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Sources of widefield fluorescence from the brain

  1. Jack Waters  Is a corresponding author
  1. Allen Institute for Brain Science, United States
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Cite this article as: eLife 2020;9:e59841 doi: 10.7554/eLife.59841

Abstract

Widefield fluorescence microscopy is used to monitor the spiking of populations of neurons in the brain. Widefield fluorescence can originate from indicator molecules at all depths in cortex and the relative contributions from somata, dendrites, and axons are often unknown. Here, I simulate widefield illumination and fluorescence collection and determine the main sources of fluorescence for several GCaMP mouse lines. Scattering strongly affects illumination and collection. One consequence is that illumination intensity is greatest ~300–400 µm below the pia, not at the brain surface. Another is that fluorescence from a source deep in cortex may extend across a diameter of 3–4 mm at the brain surface, severely limiting lateral resolution. In many mouse lines, the volume of tissue contributing to fluorescence extends through the full depth of cortex and fluorescence at most surface locations is a weighted average across multiple cortical columns and often more than one cortical area.

Introduction

Widefield fluorescence microscopy is a popular technique for monitoring activity in the mouse neocortex, often used in combination with genetically-encoded calcium indicators (Mohajerani et al., 2013; Wekselblatt et al., 2016; Allen et al., 2017; Makino et al., 2017; Mitra et al., 2018). A defining characteristic of widefield microscopes is a lack of optical sectioning. In some mouse lines, fluorescent indicator molecules are expressed at many depths in neocortex, either in multiple cell populations or throughout neurons that extend across cortical layers (Daigle et al., 2018). With no optical sectioning, fluorescence can and often does arise from multiple cortical layers and assignment of the signal to cellular or laminar populations is challenging (Allen et al., 2017). In addition, scattering by brain tissue commonly deflects photons en route to the camera chip, affecting lateral resolution (Silasi et al., 2016).

How severe are these problems? From which layers does fluorescence arise and how much does each layer contribute to total fluorescence? What volume of tissue contributes to fluorescence at a single camera pixel and what’s the resulting resolution? Here, I answer these questions for several representative mouse lines, using a Monte Carlo random-walk model to simulate the propagation of photons in brain tissue.

Monte Carlo random-walk models provide an accurate and computationally tractable solution to the radiative transport equation and have been used extensively to simulate the propagation of photons through scattering media, such as biological tissues (Zhu and Liu, 2013). Random-walk simulations of near-infrared light propagation have been used to refine light intensity, source geometry and duty cycle in photodynamic therapies (De Jode, 2000; Valentine et al., 2012) and optimize illumination parameters and estimate the volume of tissue contributing to signals in diffuse reflectance tomography (Boas et al., 2002; Fukui et al., 2003). More recently, random-walk models have been used to explore brain illumination in the visible spectrum, often near the tips of optical fibers implanted to activate or silence neurons expressing opsins. Random-walk models can accurately predict the volume of tissue in which neurons are activated or silenced and have been used to refine stimulation parameters to minimize heating (Bernstein et al., 2008; Kahn et al., 2011; Liu et al., 2015; Stujenske et al., 2015; Yona et al., 2016). Fluorescence has been simulated by separating illumination and the fluorescence detection into two processes (Chen et al., 2012; Holt et al., 2015; Hennig et al., 2016) and widefield fluorescence has been studied for columnar arrangements of fluorophores, revealing that the effects of numerical aperture and focal position within the tissue depend on the size of the column (Tian et al., 2011).

Here, I adapted code previously used to model illumination by visible and near-IR illumination (Stujenske et al., 2015; Podgorski and Ranganathan, 2016; Wang et al., 2020), simulating illumination and fluorescence emission at visible wavelengths in a ~200 mm3 volume of mouse grey matter. Spatially detailed models, containing individual tissue elements such as neurons and blood vessels, have proven invaluable for exploring optics with single-neuron resolution (Charles et al., 2019), but require substantial computational resources. I therefore modeled tissue as a spatially homogenous medium with wavelength-dependent scattering and absorption (Wang et al., 1995), a common simplification that requires fewer computational resources and has proven accurate where, as here, many photons propagate for multiple scattering lengths.

Widefield fluorescence begins with photons, usually from an incoherent source, propagating through the brain surface and into tissue. This illumination is attenuated by tissue absorption and scattering, and one might expect illumination intensity to decline with depth. Whether and at what depth illuminating photons are absorbed by fluorophore molecules depends on the illumination intensity and the density of fluorophores at different depths. After excitation, fluorescence photons propagate from the source molecule in random directions. Emitted fluorescence is subject to absorption and scattering before exiting the brain and being focused by the objective onto a detector, usually a camera. To understand how fluorophore molecules in different locations within the brain contribute to total fluorescence, I describe illumination intensity, fluorophore expression, and collection efficiency, and how these three factors change throughout the tissue for several mouse lines with GCaMP expression in laminar neuron sub-populations.

Results

Widefield illumination

I began by considering the spread of illuminating photons into brain tissue, simulating 480 nm illumination from an incoherent source focused into the brain through a cranial window by a low magnification, low numerical aperture objective, a configuration commonly used to image activity in mammalian brains using GFP-based indicators. As expected, the broad trend was of a decline in illumination intensity with tissue depth but with an increase in intensity over the initial 200 µm (Figure 1A). When the scattering coefficient was set to zero, eliminating scattering from the model, intensity declined exponentially from the tissue surface with a length constant matching that of absorption (Figure 1A). With the absorption coefficient set to zero, leaving scattering the only mechanism of attenuation, the superficial rise in intensity became larger and extended deeper into the tissue, indicating that the superficial increase in illumination intensity is a result of scattering (Figure 1A).

Excitation intensity under widefield illumination.

(A) Intensity as a function of depth, normalized to the intensity at the tissue surface. Dashed line, exponential decay described by the absorption length constant: normalized intensity = exp(- depth * length constant). (B) Trajectories in tissue for 10 photons. Tissue surface is at depth = 0. Black circle: location at which each photon was absorbed by the tissue. (C) Cosine of the mean propagation angle, relative to the optical axis and perpendicular to the tissue surface. Grey: after 300 µm of skull. (D) Intensity in brain tissue without (black) and with skull (grey; 1 mm, 300 µm and 100 µm skull), normalized to the total intensity in brain tissue.

How does scattering increase the illumination intensity in superficial tissue? Photons exit the objective and enter the tissue propagating almost perpendicular to the brain surface (Figure 1B). The propagation angle is randomized over multiple scattering events. The cosine of the mean angle of propagation (relative to the optical axis; perpendicular to the tissue surface) relaxes towards zero over ~800 µm (Figure 1C), consistent with a calculated transport length of 826 µm. By randomizing propagation directions, scattering slows propagation perpendicular to the brain surface, concentrating photons.

