Abstract
The statistics of vesicle release determine how synapses transfer information, but the classical Poisson model of independent release does not always hold at the first stages of vision and hearing. There, ribbon synapses also encode sensory signals as events comprising two or more vesicles released simultaneously. The implications of such coordinated multivesicular release (MVR) for spike generation are not known. Here we investigate how MVR alters the transmission of sensory information compared with Poisson synapses using a pure rate-code. We used leaky integrate-and-fire models incorporating the statistics of release measured experimentally from glutamatergic synapses of retinal bipolar cells in zebrafish (both sexes) and compared these with models assuming Poisson inputs constrained to operate at the same average rates. We find that MVR can increase the number of spikes generated per vesicle while reducing interspike intervals and latency to first spike. The combined effect was to increase the efficiency of information transfer (bits per vesicle) over a range of conditions mimicking target neurons of different size. MVR was most advantageous in neurons with short time constants and reliable synaptic inputs, when less convergence was required to trigger spikes. In the special case of a single input driving a neuron, as occurs in the auditory system of mammals, MVR increased information transfer whenever spike generation required more than one vesicle. This study demonstrates how presynaptic integration of vesicles by MVR can increase the efficiency with which sensory information is transmitted compared with a rate-code described by Poisson statistics.
SIGNIFICANCE STATEMENT Neurons communicate by the stochastic release of vesicles at the synapse and the statistics of this process will determine how information is represented by spikes. The classical model is that vesicles are released independently by a Poisson process, but this does not hold at ribbon-type synapses specialized to transmit the first electrical signals in vision and hearing, where two or more vesicles can fuse in a single event by a process termed coordinated multivesicular release. This study shows that multivesicular release can increase the number of spikes generated per vesicle and the efficiency of information transfer (bits per vesicle) over a range of conditions found in the retina and peripheral auditory system.
Introduction
The coding of sensory information by spikes has been studied in detail (Gollisch and Meister 2008; Kayser et al., 2009), but less is understood about coding with vesicles. This is especially true in the early stages of vision and hearing where analog voltage signals are transmitted through synapses with specialized “ribbon” structures that hold a reservoir of vesicles just behind the active zone (Matthews and Fuchs, 2010; Lagnado and Schmitz, 2015).
Classical models of synaptic transmission use binomial statistics expected when all vesicles are released independently (Del Castillo and Katz, 1954). It has often been assumed that ribbon synapses operate similarly, encoding sensory signals by modulating the mean rate of a Poisson process (Choi et al., 2005; Odermatt et al., 2012), but an accumulation of evidence now indicates that this description does not always hold (Glowatzki and Fuchs, 2002; Singer et al., 2004; G. L. Li et al., 2009; James et al., 2019; Hays et al., 2021). In retinal photoreceptors and bipolar cells, the fusion of multiple vesicles can be synchronized to within the resolution of electrophysiological recordings (<100 µs) by a process that has been termed coordinated multivesicular release (Singer et al., 2004; Hays et al., 2021).
Multivesicular release (MVR) conforms with binomial statistics in rat bipolar cells (Singer et al., 2004), but not in rod photoreceptors (Hays et al., 2021) or in bipolar cells from the retina of zebrafish where the ratio of the variance to the mean of the synaptic output at low release probabilities is not one, as expected for a Poisson process, but about three, indicating that vesicles interact (Moya-Díaz et al., 2022). MVR is also a prominent property of ribbon synapses in auditory hair cells (Keen and Hudspeth, 2006; G. L. Li et al., 2009; Grant et al., 2010; Chapochnikov et al., 2014; Niwa et al., 2021), where synchronization depends on calcium domains very close to clusters of calcium channels (Graydon et al., 2011). Although the relative importance of univesicular and multivesicular release in mammalian hair cells remains under debate (Chapochnikov et al., 2014; Niwa et al., 2021), the release statistics do not appear binomial where synchronization is on the submillisecond time scale (Glowatzki and Fuchs, 2002).
The closer together in time vesicles fuse at a single active zone, the more effectively their electrical actions will summate in the postsynaptic neuron (X. Li and Ascoli, 2008), potentially allowing for information to be transmitted by both the temporal pattern of synaptic events and by their amplitude. Evidence for this idea has been provided by imaging glutamate release at individual active zones with single-vesicle resolution, revealing that ribbon synapses of retinal bipolar cells can encode visual signals as changes in the number of vesicles released within an event, with larger and rarer events carrying the most information per vesicle (James et al., 2019; Moya-Díaz et al., 2022).
Here we explore how MVR contributes to the conversion of sensory signals into spikes. An experimental investigation is difficult because it requires spikes to be recorded while also counting vesicles released at individual synaptic inputs. We have therefore used a modeling approach in which a train of synaptic events is simulated based on experimentally measured statistics of vesicle release and then used as the input to a leaky integrate-and-fire (LIF) model of a neuron (Abbott, 1999; Burkitt, 2006a). We gather these statistics in vivo from the synapses of retinal bipolar cells as they transmit visual information to postsynaptic ganglion cells in zebrafish. A comparison with simulations in which synapses operate a pure rate-code by releasing all vesicles independently demonstrates that coordinated MVR can increase the efficiency with vesicles are used to transmit sensory information over a range of conditions found in the retina and in auditory systems. In the special case of a neuron driven by a single synapse, as occurs in the cochlea of mammals, MVR increased the efficiency of information transfer whenever spike generation required depolarization greater than that caused by a single vesicle.
