# Temporal pattern recognition in retinal ganglion cells is mediated by dynamical inhibitory synapses

Simone Ebert, Thomas Buffet, B. Semihcan Sermet, Olivier Marre, Bruno Cessac

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Simone Ebert, Thomas Buffet, B. Semihcan Sermet, Olivier Marre, Bruno Cessac. Temporal pattern recognition in retinal ganglion cells is mediated by dynamical inhibitory synapses. 2023. hal-03939794

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# Temporal pattern recognition in retinal ganglion cells is mediated by dynamical inhibitory synapses

Simone Ebert, Thomas Buffet, B.Semihcan Sermet, Olivier Marre, Bruno Cessac

► To cite this version:

Simone Ebert, Thomas Buffet, B.Semihcan Sermet, Olivier Marre, Bruno Cessac. Temporal pattern recognition in retinal ganglion cells is mediated by dynamical inhibitory synapses. Nature Communications, 2024, 15 (1), pp.6118. 10.1038/s41467-024-50506-7. hal-03939794v2

HAL Id: hal-03939794

https://inria.hal.science/hal-03939794v2

Submitted on 17 Jul 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Temporal pattern recognition in retinal ganglion
cells is mediated by dynamical inhibitory
synapses

Simone Ebert¹⁺, Thomas Buffet²⁺, B.Semihcan Sermet²,³, Olivier Marre²*, and Bruno Cessac¹*

¹Biovision and Neuromod Institute, Université Côte d'Azur,
Sophia Antipolis, France

²Sorbonne Université, INSERM, CNRS, Institut de la Vision, 17
rue Moreau, F-75012 Paris, France

³Present address: Institut Pasteur, Paris, France

*bruno.cessac@inria.fr ; olivier.marre@inserm.fr

+These authors contributed equally to this work.

Abstract

A fundamental task for the brain is to generate predictions of future
sensory inputs, and signal errors in these predictions. Many neurons have
been shown to signal omitted stimuli during periodic stimulation, even
in the retina. However, the mechanisms of this error signaling are un-
clear. Here we show that depressing inhibitory synapses enable the retina
to signal an omitted stimulus in a flash sequence. While ganglion cells,
the retinal output, responded to an omitted flash with a constant latency
over many frequencies of the flash sequence, we found that this was not
the case once inhibition was blocked. We built a simple circuit model
and showed that depressing inhibitory synapses were a necessary com-
ponent to reproduce our experimental findings. We also generated new
predictions with this model, that we confirmed experimentally. Depress-
ing inhibitory synapses could thus be a key component to generate the
predictive responses observed in many brain areas.
Temporal pattern recognition in retinal ganglion
cells is mediated by dynamical inhibitory
synapses

Simone Ebert * †1,2,3, Thomas Buffet3,*, B.Semihcan Sermet ‡3, Olivier Marre §3, and Bruno Cessac§,1,2

Abstract

A fundamental task for the brain is to generate predictions of future
sensory inputs, and signal errors in these predictions. Many neurons have
been shown to signal omitted stimuli during periodic stimulation, even in
the retina. However, the mechanisms of this error signaling are unclear.
Here we show that depressing inhibitory synapses shape the timing of the
response to an omitted stimulus in the retina. While ganglion cells, the
retinal output, responded to an omitted flash with a constant latency over
many frequencies of the flash sequence, we found that this was not the
case once inhibition was blocked. We built a simple circuit model and
showed that depressing inhibitory synapses were a necessary component
to reproduce our experimental findings. A new prediction of our model is
that the accuracy of the constant latency requires a sufficient amount of
flashes in the stimulus, which we could confirm experimentally. Depress-
ing inhibitory synapses could thus be a key component to generate the
predictive responses observed in the retina, and potentially in many brain
areas.

<footnote n="1">¹Université Côte d'Azur, Inria Biovision team, 2004 Rte des Lucioles, 06902 Valbonne, France</footnote>

<footnote n="2">²Institute for Modeling in Neuroscience and Cognition (NeuroMod), Université Côte d'Azur, 28 Av. Valrose, 06100 Nice, France</footnote>

<footnote n="3">³Sorbonne Université, INSERM, CNRS, Institut de la Vision, 17 rue Moreau, F-75012 Paris, France</footnote>

<footnote>*These authors contributed equally to this work.</footnote>

<footnote>†corresponding author: simoneeebert166@gmail.com</footnote>

<footnote>‡Present address: Netherlands Institute for Neuroscience Meibergdreef 47, 1105 BA Ams-
terdam</footnote>

<footnote>§These authors contributed equally to this work.</footnote>
# 1 Introduction

A long standing hypothesis is that visual neurons do not signal the visual scene *per se*, but rather surprising events, eg. mismatches between observation and expectation formed by previous inputs [3]. It has been observed in a number of sensory modalities that neurons strongly respond when a sequence of repetitive stimuli is unexpectedly interrupted [35, 4, 21]. In the retina, this phenomenon has been coined the Omitted Stimulus Response (OSR) [30]. When a periodic sequence of flashes suddenly ends, some ganglion cells emit a large response. Interestingly, the latency of this response shifts with the period of the flash sequence, so that the ganglion cell responds to the omitted flash with a constant latency. This suggests that the retina forms predictions of observed patterns, and responds to a violation of its internal expectation. However, the mechanisms by which the retina achieves this remain unclear and debated [29, 39, 9, 32].

Here we investigated how inhibitory amacrine cells affect the OSR and showed that depression in inhibitory synapses can account for this characteristic latency shift. To this end, we performed electrophysiological recordings of retinal ganglion cells and found that blocking inhibitory transmission from glycinergic amacrine cells selectively abolished the predictive latency shift of the OSR. To better understand how glycinergic inhibition impacts the latency of the OSR, we developed a circuit model equipped with a glycinergic amacrine cell. This model could reproduce the latency shift of the OSR when the glycinergic synapse showed short-term depression, thereby adjusting its weight to the stimulus frequency. Our model generated several predictions about the OSR, which we could confirm in experiments. The latency shift that is characteristic of the OSR is thus due to a depressing inhibitory synapse whose weight is changed by the stimulus frequency. For low frequency sequence, the synaptic weight is large and this increases the latency of the response, while for high frequency stimuli, the weight is low due to depression, and the latency is only shifted by a small amount. Our results suggest a generic circuit to generate responses to surprise that could be implemented in several brain areas.

# 2 Results

## 2.1 ON biphasic ganglion cells exhibit an Omitted Stimulus Response to dark flashes

Using a multi-electrode array of 252 electrodes, we extracellularly recorded the spiking activity of ganglion cells from the mouse retina. [20] (Figure 1 A). We presented sequences of 12 full-field dark flashes of 40 ms duration each, at frequencies of 6, 8, 10, 12 and 16 Hz, with a grey baseline illumination. We estimated the receptive fields of the same retinal ganglion cells with a checkerboard-like noise. We defined ON cells based on their receptive fields (responding to a light increase, 1 B). We focused on the response of ON cells to sequences of dark flashes.
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# 1 Introduction

A long-standing hypothesis is that visual neurons do not signal the visual scene per se, but rather surprising events, eg. mismatches between observation and expectation formed by previous inputs<sup>Barlow1961</sup>. It has been observed in a number of sensory modalities that neurons strongly respond when a sequence of repetitive stimuli is unexpectedly interrupted<sup>Ulanovsky2003, Bullock1994, McAnany2009</sup>.

In the retina, this phenomenon has been coined the Omitted Stimulus Response (OSR)<sup>Schwartz2007a</sup>. When a periodic sequence of flashes suddenly ends, some ganglion cells emit a large response. Interestingly, the latency of this response shifts with the period of the flash sequence, so that the ganglion cell responds to the omitted flash with a constant latency. This suggests that the retina forms predictions of observed patterns, and responds to a violation of its internal expectation. Several studies have proposed potential mechanisms that may underlie this phenomenon, such as oscillatory activity in bipolar cells<sup>Gao2009</sup>, summation of parallel pathways with different response polarities<sup>Werner2008</sup> or response kinetics that respond early and late<sup>Tanaka2019</sup>. The fact that there is a rebound response at the end of the flash sequence can be simply explained by a model with a biphasic filter<sup>Werner2008, Tanaka2019</sup>. Previous work has shown that this rebound response depends on the ON bipolar cell pathway<sup>Schwartz2008</sup>. However, how the latency changes with the period of the sequence, such that the response to the Omitted stimulus has a constant latency, remains unclear. None of the mechanisms proposed so far could be experimentally proven. Thus, the mechanisms by which the retina achieves this latency shift remain unclear and debated.

Here we investigated how inhibitory amacrine cells affect the OSR and showed that depression in inhibitory synapses can account for this characteristic latency shift. To this end, we performed electrophysiological recordings of retinal ganglion cells and found that blocking inhibitory transmission from glycinergic amacrine cells selectively abolished the predictive latency shift of the OSR. We then showed that the latency shift is specific to the periodicity of the stimulus and is not a consequence of stimulus duration or luminance. To better understand how glycinergic inhibition impacts the latency of the OSR, we developed a circuit model equipped with a glycinergic amacrine cell. This model reproduced the latency shift of the OSR when the glycinergic synapse showed short-term depression, thereby adjusting its weight to the stimulus frequency. In addition, our model generated several predictions about the OSR, which we could confirm in experiments. The latency shift that is characteristic of the OSR is thus due to a depressing inhibitory synapse whose weight is changed by the stimulus frequency. For low-frequency sequences, the synaptic weight is large and this increases the latency of the response, while for high-frequency stimuli, the weight is low due to depression, and the latency is only shifted by a small amount. Our results suggest a generic circuit to generate responses to surprise that could be potentially implemented in several brain areas.

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Many ON cells responded with a broad peak of activity after the stimulus stopped for all frequencies tested (n = 74). A subset of these cells (36%, n = 26, fig. 1D, see Methods) shifted the response latency according to the stimulus frequency. They exhibit an "Omitted Stimulus Response" (OSR), as it was first described in [30]: when the period of the flash train increases, the latency of the response to the last flash in the stimulus shifts by the same amount (fig. 1C,D), such that the latency of the response to the omitted stimulus is constant (fig. 1E). This indicates that the retina has a precise temporal expectation of when the next flash should have occurred and shifts the latency of its response accordingly. This is illustrated in fig. 1F, where the relation between the latency of the response and the period of the flash sequence is linear, with a slope of nearly 1 (fig. 1G). In the following we will refer to this specific relation as "latency shift". Interestingly, the ON cells showing this latency shift mostly had a biphasic response profile 1B).

## 2.2 Amacrine cells are required for the latency shift in the Omitted Stimulus Response

It remains unclear how the retinal circuit generates the OSR. Previous studies have shown that the ON bipolar cell pathway is necessary to have a response *per se* [30], but the components of the retinal circuit needed for the latency shift are yet to be determined. We hypothesized that the inhibitory cells of the retinal circuit are responsible for the shift in latency, as inhibition has been shown to shift latency in various circuits [34, 37, 38, 8]. Amacrine cells are the main class of inhibitory interneurons in the mouse retina. To investigate this further, we blocked glycinergic transmission using strychnine (2µM) and recorded the spike responses of retinal ganglion cells to flash trains of varying frequencies (see Methods). As glycinergic transmission is only employed by certain classes of inhibitory amacrine cells in the mouse retina [40] this blocks only a subset of amacrine cells.

While the response after the sequence end remained after strychnine application, we observed that the slope between response latency and stimulus period decreased from an average of 1.13 ± 0.08 in the control condition to 0.07 ± 0.18 after strychnine was added (Figure 1F and G, n = 12, see Methods). While the OSR occurred at roughly the same time in the highest frequency tested, the peak was significantly advanced after low frequency flashes compared to the control condition (Figure 1D). As a consequence, the OSR did not have a constant latency relative to the omitted stimulus after strychnine was added (Figure 1E). These results demonstrate that glycinergic amacrine cells are a key contributor to the OSR. Although they do not generate the response alone, they are crucial for the latency shift, which is a hallmark of the OSR.
## 2 Results

### 2.1 ON ganglion cells exhibit an Omitted Stimulus Response to dark flashes

Using a multi-electrode array of 252 electrodes, we extracellularly recorded the spiking activity of ganglion cells from the mouse retina<sup>Marre2012</sup> (Figure 1 A). We presented sequences of 12 full-field dark flashes of 40 ms duration each, at frequencies of 6, 8, 10, 12 and 16 Hz, with a grey baseline illumination. We estimated the receptive fields of the same retinal ganglion cells with a checkerboard-like noise. We defined ON cells based on their receptive fields (responding to a light increase, 1 B). Previous studies observed an OSR in both ON and OFF retinal ganglion cells. Given that previous pharmacological experiments revealed that ON inputs are necessary to drive an OSR<sup>Schwartz2007a</sup>, we focused on the response of ON cells to sequences of dark flashes.

