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, 33 (36), 14406-16

Stochastic Properties of Neurotransmitter Release Expand the Dynamic Range of Synapses

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Stochastic Properties of Neurotransmitter Release Expand the Dynamic Range of Synapses

Hua Yang et al. J Neurosci.

Abstract

Release of neurotransmitter is an inherently random process, which could degrade the reliability of postsynaptic spiking, even at relatively large synapses. This is particularly important at auditory synapses, where the rate and precise timing of spikes carry information about sounds. However, the functional consequences of the stochastic properties of release are unknown. We addressed this issue at the mouse endbulb of Held synapse, which is formed by auditory nerve fibers onto bushy cells (BCs) in the anteroventral cochlear nucleus. We used voltage clamp to characterize synaptic variability. Dynamic clamp was used to compare BC spiking with stochastic or deterministic synaptic input. The stochastic component increased the responsiveness of the BC to conductances that were on average subthreshold, thereby increasing the dynamic range of the synapse. This had the benefit that BCs relayed auditory nerve activity even when synapses showed significant depression during rapid activity. However, the precision of spike timing decreased with stochastic conductances, suggesting a trade-off between encoding information in spike timing versus probability. These effects were confirmed in fiber stimulation experiments, indicating that they are physiologically relevant, and that synaptic randomness, dynamic range, and jitter are causally related.

