Abstract
Experiencedependent modifications of synaptic connections are thought to change patterns of network activities and stimulus tuning with learning. However, only a few studies explored how synaptic plasticity shapes the response dynamics of cortical circuits. Here, we investigated the mechanism underlying sharpening of both stimulus selectivity and response dynamics with familiarity observed in monkey inferotemporal cortex. Broadening the distribution of activities and stronger oscillations in the response dynamics after learning provide evidence for synaptic plasticity in recurrent connections modifying the strength of positive feedback. Its interplay with slow negative feedback via firing rate adaptation is critical in sharpening response dynamics. Analysis of changes in temporal patterns also enables us to disentangle recurrent and feedforward synaptic plasticity and provides a measure for the strengths of recurrent synaptic plasticity. Overall, this work highlights the importance of analyzing changes in dynamics as well as network patterns to further reveal the mechanisms of visual learning.
https://doi.org/10.7554/eLife.44098.001Introduction
Experiencedependent changes in neural responses have been suggested to underlie the more efficient and rapid processing of stimuli with learning. Human and monkeys have been reported to process familiar stimuli with shorter response times and with less effort (Greene and Rayner, 2001; Logothetis et al., 1995; Mruczek and Sheinberg, 2007). The possible neural correlate for such behavior enhancement is the sharpening of stimulus selectivity that is achieved by broadening the distribution of activities as the stimulus becomes familiar (Freedman et al., 2006; Kobatake et al., 1998; Lim et al., 2015; McKee et al., 2013; Woloszyn and Sheinberg, 2012). Also, temporal sharpening of neural responses with experience has been observed, which can increase the resolution of discriminating stimuli in time with learning (Meyer et al., 2014; Recanzone et al., 1992).
Modifications of synaptic connections have been thought to be one of the basic mechanisms for learning. A repeated encounter of a stimulus would elicit a particular activity pattern in the network, which in turn modifies synaptic connections depending on pre and postsynaptic activities. Such modifications of synaptic connections lead to changes in neural responses that can be a substrate to differentiate learned and unlearned stimuli. The previous modeling works investigated the relationship between synaptic plasticity and changes in network activity to find a synaptic plasticity rule that can account for sharpening of stimulus selectivity observed with learning (Dayan and Abbott, 2005; Gerstner and Kistler, 2002). However, whether such rules can also explain temporal changes in neural responses is in question.
In this work, we investigate the mechanism underlying changes of response dynamics with learning. To this end, we consider neural activities recorded in inferior temporal cortex (ITC) known to be important for visual object recognition (Miyashita, 1993; Tanaka, 1996). In ITC, changes in the response properties with learning have been reported in several experiments (Freedman et al., 2006; Li et al., 1993; Lim et al., 2015; Logothetis et al., 1995; McKee et al., 2013; Woloszyn and Sheinberg, 2012; Xiang and Brown, 1998). The average over different visual stimuli of timeaveraged responses decreases with familiarity, while the distribution of responses across visual stimuli broadens with learning. The dynamics of visual responses were also found to change with familiarity – in particular, rapid successive presentation of familiar images, but not novel images, elicits strong periodic responses (Meyer et al., 2014).
Previously, we investigated synaptic plasticity in recurrently connected circuits that reproduces changes in the distribution of timeaveraged visual responses observed experimentally (Lim et al., 2015). As the distribution of timeaveraged visual responses of a single cell to multiple stimuli can be a surrogate for a spatial pattern of the network to one stimulus in a homogeneous network, the previous work mainly focused on how recurrent synaptic plasticity shapes the network pattern and stimulus tuning. Here, we extend our previous framework to understand mechanisms underlying changes of temporal patterns with learning. First, we demonstrate that the synaptic plasticity rule inferred from the timeaveraged responses is not sufficient to reproduce changes in response dynamics. Next, we show that the interaction between synaptic plasticity and negative feedback mechanisms is critical for generating stronger oscillation after learning. Using a meanfield analysis, we identify the conditions on synaptic plasticity and negative feedback to reproduce changes in response dynamics consistently observed in different experimental settings. Finally, we validate these conditions through network simulations and infer the postsynaptic dependence of synaptic plasticity from the experimental data.
Results
Effects of visual learning on response dynamics
In this section, we summarize the effects of visual experience on response dynamics obtained from three different laboratories comparing the visual response to novel (unlearned) and familiar (learned) stimuli in the monkey ITC (Lim et al., 2015; McKee et al., 2013; Meyer et al., 2014; Woloszyn and Sheinberg, 2012). Two experiments measured visual responses to the presentation of one stimulus, one in a passive viewing task (Lim et al., 2015; Woloszyn and Sheinberg, 2012) and the other in a dimmingdetection task (Freedman et al., 2006; Lim et al., 2015; McKee et al., 2013). The duration of the stimulus presentation and number of stimuli were different in the two tasks: shorter duration of stimulus presentation and a larger set of stimuli in the passive viewing task in comparison to the dimmingdetection task (Materials and methods). In both cases, the average response to familiar stimuli was lower than that to novel stimuli with a rapid decrease of the response around 150 ms after the stimulus onset in putative excitatory neurons (Figure 1A; Figure 5A,B for the dimmingdetection task). On the other hand, the response to the most preferred stimulus was found to increase for familiar stimuli with broadening of the distribution of timeaveraged activities (Figure 1B,C).

Figure 1—source code 1
 https://doi.org/10.7554/eLife.44098.019
In both the mean and maximal responses to familiar stimuli, a rebound of activity was observed around 230 ms after the stimulus onset (Figure 1A,B). This is distinctive from responses to novel stimuli showing slow decay after the transient rise. We further quantified the magnitude of the rebound before and after learning by measuring the slope of changes in the activities at each rank of stimuli (Figure 1D). It showed that the higherrank familiar stimuli exhibit the stronger rebound in putative excitatory neurons. In contrast, there is only a weak dependence between the rank of stimuli and the magnitude of rebound activity in inhibitory neurons (Figure 1—figure supplement 1).
The emergence of oscillatory responses after learning was also observed in different experimental settings. In the dimming detection task with longer stimulus presentation, the average response showed damped oscillation for familiar stimuli (Figure 5B; Freedman et al., 2006; McKee et al., 2013). In another experiment where either two novel stimuli or two familiar stimuli were presented rapidly in sequence, the peak response for the second familiar stimulus is as strong as the one for the first stimulus, while the response to the novel stimulus is suppressed at the second peak (Meyer et al., 2014). Thus, rapid successive presentation of familiar images, but not novel images, elicits strong periodic responses. Note that although all three experiments suggest stronger oscillation after learning, its strength may vary depending on a sampling of neurons and stimuli as only excitatory neurons with their most preferred stimuli exhibit strong oscillation after learning (Figure 1D).
In sum, the prominent effects of visual learning on responses of excitatory neurons are (i) reduction in average response, (ii) increase in maximum response, and (iii) stronger oscillations after learning. In the following, we show how such changes guide us to reveal a mechanism underlying visual learning that sharpens stimulus selectivity and temporal resolution of stimuli. Note that we focus on excitatory neurons only assuming that the dynamics of inhibitory neurons follow that of mean excitatory neurons, and do not contribute qualitative changes of response dynamics after learning. Such a simplification is based on the experimental observation that input changes and the magnitude of rebound activity depend weakly on the postsynaptic firing rates in inhibitory neurons (See Discussion for further justification).
Recurrent synaptic plasticity alone cannot reproduce the response dynamics
Activitydependent modifications of synaptic connections can be one of the key elements to explain changes in network patterns and response dynamics with learning. Previously, we introduced a procedure to infer synaptic plasticity rules from experimental data so that networks implementing the derived learning rules can quantitatively reproduce changes in the distribution of timeaveraged visual responses observed experimentally (Lim et al., 2015). We now extend this framework and explore whether synaptic plasticity alone would be sufficient to explain stronger oscillatory responses after learning.
To investigate the effect of learning on response dynamics, we considered a firing rate model with a plasticity rule that modifies the strength of recurrent synapses as a function of the firing rates of pre and postsynaptic neurons. Activities of neurons are described by their firing rates r_{i} for i = 1,…, N, where N denotes the number of neurons in the network. Their dynamics are described by the following equations
where Φ is a static transfer function (fI curve), and the total input current is the sum of the recurrent input $\sum {W}_{ij}^{R}{r}_{j}$ and the feedforward input $\sum {W}_{ij}^{F}{I}_{j}^{X}$. $W}_{ij}^{k$ denotes the strength of synaptic connection from neuron j to neuron i with k = R or F representing recurrent and feedforward connections, respectively. The superscript X denotes an external input, and $I}_{i}^{X$ is the external input to neuron i before learning with $W}_{ij}^{F}={\delta}_{ij$.
We assumed that the recurrent synapses are plastic, changing their strengths according to $W}_{ij}^{R}\to {W}_{ij}^{R}+\mathrm{\Delta}{W}_{ij}^{R$, which depends on the activities of both pre and postsynaptic neurons during the stimulus presentation. We further assumed that the learning rule is a separable function of pre and postsynaptic activity as
where f and g are post and presynaptic dependence of the learning rules, respectively, and ξ_{i} is the activity of neuron i averaged during the stimulus presentation before learning.
Previously, we found that synaptic plasticity in recurrent excitatory connections is sufficient to reproduce changes in the distribution of timeaveraged visual responses observed experimentally (Lim et al., 2015). Hebbiantype synaptic plasticity with a potentiation in high firing rates leads to an increase of the maximal response of excitatory neurons, while overall depression leads to a decrease of the average network response of both excitatory and inhibitory neurons (Figure 2A). With such synaptic plasticity derived from the timeaveraged activities, response dynamics in Equation (1) shows similar changes to the timeaveraged responses (Figure 2B,C). However, the temporal profile is similar before and after learning and does not show oscillations after learning. Thus, synaptic plasticity alone is not sufficient for reproducing changes in response dynamics observed experimentally, which will be shown analytically in the next section.