Materials and Methods
Modeling overview
Modeling the effects of MVR on spike generation involved the following basic steps:
1. Statistics of vesicle release in retinal bipolar cells responding to visual stimuli
Using iGluSnFR expressed in retinal bipolar cells of larval zebrafish of either sex, we measured the amplitude of synaptic events and their timing relative to a sinusoidal full-field stimulus of varying contrast (see Fig. 1A). At each contrast, we calculated (1) the average rate of vesicle release over a 30 s period R (see Fig. 1B; n = 60 synapses); (2) the probability (Pr) of events composed of different numbers of quanta, PQe (see Fig. 1C; n = 55 synapses); and (3) the “temporal jitter” (TJ) of events of each amplitude, TJQ, quantified as the SD of event times relative to any particular phase of the sinusoidal stimulus (see Fig. 1D–F; see also Step 5). Each statistic was calculated from at least 20 zebrafish.
2. Simulation of synapse output
Based on Step 1, two types of simulated synaptic output were constructed: one in which a sinusoidal stimulus was represented as a “pure” rate-code in which all vesicles were released independently and a second “hybrid code” in which amplitude also varied (see Fig. 2A). In both cases, the overall average rate of vesicle release R was fixed to values measured experimentally at a given contrast of a visual stimulus.
The output of a synapse using coordinated MVR was generated by randomly selecting a total of N events with amplitudes chosen from the distribution of quanta in an event PQe (see Fig. 2B). Each event was then given a time by sampling from the Gaussian distribution of event times with mean and variance measured experimentally (see Fig. 1F). Each synapse was constrained to generate only one or zero events per cycle of the stimulus, with the Pr of no event given by
The rate-code comparison was constructed by replacing each event consisting of more than one quantum with an equivalent number of uniquantal events, each event time now sampled from the distribution of times of uniquantal events (see Fig. 1F). The vectors describing a pure rate synapse were therefore of variable lengths corresponding to the total number of vesicles sampled within the 30 s sample period. The resulting vectors Qe and E of event quanta and event times were then passed into a conductance-based model LIF model (see Fig. 2A) and the spike output analyzed.
3. Simulation of synapse output using marked Poisson processes
For purely rate-coded synapses, we used a nonhomogeneous Poisson process as the driving force for vesicle release, in which the mean rate λ(t) varied sinusoidally in time. By definition, simple Poisson processes describe a situation in which all events occur independently and with exponentially distributed interevent times and cannot, therefore, be used to model MVR when two or more vesicles are released within a single synaptic event. To construct an amplitude-modulated Poisson process we turned to a modification known as Poisson splitting or location-dependent thinning (Williams et al., 2020), where events can be assigned a type based on their location in time. In this case, events occur with a constant rate, but the number of vesicles in each event is chosen based on when the event occurred. We could therefore drive the LIF model neuron in two distinct regimens: a pure rate case, where all information is encoded by modulating the mean rate of release of individual vesicles; and a hybrid case, where information is encoded by modulating both the rate and quantal content of synaptic events.
A key aspect of our investigation was to construct the rate and hybrid models in such a way that each released the same average number of vesicles, with differences found only in the variabilities. In other words, vesicles were released individually in the “rate-code,” but in packets of variable size in the “hybrid code.” To simulate pure rate-coded synaptic inputs, we used a sinusoidal intensity function. Variations in the amplitude of the sinusoid simulate the contrast of a visual stimulus or intensity of an auditory stimulus. The response of each synapse to stimuli of varying strengths was simulated by increasing the amplitude of the sinusoid between a total release rate of 5 vesicles s−1 at input condition 1 and 65 vesicles s−1 at input condition 10. Below, we term these conditions 10% and 100% contrast because these was the average rate of release from the active zone of a bipolar cell in the retina of a zebrafish receiving a low photopic stimulus at those contrasts (see Fig. 2D,E). The responses of a neuron receiving multiple inputs were simulated by assuming that all synapses generated responses derived from the same distributions and summing the response to all the individual inputs. By the superposition principle of Poisson processes, adding up multiple independent Poisson processes with the same underlying intensity function is mathematically equivalent to simply scaling the underlying intensity function. The underlying release function was therefore scaled in proportion to N, the number of inputs onto the cell. To simulate hybrid coding the Pr of release was also modulated as a sinusoid with an amplitude generating an average rate of release corresponding to that measured experimentally at a given stimulus strength (see Fig. 1A).
4. A conductance-based LIF model of the postsynaptic neuron
The vectors describing amplitudes and times of synaptic events were convolved with a synaptic filter to estimate the time course of the synaptic current Sin (see Fig. 2C), which was then passed through a LIF model to calculate the change in voltage and spike output. LIF models provide a computationally compact method for exploring basic physiological parameters affecting spiking, including the number of synaptic inputs, cell time constant, threshold relative to resting potential, and ion channel conductances (Gerstner et al., 1997; Abbott, 1999; Burkitt, 2006b). Voltage is governed by the following differential equation:
Where
Where s(t) is the sequence of Dirac δ function describing the timing of each event in a realization of the process, and
To compare how the MVR might shape the spike output of a neuron across a range of physiological situations encountered in early vision and hearing, we systematically varied the parameters shown in Table 1. The instantaneous depolarization in the postsynaptic neuron required to trigger a spike was re-expressed as k, the number of vesicles required to achieve that depolarization if the neuron were a perfect integrator. k is therefore dependent only on the properties of the postsynaptic neuron and is agnostic to the number of synaptic inputs N or the number of docking sites at a single input. The parameter k was varied from 1, a situation that can occur in the mammalian cochlea (Grabner and Moser, 2018), up to 100. Rather than representing the set of the excitatory conductances,
Parameters used for simulationsa
5. Analyzing the spike output of the model neuron
We concentrated on three aspects of the spiking response of the model neuron: the spike count generated by each cycle of the stimulus, the temporal accuracy of spikes, and the average rate of information transfer about changes in stimulus strength.