Many ON cells responded with a broad peak of activity after the stimulus stopped for all frequencies tested ($n = 143$ cells). A subset of cells with response after stimulus end shifted the response latency according to the stimulus frequency (27 %, $n = 40$, fig. 1 D, see Methods). They exhibited an "Omitted Stimulus Response" (OSR), as it was described in<sup>Schwartz2007a</sup>: when the period of the flash train increases, the latency of the response to the last flash in the stimulus shifts by the same amount (Figure 1C,D), such that the latency of the response to the omitted stimulus is constant (Figure 1E). This indicates that a subset of retinal ganglion cells have a temporal expectation of when the next flash should have occurred and shift their response latency accordingly. This is illustrated in Figure 1F, where the relation between the latency of the response and the period of the flash sequence is linear, with a slope of nearly 1 (Figure 1G). In the following we will refer to this specific relation as "latency shift".

To see whether there are ON cells showing this latency shift can be related to a known RGC type, we clustered them according to their response to a full-field 'chirp' stimulation, which reveals response polarity, kinetics and preference to temporal frequencies and contrasts<sup>Baden2016</sup>. We identified roughly 4 different response types which we classified as "ON-transient", "ON-transient-sustained", "ON-sustained" and "ON-OFF" (see Figure S1). This suggests that the OSR is not a response behavior specific to a given cell type but rather exhibited by a broader range of cells. While some cells showed a response to the onset of the flash sequence and/or showed small responses to flashes, the majority of cells did not respond at all to the flashed stimuli (see Figure S1C). Additionally, the total latency between the last flash and the OSR varied substantially between cells, ranging between 142 and 483 ms for the fastest frequency (see Figure S2, right). Even though the omitted stimulus responses occur late for some cells, the latency difference of 120 ms between the fastest and the lowest frequency is very close to the difference in period (110 ms) of these stimuli. For further analysis, we chose to focus on the omitted stimulus response peak characterized by this latency shift, pooling together ON cells of different types.
A

<figure><img src="image_1.png" /></figure>

C

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D

<figure><img src="image_3.png" /></figure>

B

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E

<figure><img src="image_6.png" /></figure>

F

<figure><img src="image_7.png" /></figure>

G

<figure><img src="image_8.png" /></figure>

Figure 1: Glycinergic Amacrine cells are necessary for predictive timing of the OSR. **A.** Schematic representation of the retina, with the activity of retinal ganglion cells being recorded with a multi electrode array. **B.** Temporal traces of the receptive fields of the cells that exhibit an OSR. **C.** Example of OSR. The cell responds to the end on the stimulation, after the last flash. The times of dark flashes are represented by grey shaded rectangles. The black dotted rectangle shows the timing of the omitted flash. The grey dotted rectangle shows the time period of focus in panel D. **D.** Experimental recording of the OSR in one cell in control condition (black) and with strychnine to block glycine amacrine cell transmission (red). Firing rate responses to flash trains of 3 different frequencies are aligned to the last flash of each sequence. Flashes are represented by gray patches, vertical lines indicate the maximum of the response peak, red shaded areas indicate the temporal discrepancy between control and strychnine conditions. **E.** Mean latency between OSR and the omitted flash plotted against the period of the stimulus for a population of *n* = 12 cells. Latency is expressed relatively to the latency of the response to the 16Hz stimulus in the control condition. **F.** Mean latency between OSR and last flash in the stimulus plotted against stimulus period. Control latencies shift with the period of the stimulus with a slope 1.1±0.08. With strychnine this shift is abolished (slope = 0.07±0.18). Latency is expressed relatively to the latency of the response to the 16Hz stimulus in the control condition. **G.** The slope of the latency shift decreases significantly when strychnine is added, p-value = 0.0004 (paired t-test).
## 2.2 Amacrine cells are required for the latency shift in the Omitted Stimulus Response

It remains unclear how the retinal circuit generates an OSR. Previous studies have shown that the ON bipolar cell pathway is necessary to have a response per se$^{Schwartz2007a}$, but the components of the retinal circuit needed for the latency shift are yet to be determined. We hypothesized that the inhibitory cells are responsible for the shift in latency, as inhibition has been shown to shift latency in various neuronal circuits$^{Tsodyks1998, Wehr2003, Wehr2005, Fontaine2014}$. Amacrine cells are the main class of inhibitory interneurons in the mouse retina. To investigate this further, we blocked glycinergic transmission using strychnine ($2\mu M$) and recorded the spike responses of retinal ganglion cells to flash trains of varying frequencies (see Methods). As glycinergic transmission is only employed by certain classes of inhibitory amacrine cells in the mouse retina$^{Waessele2009}$, this blocks only a subset of amacrine cells. In the following, we analyze the effect of strychnine on those ON retinal ganglion cells which exhibited an OSR with latency shift in control conditions.

While the response after the sequence end remained after strychnine application, we observed that the slope between response latency and stimulus period decreased from an average of $1.13 \pm 0.08$ in the control condition to $0.07 \pm 0.18$ after strychnine was added (Figure 1 F and G, mean $\pm$ SEM, $n = 12$, see Methods). While the OSR occurred at roughly the same time in the highest frequency tested, the peak was significantly advanced after low-frequency flashes compared to the control condition (Figure 1 D). As a consequence, the OSR peak did not have a constant latency relative to the omitted stimulus after strychnine was added (Figure 1 E). These results demonstrate that glycinergic amacrine cells are a key contributor to the OSR latency shift. Although they do not generate the response alone, they are crucial for the peak latency shift, which is a hallmark of the OSR. We also looked at the onset time of the OSR response but found that the relation between onset time and stimulus period is highly variable with an average slope of 0.39 (see Figure S3). The effect of glycine application on the onset of the OSR is also highly variable, resulting in a non-significant difference in the slope in control and strychnine conditions. Overall, these results suggest that spiking onset does not contain predictive information about the arrival of the next flash as its timing does not shift in a 1-to-1 manner with the period of the flash train.

## 2.3 Stimulus Luminance has no effect on response latency to opposite polarity stimuli

Previous works have shown that overall changes in luminance or contrast can induce temporal adaptation that could affect ganglion cell responses$^{Oesch2011, Oesch2019}$. To further understand the mechanisms of the OSR, and constrain a model that would reproduce the experimental results, we investigated whether the latency shift of the OSR is really triggered only by the periodicity of the stimulus or if it is affected by other stimulus features. Periodic flash trains of different frequen-
## 2.3 A circuit model with depressing synapses in inhibitory glycinergic amacrine cells explains the latency shift

Our experimental results provided compelling evidence that glycinergic amacrine cells provide inputs which are required to achieve the latency shift of the OSR. However, it remained unclear how the retinal circuit exhibits an OSR in a glycine-dependent way. We developed a mechanistic model in which we explicitly simulated inputs from glycinergic amacrine cells to understand their role in the latency shift of the OSR.

Since we focused on biphasic ON ganglion cells, we equipped our model with two ON inputs, one being excitatory $E^{ON}$ and mimicking ON bipolar cell input, and one being inhibitory $I^{ON}$, conveying broad delayed inhibition. This delayed inhibitory input summarizes the influence of various inhibitory pathways (horizontal cells, GABAergic amacrine cells, ON glycineergic amacrine cells) that generate the biphasic response profile (see discussion). In addition, we explicitly included a glycineergic amacrine cell with an OFF polarity, $I_{Gly}^{OFF}$, in order to provide inhibition to dark stimuli. All three units receive the visual stimulus as input, and connect onto a ganglion cell $G$ (Fig. 2 A, see Methods for details).

A characteristic feature in the Omitted Stimulus Response is that the latency shifts by the same amount as the stimulus period. It has been shown that the relative strengths of excitation and inhibition can determine the latency of the response [34, 37, 38, 8]. We reasoned that the effective strength of the inhibitory input should thus depend on the frequency of the flash sequence. This can be achieved with a dynamic synapse, i.e. a synapse whose strength varies with the frequency of the stimulation.

Several previous reports have shown that inhibitory synapses can be depressing, i.e. have a decreasing weight depending on previous inputs [16, 36, 22, 17, 14]. It has been hypothesized that the variation in synaptic strength results from varying availability of vesicles in the readily releasable vesicle pool, which gets gradually depleted upon persistent inputs [31, 5, 25]. In the retina, this has been modelled via dynamical systems of vesicle pools, where the value of one of the variables directly serves as input to the postsynaptic cell [26, 28]. To keep our model as simple as possible, we modelled the glycineergic synapse as a depressing synapse using one kinetic equation to simulate synaptic vesicle occupancy, similar to cortical models of short-term plasticity [33, 42, 11], but replaced spiking inputs by continuous presynaptic voltage. The vesicle occupancy then scales the output of the cell (see Methods).

This mechanistic model allowed us to reproduce the main properties of the recorded ganglion cells. Thanks to excitatory and inhibitory ON inputs, it has an ON biphasic impulse response. It also responds with a peak at the end of dark periodic flash stimuli, due to delayed disinhibition, because inhibition has a slower temporal filter than excitation (Figure 2 B). Our model also successfully simulated an OSR whose latency with respect to the last flash increased with the stimulus period with a slope around 1, and thus with a constant latency with respect to the omitted stimulus (Figure 2 B and C, black line).
cies are not only characterized by periodicity but also vary in terms of average luminance and duration. As flashes have the same duration of 40 ms across all frequencies but occur in different windows of time, the average illumination and stimulus duration is lower for high than for low frequencies.

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To investigate whether the latency shift of the OSR is simply a consequence of duration or different levels of average luminance, we presented two sets of stimuli: non-flashing dark step-stimuli of different lengths corresponding to the duration of flash trains presented in the control experiments, and non-flashing dark step-stimuli with different luminance levels corresponding to the average luminance during flash trains (Figure 2A,B upper panel). Both stimuli evoked an offset response after stimulus in cells that show an OSR to periodic flashes (Figure 2A,B lower panel), but the latency of this response was nearly equal across all luminance levels and durations tested (Figure 2C). This suggests that the latency shift in the OSR is specific to periodic stimuli and that luminance or duration variations are not sufficient.

We then tested two further modifications of our periodic flash trains in which mean luminance was kept constant across stimulus frequencies (Figure 2D). The first modification was to keep the luminance steady by increasing light intensity in between the dark 40ms flashes, which yielded an OSR with latency shift (Figure 2E, F, G, in blue). This suggests that overall contrast change is not necessary for the latency shift. In the second modification, we kept the average luminance constant by adjusting the duration of the flashes to half of the stimulus period. Surprisingly, we found that changing the duration of the flashes maintains the OSR peak but erases the latency scaling (Figure 2E, F, G, in green). These experimental results suggest that the retina detects periodic patterns but can only form temporal predictions for specific input patterns (see also Schwartz2008).

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Surprisingly, the responses to the stimulus with increased light intensity between the flashes were almost identical to the responses in the control stimulus. To both the control stimulus and the modification, only 4 out of 20 ON cells with OSR showed a response during the stimulus, mostly for low frequencies. We did not identify any quantifiable differences in the OSR response in these two cells compared to the remaining 16 cells that did not respond during the stimulus. Our hypothesis is that the transient increases are either too fast (for high frequencies) or too small (for low frequencies), to evoke a response above threshold.

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## 2.4 A circuit model with depressing synapses in inhibitory glycinergetic amacrine cells explains the latency shift

Our experimental results provided compelling evidence that glycinergetic amacrine cells provide inputs which are required to achieve the latency shift of the OSR and that the latency shift is specific to some stimulus patterns. However, it remained unclear how the retinal circuit achieves such selectivity in a glycinergetic dependent way. We developed a mechanistic model in which we explicitly

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We next simulated the experimental effect of strychnine with the model by removing the glycinergic amacrine cell input. Since the ON inhibitory cell of our model also includes the effect of ON glycinergic amacrine cells, we also decreased the weight of the ON inhibitory input (note however that our results did not depend on that additional modification, see discussion). Figure 2 B and C (red) show that the model replicates the experimental effect of strychnine. The slope of the latency shift decreases from 1.16 to 0.34 when $I_{Gly}^{OFF}$ is removed from the circuit.