Interactions between recurrent synaptic plasticity and slow negative feedback
Another key ingredient to explain changes in response dynamics with learning can be slow negative feedback. In a dynamical system, resonancelike behavior emerges from the interaction between strong positive feedback and relatively slow negative feedback. Thus, enhanced resonance behavior after learning observed experimentally may suggest that changes in synaptic connections strengthen positive feedback in the circuit and affect the response dynamics by interacting with a slow negative feedback mechanism. Also, the reduced response to successive stimulus presentation of novel stimuli (Meyer et al., 2014) can be caused by the slow recovery from negative feedback.
For generating a damped oscillatory response after learning, we found that specific negative feedback such as firing rate adaptation is required (Figure 3). Similar to previous works investigating the effect of adaptation on the network activity in a meanfield approach (Fuhrmann et al., 2002; Laing and Chow, 2002; Tabak et al., 2006; Treves, 1993; van Vreeswijk and Hansel, 2001), we considered a linear mechanism for adaptation where the adaptation current is a lowpass filtered firing rate represented by the variable a_{i} with time constant τ_{a} and strength k. Then the dynamics of network activity is described by the following equations:
Intuitively, interactions between recurrent synaptic plasticity and adaptationlike negative feedback in Equations (2) and (3) can reproduce two effects of visual learning, increase in maximal response and stronger oscillatory response after learning. Hebbiantype synaptic plasticity in recurrent connections provides strong potentiation in the connections among high firing rate neurons, and thus, generates a cell assembly with stronger positive feedback after learning (Figure 3A). This leads to not only an increase in the response of this cell assembly but also the emergence of oscillation under the interplay with slow adaptation currents. The strength of oscillation in the rest of the population may depend on the synaptic strengths from these high firing rate neurons.
To show this analytically, we investigated meanfield dynamics that summarize network activity with fewer variables (Materials and methods). To facilitate the analysis, we made two assumptions, linear dynamics with transfer function Φ(x) = x, and homogeneous connectivity before learning that reflects no correlation between novel stimuli and network structure. Under these assumptions, the dynamics before learning is described by average activity and adaptation, $\overline{r}=\frac{1}{N}{\displaystyle \sum _{i}{r}_{i}}$ and $\overline{a}=\frac{1}{N}{\displaystyle \sum _{i}{a}_{i}}$. After learning, with synaptic plasticity in recurrent connections following Equation (2), recurrent connections become correlated with activity pattern they learned. Increased correlation between the learned pattern and network structure can be captured by additional variables m and n, defined as $m=\frac{1}{N}{\displaystyle \sum _{i}{g}_{R}\left({\xi}_{i}\right){r}_{i}}$ and $n=\frac{1}{N}{\displaystyle \sum _{i}{g}_{R}\left({\xi}_{i}\right){a}_{i}}$, which is a variation of the pattern overlap $\frac{1}{N}{\displaystyle \sum _{i}{\xi}_{i}{r}_{i}}$ utilized previously to describe changes in dynamics with learning (Tsodyks and Feigel'man, 1988).
The variables m and n can approximately represent the activities and adaptation of high firing rate neurons as the activities and adaptation of high firing rate neurons contribute more to m and n variables with monotonically increasing presynaptic dependence ${g}_{R}\left({\xi}_{i}\right)$ (Figure 3A). Thus, potentiation of recurrent inputs in high firing rate neurons provides strong positive feedback in m, while slow adaptation mechanisms represented by n variables provide negative feedback. As the variables m and n are only present in the dynamics after learning, qualitative changes of the response dynamics in the network should be mainly led by their dynamics with strong potentiation in high rate neurons (Figure 3B). Such strong potentiation and generation of damped oscillation in high rate neurons are consistent with the observation that the rebound is strongest in those neurons (Figure 1D).
The recurrent input from high rate neurons can lead to a damped oscillatory response in the rest of the population (Figure 3A). The meanfield analysis shows that the strength of the damped oscillatory response is proportional to the strength of postsynaptic synaptic plasticity ${f}_{R}\left({\xi}_{i}\right)$ in the case of linear dynamics. If f_{R} for neuron i is positive (negative) corresponding to potentiation (depression) in recurrent inputs, an oscillation in neuron i would be in phase (out of phase) with that of high rate neurons. Previously, we proposed Hebbiantype but overall depressiondominant synaptic plasticity in recurrent connections to minimally account for the decrease in timeaveraged responses (Lim et al., 2015). However, this would lead to out of phase oscillation in the mean and maximum response, inconsistent with the data (Figure 1A,B). Instead, overall potentiation in recurrent inputs with ${\overline{f}}_{R}$ >0 is required to generate inphase oscillation in the mean and maximum response in linear dynamics (Figure 3—figure supplement 1).
Additional synaptic plasticity for reduction in average response
We showed that recurrent synaptic plasticity could account for the emergence of damped oscillation and sharpening neural activities by increasing the maximal response after learning. Furthermore, synchronous oscillations in the mean and maximum response observed experimentally suggest overall potentiation in recurrent inputs. However, potentiationdominant synaptic plasticity in recurrent connections would increase overall synaptic input and cannot reproduce a decrease in average activities with learning (Figure 3—figure supplement 1A,B). The same holds for recurrent synaptic plasticity with or without the assumption of the constant sum normalization which imposes a constraint on the presynaptic dependence (Figure 3—figure supplement 2).
Instead, reduction in average response requires changes in external inputs or other recurrent inputs such as suppression in other excitatory inputs or enhanced inhibition. Enhanced recurrent inhibition can result from an increase in inhibitory activities after learning or potentiated inhibitory connections onto excitatory neurons. The former is inconsistent with the experimental observations showing a reduction in inhibitory firing rates across different stimuli (Figure 1—figure supplement 1). Also, potentiated inhibition with learning is less likely to account for a decrease of average excitatory activities  a temporal profile of inhibitory activities after learning shows a decrease of activity almost to the baseline in the late phase of the stimulus presentation (200–250 ms after the stimulus onset). This suggests that the effect of potentiated inhibition in the late phase is weaker than in the early phase while reduction of excitatory activities was observed in the late phase (Figure 1A,B).
Another possibility is a depression in recurrent excitation through different types of synapses such as potentiation in fast AMPAlike currents and depression in slow NMDAlike currents. Depression in slow excitatory currents can lead to a decrease in excitatory activities in the late phase. However, different regulation of AMPA and NMDA currents is inconsistent with the experimental observations showing maintenance of a constant NMDAtoAMPA ratio under the changes of AMPA receptors induced chemically or by an STDP protocol (Watt et al., 2000; Watt et al., 2004).
Instead of additional changes of the recurrent synaptic inputs, we considered changes in external inputs with feedforward synaptic plasticity $\Delta {W}_{ij}^{F}={f}_{F}\left({\xi}_{i}\right){g}_{F}\left({\xi}_{j}\right)$. Together with overall potentiation in the recurrent connections, dominant depression in the feedforward connections with ${\overline{f}}_{F}$< 0 can reproduce the reduction of average responses over the stimuli with learning. In Figure 4, an example network with Hebbian learning rule in recurrent connections, uniform depression in the feedforward connection, and spike adaptation mechanisms was shown to reproduce the effects of visual learning qualitatively. With learning, the average response decreases in particular in the late phase (Figure 4A), but maximal firing rates increased and oscillation becomes prominent especially in high rates (Figure 4B,C). Also, in the successive presentation of two stimuli, the average response shows stronger oscillation after learning (Figure 4D), while the rank of individual neuronal activities changes when a new stimulus arrives (Figure 4E,F).

Figure 4—source code 1
 https://doi.org/10.7554/eLife.44098.020
Note that the mean field dynamics was derived under the assumption of linear dynamics. With synaptic or neuronal nonlinearity, some conditions identified through our mean field dynamics can be mitigated such as less dominant potentiation in recurrent inputs with learning (Figure 6—figure supplement 1). However, a network simulation with example nonlinearity still shows that the core principles on the synaptic plasticity rule remain the same as strong potentiation in recurrent connections in high rate neurons, and average depression in feedforward inputs.
Network simulation and comparison with data
In this section, we validate that network models implementing the conditions identified through meanfield equations indeed reproduce the experimental observation and allow us to infer the postsynaptic dependence of synaptic plasticity. To illustrate this, we considered electrophysiological data obtained in a passive viewing task and dimmingdetection task (Lim et al., 2015; McKee et al., 2013; Woloszyn and Sheinberg, 2012). In the dimming detection task, responses to fewer stimuli were measured, and we considered the response averaged over neurons and stimuli, which was fitted using meanfield dynamics (Figure 5). The external inputs and parameters of the $\overline{r}$ and $\overline{a}$ dynamics before learning were chosen to generate no oscillations (Figure 5A; Figure 5—figure supplement 1). Potentiation in high firing rate neurons, average potentiation of recurrent inputs and depression in feedforward inputs were found to mimic response to familiar stimuli (Figure 5B).

Figure 5—source code 1
 https://doi.org/10.7554/eLife.44098.021

Figure 5—source code 2
 https://doi.org/10.7554/eLife.44098.022
This meanfield dynamics reproduces prominent features of response dynamics before and after learning, showing damped oscillation and a decrease in average response to familiar stimuli after its peak (Figure 5C). Furthermore, we simulated the mean response to novel and familiar stimuli for a successive presentation of stimuli (Figure 5D). When novel stimuli are repeatedly shown, the peak response to the second stimuli is smaller than the response to the first, due to a slow recovery from the adaptation current. In contrast, for the serial presentation of familiar stimuli, the response to the first stimulus decays quickly and the response to the second stimulus is less affected by the adaptation current. Thus, the overall response becomes more oscillatory compared to the one for novel stimuli.
In the experimental data obtained during the passive viewing task, the duration of stimulus presentation was shorter, but the distribution of response dynamics before and after learning could be obtained (Figure 1C; Materials and methods). As in the dimming detection task, the external inputs were obtained from the responses to novel stimuli. By comparing the response dynamics at each rank of the novel and familiar stimuli, we derived the postsynaptic dependence of synaptic plasticity in recurrent and feedforward connections. Note that the synaptic plasticity was inferred from normalized firing rates averaged over neurons under the assumption that the dependence of synaptic plasticity rules on normalized firing rates is the same across different neurons (See Discussion for justification).