Temporal accuracy was quantified as “temporal jitter” (TJ), which was in turn calculated from the vector strength, which takes values between 0 and 1, with 0 being complete independence from the stimulus and 1 being perfect phase-locking (Goldberg and Brown, 1969; Baden et al., 2011). Vector strength was computed separately for events of each quantal amplitude (VSQ) from stimuli lasting 30 s stimulus and of varying contrast delivered at 5 Hz as follows:
TJQ is plotted as a function of Qe in Figure 1E.
We calculated the mutual information (Shannon, 1948) between the stimulus S and either the spike times or the total number of spikes occurring over a period of 200 ms (N, corresponding to one cycle of a 5 Hz stimulus, two cycles of a 10 Hz stimulus, or three cycles of a 15 Hz stimulus). Mutual information for spike counts was computed empirically from the joint and marginal distributions
The signal-to-noise ratio (SNR) associated with a change in the rate of a Poisson process
Imagine the mean rate of a Poisson process, R, changes by a factor a. The signal, S, generated by comparing two observation times Dt will be the change in the mean number of events counted in each period (aRDt – RDt), and the variance in that signal will be the sum of the number of events counted in each period (aR Dt + R Dt). Defining the SNR in the same way as the discriminability (d′) used in signal detection theory, we have the following:
Multiphoton imaging of glutamate release
Methods for in vivo imaging of glutamate release in the retina of zebrafish were as described previously (James et al., 2019). Transgenic larval zebrafish of either sex expressing the iGluSnFR reporter under the ribeye a promoter were imaged at 7-9 d post-fertilization after embedding in a 3% low melting-point agarose in E2 on a glass coverslip. To prevent eye movements, the fish was injected with 1 nl of α-bungarotoxin behind the eye. Imaging was conducted using a multiphoton microscope (Scientifica) equipped with a mode-locked titanium-sapphire laser (Chameleon, Coherent) tuned to 915 nm and an Olympus XLUMPlanFI ×20 water immersion objective (NA of 0.95). Fluorescence emission was also collected using a substage oil condenser (Olympus; NA of 1.4), which was essential to achieve a SNR adequate for reliable detection of single vesicles. A total of 42 zebrafish were used in this study, and all measurements were made in the afternoon.
Light emission was filtered through GFP filters (HQe525/50, Chroma Technology) before detection using GaAsP photomultipliers (H7422P-40, Hamamatsu). Photocurrents were passed to a current-to-voltage converter, after which signals from the objective and condenser were summed and digitized through ScanImage (version 3.6; Vidrio Technologies). For this work, all time-series were acquired as 128 pixel line scans imaged at 1 kHz and analyzed in custom software written within IgorPro (Wavemetrics). Stimuli were generated by an amber LED (peak wavelength of 590 nm) filtered through 590/10 bandpass filter (Thorlabs) delivered through a light-guide placed near the fish's eye, with the mean stimulus intensity of ∼320 nW mm−2. Detailed evidence that this approach can detect the release of single vesicles from individual active zones has been presented previously (James et al., 2019).
Results
Synaptic coding of a sensory stimulus: gathering release statistics for an empirically driven model
To investigate how the statistical properties of vesicle release affected the synaptic transfer of sensory information, we compared synapses using coordinated MVR with synapses operating as simple Poisson machines. The starting point was to gather experimental measurements of release statistics from retinal bipolar cells expressing the glutamate reporter iGluSnFR, and examples of such records are shown in Figure 1A. Both the rate and amplitude of glutamate transients varied widely during sinusoidal modulations in light intensity (James et al., 2019; Moya-Díaz et al., 2022).
Analyzing vesicle release from retinal bipolar cells. A, Summary of the basic steps for quantal decomposition of iGluSnFr signals. 1. Raw trace extracted from an individual active zone (linescan, 1 kHz). 2. Trace deconvolved using the estimated Wiener filter and threshold crossings used to detect events above noise. The timing of the peak is the event time t. The amplitude of the event is the peak of the deconvolved trace at time t. 3. The distribution of event amplitudes is plotted and fitted by the sum of Gaussians with peaks differing by integer multiples of a quantal value q. This example is a histogram of event amplitudes for an active zone in which 373 events were accumulated using stimulus contrasts of 20%, 60%, and 100% and a frequency of 5 Hz. Black line indicates a fit of eight Gaussians, identified using a Gaussian mixture model. The first peak had a value of 0.24, and the distance between peaks averaged 0.25, indicating the existence of a quantal event equivalent to ∼0.25. 4. Maximum-likelihood estimation of the number of quanta, q, in each event based on its amplitude in 2 and the distribution in 3. These steps are validated in much greater detail in James et al. (2019). B, Normalized change in the rate of events R (black) and average event amplitude in quanta (red) (n = 60 synapses). R includes events of any amplitude. C, Distribution of event amplitudes during a 30 s application of a 5 Hz stimulus at 20% and 100% contrast (n = 55 synapses). D, A quantal time series (black lines) in response to a full-field stimulus modulated as a sinusoid (5 Hz) at 80% contrast (red). Vertical blue dashed lines indicate a single phase of the stimulus. Smaller events show greater temporal dispersion compared with large events. E, The TJ of events of different quantal content triggered by a stimulus of 100% contrast (n = 60 synapses). F, Mean-shifted distribution of events containing 5 or more quanta (black) and of events containing one quantum (red). Data from E.