To test whether the model achieves the latency shift of the response peak thanks to the dynamical synapse, we simulated the response of the model while keeping the occupancy of the glycinergic amacrine cell synapse constant at 1. (3 A). The latency increased in all frequencies simulated, but the slope of the latency shift decreased to 0.32 (see 3 B-D). In our model, the dynamical synapse is thus essential to achieve the latency shift of the response with a slope of 1 observed experimentally. Note that there was also an overall increase in latency which can be explained by the fact that the fixed synapse is stronger than the dynamic counterpart, since it is never at full occupancy when stimulated due to depression.
simulated evoked inputs from glycinergic amacrine cells to understand their role
in the latency shift of the OSR.

We focused on ON ganglion cells, and equipped our model with two ON
inputs, one being excitatory $E^{ON}$ and mimicking ON bipolar cell input, and
one being inhibitory $I^{ON}$, conveying broad delayed inhibition. This generates a
biphasic response profile needed for a rebound response to dark flashes Werner2008.
This delayed inhibitory input summarizes the influence of various inhibitory
pathways (horizontal cells, GABAergic amacrine cells, ON glycinergic amacrine
cells) that generate the biphasic response profile (see Discussion). In addition,
we explicitly included a glycinergic amacrine cell with an OFF polarity, $I_{Gly}^{OFF}$,
in order to provide inhibition to dark stimuli. All three units receive inputs
from the outer plexiform layer (OPL), which is passed through a nonlinearity
to simulate nonlinear processing in the first synaptic retinal layer. All 3 units
synapse onto a ganglion cell G, where synaptic inputs to G are again passed
through a nonlinearity (Figure 3 A, see Methods for details).

A characteristic feature of the Omitted Stimulus Response is that the latency
shifts by the same amount as the stimulus period. In other contexts, it has been
shown that the relative strengths of excitation and inhibition can determine the
latency of the response Tsodyks1998, Wehr2003, Wehr2005, Fontaine2014. We rea-
soned that the effective strength of the inhibitory input should thus depend
on the frequency of the flash sequence. This can be achieved with a dynamic
synapse, i.e. a synapse whose strength varies with the frequency of the stimu-
lation.

Several previous reports have shown that inhibitory synapses can be depress-
ing, i.e. have a decreasing weight depending on previous inputs Li2007, Vickers2012, Nikolaev2013, Kastner2019, Hua
It has been hypothesized that the variation in synaptic strength results from
varying availability of vesicles in the readily releasable vesicle pool, which gets
gradually depleted upon persistent inputs Singer2006, Burrone2000, Oesch2011. In
the retina, this has been modeled via dynamical systems of vesicle pools, where
the value of one of the variables directly serves as input to the postsynaptic
cell Ozuysal2012, Schroeder2020. To keep our model as simple as possible, we
modeled the glycinergic synapse as a depressing synapse using one kinetic equa-
tion to simulate synaptic vesicle occupancy, similar to cortical models of short-
term plasticity TsodyksMarkram1997, Zhou2012, Henning2013, but replaced spiking
inputs by continuous presynaptic voltage. The vesicle occupancy then scales
the output of the cell (see Methods).

This mechanistic model allowed us to reproduce the main properties of the
recorded ganglion cells. Thanks to excitatory and inhibitory ON inputs, it has
an ON biphasic impulse response. It also responds with a peak at the end of
dark periodic flash stimuli, due to delayed disinhibition, because inhibition has
a slower temporal filter than excitation (Figure 3 B).

Our model also successfully simulated an OSR whose latency with respect
to the last flash increased with the stimulus period with a slope around 1, and
thus with a constant latency with respect to the omitted stimulus (Figure 3 B
and C, black line).

We next simulated the experimental effect of strychnine with the model by
<figure><img src="image_9.png" /><figcaption>Figure 2: Mechanistic model replicates latency shift and strychnine experiment.

**A.** Schematic description of the Model. It is composed of an ON excitatory input $E^{ON}$, an ON inhibitory input $I^{ON}$, and an OFF inhibitory input $I_{Gly}^{OFF}$ representing a glycinergic amacrine cell. Each of those units receives as input the convolution of the stimulus with a monophasic temporal kernel, determining the cells polarity, and connects onto a ganglion cell $G$. The response of $G$ is then passed through a nonlinearity to simulate the cells' firing rate. The synapse from $I_{Gly}^{OFF}$ to $G$ can adapt its strength to the stimulus via short-term depression. The shaded red area represents the weight of this glycinergic amacrine cell being set to zero to simulate the effect of strychnine. **B.** Simulation of the model responses to flash trains of 3 different frequencies with the full model (black, control), and the weight of $I_{Gly}^{OFF}$ set to 0 (red, strychnine). The weight of $I^{ON}$ was decreased in this simulation, accounting for the broad effect of strychnine, which likely reduces inhibition overall. The times of dark flashes are represented by grey shaded rectangles, while the black dotted rectangle shows the timing of the omitted flash. **C.** Latency of the OSR plotted against stimulus period in control and strychnine simulation. The latency is expressed relatively to the latency of the response of the full model to the 16Hz stimulus. The slope of the latency shift decreased from 1.16 to 0.34 when $I_{Gly}^{OFF}$ was set to 0 (dotted lines). **D.** Value of the slope fitted to latency shift in the full model and strychnine simulation.</figcaption></figure>
removing the glycinergic amacrine cell input. Since the ON inhibitory cell of our model also includes the effect of ON glycinergic amacrine cells, we simultaneously decreased the weight of the ON inhibitory input (note however that our results did not depend on that additional modification, see Discussion). Figure 3 B and C (red) show that the model replicates the experimental effect of strychnine. The slope of the latency shift decreases from 1.16 to 0.34 when $I_{\text{Gly}}^{\text{OFF}}$ is removed from the circuit.

To test whether the model achieves the latency shift of the response peak thanks to the dynamical synapse, we simulated the response of the model while keeping the occupancy of the glycinergic amacrine cell synapse constant at 1 (Figure 4 A). The latency increased in all frequencies simulated, but the slope of the latency shift decreased to 0.32 (see Figure 4 B-D). Without the dynamical synapse, the linear filters in the distinct pathways of our model can be summed together to one ON biphasic filter profile. Followed by the non-linearity placed in the ganglion cell our model is equivalent to a LN-model and very similar to the one proposed by Werner2008. However, these models, which are somewhat simplification of ours (they have no dynamical synapse) are not able to predict the latency shift with a slope of 1. The dynamical synapse is thus essential to achieve the latency shift of the response with a slope of 1 observed experimentally. Note that there was also an overall increase in latency which can be explained by the fact that the fixed synapse is stronger than the dynamic counterpart, since it is never at full occupancy when stimulated due to depression.

Additionally, we observed that the OSR amplitude decreased when stimulus frequency increased (Figure S4B). There are no significant changes in this relation after strychnine application, albeit the curve seems slightly flattened. Our model captures this relation accurately (Figure S4A).

Finally, we simulated the model's response to modified flash trains with constant average luminance across periods (Figure 2D). As observed in experiments, the model maintains an OSR with latency shift to periodic flash trains with increased light intensity in interflash-intervals but loses this scaling in response to flash trains where the duration of the flashes is adjusted (see Figure S5).

The model thus captures experimental findings accurately.

## 2.5 The depressing inhibitory synapse induces a latency shift

To understand how the model can account for the latency shift in the OSR, it is helpful to look at the temporal evolution of its internal variables. The ON excitatory input evokes a hyperpolarization in response to dark flashes, and cancels the depolarization evoked by the slightly slower ON inhibitory cells during the flash sequence. At the end of the flash sequence, due to differing time constants, there is a time window where depolarization due to the inhibitory delayed cell exceeds the hyperpolarization due to the bipolar cell, and triggers a spiking response of the retinal ganglion cell (Figure 5 A). This is similar to many classical rebound responses recorded experimentally, and it can be predicted with a biphasic filter. But by itself, this biphasic filter would not predict the
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>Figure 3: Short-term plasticity is the crucial component for latency shift A. Schematic description of the Model, as in Figure 2. The shaded red area now represents removing the dynamic characteristic of the glycinergic synapse. B. Simulation of the Model responses to flash trains of 3 different frequencies with dynamic occupancy (black) and the weight of $I_{Gly}^{OFF}$ held constant (red). The times of dark flashes are represented by grey shaded rectangles, while the black dotted rectangle shows the timing of the omitted flash. C. Latency of the OSR plotted against stimulus period in control and strychnine simulation. The latency is expressed relatively to the latency of the response to the 16Hz stimulus in the control condition. The slope of the latency shift decreased from 1.16 to 0.32 when the weight of $I_{Gly}^{OFF}$ was held constant (dotted lines). D. Value of the slope fitted to latency shift in the full model and without the adaptive property of the glycinergic synapse.</figcaption></figure>
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latency shift as observed experimentally (see above). As we will describe in the following paragraph, this latency shift can be explained thanks to the specific effect of the glycinergic amacrine cell equipped with a depressing synapse.

Since this glycinergic amacrine cell is an OFF cell, it inhibits the ganglion cell in response to dark flashes. This has the effect of delaying the spiking response at the end of the flash sequence and to increase its latency (Figure 5 B, black compared to grey). The latency of the response is then shifted for different stimulus frequencies because the depressing synapse changes the strength of the glycinergic inhibition and the time scale in the response.

In this synapse, the vesicle occupancy represents the amount of synaptic depression and decreases when stimulation starts (Figure 6 A, 3rd row). It then reduces the current input from $I_{\text{Gly}}^{\text{OFF}}$ to the ganglion cell (Figure 6 A, 4th row). This reduction of inhibition shifts the OSR towards an earlier response, reducing its latency (Figure 6 A, 5th row).

Fast-frequency stimuli cause stronger depression, reducing the $I_{\text{Gly}}^{\text{OFF}}$ current input by about 30 %. This has a strong impact on the latency, which is more than 100 ms shorter when the synapse is depressed. In contrast, slow-frequency stimuli cause only weak depression, reducing $I_{\text{Gly}}^{\text{OFF}}$ by about only 10 %. The latency was thus only slightly reduced in that case (compare Figure 6 A and B).

In summary, the steady-state vesicle occupancy of the synapse is determined by the stimulus frequency (Figure 6 C and D). The vesicle occupancy can then reduce the inhibitory current, yielding a large reduction for fast inputs and a small reduction for slow inputs (Figure 6 E). As a result, vesicle occupancy acts as a scaling factor to tune the inhibitory current input and thereby shifts the response latency based on stimulus frequency. This explains how the latency shift observed experimentally is achieved via glycinergic inputs.

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## 2.6 The depressing inhibitory synapse predicts other features of the Omitted Stimulus Response

Can our model give other predictions about the OSR? Since the glycinergic inhibitory synapse is more depressed at high frequency, the OSR is less inhibited, and its amplitude is thus stronger compared to low frequencies (compare Figure 6 A and B, 5th row). This trend was also observed in our experiments. Both simulated and experimental amplitudes showed a negative correlation between the response amplitude and the stimulus period (−0.87 ± 0.02, mean±SEM $n = 14$) in data and as well in simulations (−0.93).

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An important consequence of our depressing synapse model is that it needs several flashes to reach the steady state in the vesicle occupancy. If we shorten the flash sequence, the vesicle occupancy will barely reach that steady state, and this should have predictable consequences on response amplitude and latency. We simulated the response to long flash trains consisting of 12 flashes (as in the experiments and simulations above) and shorter sequences of only 5 flashes.