Consistent with the fitting of the meanfield dynamics to the data obtained in a dimming detection task, the average postsynaptic dependence of synaptic plasticity leads to potentiation in recurrent inputs and depression in feedforward inputs (Figure 6A). Furthermore, the postsynaptic dependence in recurrent connections is an increasing function of the rank of stimuli, or equivalently, the postsynaptic activities. It is notable that such a tendency is similar to the dependence of the rebound magnitude to familiar stimuli on the rank of stimuli observed experimentally (Figure 1D). Network models implementing the derived synaptic plasticity reproduce the reduction of average activities (Figure 6B) and rebound in the late phase of stimulus presentation in both average and maximal responses, although the maximal response after the initial rise is less well fitted (Figure 6C).

Figure 6—source code 1
 https://doi.org/10.7554/eLife.44098.023
We also checked whether the key conditions for synaptic plasticity change with example nonlinear inputoutput transfer function derived from the timeaveraged response to novel stimuli (Figure 6—figure supplement 1A). The derived postsynaptic dependence in both recurrent and feedforward connections is similar to that obtained under linear dynamics with more balance between depression and potentiation in recurrent synaptic plasticity (Figure 6—figure supplement 1B). Although the rebound in the average activities is less well fitted compared to that with linear dynamics, the network simulations agree with the data qualitatively (Figure 6—figure supplement 1C,D).
Alternative negative feedback mechanisms
Our mean field analysis and model fit to the data suggest firing rate adaptation mechanisms as a good candidate for slow negative feedback to explain the familiarity effect on the dynamics. Here, we explored whether two alternative negative feedback mechanisms such as delayed global inhibition or shortterm depression can replace adaptation. Delayed global inhibition may arise due to local inhibition with slow NMDA or GABA_{B}like currents in inhibitory feedback pathways, or inhibitory feedback from other areas. For instance, prefrontal cortex shows a familiarity effect with a long latency around 100 ms but with opposite sign (Rainer and Miller, 2000; Xiang and Brown, 2004), and thus, the topdown signals from this area can serve as slow negative feedback.
We considered a model of global inhibition so that all excitatory neurons receive the same slow inhibition whose strength is proportional to the average activity of excitatory neurons (Materials and methods). Under the assumption of linearity, we could derive the mean field equations similar to that with adaptation mechanisms with variables r, a and m but without variable n that mainly represents the negative feedback in high firing rate neurons (Equation (6)). Without negative feedback, m cannot generate damped oscillations after learning in both high rate neurons and the overall population. This suggests that slow negative feedback private to individual neurons or subpopulations is required to generate qualitative changes in dynamics as interacting with synaptic plasticity.
Shortterm depression in synaptic connections has also been suggested as a mechanism for negative feedback and generating oscillations in cortical circuits (Laing and Chow, 2002; Loebel and Tsodyks, 2002; Tabak et al., 2006; Wang, 2010). To see whether shortterm depression can reproduce the damped oscillatory response after learning, we considered a phenomenological model mimicking the effect of depletion of a neurotransmitter such that when the presynaptic firing is high, the synaptic input from such neuron becomes weak due to the lack of resources (Materials and methods; Tsodyks and Markram, 1997). Under the assumption that the recurrent connection is weak before learning, and the damped oscillation in the network is led by that in the high rate neurons, we searched for a parameter set of the strength and timescale of shortterm plasticity that provides the best fit to the experimental data. However, the network simulation with the bestfitted parameters cannot generate a strong rebound, unlike the adaptation mechanisms (Figure 6—figure supplement 2). Thus, a simple phenomenological model of shortterm plasticity cannot explain the qualitative changes in response dynamics observed experimentally.
Discussion
In this work, we provided a mechanistic understanding of how interactions between synaptic plasticity and a negative feedback mechanism implementing firing rate adaptation shape response dynamics with learning. The emergence of damped oscillations after learning requires strong positive feedback through potentiation in recurrent connections particularly among neurons with high firing rates. Such recurrent synaptic plasticity broadens the distribution of activities, while depression in feedforward inputs decreases average firing rates. Synaptic plasticity, therefore, enables the sparse and efficient representation of the learned stimuli. Furthermore, the strength of rebound of damped oscillation observed after learning can be a novel, graded measure for recurrent synaptic plasticity. On the other hand, adaptationlike mechanisms are critical for enhanced oscillatory responses after learning, and strongly suppresses the neural activities for the learned stimuli in particular in the late phase of the stimulus presentation. As such temporal sharpening prepares neurons to respond to the subsequent stimulus, our work suggests that the adaptation mechanisms together with synaptic plasticity may play an important role in the rapid processing of the learned stimuli.
Here, we extended our previous work inferring recurrent synaptic plasticity rules from timeaveraged data in a static model of a cortical network to timecourse data and a dynamic model with additional spike adaptation mechanisms and feedforward synaptic plasticity (Lim et al., 2015). Analyzing timecourse data allows disentangling contributions of synaptic plasticity in different connections. However, similar to the previous work, only postsynaptic dependence of the synaptic plasticity rules can be inferred from single cell recordings under the assumption that the learning rules are a separable function of pre and postsynaptic rates. Also, fitting the time course poses a limitation such that synaptic plasticity rules needed to be inferred from the data averaged over neurons due to noise. On the other hand, timeaveraged data allows to infer recurrent synaptic plasticity in different neurons, which reveals a strong correlation between neural activity and the threshold separating depression and potentiation, but no correlation when the postsynaptic activity is normalized (Lim et al., 2015). Inspired by this observation, we inferred synaptic plasticity rules from normalized firing rates under the assumption that synaptic plasticity rules are the same across different neurons when inputs and rates are normalized (Figures 1 and 6). Although a direct test of this assumption is not feasible, the relatively small variance of rebound strengths over neurons may support this assumption on the recurrent synaptic plasticity as the dependence of rebound strengths on the rank of stimuli alternatively represents learning rules in recurrent connections (Figure 6C). Furthermore, if the learning rule inferred from the timeaveraged response is the combination of recurrent and feedforward synaptic plasticity, the same learning rules of this mixture and recurrent connections across different neurons would justify the assumption on the feedforward plasticity (Figure 6—figure supplement 3).
Our work provides a reconciling perspective between two prominent classes of synaptic plasticity models suggested for familiarity detection and associative memory in ITC. Depression in the feedforward connections required to lower average response after learning reasserts the role of feedforward synaptic plasticity suggested for familiarity detection (Bogacz and Brown, 2003; Norman and O'Reilly, 2003; Sohal and Hasselmo, 2000). On the other hand, most theoretical works implementing synaptic plasticity in recurrent connections have focused on associative memory and the emergence of attractors with learning (Amit and Brunel, 1997; Pereira and Brunel, 2018; Sohal and Hasselmo, 2000). Unlike most of the previous works focusing on onetype of synaptic plasticity, our analysis proposed that both recurrent and feedforward synaptic plasticity are required to reproduce changes in spatial and temporal patterns underlying familiarity detection. A recent study investigated the memory capacity for associative memory under recurrent synaptic plasticity whose form was derived from neural activities related to familiarity detection (Pereira and Brunel, 2018). Similarly, it can be further investigated how the feedforward and recurrent synaptic plasticity rules derived from the data for familiarity detection contribute to other types of memory, and how a memory capacity changes dynamically during the stimulus presentation with slow spike adaptation mechanisms.
As a substrate for slow negative feedback, firing rate adaptation mechanisms have been suggested to be critical in generating network oscillations and synchrony (Ermentrout et al., 2001; Fuhrmann et al., 2002; La Camera et al., 2004; Laing and Chow, 2002; Tabak et al., 2006; van Vreeswijk and Hansel, 2001; Wang, 2010), and in optimal information transmission under a particular form of synaptic plasticity (Hennequin et al., 2010). The effect of synaptic plasticity on enhancing synchrony in the recurrent synaptic circuits also has been explored theoretically (Gilson et al., 2010; Karbowski and Ermentrout, 2002; Morrison et al., 2007). Consistent with these previous works, our work suggests that the interplay between synaptic plasticity and adaptation with the time constant consistent with that of cellular adaptation mechanisms (Benda and Herz, 2003) generate synchronous damped oscillations after learning. Note that our analysis based on the data obtained from single cell physiology is limited to firing rate synchrony, and how spiketime correlation between neurons changes with visual learning needs to be further explored. Also, our work emphasizes the role of adaptation in different types of recognition memory. Previously, the adaptation mechanisms in the temporal cortex have been suggested to encode the recency of stimuli, which is typically measured by suppression of the response to the repetition of a stimulus (Meyer and Rust, 2018; Miller et al., 1991; Vogels, 2016; Xiang and Brown, 1998). As the time scale of repetition suppression lasts up to seconds, it may require the adaptation mechanisms on the much longer time scale (SanchezVives et al., 2000). Thus, adaptation on various time scales (La Camera et al., 2006; Pozzorini et al., 2013) may be required for different types of recognition memory.
In our work, we assumed that inhibition minimally contributes to shaping response dynamics with learning for the following reasons. First, no dependence of input changes on postsynaptic firing rates in inhibitory neurons observed experimentally suggests that changes in inhibitory activities with learning can reflect the reduction of average excitatory activities and thereafter, excitatory inputs to inhibitory neurons without synaptic plasticity in the excitatory (E)toinhibitory (I) connections (Lim et al., 2015). On the other hand, antiHebbian synaptic plasticity in the ItoE connections can have similar effects as Hebbiansynaptic plasticity in the EtoE connections. Alternatively, overall potentiation in the ItoE connections can provide stronger negative feedback or can replace the role of feedforward synaptic plasticity. However, as the dynamics of inhibitory neurons show strong suppression almost to the baseline in the late phase of the stimulus presentation after learning (Figure 1—figure supplement 1), neither antiHebbian synaptic plasticity nor potentiation can account for an increase of maximal response of excitatory neurons in the early phase and overall reduction in activities in the late phase (Figure 1). Thus, we assumed that changes in the inhibitory pathway are less likely to induce oscillation or suppression in the excitatory neurons. It is notable that the interaction between synaptic plasticity in both recurrent excitatory and inhibitory connections was suggested to reproduce increased transient response with learning (Moldakarimov et al., 2006). Although the homeostatic inhibitory plasticity proposed in this work cannot reproduce damped oscillatory response observed in ITC, we cannot rule out the role of inhibitory synaptic plasticity that can be complementary to the mechanisms proposed in our work.
