We used a high power ‘white’ LED (Seoul Z-Power P4 star, white, 100 Lumens) to test individual R1-R6 photoreceptors’ encoding dynamics (Figures 1 and 6F). It was connected to a randomized quartz fiber optic bundle (transmission range: 180–1,200 nm), fitted with a lens (providing ~3° homogeneous light disk as seen by the flies), and attached onto a Cardan arm system for accurate positioning at the center of each tested cell’s receptive field. Its light output was driven by an OptoLED (Cairn Research Ltd, UK), which utilizes a feedback circuitry with a light-sensor. This LED has red component wavelengths, which minimizes prolonged depolarizing afterpotential (PDA) effects. Because long recordings can show sensitivity drifts, attributable to muscle activity (Appendix 4), the stimulus XY-position was regularly tested and, if needed, re-centered between long stimulus runs.

We used a bespoke 25 light-point array to measure individual R1-R6 photoreceptors’ receptive fields and responses to moving point objects (bright dots, Figure 7; dark dots, Appendix 9). Again, a custom-made Cardan arm system was used to accurately position the array’s center light-point (no. 13) at the center of each tested cell’s receptive field. The dot size and the minimum inter-dot-distance, as seen by Drosophila, was 1.7^o. Details of this device and the recording procedures are given in Appendixes 4 and 6.

Single photoreceptors’ diurnal temporal encoding gamut was tested systematically over different bandwidth and contrast distributions; using 20 distinct light intensity time series stimuli, which were presented at the center of their receptive fields. The used test stimuli was based upon 5 different 2 s long Gaussian white-noise light intensity time series patterns (generated by Matlab’s randn-function), which had ‘flat’ power spectrum up to 20, 50, 100, 200, or 500 Hz (Figure 1B), as low-pass filtered by MATLAB's filter toolbox, and the same peak-to-peak modulation (two units). These were then superimposed on four backgrounds: BG0 (0 units, dark), BG0.5 (0.5 units), BG1 (one unit) or BG1.5 (1.5 units, bright) on a linear intensity scale, giving altogether 20 unique stimulus patterns. As the two lowest backgrounds clipped downwards-modulation, prolonging dark intervals, the resulting stimuli ranged from high-contrast bursts (c = ΔI/I ~ 1.46 at BG0) to low-contrast Gaussian (c ~ 0.22 at BG1.5).

As further controls, we tested how well R1-R6 photoreceptors responded to dark contrast bursts of different bandwidths (Appendix 9) and to their bright counterparts. In these experiments, R1-R6s were adapted for 10 s to BG0.5 and BG1 before repeated stimulation. In addition, we recorded the tested cells’ responses to naturalistic light intensity time series (van Hateren, 1997a; Song and Juusola, 2014) (NS), selected from van Hateren natural stimulus collection (van Hateren, 1997a) (Figure 2—figure supplement 3). We also sampled light intensity time series from panoramic natural images, using three different velocity profiles of a published 10 s Drosophila walk (see Video 1; details in Appendix 3). These stimuli were then played back to a R1-R6 photoreceptor by the ‘white’ LED (see above).

In all these experiments,≥25 consecutive responses to each repeated stimulus were recorded.

Both the stimuli and responses were filtered at 500 Hz (KEMO VBF/23 low-pass elliptic filter, UK), and sampled together at 1–10 kHz using a 12-bit A/D converter (National Instruments, USA), controlled by a custom-written software system, Biosyst in Matlab (Mathworks, USA) environment. For signal analyses, if need, the data was down-sampled to 1 kHz.

In each recording, simulation or Poisson light stimulus series (see below), the signal was the mean, and the noise was the difference between individual traces and the signal (Juusola and Hardie, 2001a). Therefore, for a data chunk of 20 responses (n = 20 traces), there was one signal trace and 20 noise traces. The signal and noise traces were divided into 50% overlapping stretches and windowed with a Blackman–Harris 4-term window, each giving three 500-points-long samples. Because each trace was 2 s long, we obtained 60 spectral samples for the noise and seven for the signal. These were averaged, respectively, to improve the estimates.

SNR(f), of the recording, simulation, or Poisson light stimulus series was calculated from their signal and noise power spectra, <|Sf, |²> and <|Nf, |²>, respectively, as their ratio, where | | denotes the norm and <>the average over the different stretches (Juusola and Hardie, 2001a). To eliminate data size and processing bias, the same number of traces (n = 20) of equal length (2000 points) and sampling rate (1 kHz; 1 ms bin size) were used for calculating the SNR(f), estimates for the corresponding real recordings, photoreceptor model simulations and the simulated Poisson stimuli.

Information transfer rates, R, for each recording, simulation, or Poisson light stimulus series were estimated by using the Shannon formula (Shannon, 1948), which has been shown to obtain robust estimates for these types of continuous signals (Juusola and de Polavieja, 2003; Song and Juusola, 2014). We analyzed steady-state-adapted recordings and simulations, in which each response (or stimulus trace) is expected to be equally representative of the underlying encoding (or statistical) process. From SNR(f), the information transfer rate estimates were calculated as follows:

We used minimum = 2 Hz and maximum = 500 Hz (resulting from 1 kHz sampling rate and 500 points window size). The underlying assumptions of this method and how the number and resolution of spectral signal and noise estimates and the finite size of the used data can affect the resulting Information transfer rate estimates have been analyzed before (van Hateren, 1992b; Juusola and Hardie, 2001b; Juusola and de Polavieja, 2003; Song and Juusola, 2014) and are further discussed in Appendix 2. The mean and SD of each photoreceptor recording series (20 × 2000 points) was obtained by estimating R from eleven 1,000-point data chunks with 100-point overlaps.

We also tested how the Shannon method’s information transfer rate estimates of bursty responses compare with those obtained by the triple extrapolation method (Juusola and de Polavieja, 2003) using additional longer recordings. In the triple extrapolation, photoreceptor responses were first digitized (Figure 2—figure supplement 4A–B) by dividing these into time intervals, T_w, that were subdivided into smaller intervals of t_w = 1 ms. This procedure selects ‘words’ of length T_w with T_w/t_w ‘letters.’ The mutual information between the response S and the stimulus is then the difference between the total entropy, H_s:

where P_S(s_i) is the probability of finding the i-th word in the response, and the noise entropy H_N:

where P_i(τ) denotes the probability of finding the i-th word at a time t after the initiation of the trial. This probability P_i(τ) was calculated across trials of identical 20 Hz bursty stimulation. The values of the digitized entropies depend on the length of the ‘words’ T_w, the number of voltage levels v, and the size (as %) of the data file, H^T,ν,size. The rate of information transfer was obtained taking the following three successive limits (Figure 2—figure supplement 4C–E, respectively):

These limits were calculated by extrapolating the values of the experimentally obtained entropies. A response matrix for the analysis contained 2,000 points × 30 trials (note, the 10 first trials from the light onset were removed to minimize any adaptation effects). The total entropy and noise entropy of the responses were then obtained from the response matrices using linear extrapolation within the following parameter ranges: size = 5/10, 6/10,…,10/10 of data; ν = 4, 5,…,20 voltage levels; T_w⁻¹ = 2, 3,…, 7 points. As adaptation in photoreceptors approaches steady state, their output varies progressively less (Juusola and de Polavieja, 2003). Similarly, the entropies of their responses, when digitized to ≤20 voltage levels, ceases to increase with increasing data size, enabling their limits to be extrapolated in control by linear fits (Figure 2—figure supplement 4C–F) or Taylor series fits. Consequently, as few as 30 response traces (each 2,000 points long) provided similar information rate estimates to the Shannon method (Figure 2—figure supplement 4G) for 20 Hz burst stimulation. All data analyses were performed with Matlab (MathWorks).

We measured dark- and light-adapted wild-type R1-R6 photoreceptors’ receptive fields by their acceptance angles, ∆ρ, using intracellular voltage responses to random light-points in a stimulation array. These measurements were compared to those of hdc^JK910-mutants (Burg et al., 1993), in which first-order interneurones receive no neurotransmitter (histamine) from photoreceptors and so are incapable of feedback-modulating the photoreceptor output. Both the wild-type and mutant R1-R6 photoreceptors’ mean ∆ρ was about twice the mean interommatidial angle, ∆φ. The stimulus apparatus, the method and result details and theoretical electron micrograph comparisons of their mean rhabdomere sizes are explained in Appendixes 4–5.

Voltage responses of wild-type and hdc^JK910 R1-R6s to moving bright dots were evaluated against their respective classic model simulations, in which each recorded receptive field was convoluted by the same cell’s impulse response (Srinivasan and Bernard, 1975; Juusola and French, 1997) (1^st order Volterra kernels). The motion blur effects were quantified by comparing the real R1-R6 outputs to their deterministic model predictions. Details of the analysis are given in Appendix 6.

We used our recently published biophysically-realistic stochastic photon sampling model (Song et al., 2012) of a Drosophila R1-R6 photoreceptor to simulate macroscopic voltage response to different repeated light intensity time series patterns from a point source (Figures 3–4). The model has no free parameters. Its design and the general aims and details of these simulations are given in Appendixes 1 and 2. To eliminate data size bias, the signaling properties and performance of the simulations were quantified and compared to the corresponding recordings by using the same analytical routines on the same-sized data-chunks. The models were run using Matlab in the University of Sheffield computer cluster (Iceberg).

For each stimulus, its mean was adjusted to maximize information of the simulated photoreceptor outputs, mimicking the action of the photomechanical adaptations (intracellular pupil mechanism and rhabdomere contractions; Appendixes 2 and 7). This optimization set the effective mean photon rates from 8 × 10⁴ at BG1.5 to 8 × 10⁵ photons/s at BG0 (Figure 3). Thus, each of these light levels was considered to represent the optimal daylight input (that survived the photomechanical adaptations and was absorbed by a rhabdomere), in which modulation enabled the largest sample (bump) rate changes. Otherwise, more of its sampling units (30,000 microvilli) would be either underutilized or refractory (saturation). The maximum information rates of the simulated photoreceptor outputs closely followed the corresponding mean information transfer rates of the real recordings over the whole tested encoding range (Appendix 2). This implies that the central function of the photoreceptors’ combined photomechanical adaptations is to maximize their information transfer, and that the resulting estimates represent realistic maxima.

A photoreceptor’s encoding efficiency, η, was the ratio between the information rates of its voltage output, R_output, and the corresponding effective light input, R_input:

with R_output and R_input estimated by the Shannon formula (Equation 1). Details are in Appendix 2.

We developed a new ‘microsaccadic sampling’-model to predict how photomechanical rhabdomere contractions (microsaccades) move and narrow Drosophila R1-R6 photoreceptors’ receptive fields to resolve fast-moving objects. Appendix 8 gives the details of this modeling approach, which combines the stochastic photon sampling model(Song et al., 2012) with additional fixed ommatidium optics and photomechanical rhabdomere contraction parameters. The same appendix shows examples of how refractory photon sampling and rhabdomere contractions jointly improve visual acuity.

This appendix describes the basic theoretical principles of how fly photoreceptors sample photons, providing central background information for the results presented in the main paper.

Many lines of evidence imply that in a Drosophila R1-R6 photoreceptor 30,000 individual refractory sampling units (microvilli) integrate exponential photon flux changes (~10⁶ fold) from the environment into macroscopic voltage responses of biophysically limited amplitude range (~60 mV) and bandwidth (~200 Hz) (Juusola and Hardie, 2001a; Song et al., 2012; Song and Juusola, 2014; Hardie and Juusola, 2015). In essence, a light-adapted R1-R6 counts photons imperfectly, which, nonetheless, adds up highly reproducible neural representations of light changes within its receptive field (Juusola et al., 2015).

In this study, we quantify such quantal information processing through large-scale experimental and theoretical analyses. Our overriding aim is to analyze R1-R6s’ diurnal encoding range systematically; from light bursts to Gaussian white-noise stimulation to point-objects moving across their receptive fields at saccadic speeds. Because of the outstanding stability and signal-to-noise ratio of the intracellular recordings from in vivo R1-R6s (Juusola and Hardie, 2001a; Zheng et al., 2006; Song and Juusola, 2014; Juusola et al., 2016), providing apparent ergodicity, we can directly compare their voltage responses to those of biophysically realistic R1-R6 model simulations (Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015; Song et al., 2016), in which stochastically operating microvilli sampled similar stimuli (Appendix 1—figure 1). The mechanistic knowledge so obtained about the dynamics and limitations of quantal visual information processing provides us with deep new understanding of how well Drosophila, and other insect eyes, can see the world.

Appendix 1—figure 1

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We used our previously published biophysical Drosophila R1-R6 model (Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015; Song et al., 2016) to simulate voltage responses to time series of light intensities. The Matlab scripts for this model are downloadable from the repository: https://github.com/JuusolaLab/Microsaccadic_Sampling_Paper/tree/master/BiophysicalPhotoreceptorModel. The model contains four modules (Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015; Song et al., 2016):

• Random Photon Absorption Model: regulates photon hits (absorptions) in each microvillus, following Poisson statistics (Song et al., 2016) (Appendix 1—figure 1A).

• Stochastic Bump Model: stochastic biochemical reactions inside a microvillus capture and transduce the energy of photons to variable quantum bumps or failures (Appendix 1—figure 1B). Here, Gillespie algorithm provides discrete and stochastic phototransduction cascade simulations with few reactants as every reaction is explicitly simulated.

• Summation Model: bumps from 30,000 microvilli integrate to the macroscopic light-induced current (LIC) response (Appendix 1—figure 1C).

• Hodgkin-Huxley (HH) Model of the photoreceptor plasma membrane (Niven et al., 2003; Vahasoyrinki et al., 2006): transduces LIC into a voltage response (Appendix 1—figure 2).

Appendix 1—figure 2

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The formalism, assumptions and many tests of the biophysical photoreceptor model, which has no free parameters, are given in our previous publications (Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015). All its parameter values can be found and downloaded from: http://www.sciencedirect.com/science/article/pii/S0960982212006343

This appendix describes how the ‘stochastic adaptive visual information sampling’-theory (Appendix 1) predicts and explains the roles of R1-R6 photoreceptors’ photomechanical adaptations and network connections in information maximization at different stimulus conditions, as shown in Figures 1–4.

In this appendix:

• We test the hypotheses that photomechanical adaptations (intracellular pupil and rhabdomere contractions; see Appendix 7) and network connections in the Drosophila eye contribute importantly to optimizing the capture and representation of visual information.

• We first estimate through simulations how a R1-R6 photoreceptor’s intracellular pupil and rhabdomere contractions are jointly optimized for maximal information sampling by its 30,000 microvilli. The simulations predict that these mechanisms’ optimal combined photon throughput in bright conditions (to be absorbed by an average R1-R6 photoreceptor) should be different for different stimuli.

• We then compare the model predictions to corresponding intracellular recordings and find a comprehensive agreement between the theory and mean experiments for all the tested stimuli.

• This striking correspondence enables us to further estimate how the lamina network shapes information transfer of individual R1-R6 photoreceptors.

• Remarkably, our data and analyses strongly suggest that voltage output is different in each R1-R6, which are brought together in neural superposition during development to sample light changes from a small local visual area.

• These results are consistent with the hypothesis that the variability in the retinal sampling matrix dynamics and topology minimizes aliasing and noise, enabling its parallel processing to generate reliable and maximally informative neural estimates of the variable world (Barlow H, 1961; Yellott, 1982; Song and Juusola, 2014; Juusola et al., 2015).

• Finally, we explain how to calculate a photoreceptor’s encoding efficiency for different light stimuli, highlighting the assumptions and limits of this method.

In a fly photoreceptor, intracellular screening pigments form its pupil mechanism (Appendix 2—figure 1). The pupil protects a photoreceptor’s sampling units (30,000 microvilli in a Drosophila R1-R6) from saturation (Howard et al., 1987; Song and Juusola, 2014). At bright light exposure, screening pigments migrate to narrow the aperture they form collectively (Franceschini and Kirschfeld, 1971b), shielding off excess light from reaching the microvilli. This is important because midday sunshine on a photoreceptor may contain 10^6-8 photons/s, and without the pupil mechanism would deteriorate the encoding function of its finite microvillus population (Howard et al., 1987; Song and Juusola, 2014). The pupil opening and closing seem modulated by light-driven intracellular Ca²⁺-concentration changes (Hofstee and Stavenga, 1996), and show reasonably fast dynamics (from fully open to fully closed within 15 s) (Franceschini and Kirschfeld, 1976) for adapting its light throughput to ambient changes. Although our biophysical (stochastically operating) Drosophila photoreceptor model (Song et al., 2012; Juusola et al., 2015) lacks the pupil mechanism and any other photomechanical adaptations (cf. Appendix 7), their joint effects can be predicted through simulations; by assuming that their objective function is to maximize the photoreceptor’s information capture.

Appendix 2—figure 1

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We hypothesize that the intracellular pupil, besides affecting a photoreceptor’s angular and spectral sensitivity (Stavenga, 2004a) (see Appendix 4), participates in maximizing a photoreceptor’s information sampling by optimizing light input intensity to its microvilli in time. Specifically in this context, it works together with all other photomechanical adaptations within an ommatidium, including the much faster light-induced rhabdomere contractions (Videos 2–4), in protecting the microvilli from saturation. Thus, collectively, we consider the photomechanical adaptations (Appendix 2—figure 2) as a biological manifestation of a mathematical information maximization function.

Appendix 2—figure 2

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To function optimally, the photomechanical adaptations need to regulate input from the ambient illumination so that the temporal light changes they let through would cause maximal sample (quantum bump) rate changes (Song and Juusola, 2014). The higher the photoreceptor’s sample rate changes, the higher its rate of information transfer (Song and Juusola, 2014). Too bright light would saturate microvilli because most of them would be rendered refractory, reducing their dynamic sample counts. Conversely, too dim light would not utilize microvilli population fully, producing low (suboptimal) sample counts. Therefore, the optimal light intensity throughput for maximum information capture is somewhere between. This value is expected to depend upon five factors:

• Light intensity time series structure (we consider all the 20 light patterns tested in Figure 1B)

• Number of microvilli (~30,000 in a R1-R6 Drosophila photoreceptor)

• Refractory period distribution of the microvilli (full range: 50–500 ms in a R1-R6 Drosophila photoreceptor)

• Quantum bump waveform (sample duration)

• Quantum bump latency distribution (‘sample jitter’)

Detailed tests and descriptions of why and how these factors contribute to encoding in fly photoreceptors are given in our previous publications (Juusola et al., 1994; Henderson et al., 2000; Juusola and Hardie, 2001b; Juusola and Hardie, 2001a; Juusola and de Polavieja, 2003; Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015).

To test the photomechanical light-screening hypothesis, we simulated voltage responses to 20 different light patterns (Figure 1B) at 15 different light intensity (or brightness) levels, which ranged from 5 × 10⁴ to 1 × 10⁶ photons/s (5, 6, …, 9 × 10⁴; 1, 2,. .., 9 × 10⁵; 1 × 10⁶). In each simulation, the stochastic photoreceptor model generated 20 independent responses to the given 2-seconds-long (2000 points) light pattern of a given intensity, following the published procedures (Song and Juusola, 2014). These 20 responses were used to estimate the model’s rate of information transfer for that specific stimulus pattern (1/20) at that specific light level (1/15). So all together, we could have simulated 20 repeated photoreceptor outputs to 300 (20 × 15) different 2,000-points-long stimulus patterns. But because the model’s maximum information transfer rate estimates turned out to be relatively straightforward to determine for many light patterns (cf. Appendix 2—figure 3), the total number of simulations never reached this limit. Nevertheless, being computationally expensive, the stochastic simulations took months to complete.

Crucially, in all the simulations, the photoreceptor model was exactly the same. Its stochastic bump production dynamics (waveform, latency and refractory distributions) were governed by light-adapted values with every single parameter fixed, and these parameter values were unchanged in each simulation. The supplement of the reference (Song et al., 2012) lists these parameter values, which were collected from intracellular experiments or logically extrapolated to be biophysically realistic for light-adapted Drosophila photoreceptors. This supplement is downloadable from: http://www.sciencedirect.com/science/article/pii/S0960982212006343

Figure 3B shows the simulated voltage responses (traces above) that carried the maximum information transfer rates for the 20 tested light patterns (traces below) and the corresponding intensity levels (as effective photons/s) that evoked them. The simulations match the overall size, appearance and dynamics of the real recordings astonishingly well (Figure 1B and Figure 1—figure supplement 1B), indicating that the photoreceptor model, with its photomechanics optimizing light input intensity, samples and integrates light information much like its real-life counterparts. Notice that the optimal light intensity is the same for the different bandwidth (20, 50, 100, 200 and 500 Hz) stimuli within one BG. But for each BG (BG0, BG0.5, BG1 and BG1.5) this optimum is different. For example, for BG0, which results in bursty (high-contrast) stimulation, the optimal light intensity level is ~8×10⁵ photons/s. Whereas for BG1.5 of low contrast Gaussian white-noise stimulation, this is 10-times lower (~8×10⁴ photons/s).

We express these intensity levels in units of effective photons/s. This is because, theoretically, we have deduced the mean photon throughput that effectively fluxes into microvilli for a Drosophila photoreceptor to sample the best estimates of the given light stimuli. In other words, if the photomechanical screening mechanisms set the light input intensity for maximal information capture, as is our hypothesis, then these light intensity values should also closely approximate the actual photon absorption changes that drive phototransduction in the real experiments (as recorded intracellularly from wild-type R1-R6 photoreceptors, which have the normal pupil mechanism and photomechanical rhabdomere contractility; Figure 1 and Figure 1—figure supplement 1B). Note that as the preceding photomechanical light screening mechanisms eliminate photons, a photoreceptor’s photon absorption rates will always be considerably lower than the photon emission rates from the light source.

Because of the remarkable dynamic correspondence between the experiments (Figures 1–2) and the theory (Figures 3–4) over the whole tested encoding space, we now judge that this hypothesis must be largely true. Importantly, this realization opens up new ways to analyze photoreceptor function. For example, by making the general assumption that the input - photon absorptions (and light emission from our LED light source) - follows Poisson statistics, we could further estimate the lower information transfer rate bound for each tested light intensity pattern (as absorbed by an average R1-R6 photoreceptor), and consequently the upper bound for the Drosophila photoreceptor’s encoding efficiency (e.g. Figure 2D, Figure 2—figure supplement 1D and Figure 4D). More details about this assumption and the analysis are given at the end of this appendix (Appendix 2).

The reasons why and how the optimal light intensity input (that drives a photoreceptor’s information transfer maximally) is different for bursts and Gaussian white-noise stimulation are summarized in Appendix 2—figure 3. Here we assess both cases using data from the stochastic Drosophila R1-R6 photoreceptor model simulations, starting with light bursts.

Bursts

(Appendix 2—figure 3A-–D). These light intensity time series characteristically contain periods of longer dark contrasts, intertwined with brief and bright contrast events, as shown for 100 Hz bandwidth stimulation (Appendix 2—figure 3A, dark-yellow trace). Based on our previous analyses (Song and Juusola, 2014), longer dark contrasts help to recover more refractory microvilli than equally-bright stimuli without these features, improving neural information capture. This makes it more difficult for bursty stimuli to saturate the photoreceptor output. By increasing the stimulus intensity 8-fold, here from 1 × 10⁵ to 8 × 10⁵ effective photons/s, simply evoked larger macroscopic responses. These, thus, integrated more samples (bumps); as indicated by the larger (black) and smaller (blue) trace, respectively.

Because noise changes little in light-adapted photoreceptor output (Juusola et al., 1994; Juusola and Hardie, 2001b, Juusola and Hardie, 2001aJuusola and Hardie, 2001a; Song et al., 2012; Song and Juusola, 2014) (Figure 2—figure supplement 2), the larger responses to brighter bursts have higher and broader signal-to-noise ratio, SNR_output(f), (Appendix 2—figure 3B). This, in turn, results in higher information transfer rate estimates, R_output (Appendix 2—figure 3C), following Shannon’s equation (Shannon, 1948):

(A2.1) ${\displaystyle R_{output}={\int }_0^{\mathrm{\infty }}(lo{g}_2[SN{R}_{output}(f)+1])df}$

Note that with 1 kHz sampling rate used in every experiment, this estimation did not integrate information rate for frequencies from 0 to infinite, but from 2 to 500 Hz instead. However, the limited bandwidth would not considerably affect estimation results because: (i) high-frequency components have SNR <<1 and therefore contain mostly noise. (ii) Whereas even a high SNR_output(f) contains little information in its low-frequency components, below 2 Hz. Note also that we have previously shown the generality of Shannon’s information theory for estimating information transfer rates of continuous (analogue) repetitive responses, irrespective of their statistical structure (Juusola and de Polavieja, 2003; Song and Juusola, 2014). That is, for sufficient amount of data, Shannon’s equation and triple extrapolation method, which is free of signal and noise additivity and Gaussian distribution assumptions, give comparable rate estimates. Thus, these estimates should evaluate the simulations’ relative information rate differences truthfully; i.e. consistently with only small errors.

Markedly, a photoreceptor’s performance is systematically better to the brighter bursts (black line) than to the less bright ones (blue line), irrespective of their bandwidth (Appendix 2—figure 3C). Thus, for the brighter bursts, more microvilli are dynamically activated, generating larger sample rate changes. These bumps sum up larger (and more accentuated – see [Song and Juusola, 2014]) macroscopic responses, packing in more information than the corresponding responses to the less bright bursts.