We measured how changes in contrast altered three aspects of the vesicle code highlighted in Figure 1 event rate R (of any amplitude), distribution of event amplitudes PQe, and variability of event timing TJQ. An increase in contrast increased R (Fig. 1B) and shifted the distribution of Qe to larger values (Fig. 1C). R saturated at lower contrasts than Qe, such that contrasts greater than ∼50% were often encoded entirely by the amplitude of release events rather than their frequency (Fig. 1B,C). A potential role of MVR in determining the temporal accuracy of spiking in the postsynaptic neuron is immediately suggested by the observation that multiquantal events were more tightly phase-locked to the stimulus than vesicles released individually (Fig. 1D–F). The relation between TJ and Qe is shown in Figure 1E, and a comparison of the distribution of times for uniquantal and multiquantal events is shown in Figure 1F. Uniquantal events had a TJ of 21.2 ± 1.5 ms, while for events composed of 9 quanta TJ = 2.7 ± 0.6 ms, which is very similar to the precision of spikes observed in retinal ganglion cells (RGCs) of the salamander retina responding to stimuli of high-contrast (Berry et al., 1997; Uzzell and Chichilnisky, 2004).
In other studies, changes in release statistics have been measured in response to voltage-clamp stimuli rather than visual or auditory inputs, but the effects are qualitatively similar to an increase in contrast shown in Figure 1. Larger depolarizations increase the frequency of release and the Pr of larger events in rat bipolar cells (Singer et al., 2004) and mouse rod photoreceptors (Hays et al., 2021) as well as hair cells in frogs (Keen and Hudspeth, 2006; G. L. Li et al., 2009), where larger events are also more tightly phase-locked to a periodic stimulus (G. L. Li et al., 2014).
Based on the statistics gathered through experiments shown in Figure 1, we constructed two types of synaptic input to the model neuron: purely rate-coded inputs in which all vesicles were released independently (Fig. 2A, red) and hybrid inputs in which both rate and amplitude of events varied (black; see Materials and Methods). To compare how these two coding strategies performed with equivalent resources the average rates of vesicle release were fixed for both types of input at the values measured experimentally at a given contrast and frequency (Fig. 1B). Measuring the output of individual synapses to stimuli of different strengths and frequency then allowed us to make measures of the mutual information between the stimulus set and spikes generated in model neurons.
Overview of modeling. A, A LIF neuron received either rate (top) or hybrid (bottom) inputs. B, Illustration of release simulation. The number of vesicles in an event (for the MVR case) or the number of released uniquantal events (for the rate case) is sampled from the distribution PQ (in this example for a stimulus of 60% contrast). For the MVR case, each event is then given a time by sampling from a Gaussian distribution with variances set by the mean temporal precision of events, given by TJq. For the rate case, a corresponding number of event times are sampled from the distribution of uniquantal event times (bottom middle). C, The sampled event time and amplitude tuples are then convolved with a synaptic current filter. The resulting current is summed over the number of inputs to the cell. Plotted on the right are the average synaptic current input to a cell using a rate-code (red) and hybrid code (black). Note the increased temporal variability in the rate-code (SD = 360 ms for the hybrid case vs 685 ms for the rate case). D, Demonstration of the Poisson release model. Bottom, Intensity function driving the rate of vesicular events. Middle, Expected number of vesicles released in an event as a function of time. Top, Expected cumulative vesicles released as a function of time for rate and amplitude codes, offset for visualization. These functions have been equalized by design. E, Expected total vesicles released over a 1 s window as a function of stimulus “contrast.”
Interspike intervals (ISIs) in neurons of different structure
Ribbon synapses transmit to target neurons of varying size and shape and with varying degrees of convergence. In the vestibular organs of mammals and auditory papilla of amphibians, each afferent fiber collects input from ∼30 to 100 ribbons (Eatock and Songer, 2011; Graydon et al., 2014). At the other extreme, primary auditory afferents in mammals are driven by a single synapse and have input resistances of the order of gigaohms, leading to the suggestion that a single glutamatergic vesicle is sufficient to trigger a spike (Rutherford et al., 2012; Grabner and Moser, 2018). In the retina, bipolar cells transmit to RGCs that vary widely in the dimensions of their dendritic trees (determining the size of receptive fields) and membrane time constants (determining temporal integration of synaptic inputs). In the fovea of primates, for instance, midget ganglion cells receive 25-50 synaptic inputs from between one and three bipolar cells (Calkins et al., 1994; Kolb and Marshak, 2003); whereas in the periphery of the retina, RGCs have large dendritic fields receiving inputs from hundreds of bipolar cells, with up to thousands of synapses (Jacoby et al., 2000). We therefore begin by comparing spike outputs in a “small” synthetic RGC (
Comparison of vesicle codes on spike generation in a “small” cell and a “large” cell. A, Mean spike count as a function of contrast for a “small” cell (top) and “big” cell (bottom). The “small” cell was simulated with the following: inputs = 50, k = 10,
Using a stimulus of low contrast (20%), the large cell barely responded, but the small cell generated an average of one spike per cycle of the 5 Hz stimulus (Fig. 3A). The distributions of spike times were not significantly affected by the coding strategy of the synaptic inputs (Fig. 3B, middle); but when two or more spikes were generated within a cycle, the distribution of ISIs was shifted to significantly lower values when input was provided by hybrid synapses using MVR (Fig. 3B, bottom; p < 0.02; Kolmogorov–Smirnov test). This distribution, Y(ISI), could be described as a log-normal function of the following form:
The precise timing of spikes in an RGC can code information about the stimulus that neurons postsynaptic to RGCs can decode (Kaplan et al., 1987; Usrey and Reid, 1999) In cats, for instance, the efficiency with which an RGC spike drives an LGN spike depends on the ISI: ISIs shorter than ∼10 ms have the greatest efficiency, but this decreases progressively with ISI up to ∼30 ms (Usrey et al., 1998). Such ISI-based filtering of retinal spikes can shape receptive fields and may serve as a mechanism by which the information carried in ISIs is decoded (Rathbun et al., 2010; Ishii and Hosoya, 2020). The simulations in Figure 3 therefore indicate that a hybrid vesicle code driving excitation of RGCs has the potential to increase the visual information transmitted to postsynaptic targets by shortening spike intervals.