The enhanced oscillation for familiar stimuli investigated here was around 5 Hz, which is in the range of theta oscillations. Such a lowfrequency oscillation has been discussed in visual search to characterize overt exploration or sampling behaviors such as saccadic or microsaccadic eye movements (OteroMillan et al., 2008; Buzsaki, 2011) and to underlie covert shift of attention that samples different stimuli rhythmically (Dugué et al., 2015; Fiebelkorn et al., 2013; Landau and Fries, 2012). In line with these studies, Rollenhagen and Olson (2005) observed that lowfrequency oscillation became stronger when another stimulus was present together. Competitive interactions between populations representing different stimuli were suggested to generate oscillation with fatigue mechanism (Moldakarimov et al., 2005; Rollenhagen and Olson, 2005). Based on the adaptation mechanisms proposed in the current work, competition between two different familiar stimuli can generate stronger oscillation at a similar frequency. In the meanfield dynamics with two mutually inhibitory populations each of which mimics the maximum response to a single familiar stimulus, stronger oscillation but with the similar frequency with that for the single stimulus presentation was reproduced in the presentation of two stimuli (Figure 7). This may indicate lowfrequency damped oscillators for a single familiar stimulus can be a building block for a rhythmic sampling of multiple stimuli and covert attentional shift through competitive interactions.
Overall, our work resonates with perspectives emphasizing the importance of dynamics in understanding cognitive functions (Bargmann and Marder, 2013; Kopell et al., 2014). As an extension of our previous work that inferred the synaptic plasticity rules from changes in spatial patterns, additional analysis of response dynamics revealed the role of slow adaptation currents in shaping response dynamics. Different contributions to activity changes of recurrent and feedforward synaptic plasticity suggested in our work can be further utilized to examine how each synaptic plasticity engages during the progress of learning. Also, although we suggested a local circuit model for visual learning, interactions with other areas might also be important – for instance, the interactions between ITC and perirhinal cortex may form positive feedback given the adjacency of these two areas and similar familiarity effects observed experimentally (Xiang and Brown, 1998). On the other hand, prefrontal cortex showing opposite effects of familiarity with a long latency may provide slow negative feedback (Xiang and Brown, 2004). To dissect the interaction between multiple regions, one can analyze time course data investigating latencies and qualitative changes in dynamics in these areas such as the emergence of oscillatory response after learning.
Materials and methods
Meanfield dynamics
Request a detailed protocolTo derive the mean field dynamics from Equation (3), we assumed linear dynamics with Φ(x) = x and uniform recurrent connectivity before learning ${W}_{ij}^{R}={w}_{R}/N$. Note that uniform connection can be replaced by random connection, which is analogous to the state where the network connectivity is stabilized after learning of a large number of uncorrelated activity patterns, but not correlated with the stimulus of interest (Lim et al., 2015). We also assumed $\sum {g}_{k}\left({\xi}_{j}\right)}=0$ so that the sum of synaptic weights over the presynaptic neurons is preserved with learning. The external input to neuron i before learning is defined as ${I}_{i}^{X}$ with ${W}_{ij}^{F}={\delta}_{ij}$.
Before learning, the meanfield dynamics can be obtained by taking an average over neurons, which yields a twodimensional system of differential equations in terms of $\overline{r}=\frac{1}{N}{\displaystyle \sum _{i}{r}_{i}}$ and $\overline{a}=\frac{1}{N}{\displaystyle \sum _{i}{a}_{i}}$. After learning, with ${W}_{ij}^{k}\to {W}_{ij}^{k}+\frac{1}{N}{f}_{k}\left({\xi}_{i}\right){g}_{k}\left({\xi}_{j}\right)$, Equation (3) becomes
The meanfield dynamics is fourdimensional with additional variables $m=\frac{1}{N}{\displaystyle \sum _{i}{g}_{R}\left({\xi}_{i}\right){r}_{i}}$ and $n=\frac{1}{N}{\displaystyle \sum _{i}{g}_{R}\left({\xi}_{i}\right){a}_{i}}$. The dynamics of m and n can be obtained by multiplying ${g}_{R}\left({\xi}_{j}\right)$ to Equation (3) and taking the average over neurons as
With $\sum {g}_{k}\left({\xi}_{j}\right)}=0$, the second term in the first equation disappears (note that without $\sum {g}_{k}\left({\xi}_{j}\right)}=0$, this term remains and provides feedback from $\overline{r}$ to the m dynamics as in Figure 3—figure supplement 2). Then, the meanfield dynamics after learning is given as
with
In Equation (4), ${\overline{f}}_{R,F}=\frac{1}{N}{\displaystyle \sum _{i}{f}_{R,F}\left({\xi}_{i}\right)}$ is the average postsynaptic dependence of recurrent and feedforward synaptic plasticity, ${\overline{fg}}_{k}=\frac{1}{N}\sum _{i}{f}_{k}\left({\xi}_{i}\right){g}_{R}\left({\xi}_{i}\right)$ is the average of the product of post and presynaptic dependence f and g. I represent the external inputs where ${\overline{I}}_{X}=\frac{1}{N}{\displaystyle \sum _{}{I}_{i}^{X}},{I}_{FX}=\frac{1}{N}{\displaystyle \sum _{}{g}_{F}\left({\xi}_{i}\right){I}_{i}^{X}},{I}_{MX}=\frac{1}{N}{\displaystyle \sum _{}{g}_{R}\left({\xi}_{i}\right){I}_{i}^{X}}$.
To describe visual responses under the successive presentation of stimuli (Meyer et al., 2014), we consider learning of two stimuli. Changes of synaptic connections after two stimuli become $W}_{ij}^{k}\to {W}_{ij}^{k}+\mathrm{\Delta}{W}_{ij}^{k,1}+\mathrm{\Delta}{W}_{ij}^{k,2$ where superscripts 1 and 2 represent the indices of the stimuli. With the same synaptic plasticity rule as in Equation (2), ${\overline{f}}_{R,F}$ and $\overline{fg}}_{R,F$ for different stimuli are the same, and the external input is the sum of the inputs ${I}_{{}^{i}}^{X}={I}_{i}^{X,1}+{I}_{i}^{X,2}$. For simplicity, we assume that the interaction of learning two stimuli is minimal such that two stimuli are uncorrelated as $\sum _{}{f}_{k}\left({\xi}_{j}^{{l}_{1}}\right){g}_{k}\left({\xi}_{j}^{{l}_{2}}\right)}=0$ and $\sum _{}{I}_{j}^{X,{l}_{1}}{g}_{k}\left({\xi}_{j}^{{l}_{2}}\right)}=0$ for l_{1}, l_{2} = 1,2 but l_{1} ≠ l_{2}. Then, by defining the overlap variables as $m=\frac{1}{N}{\displaystyle \sum _{}\left({g}_{R}\right({\xi}_{j}^{1})+{g}_{R}({\xi}_{j}^{2}\left)\right){r}_{j}}$, $n=\frac{1}{N}{\displaystyle \sum _{}\left({g}_{R}\right({\xi}_{j}^{1})+{g}_{R}({\xi}_{j}^{2}\left)\right){a}_{j}}$, and inputs as ${I}_{FX}=\frac{1}{N}{\displaystyle \sum _{}\left({g}_{F}\left({\xi}_{i}^{1}\right)+{g}_{F}\left({\xi}_{i}^{2}\right)\right){I}_{i}^{X}}$ and ${I}_{MX}=\frac{1}{N}{\displaystyle \sum _{}\left({g}_{R}\left({\xi}_{i}^{1}\right)+{g}_{R}\left({\xi}_{i}^{2}\right)\right){I}_{i}^{X}}$, the dynamics after learning two stimuli is the same as for that stimulus given in Equation (4).
Constraints on parameters in the meanfield dynamics
Request a detailed protocolIn this section, we describe the conditions on parameters in the meanfield dynamics Equation (4) to reproduce changes of response dynamics with learning qualitatively. Changes in response dynamics showing stronger oscillation after learning imposes a condition on the m and n dynamics in Equation (4), and thus the constraints on the strength of potentiation, $\overline{fg}}_{R$, parameters for adaptation, k and τ_{A}, and time constant τ_{R} (Figure 3B). Also, response dynamics to novel stimuli such as no damped oscillation before learning and reduced response in the successive presentation of novel stimuli leads to constraints on the dynamics of $\overline{r}$ and $\overline{a}$ before learning, thus, k, τ_{A}, τ_{R}, and connectivity strength before learning w_{R} (Figure 5—figure supplement 1).
Under the linear assumption, the dynamics is characterized by the eigenvalues of the system, and the eigenvalues of the m and n dynamics are given as $\left(1+{\overline{fg}}_{R}\right)/{\tau}_{R}1/{\tau}_{A}\pm \sqrt{{\left\{\left(1+{\overline{fg}}_{R}\right)/{\tau}_{R}+1/{\tau}_{A}\right\}}^{2}4k/\left({\tau}_{R}{\tau}_{A}\right)}$. The transition to overdamped oscillation occurs when the eigenvalue becomes a complex number, that is, ${\left\{\left(1+{\overline{fg}}_{R}\right)/{\tau}_{R}+1/{\tau}_{A}\right\}}^{2}4k/\left({\tau}_{R}{\tau}_{A}\right)$ changes its sign. This provides a separatrix (red to blue region in Figure 3B). Also, the stability requiring a negative real part of eigenvalues imposes two other conditions, $\overline{fg}}_{R}<1+{\tau}_{R}/{\tau}_{A$, and $\left(1+{\overline{fg}}_{R}\right)/{\tau}_{R}1/{\tau}_{A}+\sqrt{{\left\{\left(1+{\overline{fg}}_{R}\right)/{\tau}_{R}+1/{\tau}_{A}\right\}}^{2}4k/\left({\tau}_{R}{\tau}_{A}\right)}<0$, that is, ${\overline{fg}}_{R}k1<0$ (two lines on the right side in Figure 3B).