The concentrating effect of scattering is lost when angles at the brain surface are randomized, such as by overlying skull. In mouse, widefield imaging is often performed through intact skull (Mohajerani et al., 2013; Silasi et al., 2016; Allen et al., 2017; Makino et al., 2017; Gilad and Helmchen, 2020; Valley et al., 2020). Mouse skull is ~150–300 µm thick and transparent but strongly scattering (Soleimanzad et al., 2017; Wang et al., 2018). 300 µm of skull overlaying cortex randomizes the directions of propagation (Figure 1C), eliminating the increase in intensity in superficial tissue (Figure 1D). By randomizing the propagation angles of photons arriving at the brain surface, skull weights excitation towards the most superficial fluorophore molecules (Figure 1D).

Fluorescence collection

What percentage of photons from a fluorophore molecule contribute to the image and how does this percentage change with the depth of the source? I simulated fluorescence at 560 nm, in the green-yellow spectrum, from point sources at different depths (Figure 2A). Photons that exit the tissue within the 5.7° maximum collection angle of the objective are collected and contribute to image formation. 0.58% of photons from a surface source are collected (Figure 2B). The collection percentage increases slightly with source depth to ~400 µm, due to scattering, and decreases thereafter (Figure 2B). Photons from deep within cortex can contribute as much to detected fluorescence as photons from superficial layers, with collection percentages for sources on the surface and 1 mm deep being equal.

Widefield fluorescence collection.

(A) Trajectories of 3000 photons from a point source (white circle) at 0.1 mm (left) and 0.5 mm (right) below the tissue surface. Black: trajectories of collected photons (23 photons from 0.1 mm, 22 photons from 0.5 mm). Grey: trajectories of photons absorbed in tissue or that exit tissue outside the collection angle of the objective. Dashed line, tissue surface. Histograms: sum of photons at different surface locations. 106 photons (~5000 collected) in 10 µm bins. (B) Percentage of photons collected, as a function of source depth. (C) Diameter of the patch of fluorescence at the surface, for sources at different depths. Plot illustrates the diameters that include 50% and 95% of captured photons. (D) 2-photon and widefield images of a bolus of fluorescent beads injected into mouse cortex, with the focal planes 310 µm below and at the brain surface, respectively. (E) Measured surface distribution (from the example in D) and the expected fluorescence distribution, simulated for a point source at a depth of 310 µm. Arrowheads mark the locations between which 75% of photons are expected at the surface. (F) Comparison of measured and expected diameters that include 50% (black) and 95% (grey) of photons at the surface, for three experiments with beads at depths of 165, 190, and 310 µm.

Collected photons are scattered en route to the tissue surface. Photons from a point source in the tissue form a patch of fluorescence on the surface (Figure 2A). The diameter of the patch is greater for sources at depth than near the surface. The diameter containing 50% of photons is 10 µm for a source on the brain surface and 860 µm for a 1 mm deep source; the diameter containing 95% of photons is 2.6 mm for a source on the brain surface and 3.9 mm for a 1 mm deep source (Figure 2C). Nearby sources, even in the superficial layers of cortex, produce overlapping surface distributions.

The model accurately predicted the surface distribution of photons. In three experiments, a bolus ~50–100 µm in diameter of 0.1 µm fluorescent beads was injected into mouse cortex at depths of 165, 190, and 310 µm. The diameter and depth of the distribution were measured with 2-photon fluorescence microscopy (Figure 2D). The diameter of the surface distribution, measured with widefield fluorescence, was ~1 mm (Figure 2D,E). The model slightly overestimated the spread toward the edges, but accurately predicted the distribution of the majority of photons (Figure 2E,F).

Effects of focal plane depth, numerical aperture, field of view, and skull

In Figures 1 and 2, illumination and fluorescence collection extend through all layers of cortex, peaking in the middle layers. Do illumination and collection change with system optics?

One might naively expect focusing up and down through brain tissue to change the weighting of fluorescence across cortical layers. As illustrated in Figure 3A, changing the depth of the focal plane below the tissue surface has no effect on illumination, the percentage of photons collected from different depths, or the distribution of fluorescence at the tissue surface (though, of course, adjusting the focus will change the distribution of photons on the camera chip). The lack of effect of changing the focal plane is consistent with the results of Tian et al., 2011, who found that focal plane depth mattered little when imaging large regions of uniform fluorescence, and also considered the effects of focal plane on the distribution of photons on the camera chip.

Effects of optical parameters on illumination and fluorescence collection.

Normalized illumination intensity (c.f.Figure 1A), percentage of photons collected (c.f. Figure 2B) and diameters that include 50 and 95% of surface fluorescence (c.f. Figure 2C) with the objective focused at depths of 1 and 2 mm below the tissue surface (A), with objectives of numerical aperture 0.1 and 0.5 (B), with objectives of 11 and 4.4 mm field of view (C), and when imaging through no and 300 µm of skull. In each plot, black symbols represent results with an objective with NA 0.1 and 11 mm field of view focused 1 mm below the tissue surface with no overlying skull. For collection efficiency, results from different numerical apertures are displayed on different y-axes to facilitate comparison.

Similarly, one might expect illumination and fluorescence collection to change with the numerical aperture and field of view of the microscope. I compared results with numerical apertures of 0.1 and 0.5. As expected, greater numerical aperture increases collection efficiency substantially, from a maximum collection efficiency of ~0.716% (Figure 3B). However, numerical aperture has negligible effect on illumination, weighting of collection with tissue depth or the surface distribution of fluorescence (Figure 3B). Peak illumination intensity and collection efficiency remains at ~0.3–0.4 mm below the tissue surface, in superficial layers of cortex, across a range of numerical apertures. The lack of effect of NA is consistent with published results (Tian et al., 2011).

Reducing the field of view from 11 to 4.4 mm (corresponding to an increase in objective magnification from x2 to x10; TL2X-SAP and TL10X-2P objectives) has no effect on illumination (Figure 3C) but reduces collection efficiency and the diameter of surface distribution of fluorescence (Figure 3C). These results illustrate one consequence of the large surface distribution of fluorescence: even a microscope objective with a fairly large field of view can cause vignetting.

Finally, I examined the consequences of imaging through 300 µm of skull. Skull weights illumination and fluorescence collection towards deeper layers of cortex (Figure 1D, Figure 3D) and slightly broadens the central peak of the surface fluorescence distribution (Figure 3D).