Coordinated MVR increases spike count over a range of conditions
The spike response of a target neuron will depend not only on the numbers of synaptic inputs (N) that it receives but also on the strength of these inputs. Graydon et al. (2014) have simulated transmission in the auditory system of different species with different wiring patterns and found that reliability, quantified as the coefficient of variation (CV) of the postsynaptic current, is a function of the degree of convergence and release Pr: increasing the number of inputs caused large increases in reliability, even for low Pr. In our modeling framework, synaptic strength is directly related to k, the minimum number of vesicles that would need to be summed instantaneously to depolarize the neuron to threshold. Although we systematically varied both k and N (Table 1), we found the ratio k/N to be a useful summary metric that provided insight into the effects of both synapse strength and convergence.
In the retina of guinea-pigs, medium-sized RGCs receive ∼1000-2000 inputs, and a brief burst of excitation comprising 3-65 vesicles triggers a burst of 1-6 spikes (Freed, 2005). This example therefore provides an upper limit of k ∼10 while k/N is ∼0.01. In contrast, a midget RGCs might receive just 10 inputs. If the same number of vesicles are required to trigger a spike, k/N = 1; and even if just one vesicle is sufficient, k/N = 0.1. Examples of the interaction between k/N and the time constant of the target neuron are shown in Figure 4. Increasing
Hybrid coding increased spike count over a range of physiologically relevant conditions. A, Top, Mean spike count as a function of leak time constant (tl) for a cell receiving N = 500 inputs and requiring k = 100 vesicles to spike in response to a 5 Hz stimulus of varying contrast (other parameters as in the “large” cell in Fig. 3). This count is over a 200 ms time window, and so, can be multiplied by 5 to obtain spike rates. Bottom, Spike count difference (hybrid – rate) from the data in top panel. For this ratio of k:N, the hybrid code produces more spikes than the rate-code when
The interaction between
How does this comparison of the hybrid and rate-codes relate to the physiology of the retina? Compared with other visual circuits, such as those in the cortex, the retinal output is strikingly reproducible over repeated trials of a stimulus and contrasts of 20%–40% can trigger spikes in RGCs with almost perfect reliability (i.e., close to 100% of trials) (Berry et al., 1997; Gollisch and Meister, 2008). Unsurprisingly, the reliability of individual bipolar cell synapses was lower. At 20% contrast, a 5 Hz stimulus triggered a response in 31 ± 3% of stimulus cycles (n = 48 synapses), rising to 64 ± 4% at 60% contrast (n = 56 synapses). Experimental measurements of the average number of vesicles released in each cycle are shown in Figure 1A, B. When a stimulus of 20% contrast was effective, it released an average of 2.32 ± 0.09 vesicles (equivalent to an overall average rate of 0.31 × 2.32 × 5 = 3.67 vesicles s−1), while 60% contrast released 2.84 ± 0.14 vesicles in each stimulus cycle that elicited a response (equivalent to 9.1 vesicles s−1; n = 48 synapses). Comparing these experimental measurements with the results of simulations in Figure 4 indicates that synapses of bipolar cells are operating over a range of reliabilities where coordinated MVR provides an advantage over a pure rate-code by increasing the number of spikes generated per released vesicle.
Coordinated MVR reduces spike latency over a range of conditions
Visual and auditory information is contained not only in the number of spikes generated by a stimulus but also in their timing (Gollisch and Meister, 2010; Butts et al., 2011; Rutherford et al., 2012, 2021). In vertebrate vision, spikes can be precise to within a few milliseconds in RGCs (Berry et al., 1997; Uzzell and Chichilnisky, 2004), the LGN (Reinagel and Reid, 2002), and visual cortex (Buracas et al., 1998). This level of precision allows the latency to the first spike in RGCs to transmit more information about a stimulus than the total number of spikes, at least when a stimulus drives episodic responses (Gollisch and Meister, 2008).
To assess the impact of MVR on the temporal precision of spike generation, we analyzed how
Hybrid coding reduced spike latency over a range of physiologically relevant conditions. A, Top, Mean first spike latency as a function of leak time constant (tl) for a cell receiving N = 500 inputs and requiring k = 100 vesicles to spike in response to a 5 Hz stimulus of varying contrast (other parameters as in the “large” cell in Fig. 3). Latencies were measured relative to an arbitrarily chosen phase of the sinusoidal stimulus, so it is the change in these values that is most informative. Bottom, Latency difference (hybrid – rate) from the data in top panel. For this ratio of k:N, the hybrid code produced at greater latency when tl > 15 ms. B, Top, Heat map showing the average first spike latency generated by hybrid inputs for cells of varying k/N and tl for a stimulus of 20% contrast. Latencies were averaged over values of k and N shown in Table 1. Bottom, Same as in top, but for 80% contrast. C, Same as in B, but for rate-coded inputs. D, The difference in first spike latency generated by hybrid- and rate-coded inputs in B and C. For a given tl, rate-coded inputs generated faster responses at lower k/N, while hybrid inputs generated faster responses at higher k/N (i.e., when spikes are generated by activation of a larger proportion of inputs). Note the different ranges for k/N in top and bottom panels.
Coordinated MVR increases information transmission across a range of conditions
Having established that MVR impacts both spike count and timing, we asked how these actions interact to alter the overall transmission of information (Borst and Theunissen, 1999). The mutual information was calculated between a set of nine stimuli (contrasts of 20%, 60% and 100% at frequencies of 5, 10, and 15 Hz, respectively) and each of three measures of the response in the model neuron: spike count, spike time, and the total information within the spike sequence. A neuron that encodes a total of log2(9) = 3.17 bits of information over a 200 ms time window is discriminating perfectly between the nine stimuli.