Similarly, the eigenvalues of linear dynamics of $\overline{r}$ and $\overline{a}$ before learning are given as $(1+{w}_{R})/{\tau}_{R}1/{\tau}_{A}\pm \sqrt{{\left\{\right(1+{w}_{R})/{\tau}_{R}+1/{\tau}_{A}\}}^{2}4k/\left({\tau}_{R}{\tau}_{A}\right)}$, and no oscillation before learning requires no complex eigenvalues, that is, ${\left\{\right(1+{w}_{R})/{\tau}_{R}+1/{\tau}_{A}\}}^{2}4k/\left({\tau}_{R}{\tau}_{A}\right)\ge 0$ (solid curve in Figure 5—figure supplement 1). Another condition is that the second peak is lower than the first peak in the successive presentation of two novel stimuli. To derive analytical expression, we made the following assumptions − i) neural activity changes linearly during the rising and decaying phases, and ii) during the rising phase, the adaptation variable $\overline{a}$ and external input are constant. We denote t_{0} and t_{1} as the duration of the rising and decaying phases, r_{0} and r_{1} are activities at the end of the rising and decaying phases with $\overline{r}$ = 0 and $\overline{a}$ = 0 as the baseline before the stimulus presentation. Also, if we denote I_{0} as the constant input during the rising phase, then approximately, ${r}_{0}={I}_{0}{t}_{0}/{\tau}_{eff}$ where ${\tau}_{eff}={\tau}_{R}/(1{w}_{R})$. During the decaying phase of the first stimulus presentation, $\overline{r}$ decreases linearly from r_{0} to r_{1}, and then at the end of the presentation of the first stimulus, $\overline{a}={r}_{0}\left(1\mathrm{exp}({t}_{1}/{\tau}_{A})\right)+({r}_{1}{r}_{0})\left\{1{\tau}_{A}/{t}_{1}\left(1\mathrm{exp}({t}_{1}/{\tau}_{A})\right)\right\}\equiv {a}_{1}$.
Now based on the second assumption during the rising phase of the second stimulus presentation, the input becomes ${I}_{0}{a}_{1}k$ and the expression for the second peak becomes $({I}_{0}{a}_{1}k)\frac{{t}_{0}}{{\tau}_{R}/(1{w}_{R})}+{r}_{1}$. Then the condition that the second peak is lower than the first peak gives $({I}_{0}{a}_{1}k)\frac{{t}_{0}}{{\tau}_{R}/(1{w}_{R})}+{r}_{1}<{r}_{0}$. Replacing I_{0} using ${r}_{0}={I}_{0}{t}_{0}/{\tau}_{eff}$ leads to the condition $\frac{{r}_{1}/{r}_{0}\cdot {\tau}_{R}/{t}_{0}}{1\mathrm{exp}({t}_{1}/{\tau}_{A})\left(1{r}_{1}/{r}_{0}\right)\left({\tau}_{A}/{t}_{0}\left(\mathrm{exp}({t}_{1}/{\tau}_{A})1\right)+1\right)}<(1{w}_{R})k$ (dotted curve in Figure 5—figure supplement 1).
Network simulation in Figure 4
Request a detailed protocolIn Figure 4, we illustrated the dynamics of an example network with synaptic plasticity in feedforward and recurrent connections, and spike adaptation mechanisms. The network dynamics follows Equation (3) and as in the meanfield dynamics, we assumed linear dynamics with Φ(x) = x and uniform recurrent connectivity before learning ${W}_{ij}^{R}={w}_{R}/N$. The input was modeled as a sum of a constant input ${I}_{const}$ and timevarying one which is the sum of two exponential functions ${I}_{dyn}=\mathrm{exp}(t/{t}_{1})\mathrm{exp}(t/{t}_{2})$ with its strength ${\xi}_{i}$ varying across neurons as ${I}_{i}^{X}={I}_{const}+{\xi}_{i}{I}_{dyn}$. For recurrent synaptic plasticity, Hebbian learning rule such as $\Delta {W}_{ij}^{R}=\frac{\alpha}{N\mathrm{var}\left(\xi \right)}{\xi}_{i}\left({\xi}_{j}\overline{\xi}\right)$ was considered where α is the strength of the plasticity. For feedforward synaptic plasticity, uniform scaling down of the timevarying input was considered such that ${I}_{i}^{X}$ changes to ${I}_{i}^{X}={I}_{const}+\gamma {\xi}_{i}{I}_{dyn}$ after learning.
For the successive presentation of two stimuli, the changes in the recurrent connection become $W}_{ij}^{R}\to {W}_{ij}^{R}+\mathrm{\Delta}{W}_{ij}^{R,1}+\mathrm{\Delta}{W}_{ij}^{R,2$ with uncorrelated patterns ${\xi}_{i}^{1}$ and ${\xi}_{i}^{2}$. The duration of each stimulus presentation is denoted as P_{1} and the external input correlated with one stimulus decays linearly during P_{2} when another stimulus is on. The parameters used in Figure 4 are N = 2000, w_{R} = 0, k = 1.8, τ_{R} = 5 ms, τ_{A} = 200 ms, t_{1} = 150 ms, t_{2} = 50 ms, P_{1} = 150 ms and P_{2} = 100 ms. ξ_{i} is assumed to follow a gamma distribution with shape parameter three and α = 0.9. I_{const} is adjusted so that the baseline firing rate is 5 Hz, and γ = 0.4.
Fitting experimental data in Figures 5,6
Request a detailed protocolIn Figure 5, activities in ITC neurons for the dimming detection task were fitted using the mean field dynamics given in Equation (4). Under the assumption of a homogeneous network, activities to different stimuli can serve as a surrogate for activities of different neurons to one stimulus. Thus, we took an average of firing rates over stimuli (eight novel stimuli and 10 familiar stimuli for each neuron) and over 41 neurons classified as putative excitatory neurons (see more details in Lim et al., 2015). Note that as the timecourse data without taking an average over neurons is noisy and the number of stimuli is small, only the parameters for the meanfield dynamics could be inferred from the data from the dimmingdetection task.
Before learning, the response dynamics is only determined by average variables $\overline{r}$ and $\overline{a}$, and by the parameters w_{R}, k, τ_{R}, and τ_{A}, which need to reproduce the data showing no damped oscillations before learning and suppressed response to the presentation of the second novel stimuli (Figure 5—figure supplement 1). Given w_{R}, k, τ_{R}, and τ_{A}, the external input was modeled as the sum of two exponential functions $a\mathrm{exp}(t/{t}_{1})b\mathrm{exp}(t/{t}_{2})+ba$ and their parameters are chosen such that the simulation fits the activities before learning (Figure 5A). Note that since we assume that the inhibitory activities follow the excitatory activities instantaneously, w_{R} represents ${W}^{EE}{W}^{EI}{W}^{IE}$, and can be negative. In the dynamics of m and n after learning, the strength of positive feedback is $\overline{fg}}_{R$ in Equation (4), analogous to potentiation in high firing rate neurons. Together with parameters for slow adaptation currents, $\overline{fg}}_{R$ should be chosen to generate the oscillation with the period around 150 ms (Figure 5—figure supplement 2A,B). The external input for m is also modeled as the sum of two exponential functions, and given m and n dynamics and the external input from the novel response, ${\overline{f}}_{R,F}$ were chosen to fit the magnitude of oscillation and reduction in firing rates in the mean response for familiar stimuli given the dynamics of m (Figure 5B; Figure 5—figure supplement 2C).
In the simulation of the successive stimulus presentation in Figure 5C D, all the parameters are the same as in Figure 5A B and the external inputs for the first and second stimuli have the same temporal profile except for different onsets. During the presentation of the second stimuli, the external input for the first stimulus decays exponentially with a time constant of 50 ms. The parameters used in Figure 5 are w_{R} = 0, k = 1.8, τ_{R} = 5 ms, τ_{A }= 200 ms, $\overline{fg}}_{R$ = 0.9, ${\overline{f}}_{R}$ = 0.3, ${\overline{f}}_{F}$ = −0.7, a = 6, b = 5, t_{0} = 700 ms, t_{1} = 40 ms for the mean external input and a = b = 5, t_{0} = 400 ms, t_{1} = 20 ms for the external input of the m dynamics. Note that for a wide range of w_{R} with the same parameters except a, b, t_{0}, and t_{1} adjusted to reproduce response to novel stimuli, the simulation fit the data well (Figure 5—figure supplement 3).
In the passive viewing task in Figure 6, responses to 125 novel and 125 familiar stimuli were measured, and 14 putative excitatory neurons were classified to show both potentiation and depression when the distributions of timeaveraged activities before and after learning were compared (see more details in Lim et al., 2015). Timecourse data at each rank of the stimuli in each neuron was noisy, and averaging over neurons was required to reduce noise. For this, we normalized activities in each neuron and took the average of these normalized activities over neurons at each rank (Figure 1).
To infer postsynaptic dependence of synaptic plasticity rules on normalized activities, we considered a network consisting of 125 neurons whose dynamics are described by Equation (3) and fit timecourse data before and after learning. We set the parameters to be the same as in Figure 5, and fitted external inputs ${I}_{}^{X}\left(t\right)$ and postsynaptic dependence of the feedforward and recurrent connections, ${f}_{R,F}$. The external input to each neuron was obtained to reproduce the response for novel stimuli at each rank as follows  Discretization of the dynamic equations in Equation (3) yields $\frac{{\tau}_{r}}{dt}\left({r}_{i}^{nov}(t+dt){r}_{i}^{nov}\left(t\right)\right)={r}_{i}^{nov}\left(t\right)+\Phi \left({w}_{r}{\overline{r}}_{i}^{nov}\left(t\right)k{a}_{i}^{nov}\left(t\right)+{I}_{i}^{X}\left(t\right)\right)$ where ${r}_{i}^{nov}\left(t\right)$ is the firing rate for the novel stimulus at rank i, and ${a}_{i}^{nov}\left(t\right)$ is a lowpass filtered ${r}_{i}^{nov}\left(t\right)$. Given w_{R} = 0, τ_{R} = 5 ms with the time step 5 ms to be the same as that in the data, the external input can be expressed as ${I}_{i}^{X}\left(t\right)={\Phi}^{1}\left({r}_{i}^{nov}(t+dt)\right)+k{a}_{i}^{nov}\left(t\right)$, and thus, it is determined by activities for novel stimuli.