In summary, optical parameters typically have modest effects on widefield fluorescence. That said, changing to a higher magnification objective will generally result in a greater numerical aperture and a smaller field of view and together these changes can increase collection efficiency and limit the effective point spread function, albeit by vignetting.

Fluorescence from tissue under a blood vessel

The absorption and scattering coefficients used in the model were measured in vivo and therefore account for the effects of endogenous molecules such as hemoglobin, with the absorption coefficient in vivo being ~5 times greater than that measured in vitro, largely because of absorption by hemoglobin (Johansson, 2010). Nonetheless, in the brain there will be local variations in absorption and scattering, such as in the vicinity of blood vessels, resulting in local effects that are not reflected in Figures 13.

To obtain a sense of the likely magnitude and spatial scale of local variations in illumination and fluorescence collection, I simulated the effects of surface blood vessels. Blood vessels with circular cross-sections of radius 100 and 250 µm were simulated as regions in which all photons were absorbed. From the Beer-Lambert law, 500 µm of blood transmits <<1% of incident light but 200 µm of blood transmits ~6% (2.2 × 10−3 mol/L hemoglobin, 50% hemoglobin oxygenation, hemoglobin molar extinction coefficient 27,895 cm−1M−1; Valley et al., 2020). Likely this simple simulation slightly overestimates the effects of vessels, particularly small vessels.

Illumination intensity is reduced immediately below a vessel and throughout the deeper cortical tissue, but even tissue immediately under the vessel received substantial illumination (Figure 4A–C). This result is expected given the random average direction of travel of photons in deep layers (Figure 1C). Similarly, fluorescence collection from under the vessel was reduced but remained substantial. For a large vessel of radius 250 µm, the combined effects on illumination and collection reduce fluorescence to ~5% at 500 µm depth, immediately under the vessel, and to ~45% at 1 mm. Of course, fluorescence is affected less either side of the vessel center line. Clearly even at low numerical apertures (with few oblique angles of illumination at the surface), tissue under vessels can make a substantial contribution to widefield fluorescence.

Illumination and fluorescence collection under blood vessels.

(A and B) Images illustrating illumination intensity around 100 µm and 250 µm radius surface blood vessels. (C and D) Illumination intensity (normalized to the brain surface with no blood vessel) and fluorescence collection as a function of depth below the center of the blood vessel.

Vessel diameter and content are dynamic in vivo. Under 2-photon excitation, dilation of a small vessel can cause a substantial decline in fluorescence from an underlying neuron (≥10% ΔF/F from a neuron under a 50 µm diameter vessel during sensory stimulation; Shen et al., 2012). Likewise, changes of ≥10% ΔF/F occur in widefield fluorescence near large surface vessels and can be largely separated from changes in tissue fluorescence with appropriate measurements and calculations (Valley et al., 2020).

Fluorophore expression and the volume from which fluorescence is collected

There are many mouse lines available with fluorophore in sub-populations of neurons, often cells with somata in only one or two layers of cortex. However, the axons and dendrites of most neurons extend into other layers where they may contribute to widefield fluorescence. From which layers do widefield fluorescence signals originate? What percentage of the fluorescence arises from somatic layers?

I measured expression in six mouse lines with GCaMP in laminar sub-populations of excitatory neurons: Slc17a7-Ai93 (all layers), Cux2-Ai93 (layers 2–4), Rorb-Ai93 (layer 4), Rbp4-Ai93 (layer 5), Fezf2-Ai148 (layers 5 and 6), and Ntrs1-Ai148 (layer 6). Fluorescence images of coronal sections from visual cortex were obtained from the Allen Brain Observatory (Figure 5A). As expected, there was high expression in layers with GCaMP in somata and moderate expression in other layers, presumably from GCaMP in dendrites and axons (Figure 5B).

Laminar fluorescence in GCaMP mouse lines.

(A) Fluorescence images from coronal sections of mouse primary visual cortex in six mouse lines, from the Allen Brain Observatory. (B) Fluorescence in coronal sections in panel A, as a function of depth and normalized to maximum for each mouse. (C) Widefield fluorescence in vivo, the product of expression (panel B), excitation intensity through a cranial window (Figure 1), and percentage of fluorescence photons collected (Figure 2). Widefield fluorescence is expressed by layer, as a percentage of total fluorescence from pia to the base of white matter. Asterisks: layers with most somata. (D) 2-dimensional illustrations of the volume of tissue from which photons propagate to a single location on the brain surface (black circle at 0 depth, 0 lateral distance), arriving within the collection angle of the objective lens. Lines encircle the voxels contributing the most photons, that together contribute 25, 50, 75, 90, and 95% of collected photons. Grey bands indicate the depths of layers 2/3 and 5.

Multiplying expression, illumination intensity and collection efficiency, each as a function of depth, revealed the relative contributions of different layers to widefield fluorescence (Figure 5C). The percentages of fluorescence arising from the somatic layers was high for mice with somatic expression in superficial layers and lower for mice with deep-layer expression (Slc17a7-Ai93 90%, Cux2-Ai93 76%, Rorb-Ai93 26%, Rbp4-Ai93 26%, Fezf2-Ai148 60%, and Ntsr1-Ai148 43%). There are dendrites and axons in all layers so these numbers are an upper bound on the percentage of fluorescence arising from somata.

Despite being the surface layer, layer 1 contributes >10% of fluorescence only in Cux2-Ai93 mice (Slc17a7-Ai93 5.8%, Cux2-Ai93 10.2%, Rorb-Ai93 2.8%, Rbp4-Ai93 5.2%, Fezf2-Ai148 3.4%, Ntsr1-Ai148 0.5%). The modest layer 1contribution is expected given that illumination intensity, collection efficiency, and fluorophore expression are all less in layer 1 than layer 2/3 (Figure 1A, Figure 2B, Figure 5C). For all mouse lines, the largest contribution originates from deeper layers (Slc17a7-Ai93 43% from layer 2/3; Cux2-Ai93 57% from layer 2/3; Rorb-Ai93 34% and 27% from layers 2/3 and 4; Rbp4-Ai93 ~ 30% from each of layers 2/3, 4 and 5; Fezf2-Ai148 48% from layer 5; Ntsr1-Ai148 ~ 40% each from layers 5 and 6). However, these numbers are in apparent conflict with the greater correlation between layer 1 (2-photon) and widefield fluorescence than between layer 2/3 and widefield fluorescence observed by Allen et al., 2017. The numbers cited above report steady-state fluorescence whereas Allen et al., 2017 calculated fractional changes in fluorescence (ΔF/F), common practice in the field. Axons and distal dendrites often display larger fractional changes than somata and proximal dendrites (Helmchen et al., 1996; Brenowitz and Regehr, 2007; Larkum et al., 2007; Xu et al., 2012) and are major contributors to fluorescence signals in layer 1 and in the neuropil in other layers. How much larger would the fractional change in fluorescence in the neuropil or in layer 1 need to be to substantially change the layer 1 contribution?