Appendix 2—figure 3

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However, because a Drosophila photoreceptor has a finite amount of microvilli, each of which - once activated by a photon’s energy - stays briefly refractory, its sample rate changes and thus signaling performance first increases monotonically until about 6 × 10⁵ photons/s, before gradually saturating, and eventually decreasing, with increasing burst brightness (Appendix 2—figure 3D). The photoreceptor model’s maximum information transfer rate estimate (R_max = 631 ± 31 bits/s; marked by a square) for 100 Hz bright bursts is reached at the optimal stimulus intensity of 8 × 10⁵ effective photons/s. In other words, this is the amount light the photomechanical adaptations, including the intracellular pupil mechanism and rhabdomere contractions (see Appendix 7), should let through (to be absorbed) in bright daylight for the fly to see bursty real-world events best. The corresponding performance estimate with the less bright bursts (10⁵ effective photons/s) is 493 ± 12 bits/s (circle).

We next compare the maximum information transfer rate estimates (squares) of the model simulations to those of corresponding in vivo recordings (circles) for all BG0 (bursts) and BG1 (GWN) stimuli (Appendix 2—figure 4). The simulated performance is very close to the measured mean performance for all the tested stimuli, typically falling within the standard deviation of the recordings’ information transfer.

In further inspection, two interesting observations can be drawn from this data. First, for the GWN stimuli, irrespective of their bandwidth, the maximum information transfer rate estimates of the model (dotted line) are just a few bits/s (1–10%) higher than the corresponding mean estimates of the real recordings (continuous line). These small differences are probably caused by recording noise. Second, the simulations to bursty stimuli carry less information than the corresponding best recordings, and the recordings show variations in their information transfer.

Appendix 2—figure 4

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In Appendix 2—figure 4B, the difference in information rate estimates between the corresponding recordings and simulations to the bursty stimuli is plotted for each complete recording series (thin lines) of individual cells. The thick line gives the mean difference to all these cells’ performance. Most noticeably, some photoreceptor cells carry ~100–200 bits/s more information from the bursty stimuli, but many other cells also show information rates that surpass the model’s performance (see also Figure 5). Any information surplus (cyan background) presumably comes from the lamina network (Zheng et al., 2006; Wardill et al., 2012); through gap-junctions and feedback synapses from the cells that sample information from the same small visual area (due to neural superposition [Vigier, 1907b; Vigier, 1907a; Agi et al., 2014]). The photoreceptor model lacks this network information.

Appendix 2—figure 5

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In fact, each of the six R1-R6s, which pool their inputs in the same lamina cartridge for feed-forward synaptic transmission, should show different information transfer rates. This is because the lamina connections are asymmetric (Appendix 2—figure 5). Electron micrographs have shown that R1, R2, R3, R4, R5 and R6 make different amounts of feedback synapses with the lamina interneurons (Meinertzhagen and O'Neil, 1991; Rivera-Alba et al., 2011). Most feedbacks are provided by neurons belonging to the L2/L4 circuits (Meinertzhagen and O'Neil, 1991; Rivera-Alba et al., 2011). Whilst same-cartridge connections are selectively from L2 to R1 and R2 and from L4 to R5, all R1-R6s receive feedback signals from L4 of neighboring cartridges. There are further connections from Am to R1, R2, R4 and R5, and glia are also synaptically connected to the network (Meinertzhagen and O'Neil, 1991; Rivera-Alba et al., 2011), but only R6 makes direct gap-junctions (Shaw et al., 1989) with R7 or R8. These asymmetric functional connections (Zheng et al., 2006) may largely explain the variability in photoreceptor output (Figure 1—figure supplement 1) and information rates (Figure 2—figure supplement 1C).

Our recent work (Wardill et al., 2012) further showed that during naturalistic stimulation R6 can receive up to ~200 bits/s of information from R8, as channeled through gap-junctions between these cells. Therefore, we infer here that the recordings with the highest information transfer rates (~850 bits/s) were probably of R6-type, which directly receive extra information from its R8y and R7y neighbors (Shaw, 1984; Shaw et al., 1989; Wardill et al., 2012) (Appendix 2—figure 6). Conversely, the recordings, in which information rates were lower than those of the simulations (Appendix 2—figure 4B, pink background), carried presumably more recording/experimental noise, with one potential source being minute retinal movements (see Appendixes 4, 6–9).

Our intracellular recordings establish that during bright light stimulation, the voltage output of an individual photoreceptor is highly repeatable (cf. Figure 1). Consequently, our recording system could be used to study variability among individual R1-R6 photoreceptors of the fly eye. We discovered that for the same stimuli the characteristic output waveforms and frequency distributions of one particular cell are typically different to those of another photoreceptor (Figure 5—figure supplement 1), even when recorded from the neighboring cells in the very same eye (by the same microelectrode). Because the signal-to-noise ratios of the recordings were very high (Figure 2), sometimes over 6,000, it was evident that the observed cell-to-cell variability had little to do with the quality of the recordings. Hence, in the Drosophila retina, R1-R6s show intercellular variability that is far greater than the observed small intracellular variability.

Appendix 2—figure 6

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Collectively, these results strongly suggest that every R1-R6, which is pooled in one lamina cartridge under the developmental neural superposition principle (Agi et al., 2014) to transmit information about light changes in a small area of visual space to visual interneurons (L1-L3 and Am) (Meinertzhagen and O'Neil, 1991; Zheng et al., 2006; Zheng et al., 2009; Rivera-Alba et al., 2011), has, in fact, its own unique output. Besides asymmetric connectivity within a neuro-ommatidium, some of the observed response variations may also reflect different recording locations. For example, Drosophila R1-R6s in the front of the eye might show different responsiveness to those at the back, as already shown for localized polarization-sensitivity differences (Wernet et al., 2012). Compound eyes of many insects exhibit structural adaptations that alter their lens sizes and shapes locally, such as bright or acute zones for increasing sensitivity or resolution, respectively (Land, 1998). Furthermore, electrophysiological recordings in some fly species suggest that their photoreceptor output vary across the eyes and could be tuned to the spatial and temporal characteristics of the light environment (Hardie, 1985; Laughlin and Weckström, 1993; Burton et al., 2001).

With each R1-R6 having variable ‘network-tuned’ (and possibly ‘location-tuned’) encoding properties and output, and with each image pixel being sampled through variable size rhabdomeres (see Appendix 5, Appendix 5—figure 1) and ommatidial lenses (the photoreceptors’ receptive fields vary; see Appendix 4, Figure 7—figure supplement 1 and interommatidial angles change progressively from front to back [Gonzalez-Bellido et al., 2011]), the Drosophila eye should generate reliable neural estimates of the variable world. This is because a sampling matrix made out of variable pixels (neuro-ommatidia), in which size and sensitivity show random-like constituents:

• prevents aliasing of image information (Appendix 2—figure 7); see also (Yellott, 1982; Dippé and Wold, 1985; Juusola et al., 2015).

• mixes color information to the R1-R6 motion vision channel, whitening its spectral sensitivity (Appendix 2—figure 7E) (Wardill et al., 2012), which is a prerequisite for an optimal motion detector (Srinivasan, 1985).

Aliasing effects are reduced by sampling faster and/or with finer spatial resolution, and eliminated by sampling more than twice over the highest stimulus frequency (Cover and Thomas, 1991). The Nyquist–Shannon sampling theorem establishes a sufficient condition for a sample rate that enables a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth. Specifically, it only applies to a class of mathematical functions having a Fourier transform that is zero outside of a finite region of frequencies. This condition, however, cannot be fully realized in sensory systems, which show finite spatiotemporal sampling resolution and evolved around 1/fⁿ-stimulus (Field, 1987; van Hateren, 1997b) distributions of the real-world objects and events. Because any physical transformation affects signal and noise equally (data processing theorem [Shannon, 1948; Cover and Thomas, 1991]) and because real-world low-pass filters, such as a lens, cannot cut-off sharply at an exact point, but instead gradually eliminate frequency components and exhibit a fall-off or roll-off slope, aliasing effects would not be removed completely in an ordered sampling matrix. Therefore, to prevent phantom sensations of aliased signals fooling the brain and perception of physical reality, sampling matrixes of sensory systems must entail stochastic variations.

Appendix 2—figure 7

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Whilst temporal and topological sampling matrix variations in retinae combat aliasing (Yellott, 1982; Juusola et al., 2015), their trade-off is broad-band noise (Dippé and Wold, 1985) (Appendix 2—figure 7C; the Python script for these simulations is downloadable from: https://github.com/JuusolaLab/Microsaccadic_Sampling_Paper/tree/master/AntialiasingByRandomisation). This noise, however, is much reduced (or nearly eliminated) by parallel sampling of the same information (Song and Juusola, 2014; Juusola et al., 2015). For example, noise reduction occurs naturally in the fly eye - both in time and in space. In every R1-R6 photoreceptor, 30,000 microvilli sample discrete information stochastically in time, generating virtually aliasing-free macroscopic responses of very high signal-to-noise (Figure 5—figure supplement 1). Whereas, across the lamina neuro-ommatidia of variable connectivity and spectral sensitivity, neural superposition integrates local R1-R8 signals of overlapping information from each pixel (a small largely aligned area in the visual space) to improve the signal-to-noise ratio of the sampled images (see Appendix 5). Such images should provide the brain reliable and maximally informative estimates of the environment.

A photoreceptor’s encoding efficiency, η, is the ratio between the information rates of the voltage output, R_output, and the effective light input (photon absorptions), R_input, that drove it:

As we already had determined the maximum photoreceptor output information rates, R_output (Equation A2.1; Figure 2C, Figure 2—figure supplement 1C and Figure 4C), only the corresponding information rates of the effective light stimuli, R_input, needed to be worked out. Because the output simulations’ maximum information rates matched well the corresponding mean rates of the real recordings (Appendix 2—figure 6A), we had extrapolated successfully each effective light intensity (photon absorption) time series that drove the voltage response. Therefore, we could now estimate the rate of information transfer of the effective light input by making the following assumptions:

• Photon emission from the light source (LED) follows Poisson statistics; this may or may not be true (see the discussion below).

• But if true, the effective photons, which survived photomechanical adaptations (Appendix 2—figure 2) and were absorbed by a photoreceptor and used for calculating R_input, should also follow Poisson statistics (Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015; Song et al., 2016).

Photons are thought to be emitted by the light source, such as the LEDs, at random, exhibiting detectable statistical fluctuations (shot noise). Such dynamics can be modelled by Poisson statistics (Song and Juusola, 2014). Therefore, as each light stimulus trace differs from any other, with their mean equaling their variance, we could estimate through simulations their average signals and noise, and signal-to-noise ratios, SNR_input(f). The corresponding information transfer rates, R_input, could then be estimated by Shannon’s equation (Equation A2.1). For each tested stimulus pattern, this was done by using the same amount of simulated input data as with the output data (2,000 points x 20 repetitions) to control estimation bias. More details and examples about Poisson stimulus simulation procedures are given in (Song and Juusola, 2014).

• Notice that currently there are no manmade sensors more efficient than the biological photoreceptors themselves for measuring the photon emissions from the LED light source. Therefore, we had no good direct methods to measure the LED’s photon rate changes at the same level of accuracy as the photoreceptor output that it evoked. Accordingly, calculating mutual information directly between the less accurate light input estimate and the more accurate photoreceptor output would be both impractical and erroneous.

For the simulated inputs and outputs, the data processing theorem (Shannon, 1948) dictates that R_input ≥ R_output; thus η ≤1 (≤100%). If not, then one or both estimates are biased or incorrect; information cannot be created out of nothing. However, for the efficiency estimates based on the real recordings, it is quite possible that R_output > R_input, and thus η >1 (>100%), because R1-R6s receive extra information from the network (Appendix 2—figure 5 and Appendix 2—figure 6) that is missing from the R_input estimates of an average R1-R6 photoreceptor’s photon absorptions (cf. Appendix 2—figure 4B).

We recognize that there are methodological limitations and unknowns, which may affect the accuracy and consistency of these estimates:

• Experimental and theoretical evidence suggests that photon output of some light sources might be sub-Poisson (Teich et al., 1984); meaning, not maximally random. If this were true for our LED, then our approach would slightly underestimate R_input, used in the experiments, and consequently overestimate Drosophila photoreceptors’ encoding efficiency.

• Shannon’s equation can bias information transfer rate estimates for any corresponding light input and photoreceptor output differently. This is because the signal and noise components of the input and output may deviate from the expected Gaussian by different amounts. Even though we used systematically the same amount of data for both estimates (20 × 2,000 data points), in the cases where light distribution is skewed (bursty stimuli) but the photoreceptor output is more Gaussian, it is possible that Shannon’s equation would underestimate input but not (or less so) output information, causing us to overestimate efficiency.

• Small data chunks limit analyses. In the past, we have compared information transfer rate estimates, as obtained by Shannon’s equation to those estimated through the triple extrapolation method (Juusola and de Polavieja, 2003), which is directly derived from Shannon’s information theory. For ergodic data of different distributions, and when appropriately applied, both methods provided similar estimates (Figure 2—figure supplement 4) (Juusola and de Polavieja, 2003; Song and Juusola, 2014). However, the triple extrapolation method works best with large sets of data; preferably containing ≥30 responses to the same stimulus (Juusola and de Polavieja, 2003). In the current study, because of the practical limitations (to map a photoreceptor’s whole encoding space within a reasonable time), all the selected recordings and simulations consisted responses to 20 stimulus repetitions. This data size was deemed insufficient for an accurate estimate comparison between the two methods and was not done here. In the analyses, to provide fair comparison between simulations and recordings in all tested conditions, all the data chunks (for the recordings, simulations and stimuli) were exactly the same size (20 × 2,000 points) and they were processed systematically in the same way (apart from the two exceptions we discuss next). Therefore, the data-size bias should be under control and the results comparable within these limits.

• Implementation of Shannon’s equation (Equation A2.1) in digital computers typically requires windowing of the data chunks (for signal and noise) before calculating their power spectra though Fast Fourier Transfer (FFT). Windowing combats spectral leakage (smearing), but this affects especially low-frequency signals, in which information content is low. So this trade-off can be considered reasonable, and its effect on most performance estimates is marginal. But here as the input and output information transfer is calculated separately, windowing affects more 20 Hz GWN light input than its corresponding photoreceptor output. This is because windowing clips lower frequency power from 20 Hz GWN input, whereas in the simulated and real voltage responses much of this power is nonlinearly translated (through adaptation) to higher frequencies, including those over 20 Hz. The simulated light input, of course, carries no information on frequencies > 20 Hz, but now it has also lost in windowing some of its low-frequency modulation, which the photoreceptors could translate into high-frequency voltage modulation (note, photomechanical phase enhancement can further contribute to this nonlinearity, see Appendix 3). For the two lowest intensity levels only, we judge that because of this methodological bias, the efficiency estimates for the 20 Hz GWN input-output data became unrealistic by a small margin of 10–40 bits/s, implying that R_output > R_input. Therefore, for data to these two stimuli only, we applied box-car windowing (instead of the normal Blackman-Harris type), to retain its low frequency information content, and so to reduce this bias.

Because of all these possible error and bias sources, a Drosophila photoreceptor’s encoding efficiency (η) estimates given in this publication must be considered as upper bounds. Nonetheless, for real photoreceptors, it is realistic to expect their maxima to approach 100%, and in some cells (likely R6s) be beyond, for the tested low-frequency stimuli (20 Hz). This is because of the extra information from the network, which is missing from the simulated mean photon absorption estimates. (Note that in the in vivo experiments, the light source emits at each moment 100–10,000-times more photons than what can be absorbed by the tested photoreceptor. Thus, the light source’s R_input^emitted always exceeds a photoreceptor’s R_input^absorbed).

Overall, the maximum η values are slightly higher but consistent with our previous (conservative) estimates of 90–95%, in which the light input intensity to microvilli was inferred by comparing the wild-type photoreceptor performance to that of white-eye mutants, lacking the intracellular pupil. Therefore, we conclude (again conservatively) that the error margin of these new encoding efficiency estimates may reach ±5%.

This appendix explains why the encoding of high-contrast bursts is both highly informative and reliable, proving additional insight to the results presented in Figures 1–6. It also explains how we generated the different light intensity time series from panoramic images of natural scenes, following a Drosophila‘s saccadic walking patterns (Figure 6), and how these stimuli were analyzed and used in the experiments.

Figure 2—figure supplement 3 shows that R1-R6 photoreceptors can sample more information from high-contrast bursts than from naturalistic light intensity time series (1/fⁿ-stimuli). We can explain this performance difference by the bursty stimuli’ proportionally more, and more evenly distributed, long dark contrasts. Such events enable refractory microvilli to recover efficiently from their previous light-activation so that large numbers of them are continuously available to sample ongoing light changes; i.e. to transduce photons to quantum bumps. This leads to larger sample (quantum bump) rate changes and, thus, to a higher rate of information transfer (see also: Song and Juusola, 2014).

Moreover, fast high-contrast events survive the slower intracellular pupil mechanism (Appendix 2, e.g. Appendix 2—figure 2) and photomechanical rhabdomere contractions (Appendix 7) well (Figure 8C). And consequently, fewer photons are being filtered out (lost) from high-contrast bursts than from naturalistic stimulation (Figure 2—figure supplement 3B, pink trace) or Gaussian white-noise (grey), which adapt the photoreceptors more continuously to the given light background. Therefore, at the level of the light source, bursty stimuli can have much lower power than the other two stimuli to drive photon-to-quantum bump sampling efficiently by 30,000 microvilli.

Appendix 3—figure 1

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From an information theoretic point of view, the amount of visual information that is encoded by a photoreceptor can be similar for bursty (phasic) and Gaussian (tonic) signals (Figure 2C; cf. 20 Hz 0.6-contrast bursts and 100 Hz 0.32-contrast GWN). However, when signal-detection-theoretic measures are applied, bursts outperform ‘tonic’ GWN signals in indicating visual ‘things’; i.e. the occurrence of perceptually relevant changes in light input. Bursts appear somewhat like all-or-none events (Appendix 3—figure 1), having much higher local signal-to-noise ratios in the rising or decaying phases of a photoreceptor’s voltage responses (Zheng et al., 2006). They tower over the background noise, making their detection much easier than for the tiny blips of the GWN signals. Accordingly, photoreceptors’ voltage bursts support robust transmission of behaviorally relevant visual information and should further improve the reliability of synaptic transmission and perception (Zheng et al., 2006; Zheng et al., 2009).

By combining a fly’s movement during free walking (Geurten et al., 2014) with natural image statistics, we estimated light intensity stimuli, which a Drosophila R1-R6 photoreceptor would face during locomotion through different natural scenes (Figure 6 and Video 1).

To reproduce a fly’s saccadic movements and fixations during its 10 s walk (Figure 6A), we used the published angular velocity data (Geurten et al., 2014) (Figure 6B; Appendix 3—figure 2C). This was traced from Figure 1D in (Geurten et al., 2014), using the unobscured section between 0.05–9.95 s, and re-sampled with 1 ms steps. The velocity was integrated over time to give the yaw signal (yaw(t)). Both the velocity and the yaw matched the original published data. Finally, the yaw was wrapped between 0^o and 360^o.

For generating the light intensity time series stimuli, which a walking fly would experience in different surroundings, we used six different 360^o panoramic images (high-density digital photographs of natural scenes), taken from the internet (Appendix 3—table 1). These natural scenes were arbitrarily chosen from Google image search results, and we do not know how representative their image statistics are, for example, in respect to the van Hateren database (van Hateren, 1997a). Each image’s left (0^o) and right (360^o) side were stitched together to enable continuous viewing over a full rotation. The images were preprocessed in the following way:

• Because stitching can cause errors (distortions), the lower and upper quarters of the images were discarded.

• The color images (Appendix 3—figure 2A) were reduced to gray scale, and their gamma correction was removed, enabling us to use their raw intensity values (Appendix 3—figure 2B).

• For each image, light intensity values were collected from 15 horizontal line scans taken in regular intervals (from top to bottom; Appendix 3—figure 2B).

As each image spanned 360^o horizontally, we could calculate the degree-value between 0^o and 360^o for each pixel (intensity) in the horizontal line scans (Intensity(angle)). The pixel intensity values (within the chosen horizontal line) were then sampled at the corresponding yaw positions (Appendix 3—figure 2D; in degrees) of the fly’s walk for each 1 ms time-bin (Intensity(yaw(t))). This generated unique light intensity time series (Appendix 3—figure 2E), which mimicked walk-induced photoreceptor stimulation from the given scene. In the sampling, each yaw value was automatically rounded to the closest pixels angle value (Appendix 3—figure 2C, blue). Note: this process assumes that, during a free walk, the fly head would not rotate or move vertically. The Matlab script is in: https://github.com/JuusolaLab/Microsaccadic_Sampling_Paper/tree/master/PanoramicIntensitySeries.

We also generated two sets of control light intensity time series data from the same images. first control: to compare saccadic movements to linear movements (named linear), we used the same walk’s median yaw velocity of 63.3 ^o/s (median(abs(angularvel(t)))) (Appendix 3—figure 2D, red traces). second control: we shuffled the angular velocity trace values (named shuffled; gray traces); this removed all time correlations in the velocity trace without affecting its histogram. Appendix 3—figure 2E shows two examples of the saccadic (test) and the two control light intensity time series, taken from two different horizontal scan lines (scans 8 and 15 in Appendix 3—figure 2B).

Appendix 3—figure 2

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Intensity changes for saccadic, linear and shuffled locomotion dynamics were calculated by subtracting two neighboring points in each intensity series (using Matlab ‘diff’-function). The corresponding ‘intensity change’-histograms were calculated from all 15 traces per each image. Differential histogram was calculated as the mean of the ‘intensity change’-histograms.

We found (predictably) that the differential histograms of the saccadic light intensity time series were sparser than those of the corresponding linear light intensity time series stimuli (of the same median velocity; Figure 6D). This was true for all the tested panoramic images (Appendix 3—figure 3). Saccadic sampling (blue traces) ‘burstified’ light input. This was because it increased the proportion of rare large intensity differences between two consecutive moments in comparison to linear sampling (red); i.e. saccades made the histogram flanks to reach out further. Furthermore, the fixation periods made it more likely that light intensity over the neighboring moments remained similar or the same (higher proportion of zero values). These features are obvious in Video 1.

Appendix 3—figure 3

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There are important factors to consider when selecting the stimulus series and their playback velocity for testing how self-motion affects R1-R6 photoreceptors ability to encode naturalistic stimulation.

A fly photoreceptor’s information transfer rate is limited by (i) the number of its photon sampling units (Howard et al., 1987; Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015) (30,000 and 90,000 microvilli in a typical Drosophila and Calliphora R1-R6, respectively) and (ii) the speed, (iii) reliability (jitter) and (iv) recoverability (refractoriness) of their phototransduction reactions (Juusola and Hardie, 2001b; Juusola and Hardie, 2001a; Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015). In general, the more efficiently the light stimulus utilizes the available microvilli population in generating the larger sample (quantum bump) rate changes, the higher the photoreceptor’s information transfer rate (Song and Juusola, 2014) (see Appendix 2). Consequently, the efficiency of photon sampling depends upon the stimulus speed and statistics (Juusola and de Polavieja, 2003; Zheng et al., 2009; Song et al., 2012; Song and Juusola, 2014) (Appendix 3—figure 4). For naturalistic light intensity time series stimulation (NS), we have previously shown that:

• A R1-R6 photoreceptor’s information transfer increases with stimulus playback velocity until saturation, when most of its microvilli likely become refractory for most of the time (Juusola and de Polavieja, 2003; Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015) (Appendix 3—figure 4A–C). This information increase results from the increased entropy rate in photoreceptor output (Appendix 3—figure 4B), as it reliably packs in more sample rate changes in a given time unit. The corresponding noise entropy rate (Juusola and de Polavieja, 2003), similar to noise power (Figure 2—figure supplement 2A), remains practically invariable.

• Sample rate changes in R1-R6 output further depend upon the stimulus structure (Juusola and de Polavieja, 2003; Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015) (the distribution of its dark and bright contrasts). For example, R1-R6 output information peaks at lower playback velocity (10 kHz) for NS₁, which had fewer long dark-contrast periods (to recover refractory microvilli) than for NS₂ (>20 kHz), which had more and more evenly spaced dark-contrasts (Appendix 3—figure 4).

For testing how naturalistic saccadic, linear and shuffled locomotion patterns affect Drosophila R1-R6s’ encoding performance (Figure 6F), we used the three corresponding light intensity time series stimuli (first 8,000-points) from ‘swampy forest’ panorama (line scan #8). These stimulus sequences were selected because each of them carried high-contrast modulation. In the intracellular experiments and model simulations, these stimuli were repeatedly presented one after another to each tested photoreceptor with 4 kHz playback velocity. This stimulus speed was chosen because:

• It would cover well the broad velocity range of natural visual inputs to photoreceptors, including both the slower walking and the faster saccadic flight behaviors.

• Each stimulus could be presented in 2 s, enabling us to collect 30 responses in 1 min and the three different sets of data in 3 min, keeping the recording conditions under control.