The heat plots in Figure 6 demonstrate that spike count carried more of the total information than spike time for both the synaptic coding strategies. But the relative advantages of MVR and rate-codes again depended on the time constant of the target neuron and the reliability of the inputs. In a cell of given time constant, an increase in the reliability of synapses caused the hybrid code to become more efficient at generating spikes (Fig. 4), with shorter latency (Fig. 5) resulting in more information transmission (Fig. 6). In the small cell, for instance, the spike count over a 200 ms period carried 0.07 bits more information when generated by hybrid inputs, while spike time carried 0.08 bits more, and the total information difference was ∼0.16 bits (equivalent to an information rate of 0.8 bits s−1). In a cell with a 10 ms time constant, the largest difference in information rate in favor of the hybrid code was 2 bits s−1, occurring with k/N = 0.5 (Fig. 6C).
Hybrid coding increased information in the spike output over a range of physiologically relevant conditions. A, Left, Heat map represents the information transmitted in the spike count generated by hybrid synaptic inputs for cells of varying k/N and
The rate-code carried more of the total information only in larger cells in which greater numbers of less reliable synapses converge, and the improvements were marginal. For the large neuron highlighted in Figure 3, for instance, we calculated mutual information differences (hybrid – rate) of −0.12 bits for spike count and 0.11 bits for spike time, yielding a total information difference of −0.01 bits. The largest difference in information rate in favor of the rate-code was only 0.24 bits s−1, occurring in a cell with a time constant of 50 ms and k/N = 0.2.
Together, the simulations in Figures 2–6 indicate that synapses that generate MVR can often trigger more spikes per released vesicle compared with a classical Poisson synapse in which all vesicles are released independently. In cells with time constants <15 ms, the tendency for MVR to enhance the transmission of information becomes greater as k/N falls below ∼0.8. These conditions are physiologically relevant. In the peripheral retina, for instance, α ganglion cells have membrane time constants <5 ms and 10 or fewer quanta released from thousands of synapses are sufficient to generate a spike (Freed and Sterling, 1988; O'Brien et al., 2002). More morphologically compact neurons, such as midget ganglion cells in the fovea of primates, only receive inputs from synapses from a single midget bipolar cell and are likely to have longer time constants (Sinha et al., 2017).
MVR increases the efficiency of information transmission across a range of conditions
Neurons can transmit more information by spiking at higher rates, but this comes at a relatively large energetic cost (Laughlin, 2001; Sterling and Laughlin, 2015). The release of vesicles and generation of spikes is the major consumer of energy in the brain with one estimate being of the order of ∼24,000 ATP molecules consumed per bit of information transmitted (Attwell and Laughlin, 2001; Harris et al., 2012). The efficiency with which vesicles drive the spike code is therefore likely to have been an evolutionary constraint on the vesicle code itself (Sterling and Laughlin, 2015).
To investigate the potential effects of MVR on the efficiency of information transmission, we normalized the measurements of total information summarized in Figure 6A, B as bits per vesicle and bits per spike, as shown in Figure 7A, B. Considering the amount of information per vesicle, the relative advantages of hybrid and rate-codes can be seen to follow a clear pattern: the more reliably inputs responded (i.e., the higher k/N), the broader the range of cell time constants over which hybrid-coded inputs improved the efficiency with which vesicles transferred information through spikes in the target neuron (Fig. 7A, right). The rate-code was only slightly advantageous in neurons acting as the best temporal integrators receiving the least reliably responding inputs. The highest vesicle efficiency using either synaptic code was ∼0.044 bits per vesicle.
Hybrid coding increased the efficiency of information transmission over a range of conditions. A, Left, Heat map showing the information transmitted per vesicle generated by hybrid synaptic inputs for cells of varying k/N and τ1. Middle, The same for rate-coded synaptic inputs operating at the same average release rates. Right, The difference in the efficiency of information transmission considered as bits per vesicle (hybrid – rate). Right, Color scale represents combinations of parameters in which hybrid inputs generated more spikes in green. The parameters for the specific model cells featured in Figure 3 are indicated as S (small) and L (large) in the heat plot. B, Same as in A, but considering efficiency as bits per spike. The hybrid vesicle code increases the efficiency of information transmission across a range of conditions. The pure rate vesicle code was only advantageous in LIF neurons with the longest time constants driven by the most reliably responding synaptic inputs.
A similar pattern was observed when we quantified the amount of information per spike: the more reliably inputs responded the broader the range of cell time constants over which hybrid-coded inputs increased the amount of information per spike (Fig. 7B, right). The highest spike efficiency was ∼3 bits per spike. A comparison can be made with the information transmitted by spikes in RGCs responding to white-noise stimuli, where the most sluggish transmit ∼3.5 bits/spike, while those that fire most briskly encode ∼2 bits/spike (Koch et al., 2006). The results in Figure 7 encapsulate what we believe is the most fundamental insight of this study: the potential of MVR to increase the efficiency with which vesicles are used to transmit information.
The first synapse in hearing
The results described so far have concentrated on a range of physiological parameters likely to operate in the retina because that is the context in which we measured the statistics of vesicle release. Our current understanding of the role of MVR in auditory systems is limited by a lack of measurements in response to the normal sensory input: sound. In the amphibian papilla, a voltage-clamp stimulus generates MVR events composed of up to 6 quanta with larger events being more tightly phase-locked to a sinusoidal stimulus (G. L. Li et al., 2009, 2014); while in rat inner hair cells, MVR events can be as large as 20 vesicle equivalents when triggered by depolarization with a solution high in K+ (Glowatzki and Fuchs, 2002). But other studies using voltage-clamp suggest that release from rat hair cells is purely uniquantal and that variations in the size of postsynaptic EPSCs reflect variations in the size of fusing vesicles (Chapochnikov et al., 2014; Grabner and Moser, 2018). In mammals, spikes in the afferent fiber can be triggered by just a few vesicles and in some cases just one (Rutherford et al., 2012; Grabner and Moser, 2018).