The postsynaptic dependence of the synaptic plasticity was obtained to fit the activities for familiar stimuli. As the single cell recordings do not allow inference on the presynaptic dependence, we assumed its form which is ${g}_{R,F}$ = 1 for the highest rank and 0 otherwise such that m in Equation (4) is the response to the familiar stimulus at the highest rank. In this case, discretization of the dynamic equation for familiar stimuli becomes $\frac{{\tau}_{r}}{dt}\left({r}_{i}^{fam}(t+dt){r}_{i}^{fam}\left(t\right)\right)={r}_{i}^{fam}\left(t\right)+\Phi \left({w}_{r}{\overline{r}}_{i}^{fam}\left(t\right)+{f}_{R,i}{r}_{\mathrm{max}}^{fam}\left(t\right)k{a}_{i}^{fam}\left(t\right)+{I}_{i}^{X}\left(t\right)+{f}_{F,i}{I}_{\mathrm{max}}^{X}\left(t\right)\right)$. ${f}_{R,F}$ were fitted to mimic the response to familiar stimuli at each rank  the number of unknowns is 125 times 2 (125${f}_{R}$ and 125${f}_{F}$) and the number of data points to fit is 125 times 44 where 44 is the number of time steps so it is analogous to underdetermined system. We used the least square method with larger weights in the late phase to capture the rebound better (weight 5 from 230 ms after the stimulus onset, and otherwise 1; different weights do not affect the performance qualitatively, not shown here). Note that in fitting and simulating the response to familiar stimuli, we used ${r}_{\mathrm{max}}^{fam}\left(t\right)$ from the data to prevent the fitting error in ${r}_{\mathrm{max}}^{fam}\left(t\right)$ from spreading over the network.
For nonlinear dynamics in Figure 6—figure supplement 1, the transfer function $\Phi \left(x\right)$ was obtained from the timeaveraged response for novel stimuli – for each rank of novel stimuli, we took the timeaveraged response in the time window between 75 ms and 200 ms after stimulus onset. Under the assumption that the transfer function $\Phi \left(x\right)$ is monotonically increasing and the distribution of synaptic inputs to novel stimuli follow Gaussian statistics, the transfer function is obtained by matching the input current and timeaveraged response at the same rank (Lim et al., 2015).
Models for alternative negative feedback mechanisms
Request a detailed protocolReplacing adaptation a_{i} in Equation (3) as a^{I} which is an exponential filtered $\overline{r}$ with strength k^{I} and time constant τ_{A}, we can derive the meanfield dynamics of the model for the global inhibition as
which is similar to Equation (4), but without n dynamics.
The shortterm depression is modeled by a variable x which represents the fraction of resources available after the depletion of neurotransmitters and therefore adjusts the strength of the synaptic connections (Tsodyks and Markram, 1997). The network activity is thus described by the following equations
where τ_{X} and γ represent the time constant and strength of shortterm depression. Before the stimulus presentation, x is initialized to its steady states given the parameters and baseline activity, and W^{R} before and after learning is the same as in Equation (3). To see whether shortterm depression can reproduce the oscillatory response after learning, we considered the case that the recurrent connection is weak before learning, and the oscillation in the network is led by that in the high rate neurons. With larger presynaptic dependence g_{R} for the high rate neurons, their dynamics can be approximated as
We fitted the parameters ${f}_{m}^{R}{g}_{m}^{R}$ and γ analogous to the strengths of longterm synaptic plasticity and shortterm plasticity, respectively (Figure 6—figure supplement 2). When we set ${\tau}_{R}$ = 5 ms, ${\tau}_{x}$ = 200 ms, ${I}_{m}^{X}$ was obtained from the maximal response to the novel stimuli. The best fitting parameters to the maximal response to the familiar stimuli are ${f}_{m}^{R}{g}_{m}^{R}$ = 2.56 and γ = 0.125, and the time course with the bestfitted parameters cannot generate oscillation (Figure 6—figure supplement 2).
Models for competitive interactions between two stimuli
Request a detailed protocolExperimentally, stronger oscillation at around 5 Hz was observed in the presence of another stimulus in the visual field, which was accounted for by competitive interactions between the populations selective to each stimulus (Moldakarimov et al., 2005; Rollenhagen and Olson, 2005). Following these previous works, we considered two mutually inhibitory populations where each population is selective to one of two stimuli and its dynamics follow the dynamics of m in the meanfield description under the presence of a single stimulus. Then the dynamics of two populations are given as follows:
where population indices i,j = 1 or two where i ≠ j, and w_{c} denotes the strength of the mutual inhibition, set to be 0.1. Φ is the input currentoutput rate transfer function which was assumed to be piecewise linear as Φ(x) = x for $x\ge 3$ and 0 otherwise. The remaining parameters and variables are the same as in Figure 5 as $\overline{fg}}_{R$ = 0.9, k = 1.8, τ_{R}= 5 ms, τ_{A}= 200 ms, ${I}_{m,i}=\mathrm{exp}(t/{t}_{1})\mathrm{exp}(t/{t}_{2})$ where t_{1} = 400 ms and t_{2} = 20 ms.
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Decision letter

Nicole RustReviewing Editor; University of Pennsylvania, United States

Michael J FrankSenior Editor; Brown University, United States
In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.
Thank you for submitting your article "Mechanisms underlying sharpening of visual response dynamics with familiarity" for consideration by eLife. Your article has been reviewed by two peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Michael Frank 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.
Summary:
In this paper, Lim addresses questions related to the cortical mechanisms that support learning through an innovative modelingbased approach. The specific focus of this paper is a model of how the stimulusevoked response dynamics of IT neurons along timescales of a few hundred ms differ for novel as compared to highly familiar images. Previous experimental work found that familiarity leads to a sharp reduction in firing rate following the initial peak (phasic) response, then a rebound of firing that when taken together resemble a damped oscillation. Modeling this response could provide important insights into learning mechanisms of the brain.
The author builds on her earlier model of IT familiarity acquisition, which uses changes in tuning functions to argue that familiarity plasticity resides in synaptic plasticity of recurrent connections within IT. Here she proposes 1) synaptic plasticity in the recurrent connections, 2) rate adaptation and 3) plasticity in the feedforward inputs, are sufficient to account for experimentally observed changes in visual response between novel and familiar images. In particular, this work extends the work Lim et al., 2015. It focuses on reproducing a damped oscillatory component of the visual response after learning, which was not present before learning in experimental data.
The reviewers find the work interesting and exciting, but have also identified a number of issues that must be addressed for the manuscript to be suitable for publication. They also have provided a number of suggestions for improvement.
Essential revisions:
1) The BCM type rule was derived assuming there is only plasticity in the recurrent network (Lim et al., 2015). Then it is used here with plasticity in the feedforward network. That seems inconsistent. If I understand correctly, the rule should be reinferred with plasticity both in feedforward and recurrent connections in the first place.
2) Describing this rebound/oscillatory component mechanistically is interesting, in terms of fitting the data. However, the functional implications are less clear. The work could be extended to show the functional implications of a network with the 3 ingredients: plasticity in the feedforward, in the recurrent and the rate adaptation, leading to this transition between overshoot and damped oscillations.
3) Is this model fully consistent with the experimental results that motivate it? Specifically, wouldn't turning off the image still induce an oscillatory response due to the positive/negative recurrent feedback? This seems counter to work the author cites (Meyer et al., 2014 Figure 5C, D – notice how when a familiar image is presented then left with a blank screen 'F' there is no oscillation).
4) The paper focuses exclusively on excitatory neurons – is there a good reason for this? Can the model account for both excitatory and inhibitory response dynamics?
5) The author needs to include all the information to reproduce the paper.
6) The writing should be improved for both technical expects as well as a general audience, particularly in the subsection “Interactions between synaptic plasticity and slow negative feedback”.
7) The author must provide code for the reviewers (both for the network with fitted parameters and the code for the fitting procedure) and post the code publicly after publication.
[Editors' note: further revisions were requested prior to acceptance, as described below.]
Thank you for submitting your article "Mechanisms underlying sharpening of visual response dynamics with familiarity" for consideration by eLife. Your article has been reviewed by two peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Michael Frank as the Senior Editor.
The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.
Summary:
The reviewers would like to thank the authors for all the work they did. The paper has improved as a result of these clarifications. A few remaining items should be addressed before the manuscript is accepted for publication.
Essential revisions:
1) In the first round of reviews, the reviewers pointed out that the BCM type rule was derived in 2015 assuming that plasticity was only in the recurrent network but in the current manuscript it was applied to a network with feedforward plasticity; the reviewers asked whether the rule should be rederived. The author reply focused on a normalization procedure applied to the neural data. It is not clear to the reviewers how this normalization procedure relates to the issues raised about recurrent versus feedforward processing. Please justify the use of the BCM type rule in the model with multiple types of plasticity.
2) In the first round of reviews, the reviewers requested that the work be extended to show the functional implications of the proposed network. The authors responded by incorporating a paragraph into the Discussion highlighting the bridge between two classes of models, and these are nice points to make. However, the reviewers would like to clarify their request to complement the current presentation, which focuses on the network architectures required to recapitulate an experimentallyobserved phenomenology, with more insight into the functional implications of this work. For example, beyond constraining mechanistic models, why do we care about the damped oscillatory response?
What are its functional implications for representation in IT and/or behavior? What types of functions is a network with the 3 proposed ingredients capable of?
https://doi.org/10.7554/eLife.44098.026Author response
Essential revisions:
1) The BCM type rule was derived assuming there is only plasticity in the recurrent network (Lim et al., 2015). Then it is used here with plasticity in the feedforward network. That seems inconsistent. If I understand correctly, the rule should be reinferred with plasticity both in feedforward and recurrent connections in the first place.
Thank you for pointing out the lack of clarity concerning connection to the previous work (Lim et al., 2015). As noted by the reviewers, one of the main findings in my previous work (Lim et al., 2015) was that when the synaptic plasticity was inferred from changes of time averaged response with learning, the postsynaptic firing rate separating depression and potentiation, denoted as a threshold θ, was strongly correlated with mean and standard deviation of postsynaptic firing rates. This is reminiscent of the BCM rule claiming the dynamic evolution of θ depending on the postsynaptic activities, although our work compared snapshots of statistics before and after learning, and examined θ across different neurons, that is, the spatial version of the BCM rule. Such a correlation between θ and postsynaptic activities may arise from similar synaptic plasticity rule across different neurons when input currents and firing rates are normalized. Author response image 1, adapted from the previous paper (Figure 4 in Lim et al., 2015) shows that when firing rates and inputs were normalized by the mean and standard deviation of them before learning, such a correlation disappeared (g and h compared to e and f). This may suggest the same synaptic plasticity rule across different neurons when postsynaptic rates were normalized (c), and as overall firing rates changes across different neurons, the threshold changes proportionally as θ = σθ’+μ where θ’ is the threshold for normalized firing rate, and μ and σ are the mean and standard deviation of activities.