• It evokes high R1-R6 information transfer, which for many high-contrast NS sequences approaches their maxima (Juusola and de Polavieja, 2003; Zheng et al., 2009) (cf. Appendix 3—figure 4D–E). Theoretically, Drosophila R1-R6 output information rate cannot exceed ~850 bits/s (Figure 2C), which was evoked by 100 Hz bursts. Such stimulus entailed the right mix of bright and dark contrasts to optimally utilize a R1-R6’s frequency and amplitude ranges.

These stimuli evoked comparable responses (of high information rates) both from R1-R6 photoreceptors in vivo and the biophysically realistic R1-R6 model (Appendix 1). The recordings and the simulations showed consistently that the voltage responses to saccadic (i.e. the most bursty) light intensity time series had the highest information transfer rate (Figure 6F; Figure 6—figure supplement 1).

Appendix 3—figure 4

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Finally, we note that it is possible that in scenes with different spatial structure (particularly lower spatial frequency structure), flies would use different turn velocities to bring contrast features into ideal sampling range (irrespective of saccades making sampling shorter). Future studies need to explore whether such a match with saccade statistics exists.

This appendix describes in detail a new method to measure a Drosophila photoreceptor’s receptive field, and provides important background information about the experimental and theoretical results presented in Figures 7–9.

In this appendix:

• We test the hypothesis that in the Drosophila eye visual information is integrated laterally in dim conditions, and fed back synaptically to its photoreceptors, contributing to their spatial responsiveness.

• We measure dark- and moderately light-adapted wild-type R1-R6 photoreceptors’ receptive fields by their acceptance angles, ∆ρ, using intracellularly recorded voltage responses to light flashes, delivered from randomized positions of an orthogonal stimulation array.

• We compare these measurements to those of histamine-mutants (Burg et al., 1993; Melzig et al., 1996; Melzig et al., 1998) (hdc^JK910), in which first-order interneurons are blind (receiving no neurotransmitter from photoreceptors) and so incapable of feedback-modulating photoreceptor output.

• We show that the average acceptance angles of dark-adapted wild-type photoreceptors are 10.9% broader than those of the mutant, while light-adapted cells show no such difference.

• We characterize slow spontaneous retinal movements in the Drosophila eye and show how this activity can influence intracellular photoreceptor recordings.

• Our results suggest that in dim conditions spatial information is pooled in the lamina and fed-back to wild-type photoreceptors. Such excitatory lateral synaptic modulation, which is missing in the mutant, increases spatial sensitivity, broadening the photoreceptors’ receptive fields.

Visual acuity is defined as the minimum angle that the eye can resolve. In the fly compound eye, if each ommatidium constitutes a sampling point in space, then the eye’s maximal spatial resolution is set by the density of its ommatidial array (Snyder et al., 1977). Suppose a regular pattern of black and white stripes is presented to a fly. The maximum spatial frequency that the fly can resolve, ν_s, is achieved when one ommatidium points to a black stripe and its adjacent ommatidium points to the next white stripe (Appendix 4—figure 1A). Thus, the interommatidial angle (Snyder and Miller, 1977), ∆φ, is the key parameter in determining ν_s. For the compound eyes with hexagonal layout, as is the case of most flies, the effective interommatidial angle, ∆φ_e (Appendix 4—figure 1B), can be calculated as:

Thus, the upper limit of the fly eye’s visual acuity is given by:

Whether this limit is achieved or not depends upon the spatial performance of a photoreceptor (Snyder, 1977). However, when estimating a photoreceptor’s receptive field, which is quantified by its width at half-maximum, or acceptance angle (Warrant and McIntyre, 1993), ∆ρ, we need to consider several contributing factors.

Firstly, since the ommatidium lens and a photoreceptor’s rhabdomere are very small, optical quality is strongly affected by light diffraction, of which airy pattern (the point-spread function) depends upon light wavelength, λ, lens diameter, D, rhabdomere diameter, d, and focal distance, f (Appendix 4—figure 1C). Theoretically, the blurring functions at the ommatidium lens and rhabdomere tip are both Gaussian and therefore can be combined (Snyder, 1977) to yield a simple approximation of ∆ρ:

However, owing to the rather complex waveguide properties of small-diameter rhabdomeres, this formula is somewhat inaccurate. Van Hateren (van Hateren, 1984) and Stavenga (Stavenga, 2003b; Stavenga, 2003a) found that along a fly photoreceptor’s rhabdomere only a limited number of light patterns (modes) could be formed and that this number depends upon the incident angle of light, leading to a smaller actual ∆ρ than what Equation A4.3 implies.

Another contributing factor is the spatial cross talk, in which a photon escapes the rhabdomere it first travels in and enters an adjacent rhabdomere (Horridge et al., 1976). Such an effect is likely to happen when the cross-talk index of the ommatidia/rhabdomere structure is less than three (Wijngaard and Stavenga, 1975). This was indeed reported for Drosophila (Gonzalez-Bellido et al., 2011), suggesting that its neural images might have lower resolution than theoretically calculated from the optics.

Lastly, the intracellular pupil mechanism further affects ∆ρ estimation. Inside each photoreceptor cell, there are tiny pigment granules that migrate toward its rhabdomere boundary upon light adaptation (see Appendix 2, Appendix 2—figure 1). These pigments absorb and scatter light that travels inside the rhabdomere, reducing the light influx absorbable by its rhodopsin molecules (Kirschfeld and Franceschini, 1969; Boschek, 1971; Roebroek and Stavenga, 1990). Consequently, the pupil mechanism shapes a photoreceptor’s angular and spectral sensitivity (Stavenga, 2004a). Moreover, in Appendix 2, we show by experiments and theory that it further helps to maximize a photoreceptor’s information transfer; by optimizing the light intensity passing into the rhabdomere.

Appendix 4—figure 1

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The fly compound eyes are small and size-constrained, presumably to save energy and improve survival (Land, 1998; Laughlin et al., 1998; Niven et al., 2007). This puts their sensitivity/acuity trade-off under intense evolutional pressure (Snyder et al., 1977; Laughlin, 1989; Nilsson, 1989; Warrant and Mcintyre, 1992). While an increase in ommatidium size would improve photon capture, it would also result in fewer sampling points (image pixels) in the eye, lowering the resolution of its neural responses (neural images of the world). In dim conditions, where photon noise is relatively large compared to available information (signal), the task to enhance visual reliability and sensitivity becomes challenging. Optical mechanisms, including the widening of photoreceptor receptive fields by pupil opening (Williams, 1982; Laughlin, 1992; Nilsson and Ro, 1994; Stavenga, 2004a), can increase the amount of light collected in each ommatidium only to some extent. Yet under dim illumination, insect visual behaviors appear remarkably robust (Pick and Buchner, 1979; Warrant et al., 1996; Honkanen et al., 2014), suggesting that their eyes’ neural mechanisms could successfully overcome the apparent shortfall in photon supply (Warrant, 1999).

Sensitivity can be increased neurally at the cost of decreasing acuity by (i) increasing photoreceptors’ voltage/light intensity gain (Laughlin and Hardie, 1978; Matić and Laughlin, 1981; Song et al., 2012), (ii) increasing their integration time (temporal summation) (Skorupski and Chittka, 2010; Song et al., 2012) and (iii) spatially summing information, or reducing lateral inhibition from neural neighbors (Srinivasan et al., 1982; van Hateren, 1992c; 1993b). Experimentally, spatial summation has been shown to occur in the directionally-selective motion-detecting (DSMD) neurons of the fly lobula plate (Srinivasan and Dvorak, 1980), but it is possible that such signals might also reflect upstream processing in the earlier optic neuropiles (the lamina, medulla and lobula).

Although the fly photoreceptor biophysics for adapting temporal summation are well characterized (Juusola et al., 1994; Juusola and Hardie, 2001b, Juusola and Hardie, 2001aJuusola and Hardie, 2001a; Song et al., 2012; Song and Juusola, 2014; Hardie and Juusola, 2015; Juusola et al., 2015) (see Appendixes 1–3), the neural substrate for spatial summation is less well understood. In the lamina, electrical couplings by gap-junctions were found only between the photoreceptor axons that share the same optical axis (Ribi, 1978; Shaw, 1984; van Hateren, 1986; Shaw et al., 1989) in neural superposition. Hence, these presynaptic connections probably cannot distribute spatial information. Nonetheless, postsynaptically, the evidence is more suggestive. Intracellular responses of the histaminergic interneurons (large monopolar cells, LMCs) to narrow (point source) and wide-field light stimuli match well the theoretical predictions of spatiotemporal summation (Dubs et al., 1981; van Hateren, 1992a, 1992b). This notion was further advocated by the structural study in the nocturnal bee Megalopta genalis (Greiner et al., 2005) lamina, which revealed extensive synaptic connections between adjacent cartridges. Finally, early functional studies of the housefly (Musca domestica) photoreceptors (Dubs et al., 1981) indicated that quantum bumps, recorded to dim light at the behavioral threshold, contain additional small-amplitude events. These were judged not to be generated by the impaled cells but by single photon captures in their neighbors; with the receptive fields being wider than what were expected from the optics alone (Dubs, 1982).

In this appendix, we test whether or how spatial information is integrated laterally and fed back synaptically to photoreceptors, contributing to their acceptance angles, ∆ρ. The tight coupling between feed-forward and feedback pathways in the photoreceptor-lamina circuit is known to have crucial roles in maintaining robust adaptation and temporal coding efficiency (Zheng et al., 2006; Nikolaev et al., 2009; Zheng et al., 2009). Theoretically, similar spatial information regulation should further improve fly vision. Specifically here, we take advantage of Drosophila genetics and compare R1-R6 photoreceptor outputs of wild-type and hdc^JK910 mutant. Synaptic transmission from hdc^JK910 photoreceptors is blocked, making their interneurons effectively blind (Dau et al., 2016). Therefore, feedback from the mutant LMCs (and possibly from amacrine cells (Zheng et al., 2006; Hu et al., 2015), Am, which also receive histaminergic input from photoreceptors) to R1-R6s cannot contain any lateral modulation, neither inhibitory nor excitatory.

We show that the dark-adapted wild-type R1-R6 photoreceptors’ mean acceptance angles are 10.9% broader than in the mutant, while no significant differences are found between the light-adapted cells. We further show how stimulus history and retinal movements affect the receptive fields in the Drosophila eye. Our results suggest that in dim conditions spatial information is pooled in the lamina and channeled back to R1-R6 photoreceptors in the form of excitatory synaptic modulation, which increases spatial responsiveness by broadening the cells’ receptive fields.

A photoreceptor’s receptive field can be estimated electrophysiologically by measuring its intracellular response amplitudes, V_n, to a light flash intensity, I_n, at varying angular positions, α_n. From all these V_n, I_n, and α_n values generated by a complete scan, the receptive field width can be computed by three different methods as comparatively reviewed below.

25 LED light-point array and LED pads

A R1-R6 photoreceptor’s receptive field was scanned by using an array of 25 light-points, mounted on a Cardan arm (Appendix 4—figure 2). Each light-point (small light guide end) subtended an angle of 1.7° as seen by the fly, transmitting its light output from its specific LED (1/25). The system was controlled by 2 channels, both with voltage inputs ranging from 0 V to 10 V. Channel 0 was used to select the light-point while Channel 1 was used to linearly set its intensity.

Appendix 4—figure 2

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Appendix 4—figure 3A shows a typical light-point’s spectral density measured at the light-guide end. Each light-point had a narrow spectral Peak1 at ~450 nm and a broader Peak2 at ~570 nm, in which intensities and wavelengths are listed in Appendix 4—table 1. Based on their relatively small variations, all 25 light-points provided reasonably uniform light input, except the 4-times brighter No.22 (see below). This is because a fly photoreceptor’s response amplitudes differ only marginally until light intensity changes several-fold, as defined by the sigmoidal V/log(I) relationship (Matić and Laughlin, 1981). Standard light flashes, containing ~2 × 10⁶ photons/s at Peak1 and ~3 × 10⁶ photons/s at Peak2, were produced by setting Channel 1 to an input value of 2 V. Here, the estimated photon counts are given at the light source, not at the level of photoreceptor sampling. Moreover, in the experiments, to evoke subsaturating responses, we used a neutral density filter plate to cut the light-point intensity by 100-fold.

Appendix 4—table 1

Light- Point	Peak1 wavelength (nm)	Peak1 intensity (106 photons/s)	Peak2 wavelength (nm)	Peak2 intensity (106 photons/s)
No.1	448	2.720	571	2.805
No.2	452	1.790	570	2.818
No.3	448	2.618	565	2.900
No.4	451	1.840	576	3.020
No.5	451	2.570	575	3.710
No.6	451	2.214	572	3.640
No.7	452	1.430	575	2.020
No.8	446	2.203	570	2.990
No.9	453	1.465	571	2.350
No.10	451	3.300	578	5.100
No.11	453	1.877	575	3.080
No.12	455	1.763	575	3.020
No.13	451	2.334	575	3.440
No.14	451	2.009	576	2.634
No.15	454	2.400	568	4.480
No.16	452	2.390	572	4.165
No.17	455	3.190	566	3.010
No.18	452	1.990	578	3.320
No.19	455	1.958	578	3.336
No.20	454	1.745	569	2.670
No.21	450	2.642	573	2.314
No.22	452	9.520	572	13.300
No.23	452	2.420	575	3.380
No.24	452	2.658	573	3.284
No.25	452	1.670	570	2.750

Appendix 4—figure 3

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Light-point No.22 was 4-fold brighter than the others. However, no attempt was made to correct its intensity for three reasons. Firstly, it was located at the tested receptive fields’ periphery, and thus had limited influence on the measurements. Secondly, because this ‘error’ occurred stereotypically in every experiment, the brighter No.22 would not bias the comparative studies (see below). Lastly, having one brighter light-point was beneficial for other experiments, as will be shown in Appendix 6.

Two Lamina LED pads, each with 39 similar LEDs, provided ambient illumination to moderately light-adapt the tested photoreceptors. The pads were located at the outer half and outside each tested cell’s receptive field (Appendix 4—figure 2). Thus, a large portion of their light projected onto the neighboring photoreceptors. But the pads also illuminated the whole recording chamber, revealing its spatial structure and possibly inducing spatial processing in the lamina network. Light from each of the pad’s LEDs peaked at 460 nm (Appendix 4—figure 3B), delivering estimated ~2 × 10⁵ photons/s.

Pseudo-random receptive field scans

Before recording intracellular voltage responses from a R1-R6 photoreceptor, we located its receptive field center. This was done by flashing the light-point No.13 (at the center of the array) and moving the array (with the Cardan arm along its XY-axes) until the maximum response amplitude was elicited. The array was then locked at this position.

In the dark-adaptation experiments, the photoreceptor faced darkness (Appendix 4—figure 4A) for 30–60 s before its receptive field was measured. In the light-adaptation experiments, preselected background illumination (using the LED pads: Appendix 4—figure 2) was turned on 30–60 s before the corresponding receptive field measurement.

Appendix 4—figure 4

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A complete scan of a photoreceptor’s receptive field comprised 25 subsaturating flashes from all the light-points, one after another in a pseudo-random order (Appendix 4—figure 4B). Each flash lasted 10 ms, and was 490 ms apart from the next one (Appendix 4—figure 4C). Although this inter-flash-interval largely rescued the photoreceptor sensitivity, spatiotemporal adaptation might have still affected their responses. For instance, a flash near the center of the receptive field would light-adapt the cell more than one at the periphery, possibly causing the response to the next flash to be artificially smaller. Therefore, by randomizing the order of flash positions - with the Matlab command randperm(25) - we could reduce this kind of potential adaptation effects.

Channel 0 input was turned on only when Channel one was set to zero V; that is, in the resting period when all the light-points were off. Otherwise, the transitions of Channel 0 input values would generate running dot images. Each tested photoreceptor’s responses to 2–5 repetitions of pseudorandom scans were averaged (Appendix 4—figure 4D) before the acceptance angle (or half-maximum width), ∆ρ, of its receptive field was determined (Appendix 4—figure 5).

Appendix 4—figure 5

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In every experiment, we first assessed the recorded photoreceptor’s receptive field after dark-adaptation (Figure 7—figure supplement 1A). Wild-type R1-R6s’ mean acceptance angle, measured as their receptive fields’ half-maximum width, ∆ρ, was 9.47 ± 0.36° (± SEM, n = 19 cells), ranging from 7.00° to 11.65°. Interestingly, hdc^JK910 R1-R6’s receptive fields were 10.9% narrower (p =0.0397, two-tailed t-test). Their mean, minimum and maximum acceptance angles were 8.44 ± 0.32° (n = 18 cells), 6.18° and 11.50°, respectively.

Because each photoreceptor’s flash response amplitudes, V_n, were directly used to estimate its receptive field (Figure 7—figure supplement 1B), rather than being converted to angular sensitivities (see above), the obtained ∆ρ metric depended upon the cell’s output/input characteristics and the test flash intensity. To ensure that wild-type and hdc^JK910 photoreceptors’ ∆ρ comparison was unbiased by variable on-axis light sensitivities, we also compared their maximum response amplitudes, V₀, and V₀/∆ρ relations.

The corresponding V₀ values were very similar (Figure 7—figure supplement 1B) and mostly within 20–35 mV sub-saturated linear range of the photoreceptors’ V/log(I) curves (Dau et al., 2016). Moreover, in both wild-type and the hdc mutant, the linear correlations between V₀ and ∆ρ reflected only a weak trend of more sensitive photoreceptors (larger V₀) having wider receptive fields (larger ∆ρ) (Figure 7—figure supplement 1C,D).

Together, these findings indicate that the narrower ∆ρ of dark-adapted hdc^JK910 photoreceptors neither resulted from altered phototransduction nor was an artefact of this measurement method.

A photoreceptor’s ∆ρ measured under light-adaptation (at specific ambient illumination; Appendix 4—figure 2) should be smaller than during dark-adaption. There are four reasons for this difference:

• Light-adaptation steepens a photoreceptor’s V/log(I) function (Laughlin and Hardie, 1978; Matić and Laughlin, 1981; Eguchi and Horikoshi, 1984). This reduces the difference between I₀ and I_a50 (or the effective intensity that could evoke response amplitude V₀/2 ), which in turn leads to a smaller α₅₀ (or the corresponding angular position of I_a50) and thus to a smaller ∆ρ, as reported by the chosen method.

• Because the test flash intensity was kept unchanged, their contrast would be lower during light-adaptation than in the dark-adaption experiments, further reducing the I_o/I_α50 ratio, α₅₀ and ∆ρ.

• Light adaptation activates screening pigment migration, narrowing the intracellular pupil (cf. Appendix 2, Appendix 2—figure 1). The narrower pupil effectively reduces the amount of light from off-axis angles that can be absorbed by rhodopsin-molecules in the rhabdomere (Hardie, 1979; Smakman et al., 1984; Stavenga, 2004a; Stavenga, 2004b), reducing ∆ρ.

• Theoretical studies and some experimental data suggest that in dim conditions neural signal summation from neighboring cells may enhance sensitivity. But in bright conditions, lack of summation, increased lateral inhibition or both improve image resolution (Srinivasan et al., 1982; van Hateren, 1992c; 1993a; Warrant, 1999; Klaus and Warrant, 2009).

To quantify how moderate ambient light affects the fly eye’s spatial responsiveness, we analyzed the receptive fields of six wild-type (n = 6) and eight hdc^JK910 (n = 8) photoreceptors both at their dark- and light-adapted states.

At the dark-adapted state, the acceptance angles of wild-type and hdc^JK910 R1-R6s’ receptive fields, ∆ρ, were 9.65 ± 1.06° and 8.16 ± 0.62° (mean ± SEM), respectively (Box 4.8A). However, owing to the smaller test and control group sizes than in Figure 7—figure supplement 1A, this average difference (15.44%), though similar, was now statistically insignificant (p=0.258, two-tailed t-test).

At the light-adapted state, under the given ambient illumination (Figure 7—figure supplement 2B), the corresponding ∆ρ values were 7.70 ± 0.52° for wild-type photoreceptors and 6.98 ± 0.46° for their hdc^JK910 counterparts. Thus, light-adaptation significantly reduced ∆ρ values from dark-adaptation (p = 3.49×10⁻⁴, paired two-tailed t-test). Switching from the dark- to light-adapted states, wild-type photoreceptors’ receptive fields narrowed down by 18.44 ± 3.5% (Figure 7—figure supplement 2C), slightly more than those of mutants, which changed by 13.68 ± 3.37%. Yet, none of these parameters differed significantly between the wild-type and mutant photoreceptors.

Based on the ommatidium dimensions, as extracted from histological images of fixed/non-living retinae, and the waveguide optic theory, Stavenga (Stavenga, 2003b) calculated that the acceptance angles or dark-adapted Drosophila R1-R6 photoreceptors should be from 3.8 to 5.0^o (as amended for 16.5 µm diameter ommatidium lens). Yet, our current (∆ρ = 9.47^o; Figure 7—figure supplements 1 and 2) and earlier (Gonzalez-Bellido et al., 2011) measurements (∆ρ = 8.23^o; using Method two above) clearly showed that their acceptance angles in vivo are in fact about twice as large. What kind of physical mechanism(s) could explain this discrepancy between the theory and measurements?

We briefly introduce here some key points of the new ‘microsaccadic sampling hypothesis’, which is examined in detail in Appendixes 7–8.

• Living R1-R6 photoreceptors are not still but transiently contract to light (Hardie and Franze, 2012) (Video 3). We show in Figure 8 (see also Appendixes 7–8) that this causes considerable horizontal rhabdomere movements (up to 1.4 µm, peaking ~60–150 ms after a flash onset and returning back slower). As the lens system stays practically put, the rhabdomere tips shift away from the central axis, skewing the light input and narrowing the photoreceptors’ receptive fields dynamically.

• Rhabdomere contractions also move their tips axially; transiently down the focal plane (Video 2).

  • In a dark-adapted state, rhabdomere tips are elongated upwards (closer to the ommatidium lens), and possibly out of focus, collecting light through the lens system over a wider space. Thus, R1-R6s’ acceptance angles would be broader for light flashes spaced by normal (500 ms) intervals, which recover refractory microvilli, returning rhabdomeres to their old positions. But during a bright passing light stimulus, which progressively contracts R1-R6s, their acceptance angles dynamically narrow as the rhabdomeres draw a bit deeper in the retina.

  • At a moderate light-adaptation state (Figure 7—figure supplement 2), the intracellular pupil mechanism has reduced light input and the rhabdomere lengths should occupy a position (or set-point), which allows further contractions to light increments (cf. hair cells in the inner ear [Howard et al., 1988]). However, here, R1-R6s’ acceptance angles would still be broader for flashes with 500 ms intervals. Thus, the rhabdomeres would return to their pre-flash positions, which are closer to the lens than during a bright passing light stimulus.

• Photomechanical R1-R6 contractions are partially levered by the adherence junctions (Tepass and Harris, 2007) from their rhabdomeres to the above cone cells and epithelial pigment cells, which form the inner wall of the ommatidium underneath the lens (Figure 8F). Thus, as the photoreceptors contract to light, their adherence junctions appear to pull the pigments cells, moving and narrowing the aperture (and the light beam) in the front of their rhabdomere tips (Video 4).

Despite a Drosophila’s head and thorax being immobilized to the conical holder (Appendix 4—figure 4A), its eyes could still move affecting the electrophysiological recordings (Kirschfeld and Franceschini, 1969). Retinal movements, caused by spontaneous intraocular muscle activity, have been described in larger flies (Franceschini et al., 1991; Franceschini and Chagneux, 1994; Franceschini et al., 1995; Franceschini and Chagneux, 1997; Franceschini, 1998) and treated by different methods, including cooling, anesthesia and fixing their slightly pulled-out antennae (Smakman et al., 1984).

Here we report possibly related but slower retinal movements in fixed Drosophila preparations in vivo. Appendix 4—figure 6A shows an example, in which the optical axis of a R1-R6 photoreceptor moved between two consecutive receptive field scans. In the first scan, the receptive field center, which was localized by the largest flash response, corresponded to the light-point No.12. However, the second receptive field scan indicated that the cell’s optical axis pointed toward the light-point No.10. This displacement corresponds to an angular movement of ~3^o. We found that about 50% of photoreceptors, in which receptive fields were scanned more than once (8/18 wild-type and 8/16 mutant cells), displayed similar retinal movements in the range of 1–3.5^o. Moreover, these movements occurred in both front-to-back and back-to-front directions, validating that they were not equipment related artefacts; for example, not caused by gravitational drift in the 25 light-point stimulus array (Appendix 4—figure 2).

It has been suggested that recordings from damaged fly photoreceptors may result in (i) extraordinarily wide acceptance angles, (ii) diminishing sensitivity (Wilson, 1975), or (iii) markedly asymmetrical receptive fields, attributed to artificial electrical coupling between neighboring cells (Smakman and Stavenga, 1987). To ensure that high-quality ∆ρ measurements were presented in this study, we only considered data from photoreceptors in which intracellular responses were stable and repeatable, and their receptive fields reasonably symmetrical. However, we acknowledge that Drosophila eye movements can inadvertently affect the receptive field assessment accuracy.