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Our simulations predicted that the amplitude of the OSR decreases when the stimulus contains only 5 flashes. We tested that in experiments and found the
## 2.4 The depressing inhibitory synapse induces a latency shift

To understand how the model can account for the latency shift in the OSR, it is helpful to look at the temporal evolution of its internal variables. The ON excitatory input evokes a hyperpolarization in response to dark flashes, and cancels the depolarization evoked by the slightly slower ON inhibitory cells during the flash sequence. At the end of the flash sequence, due to differing time constants, there is a time window where depolarization due to the inhibitory delayed cell exceeds the hyperpolarization due to the bipolar cell, and triggers a spiking response (Figure 4 A). This is similar to many classical rebound responses recorded experimentally, and it can be predicted with a biphasic filter. But by itself, this biphasic filter would not predict the latency shift as observed experimentally. As we will describe in the following paragraph, this latency shift is due to the specific effect of the glycinergic amacrine cell equipped with a depressing synapse.

Since this glycinergic amacrine cell is an OFF cell, it inhibits the ganglion cell in response to dark flashes. This has the effect of delaying the spiking response at the end of the flash sequence and to increase its latency (Figure 4 B, black compared to grey). The latency of the response is then shifted for different stimulus frequencies because the depressing synapse changes the strength of the glycinergic inhibition. In this synapse, the vesicle occupancy represents the amount of synaptic depression and decreases when stimulation starts (Figure 5 A, 3rd row). It then reduces the current input from $I_{Gly}^{OFF}$ to the ganglion cell (Figure 5 A, 4th row). This reduction of inhibition shifts the OSR towards an earlier response, reducing its latency (Figure 5 A, 5th row).

Fast frequency stimuli cause stronger depression, reducing the $I_{Gly}^{OFF}$ current input by 30%. This has a strong impact on the latency, which is more than 100 ms shorter when the synapse is depressed. In contrast, slow frequency stimuli cause only weak depression, reducing the $A_{Gly}$ by only 10%. The latency was thus only slightly reduced in that case. (compare 5 A and B).

In summary, the steady state vesicle occupancy of the synapse is determined by the stimulus frequency (5 C and D). The vesicle occupancy can then reduce the inhibitory current, yielding a large reduction for fast inputs and a small reduction for slow inputs (5 E). As a result, vesicle occupancy acts like a scaling factor to tune the inhibitory current input and thereby shifts the response latency based on stimulus frequency. This explains how the latency shift observed experimentally is achieved via glycinergic inputs.
same tendency: the OSR amplitude was smaller in all but the lowest frequency tested (see Figure 7 A)

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Another model prediction was that the slope of the relation between OSR latency and stimulus period should decrease for shorter flash trains, reaching only a value of 0.67 for 5 flashes, compared to 1.16 when 12 flashes were presented (see Figure 7 B, left). In our model, this is a consequence of the dynamics of the depressing synapse.

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In the 5-flashes scenario, our model predicts that the stimulus is too short for the synapse to reach a reliable steady-state occupancy that is not perturbed by the oscillations due to the flashes. (Figure 7 C). This perturbs the response latency scaling and changes the slope of the relation between latency shift and stimulus period (Figure 7 D) for short flash trains.

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In our experiments, while there was no difference for low-frequency stimuli, the absolute latency of the OSR was much larger after 5 flashes than after 12 when the stimulus frequency was high (see Figure 7 B). This change in latency led to a reduction of the mean ± SEM slope value from 0.84±0.02 to 0.69±0.04 in experiments, consistent with the model prediction. These agreements provide further evidence for the validity of our model, and for the key role of a depressing inhibitory synapse.

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# 3 Discussion

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The Omitted Stimulus Response is an example of sophisticated feature detection that takes place already in the retina. This phenomenon implies that retinal ganglion cells can carry a dynamic prediction of their future visual input with high temporal precision, and selectively respond when this prediction is not matched (Figure 8A). Although high-contrast full-field periodic flashes are artificial stimuli that are unlikely to occur in natural scenes, they isolate temporal aspects of visual input patterns. The underlying mechanisms of temporal processing in the rather artificial OSR may be embedded in more complex networks detecting spatiotemporal patterns in more realistic scenes.

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With this work, we provide evidence that the latency shift of the OSR, which allows a constant latency relative to the omitted stimulus, is generated by inhibition from glycineric amacrine cells and triggered by the periodicity of the stimulus. Using computational modeling, we show how inhibition can enable retinal ganglion cells to respond to the missing flash at the end of a sequence. Short-term depression in inhibitory synapses allows shifting the latency of this response (Figure 8B,C).

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Several theoretical models have been proposed to elucidate the mechanisms behind the Omitted Stimulus Response. Werner and Passaglia Werner2008 proposed a dual LN-model with biphasic ON-OFF pathway interactions, which accurately captures the response peak after the stimulus ends via the rebound phase of the pathway selective to the opposite polarity than the stimulus. However, it fails to shift the peak latency as a function of the stimulus period with a slope of 1, which is a defining feature of the OSR. This slope value is necessary
<figure><img src="image_14.png" /><figcaption>Figure 4: ON components of the model produce a peak after stimulus end while the glycinergic OFF input shifts the latency. **A.** - **B.** Internal model responses to a 6 Hz dark flash stimulus. The glycinergic OFF synapse is dynamic. From top to bottom: Stimulus Intensity, Bipolar and Amacrine voltage responses, ganglion cell voltage and firing rate. **A.** ON excitation and inhibition hyperpolarize in response to dark flashes. When both inputs are subtracted in the Ganglion cell, its voltage sum hyperpolarizes during flash presentation, followed by an overshoot of disinhibition due to the slower response profile of the inhibitory input. After passing the voltage through a rectification function, only the disinhibitory peak after stimulus end remains in the firing rate. **B.** The voltage of the glycinergic OFF input depolarizes in response to dark flashes, passing additional inhibition onto the ganglion cell. This lowers the GC voltage response and increases the latency between peak and stimulus end in the firing rate. Last two panels compare the models' simulation and peak time-point with (black) and without (grey) the input from $I_{Gly}^{OFF}$.</figcaption></figure>
to have a response of constant latency with respect to the omitted stimulus. When removing the depressing synapse, our model is amenable to a biphasic LN model, since the responses of our intermediate units are then linear and could be represented by a single linear filter as well. Our model then simulates the OSR in the same manner as this previous study, but the depressing inhibitory synapse was necessary to obtain the slope of 1, which is the signature of a predictive latency shift.

Gao and Berry*Gao2009* proposed intrinsic oscillatory activity in ON bipolar cells that evoked a latency shift via resonance tuned to the stimulus frequency. However, such oscillatory activity was not found in bipolar cells*Deshmukh2019*. Further, our experiments show that glycinergic amacrine inhibition is necessary for the latency scaling of the OSR, which cannot be explained by this model.

More recently, Tanaka et al.*Tanaka2019* proposed that the OSR with its latency shift can arise in a deep neural network model via summation of multiple excitatory inputs with different time constants. It is difficult to evaluate whether the model accurately captures the latency shift as observed in experiments, with the correct slope value. The explanation behind this model is that the OSR latency is determined by the sum of 2 ON bipolar cells which are activated only by certain stimulus frequencies due to different temporal filtering. This purely excitatory mechanism of latency scaling is not in line with our experimental findings, suggesting that amacrine cells likely contribute to temporal filtering as well. Our hypothesis is thus that the components they isolated correspond to a mix of bipolar and amacrine cell properties.

In contrast to those previous models of the OSR, we explicitly included an inhibitory input whose contribution to the peak latency is dependent on the stimulus frequency via short-term plasticity. By doing so, we can propose a mechanistic explanation and match the latency shift of the OSR as well as various other response properties of the experimentally observed OSR.

Previous experimental studies*Schwartz2007a, Schwartz2008, Werner2008* reported that the OSR is found in a higher proportion of retinal ganglion cells than what we experimentally observed in this study. This difference could come from the fact that we define OSR as a response with a latency shift having a slope of at least 0.7, while it is not clear whether previous studies took multiple frequencies into account when classifying the OSR. Schwartz et al.*Schwartz2008* also showed that blocking inhibition from amacrine cells had no effect on the OSR. But again, this study only investigated the presence or absence of the OSR under amacrine blockade, and did not investigate if the latency of the OSR shifted with the stimulus frequency. In addition, some previous studies were mostly carried out in salamander*Schwartz2007a, Schwartz2008*, where the underlying mechanisms may be different from the mouse.

In order to realistically simulate the model's response with glycinergic amacrine cells blocked, we had to decrease the weight of the inhibitory ON input $I_{ON}$ in our simulations. Leaving the weight of this input untouched while setting $w_{I_{OFF}}$ to 0, we still obtain a decrease in latency shift but this configuration generated a response to each flash of the sequence, something we did not observe.
<figure><img src="image_15.png" /><figcaption>Figure 5: Synaptic depression scales OFF glycinergic input to stimulus frequency and thereby shifts the latency of the response. **A.** Impact of occupancy scaling on $I_{Gly}^{OFF}$ current input to G for a fast (16 Hz, left) and a slow (6 Hz, right) stimulus. From top to bottom: Stimulus Intensity, $I_{Gly}^{OFF}$ voltage, vescile occupancy, current input, G voltage and firing rate. Last 3 panels compare simulations with dynamic occupancy (solid lines) to when the occupancy is held constant (dotted lines). Depression has the effect to advance the OSR peak, more so for fast than slow frequencies. **B.** Occupancy traces to flash stimuli of different frequencies aligned to the last flash. Dots indicate the occupancy level at stimulus end. **C.** Level of occupancy after stimulus end scales with the period of the stimulus. **D.** $I_{Gly}^{OFF}$ current input is decreased by short-term depression, more so for fast than slow frequencies. Dotted line shows current with fixed occupancy, solid line with dynamic occupancy.</figcaption></figure>
experimentally. We therefore deemed this configuration as less realistic than decreasing also the weight of the ON inhibitory cell, since strychnine is likely to affect glycinergic ON inhibition as well. Additionally, the components of our circuit might represent several cell types pooled together, and more detailed circuit models might give similar predictions. For example, we chose to simulate synaptic depression via a modified version of cortical STP-models with only 2 parameters rather than the more complex systems used in the retina previously Schröeder2020. Overall, we chose to only include the minimal components necessary to specifically explain the peak latency shift in the OSR and its abolishment via strychnine and arrived at a model with (still) 19 parameters.

In addition, bath application of strychnine acts on the whole retinal network and likely has side effects such as changes (increases) in the baseline activity across bipolar, other amacrine and ganglion cells due to a reduction of maintained inhibition. However, these maintained effects, although they would likely decrease absolute latencies, should not depend on the stimulus and are thus unlikely to explain changes in the latency shift relative to stimulus period. For simplicity, we thus do not take these side effects into account in our modeling approach and only simulate the minimal amount of direct inputs we found necessary for an OSR with latency shift.

Our present model accounts only for an OSR to dark-type flashes in ON cells. It has however been reported as well that OFF cells emit a similar response after cessation of OFF-type stimulation which our model as it is does not explain. This could be obtained by adding another independent OFF pathway that would deliver an input to the same ganglion cell. This pathway would trigger a response during the flashes, while the circuit described in our model would generate an OSR that scales with latency.

We experimentally identified an important role for glycinergic inhibition in the latency shift of the OSR in experiments. The role of GABAergic inhibition in generating the OSR is less clear. In principle, depressing GABAergic synapses could play a similar role as glycinergic synapses or be the source of disinhibition needed for the rebound response. We tried to block GABAergic inputs with Gabazine to test this hypothesis experimentally. We indeed found a small number of cells that also lost their latency scaling and others that lost the entire OSR after application of gabazine (data not shown), supporting both hypotheses. However, we observed a large heterogeneity in the effect of gabazine on the OSR across experiments, so these results remain inconclusive (see Figure S7.

In this study, we focused on the OSR defined as the response to the abrupt cessation of a periodic stimulus, following several previous studies Schwartz2007a, Werner2008, Schwartz2008, Gao2008. It has however been shown that retinal ganglion cells in both mouse and salamander emit an OSR to more complex pattern violations, for example in response to an omission in the middle of a periodic stimulus sequence Schwartz2007a, which we did not test here. We would expect to observe such a response if the overall latency of the OSR for a given frequency was shorter than twice the stimulus period. In a stimulus where one flash is omitted in the middle of a sequence, this would allow for the OSR to signal this omission before flash
## 2.5 The depressing inhibitory synapse predicts other features of the Omitted Stimulus Response

Can our model give other predictions about the OSR? Since the glycinergic inhibitory synapse is more depressed at high frequency, the OSR is less inhibited, and its amplitude is thus stronger compared to low frequencies (compare Figure 5 A and B, 5th row). This trend was also observed in our experiments. Both simulated and experimental amplitudes showed a negative correlation between the response amplitude and the stimulus period ($-0.87 \pm 0.02$, *n* = 14) in data and as well $-0.87$ in simulations).