Inspired by this previous observation, we inferred synaptic plasticity from normalized activities when it was allowed – in the passive viewing task in Figures 1 and 6, we normalized activities in each neuron using the mean and standard deviation of activities before learning, and averaged such normalized activities over different neurons. Note that averaging over neurons was required to reduce noise in the timecourse data, in contrast to the previous work comparing the timeaveraged responses and deriving recurrent synaptic plasticity rule in individual neurons. Under the assumption that synaptic plasticity rule is the same across different neurons when inputs and rates are normalized, the correlation between the threshold and postsynaptic activities naturally arises even if depression occurs mainly in the feedforward connections and potentiation occurs in the recurrent connections.
We now add a sentence in Results and the paragraph in Discussion to clarify this as follows:
Results: “… Note that the synaptic plasticity was inferred from normalized firing rates averaged over neurons under the assumption that the dependence of synaptic plasticity rules on normalized firing rates is the same across different neurons (See Discussion for justification).”
Discussion: “Here, we extended our previous work inferring recurrent synaptic plasticity rules from timeaveraged data in a static model of a cortical network to timecourse data and a dynamic model with additional spike adaptation mechanisms and feedforward synaptic plasticity (Lim et al., 2015). […] In this case, the dependence of synaptic plasticity rules on postsynaptic rates scales proportionally to changes of a range of firing rates, resulting in a correlation between the threshold and neural activity even with synaptic plasticity in different connections, consistent with the previous observation from timeaveraged responses (Lim et al., 2015).”
2) Describing this rebound/oscillatory component mechanistically is interesting, in terms of fitting the data. However, the functional implications are less clear. The work could be extended to show the functional implications of a network with the 3 ingredients: plasticity in the feedforward, in the recurrent and the rate adaptation, leading to this transition between overshoot and damped oscillations.
We thank the reviewers for pointing out the lack of clarity. The current work proposed the conditions on synaptic plasticity in recurrent and feedforward connections, and spikeadaptation mechanisms for reproducing the time course activities. Recurrent synaptic plasticity broadens the distribution of activities as typical Hebbian synaptic plasticity, while depression in feedforward inputs decreases average firing activities. Thus, synaptic plasticity enables the sparse and efficient representation of the learned stimuli. On the other hand, adaptationlike mechanisms are critical for shaping the dynamics as the network cannot generate oscillatory response without slow negative feedback (Figure 2). It has been suggested that stronger oscillatory response after learning might be important for putting neurons to be ready for the following stimuli as suppressing activity strongly in particular in the late phase of the stimulus presentation. Thus, the slow adaptation mechanisms together with synaptic plasticity may play an important role in the rapid processing of the learned stimuli.
The functional role of these three main ingredients have been investigated previously in relation to different types of recognition memory. For familiarity detection, different forms of feedforward synaptic plasticity have been explored to reproduce a lower response for familiar stimuli, but without considering response dynamics (Bogacz and Brown, 2003; Norman and O'Reilly, 2003; Sohal and Hasselmo, 2000). On the other hand, most theoretical works implementing synaptic plasticity in recurrent connections have focused on associative memory and the emergence of attractors with learning (Amit and Brunel, 1997; Pereira and Brunel, 2018; Sohal and Hasselmo, 2000). Finally, the adaptation mechanisms in the temporal cortex have been suggested to encode the recency of stimuli, which is typically measured by suppression of the response to the repetition of a stimulus (Meyer and Rust, 2018; Miller, Li and Desimone, 1991; Vogels, 2016; Xiang and Brown, 1998). As the time scale of repetition suppression lasts up to seconds, the spike adaptation mechanism considered in the current study may only encode the recency signal on a shorter time scale.
Most of these works focused on one of the three ingredients, except Sohal and Hasselmo, 2000, whose model contained feedforward and recurrent synaptic plasticity as well as spike adaptation mechanisms on a longer time scale. Still, as other works, Sohal and Hasselmo proposed each ingredient for a different type of memory, and did not investigate their interactions. On the other hand, we focused on familiarity detection and investigated how the three ingredients shape response dynamics together. Recently, Pereira and Brunel, 2018, have investigated the capacity of associative memory with recurrent synaptic plasticity whose form was derived from neural activities related to familiarity detection. Similarly, it can be further investigated how the three ingredients derived in the current study contribute to other types of memory like associative memory and recency effect, and how a memory capacity for familiarity detection changes dynamically during the stimulus presentation with the spike adaptation mechanisms. However, this is beyond the scope of the current paper.
The functional implications of each mechanism are summarized in the first paragraph in Discussion and to discuss them related to the previous works, we modified the paragraph in Discussion as follows:
“Our work provides a reconciling perspective between two prominent classes of synaptic plasticity models suggested for familiarity detection and associative memory in ITC. […] Similarly, it can be further investigated how the feedforward and recurrent synaptic plasticity rules derived from the data for familiarity detection contribute to other types of memory, and how a memory capacity changes dynamically during the stimulus presentation with slow spike adaptation mechanisms.”
3) Is this model fully consistent with the experimental results that motivate it? Specifically, wouldn't turning off the image still induce an oscillatory response due to the positive/negative recurrent feedback? This seems counter to work the author cites (Meyer et al., 2014 Figure 5C, D – notice how when a familiar image is presented then left with a blank screen 'F' there is no oscillation).
To reveal the mechanisms underlying changes in response dynamics with learning, we mainly considered the experimental results obtained from three different laboratories. We note that different experimental settings may lead to quantitatively different results even if the underlying principle is the same.
The data obtained from a passive viewing task with a larger number of stimuli suggests that oscillation is originated from the response dynamics of excitatory neurons to their most preferred stimuli about the top 5% of the stimuli (Figure 1C). As different data sets from the dimmingdetection task or with the successive presentation of two stimuli (Meyer et al., 2014) employed the smaller number of stimuli (10 familiar stimuli for each neuron in the dimming detection task, and on average 6.5 times 2 familiar stimuli for Meyer et al., 2014) in comparison to 125 stimuli in the passive viewing task, it requires sampling at least ten times more neurons to see the oscillation. Furthermore, as addressed in the reply to point 4 below, damped oscillation is not prominent in inhibitory neurons. Thus, averaging response dynamics over excitatory neurons and inhibitory neurons can mask oscillation.
The response to a short presentation of familiar stimuli shown as blue curves in Figure 5C, E, and G (adapted from Meyer et al., 2014) is less consistent as panels C and E do not show oscillation while panel G shows oscillation. Such inconsistency may arise from sparse sampling from highly oscillatory excitatory neurons and averaging the response over both excitatory and inhibitory neurons. Similarly, in Figure 5D compared to Meyer et al., 2014, the network with the parameters inferred from one experimental setting might be difficult to reproduce the data from another experiment quantitatively. Instead, we focused on inferring the mechanisms underlying visual learning from the common qualitative features across the different experiments showing stronger oscillation after learning although their magnitude may depend on different sampling of neurons and stimuli.
To clarify this, we added the following sentence in “Effects of visual learning on response dynamics” section in Results:
“… Note that although all three experiments suggest stronger oscillation after learning, its strength may vary depending on a sampling of neurons and stimuli as only excitatory neurons with their most preferred stimuli exhibit strong oscillation after learning (Figure 1D).”
4) The paper focuses exclusively on excitatory neurons – is there a good reason for this? Can the model account for both excitatory and inhibitory response dynamics?
We thank the reviewers for bringing up the lack of clarity in simplification on the inhibitory dynamics in the model and the possible role of inhibitory dynamics and synaptic plasticity in shaping response dynamics. As the reviewers noted, the dynamics of inhibitory neurons follow that of mean excitatory neurons in the model, and the recurrent inputs to excitatory neurons reflect the feedback through inhibitory neurons as the connectivity strength w_{R} represents W^{EE} _{−} W^{EI} W^{IE},and can be negative. Such a simplification is permitted under the assumption that inhibitory dynamics do not provide a major contribution to the emergence of oscillation after learning, which can be justified for the following reasons. First, no dependence of input changes on postsynaptic firing rates in inhibitory neurons observed experimentally (Author response image 1D) suggests that changes in inhibitory activities with learning can reflect the reduction of average excitatory activities and thereafter, excitatory inputs to inhibitory neurons without synaptic plasticity in the excitatory (E)toinhibitory (I) connections (Lim et al., 2015). On the other hand, antiHebbian synaptic plasticity in the ItoE connections can have similar effects as Hebbiansynaptic plasticity in the EtoE connections. Alternatively, overall potentiation in the ItoE connections can provide stronger negative feedback or can replace the role of feedforward synaptic plasticity. However, as the dynamics of inhibitory neurons show strong suppression almost to the baseline in the late phase of the stimulus presentation after learning (150200 ms after the stimulus onset in Figure 1—figure supplement 1), neither anti Hebbian synaptic plasticity nor potentiation can account for an increase of maximal response of excitatory neurons in the early phase or overall reduction in activities in the late phase (Figure 1). Thus, although inhibitory dynamics or synaptic plasticity can be complementary to the mechanisms addressed in the paper, we think that it cannot be a major factor to lead to oscillation with stronger positive or negative feedback, or reduction in activities with learning.
Another reason why we did not model the inhibitory dynamics explicitly is difficulty in fitting the data quantitatively – in the passive viewing task, as many stimuli were presented with a short interstimulus interval (200 ms for the stimulus presentation and 50 ms for the interval between the stimuli). Thus, the baseline activities before the stimulus presentation may reflect the residual activities in response to the previous stimulus. Indeed, inhibitory neurons show a more prominent effect having the baseline around 30 Hz which is too high compared to 10 Hz in Meyer et al. or other experiments. Such distortion in the temporal profiles hinders fitting the time course of inhibitory neurons quantitatively.