The slow retinal movements and drifts that shift R1-R6 photoreceptors’ receptive fields are likely driven by eye muscle (Hengstenberg, 1971) activity. These movements can modulate light input to photoreceptors, causing spontaneous dips and peaks in their output during continuous repetitive stimulation, as is sometimes seen during long-lasting intracellular recordings (Appendix 4—figure 6B). Because this additional input modulation seems largely occur in the timescale of seconds, it should reduce mostly the low-frequency signal-to-noise ratio in the R1-R6 output. In this study, to obtain as good estimates as possible of the Drosophila photoreceptors’ encoding capacity, we only used data from the very best (most stable) recording series. These recordings (Figures 1–2; Figure 1—figure supplement 1; Figure 2—figure supplement 1) showed very little or no clear signs of such perturbations.

Appendix 4—figure 6

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Furthermore, in Appendixes 7–8, we quantify how all Drosophila photoreceptors exhibit fast light-triggered photomechanical micro-saccades, peaking ~100 ms after the stimulus onset and lasting 0.2–3 s, depending upon the stimulus intensity. These microsaccades directly modulate light input from the moving objects and consequently photoreceptor output, and we show through simulations and recordings how they can improve the spatiotemporal resolution of neural images (Figures 8 and 9; Figure 8—figure supplement 1 and Figure 9—figure supplement 1).

In this appendix, we described how receptive fields (spatial responsiveness) and acceptance angles (∆ρ) of wild-type and synaptically-blind hdc^JK910 R1-R6 photoreceptors were estimated, using intracellular voltage responses to new light-point array stimulation. Their characteristics in the dark- and moderately light-adapted states, and after prolonged light stimulation, were compared to test the hypothesis that spatial information summation in the lamina contributes to Drosophila photoreceptor function. We found that the dark-adapted wild-type R1-R6s show wider receptive fields. But in steady illlumination, the two photoreceptor groups’ ∆ρ-estimates adapted similarly.

Could the difference between the dark-adapted wild-type and hdc^JK910 receptive field widths result from recording artefacts? It is well known that LMCs’ hyperpolarizing intracellular responses to light pulses depolarize the surrounding extracellular space (Shaw, 1975), seen as the on-transient in the electroretinogram (ERG) recordings (Heisenberg, 1971). Theoretically, these signals could be picked up by recording microelectrodes, adding artificial components to the intracellularly measured V_n, and so making wild-type photoreceptors’ receptive fields appear wider (Hardie et al., 1981). However, we can essentially rule out this notion because the Gaussian functions, which quantified the actual recordings, were fitted to their real flank amplitudes rather than to zero (Appendix 4—figure 5). Consequently, any extra DC component would not affect the resulting ∆ρ-estimates. Furthermore, our past comparative study, which included different synaptic mutant flies, failed to find clear signs for ERG contamination in high-quality intracellular wild-type photoreceptor recordings (Zheng et al., 2006). Whereas by lacking neurotransmitter histamine, hdc^JK910 LMCs cannot respond to light (Burg et al., 1993; Melzig et al., 1996; Melzig et al., 1998), and thus hdc^JK910 photoreceptor recordings cannot be ERG contaminated. Hence, we conclude that ERG signals could only have marginal contribution to our results at most.

In fact, the dark-adapted photoreceptors’ ∆ρ-estimates constituted the most reliable data in this appendix, with the largest number of samples (n_wild-type = 19, n_hdc = 18 cells) obtained through consistent recording protocols. In every experiment, the receptive field assessment in the dark-adapted state was strictly the first examination, following the standard stimulus centering procedure. This minimized any potential downgrade in the recording quality or variation in the stimulation history. Notably, our estimate of WT Drosophila R1-R6 photoreceptors’ average receptive field half-width in the dark-adapted state, ∆ρ = 9.47 ± 0.36° (n = 19 cells; see Method 3, above), is reasonably similar to the previous estimate of 8.23 ± 0.54° (n = 11 cells) (Gonzalez-Bellido et al., 2011), which was obtained through a less stationary recording apparatus/method with more assumptions (see Method 2, above).

The dominant factors determining a fly photoreceptor’s receptive field are optical, waveguide properties and, particularly for the chosen measurement method, the phototransduction characteristics (Snyder, 1977; Land, 1997; Stavenga, 2003b, 2003a). For blowflies, it has been shown that the receptive field shape can be largely derived from the optical structure dimensions with the waveguide theory (Smakman et al., 1984). Given the hdc^JK910 mutants’ seemingly normal ommatidial and rhabdomere optics, as seen in vivo (Appendix 7) and under electron microscopy (Appendix 5; R1-R6 rhabdomere diameters, d, were ~96% of the wild-type), and their wild-type like photoreceptor voltage/intensity relations to brief light pulses (Dau et al., 2016), it is reasonable to expect that their ∆ρ-estimates would be close to wild-type. This should especially be true in light-adaptation, which is predicted to make photoreceptor output more independent of its neighbors (Atick, 2011; van Hateren, 1992c, 1992b). And indeed, we found ∆ρ-estimates of the light-adapted wild-type and hdc^JK910 photoreceptors alike. But because of this conformity, the 10.9% difference between their dark-adapted acceptance angles requires an additional explanation. Although at the flanks this difference increases (Figure 7—figure supplement 1A), it still may seem rather small when compared to the measured cell-to-cell variation within each genotype, with the respective maxima being 66% and 88% wider than the minima, and its statistical significance becomes less with fewer samples (Figure 7—figure supplement 2A). Nevertheless, the finding is conceptually important as it supports an expansion in the classic spatial vision paradigm; from the optical constraints to spatial information summation in the network (Stöckl et al., 2016).

The dark-adapted wild-type photoreceptors’ wider receptive fields are consistent with what we know about how synaptic inputs are channeled from lamina interneurons to R1-R6 axons (Meinertzhagen and O'Neil, 1991; Sinakevitch and Strausfeld, 2004; Zheng et al., 2006, 2009; Abou Tayoun et al., 2011; Rivera-Alba et al., 2011; Hu et al., 2015). Thus, the corresponding narrower receptive fields of mutant photoreceptors seem most sensibly attributed to the missing excitatory feedback modulation from their interneurons (Zheng et al., 2006; Nikolaev et al., 2009; Zheng et al., 2009; Dau et al., 2016). As shown by intracellular recordings (Zheng et al., 2006; Dau et al., 2016), feedforward and feedback signals dynamically contribute to photoreceptor and interneuron outputs in vivo. When the probability of light saturation is low, the stronger synaptic transmission in both pathways helps to amplify their response amplitudes.

Therefore, taken together with the findings of Dubs et al. (1981) and Dubs (1982), these results suggest that under dim illumination, lateral excitation spreads synaptically within the lamina of the fly visual system. Spatial information summation is likely implemented by the first-order interneurons and fed back to photoreceptors through connections (Meinertzhagen and O'Neil, 1991; Rivera-Alba et al., 2011) that utilize excitatory neurotransmitters (Zheng et al., 2006; Hu et al., 2015). This model is further supported by our anatomical observations (Appendix 5 and Appendix 7), which imply that there are no major developmental defects in hdc^JK910 retina and that their lens systems and rhabdomere sizes are broadly wild-type-like.

This appendix shows how R1-R6 rhabdomere diameters vary systematically and consistently in Drosophila ommatidia and provides supporting background information for the results presented in Figures 7–9 and Appendix 4.

In this appendix:

• We measure wild-type and hdc^JK910 histamine-mutant (Burg et al., 1993; Melzig et al., 1996; Melzig et al., 1998) R1-R6 photoreceptors’ rhabdomere sizes from the electron micrographs of their retinae.

• We compare these measurements to their electrophysiologically measured receptive field estimates (Appendix 4).

• We show that the mean wild-type R1-R6 rhabdomere diameter, d_R1-R6, is only ~4.1% wider than in hdc^JK910 mutant eyes. This difference may contribute in part to their 10.9% wider average acceptance angle (∆ρ) in a dark-adapted state (Appendix 4), but cannot fully explain it (see also Appendix 7).

• We further show that in both phenotypes R1, R3 and R6 rhabdomeres are systematically larger than R2 and R4 rhabdomeres. As for the maximum difference, the mean R1 rhabdomere diameter (d_R1 = 1.8433 ± 0.1294 µm, mean ± SD) is about 18% wider than that of R4 (d_R4 = 1.5691 ± 0.0915 µm, n = 25, p = 2.3419×10⁻¹¹, 2-tailed t-test).

• These findings imply that each R1-R6 photoreceptor should have a different receptive field size (coinciding with their considerable ∆ρ variation seen in Appendix 4, Figure 7—figure supplement 1C).

• Our results further suggest an asymmetric information integration model, in which the neural superposition of different-sized overlapping receptive fields (of the neighboring R1-R6s) has a potential to contribute in enhancing Drosophila’s visual acuity beyond the presumed optical limits of its compound eyes (as revealed by behavioral experiments in Appendix 9).

Neural superposition eyes provide more samples from local light intensity changes for each image pixel, represented by large monopolar cell (L1 and L2) outputs. In the conventional viewpoint, each pixel’s signal-to-noise improves by $\sqrt{6}$ because its L1 and L2 receive similar inputs from six ‘physiologically identical’ R1-R6 photoreceptors, which sample information from the same small area in the visual space. Thus, the conventional assumptions and limits for neural superposition performance are:

• Each R1-R6 functions virtually identically, generating similar outputs to the same light input

• Each R1-R6 in superposition has an identical receptive field size and shape

• The receptive fields in superposition overlap perfectly

• Each image pixel represents sampling and processing within its inter-ommatidial angle

• Inter-ommatidial angle sets the visual resolution of the Drosophila eye

This appendix presents anatomical and theoretical evidence that these assumptions and limits are overly simplistic and suggests ways the real neural images could be sharpened beyond them to improve Drosophila vision.

Drosophila R1-R6 photoreceptors’ rhabdomere sizes vary systematically and consistently in each ommatidium (Appendix 5—figure 1B). R1 and R6 rhabdomere cross-sectional areas are always the largest and R4 rhabdomeres the smallest (Appendix 5—table 1).

Theoretically, a fly photoreceptor’s receptive field size depends upon its rhabdomere diameter, d (Equation A4.3). This relationship was recently supported experimentally by comparing the rhabdomere diameters and acceptance angle estimates, ∆ρ, of Drosophila R1-R6 photoreceptors to those of killer fly (Coenosia attenuata), both of which eyes have rather similar ommatidial lens sizes (16–17 vs 14–20 µm) and focal lengths (21.36 vs 24.70 µm) (Gonzalez-Bellido et al., 2011), cf. Equation A4.3. In ♀ Drosophila, maximum d was ~2 µm and in ♀ Coenosia ~1 µm, while Drosophila’s mean ∆ρ-estimate was 8.23 ± 0.54^o and Coenosia’s 2.88 ± 0.07^o (Gonzalez-Bellido et al., 2011). Thus, the wider rhabdomere tip correlates strongly with the wider receptive field.

Accordingly, with each Drosophila ommatidium hosting R1-R6 rhabdomeres of distinct size differences (Appendix 5—figure 1B, left; Appendix 5—table 1), the receptive fields of the neighboring R1-R6, which are pooled together in neural superposition, should differ in size and overlap broadly. These observations and analysis concur with the broad variability of the intracellularly measured wild-type R1-R6s’ receptive field widths (Appendix 4:Figure 7—figure supplement 1A,C).

However, although collectively the mean wild-type R1-R6 rhabdomere cross-sectional areas (Appendix 5—tables 2,3) are larger than their hdc^JK910 counterparts (Appendix 5—figure 1B), their corresponding diameter differences are small. The average wild-type R1-R6 rhabdomere diameter, (WT d_R1-R6 = 1.70 ± 0.15 µm; mean ± SD, n = 150 rhabdomeres; Figure 5) is only ~4.1% wider than in hdc^JK910 mutant eyes (hdc^JK910 d_R1-R6 = 1.64 ± 0.10 µm; n = 150 rhabdomeres), as extrapolated from the ellipsoid rhabdomere area fits. Thus, hdc^JK910 photoreceptors’ smaller average rhabdomere diameters can contribute to their ~ 10.9% narrower ∆ρ (Appendix 4:Figure 7—figure supplement 1A,D), but cannot fully explain it (Appendix 5—figure 1B, right).

In the Drosophila compound eye, R1-R6 photoreceptors’ mean acceptance angle (∆ρ ~9.5^o) is on average about twice as wide (see Appendix 4) as its mean inter-ommatidial angle (∆φ ~4.5^o) (Gonzalez-Bellido et al., 2011). Such an eye design could potentially facilitate spatial hyperacuity through neural image processing. In the vein of previous suggestions for manmade optoelectrical systems (Luke et al., 2012) and retinae of other species (Zurek and Nelson, 2012), we consider three alternative hypothetical scenarios based upon neighboring R1-R6s’ overlapping receptive fields (RFs) (Pick, 1977).

The first case (Appendix 5—figure 2, left) considers RF variations of the photoreceptors in neural superposition. An image of an object (here, a thin 1^o vertical bar, grey) stimulates simultaneously eight photoreceptors (R1-R8), which gather light information about the same area in the visual space by their overlapping RFs (for clarity only R1-R3’ RFs are shown; orange Gaussians). However, because the rhabdomere diameters, d, vary considerably and consistently between them (e.g. R1 and R6 rhabdomere diameters areas are ~18% wider than those of R4s; Appendix 5—figure 1), so could also be their RF sizes (see Appendix 4, Equation A4.3), causing overlaps. Six of these inputs (R1-R6) are pooled in the lamina. Consequently, even a small (1^o) displacement of the vertical bar stimulus (grey) could lead to variable but specific light intensity modulations in each of the six converging input channels. Their signals to LMCs (L1-L3), which in high signal-to-noise conditions transforms input modulations into phasic responses (Zettler and Järvilehto, 1972; Järvilehto and Zettler, 1973; Zheng et al., 2006; Zheng et al., 2009; Wardill et al., 2012), could therefore be different before and after the bar displacement and possibly neurally detectable.

In the second case (Appendix 5—figure 2, middle), six photoreceptor cells of the same type (say R2s) in the neighboring ommatidia gather light information from the neighboring small visual areas (~4.5^o apart, as separated by the interommatidial angle), but their receptive fields (~9.5^o half-widths) overlap; for clarity only three R2s are shown: orange, blue and red. Lateral connections (L4, Lawf and Am cells) between lamina neuro-ommmadia could then be used by LMCs to compare their outputs, enhancing the spatial resolution of each neural channel (see Appendix 2, Appendix 2—figure 5).

In the third case (Appendix 5—figure 2, right), R1-R6 photoreceptor cells in the same ommatidium gather light information from the neighboring small visual areas, but their receptive fields overlap; again for clarity only three: orange (R1), blue (R2) and red (R3) are shown. Lateral connections (L4, Lawf and Am cells) between adjacent lamina neuro-ommatidia may enable LMCs to compare their outputs, enhancing the spatial resolution of each neural channel.

Appendix 5—figure 2

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All these circuit models could theoretically contribute to motion vision hyperacuity, which occurs when a stationary Drosophila eye resolves object motion finer than its ~4.5^o inter-ommatidial angle (the average sampling point or photoreceptor spacing). And crucially, in Appendix 10, we use a flight simulator system to demonstrate and quantify Drosophila hyperacute optomotor behavior to sub-interommatidial stimuli (1-4^o). However in Appendix 7-8, we further provide decisive evidence that the spatiotemporal resolution of the early neural images is improved by synchronized and coherent photomechanical rhabdomere contractions (Hardie and Franze, 2012), which move and narrow R1-R6s’ receptive fields. Together with refractory information sampling, this enables photoreceptors to encode space in time. Therefore, as the RFs narrow with moving stimuli, this reduces the overlap between the neighboring RFs and, consequently, affects the potential resolving power of the circuit models in Appendix 5—figure 2.

We conclude that at the photoreceptor level the overlapping RFs provide neither necessary nor sufficient mechanistic explanations for the Drosophila spatiotemporal hyperacuity. However, at the lamina interneuron level, such connectivity arrangements may further enhance hyperacute vision. It is also possible that any kind of retinal image enhancement would be further coordinated centrally to match the visual needs of a locomoting fly. In walking blowflies, intraocular muscles in both the left and right eye seem to contract synchronously with increasing rates, causing vergence eye movements (Franceschini et al., 1991; Franceschini and Chagneux, 1994; Franceschini et al., 1995; Franceschini and Chagneux, 1997; Franceschini, 1998). Finally, we note that in lobula plate motion sensitive cells, responses to moving visual stimuli increase with locomotion (Chiappe et al., 2010; Haag et al., 2010; Maimon et al., 2010; Tang and Juusola, 2010), although there is currently no evidence to relate this phenomenon to hyperacuity, as characterized here.

Temporal output modulation through gap-junctions between R1-R6 and R7-R8 photoreceptor axons could further contribute, as a possible network mechanism, to the acuity improvements that we report in this publication (Figures 7–8; see Appendix 6). Drosophila R1-R6s have larger rhabdomeres, each with ~30,000 microvilli, whereas those of R7s and R8s contain only ~15,000. Owing to superposition in each neuro-ommatidium, both of these photoreceptor classes integrate photons from the same small area in space, but for given light changes, the macroscopic R1-R6 output rises and decays faster than those of R7s and R8s. This is because R1-R6 rhabdomeres integrate twice as many samples (quantum bumps) from the same stimulus and their membranes have likely smaller time constant (Anderson and Laughlin, 2000). Therefore, at each moment in time, R1-R6 and R7-R8 outputs carry a dynamic phase difference. If their responses were to antagonize each other through the gap-junctions between R6 and R7/R8 axons (Shaw, 1984; Shaw et al., 1989; Wardill et al., 2012), similar to the crosstalk between Calliphora R7 and R8 outputs (Hardie, 1984), phasic R1-R6 output components could be enhanced even further.

This appendix describes a new method to measure Drosophila photoreceptor output to moving dots, and shows how these responses provide much higher visual resolution and motion blur resistance than what is predicted by the classic theories, supporting the results in Figures 7–9.

In this appendix:

• We measure how well dark- and moderately light-adapted wild-type Drosophila R1-R6 photoreceptors resolve bright dots (point-objects), which cross their receptive fields at different speeds.

• We compare these intracellular recordings to those of histamine-mutants, hdc^JK910 (Burg et al., 1993; Melzig et al., 1996; Melzig et al., 1998), in which first-order interneurons are blind (receive no neurotransmitter from photoreceptors) and thus incapable of feedback-modulating the photoreceptor output.

• We further record voltage responses of blowfly (Calliphora vicina) R1-R6 photoreceptors to moving point-objects, as an additional test of our experimental setup, stimulus paradigm and mathematical analyses, validating this method.

• We evaluate the wild-type and mutant recordings against their respective classic model simulations, in which each recorded receptive field is convolved by the same cell’s impulse response.

• Our results indicate that both wild-type and hdc^JK910 R1-R6s resolve moving dots about equally well, and significantly better than the corresponding classic model simulations.

• These findings demonstrate that the classic deterministic photoreceptor models (Srinivasan and Bernard, 1975; Juusola and French, 1997; Land, 1997) for resolving moving objects grossly underestimate the visual resolving power of real photoreceptors.

• Consequently, the classic theory overestimates the effects of motion blur on Drosophila vision during saccadic behaviors.

A single photoreceptor’s voltage responses can give important insight into neural image processing behind a fly’s ability to detect small objects, whether in high-speed chasing flights or against a cluttered background (Burton and Laughlin, 2003; Brinkworth et al., 2008). Theoretically, when a point-object moves uniformly across an array of photoreceptors, each cell would produce a similar response. But these responses would be displaced in time, t, which it takes for the object to travel between two adjacent cells’ receptive field centers (Srinivasan and Bernard, 1975). Thus, the response of the whole array, as a collective neural representation of the moving point-object, would be a travelling pattern with a mirrored waveform. Mathematically, this can be extrapolated from a single photoreceptor’s response. We now apply this classic approach to simplify the questions about neural images of moving point-objects and compare its predictions to R1-R6s’ spatiotemporal responses.

First, we consider the problem of neural latency compensation in motion perception. This is related to the flash-lag effects observed in humans (Krekelberg and Lappe, 2001; Nijhawan, 2002). Due to the inevitable phototransduction delays, every sighted animal should encounter this problem and Drosophila is not an exception. At 19°C, its photoreceptors’ voltage responses rise ~10 ms from the light flash and peak 15–30 ms later (Juusola and Hardie, 2001b). Given that a fly’s saccadic turning speed (Fry et al., 2003) in flight can exceed 1000 ^o/s, such delays need compensating by network computations. Otherwise, neural images of its surroundings could lag behind their actual positions by more than 25^o, making fast and accurate visual behaviors seemingly infeasible.

Such compensations have been shown to occur early on in vertebrate eyes. In the tiger salamander and rabbit retina, ganglion cells’ firing rates lag behind flashing but not moving bars (Berry et al., 1999). Whether similar processing happens in insect eyes is unknown. By analyzing Calliphora, wild-type Drosophila and hdc^JK910 R1-R6 output to a point-object crossing their receptive fields, we find their time-to-peak values broadly similar to those evoked by light flashes. Therefore, these lag times are not, or at most weakly, compensated by the signal spread between photoreceptors.

Second, we examine whether R1-R6 output to point-object motion displays directional preference, as suggested by the asymmetric synaptic feedback to them (Meinertzhagen and O'Neil, 1991; Rivera-Alba et al., 2011). While both L1 and L2 monopolar cells mediate a major neural pathway in the lamina, L2s show richer connectivity. Only L2 projects feedback to R1-R6 and have reciprocal connections with L4, which in turn connects to L4s of the neighboring neural cartridges (Braitenberg and Debbage, 1974), providing further feedback to photoreceptors (Meinertzhagen and O'Neil, 1991; Rivera-Alba et al., 2011). We find that whilst the photoreceptors’ peak responses show no clear directional preference, their rise and delay time courses to front-to-back and back-to-front moving point-objects often differ significantly. Although it is still possible that these differences may in part be augmented by the asymmetric network feedback, we show in Appendixes 7–8 that they actually originate from photomechanical R1-R8 contractions (Hardie and Franze, 2012).

Third, we investigate whether network regulation affects R1-R6 cell’s spatiotemporal acuity. By using the classic approaches (Srinivasan and Bernard, 1975; Juusola and French, 1997; Land, 1997), we estimate the theoretical blur effects and the eye’s ability to resolve bright dots moving at certain speeds. Furthermore, we apply the Volterra series, a widely used ‘black-box’ modeling method (Marmarelis and McCann, 1973; Eckert and Bishop, 1975; Gemperlein and McCann, 1975; Juusola et al., 1995b; Korenberg et al., 1998), to simulate wild-type and hdc^JK910 R1-R6 output to these point-objects (Juusola et al., 2003; Niven et al., 2004). Remarkably, the simulations make it clear that these models cannot predict the recordings accurately (see Appendix 1 and Figures 7 and 8G–I).

Spatiotemporal resolution of the eye is thought to be determined by two components with special characteristics: the static spatial resolution of light input, as channeled through the optics (Srinivasan and Bernard, 1975; Hornstein et al., 2000), and the temporal response dynamics of photoreceptors. These characteristics are further influenced by the photoreceptors’ adaptation state and synaptic feedback. The classic approaches suggest that because wild-type R1-R6s’ acceptance angles (∆ρ) are 10.9% wider than those of hdc^JK910 but their response dynamics are similar (see Appendix 4), they should produce blurrier images (of wider spatial half-width, S). Moreover, as hdc^JK910 R1-R6s lack synaptic feedback modulation (Dau et al., 2016), their predicted higher acuity should reflect differences in spatiotemporal photon sampling dynamics. Our recordings show, however, that both wild-type and hdc^JK910 R1-R6s resolve moving dots at least twice as well what the classic theory predicts, and that any resolvability difference between these cells largely disappears against a lit background. Thus, in dim conditions, lateral summation within the network may sensitize R1-R6 output by trading-off acuity, whereas in bright conditions more independent photoreceptor output sharpens neural images. Nonetheless, the classic theory cannot account for these dynamics, as it greatly overestimates the effect of motion blur on photoreceptor output.

We later demonstrate in Appendixes 7–8 how and why the model simulations (of this appendix) differ from the corresponding recordings. Essentially, this is because the classic theoretical approaches do not incorporate two interlinked biophysical mechanisms that are critical for high acuity. (i) Rapid photomechanical photoreceptor contractions (Hardie and Franze, 2012) accentuate light input dynamically by shifting (front-to-back) and narrowing the cell’s receptive field as moving bright point-objects enter in its view. While (ii) stochastic refractory photon sampling by microvilli accentuates the temporal dynamics in R1-R6 output. These mechanisms work together to improve the acuity and resolvability of moving objects far beyond the predictions of the classic models.

The 25 light-point array and LEDs pads, which we used for creating images of moving objects and providing ambient illumination, respectively, are described in Appendix 4. In the Drosophila experiments, the 25 light-point array was placed 6.7 cm away from the fly, subtending an angle of 40.92^o. This gave each light-point (dot) 1.7^o size and minimum inter-dot-distance. In the Calliphora experiments, these parameters were 17 cm (distance) and 16.73^o (viewing angle).