An important consequence of our depressing synapse model is that it takes several flashes to reach steady state in the vesicle occupancy. If we shorten the flash sequence, the vesicle occupancy will not reach that steady state, and this should have predictable consequences on response amplitude and latency. We simulated the response to long flash trains consisting of 12 flashes (as in the experiments and simulations above) and shorter sequences of only 5 flashes.

Our simulations predicted that the amplitude of the OSR decreases when the stimulus contains only 5 flashes. We tested that in experiments and found the same tendency: the OSR amplitude was significantly smaller in all but the lowest frequency tested (see Figure 6 A).

Another model prediction was that the slope of the relation between OSR latency and stimulus period should decrease for shorter flash trains, reaching only a value of 0.67 for 5 flashes, compared to 1.16 when 12 flashes were presented (see Figure 6 B, left). In our model, this is a consequence of the dynamics of the depressing synapse.

In the 5-flash scenario, our model predicted that the stimulus is too short for the synapse to reach a steady state occupancy when the stimulus frequency is high (Figure 6 C). $I_{Gly}^{OFF}$ hence provides a larger inhibitory input than for a longer sequence. This increases the response latency and changes the slope of the relation between latency shift and stimulus period (Figure 6 D).

In our experiments, while there was no difference for low frequency stimuli, the absolute latency of the OSR was much larger after 5 flashes than after 12 when the stimulus frequency was high (see Figure 6 B). This change in latency led to a reduction of the slope value from $0.84 \pm 0.02$ to $0.69 \pm 0.04$ in experiments, consistent with the model prediction. The agreements between the model predictions and experiments provide further evidence for the validity of our model, and for the key role of a depressing inhibitory synapse.
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sequence continues. According to absolute latencies of cells recorded in this study, several cells should signal omissions in the middle of a flash stimulus up to frequencies of 12 Hz. (see Figure S7).

Dynamical synapses have previously been proposed to enable neuronal circuits in the retina to form expectations of future inputs$^{Hosoya2005Johnston2019}$ and are thus a plausible candidate to play an important role in the OSR. Previous works have shown that inhibitory synapses can be depressing$^{Kastner2011, Kastner2013b, Nikolaev2013}$. In particular, glycinergic synapses that input to bipolar cells can be depressing$^{Huang2022}$. However, there is no method to experimentally remove the depressing nature of the synapse without affecting the inhibitory weight, so we could not show experimentally that the depressing nature of the synapse is necessary for the OSR.

Adaptation in excitatory ribbon synapses is a well-studied phenomenon to reliably encode luminance and contrast and could be the source of the OSR latency shift as well. While a more simple model with depression in bipolar cell terminals can provide an OSR with latency shift as well (see Figure S6), such a model is not congruent with our findings that stimulus luminance and contrast are neither necessary nor sufficient for the OSR latency shift and cannot readily explain our experimental observations under strychnine. While it has been shown that GABAergic inhibition modulates gain changes in ribbon synapses$^{Oesch2019}$, glycinergic effects at this stage have not been observed so far. Therefore we conclude that, even though plasticity in bipolar cells certainly plays an important role in retinal computations, the idea of inhibitory plasticity provides a simpler explanation of this specific phenomenon.

In addition, our model predicts that the depressing inhibitory synapse should have several functional consequences, that we verified in the data. In particular, a key prediction of the depressing synapse is that the OSR requires a long enough flash sequence to accurately shift the latency and we confirmed this prediction experimentally.

Ultimately, our results might be of relevance to understanding neuronal mechanisms of predictive coding beyond the retina. Very similar surprise responses exist in other sensory domains, such as the mismatch negativity response in the auditory cortex$^{Naatanen1993, Garrido2009, Ulanovsky2003, Li2017}$, where neural activity is enhanced following a "deviant" tone in a sequence of "standard" tones. A recent study suggested that synaptic adaptation could be a key contributor to this phenomenon$^{Amsalem2020}$. Following the predictive coding theory, one possible explanation is that this response emerges from an interaction between feed-forward and feedback connectivity$^{Rao1999, Millidge2021}$.

Here we show that a purely feed-forward micro-circuit can generate this response to a violation of prediction via an interplay of excitation and inhibition, where synaptic depression takes place in inhibitory connections. All the components used in this micro-circuit are generic and can be found in other sensory areas$^{Deneve2016, TsodyksMarkram1997, Abbott1997}$, and it is thus likely that a similar circuit could be at work at the cortical level, for more complex pattern recognition than full-field flashes.
<figure><img src="image_16.png" /><figcaption>Figure 6: Latency shift decreases for shorter stimuli because of lacking steady state occupancy. A. Amplitude of the OSR against stimulus period for 12 and 5 flashes in the stimulus in simulations (left) and experiments (right). Amplitudes to 6 Hz and 10 Hz stimuli were significantly different after Bonferroni-Holm correction [12] (6 Hz: *p* = 0.000006, 10 Hz: *p* = 0.001). B. Latency against stimulus period in simulations (left) and experiments (right). Simulated slopes decreased from 1.16 after 12 flashes to 0.67 after 5 flashes. Experimental slopes decreased from 0.84±0.02 to 0.69±0.04. The latency after 12 and 5 flashes was significantly different for 10 Hz (*p* = 0.03), 12 Hz (*p* = 0.04) and 16 Hz stimuli (*p* = 0.02). C. Temporal traces of vesicle occupancy to all frequencies simulated, for 12 Flashes (upper) and 5 Flashes (lower). Dots indicate occupancy at stimulus end. Traces do not reach a steady state for 5 flashes. D. Scaling of occupancy with stimulus period in 5- and 12-flash scenario.</figcaption></figure>

**3 Discussion**

The Omitted Stimulus Response is an example of sophisticated feature detection that takes place already in the retina. This phenomenon implies that retinal ganglion cells can carry a dynamic prediction of their future visual input with high temporal precision, and selectively respond when this prediction is not matched.

With this work, we provide evidence that the latency shift of the OSR, which allows a constant latency relative to the omitted stimulus, is generated by inhibition from glycinergic amacrine cells. Using computational modelling, we show how inhibition can enable retinal ganglion cells to respond to the missing flash at the end of a sequence. Short-term depression in inhibitory synapses allows shifting the latency of this response.
# 4 Methods

## 4.1 Experimental Setup

### 4.1.1 Recordings

Recordings were performed on isolated retinas from 8 C57BL6/J adult mice aged between 2 and 7 months. Strychnine Experiments were performed on two males (age 84 and 52 days) and one female (85 days). Luminance experiments were performed on two retinas from one female (161 days). Gabazine experiments were performed on two females (58 and 163 days) and one male (185 days). Experiment with different flashnumbers was performed one a female mouse (30 days). The animals were housed in enriched cages with ad libitum food, and watering. The ambient temperature was between 22 and 25 C, the humidity was between 50 and 70% and the light cycle was 12-14h of light, 10-12h of darkness. Animals were killed according to institutional animal care standards of Sorbonne Université. The retina was isolated from the eye under dim illumination and transferred as quickly as possible into oxygenated Ames' medium (Merck, A1420). The retina was extracted from the eye cup and lowered with the ganglion cell side against a multi-electrode array whose electrodes were spaced by 30 µm<sup>Marre2012</sup>. During the recordings, the Ames' medium temperature was maintained at 37°C. Raw voltage traces were digitized and stored for off-line analysis using a 252-channel preamplifier (MultiChannel Systems, Germany) at a sampling frequency of 20kHz. The activity of single neurons was obtained using Spyking Circus V 1.1.0, a custom spike sorting software developed specifically for these arrays<sup>Yger2018</sup>.

### 4.1.2 Visual stimulation

Visual stimuli were presented using a white LED and a Digital Mirror Device (DMD). Flash sequences contained 5 or 12 flashes of 5 different frequencies (6Hz, 8Hz, 10Hz, 12Hz, 16Hz). Polarities were either switched from grey to black (dark flashes) or from grey to white (bright flashes). 60 trials were conducted for each stimulus, with 2-4 s between each trial. The order of magnitude of the background illumination was $10^6$ R*.

### 4.1.3 Spike Triggered Average

We displayed a random binary checkerboard during 40 min to 1h at 40 Hz to map the receptive fields of ganglion cells. A three dimensional STA (x, y and time) was sampled averaging over the stimulus preceding each spike for a time window of 1 s, divided into N = 40 time bins. Temporal and spatial components were isolated via Singular Value decomposition and reconstructed from Eigenvectors. STA analysis was carried out in Python.
Previous experimental studies [30, 29, 39] reported that the OSR is found
in a higher proportion of retinal ganglion cells than what we observed in this
study. This difference could come from the fact that we define OSR as a response
with a latency shift having a slope of at least 0.7, while it is not clear whether
previous studies took multiple frequencies into account when classifying the
OSR. Schwartz et al. [29] also showed that blocking inhibition from amacrine
cells had no effect on the OSR. But again, this study only investigated the
presence or absence of the OSR under amacrine blockade, and did not investigate
if the latency of the OSR shifted with the stimulus frequency. In addition, some
previous studies were mostly carried out in salamander, where the underlying
mechanisms may be different from the mouse.

Several theoretical models have been proposed to elucidate the mechanisms
behind the Omitted Stimulus Response. Werner and Passaglia [39] proposed a
dual LN-model with biphasic ON-OFF pathway interactions, which accurately
captures the response peak after stimulus end via the rebound phase of the
pathway selective to the opposite polarity than the stimulus. However, it fails
to shift the peak latency as a function of the stimulus period with a slope of 1,
which is a defining feature of the OSR. This slope value is necessary to have a
response of constant latency with respect to the omitted stimulus.

A slope value of 1 indicates that the cell responds with a constant latency to the omitted stimulus, while a slope value of 0 indicates a response with a constant latency relative to the last flash. This slope value is thus a defining feature of the OSR.

When removing the depressing synapse, our model is amenable to a biphasic
LN model, since the responses of our intermediate units are then linear and could
be represented by a single linear filter as well. Our model then simulates the
OSR in the same manner as this previous study, but the depressing inhibitory
synapse was necessary to obtain the slope of 1, which is the signature of a
predictive latency shift.

Gao and Berry [9] proposed intrinsic oscillatory activity in ON bipolar cells that evoked a latency shift via resonance tuned to the stimulus frequency. However, such oscillatory activity was not found in bipolar cells [7]. Our experiments where we blocked glycinergic transmission, while leaving bipolar cells intact, show that intrinsic properties of bipolar cells are not sufficient to generate a predictive latency shift.

More recently, Tanaka et al. [32] proposed that the OSR with its latency shift
can arise in a deep neural network model via summation of multiple excitatory
inputs with different time constants. It is difficult to evaluate whether the
model accurately captures the latency shift as observed in experiments, with
the correct slope value. The explanation behind this model is that the OSR
latency is determined by the sum of 2 ON bipolar cells which are activated only
by certain stimulus frequencies due to different temporal filtering. This purely
excitatory mechanism of latency scaling is not in line with our experimental
findings, suggesting that amacrine cells likely contribute to temporal filtering as
well. Our hypothesis is thus that the components they isolated correspond to a
mix of bipolar and amacrine cell properties.
### 4.1.4 Pharmacology

To block glycinergic transmission, we dissolved strychnine (Sigma-Aldrich, S8753) in Ames' medium at a concentration of 2µM, and perfused the retina with the solution at least 15 minutes before the recording.

### 4.1.5 Latency Analysis

To determine slope of latency shift, we measured the latency between the peak firing rate and the end of the last flash in the stimulus for all frequencies tested. We plotted these latencies against the respective period of the stimulus and fitted a straight line to determine the slope of the latency shift using SciPy's optimization package SciPy2020. Cells where classified as having an OSR in the control condition when the slope what at least 0.7 or higher. All cells where the peak time point could not be unambiguously determined in any condition were excluded from the analysis.