In summary, we made a simplification of the dynamics of inhibitory neurons based on the assumption that changes in inhibitory activities with learning can be explained by that of excitatory neurons, and inhibitory dynamics or synaptic plasticity does not provide a major contribution to the emergence of the oscillation. Also, the limitation of the current experimental settings poses difficulty in fitting the inhibitory dynamics quantitatively. To clarify this, we modified the text in Results about modeling excitatory dynamics only, the candidate mechanisms for reduction of average activities with learning and a paragraph in Discussion for the role of inhibitory dynamics or synaptic plasticity as follows:
Results: “In sum, the prominent effects of visual learning on responses of excitatory neurons are i) reduction in average response, ii) increase in maximum response, and iii) stronger oscillations after learning. […] Such a simplification is based on the experimental observation that input changes and the magnitude of rebound activity depend weakly on the postsynaptic firing rates in inhibitory neurons (see Discussion for further justification).”
Results: “Instead, reduction in average response requires changes in external inputs or other recurrent inputs such as suppression in other excitatory inputs or enhanced inhibition. […] This suggests that the effect of potentiated inhibition in the late phase is weaker than in the early phase while reduction of excitatory activities was observed in the late phase (Figure 1A, B).”
Discussion: “In our work, we assumed that inhibition minimally contributes to shaping response dynamics with learning for the following reasons. […] Thus, we assumed that changes in the inhibitory pathway are less likely to induce oscillation or suppression in the excitatory neurons…”
5) The author needs to include all the information to reproduce the paper.
We modified the Materials and methods section significantly and published the codes and data (see the reply to point 7).
6) The writing should be improved for both technical expects as well as a general audience, particularly in the subsection “Interactions between synaptic plasticity and slow negative feedback”.
We highly appreciate the reviewers’ constructive suggestions to improve the clarity in the paper. Following the first three suggestions, we modified the relevant texts in “Interactions between recurrent synaptic plasticity and slow negative feedback” section and created a new section, “Additional synaptic plasticity for a reduction in average response” in Results.
With regard to the last suggestion, we added a new paragraph in Discussion as addressing the relation to the BCMrule (see the relevant paragraph in point 1).
7) The author must provide code for the reviewers (both for the network with fitted parameters and the code for the fitting procedure) and post the code publicly after publication.
In the original submission, I uploaded the code and data on Github and provided this information in Data availability. However, I did not include this information in the manuscript due to my carelessness, and now I added this information in Materials and methods as follows: “Code availability. The data analysis and network simulations were performed in MATLAB. The data, codes for fitting the data and network simulations are available at https://github.com/slimcompneuro/Dynamics_NovelvsFamiliar.”
[Editors' note: further revisions were requested prior to acceptance, as described below.]
Essential revisions:
1) In the first round of reviews, the reviewers pointed out that the BCM type rule was derived in 2015 assuming that plasticity was only in the recurrent network but in the current manuscript it was applied to a network with feedforward plasticity; the reviewers asked whether the rule should be rederived. The author reply focused on a normalization procedure applied to the neural data. It is not clear to the reviewers how this normalization procedure relates to the issues raised about recurrent versus feedforward processing. Please justify the use of the BCM type rule in the model with multiple types of plasticity.
Thank you for pointing out the lack of clarity. In the previous response, I addressed that under the assumption of the same learning rule across different neurons for normalized firing rates and input currents, a correlation between activity and the threshold separating the depression and potentiation emerges as observed in the previous work based on timeaveraged response. However, the contribution of different synaptic plasticity such as feedforward or recurrent connections cannot be dissected using timeaveraged response, and changes in temporal dynamics such as synchronous oscillations emerging after learning were further required.
In the time course data, as the response at each rank of stimuli in individual neuron was noisy, inferring both feedforward and recurrent synaptic plasticity in each neuron was not feasible. Instead, we assumed the BCMtype rules in each synaptic plasticity, that is, the same learning rule across different neurons as a function of the normalized firing rate. To validate this assumption, it may require more trials for the same stimulus or a larger set of stimuli so that averaging over a larger number of trials or stimuli at a similar rank can reduce noise and inference of synaptic plasticity in individual neurons would be allowed. Such a direct reinference is not feasible in the current data set, given that oscillation is prominent in the top 5% of preferred stimuli, that is, 56 stimuli out of 125 stimuli, and averaging over stimuli would diminish the dependence of the learning rule on the postsynaptic activity.
On the other hand, as pointed in Figure 6A and its surrounding text, the rebound strength of damped oscillation for learned stimuli was similar to the postsynaptic dependence of recurrent synaptic plasticity. Although such rebound strengths at each rank of stimuli vary over neurons, its standard error of the mean was relatively small compared to the mean (shaded area compared to the solid line in Figure 1D). This may suggest a similar recurrent synaptic plasticity rule across different neurons as a function of the rank of stimuli, or equivalently normalized firing rates (Figure 6—figure supplement 3). If the learning rule inferred from timeaveraged activities is the combination of recurrent and feedforward synaptic plasticity, the same synaptic plasticity of this mixture and recurrent connections across different neurons (Figure 6—figure supplement 3A and B) would lead to the same synaptic plasticity of feedforward connections as well (Figure 6—figure supplement 3C). Thus, a BCMtype of synaptic plasticity rules observed in timeaveraged response and relatively small noise in rebound strengths across different neurons might provide indirect support for similar synaptic plasticity over neurons for both feedforward and recurrent synaptic plasticity.
To clarify this point, I modified the text in the Discussion (second paragraph) and added a supplementary figure (Figure 6—figure supplement 3).
2) In the first round of reviews, the reviewers requested that the work be extended to show the functional implications of the proposed network. The authors responded by incorporating a paragraph into the Discussion highlighting the bridge between two classes of models, and these are nice points to make. However, the reviewers would like to clarify their request to complement the current presentation, which focuses on the network architectures required to recapitulate an experimentallyobserved phenomenology, with more insight into the functional implications of this work. For example, beyond constraining mechanistic models, why do we care about the damped oscillatory response?
What are its functional implications for representation in IT and/or behavior? What types of functions is a network with the 3 proposed ingredients capable of?
I appreciate the reviewers for raising this issue again – in this revision, I found that I missed literature discussing the prevalence of lowfrequency oscillation in the brain and their functional roles (Buzsaki, 2011). The frequency of damped oscillation analyzed in this work is around 5Hz, which is in the range of theta oscillations. Closely related to the visual response in ITC investigated in this work, such a lowfrequency oscillation has been discussed in visual search to characterize overt exploration or sampling behaviors such as saccadic or microsaccadic eye movements (OteroMillan, Troncoso et al., 2008; Buzsaki, 2011). Similarly, it was suggested that covert shift of attention samples different stimuli rhythmically at a similar frequency range (Landau and Fries, 2012; Fiebelkorn, Saalmann et al., 2013; Dugue, Marque et al., 2015).
In line with these studies, a lowfrequency oscillation at the theta range has been observed in several electrophysiological studies in ITC while monkeys passively viewed the images or performed attention tasks (Nakamura, Mikami et al., 1991; Nakamura, Mikami et al., 1992; Sheinberg and Logothetis, 1997; Freedman, Riesenhuber et al., 2006; Woloszyn and Sheinberg, 2012). In particular, Rollenhagen and Olson observed that lowfrequency oscillation became stronger when an object eliciting an excitatory response was present together with a flanker stimulus that alone elicits little or no activity (Rollenhagen and Olson, 2005). The authors and Moldakarimov et al. in the following theoretical study suggested competitive interactions between populations representing each stimulus can generate such oscillation together with fatigue mechanisms (Moldakarimov, Rollenhagen et al., 2005; Rollenhagen and Olson, 2005). The frequency of enhanced oscillation was around 5 Hz, consistent with other electrophysiology and behavior studies, and thus, the oscillatory response may suggest perceptual alternation between different stimuli and covert shift of attention.
Interestingly, the frequency of damped oscillation in the presentation of a single familiar stimulus is similar to that observed during the visual search. Based on the adaptation mechanisms proposed in the current work which determines the frequency of oscillation, competition between two different familiar stimuli can generate stronger oscillation at a similar frequency. To show this, I utilized the meanfield dynamics considered in Figure 5, which generated damped oscillation in the presentation of a single familiar stimulus. Considering two mutually inhibitory populations each of which mimics the maximum response to a single familiar stimulus (Figure 7A), the experimental observation was reproduced qualitatively – the onset of the second stimulus transiently suppressed the response to the first stimulus and the oscillation during the presentation of both stimuli becomes stronger (Figure 7B). Furthermore, the oscillation frequency for the single stimulus presentation and presentation of two stimuli is similar around 5 Hz. This may indicate that lowfrequency damped oscillators for a single familiar stimulus can be a building block for a rhythmic sampling of multiple stimuli and attentional shift through competitive interactions.
To discuss this possible functional role, I added a new paragraph in the Discussion (sixth paragraph), Figure 7, and a section describing the competition model in Materials and methods (subsection “Models for competitive interactions between two stimuli”).
https://doi.org/10.7554/eLife.44098.027Article and author information
Author details
Funding
National Natural Science Foundation of China (Fund for International Young Scientists – 31650110468)
 Sukbin Lim
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
Acknowledgements
The author is grateful to Nicolas Brunel for valuable feedback on the manuscript and discussions with the initial suggestion of the project, David Sheinberg and David Freedman for sharing their data, Loreen Hertäg and Panagiota Theodoni for valuable feedback on the manuscript, John Rinzel for valuable discussion, and anonymous reviewers whose comments helped to improve the manuscript significantly. This research was supported by Research Fund for International Young Scientists at National Natural Science Foundation of China, 31650110468, and the author acknowledges the support of the NYUECNU Institute of Brain and Cognitive Science at NYU Shanghai.
Senior Editor
 Michael J Frank, Brown University, United States
Reviewing Editor
 Nicole Rust, University of Pennsylvania, United States
Publication history
 Received: December 3, 2018
 Accepted: August 7, 2019
 Accepted Manuscript published: August 8, 2019 (version 1)
 Version of Record published: August 27, 2019 (version 2)
Copyright
© 2019, Lim
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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