Images of one moving point-object (dot) were produced by briefly turning each light-point on and off, one after another in an incremental (for front-to-back direction) or decremental order (for back-to-front direction). Accordingly, Channel 0 input was driven with increasing or decreasing ‘ramp’ (Appendix 6—figure 3A), while Channel one input was set to 2 V. The travelling time of an object, or duration of the ‘ramp’, was between 50 ms and 2 s, resulting in object speeds within naturalistic range (Schilstra and Hateren, 1999; Hateren and Schilstra, 1999; Fry et al., 2003): from 20 to 818 ^o/s for Drosophila and 8 to 334 ^o/s for Calliphora.

The ability to resolve two moving point-objects of Drosophila photoreceptors were tested in dark-and light-adaptation conditions. In light-adaptation experiments, two 39-LED pads, on both sides of the 25 light-point array, provided background illumination (see Appendix 4, Appendix 4—figure 2). The two dots in the 25 light-point array were separated by 6.8^o (four dark points in between) and moved together at different speeds; typically, 205, 409 or 818 ^o/s. Each stimulus was presented 8–10 times to the fly and the resulting photoreceptor responses were averaged before being analyzed.

To evaluate how well the classic theory of fly compound eye optics/function (Srinivasan and Bernard, 1975; Juusola and French, 1997; Land, 1998) explains single Drosophila R1-R6 photoreceptors ability to resolve moving dots, we needed to estimate each photoreceptor’s linear impulse response (the first Volterra kernel) separately. The cell’s voltage response to moving dots could then be predicted by convolving each recorded receptive field by the same cell’s impulse response

Light-point No.13 intensity was controlled by setting Channel 0 input to 5 V and modulating Channel one input with a Gaussian white-noise (GWN) time series, which had the mean value of 2.5 V and cut-off frequency of 200 Hz. With these settings, light-point No.13 delivered 2.5 × 10⁶ photons/s at Peak1 (451 nm) and 3.75 × 10⁶ photons/s at Peak2 (575 nm) on average (cf. Appendix 4—Table 1). Finally, these intensities were reduced 100-fold by neutral density filtering

The principal assumptions of the Volterra series method are that the system has finite memory and is time-invariant (Schetzen, 1980). That is, (i) the relationship between output (photoreceptor voltage response) y(t) and input (light stimuli) u(t) is characterized by an unchanging impulse response and (ii) y(t) depends only on current and past values of u(t - τ) → u(t) with limited regression time, τ. The continuous form of this input/output relationship is described by the following equation:

where k₀, k₁ and k₂ are the zero-, first- and second-order time-invariant kernels, which define the system’s impulse response. T is the finite system memory limit.

Note that the model order is not limited, as expressed only up to second-order in Equation A6.1, but instead could be extended arbitrarily further. However, it has been shown that a light-adapted fly photoreceptor’s response to GWN light intensity time series stimulation, as used in these experiments, can be approximated well by the linear terms (Juusola et al., 1994; Juusola et al., 1995a).

Therefore, the estimation of system output was simplified to a linear convolution of input with zero- and first-order kernels. Each measurement of photoreceptor voltage response and light stimuli could be fitted into the discrete and simplified form of Equation A6.1 as:

The group of Equation A6.2, which approximates $N$values of photoreceptor output, was then re-arranged into matrix form:

Equivalently, Equation A6.3 could be symbolized as:

where vector $Y$contained a sequence of N output values, P was the regression matrix constructed from the lagged input values, and the column θ elements were the kernel values. The problem of determining a photoreceptor’s Volterra series model was hence broken down to designing input stimuli$u\left(t\right)$ and measuring output values $y\left(t\right)$ to construct matrices P and Y of Equation A6.4, and estimating θ.

u(t) was a GWN series with 200 Hz bandwidth, which thus tested the whole frequency range of photoreceptor output. Initially, each tested photoreceptor was steady-state-adapted to the chosen light background (the average brightness of the GWN stimuli) for 30–60 s (see also Appendix 4). Input was then delivered from the light-point No.13, by setting Channel 0 to 5 V and modulating Channel one input by the GWN series around the mean value of 2.5 V. Each time series was 3-second-long and was repeated 8–10 times before the responses were averaged. The first 1.5 s of the recorded data was used to estimate the kernel values.

Photoreceptor output y(t) was sampled at 10 kHz. It was then preprocessed by removing the mean value and trends, and down-sampled.

Once the matrices Y and P of Equation A6.4 are constructed, there are several approaches to estimate θ with minimal error, such as the least squares regression by using Gram-Schmidt orthogonalisation (Korenberg et al., 1988; Korenberg and Paarmann, 1989) or Meixner functions (Asyali and Juusola, 2005). Here, θ was approximated by the single value decomposition method (Golub and Reinsch, 1970; Lawson and Hanson, 1974), in which the factorization of matrix P and the calculation of its Moore-Penrose pseudoinverse matrix, P⁺, were carried out by the command pinv(P) in MATLAB. The linear least-squares estimation of θ, $\widehat{\theta }$, was given by:

The computed kernels and the second half of GWN stimuli were then substituted to Equation A6.2 to yield the model prediction of the photoreceptor response. The accuracy, or fitness, F, of the prediction was quantified by the complement of its mean squared error:

where $y$ were the actual data measured from the photoreceptor voltage response and y’ were the values simulated by the mathematical model.

After determining and testing the Volterra model, we next approximated the light stimuli (input) delivered by the point-objects crossing a photoreceptor’s receptive field. Since a photoreceptor’s voltage response was assumed to be linearly correlated to light input, the response amplitudes to the subsaturating light flashes during the receptive field scans (see Appendix 4) were also considered linear measurements of the effective intensity from each light-point. Therefore,$u_m\left(t\right)$, created by one moving point-object, was modelled as 25 intensity steps, in which amplitudes were proportional to their corresponding flash responses (Appendix 6—figure 1). The temporal width of each step was calculated according to the object speed. Similarly, $u{\text{'}}_m\left(t\right)$ of two moving point-objects was constructed from the superimposition of $u_m\left(t\right)$ and $u_m(t+\Delta )$, where $\Delta$ was calculated according to the point-objects’ speed and their separation angle.

Appendix 6—figure 1

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Lastly, a photoreceptor’s voltage response to point-object motion was simulated by substituting input $u_m\left(t\right)$ or $u{\text{'}}_m\left(t\right)$ and the kernels values to the zero- and first-order terms of Equation A6.2.

Neural images in the fly retina, lamina and medulla are generated by retinotopically mapping the surrounding light intensity distribution. This means that light coming from each point in space is sampled and processed by one neural cartridge (or neuro-ommatidia) (Meinertzhagen and O'Neil, 1991). While a stationary object might be seen by several photoreceptors belonging to neighboring ommatidia due to their large acceptance angles (Appendix 4) and overlapping receptive fields (Appendix 5), the object position is almost certainly perceived on the photoreceptor’s optical axis. This position, along its corresponding lamina/medulla cartridge below, produces the largest/fastest intracellular responses (Appendix 6—figure 2; see also Appendix 4) as it channels the maximum light influx into the rhabdomere (see Appendix 2).

Appendix 6—figure 2

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Furthermore, it is customarily assumed that a moving point-object’s position would be associated with the peak of its neural image. However, this does not necessarily mean that a R1-R6’s response maximum would indicate the object position. Rather, it is more plausible - especially during high signal-to-noise ratio conditions (bright stimulation) - that the lamina circuitry (cf. Appendix 2, Appendix 2—figure 7) would be amplifying more the photoreceptor signal derivative. This is because the large monopolar cells (LMCs) are then more tuned to responding to the rate of light changes (Zettler and Järvilehto, 1972; van Hateren, 1992b; Juusola et al., 1995a; Zheng et al., 2006).

In fact, neural latency might be compensated at the subsequent processing stages in the visual system, so that the peak of the travelling network response wave would closely follow the object’s actual position, as is the case of the vertebrate ganglion cells (Berry et al., 1999). Theoretically, if such ‘correction’ occurred maximally at the single neuron level, it would mark the coincidence of two events. (i) The neuron’s response would peak as (ii) the object passes its receptive field center.

To examine whether, or to what degree, neural images of moving objects are compensated for latency at the first processing stage in the fly R1-R6 photoreceptors, we measured their intracellular voltage responses while presenting the fly with a bright dot moving at different speeds.

Appendix 6—figure 3

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Appendix 6—figure 3B depicts a typical response waveform of a blowfly (Calliphora vicina) R1-R6 to a bright moving dot (the point-object in Appendix 6—figure 3A). Let x be the time needed for it to travel through the 25 light-point array, t₁ be the moment when the dot pass the cell’s optical axis, i.e. the corresponding light-point is turned on, and t₂ be when the intracellular response peaks. With varying $x$, and thus the dot speed, t₁, can be computed as:

where the coefficient $a$ is a constant. The aim was to align the 25 light-point array so that the point No.13 lies at the tested photoreceptor’s receptive field center. Therefore in theory, a is approximately 0.48. However, the light-point No.13 might, in fact, be off-axis. For example, the cell’s receptive field center could lie in between No.13 and No.12, causing inaccuracy in the calculation of a, t₁ and lag time b, which is given by:

To overcome this ambiguity, we plotted t₂ against$x$, given that:

Appendix 6—figure 3C illustrates an example of the relationship between t₂ and $x$obtained from a Calliphora R1-R6. The two parameters fitted exceedingly well to a linear relationship (adjusted R-squared >0.9999), in which coefficient a and lag time b were found as 0.486 and 14.62 ms, respectively. These data show that in this particular case, indeed light-point No.13 was close to the center of the cell’s receptive field and that lag time b was virtually unchanged for different object speeds. The on-axial position of the light-point No.13 was later confirmed by 11 receptive field scans, all of which indicated that response elicited by a light flash from No.13 was the largest (data not shown).

The same photoreceptor was also stimulated by repeating a light flash, to which its voltage response peaked 15 ms later. The small difference between the lag time of motion response and the response time-to-peak to a flash does not readily imply neural network latency compensation. In case of the moving stimuli, photoreceptor was stimulated when the dot entered its receptive field, causing its intracellular voltage to start depolarizing before the dot reached the cell’s optical axis. Conversely, the photoreceptor’s response to light impulse was only elicited after the stimulus onset, making its time-to-peak slightly longer than the lag time.

In the classic flash-lag psychological experiment, where a flashing bar and another uniformly illuminated one travelled together, the former was perceived to be trailing (Nijhawan, 1994; Brenner and Smeets, 2000). Thus, it is probable that at some stage in the visual system, the voltage response peak (maximum) caused by moving object would display shorter delay than those elicited by increasing light intensity. In the present study, the light-point No.22 was 4-fold brighter than the others, as discussed in Appendix 4, and indirectly played the role of the flashing bar, causing a ‘local peak’ in a photoreceptor’s voltage response (Appendix 6—figure 3B). Hence, to further examine neural latency of R1-R6 output, we next assessed the lag time, b’, corresponding to this peak in the response. Given t₃ is the moment when No.22 was turned on, which can be calculated as:

and is the time of the local response peak (Appendix 6—figure 3), lag time is defined as their difference:

The relationship between t₄ and x could also be described by linear fitting with almost zero residue (Appendix 6—figure 3D), yielding a’ and b’ values of 0.83 and 13.29 ms, respectively.

These data exemplify that a photoreceptor’s response maxima, no matter whether caused by a point-object moving across its receptive field or by an unexpected increase in light intensity, show similar lag time characteristics. Both b and b' were independent of the object speed and comparable to the response time-to-peak, as induced by a comparable flash. These features were reproducible and general; observed in all seven tested Calliphora photoreceptors, without exception (Appendix 6—table 1).

Drosophila photoreceptors’ voltage responses did not clearly exhibit the ‘local peak’ to the light-point No.22; possibly owing to their slower temporal dynamics. Nevertheless, the temporal position of the ‘global peak’, measured by t₂ of wild-type (n = 12) and hdc^JK910 (n = 3) photoreceptor outputs, consistently showed linear correlation to x and comparable lag-time/time-to-peak values (Appendix 6—table 2). Their corresponding maxima showed slightly larger lag time variations, and thus the linear fits were not as error-free as with the Calliphora data. Nonetheless, overall, the mathematical relation between their peak response lag time and the object speed appeared similar. The comparable wild-type and hdc^JK910 R1-R6 output maxima to the tested point-object velocities, as recorded from their somata, suggests that their response dynamics mostly reflect similar phototransduction processing, with possibly only marginal influence from the lamina network.

Altogether, these data imply that fly phototransduction machinery (see Appendixes 1–2) samples intensity changes and object motion much the same way. Because its peak responses lag behind the actual positions of the moving objects, the neural latency of moving objects is most likely compensated downstream by image processing within the interneuron networks, starting with the LMCs (cf. Appendix 2, Appendix 2—figure 7E).

As summarized in Appendix 6—table 2, Drosophila photoreceptors’ maximum responses to a front-to-back or back-to-front moving bright dot did not exhibit clear signs of latency compensation, as indicated by their similar time-to-peak durations (estimated from the population means of individual unpaired recordings). Interestingly, in the paired recordings, however, the response rise and decay time-courses often showed considerable latency modulation.

Appendix 6—figure 4

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When a R1-R6 contracts to light input, its receptive field moves front-to-back (Appendixes 7–8). Thus, with the ommatidium lens inverting images, its responses to the back-to-front dot motion raise systematically slightly earlier (Appendix 6—figure 4E,F). This rise-time lag reduces because the dot moves against the receptive field motion, whilst the rise-time lag increases during comparable front-to-back motion when the dot moves along the receptive field motion. In other words, a dot stayed a bit longer within a R1-R6’s receptive field during front-to-back motion than back-to-front motion. Such phasic differences were consistently observed in most recordings over the tested speed range. For example, 205 ^o/s back-to-front movement evoked narrower temporal response half-widths in 8/10 R1-R6s than the opposite movement. Similarly, 409 ^o/s back-to-front movement evoked narrower temporal response half-widths in 6/10 R1-R6s (in 2 cells, these were identical; and wider in 2).

Appendix 6—figure 4 depicts intracellular responses to a moving dot, passing a photoreceptor’s receptive field front-to-back and back-to-front at (A) 409, (B) 205, (C) 136 and (D) 102 ^o/s.

Although their time-to-peak values appeared similar, the response rise and decay dynamics showed clear differences (Appendix 6—figure 4E–H), which correlated with the dot speed and motion direction. We shall later show in Appendix 7, using high-speed video recordings of photoreceptor rhabdomeres, that their photomechanical contractions (Hardie and Franze, 2012) occur in back-to-front direction. Light input modulation by these directional microsaccades can much explain the phasic differences in photoreceptor output to different directional point-object motions.

In summary, a prominent feature of R1-R6s’ voltage responses to opposing object motion directions is their similar time-to-peak values. This was found in all somatic recordings of Calliphora and Drosophila photoreceptors. Intriguingly, though, we further identified small (2–10 ms) but significant differences in the response rise and decay to front-to-back and back-to-front object motion. These phasic differences in photoreceptor output can be largely explained by each cell’s directional photomechanical contractions, and we later show how these contribute to improving the fly’s visual acuity (Appendixes 7–8). It is plausible that these directional preferences would be further enhanced downstream at the level of network processing. During bright stimulation, LMCs respond most strongly to the rate of change in photoreceptor output (Juusola et al., 1995a; Zheng et al., 2006; Zheng et al., 2009; Wardill et al., 2012), with the rich connectivity of the optic lobes proving further possibilities for the required phase coding (Meinertzhagen and O'Neil, 1991; Rivera-Alba et al., 2011; Wardill et al., 2012; Behnia et al., 2014).

We showed in Appendix 4 that dark-adapted hdc^JK910 photoreceptors have narrower receptive fields (acceptance angles) than their wild-type counterparts but broadly similar response dynamics (Figure 7—figure supplement 1). Thus, the prediction is that hdc^JK910 R1-R6s should produce slightly sharper neural images than their wild-type counterparts after dark-adaptation. Classic theoretical approaches have been used to predict how the spatial and temporal factors might jointly affect visual acuity (Srinivasan and Bernard, 1975; Juusola and French, 1997). Accordingly here, we first predict with them the motion blur effects on wild-type and hdc^JK910 R1-R6 outputs. Later on, we test the ability of these cells to distinguish two dots moving together, separated by less than the cell’s acceptance angles.

Since a fast moving bright dot can stimulate several photoreceptors virtually at the same time (Appendix 6—figure 5A), theoretically, it should not be perceived as a single point but a streak, of which length is a function of object speed. This motion blur effect is classically quantified by the spatial half-width S of object’s neural image. Because the spatial response in the retina has a similar waveform with the temporal response of a single photoreceptor (Srinivasan and Bernard, 1975; Juusola and French, 1997), S can be calculated as:

where $w$ is the object speed and T_h (cf. Appendix 6—figure 4G) is the temporal half-width of a single photoreceptor response.

Appendix 6—figure 5

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Appendix 6—figure 5B illustrates the predicted relationship between the object speed and neural image resolution in wild-type and hdc^JK910 Drosophila. These estimates imply that the spatial half-width of wild-type neural images should be 1-2^o wider than that of the hdc^JK910 during both the dim and bright conditions, reflecting wild-type R1-R6s’ wider acceptance angles (∆ρ) (see Appendix 4, Figure 7—figure supplements 1A and 2B). This prediction agrees with the previous theoretical works (Srinivasan and Bernard, 1975; Juusola and French, 1997), which used similar methods to indicate two distinct regions of image resolution. Thus, theoretically, at low object speeds, visual acuity should be mostly determined by a photoreceptor’s spatial receptive field, but at high speeds, the motion-blur effect should increase rapidly, becoming the dominating factor. The corresponding trend differences (as separated by a thin dotted line) suggest that the point-object speed threshold dividing the two regions would be about 100–120 ^o/s.

Remarkably, however, we next demonstrate how these theoretical predictions greatly overestimate motion blur effects in R1-R6 output, and that these cells can, in fact, resolve image details finer than the half-width of their receptive fields, even at very high saccadic speeds.

Appendix 6—figure 6

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In the second type of experiment, two bright dots, which were less than the half-width of a R1-R6’s receptive field (6.8^o) apart, crossed its receptive field at 409 ^o/s (Appendix 6—figure 6A). Each tested photoreceptor’s ability to distinguish the dots was assessed whether its response showed two clear peaks (Appendix 6—figure 6B, solid line) or only one (dotted line). Quite unexpectedly, even at the low room-temperature of 19°C, where phototransduction is slower than at the flies’ preferred temperature of 25°C (Sayeed and Benzer, 1996; Juusola and Hardie, 2001b), 12/18 of wild-type R1-R6 photoreceptors and 15/16 hdc^JK910 R1-R6s could clearly resolve the two dots. (Note that at 25°C, every tested R1-R6 resolved them well; Figure 9—figure supplement 1E–F). Amongst the wild-type responses, the trailing peak was often larger than the leading one (Appendix 6—figure 6B, solid line), whereas all but one hdc^JK910 R1-R6 had the larger leading peak (Appendix 6—figure 6C). This observation suggests that excitatory synaptic feedback modulation, which hdc^JK910 photoreceptors lack, may enhance the second peak in the wild-type responses. Resolvability was further quantified by D-values:

Where P is the amplitude of the smaller peak and d is the depth of the response dip between the two peaks (Appendix 6—figure 6C). In darkness, D-values measured from the mutant photoreceptors were, on average, more than double those of wild-type (D_wild-type = 4.51 ± 2.33%, D_hdc = 10.5 ± 5.23%), indicating that hdc^JK910 R1-R6s resolve the two points more clearly than their wild-type counterpart (Appendix 6—figure 6D). Under light-adaptation (ambient illumination), while R1-R6s of both genotypes exhibited significant improvements in their image resolution (D_wild-type = 9.81 ± 3.7%, D_hdc = 14.85 ± 6.95%), the difference between the two groups decreased and was at the margin of statistical significance (Appendix 6—figure 6E; p=0.058, t-test). Taking into account only the cells in which D-values were measured in both dim and bright conditions, the enhancement of D-values to the ambient light change was quantified by their relative change:

On average, wild-type D-values improved by 262%, ranging from 43% to 604%. These changes appeared to be markedly larger than those observed in hdc^JK910 photoreceptors, which varied from 4% to 89% and averaged as 31%. Yet, the difference between the two groups was not statistically significant because of the large individual variations (Appendix 6—figure 6F).

In Figure 7, we further analyze the resolvability of those high-quality wild-type and hdc^JK910 R1-R6s, from which we recorded the impulse response and receptive field measurements at the two adapting backgrounds - dim and bright at 25°C, as well as responses to both 205 and 409 ^o/s moving dots. Such data allowed us to compare the classic theory to the real recordings even more thoroughly.

Together, these results show that the theoretical spatial half-width, S, grossly underestimates R1-R6 photoreceptors’ image resolution. Recordings clarify that two bright dots that travel 409 ^o/s can, in fact, be resolved by a single photoreceptor, even when the dots (6.8^o separation) are less than the photoreceptor’s acceptance angle (∆ρ = 9.5^o) apart. Therefore, a R1-R6 photoreceptor’s real spatial half-width for the same high (saccadic) speed must be less than half of the theoretical estimate (~15^o; Appendix 6—figure 5B). In other words, the classic theory overestimates the role of motion blur on Drosophila vision, as its R1-R6 photoreceptors resolve fast-moving dots beyond the predicted motion blur limit.

The recordings further indicate, consistent with hdc^JK910 R1-R6s’ marginally narrower acceptance angles (Appendix 4, Figure 7—figure supplement 1 and 2), that their spatiotemporal resolution is somewhat better than that of wild-type photoreceptors, both in dim and moderately bright conditions. However, when ambient light intensity was changed, the spatiotemporal resolutions of wild-type R1-R6s improved more. Here, possible contributing factors include:

• Slight (~4%) differences in the photoreceptors’ rhabdomere diameters (see Appendix 5)

• Dynamic and homeostatic regulation of [Ca²⁺]_i, membrane properties and synaptic feedback (Dau et al., 2016)

• Intracellular pupil (see Appendix 2 and Appendix 4)

• Differences in photomechanical rhabdomere contractions (see Appendixes 7–8)

• Electrical coupling between the cells

Their potential roles are further discussed in Appendixes 7–8

Volterra kernels of each photoreceptor model were computed from the first half (1.5 s) of GWN data (https://github.com/JuusolaLab/Microsaccadic_Sampling_Paper/tree/master/VolterraModelOfPhotoreceptor), before the other half of recorded light stimuli and voltage responses were used to validate the model. Because the output simulation accuracy depends upon input statistics and the model computation specifications, the system identification process was optimized by selecting suitable parameters.

Firstly, to test whether the selected 200 Hz input bandwidth was appropriate (Appendix 6—figure 7A), we analyzed the resulting signal-to-noise (SNR) ratio of photoreceptor output (Appendix 6—figure 7B). SNR decayed below 1 at around 66 Hz; at which point photoreceptor response contained more noise than signal. Thus, the GWN stimuli predictably activated a R1-R6 photoreceptor’s whole frequency range.

Secondly, we assessed different sampling rates. According to the Nyquist-Shannon sampling theorem, a signal without frequencies higher than B Hz can be perfectly sampled and reconstructed (Shannon, 1948) by sampling rate F_s of 2B Hz. Because the bandwidth of interest was 0–66 Hz, the data could be processed, in theory, at any sampling rate from 132 Hz to the recorded rate of 10 kHz, without compromising its information content.

Appendix 6—figure 7

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We found that higher sampling rates yielded models, which predicted R1-R6 output with slightly higher accuracy. However, their kernels also exhibited larger fluctuations, and the kernels did not decay to zero over time, most likely due to high-frequency noise. For F_s = 1,000 Hz and higher, such fluctuations undermined the physiological meaning of the Volterra first-order kernel (Appendix 6—figure 7C), which is the photoreceptor’s impulse response (Victor, 1992). Thus, the kernels computed from too richly-sampled data would be useful only for response prediction to this particular GWN stimulus.

On the other hand, while computations performed with lower F_s data would produce smoother kernels, a low sampling rate would also limit the model’s other applications. For example, Volterra series models were used to simulate photoreceptor response to the image of moving objects created by the 25 light-point array. For an object moving at 409 ^o/s, its travelling time across the array was 100 ms, or 4 ms per light-point. As the simulation required at least two data-points per light-point, F_s was chosen to be 500 Hz, at which rate reasonably smooth kernels could still be produced (Appendix 6—figure 7C). Moreover, because the first-order kernel values decayed to zero at 50–60 ms, it was deemed that a 80 ms kernel length was sufficient for the computations.

Volterra series models, computed from data sampled at 500 Hz, could consistently predict response of Drosophila photoreceptors to GWN stimuli (for example, see Appendix 6—figure 7E). On average, the model simulation accuracy, given by Equation A6.6, was ~86% for both wild-type and hdc^JK910 photoreceptors (Appendix 6—figure 7D). These high F values confirmed that a linear Volterra series model could approximate light-adapted Drosophila photoreceptor output to the test stimulation appropriately.

By approximating the light input directly from the receptive field measurements (Appendix 6—figure 1) and the corresponding R1-R6 output by Volterra series (Appendix 6—figure 7C), we could estimate each tested Drosophila photoreceptor’s responses to moving bright dots. This was done by convolving the extrapolated light stimuli with the corresponding impulse responses.

