The Impact of Multivesicular Release on the Transmission of Sensory Information by Ribbon Synapses

The statistics of vesicle release determine how information is transferred at the synapse but the classical Poisson model of independent fusion does not hold at the first stages of vision and hearing. There, ribbon synapses encoding analogue signals can coordinate the release of two or more vesicles as a single event. The implications of such multivesicular release (MVR) for spike generation are not known. Here we investigate the hypothesis that MVR might provide advantages over Poisson synapses. We used leaky integrate-and-fire models incorporating the statistics of release measured experimentally from glutamatergic synapses of retinal bipolar cells 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 spike) over a range of conditions mimicing retinal ganglion cells of different size. MVR was most advantageous in neurons with short time-constants and reliable synaptic inputs, when a lower degree of convergence was required to trigger spikes. In the special case of a single input driving a neuron with short time-constant, as occurs at the first synapse in hearing, MVR increased information transfer whenever spike generation required more than one vesicle. This study demonstrates how presynaptic integration of vesicles by MVR has the potential to compensate for less effective summation post-synaptically to increase the efficiency with which sensory information is transmitted.

. We gather these statistics from the ribbon-type synapse of

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Distribution of event amplitudes during a 30 s application of a 5 Hz stimulus at 80% contrast (n = 55 144 synapses), truncated to only include events containing fewer than 11 quanta. D. A quantal time series (black 145 lines) in response to a 5 Hz, 80% contrast full-field stimulus (red), with blue dashed lines present only for ease 146 of visibility. Note that events composed of four or more vesicles occur in a temporally small window during 147 each cycle, while lower quantal events are more temporally dispersed. E. The temporal jitter as a function of 148 quanta in event for a 100% contrast stimulus (n = 60 synapses). F. Mean-shifted distribution of events 149 containing 5 or more quanta (black) and of events containing one quantum (red) in response to a 30 s, 5 Hz,

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The output of a synapse employing coordinated MVR was generated by randomly 152 selecting a total of N events with amplitudes chosen from the distribution of quanta in an 153 event P(Qe) (Fig. 2B). Each event was then given a time by sampling from the Gaussian 154 distribution of event times with mean and variance measured experimentally i.e by TJ(Qe) 155 shown in Fig. 1F. Each synapse was constrained to generate only one or zero events per 156 cycle of the stimulus, with the probability of no event given by ! ( , ). The output of each 157 synapse was therefore described as a vector E of event times and a vector Qe of event

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The rate-code comparison was constructed by replacing each event consisting of 175 more than one quantum with an equivalent number of uni-quantal events, each event time 176 now sampled from the distribution of times of uniquantal events (Fig. 1F). The vectors 177 describing a pure rate synapse were therefore of variable lengths corresponding to the 178 total number of vesicles sampled within the 30 s sample period. The resulting vectors Qe 179 and E of event quanta and event times were then passed into a conductance-based 180 model LIF model (Fig. 1)

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A key aspect of our investigation was to construct the rate and hybrid models in such 197 a way that each released the same average number of vesicles, with differences found 198 only in the variabilities. In other words, vesicles were released individually in the "rate 199 code", but in packets of variable size in the "hybrid code". To simulate pure rate-coded 200 synaptic inputs case, we used a sinusoidal intensity function. The response of each 201 synapse to varying contrasts was simulated by increasing the amplitude of the sinusoid 9 between a total release of between 5 vesicles s -1 at input condition 1 (which we term 10% 203 contrast below) and 65 vesicles s -1 at input condition 10 (100% contrast; Fig. 2D and E).

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for the rate case. Responses from multiple cells were assumed to come from the same 205 distribution, and as such we simulated the responses of multiple BCs onto a single RGC 206 by summing the response to all the individual synaptic inputs. To simulate hybrid coding 207 the probability of release was also modulated as a sinusoid with an amplitude generating 208 an average rate of vesicle corresponding to that measured experimentally at a given 209 stimulus contrast (Fig. 1A).

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Where " is leak conductance, $ is excitatory conductance, $ is the excitatory reversal

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To compare how the MVR might shape the spike output of a postsynaptic cell across 243 a range of physiological values, we systematically varied the parameters shown in Table   244 1. Note that here, rather than representing the set of the excitatory conductances, g / , we 11 computed the approximate leak conductance required for the cell to spike in response to k where ! # is the phase of the i th event of quantal content Q, and T is the stimulus period.