### 4.1.6 Statistical Analysis

Statistical testing was performed using SciPy's stats package SciPy2020. Welch's t-test for independent samples with unequal variance was used for slope comparisons between conditions. For comparison of amplitudes and latencies between different flash numbers, paired two-sided t-tests with Bonferroni-Holm correction were used such that significance levels $\alpha$ were adjusted to $\frac{\alpha}{m+1-k}$ for the $k^{th}$ p-value of $m$ total comparisons. Pearson correlation coefficients were calculated using Python's numpy build-in functions.

## 4.2 Modeling

### 4.2.1 Model Implementation

The 3 pathways of Fig. 3 receive an input from the Outer Plexiform Layer (OPL) written as a temporal convolution of the OSR stimulus, $s(t)$ (dimensionless), with a linear filter of the form:

$$ \alpha(t) = \frac{t}{\tau_{OPL}^2} \exp(-\frac{t}{\tau_{OPL}}) H(t), \quad (1) $$

where $\tau_{OPL}$ is the characteristic time of integration (in $s$) in photoreceptors and $H(t)$ the Heaviside function.

Thus, the output of the OPL reads:

$$ F(t) = [\alpha * s](t), \quad (2) $$

where $*$ is the space-time convolution. Note that, the stimulus being spatially uniform, the space integration reduces to a constant, so that the detailed shape of the spatial RF plays a trivial role here.
In contrast to those previous models of the OSR, we explicitly included an inhibitory input whose contribution to the peak latency is dependent on the stimulus frequency via short-term plasticity. By doing so, we can propose a mechanistic explanation and match the latency shift of the OSR as well as various other response properties of the experimentally observed OSR.

In order to realistically simulate the models response with glycinergic amacrine cells blocked, we had to decrease the weight of the inhibitory ON input $I_{ON}$ in our simulations. Leaving the weight of this input untouched while setting $w_{Gly}^{OFF}$ to 0, we still obtain a decrease in latency shift but this configuration generated a response to each flash of the sequence, something we did not observe experimentally. We therefore deemed this configuration as less realistic than decreasing also the weight of the ON inhibitory cell, since strychnine is likely to affect glycinergic ON inhibition as well. The components of our circuit might represent several cell types pooled together, and more detailed circuit models might give similar predictions. For example, we chose to simulate synaptic depression via a modified version of cortical STP-models with only 2 parameter rather than the more complex systems used in the retina previously [28]. We aimed at finding the minimal components necessary to obtain our results.

Dynamical synapses have previously been proposed to enable neuronal circuits in the retina to form expectations of future inputs [13] and are thus a plausible candidate to play an important role in the OSR. Previous works have shown that inhibitory synapses can be depressing [16, 15, 23]. In particular, glycinergic synapses that input to bipolar cells can be depressing [14]. However, there is no method to experimentally remove the depressing nature of the synapse without affecting the inhibitory weight, so we could not show experimentally that the depressing nature of the synapse is necessary to the OSR. However, our model predicted that the depressing inhibitory synapse should have several functional consequences, that we verified in the data. In particular, a key prediction of the depressing synapse is that the OSR requires a long enough flash sequence to accurately shift the latency, which coincides with the time needed to reach a steady state in the synaptic weights, and we confirmed this prediction experimentally.

Ultimately, our results might be of relevance to understand neuronal mechanisms of predictive coding beyond the retina. Very similar surprise responses exist in other sensory domains, such as the mismatch negativity response in the auditory cortex [24, 10, 35, 19], where neural activity is enhanced following a 'deviant' tone in a sequence of 'standard' tones. A recent study suggested that synaptic adaptation could be a key contributor to this phenomenon [2]. Following the predictive coding theory, one possible explanation is that this response emerges from an interaction between feed-forward and feedback connectivity [27, 22]. Here we show that a purely feed-forward micro-circuit can generate this response to a violation of prediction via an interplay of excitation and inhibition, where synaptic depression takes place in inhibitory connections. All the components used in this micro-circuit are generic and can be found in other sensory areas [6], [33], [1], and it is thus likely that a similar circuit could be at
The OPL response is then passed through a sigmoidal nonlinarity to account for nonlinear processing steps in early bipolar cell processing, given by:

$$ \sigma_{ab}(F) = \frac{S_X}{1 + e^{-a(F-b)}} \qquad (3) $$

where a and b are parameter defining the shape of the nonlinearity (they depend on X but we didn't add this dependence to alleviate notations). $|S_X| = \frac{S_{mV}}{\tau_X}$ is a scale factor which scales the input into each unit to $\frac{mV}{s}$ via $S_{mV} = 20mV$ and the time constant $\tau_X$ of each unit, such that the amplitude of the response is normalized to the time constant of the respective unit. For OFF cells, the OPL inputs are multiplied by -1 before rectification to reverse polarity. The rectified signal is then integrated into each pathways via a linear dynamical system:

$$ \frac{dV_X}{dt} = -\frac{V_X}{\tau_X} + \sigma_{ab}(F(t)), \quad X = E^{\text{ON}}, I^{\text{ON}}, I_{\text{Gly}}^{\text{OFF}}. \qquad (4) $$

where $V_X$ is the voltage of cell X (in Volt) and $\tau_X$ its characteristic time constant (in s). The Current $I_X$ of unit X is computed as

$$ I_X = \frac{w_X p_\theta(V_X)}{c_m} \qquad (5) $$

with a membrane capacitance set to $c_m = 0.1nF$.

Note that this dynamical system is non autonomous as $F(t)$, the input, explicitly depends on time.

Next, all pathways provide input to the ganglion cell G:

$$ \frac{dV_G}{dt} = -\frac{V_G}{\tau_G} + w_{\text{EON}}p_{\theta}(V_{\text{EON}}) + n w_{\text{I}^{\text{OFF}}_{\text{Gly}}}p_{\theta}(V_{\text{I}^{\text{OFF}}_{\text{Gly}}}) + w_{\text{ION}}p_{\theta}(V_{\text{ION}}). \qquad (6) $$

where $w_{\text{EON}}, w_{\text{I}^{\text{OFF}}_{\text{Gly}}}, w_{\text{ION}}$ are synaptic weights (in Hz). Voltages are rectified before integrated in the ganglion cell membrane potential via:

$$ p_{\theta}(V) = \begin{cases} V - \theta & \text{if } V \geq \theta : \\ 0 & \text{otherwise.} \end{cases} \qquad (7) $$

where $\theta$ is a threshold (in V) that differs between pathways.

The synaptic weight from $I_{\text{Gly}}^{\text{OFF}}$ to G is modulated by a dimensionless variable $n$, used to simulate synaptic short-term plasticity. $n$, which interprets as a vesicle occupancy in the glycergic amacrine synapse, obeys the kinetic equation Henning2013 :

$$ \frac{dn}{dt} = (1 - n)k_{\text{rec}} - \beta k_{\text{rel}} p(V_{\text{I}^{\text{OFF}}_{\text{Gly}}}, \theta_{\text{I}^{\text{OFF}}_{\text{Gly}}})n. \qquad (8) $$

$k_{\text{rec}}$ and $k_{\text{rel}}$ are rate constants (in Hz) for vesicle release and replenishment and $\beta$ (in $V^{-1}$) is a scaling factor. Finally, the voltage response is passed through the piece-wise linear function $p$ to obtain the firing rate:

$$ R(t) = s_G p(V_G(t), \theta_G), \qquad (9) $$
work at the cortical level, for more complex pattern recognition than full-field
flashes.

# 4 Methods and Materials

## 4.1 Experimental Setup

### 4.1.1 Recordings

Recordings were performed on C57BL6/J adult mice of either sex. Animals were killed according to institutional animal care standards. The retina was isolated from the eye under dim illumination and transferred as quickly as possible into oxygenated Ames' medium (Merck, A1420). The retina was extracted from the eye cup and lowered with the ganglion cell side against a multi-electrode array whose electrodes were spaced by 30µm, as previously described. [20] During the recordings, the Ames' medium temperature was maintained at 37°C. Raw voltage traces were digitized and stored for off-line analysis using a 252-channel preamplifier (MultiChannel Systems, Germany) at a sampling frequency of 20kHz. The activity of single neurons was obtained using Spyking Circus, a custom spike sorting software developed specifically for these arrays. [41]

### 4.1.2 Visual stimulation

Visual stimuli were presented using a white LED and a Digital Mirror Device (DMD). Flash sequences contained 5 or 12 flashes of 5 different frequencies (6Hz, 8Hz,10Hz,12Hz,16Hz). Polarities were either switched from grey to black (dark flashes) or from grey to white (bright flashes). 60 trials were conducted for each stimulus, with 2-4s between each trial. The order of magnitude of the background illumination was 10⁶ R*.

### 4.1.3 Pharmacology

To block glycinergic transmission, we dissolved strychnine (Sigma-Aldrich, S8753) in Ames' medium at a concentration of 2µM, and perfused the retina with the solution at least 15 minutes before the recording.

### 4.1.4 Latency Analysis

To determine slope of latency shift, we measured the latency between the peak firing rate and the end of the last flash in the stimulus for all frequencies tested. We plotted these latencies against the respective period of the stimulus and fitted a straight line to determine the slope of the latency shift. Cells where classified as having an OSR in the control condition when the slope was at least 0.7 or higher. All cells where the peak time point could not be unambiguously determined in any condition were excluded from the analysis.
where $s_G$ is a scaling factor. The model was implemented with custom Python code.

### 4.2.2 Parameter Optimization

First, time constants and weights were fitted such that the linear response $V_G$ of the model (without nonlinearities) to an impulse stimulus best resembles the temporal STA of one example cell with OSR. This was done using an evolutionary optimization algorithm using the CMAES (Covariance Matrix Adaptation Evolutionary Strategy) Python toolbox$^{Hansen2019}$. Synaptic plasticity is removed from the model by setting $\beta = 0$. The slope of the ganglion cell nonlinearity $S_G$ was then chosen as to match experimentally observed firing rates. Parameters of the occupancy equation (8) were manually chosen as to yield a slope of 1. Thresholds for synaptic rectifications were calculated such that the rest potential of G remained at 0 without input. Slopes and thresholds for non-linear processing within units were manually chosen. Values were obtained by screening over a wide range of combinations of $\beta$ and the ratio of recovery and release rate $\frac{k_{rec}}{k_{rel}}$. All parameters used in the simulations are listed in Table 1.

## 5 Data Availability

The data generated in this study have been deposited in the Zenodo database under access code 10.5281/zenodo.11396185. Due to large file sizes, raw datasets are available from the corresponding author upon request. Source data for all Figures are provided with this paper.

## 6 Code Availability

The code used for the computational model is accessible on gitlab.

## 7 Acknowledgments

We thank Romain Brette, Matthias Henning and Romain Veltz for helpful discussions about the model, and Matias Goldin and Brice Bathellier for critical reading of the manuscript. We thank Giulia Spampinato for allowing us to use her excellent artwork. This work has been funded by a PhD fellowship from the interdisciplinary Institute for Modeling in Neuroscience and Cognition (NeuroMod) of Université Côte d'Azur to S.E., funded by the National Research Agency (ANR-15- IDEX-01) and, by an ERC grant (No 101045253, DEEP-RETINA) to O.M., ANR grants (DECORE, ANR-18-CE37-0011, and PerBaCo, ANR-22-CE37-0016-02) to O.M., a grant from Retina France to O.M., and ANR ShootingStar (ANR-20-CE37-0018-04) to O.M. and B.C. T.B. was funded by a PhD fellowship from ENS and supported by the Fondation pour la Recherche Médicale, grant number FDT202304016465.
## 4.2 Modeling

The 3 pathways of Fig. 2 receive an input from the Outer Plexiform Layer (OPL) written as a temporal convolution of the OSR stimulus, $s(t)$ with a linear filter of the form:

$$ \alpha_X(t) = \frac{t}{\tau_X^2} \exp(-\frac{t}{\tau_X}) H(t), \quad X = E^{ON}, I^{ON}, I_{Gly}^{OFF}, \quad (1) $$

where $\tau_X$ is cell X characteristic time of integration (in $s$) and $H(t)$ the Heaviside function.