The model predictions for a single moving stimulus were far less consistent than those for GWN stimuli. Appendix 6—figure 8A,B show representative simulations with broadly acceptable and clearly unacceptable accuracies, respectively, together with the corresponding intracellular recordings.

From both the recordings and simulations, we further calculated the theoretical dot motion effects on the neural image resolution, or spatial half-width, S (Appendix 6—figure 8C). As explained above (cf. Appendix 6—figure 5), the classic theory can only broadly suggest the relative differences between wild-type and mutant performances. Here, its application to the simulations further underestimated the spatial half-width predictions of wild-type recordings and over-estimated those of the hdc mutant.

Appendix 6—figure 8

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Most critically, however, Volterra series models consistently failed to predict the fast phasic components of the recorded voltage responses, and thus their real resolvability, to two fast moving dots (Appendix 6—figure 8D; see also Figure 7). The model simulations, and hence its underlying classic theory, always predicted lower resolvability than what we saw in the actual recordings. Further investigations (Appendixes 7–8) revealed that this discrepancy reflected the missing biophysical mechanisms of the empirical black-box models (see Appendix 1). Specifically, the used photoreceptor models lacked: (i) the photomechanical rhabdomere movements, which shift and narrow a R1-R6’s receptive fields, and (ii) the refractory sampling, which allows many microvilli (after the first dot) to recover from refractoriness (Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015) to respond to the second dot. Moreover, by tuning and validating the Volterra kernels to GWN stimuli at relative steady-state, we inadvertently limited its exposure to (iii) excitatory dynamic synaptic feedback modulation (Zheng et al., 2006; Dau et al., 2016), which accentuates sudden changes in photoreceptor output. For these reasons, the responses of real R1-R6s, which naturally utilize the given mechanisms, showed systematically larger widths and second-peaks, providing higher resolvability.

We show in Figure 8G–I, Figure 8—figure supplement 1 and Appendixes 7–8 that a new biophysically realistic microsaccadic sampling model, which allows for realistic refractory quantal phototransduction (Song and Juusola, 2014) and photomechanical rhabdomere contractions (Hardie and Franze, 2012), yields (significantly better) theoretical predictions that closely approximate the real R1-R6 output. Importantly, in Appendix 9, we further show that R1-R6 output to two dark dots, moving at saccadic speeds, has the same relative resolution as their output to the corresponding two bright dots. Collectively, our results demonstrate that Drosophila photoreceptors resolve fast moving objects far better than what was believed previously.

In this appendix, we used intracellular recordings and classic theoretical approaches to study how fly photoreceptors encode moving bright dots. Model simulations about each tested R1-R6s’ spatiotemporal responses were compared to the actual recordings to the same stimuli. We found that both wild-type and hdc^JK910 photoreceptors resolved moving dots nearly equally well, and significantly better than the corresponding deterministic simulations. These findings demonstrate that the classic dynamic photoreceptor models (Srinivasan and Bernard, 1975; Juusola and French, 1997; Land, 1997), which lack knowledge about the underlying phototransduction biophysics and photomechanics, grossly underestimate the spatiotemporal resolution of the real cells.

Animals counter self-motion blur effects by moving their eyes. This compensates for head and body movements by keeping the neural image position near stationary as long as possible (Land, 1999). Interestingly here, a fly photoreceptor’s response to two moving point-objects represents an opposite case where image motion, in fact, improves acuity. In the classic theory, to resolve two stationary objects, at least three photoreceptors are required so that the intensity difference in between can be detected. Because Drosophila photoreceptors’ interommatidial angles (Land, 1997; Gonzalez-Bellido et al., 2011) vary from 3.4^o to 9.0^o and their average acceptance angle is ~9.5^o (Appendix 4), its eye should not resolve two point-objects 6.8^o apart. Nevertheless, responses of single photoreceptors, during even very fast (saccadic-speed) (Geurten et al., 2014) movements, show large enough dips (in their temporal dynamics) to indicate that the objects are resolved neurally. In the classic theory instead, the outputs of several adjacent photoreceptors had to be processed together to distinguish two moving point-objects from one stationary object, in which brightness changes over time. This example highlights the inseparability of spatiotemporal information processing and acuity.

The unique advantages of the present study were the bespoke equipment and stimulus paradigm. These allowed high-quality photoreceptor recordings with precisely controlled moving point-objects stimulation. Therefore, we could directly test and compare the theoretically predicted relationship between the neural image resolution and the object speed (Srinivasan and Bernard, 1975; Juusola and French, 1997) to the experimental data. However, the equipment also had limitations to be improved in future research. Wider object speed range is necessary, especially for testing insect eyes with fast responses. Owing to the long transient time, each light-point now required 2 ms switching period. Consequently, the minimum travelling time was 50 ms and the object speed limit in Calliphora experiments was 334 ^o/s, which is far slower than observed during the flies’ saccadic flight behaviors (Schilstra and Hateren, 1999; Hateren and Schilstra, 1999) (2,000–4,000 ^o/s). Whilst positioning the light-point array closer to the fly eye would increase object angular speed, it would compromise resolution as fewer light-points would then lie within a tested cell’s receptive field.

In Appendixes 7–9, we show how both the enhanced resolvability of moving point-objects and the phasic modulation of their rising and decaying phases, as was shown here, emerge from the joint contributions of photomechanical rhabdomere contraction and its refractory information sampling.

This appendix describes a new powerful high-speed video recording method to measure photomechanical rhabdomere movements in situ, and provides important experimental and theoretical background information for the results presented in Figures 8–9.

In this appendix:

• We utilize the optical cornea-neutralization technique (Franceschini and Kirschfeld, 1971b; Franceschini and Kirschfeld, 1971) with antidromic deep-red (740 or 785 nm peak) illumination to observe deep pseudopupils (photoreceptor rhabdomeres that align with the observer’s viewing axis) in the Drosophila eye. We use an ultra-sensitive high-speed camera with a purpose-built microscope system to record fast rhabdomere movements across the compound eyes, while delivering blue-green stimuli (470 + 535 nm peaks) orthodromically into the eye.

• We show that light-activation moves rhabdomeres (Video 3) side-ways (horizontally) both in dark- and light-adapted eyes. This movement starts after a 8–20 ms delay from the light stimulus onset, and reaches its peak in about 70–150 ms. Because these movements have fast onset and light intensity-dependency, which are similar to those of the R1-R6 photoreceptors’ intracellular voltage responses to comparable stimuli, they must result from individual photoreceptors’ photomechanical contractions; see (Hardie and Franze, 2012).

• We show that trp/trpl-mutant photoreceptors, which have normal phototransduction reactions but lack the light-gated ion channels, also contract to light. Since these photoreceptors cannot produce electrical responses and thus communicate electrically or synaptically with other cells, including eye muscles, their contractility cannot be caused by eye muscle activity but must be intrinsic, supporting the earlier hypothesis (of phototransduction reactants interacting locally with the plasma membrane) (Hardie and Franze, 2012).

• We show that light moves rhabdomeres fast in the back-to-front direction, while darkness returns them back to their original positions slower. Because the ommatidium lens inverts images, R1-R8 photoreceptors’ receptive fields move in the opposite direction - front-to-back after light and back-to-front after darkness. Therefore, when front-to-back moving bright dots cross the eyes, the photoreceptors’ receptive fields move along. But when bright dots cross the eyes in the back-to-front direction, the photoreceptors’ receptive fields move against them (cf. Appendix 6).

• At the level of rhabdomere tips, the horizontal movements can be up to 1.4 µm, as measured occasionally in light-adapted eyes. Therefore, given the known optical dimensions, these photomechanical microsaccades can rapidly shift R1-R6 photoreceptors’ receptive fields by ~5^o. Remarkably, such a large image pixel displacement reaches the average interommatidial angle, ∆φ ~4.5-5^o, in the Drosophila eye (cf. Appendix 4; Appendix 4—figure 1).

• We show that the light stimulus also contracts rhabdomeres axially (Video 2; inwardly: 0.5–1.7 µm), down away from the lens. This transient increase in focal length should contribute in narrowing R1-R6’s receptive fields dynamically. We further show that specific cone- and pigment-cells inside each ommatidium form an aperture, which is connected to the rhabdomere tips. During light stimulation, this aperture moves laterally with the rhabdomeres but only half as much (Video 4). And since the ommatidium lens remains practically immobile, the light beam falling upon the rhabdomeres is shaped dynamically. These observations mean that a R1-R6’s receptive field must both move and narrow during dynamic light stimulation.

• We show that rhabdomeres of hdc^JK910 histamine-mutant (Burg et al., 1993; Melzig et al., 1996; Melzig et al., 1998) R1-R6 photoreceptors, in which visual interneurons are blind (receive no neurotransmitter from photoreceptors), have broadly wild-type-like contraction dynamics, again refuting the role of eye muscle activity in the data. But interestingly, their light-sensitivity is about 10-fold reduced, similar to their voltage responses (Dau et al., 2016). In part, this may reflect hdc^JK910 photoreceptors’ smaller size. Given that hdc^JK910 rhabdomere diameters are ~4% smaller than in wild-type (Appendix 5), their length should also be reduced in the same proportion. As the average wild-type R1-R6 is ~100 µm, hdc^JK910 R1-R6s should be ~4 µm shorter. And indeed we find in situ that hdc^JK910 rhabdomere tips are ~4 µm further away from the lens than the wild-type tips. In addition, the higher [Ca²⁺]_i, caused by tonic excitatory synaptic feedback overload (Dau et al., 2016), may further affect their mobility, possibly retaining them in a slightly more contracted state.

Atomic force microscopy (AFM) at the dissected Drosophila eyes’ corneal surface (Hardie and Franze, 2012) has shown up to 275 nm radial movements to brief light pulses, caused by transient photomechanical R1-R8 photoreceptor contractions. Such movements are too small and fast to see with the naked eye, and were initially considered: (i) only to participate in gating photoreceptor’s transduction-channels, and (ii) possibly too small to affect fly vision in general. In this appendix, we use high-speed video microscopy to show that in vivo the underlying photomechanical rhabdomere (light sensor) movements are larger both laterally (horizontally: 0.3–1.4 µm) and axially (inwardly: 0.5–1.7 µm). Because these movements are also synchronous, ubiquitous, robust and reproducible, they influence how the fly eyes sample visual information about the world.

Dark-adapted dissociated photoreceptors rapidly contract to light (Hardie and Franze, 2012) (Video 2). It has been suggested that this contraction results from light-induced phosphatidylinositol 4,5-bisphosphate (PIP₂) cleaving, which modulates their rhabdomere membrane volume and so participates in gating the phototransduction-channels (trp and trpl) (Hardie and Juusola, 2015).

Here, we directly test the hypotheses that (i) the photomechanical photoreceptor contractions occur also in intact flies in normal stimulus conditions, and (ii) these movements serve the purpose of modulating light input to photoreceptors and thus photoreceptor output. We do this by recording high-speed video of how Drosophila photoreceptor rhabdomeres move to different light stimuli in vivo, and by analyzing and characterizing how these movements affect R1-R6s’ receptive fields. Later on, in Appendix 8, we include their light input parameter changes in biophysically-realistic mathematical models to predict R1-R6 voltage output to moving visual stimuli.

We used the optical cornea-neutralization method to monitor how light stimuli evoke Drosophila photoreceptor rhabdomere movements. The imaging system was constructed upon an upright microscope (Olympus BX51), secured to a XY-micrometer stage on an anti-vibration table (MellesGriot, UK) (Appendix 7—figure 1). To minimize light pollution in the recordings, the system was light-shielded inside a black Faraday cage with black lightproof curtains in the front, and the experiments were performed in a dark room. For collecting and recording deep pseudopupil images, the system was equipped with a 40x water immersion objective (Zeiss C Achroplan NIR 40x/0.8 w, ∞/0.17, Germany) and an ultra-sensitive high-speed camera (Andor Zyla, UK), respectively.

Appendix 7—figure 1

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A Drosophila was gently fastened to an enlarged fine-end of a 1 ml pipette tip by puffing air from a 100 ml syringe at the large end until the fly head and ~1/5 of the thorax emerged outside (Appendix 7—figure 1A). The head and thorax were carefully fixed (from the proboscis and cuticle) to the pipette wall in a preferred orientation by melted beeswax, without touching the eyes. The fly was then positioned with a remote-controlled XYZ-fine resolution micromanipulator (Sensapex, Finland) underneath the water immersion objective, using both visual inspection and live video stream on a computer monitor.

Antidromic illumination (through the fly head) revealed the deep pseudopupils of the fly eyes. It was provided with a high-power deep-red light source (740 nm LED with 720 nm high-pass edge-filter; or 785 nm LED with ±10 nm bandpass filter), driven by a linear current LED driver (Cairn OptoLED, UK). Note that very bright deep-red illumination, which is a prerequisite for good signal-to-noise ratio high-speed video imaging, activates R1-R8 photoreceptors only marginally. This is because their different rhodopsins’ absorbance maxima are at much lower wavelengths (Britt et al., 1993; Wardill et al., 2012). The photoreceptors’ near insensitivity to >720 nm red light was confirmed in vivo by ERG recordings (Appendix 7—figure 2).

Orthodromic light stimulation (through the 40x objective into the eye), which evoked the photoreceptor contractions, was delivered by two high-power LEDs: 470 nm (blue) and 545 nm (green), each separately controlled by its own driver (Cairn OptoLED, UK). These peak wavelengths were selected to activate R1-R6s’ rhodopsin (Rh1) and its meta-form near maximally, and so through joint stimulation to minimize desensitization by prolonged depolarizing after-potentials (PDA) (Minke, 2012). Simultaneous stimuli from the two LEDs were merged into one focused beam by a 495 nm dichroic mirror and low-pass-filtered at 590 nm. Pseudopupil signals of the observed fly eye (left or right) were split spectrally by another dichroic mirror (600 nm), and essentially only red image intensity information (≥600 nm) was picked up by the high-speed camera.

Appendix 7—figure 2

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Light stimulus generation was performed by a custom-written Matlab (MathWorks, USA) program (Biosyst; M. Juusola, 1997–2015) (Juusola and Hardie, 2001a; Juusola and de Polavieja, 2003) with an interface package for National Instruments (USA) boards (MATDAQ; H. P. C. Robinson, 1997–2008). The length of the light stimuli (including the continuous deep-red background and the blue/green stimulus patterns) was made to match the number of frames to be acquired by the Andor camera, and the stimuli were externally triggered by the camera software (Solis). During the recordings, the frames were first buffered in the RAM in high-speed and then transferred on the computer’s hard drive. Light stimulus intensity could be attenuated by a neutral density filter set (Thorn Labs, USA), covering a 5.3 log intensity unit range.

High-speed video microscopy (Appendix 7—figure 1 e.g. Video 3) from intact wild-type Drosophila eyes (n >> 100 flies) showed repeatedly and unequivocally that:

• Full-field light flashes evoked rapid local R1-R7 rhabdomere movements within those seven ommatidia, which at the center of the imaged view, faced the blue/green stimulus source directly (Appendix 7—figure 3A, orange area). Rhabdomeres in few other neighboring ommatidia also moved marginally (yellow area), but not obviously in other ommatidia. This meant that only the ommatidia that aligned with the blue/green stimulation absorbed the incident light, while those to one side reflected it. This local area, which showed photomechanical rhabdomere movements, closely matched Drosophila’ normal pseudopupil (Appendix 7—figure 3B).

• The rhabdomere movement was in the back-to-front direction (Appendix 7—figure 1B–D), whilst in darkness, the rhabdomeres returned in front-to-back to their original positions more slowly. These dynamics and their directions were similar in both the left and right eye.

• Because light always moved the rhabdomeres back-to-front, the corresponding neural images of the left and the right eye comprise left-right mirror symmetry; i.e. against the vertical (sagittal) plane, the rhabdomeres in the left and right eye display mirror symmetric motion. We show later in Appendix 8 how this symmetry may allow Drosophila photoreceptors to encode orientation information during saccades or image rotation.

• The rhabdomere movement directions seemed homogeneous (at least in the first approximation) across each tested eye, appearing similar in its different regions: whether measured at its up, down, front or back ommatidia. Such ‘pixel interlocking’ across the whole eye’s visual field may help to preserve, or enhance, the neural images’ spatial resolution of the world.

Appendix 7—figure 3

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To accurately quantify the size and direction of the observed rhabdomere movements in time we devised specific image-analysis procedures. First, the stored images (raw data frames of each recording) in the hard drive were exported as a tiff stack, in which pixel intensity range was set by the frames’ minimum and maximum values, using the camera software (Andor SOLIS). ImageJ software was then used to convert the tiff-stack into a single tiff-file. The Matlab scripts to process and analyze the images are downloadable from the repository: (https://github.com/JuusolaLab/Microsaccadic_Sampling_Paper/tree/master/AnalyzeRhabdomereMovement). These methods included (Appendix 7—figure 4A):

1. Loading the image stack.

2. Subtracting the median and mean from each frame and setting its negative values to (0. 0) to remove the dark noise background. This process was repeated for every frame.

3. Calculating 2D cross-correlation between each frame and the reference frame.

4. iv. Selecting the cross-correlation values, which were ≥95% of the maximum (peak) value. This was repeated for every frame.

5. Calculating the weighted average position of the peak by using all the positions of the previous selection and using the cross correlation values as weights both in x- and y-direction. This was repeated for every frame.

6. Subtracting the reference frame position from every frame.

Appendix 7—figure 4

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In this study, the rhabdomere displacement measurements are given in microns (µm) and the resulting receptive field movements in degrees (^o). Appendix 7—figure 5A shows a whole image of a Drosophila’s left eye, as focused upon its rhabdomeres in the center and magnified by the microscope system to use the camera’s full 2048 × 2,048 pixel range. By placing a high-resolution µm-graticule on the same focal plane (Appendix 7—figure 5B), we calibrated that the whole image is 303 × 303 µm. After converting the recorded rhabdomere displacements from pixels (Appendix 7—figure 4) into microns, we then used the published parameters (Stavenga, 2003b) about the Drosophila ommatidium optics (Appendix 7—figure 5C) to translate these measurements into corresponding receptive field movements in degrees.

Drosophila ommatidium optical parameters were described by (Stavenga, 2003b) and (Gonzalez-Bellido et al., 2011). Its biconvex facet lens focuses light to a rhabdomere (grey rectangle) tip. The outer and inner lens curvatures, r₁ = -r₂, are 11 µm, and its thickness, l₁, is 8 µm. Distance from lens to the rhabdomere, l₂, is 15 µm. Reflective indices, n, for the object space, lens and image space, respectively, are: n₁ = 1, n₂ = 1.45 and n₃ = 1.34.

We used standard ray transfer matrix analysis (Laufer, 1996) to determine optical properties between the lens surface, P₁, and the rhabdomere tip, P₂. Both of these are represented as vectors of their positions, y, and angles, θ: ${\displaystyle P_1=\left[\begin{array}{c}{y}_1\\ {\theta }_1\end{array}\right]}$and ${\displaystyle P_2=\left[\begin{array}{c}{y}_2\\ {\theta }_2\end{array}\right]}$. Then, the optical system of the facet lens follows equation ${\displaystyle P_2=M{P}_1}$, where

${\displaystyle M=\left[\begin{array}{cc}0.23& 1.61\ast {10}^{-5}\\ -3.63\ast {10}^4& 0.71\end{array}\right]}$, obtained from the ray transfer matrix analysis.

The transform matrix clarifies that the distance, y₂ (at P₂), mostly depends upon the angle θ₁ (of P₁). Thus, 1 µm movement gives 1 × 10⁻⁶/1.61 × 10⁻⁵ = 0.0621 (rad) angular change, which is 3.56 °/µm. This movement is an inverse of the visual field movement. Note that by using the comparable optical parameter values of (Gonzalez-Bellido et al., 2011) (and considering the normal lens f-value variation across the Drosophila ommatidia), gives practically the same movement ratio (±5% error).

Appendix 7—figure 5

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We then tested whether the rhabdomere contractions were generated by the photoreceptors themselves (photomechanically) or by eye muscle activity. This was done by recording in trp/trpl null-mutants, which express normal phototransduction reactants but lack completely their light-gated ion channels. Consequently, these photoreceptors did not generate electrical responses to light, and their eyes showed no ERG signal (Appendix 7—figure 6A). Nonetheless, high-speed video recordings revealed that trp/trpl-mutant photoreceptors contracted photomechanically (Appendix 7—figure 6B; see also Video 2). These observations are consistent with the hypothesis of the light-induced phosphatidylinositol 4,5-bisphosphate (PIP₂) cleaving from the microvillar photoreceptor plasma membrane causing the rhabdomere contractions (Hardie and Franze, 2012).

Appendix 7—figure 6

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Using the high-speed video microscopy, we next tested whether the Drosophila lens system or any other ommatidium structures moved during the rhabdomere movements (Appendix 7—figure 7). In the experiments, a z-axis micromanipulator (Sensapex, Finland) was used to shift and reposition Drosophila in piezo-steps vertically. This allowed the focused image, as projected on the camera, to scan through each studied ommatidium, providing exact depth readings in µm. We then recorded any structural movements inside the ommatidia at different depths; from their corneal lens down to the narrow base, where the cone and pigment cells form an intersection between the crystalline cone and the rhabdomere tips (Tepass and Harris, 2007).

Appendix 7—figure 7

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We found that when the rhabdomeres moved photomechanically (Appendix 7—figure 7B, red trace; Video 4) the corneal lens and the upper ommatidium structures were essentially immobile (grey), and normally remained so throughout the recordings. However, clear stimulus-induced movements were detected at the basal cone/pigment cell layer (orange; also inset) that connects to the rhabdomere tips with adherens junctions (Tepass and Harris, 2007). Although it is less clear how much these structures reflected the rhabdomere motion underneath or were pulled by it, it is quite certain that they formed an aperture in the light path, which moved less than the light-sensors (rhabdomeres) below (orange vs. red). In Appendix 8, we analyze how such an interaction might dynamically narrow the R1-R6s’ receptive fields to visual motion.

Overall, these results further verified that in normal stable recordings the used blue/green light flash was not evoking eye muscle activity, which would otherwise move the whole eye.

Light intensity-dependence of rhabdomere movements (in vivo dynamics)

Through a wide-ranging testing regime, we further discovered (Appendix 7—figure 8 and Appendix 7—figure 9) that:

• Light-induced R1-R7 rhabdomere movements were robust and repeatable. Appendix 7—figure 8A shows 10 trials (thin grey traces) and their mean (black) to a 10 ms bright flash measured from the same ommatidium. Between each flash, the eye was dark-adapted for 30 s. Characteristically, the rhabdomeres contracted to every light flash without a failure. Whilst these movements showed amplitude variations, their dynamic behavior was similar. Here, they reached their peak (mean = 0.806 µm, Appendix 7—figure 8B) in about 140 ms and then decayed back to the baseline slower, mean τ_r ~190 ms (Appendix 7—figure 8C).

• Dark-adapted R1-R7 rhabdomeres’ maximum movement range (Appendix 7—figure 9A–I) was considerably larger (0.3–1.2 µm) than the displacement range measured ex vivo by atomic force microscope (Appendix 7—figure 9B, AFM_max ≤0.275 µm) (Hardie and Franze, 2012) on the corneal surface. This difference is hardly surprising. AFM measures axial (inward) cornea displacements, presumably resulting from a large number of simultaneous photoreceptor contractions underneath, whereas our high-speed video microscopy method measures orthogonal (horizontal) rhabdomere movements locally at their source. Owing to the slight excitation caused by the bright 740 nm red-light background needed for in vivo imaging (Appendix 7—figure 9B), the actual rhabdomere movements in full dark-adapted conditions could be even larger.

Appendix 7—figure 8

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• The rhabdomere movement recordings (thin grey traces) from single ommatidia of individual flies vary more than the corneal AFM data (black traces). The sizable variations in their movement range and fine dynamics (such as minor oscillations) imply both considerable trial-to-trial (Appendix 7—figure 8) and fly-to-fly variability (Appendix 7—figure 9). Much of this is clearly physiological, as rhabdomere movement sizes and waveforms to specific stimuli were similar in one fly but often slightly different to those seen in another fly. However, because of the extreme sensitivity of our method (Appendix 7—figure 4, providing subpixel movement resolution), some of the variations clearly reflected experimental noise. Such noise included microscopic mechanical vibrations in the recording system, minute spontaneous eye muscle activity (see Appendix 4, Appendix 4—figure 6), and Poisson-noise, in which the image signal-to-noise ratio - as captured by the camera’s CMOS sensor – reduced the more the faster the sampling. Appropriately, the average responses (red) to different intensity flashes were smoother, yet still remained much larger than in the AFM data.

Appendix 7—figure 9

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• The average rise and decay time courses of the normalized rhabdomere movement recordings followed closely those of the normalized AMF recordings (Appendix 7—figure 9J). Such dynamic conformity strongly suggests that both the methods capture accurately photomechanical R1-R8 photoreceptor contractions in their fast natural time resolution. But these observations also provided further evidence that ex vivo AFM data underestimate the actual magnitude of rhabdomere movements within ommatidia. In fact, it seems possible that to maximize neural images’ spatial resolution, the eye’s architectural design dampens the lens system movement, while its sensors (rhabdomeres) contract. This would inadvertently impede the AFM signal (axial movement), and any horizontal lens shift (Appendix 7—figure 7), measured on the corneal surface.