Neuropil occupies a larger fraction of the volume of layer 1 than of other layers (neuropil/soma ratio is 0.994 in layer 1 and 0.77–0.84 in deeper layers in albino rat; Gabbott and Stewart, 1987) so if the fractional change in fluorescence in the neuropil is increased, layer 1 will contribute a larger percentage of the total change in fluorescence. However, the change is modest. When ΔF/Fneuropil = 10 * ΔF/Fsoma, layer 1 contributes 6.9% of total fluorescence in Slc17a70Ai93 mice, only ~1% more than when ΔF/Fneuropil = ΔF/Fsoma.

The effect of increasing the fractional change in layer 1 is greater. If ΔF/F were 10 times greater in layer 1 than in other layers, layer 1 would account for 39% of total fluorescence in Slc17a7-Ai93 mice. However, a 10x difference seems unlikely. While an action potential can evoke cytosolic calcium transients of ~1 µM in cerebellar granule cells axons (Brenowitz and Regehr, 2007), even bursts of action potentials evoke more modest changes (~250 nM,≤3 times greater than in the soma) in the distal apical dendrites of layer 2/3 and 5 pyramidal neurons (Schiller et al., 1995; Waters et al., 2003). The model predicts that layer 1 contributes a minority of the resting fluorescence and likely also of the fractional change in fluorescence in most mouse lines. There are several possible explanations for the observation of Allen et al., 2017 that the widefield fluorescence correlates more closely with layer 1 than layer 2/3 signals: perhaps expression of GCaMP6f in vGluT1-Cre;Ai93 mice is stronger in layer 1 than in layer 2/3; maybe the olfactory go/no-go decision-making task studied in Allen et al., 2017 drives a very large ΔF/F in axons and dendrites in layer 1; or are deep-layer pyramidal neurons and their distal apical dendrites in layer 1 are more active than layer 2/3 neurons in this behavioral task?

Fluorescence photons propagating to each location on the brain surface originate from a large volume of underlying tissue, a result of scattering of fluorescence photons en route to the brain surface (Figure 5D). In Fezf2-Ai148 and Ntsr1-Ai148 mice, 95% of collected photons arriving at each 10 µm surface pixel are from 1.97 mm3 of underlying tissue, including the full 1 mm depth of cortex and a radius of >1 mm in deep layers. The most compact source volume was 1.08 mm3 in Cux2-Ai93 mice, with photons from all layers and a radius of 830 µm in layer 4. Clearly, nearby surface pixels sample fluorescence from overlapping volumes of tissue. Only pixels >~ 1 mm apart report fluorescence from non-overlapping volumes of tissue. The extremely large volume of contributing tissue is remarkable and underlines the sensitivity of widefield fluorescence imaging to light scattering by brain tissue. The extreme spread of fluorescence from even superficial sources suggests caution when localizing active regions of cortex using widefield fluorescence.

Discussion

The random-walk model provided several quantitative estimates that assist in the interpretation of widefield fluorescence measurements from brain tissue. Firstly, illumination intensity and fluorescence collection do not decay monotonically from the tissue surface when imaging through a cranial window. Each peaks at a depth of ~3–400 um, in layer 2/3 in mouse cortex, and layer 1 contributes <10% of fluorescence in most mouse lines. Interestingly, although the presence of skull overlying cortex has little effect on resolution, expressed as the surface distribution of photons, skull shifts illumination and collection towards a monotonic decay, thereby weighting widefield measurements more towards fluorescence from layer 1. Finally, a volume of ~1–2 mm3 of tissue contributes to fluorescence, resulting in resolution on the millimeter scale. Photons from a point source are commonly spread across >1 mm of the cortical surface and the surface distribution can exceed 2 mm in diameter in mice with deep expression. In mice with layer-enriched indicator expression, the main source of fluorescence is commonly the somatic layer in mice with expression in layer 2/3 neurons and outside the somatic layer in mice with expression mainly in neurons in layers 4–6.

Can widefield fluorescence provide finer spatial precision than ~1 mm? The Monte Carlo simulation indicates that there is no simple way to adapt illumination or collection to provide fine spatial precision. Using a higher magnification objective with a field of view of only several millimeters may reduce the measured surface spread but operates by vignetting the image and may thereby shift the apparent location of active tissue. Illuminating a small region of the brain surface will not restrict the excitation volume, much as a laser spot on the brain surface activates opsins > 1 mm away (Guo et al., 2014). Spatial precision could be obtained by limiting expression of fluorescent indicator to <1 mm of tissue, with virus for example, but would sacrifice the ability to monitor activity across much of cortex, a key application of widefield imaging.

The Monte Carlo model does not explicitly simulate the temporal dynamics of widefield fluorescence, but temporal information can help locate active tissue. The expansion of activity from a small initial region of tissue can be monitored with fast indicators, such as voltage indicators, enabling the center of the initiation site to be located with fine spatial precision (Petersen et al., 2003; Mohajerani et al., 2013). In addition, widefield fluorescence can locate with high spatial precision sites at which waves of activity converge. For example, the border between visual areas can be located to within tens of micrometers with GCaMP6s and a stimulus that drives converging waves of activity either side of the border (Zhuang et al., 2017). In contrast, the model indicates that locating a border from activity on only one side of the border is extremely imprecise, on the order of a millimeter.

In summary, widefield fluorescence at the brain surface is a weighted sum of photons from fluorophores distributed through 1–2 mm3 of underlying cortical tissue. Illumination intensity and collection efficiency peak not at the tissue surface, but in layer 2/3. Most fluorescence arises from the somatic layer in mice with expression in layer 2/3 neurons and from outside the somatic layer in mice with expression mainly in neurons in layers 4–6. The contributing volume extends laterally, by a radius of ~1 mm, several times larger than the width of a cortical column and comparable to the diameters of some cortical areas (~0.5–3 mm in mice). Widefield fluorescence measured at most surface locations is a weighted average across multiple cortical columns and often more than one cortical area.