Thus, the inputs read:

$$ F_X(t) = S_X[\alpha_X * s](t) \quad (2) $$

where $S_X$ is a scale factor and * the space-time convolution. If $S_X$ is negative, $X$ is an OFF cell. Note that, the stimulus being spatially uniform, the space integration reduces to a constant, so that the detailed shape of the spatial RF plays a trivial role. The OPL response is then integrated into all pathways via a linear dynamical system:

$$ \frac{dV_X}{dt} = -\frac{V_X}{\tau_X} + F_X(t), \quad X = E^{ON}, I^{ON}, I_{Gly}^{OFF}. \quad (3) $$

where $V_X$ is the voltage of cell X (in Volt).

Next, all pathways provide input to the ganglion cell $G$:

$$ \frac{dV_G}{dt} = -\frac{V_G}{\tau_G} + w_{E^{ON}} V_{E^{ON}} + n w_{I_{Gly}^{OFF}} p(V_{I_{Gly}^{OFF}}, \theta_{I_{Gly}^{OFF}}) + w_{I^{ON}} V_{I^{ON}}. \quad (4) $$

where $w_{E^{ON}}, w_{I_{Gly}^{OFF}}, w_{I^{ON}}$ are synaptic weights (in Hz). Voltages are rectified before integrated in the ganglion cell membrane potential via:

$$ p(V, \theta) = \begin{cases} V - \theta; & \text{if } V \ge \theta \\ 0; & \text{otherwise.} \end{cases} \quad (5) $$

where $\theta$ is a threshold (in Volts).

The synaptic weight from $I_{Gly}^{OFF}$ to $G$ is modulated by a dimensionless variable $n$, used to simulate synaptic short-term plasticity. $n$, which interprets as a vesicle occupancy in the glycinergic amacrine synapse, obeys the kinetic equation [11]:

$$ \frac{dn}{dt} = (1 - n)k_{rec} - \beta k_{rel} p(V_{I_{Gly}^{OFF}}, \theta_{I_{Gly}^{OFF}})n. \quad (6) $$

$k_{rec}$ and $k_{rel}$ are rate constants (Hz) for vesicle release and replenishment and $\beta$ ($V^{-1}$) is a scaling factor. Finally, the voltage response is passed through the piece-wise linear function $p$ to obtain the firing rate.

$$ R(t) = s_G p(V_G(t), \theta_G), \quad (7) $$
## 8 Author contributions

S.E., T.B., O.M. and B.C. designed the study. T.B. and B.S.S. performed the experiments. S.E. and T.B. analyzed the data with help from O.M. and B.C.

S.E. did the model with help from T.B., O.M. and B.C. S.E., T.B., O.M. and B.C. wrote the paper.

## 9 Competing interests

The authors declare no competing interests.

<table><caption>Table 1: Model parameter values used in simulations.</caption><thead><tr><th>Parameter</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>τ<sub>OPL</sub></td><td>0.003</td><td>s</td></tr><tr><td>τ<sub>EON</sub></td><td>0.08</td><td>s</td></tr><tr><td>τ<sub>ION</sub></td><td>0.085</td><td>s</td></tr><tr><td>τ<sub>OFF</sub><sub>Gly</sub></td><td>0.12</td><td>s</td></tr><tr><td>τ<sub>G</sub></td><td>0.11</td><td>s</td></tr><tr><td>a<sub>ON</sub></td><td>14.0</td><td>1</td></tr><tr><td>a<sub>OFF</sub></td><td>12.0</td><td>1</td></tr><tr><td>b<sub>ON</sub></td><td>-0.5</td><td>1</td></tr><tr><td>b<sub>OFF</sub></td><td>0.5</td><td>1</td></tr><tr><td>w<sub>EON</sub></td><td>50.0</td><td>Hz</td></tr><tr><td>w<sub>ION</sub></td><td>-65.0 / 36.0</td><td>Hz</td></tr><tr><td>w<sub>OFF</sub><sub>Gly</sub></td><td>-53.0 / 0.0</td><td>Hz</td></tr><tr><td>S<sub>EON</sub></td><td>250.0</td><td>mVs<sup>-1</sup></td></tr><tr><td>S<sub>OFF</sub><sub>Gly</sub></td><td>-235.3</td><td>mVs<sup>-1</sup></td></tr><tr><td>S<sub>ION</sub></td><td>166.7</td><td>mVs<sup>-1</sup></td></tr><tr><td>θ<sub>EON</sub></td><td>26.0</td><td>mV</td></tr><tr><td>θ<sub>ION</sub></td><td>-20.0</td><td>mV</td></tr><tr><td>θ<sub>OFF</sub><sub>Gly</sub></td><td>0.0</td><td>mV</td></tr><tr><td>k<sub>rel</sub></td><td>5.0</td><td>Hz</td></tr><tr><td>k<sub>rec</sub></td><td>10.0</td><td>Hz</td></tr><tr><td>β</td><td>0.0826</td><td>mV<sup>-1</sup></td></tr><tr><td>θ<sub>G</sub></td><td>0.0</td><td>V</td></tr><tr><td>s<sub>G</sub></td><td>2200</td><td>HzmV<sup>-1</sup></td></tr></tbody></table>
where $s_G$ is a scaling factor.

Parameter values where then chosen such that simulations match the mean latencies and amplitudes of the OSR response observed in experiments and are listed in 1.

<table><caption>Table 1: Model parameter values used in simulations</caption><thead><tr><th>Parameter</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>τ<sub>ON</sub></td><td>0.05</td><td>s</td></tr><tr><td>τ<sub>ION</sub></td><td>0.08</td><td>s</td></tr><tr><td>τ<sub>OFF</sub><sup>Gly</sup></td><td>0.08</td><td>s</td></tr><tr><td>τ<sub>G</sub></td><td>0.1</td><td>s</td></tr><tr><td>w<sub>ON</sub></td><td>50.0</td><td>Hz</td></tr><tr><td>w<sub>ION</sub></td><td>-95.0</td><td>Hz</td></tr><tr><td>w<sub>OFF</sub><sup>Gly</sup></td><td>-82.0</td><td>Hz</td></tr><tr><td>S<sub>ON</sub></td><td>1.0</td><td>Vs<sup>-1</sup></td></tr><tr><td>S<sub>OFF</sub><sup>Gly</sup></td><td>-0.625</td><td>Vs<sup>-1</sup></td></tr><tr><td>S<sub>ION</sub></td><td>0.625</td><td>Vs<sup>-1</sup></td></tr><tr><td>θ<sub>OFF</sub><sup>Gly</sup></td><td>0.0</td><td>V</td></tr><tr><td>k<sub>rel</sub></td><td>4.5</td><td>Hz</td></tr><tr><td>k<sub>rec</sub></td><td>1.0</td><td>Hz</td></tr><tr><td>β<sub>ON</sub></td><td>13.6</td><td>V<sup>-1</sup></td></tr><tr><td>θ<sub>G</sub></td><td>0.0</td><td>V</td></tr><tr><td>s<sub>G</sub></td><td>2200</td><td>HzV<sup>-1</sup></td></tr></tbody></table>

# 5 Acknowledgments

We thank Romain Brette, Matthias Henning and Romain Veltz for helpful discussions about the model, and Matias Goldin and Brice Bathellier for critical reading of the manuscript. This work has been funded by a PhD fellowship from the Neuromod Institute, Université Côte d'Azur to S.E., by an ERC grant (No 101045253, DEEPRETINA) to O.M., ANR grants (DECORE, ANR-18-CE37-0011, and PerBaCo, ANR-22-CE37-0016-02) to O.M., a grant from Retina France to O.M., and ANR ShootingStar (ANR-20-CE37-0018-04) to O.M. and B.C. T.B. was funded by a PhD fellowship from ENS.