Only in 2 out of 21 tested Drosophila eyes, the rhabdomeres moved unmistakably (twitched) to a very dim 10 ms blue/green LED flash, in which intensity was reduced ~200,000 fold by neutral density filters. Therefore, in these two positive occasions: (i) the resulting response must have been quantal with (ii) the 10 ms flash maximally containing ~1–3 absorbed photons. Furthermore, because this flash only succeeded in ~1/10 eyes, its average maximum intensity could only be ≤3/10 photons/10 ms, i.e. ≤0.03 photons/ms. This means that the brightest flash (logI(0)), which was not filtered, could maximally contain ≤6,000 photons/ms, or ≤6 million photons/s, making the used light intensity range natural and directly comparable to that used for the intracellular recordings (Figures 1–2 and 6–9).

This reasoning is in line with the similar LED driver settings used in all the experiments, and the similar V/log(I) and (µm)/log(I) functions, which resulted from these experiments.

As further controls, we measured photomechanical R1-R8 rhabdomere contractions of freshly dissociated ommatidia (Hardie and Franze, 2012) to green (480 nm) light flashes using high-speed video recordings with infrared 850 nm background illumination (Appendix 7—figure 10). The benefit of this in vitro method was that it provided a clear side-view of the tested wild-type and mutant rhabdomeres, enabling us to estimate their axial (longitudinal inward) contraction component; or how much the rhabdomere tip moved away from the ommatidium lens (Video 2). In vivo, such fast lengthwise light-sensor movements should contribute to R1-R6 photoreceptors’ transiently narrowing receptive fields (see Appendix 8).

We found that after dark-adaptation bright flashes could evoke 0.8–1.7 µm longitudinal rhabdomere contractions. These were characteristically accompanied by synchronous (about equally large) crosswise movement (or twist), which likely forms the basis of the sideways rhabdomere displacement; seen during the in vivo recordings (e.g. Appendix 7—figure 1).

Appendix 7—figure 10

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Given the slightly reduced back-to-front rhabdomere mobility of hdc^JK910 photoreceptors, we next asked whether prolonged light-adaptation itself would reduce wild-type photoreceptors’ rhabdomere movement. To study this question, we examined how the rhabdomeres in seven individual flies responded to different light impulses at different adaptation states.

First, to obtain the baseline responses in each fly eye, we recorded their rhabdomere movements to a bright and a very bright full-field green-blue flash after 30 s of dark-adaption (Appendix 7—figure 12A and B, respectively). As before, we found that the brighter the light flash, the larger and the faster their rhabdomere movements were on average.

Interestingly, however, when the flies were adapted to a moderate or bright blue (470 nm) light field for 30 s, which converts most (if not all) rhodopsin Rh1 to its active meta-form (causing PDA, prolonged depolarizing afterpotential), the flashes now evoked only weak or no rhabdomere movement (Appendix 7—figure 12C–D). Such reduced mobility somewhat resembled that in some hdc^JK910 rhabdomeres (Appendix 7—figure 11D). These observations can be explained, at least in part, with the basic molecular model proposed for rhabdomere contraction (Hardie and Franze, 2012). Here, meta-rhodopsin would continuously activate G-protein and in turn phospholipase C (PLC). PLC would then cleave most PIP₂ off the microvillar membrane, causing a tonic photoreceptor contraction, which facilitates light-gated channel openings and thus increases Ca²⁺ influx. But because a 10 ms bright green (545 nm) light pulse would convert only some fraction of meta-rhodopsin back to its non-activated form, this effect would be small proportionally, and could only partially rescue the rhabdomere contractibility.

Appendix 7—figure 12

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On the other hand, under more natural green light-adaptation (Appendix 7—figure 12E&ndash;H), the eyes’ normal back-to-front rhabdomere contractibility to light increments was retained, and sometimes even increased, in respect to their dark-adapted baseline responses (Appendix 7—figure 12A–B). Consequently in every fly eye (7/7), the rhabdomeres moved more when green-adapted than when moderately blue light-adapted (Appendix 7—figure 12C), as quantified by their flash-induced maximum displacements (Appendix 7—figure 12I).

These results indicate that in normal spectrally-broad natural environments, light increments (positive contrasts) will evoke fast evasive rhabdomere movements, steering them away from pointing directly to a bright light source. This novel photomechanical adaptation should together with the slower screening pigment migration (intracellular pupil mechanism, Appendix 2) help to recover (resensitize) a rhabdomere’s refractory sampling units (30,000 microvilli). Thus, the rhabdomere movements likely participate in optimizing photon sampling for maximum information capture (Appendixes 1–2). This further means that a rhabdomere’s state of contraction is constantly being reset to the ongoing light input, providing the capacity to respond to the next stimulus increment. Therefore, although being slower, in many sense, Drosophila photoreceptors’ mechanical adaptation resembles the inner ear hair-cells’ adaptive resensitization (Howard et al., 1988; Corey et al., 2004).

This appendix describes a new ‘microsaccadic sampling’-hypothesis that predicts a Drosophila photoreceptor’s voltage responses to moving dots, and provides important background information about the experimental and theoretical results presented in Figures 7–9.

In this appendix:

• We use our biophysical Drosophila R1-R6 model (Appendix 1), with different degrees of photomechanical rhabdomere movements modulating light input (Appendix 7), to simulate photoreceptor voltage output to moving bright dots that cross its receptive field in different directions, speeds and inter-distances.

• By comparing the model simulations to intracellular recordings, we reveal the likely biomechanics that allow R1-R6s to resolve adjacent dots at saccadic velocities (Appendix 6).

• We show that when a rhabdomere contracts away from the ommatidium lens’s focal point, its receptive field must move and narrow dynamically. Together these processes actively reshape both the light input and photoreceptor output to separate and sharpen neighboring visual objects in time, improving their resolvability.

• Crucially, with such photomechanical light input modulation, the model photoreceptor output closely approximates that of the real R1-R6s, as recorded to two moving bright dots crossing their receptive fields at different speeds (Figures 7–9; Appendix 6).

• Hence, with refractory photon sampling and photomechanical rhabdomere movements, we can correctly predict and convincingly explain visual acuity of R1-R6s to moving objects.

Based on the combined results in Appendix 1-7, we develop a new ‘microsaccadic sampling’-hypothesis, which predicts how photomechanical rhabdomere contractions (microsaccades) move and narrow Drosophila R1-R6 photoreceptors’ receptive fields (RFs) to resolve fast-moving objects. We present extensive analytical and experimental evidence to show how these mechanisms operate with the photoreceptors’ refractory information sampling to reduce light-adaptation and to increase the spatiotemporal resolution of their voltage responses, improving visual acuity.

Using the results in Appendix 1-7, we can now work out the biomechanics, which allow a R1-R6 to resolve two close bright dots crossing its receptive field at saccadic speeds. We do this systematically by comparing the output of our biophysical model (Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015) (Appendix 1), in which input is modulated by different degrees of rhabdomere photomechanics (Appendix 8—figure 1A-C), to the corresponding recorded real R1-R6 output (Appendix 8—figure 1D). Specifically, we consider three input modulation models:

1. Stationary rhabdomere model (receptive field is fixed)

2. Photomechanical rhabdomere model (receptive field moves)

3. Photomechanical rhabdomere model (receptive field moves and narrows)

In the following, to make these different models (A-C) directly comparable, we first present the findings for two bright dots, which cross the receptive field at 205 ^o/s (Appendix 8—figure 1), before generalizing the results for a vast range of stimuli and giving more examples. Note that these simulations and recordings were performed at 19–20°C. Later on in this appendix, we show how at the Drosophila’s preferred temperature range (24–25°C) (Sayeed and Benzer, 1996) these dynamics are naturally faster (Juusola and Hardie, 2001b) and improve visual acuity further. The scripts for light stimulus calibrations and for simulating responses to two moving dots are in the repository: https://github.com/JuusolaLab/Microsaccadic_Sampling_Paper/tree/master/CalibrateLightInput-PhotoreceptorMovement.

This approach is broadly analogous to the classic theory (Appendix 4 and Appendix 6). It was implemented in four steps (Appendix 8—figure 1):

1. Two bright dots, which were 6.8^o apart, crossed a R1-R6’s RF (∆ρ = 8.1^o) front-to-back at the saccadic speed of 205 ^o/s.

2. Concurrently, the ommatidium lens focused their light onto a rhabdomere tip.

3. The resulting dynamic light input at the rhabdomere tip was a convolution of the two dot intensities with the cell’s receptive field over time (Srinivasan and Bernard, 1975; Juusola and French, 1997).

4. The light input (photons/s) drove the photon sampling and refractory quantum bump (QB) production of 30,000 microvilli (Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015), which formed the rhabdomere. The resulting macroscopic photoreceptor output (Hardie and Juusola, 2015) dynamically integrated the QBs.

Appendix 8—figure 1

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Characteristically in this approach, input modulation reduced to a single peak as the RF convolution fused the light from the two dots together (iii). This made them irresolvable to the discrete photon sampling (iv). Specifically here, light input could not separate the two dots because the given receptive field half-width (8.1^o) was wider than the distance between the dots (6.8^o). The resulting model output, thus, failed to capture the resolvability of the real R1-R6 output (Appendix 8—figure 1, iv).

Markedly, the model prediction (Appendix 8—figure 1A, iv) much resembled those of the deterministic Volterra-models, in which similarly broad RFs were used in the calculations (see Appendix 6).

In this case (Appendix 8—figure 1B), we kept the cell’s receptive field shape the same (i; ∆ρ = 8.1^o) but included the light-induced fast horizontal (back-to-front) rhabdomere movement in the model (ii). The given model parameters (Appendix 8—table 1) were fixed to closely approximate the experimentally observed rhabdomere movement dynamics (see Appendix 7). Here, the following deductions were made

• Each photoreceptor contracted independently to light. Although this movement is linked to the synchronous contractions of its neighbors inside the same ommatidium, such cooperativity makes no difference to the model.

• Rhabdomere movement started 8 ms after the first dot reached the outer rim of a photoreceptor’s receptive field, called the trigger zone. This delay matched both the delay in R1-R6 output (Appendix 7: Appendix 7—figure 11) and the apparent dead-time in AFM data (Hardie and Franze, 2012) to a bright light flash (Appendix 7: Appendix 7—figure 9J). The trigger zone was 14.6^o from the photoreceptor receptive field center, matching the typical spatial threshold where dark-adapted wild-type R1-R6s responded faintly to subsaturating peripheral light flashes (Appendix 4, Figure 7—figure supplement 1).

• Maximum horizontal rhabdomere movement was set to be 0.58 µm, corresponding to a 1.6^o shift in its receptive field. This value is close to the measured average of the maximum light-induced rhabdomere movements in wild-type fly ommatidia (Appendix 7, Figure 8D).

• Rhabdomere movements had two phases. In the first phase, a rhabdomere moved 1.6^o in back-to-front direction for 100 ms, reaching its maximum displacement. This caused a receptive field to shift in the opposite, α (front-to-back) direction. Importantly, the first phase could not be disturbed. In the second phase: the rhabdomere slowly returned to the original position in 500 ms. The second phase could be disturbed. Both the phases followed linear motion.

As in the first case, the moving receptive field model (Appendix 8—figure 1B) was implemented for the same stimulus in four steps (i-iv):

1. Two bright dots, 6.8^o apart, crossed a photoreceptor’s RF (∆ρ = 8.1^o) front-to-back at the saccadic speed of 205 ^o/s.

2. The ommatidium lens focused their light onto a rhabdomere tip. But here, after 8 ms delay, the rhabdomere started to move back-to-front as it contracted photomechanically.

3. The resulting dynamic light input was, therefore, a convolution of the two dot intensities and the cell’s receptive field, which moved at different speeds in the same direction (front-to-back).

4. The light input drove the photon sampling and refractory QB production of 30,000 microvilli, while the resulting macroscopic photoreceptor output summed up the QBs.

We found that the resulting receptive field movement caused (iii) the light input rise and decay slightly later than when the rhabdomere was immobile (cf. green and dotted grey traces). However, because the two dots were close and crossed the cell’s receptive field fast, the given co-directional receptive field motion failed to separate the light from them. Thus, (iv) the resulting photoreceptor output showed a single peak, which was slightly broader than the output from the immobile model.

There is a large disparity between the measured (Appendix 4: ∆ρ = 7.00–11.65°) and the optical waveguide theory derived (Stavenga, 2003b) (∆ρ = 3.5–5.3^o) acceptance angles of dark-adapted R1-R6s. Even Snyner’s simple formula (Snyder, 1977) (Appendix 4: Equation A4.3), which overestimates (van Hateren, 1984; Stavenga, 2003b) ∆ρ from the measured Drosophila ommatidium optical dimensions, gives a theoretical upper bound (∆ρ <5^o) that is smaller than the smallest intracellularly measured values.

These upper bounds for green light (545 nm) were obtained for the smallest and largest ommatidium lens (16–17 µm) with average rhabdomere diameter EM measurements (1.7 µm) (Appendix 5), using the experimentally estimated focal length (21.36 µm) (Gonzalez-Bellido et al., 2011).

Moreover, interestingly, Götz estimated from Drosophila optomotor behavior, using the early flight simulator system (Götz, 1964), that in bright illumination R1-R6 ∆ρ would be 3.5^o.

To resolve the paradox between the conflicting experimental and theoretical ∆ρ-estimates, which in the past were based upon histological measurements of fixed/stained (dead/immobile) retinal structures, we hypothesized that the photomechanical rhabdomere contractions not only move a photoreceptor’s RF but also dynamically narrow it (Appendix 8—figure 1C). What is more, we reasoned that the RF narrowing should depend upon stimulus history; the cell’s ongoing light exposure. Therefore, our specific prediction was that when moving bright dot stimuli entered a R1-R6’s RF, the resulting dynamic input modulation would transiently sharpen R1-R6 output, improving its temporal resolution.

Again, the feasibility of the hypothesis was assessed by analyzing and comparing the resulting biophysical model output to real R1-R6 recordings. The model was implemented in four steps (Appendix 8—figure 1C):

1. Two bright dots, 6.8^o apart, crossed a photoreceptor’s RF (∆ρ = 8.1^o) front-to-back at the saccadic speed of 205 ^o/s.

2. The ommatidium lens focused their light onto a rhabdomere tip. After 8 ms delay, the rhabdomere started to move back-to-front as it contracted photomechanically. And now, with this movement, its acceptance angle, ∆ρ, also narrowed transiently, from 8.1^o to 4.0^o (Appendix 8—table 1). In the model, the further away the rhabdomere moved from its starting position at the focal plane, the more its receptive field narrowed (or skewed).

3. The resulting dynamic light input was, therefore, a convolution of the two dot intensities and the cell’s RF, which narrowed and moved at different speeds in the same direction (front-to-back).

4. The light input drove the microvillar photon sampling and refractory QB production, which were summed up over the whole rhabdomere to a macroscopic photoreceptor voltage output.

Importantly, the predicted photoreceptor output showed now two distinct peaks, indicating that the two dots (iv) were resolved neurally. Moreover, the simulations closely resembled the recordings to the similar stimulus (cf. Appendix 8—figure 1C-D).

In another test (Appendix 8—figure 1D), we estimated the same R1-R6’s light input (iii) from its RF (i; through programmed look-up table operations, see Appendix 6—figure 1) and used this to predict its output (iv; blue dotted trace). We discovered that the simulated output was indeed similar to the cell’s actual recorded output to the same stimulus (black trace), with the timing of their two peaks matching closely. This close dynamic correspondence between the simulations and recordings was robust and reproducible in different tested stimulus conditions (Appendix 8—figure 2C-D), meaning that the given model structure likely incorporated the basic biophysical mechanisms that R1-R6s use in encoding moving stimuli.

Appendix 8—figure 2

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In summary, for the biophysical model to match up the real R1-R6 cells in resolving two bright moving dots, its receptive field must move and transiently narrow from its original size (Appendix 4: ∆ρ_start = 7.00–11.65 °) to the size predicted by the optical waveguide theory (∆ρ_end = 3.5–5.3^o). Moreover, within this dynamic ∆ρ change range, the resulting model outputs become realistic and robust. Using this modeling approach, we could appropriately predict the real photoreceptors’ voltage responses to the different moving dot stimuli (Appendix 6), irrespective of the tested dot speed, direction (front-to-back or back-to-front) and inter-dot distance. For example, by replacing the mean measured rhabdomere displacements with some of the larger values (Appendix 7), the simulations resolved moving dots similarly well to the recordings even at very high stimulus speeds 400–800 ^o/s.

From the neural coding point of view, this broad agreement between our ‘microsaccadic sampling’-hypothesis and the experiments makes it almost certain that photomechanical rhabdomere contractions (Appendix 7) move and narrow R1-R6 photoreceptors’ RFs to enhance visual acuity. But from the viewpoint of reducing light-adaptation, these processes seem like by-products of a simple evasive action, which steers the rhabdomere away from pointing directly to the light source (to recover more refractory microvilli; see Appendix 2). Nevertheless, while elementary optics makes it clear why a horizontal rhabdomere motion must move a R1-R6’s receptive field in the opposite way, it is harder to see what physical mechanisms could narrow it. We next consider four potential processes within the ommatidium lens system that could just do this.

Four hypothetical mechanisms, together or separately, could explain the required RF narrowing:

1. When a rhabdomere moves back-to-front (Appendix 8—figure 3), it moves away from the center axis, which remains fixed because the ommatidium lens system does not move (see Appendix 7, Appendix 7—figure 7). Therefore, as the rhabdomere tip moves horizontally (Video 3), the light input point-spread function (airy disc) should fall only partly upon it. This may clip or skew the rhabdomere’s RF (acceptance angle, ∆ρ), narrowing it.

2. Besides moving rhabdomeres horizontally (Appendix 7), photomechanical photoreceptor contractions also move them 0.5–1.7 µm inwards (Video 2; Appendix 8—figure 3B). In a dark-adapted state, the rhabdomeres are elongated towards the lens with their tips possibly not being at the focal point. Hence, in this position, the rhabdomeres should collect light from broader angles (Appendix 4, from the brief test pulses: Appendix 4—figure 4), and partially recover (re-elongate) before the next pulse comes. But during more continuous light stimulus, their contraction pulls their tips inwards, towards the possible focal point of the lens, which could narrow ∆ρ towards its theoretical values (3.5–5.3^o).

3. Rhabdomere tips are linked by adherence junctions to the cone cells (above them) and pigment cells (at their upper corners) (Tepass and Harris, 2007) (Appendix 8—figure 3C). When the rhabdomeres contract these connections likely pull the pigment cells above, generating a dynamic aperture (Video 4), which moves and possibly tightens, to narrow ∆ρ (see Appendix 7, Appendix 7—figure 7).

4. In dark-adaptation, the waveguide crosstalk between neighboring rhabdomeres could broaden their receptive fields. But light-induced horizontal rhabdomere movement may eliminate the crosstalk between the neighbors, narrowing ∆ρ towards the theoretical values (3.5–5.3^o).

Appendix 8—figure 3

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The microsaccadic sampling-hypothesis, as implemented by our biophysically realistic photoreceptor model (Appendix 1) with combined photomechanical rhabdomere dynamics, makes important predictions about the coding benefits of moving and narrowing R1-R6 receptive fields that can be tested experimentally.

The first prediction is that, for a given stimulus or saccadic velocity, R1-R6 output to a back-to-front moving bright dot should appear before the output to a front-to-back moving dot. This is because the back-to-front moving dot should enter and exit a contracting photoreceptor's front-back moving receptive field earlier; whereas the dot moving in the opposite direction should stay marginally longer inside its RF. Appendix 8—figure 4 compares the theoretical predictions (output simulations) of the same three models as earlier (A, B and C; their details are above) and corresponding exemplary intracellular recordings (D) for these two stimuli.

Both the full model simulations (C) and many recordings (D) indicate that this prediction is indeed what happens for a R1-R6 with a symmetrical RF (i). The responses (red traces) to back-to-front moving dots rise and decay faster than the responses (blue traces) to front-to-back moving dots. Similar response dynamics of another intracellular recording series from another R1-R6 are highlighted in Appendix 6 (Appendix 6—figure 4). Notice, however, that these results are explicitly true for symmetrical receptive fields. If, on the other hand, a R1-R6’s RF was asymmetrical - say, profoundly skewed towards the front of the eye, then its response to the front-to-back moving dot might, in fact, rise earlier, or there could be little difference between the responses. Thus, it is the mathematical relationship between the scale of RF asymmetricity and the scale of the rhabdomere back-to-front movement, which ultimately sets whether a front-to-back or back-to-front stimulus would win. Notice also that dynamic photomechanical rhabdomere movements and eye muscle activity make RF recordings difficult to perform, and consequently, experimental inaccuracies and limitations can influence the results. Thus, some of the natural variations in the recordings may result from imprecise stimulation control. For example, imperfect positioning of a 25 light-point stimulus array - either off-center of a cell’s receptive field or if not aligned perfectly parallel in respect to the eye’s back-to-front axis - could bias a recording (more about this variation and the cell numbers in Appendix 6).

Appendix 8—figure 4

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Interestingly, for both opposing object directions, the narrowing of a R1-R6’s receptive field (Appendix 8—figure 4C-D) makes its voltage responses briefer than what would be the case without this process (A-B). Therefore, the resulting faster temporal photoreceptor output dynamics combat the effects of motion blur, supporting the theoretical and experimental results in Appendix 6 (Appendix 6—figure 8).

The second prediction is that, for high (saccadic) speeds, R1-R6s resolve two front-to-back moving bright dots better than when these move back-to-front (Appendix 8—figure 5). Thus, the normal back-to-front rhabdomere movement should improve the fly eye’s spatiotemporal resolution during fast forward locomotion or object motion. This is indeed what we saw in the full model simulations (Appendix 8—figure 5D) and in some stable experimental recordings (Appendix 8—figure 5E). Because of the back-to-front rhabdomere movement, which was inverted by the ommatidium lens, the light input (Appendix 8—figure 5C) for two front-to-back moving dots were separated further apart as intensity spikes (blue trace) than that for the opposite motion (red). Consequently, the resolvability in the resulting R1-R6 output (Appendix 8—figure 5D) also became greater for front-to-back moving stimuli. This of course further meant that in comparison to the case of the immobile rhabdomere with the same narrow acceptance angle (∆ρ = 4^o), the neural resolvability of the back-to-front moving rhabdomere, which kept the same stimulus longer within its receptive field, would be still better.

Appendix 8—figure 5

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We next used the complete photoreceptor model (above) to estimate how well a typical R1-R6 photoreceptor can resolve two bright dots, which are less than the average acceptance angle (∆ρ) apart, moving together at increasingly fast (saccadic) velocities. This time, however, the simulations were performed at the flies’ preferred temperature (Sayeed and Benzer, 1996) of 25°C, rather than at 19°C (as in the previous data). We have shown earlier that warming accelerates R1-R6s’ phototransduction dynamics and refractory microvilli recovery (Juusola and Hardie, 2001b; Song et al., 2012; Song and Juusola, 2014). Because the resulting increase in their sample (quantum bump) rate changes improves information transfer rate (Juusola and Hardie, 2001b; Song et al., 2012; Song and Juusola, 2014), we expect here that their output to moving dots should also show improved resolvability. We later compare these estimates to the measured head/body-saccade speeds of freely locomoting Drosophila (Fry et al., 2003; Geurten et al., 2014).

Appendix 8—figure 6 shows the simulated light input (C) and photoreceptor output (D) to the dots (6.8^o apart) crossing a R1-R6 photoreceptor’s RF (∆ρ_start = 8.1^o, ∆ρ_end = 4.0^o) in front-to-back direction at 205 (left), 409, 600, 700, 800 and 1000^o/s (right). We found that the slower the dots moved (A), the better the predicted photoreceptor output distinguished them as two separate events (peaks) in time (D). Remarkably, the output resolved the dots at speeds until ~600 ^o/s (cyan background). As a neural threshold for representing sub-RF details, this image speed is indeed very high. It means that Drosophila should lose little neural image detail during its normal saccadic body rotations during walking; the measured rotation speed range is ~200–800 ^o/s (Geurten et al., 2014). At the higher speeds, the two response peaks fused into one. Notice that because the predicted light input (as modulated by the rhabdomere contraction) resolved the dots even at 1,000 ^o/s (Appendix 8—figure 6C), the resolution limit in the photoreceptor output (Appendix 8—figure 6D) resulted from its intrinsic signal integration time limit; for the given (experimentally measured) quantum bump size, latency and refractoriness distributions (Juusola and Hardie, 2001a; Song et al., 2012; Song and Juusola, 2014). Notice also how the response amplitude and half-width were reduced more the faster the dots crossed the receptive field. Thus, the rhabdomere then simply captured and integrated fewer photons in a given time unit.

Appendix 8—figure 6

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Given that R1-R6 output shows unexpectedly high acuity even at very fast saccadic velocities (Appendix 8—figure 6), we asked how well these cells could in fact resolve slower moving point-objects. Could a normal R1-R6 encode image details, which were less than the average interommatidial angle apart? That is, could Drosophila actually see the world in finer resolution than their compound eyes maximum sensor (or pixel) spacing, which is the limit predicted by the classic optical theory (Land, 1997)?