Materials and methods

Monte carlo model

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Photon trajectories, light intensities and tissue heating were calculated using a Monte Carlo random-walk model implemented in Python. The model was almost identical to that in several previous studies (Wang et al., 1995; Stujenske et al., 2015; Podgorski and Ranganathan, 2016; Wang et al., 2020). Individual photons or packets of photons moved stochastically through the 3-dimensional volume, in which they were subjected to absorption and scattering by the tissue. Scattering angles relative to the optical axis were calculated with the Henyey-Greenstein phase function.

For most simulations, the radius of the volume was 8 mm and the tissue depth 4 mm. The cranial window was modelled as a 7.5 mm glass coverslip, surrounded by skull. Intact skull was modeled as a 150 µm-thick layer of bone. The tissue surface was planar and in contact with the glass coverslip and skull. Each voxel of the model was 10 × 10 × 10 µm.

Absorption and scattering coefficients and anisotropy parameters were from the literature. Absorption and scattering coefficients used here were measured from human grey matter in vivo and the absorption coefficient is ~5 times greater than that measured in vitro, likely because of absorption by blood (Johansson, 2010). Values for grey matter were from Johansson, 2010, for skull from Firbank et al., 1993 and Ugryumova et al., 2004. For 480 nm illumination, absorption and scattering coefficients and anisotropy were: grey matter 0.37 mm−1, 11 mm−1 and 0.89; skull 0.12 mm−1, 35 mm−1 and 0.9. For 560 nm fluorescence photons in grey matter, absorption coefficient 0.26 mm−1, scattering coefficient 10 mm−1, and anisotropy 0.89. A recent study concluded that the scattering was greater in mouse cortical slices, with scattering coefficient 21.1 mm−1 at 473 nm (Yona et al., 2016). Using this increased scattering coefficient here resulted in similar results, but with maximum illumination intensity through a cranial window at a more superficial location, 130 µm below the tissue surface.

From a scattering coefficient of 11 mm−1, transport length in mouse cortical grey matter at 480 nm is (1/11) / (1–0.89)=826 µm. Transport length is the distance over which the direction of propagation of photons is randomized as a result of scattering.

Mesoscale widefield imaging is typically performed through a low-magnification, long working distance, dry, low numerical aperture (NA) objective, often a dissecting microscope lens or camera lens. Here I simulated one such objective, TL2X-SAP from Thorlabs, for which optical parameters are readily available: magnification 2, numerical aperture 0.1, working distance 56.3 mm, effective focal length 100 mm, field number 22. The optical axis of the objective was perpendicular to the tissue surface. Photons exiting the objective and arriving at the tissue surface were tilted at a maximum angle of 5.74° (NA = n sinθ, n = 1) to the optical axis.

Simulations were also performed with the numerical aperture and field of view of a higher magnification objective from the same series, TL10X-2P. For TL10X-2P, magnification 10, numerical aperture 0.5, working distance 7.7 mm, effective focal length 20 mm, field number 22.

Collection was simulated for photons from sources near the center of the field of view. Towards the periphery of the field of view, photons at the steepest collection angles can pass outside the radius of the front window of the objective, reducing collection efficiency. The decline in collection for off-center photons will depend on the objective. The Thorlabs x2 objective has a 7 mm radius front window and 56.3 mm working distance so collection efficiency will be reduced for sources 56.3 * tan(5.7°) = ~1.5 mm from the center of the field of view. Dissecting microscope and camera lenses, both often used in widefield microscopes, typically have larger front windows, some tens of millimeters in radius. Such super-large diameter objectives can offer more consistent collection over fields of view in excess of several millimeters.

Monte Carlo code, including figures, is available at https://doi.org/10.6084/m9.figshare.12317414.v1.

Measured surface distributions

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0.1 µm diameter fluorescent polystyrene beads (Molecular probes) were injected into the cortex of an anesthetized adult mouse (2% isoflurane) with a cranial window sealed with a 5 mm diameter coverglass. Injection was performed through a glass patch pipette with the tip bumped to prevent blockage, inserted into the brain under 2-photon visual guidance through a ~ 0.5–1 mm hole drilled in the coverglass. Beads were injected with positive pressure. 2-photon and widefield images were acquired through a Nikon x16/NA0.8 objective. The depth of the center of the injection was determined from a 2-photon z-stack and the corresponding expected distribution calculated using the model, assuming a point source at the appropriate depth and a TL10X-2P objective.

Animal experiments were performed in accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health. All animals were handled according to Allen Institute for Brain Science institutional animal care and use committee protocol 1806.

Expression patterns

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GCaMP6f expression was measured in six mouse lines: Slc17a7-IRES-Cre;Camk2a-tTA;Ai93(TITL-GCaMP6f), Cux2-CreERT2;Camk2a-tTA;Ai93(TITL-GCaMP6f), Rorb-IRES2-Cre;Camk2a-tTA;Ai93(TITL-GCaMP6f), Rbp4-Cre_KL100;Camk2a-tTA;Ai93(TITL-GCaMP6f), Fezf2-CreER2;Ai148(TIT2L-GC6f-ICL-tTA2), and Ntrs1-Cre_GN220; Ai148(TIT2L-GC6f-ICL-tTA2). Abbreviated names: Slc17a7-Ai93, Cux2-Ai93, Rorb-Ai93, Rbp4-Ai93, Fezf2-Ai148, and Ntrs1-Ai148.

Fluorescence in 2-photon images of fixed, coronal sections was used to estimate GCaMP expression. Images were obtained from the Allen Institute (http://observatory.brain-map.org/visualcoding/transgenic). For each mouse, an image was selected of primary visual cortex between the AM/PM and LM/AL borders, at ~2.7 mm posterior from bregma. Images were aligned manually and rotated to place the brain surface parallel to one edge of the image. To correct inter-mouse variability, images were scaled such that the brain surface and layer 6-white matter border were at 0 and 1 mm depth. To estimate expression, fluorescence was summed over a 0.75 mm-wide strip of cortex, perpendicular to the brain surface.

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    Supralinear Ca2+ influx into dendritic tufts of layer 2/3 neocortical pyramidal neurons in vitro and in vivo
    1. J Waters
    2. M Larkum
    3. B Sakmann
    4. F Helmchen
    (2003)
    The Journal of Neuroscience 23:8558–8567.
  39. 39
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Decision letter

  1. Ryohei Yasuda
    Reviewing Editor; Max Planck Florida Institute for Neuroscience, United States
  2. John R Huguenard
    Senior Editor; Stanford University School of Medicine, United States

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

This manuscript characterizes the source of fluorescence observed in typical widefield imaging experiments using a Monte Carlo simulation. The simulation includes the propagation of photons in the brain. The model was further validated experimentally by beads injected into the mouse brain and transgenic mice expressing GCaMP in a different subset of neurons. The main conclusion is that widefield fluorescence at the brain surface is a weighted sum of photons from fluorophores distributed throughout a large area (millimeters) of cortical tissue. This work will be useful for the community when interpreting fluorescence widefield imaging in the brain.