Despite these uncertainties, transmission from auditory hair cells in mammals presents an interesting special case because there is no convergence onto the target. Each Type I afferent fiber senses glutamate released from just one ribbon synapse; and in this situation, the stochasticity of the release process will limit the reliability of transmission (Graydon et al., 2014). We therefore investigated the situation of N = 1 synapse and considered two broad scenarios: (1) k = 1 where any vesicular event, regardless of quantal content, is capable of generating a spike; and (2) k > 1, where some (but not all) multivesicular events are capable of generating a spike from rest. Here we used the release measurements taken from BCs: hair cells may have differing release statistics.
The transmission of information was strongly dependent on both the number of vesicles required to generate a spike, k, and the membrane time constant, but again the nature of this dependence differed for synapses using a pure rate-code compared with those also using MVR (Fig. 8A). Rate coding produced the maximum mutual information in the simulations when k = 1, where the spike sequence in the afferent reproduced the vesicle sequence leaving the synapse (Fig. 7A, red). In this situation, a multivesicular event is no more effective than a univesicular event, so the hybrid code produces fewer spikes per vesicle and reduces the efficiency of information transmission (Fig. 8A, black).
Spike count information for amplitude (black) and rate (red) inputs as a function of
As the gain of synaptic transmission decreased and more vesicles were required to generate a spike (k > 1), trends altered. Increasing k reduced the spike count and effectively abolished spiking at k > 3 when tau = 1 ms (Fig. 8A,B). Essentially, this is because the very short time constant of the target neuron (mimicking an afferent fiber) did not allow for effective summation of vesicles. Hybrid coding, however, expanded the range of responses by increasing the number of spikes a stimulus could generate, maximizing at a value when most events at higher contrast individually generated a spike (approximately k = 4 for this range of conditions, as seen in Fig. 8B,D). This switch in the relative efficiency of the two synaptic coding strategies starkly illustrates a key functional advantage of the hybrid code: presynaptic integration of vesicles by MVR compensates for situations where the integration time of the postsynaptic neuron is short and limits summation postsynaptically.
The heat map in Figure 8D demonstrates that the increase in the efficiency of information transmission caused by MVR was most dramatic in target neurons with time constants less than ∼10-15 ms in which a spike could be triggered by the arrival of 3-5 vesicles. For 5 < k < 10, MVR still used vesicles more efficiently than a pure rate-code (Fig. 8D), despite the fact that not all MVR events were capable of generating a spike even at the highest contrasts. Hair cells in rats and the amphibian papilla can generate MVR events with quantal contents in this range (Glowatzki and Fuchs, 2002; Keen and Hudspeth, 2006; G. L. Li et al., 2009; Graydon et al., 2011), suggesting that the advantages of a hybrid code might be exerted over a broad range of k in auditory systems.
Discussion
This study indicates that, compared with regimens in which all vesicles are released independently, MVR can increase the efficiency with which information is transmitted over a range of conditions operating in the first stages of vision and hearing (Figs. 4–8). Two aspects of the process driving spikes interacted to determine the relative efficiencies of hybrid and rate-codes: the time constant of the target neuron and the reliability of the synaptic inputs. MVR tended to be advantageous when (1) the neurons' time constant was shorter, causing less postsynaptic summation of synaptic potentials, and (2) individual synaptic inputs were more reliable so that a lower degree of convergence was required to depolarize the target to threshold for a given stimulus strength.
Potential problems with Poisson synapses as transmitters of early sensory information
It has long been recognized that a potential drawback of a pure rate-code in which all vesicles are released independently is the time scale on which it can transmit information: the more variable the response to a stimulus, the longer the observation time required to detect it to a given degree of certainty (Gerstner et al., 1997; Stein et al., 2005). At synapses of bipolar cells, the maximum sensitivity to changes in contrast occurs around an average release rate R of 20 vesicles s−1 and a 10% increase in contrast increases release by a factor of a = 1.8 (James et al., 2019). If release events are Poisson distributed, detecting that increase with a SNR of 2 would require counting an extra 14 vesicles over an observation time (Δt) of ∼900 ms (Eqs. 7–9). But vision operates much more rapidly: our visual system can process a scene in <150 ms (Thorpe et al., 1996).
The convergence of bipolar cell synapses onto RGCs is one feature of the retinal circuit that will shorten the time required to detect a change in the stimulus. N equivalent Poisson inputs allow a given SNR to be achieved with a time window that varies as 1/√N (Gerstner et al., 1997; Faisal et al., 2008; Rusakov et al., 2020) so, continuing with the example above and considering a time window of 100 ms, the output of 50 synapses would provide a SNR of 2, but this would require the release of N*(1 – a)*R*Δt = 80 extra vesicles. This is a significant cost given that excitatory transmission is a major consumer of ATP in the brain (Attwell and Laughlin, 2001).
A similar problem arises at the first synapse in vision, where the assumption of Poisson release from rod photoreceptors indicates that reliable transmission of the hyperpolarizing response to a single photon would require a basal release rate of ∼100 vesicles s−1 (Rao-Mirotznik et al., 1998). Schein and Ahmad (2006) proposed that a more efficient solution would be if release occurred at regular intervals so that a random pause could be distinguished more reliably from the absorption of a photon. Hays et al. (2021) have recently provided direct evidence for this mechanism. At the resting membrane potential in darkness (−40 mV), there was a high Pr of multivesicular events from rods, each containing ∼17 vesicles, and these were nearly abolished by a small membrane hyperpolarization mimicking a single-photon response. These results suggest that the most fundamental function of the ribbon in rods, at least from an information-processing point of view, is as a synaptic clock that reduces stochastic noise.