# 6 Author contributions

S.E., T.B., O.M. and B.C. designed the study. T.B. and B.S.S. performed the experiments. S.E. and T.B. analyzed the data with help from O.M. and B.C. S.E. did the model with help from T.B., O.M. and B.C. S.E., T.B., O.M. and B.C. wrote the paper.
<figure><img src="image_2.png" /><figcaption>Figure 1: **Glycinergic Amacrine cells are necessary for predictive timing of the OSR.** A. Schematic representation of the retina, with the activity of retinal ganglion cells being recorded with a multi electrode array. B. Temporal traces of the receptive fields of the cells that lose the latency shift with strychnine, *n* = 12. Bold trace shows mean of all cells. C. Example of OSR. The cell responds to the end on the stimulation, after the last flash. The times of dark flashes are represented by grey shaded rectangles. The black dotted rectangle shows the timing of the omitted flash. The black dotted rectangle shows the time period of focus in panel D. E. Experimental recording of the OSR in one cell in control condition (black) and with strychnine to block glycineergic amacrine cell transmission (red). Firing rate responses to flash trains of 3 different frequencies are aligned to the last flash of each sequence. Flashes are represented by grey patches, vertical lines indicate the maximum of the response peak, red shaded areas indicate the temporal discrepancy between control and strychnine conditions. E. Mean ± SEM latency between OSR and the omitted flash plotted against the period of the stimulus for a population of *n* = 12 cells. Latency is expressed relatively to the latency of the response to the 16Hz stimulus in control condition. F. Mean ± SEM latency between OSR and last flash in the stimulus plotted against stimulus period for a population of *n* = 12 cells. Control latencies shift with the period of the stimulus with a slope 1.13 ± 0.08. With strychnine this shift is abolished (slope = 0.07 ± 0.18). Latency is expressed relatively to the latency of the response to the 16Hz stimulus in the control condition.</figcaption></figure>
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<figure><img src="image_3.png" /><figcaption>Figure 2: Latency scaling of the OSR is selective to specific input patterns. A. Firing rate responses of one example cell to dark step stimuli with different durations equivalent to the duration of flash trains with frequencies 6-16 Hz. B. Firing rate responses of one example cell to dark step stimuli with different light intensities equivalent to the mean light intensity of flash trains with frequencies 6 to 16 Hz. C. Mean ± SEM between response latency and corresponding stimulus period for step stimuli with duration or luminance modulation comparable to the stimulus composed of periodic flashes, *n* = 20. D. Schematic description of the stimulus modifications for constant luminance across frequencies. "Duration" describes a modified stimulus in which the duration of each flash is set to half of the stimulus period. "Intensity" describes a stimulus modification in which the intervals between flashes are of brighter intensity to maintain a constant average luminance level E. Response traces to flash trains of 3 different frequencies of each modification shown in D. F. Mean ± SEM scaling between response latency and stimulus period for all conditions, *n* = 20 cells.</figcaption></figure>
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**G.** Fitted slope between peak latency and stimulus period for *n* = 20 cells, illustrated as a boxplot (the band indicates the median, the box indicates the first and third quartiles and the whiskers indicate ±1.5 interquartile range). Black/blue/green circles show individual datapoints. Control mean ± SEM 0.89 ± 0.03, intensity mean ± SEM 0.74 ± 0.06, duration mean ± SEM -0.13 ± 0.01 Stimuli with intensity modulation lead to no significant change in slope (*p* = 5.22e-2, two-sided Welch t-test) while duration modulations decrease the slope significantly (*p* = 7.2e-23, two-sided Welch t-test) Source data are provided as a Source Data file.
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<figure><img src="image_4.png" /><figcaption>Figure 3: **Mechanistic model replicates latency shift and strychnine experiment.** **A.** Schematic description of the Model. It is composed of an ON excitatory input $E^{ON}$, an ON inhibitory input $I^{ON}$, and an OFF inhibitory input $I_{Gly}^{OFF}$ representing a glycinergic amacrine cell. Each of those units receives as input the convolution of the stimulus with a monophasic temporal kernel, determining the cells polarity, and connects onto a ganglion cell *G*. The response of *G* is then passed through a nonlinearity to simulate the cells' firing rate. The synapse from $I_{Gly}^{OFF}$ to *G* can adapt its strength to the stimulus via short-term depression. The shaded red area represents the weight of this glycinergic amacrine cell being set to zero to simulate the effect of strychnine. **B.** Simulation of the model responses to flash trains of 3 different frequencies with the full model (black, control), and the weight of $I_{Gly}^{OFF}$ set to 0 (red, strychnine). The weight of $I^{ON}$ was changed from -65 to -36 Hz in this simulation, accounting for the broad effect of strychnine, which likely reduces inhibition overall. The times of dark flashes are represented by grey shaded rectangles, while the black dotted rectangle shows the timing of the omitted flash. **C.** Latency of the OSR plotted against stimulus period in control and strychnine simulation. The latency is expressed relatively to the latency of the response of the full model to the 16 Hz stimulus. The slope of the latency shift decreased from 1.13 to 0.30 when $I_{Gly}^{OFF}$ is set to 0 (dotted lines). **D.** Value of the slope fitted to latency shift in the full model and strychnine simulation. Source data are provided as a Source Data file.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 4: **Short-term plasticity is the crucial component for latency shift.** **A.** Schematic description of the Model, as in Figure 3. The shaded red area now represents removing the dynamical characteristic of the glycinergic synapse. **B.** Simulation of the model responses to flash trains of 3 different frequencies with dynamic occupancy (black) and the weight of $I_{Gly}^{OFF}$ held constant (red). The times of dark flashes are represented by grey shaded rectangles, while the black dotted rectangle shows the timing of the omitted flash, as in Figure 3. **C.** Latency of the OSR plotted against stimulus period in control and strychnine simulation. The latency is expressed relatively to the latency of the response to the 16 Hz stimulus in the control condition. The slope of the latency shift decreased from 1.13 to 0.31 when the weight of $I_{Gly}^{OFF}$ was held constant (dotted lines). **D.** Value of the slope fitted to latency shift in the full model and without the adaptive property of the glycinergic synapse. Source data are provided as a Source Data file.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 5: ON components of the model produce a peak after stimulus end while the glycinergic OFF input shifts the latency. From top to bottom: Stimulus intensity, Bipolar and Amacrine voltage responses, ganglion cell voltage and firing rate. **A.** Internal model responses of ON components to a 6 Hz dark flash stimulus without OFF inhibition. ON excitation and inhibition hyperpolarize in response to dark flashes. When both inputs are subtracted in the ganglion cell, its voltage sum hyperpolarizes during flash presentation, followed by an overshoot of disinhibition due to the slower response profile of the inhibitory input. After passing the voltage through a rectification function, only the disinhibitory peak after stimulus end remains in the firing rate. **B.** Effect of additional OFF inhibition. The voltage of the glycinergic OFF input depolarizes in response to dark flashes, passing additional inhibition onto the ganglion cell. This lowers the GC voltage response and increases the latency between peak and stimulus end in the firing rate. Last two panels compare the models' simulation and peak time-point with (black) and without (grey) the input from $I_{\text{Gly}}^{\text{OFF}}$. Source data are provided as a Source Data file.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure 6: Synaptic depression scales OFF glycinergic input to stimulus frequency and thereby shifts the latency of the response. Responses shown are zoomed in around the end of the flash sequence. A. Impact of occupancy scaling on $I_{Gly}^{OFF}$ current input to G for a fast (16 Hz, left) and a slow (6 Hz, right) stimulus. From top to bottom: Stimulus intensity, $I_{Gly}^{OFF}$ voltage, vesicle occupancy, current input, G voltage and firing rate. Last 3 panels compare simulations with dynamic occupancy (solid lines) to when the occupancy is held constant (dotted lines). Depression has the effect to advance the OSR peak, more so for fast than slow frequencies. Current of unit X is computed with equation 5 in Methods. B. Occupancy traces to flash stimuli of different frequencies aligned to the last flash. Dots indicate the occupancy level at stimulus end. C. Level of occupancy after stimulus end scales with the period of the stimulus. D. $I_{Gly}^{OFF}$ current input is decreased by short-term depression, more so for fast than slow frequencies. Dotted line shows current with fixed occupancy, solid line with dynamic occupancy. Source data are provided as a Source Data file.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 7: Latency shift decreases for shorter stimuli because of lacking steady state occupancy. A. Mean ± SEM amplitude of the OSR against stimulus period for 12 and 5 flashes in the stimulus in simulations (left) and experiments (right). Amplitudes to 6 Hz and 10 Hz stimuli were significantly different according to two-sided t-test with Bonferroni-Holm correction<sup>Holm1979</sup> (16 Hz: *p* = 0.000006, 10 Hz: *p* = 0.001). B. Latency against stimulus period in simulations (left) and experiments (right). Simulated slopes decreased from 1.13 after 12 flashes to 0.63 after 5 flashes in simulations. Experimental slopes decreased from 0.84 ± 0.02 to 0.69 ± 0.04, mean±SEM. The latency after 12 and 5 flashes was not significantly different according to two-sided t-test with Bonferroni-Holm correction<sup>Holm1979</sup> (6 Hz: *p* = 0.2, 8 Hz: 0.14, 10 Hz: *p* = 0.044, 12 Hz: *p* = 0.031, 16 Hz: 0.024). C. Temporal traces of vesicle occupancy to all frequencies simulated, for 12 flashes (upper) and 5 flashes (lower). Dots indicate occupancy at stimulus end. Traces do not reach a steady state for 5 flashes. D. Scaling of occupancy with stimulus period in 5- and 12-flashes scenario. Source data are provided as a Source Data file.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure 8: Mechanistic neuronal circuit explains the latency shift of the Omitted Stimulus Response (OSR) via depressing inhibition. A. Schematic responses of components shown in B to a slow-frequency and a fast frequency stimulus. Black rectangles represent dark flashes in a periodic sequence. The dotted rectangle represents an omitted flash at the end of the sequence. For both stimulus speeds, the upper panel shows inputs from the IPL. ON (orange) inputs are combined into one trace and OFF inhibitory input is shown in blue. ON inputs generate a peak response after stimulus end. OFF inhibitory input is activated by the dark flash sequence and then slowly decrease after stimulus end, overlapping with the ON peak. The lower panel shows the RGC firing rate. Without OFF inhibition (dotted black), the RGC emits a peak at the same time as the ON inputs. Adding OFF inhibitory inputs (solid black) generally decreases this response and push the peak backwards. The impact of inhibition depends on the stimulus frequency due to synaptic depression. At slow frequency inputs, synaptic depression is not activated. Inhibitory inputs remain strong and shift the latency of the OSR (blue arrow) to a later time. Fast-frequency stimuli trigger strong synaptic depression, leading to a depletion of inhibitory inputs. The latency remains unchanged. B. Schematic description of the circuit. A retinal ganglion cell (RGC, in black), which emits an OSR with latency shift, receives 3 inputs in the IPL (inner plexiform layer). Orange units are ON inputs, which provide excitation (filled circle) and inhibition (empty circle). The blue unit provides OFF inhibition and has a dynamical synapse which depresses after activation.</figcaption></figure>
C. Latency of the OSR to the last flash in the stimulus plotted against stimulus period. A RGC without depressing inhibitory inputs (dotted black) will emit a response at roughly the same time after stimulus end. It thus merely signals the end of the stimulus. With depressing inhibition (solid black), the latency is shifted backwards for slower frequencies (with longer periods), which leads to a to a 1-to-1 scaling between latency and stimulus period. Via this mechanism, the latency of the OSR with respect to the omitted flash remains constant across frequencies, indicating that the RGC signals the omitted stimulus. The latency can thus provide a prediction of the time when the flash should have occurred.
Supplementary Figures

<figure><img src="image_10.png" /><figcaption>Figure S1: **ON cells that exhibit an OSR belong to various cell types.** Manual clustering of chirp responses from all ON cells with OSR yielded 4 broad cell types that show an OSR: ON transient, ON transient/sustained, ON sustained and ON-OFF. Shown are 35 cells with a response to the chirp stimulus and have a spike-triggered average to checherboard stimulation. 5 other cells which are included in the statistics in the main paper but do not have a chirp response or STA are not shown in this figure. **A.** Response traces to a chirp stimulus. **B.** Temporal spike triggered average obtained after STA analysis to white noise-checkerboard stimulus. **C.** OSR after control stimulation with 12 Hz flash train (firing rate). **D.** Scaling between response latency and stimulus period for frequencies of 6,8,10,12,16 Hz. Black line has a slope of 1 for reference. Source data are provided as a Source Data file.</figcaption></figure>
<figure><img src="image_11.png" /></figure>

Figure S2: Absolute latency of the OSR after all frequencie tested of n = 35 cells included in our study. Shaded colored areas show the density, individual datapoints are shown in light blue. Dotted black lines indicate 2T for each period T = 1/7. 6 Hz: max = 615 ms, min 216 ms, median = 340 ms; 8 Hz: max = 547 ms, min 189 ms, median = 232 ms; 10 Hz: max = 529 ms, min 178 ms, median = 220 ms; 12 Hz: max = 497 ms, min 159 ms, median = 207 ms; 16 Hz: max = 483 ms, min 142 ms, median = 188 ms; Source data are provided as a Source Data file.
<figure><img src="image_12.png" /><figcaption>Figure S3: Spiking onset is not a consistent quantity of the OSR latency shift. A. Response onset latency against stimulus period in control conditions in all cells that show an OSR in their peak timing. Mean 0.39 ± 0.11, compared to thick dotted line which has a slope of 1. All latencies are referenced to the latency to the fastest frequency in control condition. B. Response onset latency against stimulus period in strychnine conditions in all cells that show a latency shift in their peak timing. Mean 0.15 ± 0.36, thick dotted line has a slope of 0. All latencies are referenced to the latency of the fastest frequency in control condition. C. Slope quantification, no significant difference slope in response onset between control and strychnine, p = 0.056. Source data are provided as a Source Data file.</figcaption></figure>
<figure><img src="image_13.png" /></figure>

Figure S4: Peak amplitude to different stimulus frequencies are not systematically impacted by strychnine. A. Amplitude of the OSR against stimulus period for control and strychnine conditions in simulations. B. Same for experimentally measured amplitudes, not significantly different after Bonferroni-Holm correction<sup>Holm1979</sup> (6 Hz: p = 0.26, 16 Hz: p = 0.975). Source data are provided as a Source Data file.
<figure><img src="image_14.png" /><figcaption>Figure S5: Model predicts the selectivity of latency scaling to transient periodic flashes. A. Simulated response traces of the model to flash trains of 3 different frequencies in control condition (black) and with modulations of flash-duration (green) and inter-flash brightness (blue). Stimuli are shown in the upper panels, simulated firing rate below. Vertical lines highlight the peak time-point, shaded areas show the latency shift compared to the control response. B. Latency of the OSR plotted against stimulus period for the 3 stimulus types. Solid lines are datapoints, dotted lines show linear fit between latency and period. Slope control: 1.13, slope duration modulation: 0.05, slope intensity modulation: 1.06.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Figure S6: Model with a biphasic ON bipolar cell can simulate the latency shift of the OSR via excitatory plasticity. A. Schematic description of the model with one biphasic ON unit that has a plastic synapse. B. Response traces to 3 stimulus frequencies with the purely excitatory model with plasticity (black) compared to a model without plasticity (magenta). C. Scaling between response latency and stimulus period in both model variations. Slope full model: 0.98, slope without plasticity: 0.37. Parameter used for the simulation: τ<sub>OPL</sub> = 0.1, τ<sub>OPL2</sub> = 0.1, τ<sub>EON</sub>, τ<sub>G</sub> = 0.05, a<sub>ON</sub> = 14.0, b<sub>ON</sub> = 0.0, w<sub>EON</sub> = 200.0, S<sub>EON</sub> = 0.5, θ<sub>EON</sub> = 0, k<sub>rel</sub> = 50.3, k<sub>rec</sub> = 1.0, β = 13.6, θ<sub>G</sub> = 0.0, s<sub>G</sub> = 2200. Source data are provided as a Source Data file.</figcaption></figure>
<figure><img src="image_16.png" /></figure>

Figure S7: Gabazine has various effects on the OSR. **A.,C.,E.** Response traces to flash trains of 3 different frequencies in control (black) and gabazine (shades of purple) conditions. **B.,D.,E.** Mean relative latency to the last flash of the stimulus plotted against stimulus period for control (black) and gabazine (shades of purple) conditions. Dotted line shows slope of 1. **A.,B.** Example cell where OSR remains largely unaffected by gabazine. (Slope control = 0.71, gabazine = 0.4, n = 2 cells) **C.,D.** Example cell where OSR slope decreases with gabazine. (Slope control = 0.97, slope gabazine = 0.35, n = 4 cells). **E.,F.** Example cell where OSR dissapears though gabazine. (Slope control = 0.96, n = 4 cells). Source data are provided as a Source Data file.