Decision letter after peer review:

Thank you for submitting your article "Sources of widefield fluorescence from the brain" for consideration by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and John Huguenard as the Senior Editor. The reviewers have opted to remain anonymous.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

We would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). Specifically, when editors judge that a submitted work as a whole belongs in eLife but that some conclusions require a modest amount of additional new data, as they do with your paper, we are asking that the manuscript be revised to either limit claims to those supported by data in hand, or to explicitly state that the relevant conclusions require additional supporting data.

Our expectation is that the authors will eventually carry out the additional experiments and report on how they affect the relevant conclusions either in a preprint on bioRxiv or medRxiv, or if appropriate, as a Research Advance in eLife, either of which would be linked to the original paper.

Your manuscript characterizes the source of fluorescence observed in typical widefield imaging experiment uses a Monte Carlo model to simulate the propagation of photons in the brain. These simulations include several lines of transgenic mice, that exhibit different laminar expression patterns. The main conclusions is that widefield fluorescence at the brain surface is a weighted sum of photons from fluorophores distributed throughout a large volume of underlying cortical tissue and only pixels more than 1 mm apart report fluorescence from non-overlapping volumes of tissue.

While reviewers agree that the manuscript includes important information about widefield imaging for the neuroscience community, they also find several concerns that can be addressed by additional analyses (see below). In particular, there was a significant concern about the lack of experimental validation of the simulation. We suggest that you find imaging data of point sources or sparse neurons in the cortex in literature and use them for validation of the simulation results. In case such data is not available, please revise the title and the last sentence of Abstract to include "by Monte Carlo simulation", and clarify the limitations of the current simulation and how this work fits within the field.

Reviewer #1:

Widefield fluorescence microscopy is increasingly used in neuroscience research to monitor the activity of large populations of neurons across the brain, but the spatial extent of signals detected by this technique is not well understood. This manuscript simulated light propagation through brain using a Monto Carlo model of photon interaction with tissue, which is similar to previous published models and incorporated several key parameters from the literature. Conducting this simulation under the constrain of the typical imaging conditions of widefield fluorescence microscopy, the author calculated how illumination intensity and collection efficiency will change as a function of depth. Furthermore, the author multiplied these model-derived coefficients with GCaMP expression levels in several layer-selective mouse lines evaluated from coronal tissue sections by Allen Brain Observatory, and obtained quantitative estimations of the spatial extent of signals that would contribute to widefield imaging in these lines. The main conclusions appear to be that "widefield fluorescence at the brain surface is a weighted sum of photons from fluorophores distributed throughout a large volume of underlying cortical tissue" and "only pixels more than 1 mm apart report fluorescence from non-overlapping volumes of tissue".

In general, the imaging field will welcome a quantitative estimation of the spatial extent of collected signals using simulation models as described in this manuscript. Such quantitative information will help interpret the experimental data collected by wide-field microscopy in related mouse lines, particularly regarding the spatial organization and regional boundary of cortical activity patterns. The modeling and estimation steps in this manuscript are well laid out and justified. The simulation outcomes, some are not obvious, are also explained with an in-depth consideration of imaging conditions and biological factors. There are a couple of remaining concerns about the significance and strength of the author's conclusions.

First, the general qualitative conclusions of the paper, such as "widefield fluorescence at the brain surface is a weighted sum of photons from fluorophores distributed throughout a large volume of underlying cortical tissue", and "Most fluorescence arises from the somatic layer in mice with expression in layer 2/3 neurons and from outside the somatic layer in mice with expression mainly in neurons in layers 4-6", are mostly in line with the general understanding and expectation in the field. The impact statement of the author, "Deep layer cortical neurons are often a major source of fluorescence in widefield imaging experiments from transgenic mouse lines", also doesn't appear to add much new insight. I'm wondering whether some of the less obvious simulation results, such as the non-monotonic changes of illumination intensity (Figure 1) and collection efficiency (Figure 2), will add some new predictions for wide-field microscopy.

Second, the quantitative estimates, such as the 1 mm lateral extent of signal spread, are purely based on simulation. As this is an important parameter relatable to the scale of cortical columns and area size, it would be ideal to obtain some experimental validation. For example, maybe one can take advantage of potentially existing wide-field imaging data where a small amount of virus is used to express GCaMP in a local volume, which is an experimental design touched upon by the author in the Discussion.

Reviewer #2:

The author evaluates using Monte Carlo simulation of the excitation and emission of photons from functional imaging indicators, such as GCAMP. There is also data from leading mouse lines but the use of mostly to model different GCAMP distributions (based on actually expression) rather than an experimental confirmation. The author primarily concerns himself with the occurrence of wide-field single photon fluorescence events. While there has been some theoretical work on scattering in the past, this manuscript combines simulation results with density measurements using mouse lines that target expression to various layers. The work helps to address long-standing questions in the field concerning the relative laminar contribution and resolution of wide field functional imaging experiments.

While the paper is notable for addressing an important question, it makes heavy use of Monte Carlo simulation. Such results lack important ground truth conclusions. Nonetheless, the theoretical treatment of scattered photons combined with some experimental data on expression is a significant contribution. The paper is also relatively easy to read.

Overall the paper does place important limits on the resolution of wide field microscopy, while the effective PSF is large for fluorescence originating at deep sites, the author does articulate that the center of activation and borders (when comprised of travelling activation fronts) can contain much higher resolution information.

The Abstract and title do not really conclude much, they could be more definitive about actual findings

Introduction.

In the first paragraph, the author should say fluorescent photons propagate from the source randomly, not necessarily towards the brain surface.

Figure 1. The figure could use better labelling, so that one does not have to actively consult the Legend.

Figure 1D for the access labelled intensity is assumed that this is a linear scale, but this should be indicated more directly.

Figure 2 indicates the fate of wide-field fluorescence at sources of different depths. Surprisingly, the percentage of collected photon is relatively similar between 0 and 1mm depth. What changes is the radius of emitted fluorescence at the surface. This to me is clearly demonstrated by the Monte Carlo simulation, but it may be appropriate to backup these measurements with some empirical findings. One could imagine embedding beads or other fluorescent objects at different depths in brain tissue (or best a live mouse) and examining collected fluorescence (a fluorescent pipette?).