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VS can then be easily converted to Temporal Jitter (TJ) by: We calculated the mutual information (Shannon, 1948) between the stimulus S and 273 either the spike times or the total number of spikes occurring over a period of 200 ms (N,

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We measured how changes in contrast altered three aspects of the vesicle code

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Using a stimulus of low contrast (20%), the big cell barely responded but the small 395 cell generated an average of one spike per cycle of the 5 Hz stimulus (Fig. 3A). The 17 distributions of spike times were not significantly affected by the coding strategy of the 397 synaptic inputs (Fig. 3B, middle) but when two or more spikes were generated within a 398 cycle the distribution of interspike intervals (ISI) was shifted to significantly lower values 399 when input was provided by hybrid synapses employing MVR (Fig. 3B, bottom;

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Counts were averaged over values of k and N shown in Table 1. Bottom: as top but for 80% contrast. C. As B 476 but for rate-coded inputs. Note again that the average rate of vesicle release was the same as in B for a given 477 contrast. D. The difference between the counts generated by hybrid-and rate-coded inputs in B and C. Note 478 that, for a given τ $ , rate-coded inputs generate more spikes at lower k/N and hybrid inputs were more efficient 479 at higher k/N.

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How does this comparison of the hybrid and rate codes relate to the physiology of the

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Having established that MVR impacts both spike count and timing we asked how these 538 effects interact to alter the transmission of information (Borst and Theunissen, 1999).

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The mutual information was calculated between a set of nine stimuli (contrasts of 20%,

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The heat plots in Fig. 6 demonstrate that spike count carried more of the total 562 information than spike time for both the synaptic coding strategies. But the relative 563 advantages of MVR and rate codes again depended on the time-constant of the target 564 neuron and the reliability of the inputs driving spikes. In a cell of given time-constant, an 565 increase in the reliability of inputs caused the hybrid code to become more efficient at 566 generating spikes (Fig. 4) with shorter latency (Fig. 5) resulting in more information 567 transmission (Fig. 6). In the small cell, for instance, the spike count over a 200 ms period

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As the gain of synaptic transmission decreased and more vesicles were required to 664 generate a spike (k > 1), the picture began to change. Increasing k reduced the spike 665 count and effectively abolished spiking at k > 3 when tau = 1 ms ( Fig. 8A and B).

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The heatmap in Fig. 8D demonstrates that the increase in the efficiency of information 676 transmission caused by MVR was most dramatic in a target neuron with time-constants 677 less than about 10-15 ms in which a spike could be triggered by the arrival of 3-5 vesicles.

Discussion 685
The motivation behind this study was to understand how the unusual statistics of vesicle 686 release from ribbon synapses affected the conversion of analogue sensory signals into 687 spikes. We compared two different regimes of synaptic coding known to operate in 688 different parts of the brain: independent release generating a pure rate code and a hybrid 689 code in which information is contained in both the rate and amplitude of synaptic events.

690
The results indicate that MVR can increase the efficiency with vesicles are used to 691 transmit sensory information over a range of conditions mimicking transmission of visual 692 signals to retinal ganglion cells of different sizes (Figs. 4, 6-7). In the special case of 693 auditory hair cells driving afferent fibers through a single synapse, MVR increased the 694 efficiency of information transfer whenever spike generation required depolarization 695 greater than that caused by a single vesicle (Fig. 8).

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Two aspects of the process driving spikes interacted to determine the relative 697 efficiency of a pure rate-code compared to a hybrid code: the time-constant of the target 698 neuron and the reliability of the synaptic inputs. MVR tended to be advantageous when i) 699 the neurons time-constant was shorter, causing less post-synaptic summation of synaptic 700 potentials at physiological rates of vesicle release, and ii) individual synaptic inputs were 701 more reliable so that a lower degree of convergence was required to depolarize the target 702 to threshold for a given stimulus strength.
30 What do ribbon synapses employ MVR to transmit sensory signals?

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Neurons represent sensory stimuli, at least in part, using a rate-code, where information is 705 contained in the number of spikes over a given time-window (Rieke and Warland, 1999).

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But it has long been recognized that a potential drawback of a pure rate-code is the time-

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The convergence of bipolar cell synapses onto RGCs is of course one features of the 720 retinal circuit that will shorten the time-scale of information transmission using a rate-code.

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The potential problems with a pure rate code highlighted above are closely linked to 729 the idea that the firing rate of a neuron or release rate of a synapse encodes the sensory

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To put the statistics of vesicle release into a functional context we also need an 779 understanding of the spike code that it drives. The most decisive next step would be to