The potential problems with a pure rate-code highlighted above are, however, closely linked to the idea that information about a sensory variable is transmitted continuously. Indeed, the retina can also act as a “feature detector,” when RGCs fire in bursts driven by fusillades of vesicles released from bipolar cells (Berry et al., 1997; Keat et al., 2001; Freed, 2005). Synapses of bipolar cells in zebrafish also signal visual events in bursts (Fig. 1A,C) and larger MVR events achieve millisecond precision similar to spikes in RGCs (Fig. 1E,F). This comparison highlights one of the potential advantages of representing a stimulus using synaptic symbols of different amplitude: an unexpected symbol immediately imparts new information.
MVR at the ribbon synapse of hair cells
A functional role of MVR in hair cells is strongly suggested by the observation that larger synaptic events are more strongly phase-locked than smaller ones (G. L. Li et al., 2014). Our simulations also indicate that where a single synapse drives an auditory afferent, coordinated MVR would increase the efficiency with which information is transferred whenever the summation of inputs from more than one vesicle is required to trigger a spike (Fig. 8).
The effects of release statistics on the reliability of transmission have also been investigated using models that incorporate glutamate diffusion and the ultrastructure of connections (Graydon et al., 2014). Quantifying the reliability of signaling as the CV of the postsynaptic current, the greatest improvement of MVR over univesicular release came with fewer inputs of highest reliability, equivalent to the metric k/N used in the present study. Here we quantified the quality of transmission as the mutual information rather than CV but also find that MVR is most advantageous in neurons with reliable synaptic inputs, when a lower degree of convergence is required to trigger spikes (Figs. 6–8). Only when arrival of a single vesicle triggered a spike did the pure rate-code transmit information more efficiently (Fig. 8).
Improved models
An obvious limitation of the LIF model we used is that we only considered excitation. Feedback inhibition from amacrine cells synapsing directly onto the terminal compartments of bipolar cells will be a key determinant of their output to RGCs (G. L. Li et al., 2007), while feedforward inhibition to RGCs increases the temporal precision of spikes and also causes firing in bursts (Johnston and Lagnado, 2015; Murphy-Baum and Taylor, 2018). Network models incorporating a wider range of biophysical parameters will help us understand how excitation and inhibition interact to determine the spike code leaving the retina.
A second limitation is that we have only been able to use the statistics of release measured from bipolar cells in the retina of zebrafish. Auditory systems operate at frequencies at least one order of magnitude higher than vision, and more realistic simulations would need knowledge of the statistics of release from hair cells responding to sound. In the amphibian papilla of bullfrogs, a pure tone has been mimicked by applying sinusoidal command voltages to hair cells while recording spikes in the connected afferent (G. L. Li et al., 2014). There, the TJ in large synaptic events is ∼0.3 ms using a stimulus of 400 Hz, equivalent to a vector strength of ∼0.45 (Eq. 5). At the ribbon synapse of bipolar cells stimulated at 5 Hz, even univesicular events displayed a vector strength of 0.75 (Fig. 1E). Models of MVR at the synapse of hair cells that take into account the distribution of vesicles and the kinetics of calcium-triggered exocytosis indicate that the temporal precision of MVR derives from the most obvious function suggested by the ultrastructure of the ribbon: the holding of a reservoir of vesicles just behind the active zone (Wittig and Parsons, 2008).
MVR at “classical” synapses
MVR occurs in many brain regions (Rudolph et al., 2015), including the hippocampus (Christie and Jahr, 2006), cerebellum (Auger et al., 1998), and somatosensory cortex (Huang et al., 2010). A recent combination of electrophysiology with correlative light- and electron-microscopy has even led to the suggestion that MVR may contribute to synaptic transmission throughout the nervous system (Holler et al., 2021). MVR adheres to binomial statistics in parallel fibers in the cerebellum (Malagon et al., 2016) and Schaeffer collaterals in the hippocampus (Dürst et al., 2022), indicating that it reflects a transient increase in Pr to very high values but with vesicles still being released independently. This may reflect a basic difference with coordinated MVR at sensory synapses where docking sites are organized around the ribbon structure and which often do not adhere to binomial statistics (Glowatzki and Fuchs, 2002; Hays et al., 2021; Moya-Díaz et al., 2022).
Whatever the underlying statistics, the functional implications of MVR are similar at all synapses because the closer together in time vesicles are released the more effectively they will summate postsynaptically (Dayan and Abbott, 2005; X. Li and Ascoli, 2008). This idea has important implications for understanding how information is transmitted in the brain because MVR events with different quantal content can be considered different symbols in the vesicle code. In retinal bipolar cells, larger and rarer events carry more information about a visual stimulus than smaller ones but are also more efficient in carrying more bits per vesicle (James et al., 2019). It has recently been demonstrated that the retinal neuromodulator dopamine adjusts the distribution of MVR events to alter the efficiency of this amplitude code (Moya-Díaz et al., 2022). Recent modifications in iGluSnFR that improve SNR in the brain of mammals provide a promising method to investigate how the vesicle code might be modulated in other parts of the brain (Aggarwal et al., 2022; Dürst et al., 2022).
Footnotes
This work was supported by Wellcome Trust 221936/Z/20/Z; and European Community International Training Network “Switchboard.” We thank all the laboratory folk for discussions at various points.
The authors declare no competing financial interests.
- Correspondence should be addressed to Leon Lagnado at l.lagnado{at}sussex.ac.uk