Figure 3 Using data from various Allen Institute mouse lines, Waters, again, simulated photon collection at the surface for different scenarios. In all lines, even with relatively restricted expression, the contribution of photons at the surface was from a very wide area. These detected photons in all mouse lines could be from sources as far apart as 1mm. While there was data used from actual mice (distribution), the paper does not contain empirical measurements. Here, again, this is plugging-in density values and making estimates using the Monte Carlo model. I would feel better about these strong conclusions if there could be some actual measurements from discrete fluorescent sources. A couple of data points would go a long way to convincing one that these models take everything into consideration: skull, cover slip, age of tissue and white matter content etc. The author could add some empirical measurements to the current manuscript.

The authors should discuss papers that report differences in wide field maps across cortical lamina and whether these are still expected given their findings (Allen et al., 2017, already cited but for another point).

Perhaps, the author would like to discuss and expand upon a previous empirical study performed by Silasi et al., 2016, Figure 3B, which measured the point-spread function of sub-resolution beads with and without the bone and overlying coverslip/dental cement preparation. Such work does demonstrate that some experimental measurements would be possible albeit looking at fluorescence coming from a single deep tissue source in vivo would be most informative. Silasi et al., 2016, which is already cited but not for the PSF and bone measurement

Reviewer #3:

General assessment: To characterize the source of fluorescence observed in typical widefield imaging experiments, Waters uses a Monte Carlo model to simulate the propagation of photons in the brain. These simulations include several lines of transgenic mice, that exhibit different laminar expression patterns. One limitation of the current study is that it provides little background to contextualize it within the broader literature on widefield imaging. In addition, there is limited detail about how the model's simplifying assumptions might influence the predicted spatial distribution of the fluorescence signal. Changes to the text would improve the article, broaden the potential audience and be useful to many readers. With successful modifications, the article could in principle be a candidate for publication in eLife.

1) It would be useful to place the current article in the context of other widefield imaging studies. A reader would want to know the limits of previous studies and the reason the current study needed. If space allows, a brief scholarly survey could be provided. For example, the authors could discuss other models that have been used to evaluate the performance of optical imaging methods (such as NAOMi, described in doi: https://doi.org/10.1101/726174), as well as experiments to characterize the source of fluorescence in single photon calcium imaging experiments. For example, Allen et al., 2017 (cited in the current article), performed a comparative 1P and 2P volumetric imaging from the same region which enabled them to determine the relative contributions of layer 1 vs. 2/3 in widefield imaging.

2) It would be worth mentioning how the predictions of the model might be experimentally tested.

3) In the Materials and methods section, the author mentions that their simulations do not take into account the effect of cerebral vasculature. It would be useful to move this topic to a more prominent location in the text and to discuss the potential consequences of this simplifying assumption.

4) The author mentions that the model does not take into account the observation that fractional changes in calcium fluorescence in neuropil are often larger than in the soma. It would be useful to discuss this topic in more detail. How might this omission effect their interpretation of sources of fluorescence changes in widefield imaging experiments? Is it possible to estimate the magnitude of this effect or to include this feature in the current or future simulations? Could layer 1, which is primarily axons and dendrites, potentially contribute a great degree to fluorescence changes in 1P imaging than layer 2/3?

https://doi.org/10.7554/eLife.59841.sa1

Author response

While reviewers agree that the manuscript includes important information about widefield imaging for the neuroscience community, they also find several concerns that can be addressed by additional analyses (see below). In particular, there was a significant concern about the lack of experimental validation of the simulation. We suggest that you find imaging data of point sources or sparse neurons in the cortex in literature and use them for validation of the simulation results. In case such data is not available, please revise the title and the last sentence of Abstract to include "by Monte Carlo simulation", and clarify the limitations of the current simulation and how this work fits within the field.

I added a data set to test the accuracy of the model, injecting beads into cortex in 3 mice, measuring the distribution and depth of each injection with 2-photon microscopy, and comparing the widefield fluorescence surface distribution with the distribution predicted by the model. The experiment is beset with practical difficulties (for example, the bolus is rarely spherical and there are usually a few beads in the injection tract) and the model isn’t a perfect match (I assumed a point source and similar but not identical objective) so I think it’s a fairly course comparison. Nevertheless, the model accurately predicted the shape and width of the central peak of the surface distribution. The tails of the distribution were not accurately predicted by the model, with the model predicting a larger spread, but the tails contain only ~25% of the photons. I believe the results indicate that the model is sufficiently accurate to support the conclusions of the paper. The comparison is presented in Figure 2.

Reviewer #1:

[…] First, the general qualitative conclusions of the paper, such as "widefield fluorescence at the brain surface is a weighted sum of photons from fluorophores distributed throughout a large volume of underlying cortical tissue", and "Most fluorescence arises from the somatic layer in mice with expression in layer 2/3 neurons and from outside the somatic layer in mice with expression mainly in neurons in layers 4-6", are mostly in line with the general understanding and expectation in the field. The impact statement of the author, "Deep layer cortical neurons are often a major source of fluorescence in widefield imaging experiments from transgenic mouse lines", also doesn't appear to add much new insight. I'm wondering whether some of the less obvious simulation results, such as the non-monotonic changes of illumination intensity (Figure 1) and collection efficiency (Figure 2), will add some new predictions for wide-field microscopy.

I have rewritten the impact statement and Abstract to emphasize new insights.

Second, the quantitative estimates, such as the 1 mm lateral extent of signal spread, are purely based on simulation. As this is an important parameter relatable to the scale of cortical columns and area size, it would be ideal to obtain some experimental validation. For example, maybe one can take advantage of potentially existing wide-field imaging data where a small amount of virus is used to express GCaMP in a local volume, which is an experimental design touched upon by the author in the Discussion.

I’ve obtained validation results from 3 mice, discussed above and added to Figure 2. The new results support the prediction, made by the model, that signal spreads over 1 mm or more laterally.

Reviewer #2:

[…] The Abstract and title do not really conclude much, they could be more definitive about actual findings

I’ve rewritten the Abstract to summarize more results.

Introduction.

In the first paragraph, the author should say fluorescent photons propagate from the source randomly, not necessarily towards the brain surface.

I’ve rewritten this statement.

Figure 1. The figure could use better labelling, so that one does not have to actively consult the Legend.

I’ve added panel titles and labels.

Figure 1D for the access labelled intensity is assumed that this is a linear scale, but this should be indicated more directly.

I’ve added ‘linear scale’ to the axis title.