We tested this hypothesis theoretically by using the full ‘microsaccadic sampling’-model (Figure 9). In these simulations, two bright dots were now either 1^o, 2^o, 3^o or 4^o apart. Thus the dot spacing was less than the Drosophila compound eye’ average interommatidial angle (∆φ ~4.5-5^o). The dots were then moved across a R1-R6 photoreceptor’s RF (∆ρ_start = 8.1^o; ∆ρ _end = 4.0^o) at different speeds, ranging from 5 (slow gaze fixation) to 400 ^o/s (very fast body saccade).

The model predicted that a typical R1-R6 photoreceptor would resolve the dots in hyperacute details (Figure 9) over a broad range of velocities. These theoretical predictions were broadly confirmed by intracellular recordings (Figure 9—figure supplement 1), whilst flight simulator experiments verified that Drosophila indeed have hyperacute vision (Figure 10).

To quantify how refractory photon sampling contributes to the sharpening of the macroscopic responses during moving hyperacute 2-dot stimuli, we further compared the outputs of two different photoreceptor models for the same stimuli (Appendix 8—figure 7), with the brightness as in Appendix 8—figure 1. For both cases, the resulting dynamic light input – reflecting the narrowing and moving receptive field, as caused by photomechanical rhabdomere contraction - was the same, but the models’ photon sampling differed. The test model had 30,000 stochastically operating refractory microvilli and the control was a comparable mock model, which converted every incoming photon into a quantum bump.

Appendix 8—figure 7

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Firstly, we found that the refractory sampling consistently improved the response resolution beyond that of the control for bright hyperacute dots (inter-dot-distance <4.5^o) at slow velocities (≤20 ^o/s) (Appendix 8—figure 7A–B). Thus, refractoriness enhances neural image resolution during slow self-motion or when high-resolution objects move slowly. Its effects were particularly well seen in the differing rising phases of the normalized light-induced current (LIC) responses of the two models. With the slow moving stimuli, the rising responses of the refractory sampling model (black traces) always led those of the non-refractory model (red).

Additionally, in other trials, we found that when the dots were more than the average acceptance angle apart (∆ρ_start ≥ 9.5^o) but moved across a R1-R6 photoreceptor’s receptive field at very fast saccadic speeds (≥400 ^o/s), the refractoriness often enhanced neural image resolution beyond that of the controls (Appendix 8—figure 7C). This observation is consistent with our previous finding that stochastic refractoriness of light-activated microvilli exerts a memory of past events in bump integration (Song and Juusola, 2014). This memory accentuates certain stimulus features relative to others so that a R1-R6 samples information from different inter-dot-distance/speed-combinations differently. Ultimately, it could well be that the real R1-R6s’ refractory photon sampling statistics are adapted (through their visual lifestyle) to the statistics of moving high-resolution natural images. Of course, here, the used 2-dot stimuli and the models, which were isolated from the lamina network feedbacks, are too simple to fully explore such statics and the intricacies of hyperacute Drosophila vision.

The two most important biophysical factors of Drosophila photoreceptors, which lead to motion hyperacuity - whereupon space is encoded in time - are their sufficiently narrow receptive fields (∆ρ_end < 5^o) and refractory photon sampling (quantum bump dynamics). Therefore, theoretically, as R1-R6s’ receptive fields should narrow when an object crosses them, irrespective of its motion direction; Drosophila is expected to have hyperacute vision for both horizontal and vertical motion.

However, as we considered in Appendix 8—figure 4, R1-R6 photoreceptors’ neural resolvability should be the best for front-to-back moving objects. In this case, due to their back-to-front sweeping rhabdomeres, R1-R6s’ receptive field can broaden slightly in horizontal direction. This dynamic may in part contribute to the curious observation that L2 monopolar cell terminals’ receptive fields (in the medulla) are anisotropic, elongated in horizontal (yaw) direction and narrower in vertical (pitch) direction, as measured by calcium-imaging experiments (Freifeld et al., 2013).

As we showed in Appendix 7, light increments evoke mirror symmetric back-to-front rhabdomere movements in the left and right fly eye. Interestingly, during fast saccadic body rotations, this phenomenon could surprisingly help a fly’s visual orientation (Appendix 8—figure 8). The microsaccadic sampling-hypothesis predicts that image rotation causes a phasic difference in photoreceptor outputs between the left and the right eye, with the signals always arriving slightly faster from the eye, towards which the fly rotates. Because this difference depends upon the rotation speed, it could be used for signaling changes in the fly’s heading direction or to improve visual navigation. For example, when flying across more homogenous surroundings, such as an open field with few distinctive visual landmarks, the central brain could use saccadic turns to recalibrate the fly’s head-direction in its internal world map near instantaneously; matching the intended direction to the new direction, as pointed by the global phase difference between the left and right eye signals.

Appendix 8—figure 8

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This appendix describes how photomechanical rhabdomere movements affect Drosophila R1-R6 photoreceptors’ information capture, compares microsaccadic information sampling of dark and bright objects and provides useful background information about the experimental and theoretical results presented in Figures 1–9.

In this appendix:

• We explain why and how rhabdomere movement noise influences R1-R6 output mostly at low frequencies, causing relatively little information loss.

• We test and compare how microsaccadic sampling affects encoding of bursty bright or dark image contrasts, using intracellular recordings.

• We further examine how well R1-R6s encode two dark moving point-objects (dots), and compare these recordings with those to corresponding bright moving dots.

• The results confirm that Drosophila R1-R6 photoreceptors resolve both bright and dark moving hyperacute patterns (<interommatidial angle, ∆φ ~4.5-5^o), and can respond to bright or dark point-objects, which are less than their acceptance angles (∆ρ ~ 9.5^o) apart, even at high saccadic velocities. Thus, microsaccadic sampling hypothesis provides a robust functional explanation for Drosophila‘s hyperacute vision (Appendix 10).

• The results support the idea that a fly’s optimal viewing strategy would involve fixating on dark features, which recover refractory microvilli, and then shifting gaze to bright features, to maximize information capture. This of course would require that it can neurally shift attention (across the eyes) to visual objects of interest, as some results suggest (Tang et al., 2004; van Swinderen, 2007; Tang and Juusola, 2010; Paulk et al., 2014; Seelig and Jayaraman, 2015).

Photomechanical rhabdomere contractions (microsaccades; Appendix 7) can maximally shift the center of a R1-R6 photoreceptor’s receptive field by ~5^o, and through this self-induced light input modulation (Figure 8) cause variations (noise) in its voltage output. Such ‘rhabdomere movement noise’ is inevitable if the photoreceptor signal is classified and estimated as the average of the repeated responses, just as we did in the performance calculations (e.g. Figure 2).

The condition itself bears resemblance to taking snapshots of a stationary scene from different positions and averaging these. The mean image shows an obvious smear, even if the positions were only a fraction of a photoreceptor’s receptive field (‘pixel’) apart. However, during repeated light stimulation, the rhabdomere movements adapt rapidly (Figure 8E, Figure 2—figure supplement 2), with this noise affecting less the subsequent performance estimates. Thus, when quantifying the photoreceptor performance to repeated light intensity time series stimulation (e.g. Figure 2), we removed the first 3–10 responses, in which these movements had the largest effect. In the recordings, this noise would then be rather constant across the collected responses.

Rhabdomere movement noise is missing from the simulated R1-R6 output (Figures 8–9). Therefore, given that the stochastic photoreceptor model’s transduction noise is adapted to the mean light intensity (Appendix 2), similarly to that of the recordings (Figure 2—figure supplement 2A–B), we could isolate it as the difference between the recorded and simulated R1-R6 output (Figure 2—figure supplement 2C–D). The analysis suggests that rhabdomere movement noise affects mostly low-frequency R1-R6 output, reducing its signal-to-noise ratio, and importantly, it effectively matches the rhabdomere jitter in high-speed video footage (Figure 2—figure supplement 2E,F).

The contractions deviate the rhabdomere from directly facing the light source, reducing photon influx especially during bright stimulation (Figure 8C–D). Such evasive action, however, has surprisingly little detrimental effect on the R1-R6s’ information transfer. This is because bright stimulation (>10⁶ photons/s) contains too much light to be transduced by 30,000 microvilli into quantum bumps, and R1-R6s actively screen off excess photons to maximize information in their voltage output. In Appendix 2, we showed that R1-R6s’ photomechanical adaptations (the contractions and intracellular pupil mechanism) are jointly optimized with refractory sampling (to modulate quantum efficiency [Song et al., 2012; Song and Juusola, 2014]) for maximal information intake at different stimulus conditions. Moreover, owing to bump adaptation and microvilli refractoriness, which accentuate light fast changes in macroscopic voltage output (Song et al., 2012; Song and Juusola, 2014; Juusola et al., 2015) (e.g. (Song and Juusola, 2014): Figures 9–10, improving high-frequency resolution), slower signals in return become compressed. Importantly, this low-frequency response range (<~10 Hz), where also rhabdomere movement noise mostly resides (Figure 2—figure supplement 2D), carries relatively little information (Song and Juusola, 2014) (about the behaviorally more relevant faster changes in the world).

Recordings and simulations (Figures 1–2) showed unequivocally that R1-R6s information capture is maximized for high-frequency saccade-like bursts with dark fixation intervals. This suggests that the optimal daytime viewing strategy would be to fixate on dark features in the visual scenes, as this recovers refractory microvilli, and then rapidly move gaze to over bright features, as this increases quantum bump (sample) rate changes and thus information capture in time. And indeed, in behavioral experiments, Drosophila readily fixates on and track dark objects, such as vertical bars (Götz, 1980; Tang and Juusola, 2010; Bahl et al., 2013). But because the fly eye photoreceptors sample a continuous panoramic view of the world, many of them - at any one time - would unavoidably face bright contrasts, which reduce their sensitivity even when their photomechanical adaptations (Appendix 2) operate maximally. We therefore also tested by intracellular R1-R6 recordings how encoding of dynamic bright or dark contrast changes may differ.

Appendix 9—figure 1

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Appendix 9—figure 1A shows examples of consecutive responses recorded from a R1-R6 to repeated high-frequency saccadic bright or dark contrast bursts (with 100 Hz cut-off). Expectedly, following the stochastic adaptive visual information sampling theory (Appendixes 1–2), the responses to bright (positive) contrasts after dark ‘fixation’ periods (background, BG) were significantly larger than those to dark (negative) contrasts after bright ‘fixation’ periods. Notice, however, that although in terms of absolute light intensity (I) changes (or peak-to-peak amplitude modulation) the two stimuli were equal, the negative bursts had smaller absolute contrast values (${\displaystyle \mathrm{C}=\mathrm{\Delta }\mathrm{I}/\mathrm{I}}$) than the positive ones. This is because the darkening bursts reached their absolute contrast maximum (darkness, −1) only occasionally, whereas the corresponding brightening bursts reached higher absolute contrasts (>1; owing to their lower mean light intensity).

To counter this bias, we used three sets of stimuli to examine individual R1-R6s’ response dynamics to both positive and negative bursts of equal or different contrast distributions (Appendix 9—figure 1B). First (top row), the photoreceptors were stimulated with positive contrast bursts (peak-to-peak modulation = 1 intensity units), which contained high-frequency saccade-like events on a dark background, having different cut-off frequencies (from 20 to 500 Hz, as in Figure 1). In the second set (middle), the same stimuli were superimposed on a bright background (one unit). Finally (bottom), the stimulus modulation was inverted (to negative contrast bursts) and superimposed on the same bright background (one unit). Thus, for the second and third sets, the stimulus contrasts were equal but opposite.

We found (again in agreement with the theory) that whilst the responses were always the largest to positive contrast bursts on a dark background, the corresponding responses to the positive and negative contrast bursts on bright background, although smaller, were about the same size (Appendix 9—figure 1B). Since we further know that the larger responses contain more quantum bumps (Figure 2), with the average bumps light-adapting to about the same size (e.g. Figure 2—figure supplement 2A–B), the responses’ signal-to-noise ratios (Appendix 9—figure 1A) and information transfer rates (Appendix 9—figure 1D) were predictable. R1-R6s’ signaling performance was the greatest to the larger positive contrast bursts on a dark background (black), and more than halved to the smaller corresponding positive (grey) and negative (light grey) contrast bursts over the test bandwidths. Notably, the responses to the opposite but equal positive and negative contrast bursts carried effectively equal information contents, underscoring the importance of contrast invariance at the primary visual encoding stage (Juusola, 1993; Song et al., 2012; Juusola et al., 2015).

Therefore, given the fast speed of adaptation (microvilli refractoriness and dynamic quantum bump size modulation) and its photomechanical counterbalancing (Appendixes 2, 7), the sensitivity of neighboring photoreceptors across the eyes can differ greatly at any one moment, depending upon whether they face dark or bright contrasts. This realization also implies that when a fly moves its gaze in saccades, the dark and bright spatial contrast differences in the world should be automatically translated into large temporal contrast changes between the neighboring retinotopic image pixels (neuro-ommatidia). Enhancement of local differences and similarities in neural images by spatiotemporal synaptic (Zheng et al., 2006; Freifeld et al., 2013) and gap-junctional (Wardill et al., 2012) co-processing (including network adaptation [Nikolaev et al., 2009; Zheng et al., 2009]) across the first optic ganglia, the lamina and medulla, should further improve object detection and fly vision.

Natural scenes are rich with dark features: shadows, object boundaries, surfaces of lesser reflectance etc., which have shaped visual circuit functions, perception and behaviors (Barlow H, 1961; Yeh et al., 2009; Joesch et al., 2010; Ratliff et al., 2010; Kremkow et al., 2014; Song and Juusola, 2014). Consequently, a fly’s self-motion generates both dark and bright moving features travelling across its eyes. We have shown that R1-R6s can resolve fast-moving and hyperacute bright dots (Figures 7–9 and Figure 9—figure supplement 1). But how well can these cells resolve dark moving dots?

We studied this question with the 25 light-point stimulus array (explained in Appendix 4 and Appendix 6). As before, the stimulus array was first carefully placed at the studied R1-R6’s receptive field center, but this time, all the light-points were switched on, and we generated two travelling dark points of specified speeds and interdistances. As during these experiments the cells were light-adapted (depolarized) by the lit stimulus array, the two moving dark dots evoked hyperpolarizing responses.

Appendix 9—figure 2A shows R1-R6s’ characteristic responses to two dark (black traces) and bright (red) dots of specific speeds (102, 205 and 409 ^o/s) and interdistances (3.4, 5.1 and 6.8^o apart), recorded from the same cells. In all these cases, the hyperpolarizing responses resolved the two dots, generating two troughs separated by a peak, but these responses were considerably smaller than those to the corresponding bright dots. However, when normalized, the photoreceptors’ relative neural resolvability of the dark dots matched that of the bright dots (Appendix 9—figure 2B).

Thus, in concordance with the behavioral experiments (Figure 10), these and other intracellular recordings established that Drosophila R1-R6 photoreceptors see both bright and dark moving hyperacute patterns (<interommatidial angle, ∆φ ~4.5-5^o), and can resolve point-objects, which are less than their acceptance angles (∆ρ ~ 9.5^o) apart, even at high saccadic velocities.

Appendix 9—figure 2

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Our results indicate that R1-R6 photoreceptors’ information transfer adapts to the context of stimulus statistics; with refractory microvilli, fast quantum bump adaptation (Henderson et al., 2000; Juusola and Hardie, 2001a; Song et al., 2012) and photomechanical microsaccades maximizing encoding of phasic information from high-contrast bursts. Remarkably, the extraction of phasic stimulus features, which characterize object boundaries and line elements in visual scenes, already starts during sampling and integration of visual information in the microvilli, at the first visual processing stage. The darker periods in stimuli relieve the effects of microvilli refractoriness, enabling greater sensitivity: more and slightly larger samples (quantum bumps) can be generated transiently to the next light change (Figure 1). This increases the signal-to-noise ratio of the integrated macroscopic response, especially in its phasic (fast rising/decaying) components (Appendix 3, Appendix 3—figure 1). However, unlike later information processing in the network, during which presynaptic inputs are often translated to postsynaptic spike-bursts of high sparseness for specific features, the neural code of photoreceptors must consider all stimulus features together. It adapts to allocate information in high-contrast bursts into continuous Gaussian broadband voltage signals (Figure 2A–B), utilizing the output range optimally.

In the viewpoint of efficient coding, stochastic refractory sampling, fast quantum bump adaptation and photomechanical contractions benefit vision in three important ways:

• They exchange redundant information in mean voltage to more useful information in relative modulation, enabling photoreceptors to encode reliable estimates of the world within their limited output ranges, despite strongly and quickly changing intensities.

• They lower the metabolic cost of information with fewer bumps integrating a lower membrane potential, consuming less ATP (Song and Juusola, 2014).

• And when linked to bursty saccadic head/body movements, they increase high-frequency information capture from the world and reduce motion blur.

These results further imply that saccadic behaviors enable the fly eye to convey to the fly brain a far more efficient and accurate neural image of the variable world than what was believed before. Thus, saccades not only contribute to gaze-stabilization (Land, 1973; Fox and Frye, 2014), which historically is considered to be their major function (Land, 1999), but they also “burstify” light input for efficient and accurate sampling.

This appendix describes the used optomotor behavioral paradigm in a classic Drosophila flight simulator system to study visual resolution, and provides important background information about the experimental and theoretical results presented in Figure 10 in the main paper.

In this appendix:

• We test in open-loop conditions whether wild-type Drosophila can generate yaw-torque (optomotor responses) to hyperacute vertical black-and-white stripe-scenes that rotate clockwise and counterclockwise at 45 ^o/s.

• Our results clearly indicate that wild-type Drosophila have hyperacute vision (seeing finer image details than the average interommatidial angle, ∆φ ~4.5, of their compound eyes), with the measured behavioral responses closely following the prediction of our new ‘microsaccadic sampling’-hypothesis (see Appendix 8).

Wild-type ‘Berlin’ Drosophila were raised on standard food medium at 25°C and 60% relative humidity with a 12 hr light and 12 hr dark cycle, with light on at 8 a.m. In the experiments, we used 2- to 3-day-old female flies. Under cold-anesthesia (lasting <3 min), a small copper-wire hook was fixed with a droplet of UV-light sensitive glue (Loctite) between each fly’s head and thorax. After preparation, flies were left to familiarize themselves with their hooks overnight in single vials, which provided them water and sucrose.

A custom-built, computer controlled flight simulator system (Wardill et al., 2012) was used to study Drosophila’s optomotor behavior. A tethered Drosophila was connected to the torque-meter (Tang and Guo, 2001) by a small clamp holding the copper-wire hook, which fixed the fly’s head in a rigid position and orientation, but allowed stationary flight (Götz, 1964; Heisenberg and Buchner, 1977). The torque meter transduced yaw torque into electrical voltage.

A fly, tethered from the torque meter, was lowered by a mechanical micromanipulator in the center of a white featureless plastic hollow cylinder (a diffuser). Inside it, we placed high-resolution visual patterns (bars, stripe patterns, etc.), which were laser-printed on a transparent film, forming a 360^o panorama around the fly's long axis. The panorama could be rotated around its vertical axis by a servomotor. Outside, the diffuse cylinder faced a surrounding ring-shaped light-tube (special full-band: 350–900 nm) that provided uniform illumination on the panorama. The light intensity during the panoramic motion stimulation, although bright, was always less (0.5–1.5 log-intensity units) than the direct stimuli used in the intracellular recordings (cf. Figure 1).

Inside the flight simulator, a flying fly saw a continuous (360^o) stripe-scene (black-and-white bars) of predetermined spectral and spatial resolution, which was free of motion artefacts, flashing or aliasing. After one second of viewing the still scene, it was spun to right (clockwise) by a linear stepping motor (in which output was recorded simultaneously by a separate potentiometer coupled to the motor) for two seconds, stopped for two seconds, before rotating to left (counterclockwise) for two seconds, and stopped again for a second. This eight-second stimulus was repeated 10–25 times and each trial, together with the fly’s coincident yaw torque responses, was sampled at 1 kHz and stored in a PC’s hard-drive for later analysis, using custom-written software (Biosyst) (Juusola and Hardie, 2001a). Presumably to stabilize gaze, flies tend to follow the scene rotations, generating yaw torque responses (optomotor responses to right or left), the strength of which is believed to reflect the strength of their motion perception (Götz, 1964; Heisenberg and Buchner, 1977; Wardill et al., 2012). The fixed stimulus parameters for moving stripe scenes, as shown in the figures, were: azimuth ±360°; elevation ±45°; velocity, 45, 50, 200 or 300 °/s; contrast, 1.0, as seen by the fly. Figure 10A show the averages (n = 9 flies) of the mean optomotor responses (n = 22–35 trials for each fly).

We first tested optomotor responses of wild-type flies to black-and-white stripe-scenes (spectral full-width: 380–900 nm) of three different spatial resolutions (wavelength: 1.16^o, 2.88^o and 14.4^o), rotating at 45^o/s, as shown in Figure 10A–C. To verify that air flow, or some hidden features in the stimulus panorama, was not affecting optomotor responses, we used the white diffuser cylinder alone, which showed no clear contrast to human eye, as the control stimulus. These control field rotation experiments were repeated using the same flies (Figure 10—figure supplement 1). We found by that the white control stimulus did not evoke torque responses.

We also tested optomotor responses of five flies to 3.9^o (hyperacute) and 14.4^o (control) wavelength panoramic stipe-scenes, rotating at 50, 200 and 300 ^o/s (Figure 10D–F). The results were consistent with the predictions of the full photoreceptor model (cf. Figure 9A, two dots 4^o apart), which incorporated both the refractory photon sampling and photomechanical rhabdomere motion dynamics.

Quantifying optomotor behavior. The optomotor responses of individual flies to the same repeated field rotations vary in strength and repeatability (Figure 10—figure supplement 1A), but their visual performance to different spatial resolution stripe scenes is clearly different. These differences can be quantified by measuring the mean torque response of a single fly to stimulus repetitions and by averaging the mean responses of the many flies of the same stripe scene resolution (Figure 10—figure supplement 1B; here 9). This reduces noise and non-systematic (arbitrary) trends of single experiments, revealing the underlying response strength and optomotor behavior characteristics. These population responses are shown in Figure 10 for a straightforward comparison.

In open-loop experiments, a fly’s torque response returns gradually to baseline after the optomotor stimulus stops, but this can take seconds (varying with individual flies). Accordingly, in our experiments, which contain only brief 2-s-long inter-stimulus-intervals, the torque responses typically recover only fractionally (10–70%) during these still periods toward the baseline. Therefore, for comparing the optomotor behavior different stripe scene resolutions, we used the maximum range (or peak-to-peak) of the torque response, evoked by the combined leftward and rightward field rotation stimulus. The maximum range and variability in the torque responses to the same optomotor stimulus are shown with controls in Figure 10—figure supplement 1C and D, respectively.

Markedly, the optomotor responses to hyperacute stripe-scenes were not caused by aliasing. This is because perceptual aliasing (such as the wagon-wheel effect or Moiré patterns), if induced by the rotating hyperacute scenes, would have been perceived as slowed down image rotation, eventually reversing to the opposite direction (the reverse rotation effect). And thus, if the tested flies had seen such motion patterns, they would have consequently followed them slower and rotated against the real scene rotation direction. Such optomotor behavior was never observed in our experiments.

In 1976, Buhner probed Drosophila’s visual acuity by stimulating the upper frontal part in one of its eyes with small local moving grating patterns (covering about 50 ommatidia) while a fly walked on track-ball (Buchner, 1976). Notably, the aim of his study was not to find the finest resolution what a Drosophila can resolve but instead to deduce the likely columnar organization of its directionally sensitive elementary motion detectors from a fixed fly’s tendency to follow moving stimulus patterns. Thus, this was also an open-loop paradigm, but the used microscope-mediated local grating stimulation was very different from the global hyperacute panoramic visual scenes of our study. Specifically, we note that in Buchner’s study:

• Visual acuity was not tested below the interommatidial angle (∆φ ~4.5); with the overall results deduced by eliminating the presumed boundary elements and contrast attenuation from the data.

• The used mean stimulus light intensity (luminance; 16 cd/m²) was low. Therefore, the resulting image grating at the level of individual photoreceptors would have been dim and spatiotemporal signal-to-noise ratio of light input and photoreceptor output low. Based on our intracellular data (Juusola and Hardie, 2001a; Song et al., 2012), this dim light intensity would have made it practically impossible for R1-R6 photoreceptors to resolve very fine (or hyperacute) visual patterns.

• The sensitivity and the time resolution of the used trackball system (Buchner, 1976) seem significantly less than in our bespoke torque meter (Tang et al., 2004), requiring extensive data averaging. This would have made it more difficult for the trackball system to resolve the weaker (small amplitude) behavioral responses to fine spatial contrast changes (Figure 10A).

More recently, because of the historical belief that interommatidial angle limits a fly’s visual acuity, many experimentalists have started using coarse LED-matrixes, typically with 4.5-5^o maximum resolution, to probe visual learning and optomotor responses. As our study here shows, these kinds of visual stimuli are very different from the panoramic high-resolution printed scenes with thin continuous lines and symbols and thus are expected evoke quite different neural responses.