Figure 2 indicates the fate of wide-field fluorescence at sources of different depths. Surprisingly, the percentage of collected photon is relatively similar between 0 and 1mm depth. What changes is the radius of emitted fluorescence at the surface. This to me is clearly demonstrated by the Monte Carlo simulation, but it may be appropriate to backup these measurements with some empirical findings. One could imagine embedding beads or other fluorescent objects at different depths in brain tissue (or best a live mouse) and examining collected fluorescence (a fluorescent pipette?).

I followed the reviewer’s suggestion, embedding beads in a live mouse. During experiments, I was unable to visualize the pipette tip deeper than ~400 μm and was therefore restricted to measurements from superficial tissue. The results indicate that the model accurately predicts the effects of tissue for superficial fluorescence sources. Though I cannot provide direct experimental support, it is likely that the model is also accurate for deeper sources.

Figure 3 Using data from various Allen Institute mouse lines, Waters, again, simulated photon collection at the surface for different scenarios. In all lines, even with relatively restricted expression, the contribution of photons at the surface was from a very wide area. These detected photons in all mouse lines could be from sources as far apart as 1mm. While there was data used from actual mice (distribution), the paper does not contain empirical measurements. Here, again, this is plugging-in density values and making estimates using the Monte Carlo model. I would feel better about these strong conclusions if there could be some actual measurements from discrete fluorescent sources. A couple of data points would go a long way to convincing one that these models take everything into consideration: skull, cover slip, age of tissue and white matter content etc. The author could add some empirical measurements to the current manuscript.

I added three measurements of surface fluorescence in a live mouse, imaged through a coverslip. As discussed above, the measured and predicted (by the model) distributions were reasonably well matched. These results provide additional confidence that the model takes all the relevant parameters into account, including coverslip, age of tissue, white matter content. I did not attempt to measure the scattering effects of skull, but most of the paper concerns simulations of widefield fluorescence through a cranial window.

The authors should discuss papers that report differences in wide field maps across cortical lamina and whether these are still expected given their findings (Allen et al., 2017, already cited but for another point).

I have added new simulations and associated discussions on laminar differences, including the observations of Allen et al. These topics are addressed in the fourth paragraph of the Results subsection “Fluorophore expression and the volume from which fluorescence is collected”.

Perhaps, the author would like to discuss and expand upon a previous empirical study performed by Silasi et al., 2016, Figure 3B, which measured the point-spread function of sub-resolution beads with and without the bone and overlying coverslip/dental cement preparation. Such work does demonstrate that some experimental measurements would be possible albeit looking at fluorescence coming from a single deep tissue source in vivo would be most informative. Silasi et al., 2016, which is already cited but not for the PSF and bone measurement

I have added new results measuring lateral spread of signal from beads. Unlike Silasi et al., 2016, the new measurements were through a cranial window, not through skull.

Silasi et al., 2016, reported fluorescence 48.6 ± 5.7 µm in diameter with an unknown number and spread of 10 µm beads on the brain surface. Without knowing the spread at the brain surface, it’s impossible to determine the effect of skull on lateral resolution. Furthermore, Silasi et al., 2016, do not indicate whether the diameter measurement was FWHM or some other measure of diameter. In short, it’s hard to interpret the Silasi results, limiting my ability to compare and discuss.

Reviewer #3:

1) It would be useful to place the current article in the context of other widefield imaging studies. A reader would want to know the limits of previous studies and the reason the current study needed. If space allows, a brief scholarly survey could be provided. For example, the authors could discuss other models that have been used to evaluate the performance of optical imaging methods (such as NAOMi, described in doi: https://doi.org/10.1101/726174), as well as experiments to characterize the source of fluorescence in single photon calcium imaging experiments. For example, Allen et al., 2017 (cited in the current article), performed a comparative 1P and 2P volumetric imaging from the same region which enabled them to determine the relative contributions of layer 1 vs. 2/3 in widefield imaging.

I have expanded the Introduction to provide context, including a brief summary of previous modeling studies. I also ran additional simulations to provide insight into the relative contribution of layer 1, discussed further under point 4, below.

2) It would be worth mentioning how the predictions of the model might be experimentally tested.

The revised paper includes a small data set that tests some of the key predictions.

3) In the Materials and methods section, the author mentions that their simulations do not take into account the effect of cerebral vasculature. It would be useful to move this topic to a more prominent location in the text and to discuss the potential consequences of this simplifying assumption.

The literature includes estimates of the effects of vasculature on 2-photon fluorescence from underlying neurons, but no estimates for widefield fluorescence, to my knowledge. For the revised manuscript I implemented a simple model of vasculature, resulting in a new section in the Results (subsection “Fluorescence from tissue under a blood vessel”) and a new figure (Figure 4). That widefield fluorescence can arise from under the vessel is hardly surprising and the results are really only a first guess given the exceedingly simple nature of the vascular model, but the simulation provides quantitative estimates of the effects of surface vasculature on widefield fluorescence and adding results on the effects of vasculature places the topic in a more prominent location.

4) The author mentions that the model does not take into account the observation that fractional changes in calcium fluorescence in neuropil are often larger than in the soma. It would be useful to discuss this topic in more detail. How might this omission effect their interpretation of sources of fluorescence changes in widefield imaging experiments? Is it possible to estimate the magnitude of this effect or to include this feature in the current or future simulations? Could layer 1, which is primarily axons and dendrites, potentially contribute a great degree to fluorescence changes in 1P imaging than layer 2/3?

I have run additional simulations with modified neuropil and layer 1 signals, addressing this topic at some length in the revised Results section (subsection “Fluorophore expression and the volume from which fluorescence is collected”, fourth paragraph).

https://doi.org/10.7554/eLife.59841.sa2

Article and author information

Author details

  1. Jack Waters

    Allen Institute for Brain Science, Seattle, United States
    Contribution
    Conceptualization, Software, Formal analysis, Funding acquisition, Validation, Visualization, Methodology, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    jackw@alleninstitute.org
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-2312-4183

Funding

Allen Institute for Brain Science

  • Jack Waters

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

I thank the Allen Institute founder, Paul G Allen, for his vision, encouragement, and support. I thank Kevin Takasaki, Doug Ollerenshaw, Jun Zhuang and Natalia Mesa for comments on the manuscript, and Soumya Chatterjee, Bryan MacLennan and Natalia Mesa for assistance with imaging experiments.

Senior Editor

  1. John R Huguenard, Stanford University School of Medicine, United States

Reviewing Editor

  1. Ryohei Yasuda, Max Planck Florida Institute for Neuroscience, United States

Publication history

  1. Received: June 9, 2020
  2. Accepted: October 22, 2020
  3. Version of Record published: November 6, 2020 (version 1)

Copyright

© 2020, Waters

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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