Figures

Figure 1.
Figure 1.
Stochastic firing properties of BCs in the cochlear nucleus. A–C, Representative current-clamp recording from a BC in response to ANF stimulation. A, ANF stimulation (vertical markers) at 200 Hz triggers BC spikes or EPSPs. Arrows indicate −60 mV for each trace. B, Raster plot of spike times over 25 trials, showing a sustained, but irregular, response. C, Probability of spiking for stimulation trains of different frequency. At 100 Hz, the probability of spiking (Pspike) was nearly 100% after stimulation, whereas at 333 Hz, Pspike was nearly 0%. At intermediate stimulation rates, Pspike took on intermediate values. D, Average Pspike for six experiments similar to A. On average, Pspike decreased gradually over the course of a train at all frequencies.
Figure 2.
Figure 2.
Variability in EPSCs during trains of activity. A–C, Representative voltage-clamp recording. A, Single trial of a 40-pulse, 200 Hz train. Inset, Magnified view of the same trace. EPSC amplitude is quite variable from pulse to pulse, even at steady state. B, EPSC amplitudes from 24 trials similar to A. Open circles represent EPSCs on single trials, and closed circles represent the overall average. C, EPSC mean ± SD for trains of multiple frequencies. These amplitudes were used to drive dynamic-clamp experiments in Figure 3 and were fit using the model of stochastic release in Figure 4. D, EPSC mean ± SEM for 6 cells recorded in voltage clamp. E, Variability in EPSC represents a large fraction of the EPSC amplitude at steady state. Mean CV (SD/mean) is plotted over the train for 6 cells recorded in voltage clamp. The steady-state CV for pulses 11–40 is shown at right.
Figure 3.
Figure 3.
Stochastic EPSC amplitude increases the dynamic range of synaptic transmission. A–D, Representative dynamic-clamp recording. A, Synaptic conductances used to drive dynamic-clamp experiments. Synaptic conductances were based on EPSCs measured in separate voltage-clamp experiments shown in Figure 2A–C. On different dynamic clamp trials, either the overall average amplitude (left, average of 20 trials) or amplitudes measured on individual trials (right shows five examples) were convolved with a unitary EPSC (left, inset). B, Sample dynamic clamp trials, with conductances drawn from the overall average EPSC on each trial (left), or the EPSC amplitudes measured in individual trials (right, each trace uses a unique set of conductances, shown in A). Spiking was highly repeatable using the average conductance compared with the individual conductances. For the average conductance (left), the 39th pulse in the 100 Hz train showed nearly 100% reliable spiking (asterisk below traces), whereas the 38th and 40th failed to elicit spikes, even though differences in the average conductance are imperceptible over this range (A). Spiking was much more variable when using the conductances from individual trials (right). Arrowheads to the left of traces indicate −60 mV. C, Raster diagram of spike times from 32 trials using the average (left) or individual (right) conductances. Continuous vertical lines indicate highly regular firing. D, Pspike for dynamic clamp trials driven with average versus individual conductance for 100 Hz trains, calculated from the rasters in C. The average conductance led to sharp oscillations in Pspike (closed circles) compared with the individual conductances (open circles), which showed a gradual decline. E, Relationship between Pspike and average pulse conductance GAMPA. GAMPA was the same for dynamic clamp conductances based on either individual voltage-clamp trials (A–C, right) or the overall average (A–C, left) for trains of 50, 100, and 200 Hz. Pspike values are derived from the same analysis as in D but are plotted against the average conductance for that pulse. Lines are sigmoidal fits to the data using Equation 1, and the derived measure of dynamic range is indicated by the dumbbells above the graph. F, Pspike as a function of conductance amplitude, regardless of position in the train. Synaptic conductances from the experiments of A and B were sorted by amplitude across all trials, then binned to calculate Pspike. Data from average trials are shown with solid symbols, and from individual trials are shown with open symbols. Lines are sigmoidal fits to the data as in E, with dynamic ranges indicated by the dumbbells above the graph. The average difference in dynamic range was 0.32 ± 0.10, which was not significant (p = 0.12, N = 7 cells). G, Dynamic range increased when stochastic properties of neurotransmitter release were included in dynamic-clamp trials. We fit sigmoidal curves (Eq. 1) to measure the dynamic range for individually variable trials (open circles, open bars) and the average trials (closed circles, solid bars). The dynamic range increased significantly when considering Pspike as a function of average conductance amplitude for individual pulses (p < 0.001), but not when considering Pspike as a function of conductance amplitude regardless of train position (p = 0.12). Data are averages from seven cells.
Figure 4.
Figure 4.
Stochastic model of neurotransmitter release. A, Diagrammatic view of deterministic (left) and stochastic (right) models of release. The deterministic model tracked the average behavior of a synapse, using fixed rates of release and recovery of a pool of vesicles, as well as desensitization and recovery of postsynaptic receptors (see Materials and Methods). The stochastic model tracked multiple sites, each with its own pool of vesicles and receptors. Release and recovery were governed by binomially distributed random processes. The deterministic model used seven parameters, and two parameters were added for the stochastic model. B, Activity of a single release site, showing fluctuations in vesicle pool size (NV) and extracellular glutamate concentration during a train of activity. C, The stochastic model captured both mean and variance of synaptic transmission. Symbols show mean (top) and SD (bottom) of voltage-clamp data from the cell depicted in Figure 2A–C. Solid lines show mean and SD of conductances given by the stochastic model.
Figure 5.
Figure 5.
Dynamic range increases with synaptic variance. Data are results of dynamic-clamp experiments run using the deterministic (solid symbols) and stochastic (open symbols) models of neurotransmitter release, with model parameters held constant, except for the number of release sites (NS). As NS increased, the conductance variability decreased. A–C, Spike probability for each pulse (Pspike) as a function of the pulse's average synaptic conductance (GAMPA) in a representative experiment. For the deterministic model (solid symbols), dynamic range was uniformly narrow. For the stochastic model, the dynamic range was greater for low NS. Dynamic ranges for the different conditions are indicated using the dumbbells above each plot. D, Dynamic range as a function of NS for five experiments. Dynamic range was widest for the smallest number of release sites and narrowed with increasing NS. Dynamic range was most narrow with the deterministic model. E, Dynamic range as a function of synaptic variance. Dynamic ranges from D are plotted against the CV of the steady-state synaptic conductances for different NS (mean ± SEM of five experiments).
Figure 6.
Figure 6.
Stochastic properties of release uncover high-frequency activity. A–D, Data from a representative dynamic-clamp experiment using a 75 Hz Poisson-distributed train of activity to drive the conductance model. A, B, Responses of a BC driven by deterministic (A) or stochastic (B) model conductances. The actual (A) or average (B) conductances are shown above the rasters. For scale, the final conductance in the train was 20 nS. With the deterministic model (A), responses were highly bimodal, either reliably firing or reliably failing to fire on nearly every trial. By contrast, responses to the stochastic model (B) were much more variable. Many pulses produced spikes in B that failed to do so in A. Responses are shown at steady state, beginning with the 10th pulse. C, Conductances at short intervals tended to be smaller. Conductance amplitudes were from the deterministic model. D, Pspike as a function of preceding interval, revealing a wider dynamic range for trials using the stochastic model (open circles) compared with the deterministic model (closed circles). Lines are sigmoid fits to the data to quantify the dynamic range, which is indicated using dumbbells above the graph. E, Average dynamic ranges from five experiments using deterministic (closed circles, solid bar) and stochastic models (open circles, open bar). The increase is statistically significant (p = 0.003, t test).
Figure 7.
Figure 7.
Increased variability also drives an increase in jitter, causing a trade-off. A–C, Data from a representative dynamic-clamp experiment illustrating the effects of synaptic variability on jitter. A, Spike latency after synaptic conductances in regular, 50 Hz trains (similar to the experiments of Fig. 5). Each horizontal line shows the spike latencies from steady-state pulses 11–40 of a single trial all overlaid, with a small vertical displacement to avoid perfect overlap. Spike latencies have a resolution of 20 μs. The black line at left indicates the time of the peak of the synaptic conductance (Fig. 3A, left, inset). The variability of synaptic conductances was controlled by changing the number of release sites (NS). Spike latencies were more variable for smaller NS (i.e., more variable conductance amplitude). The deterministic model had the least jitter. B, Latency histogram of spikes from A. Markers indicate overall mean and SD of the latency. The mean was unaffected by the variability of synaptic conductance, but the SD (i.e., the jitter) increased with decreasing NS. C, Effect of individual synaptic conductance GAMPA on spike latency. Spike latency is inversely related to GAMPA. Thus, variability in synaptic conductance results in variability in spike latency. D, Spike jitter as a function of the number of release sites, from five experiments similar to A–C. E, Trade-off in spike jitter and dynamic range. As dynamic range increases, so does jitter. Jitter data are from D, and dynamic range data are from Figure 5D. The measurements of dynamic range and jitter from current-clamp experiments in Figure 8 are also included for comparison (black +).
Figure 8.
Figure 8.
Dynamic range and jitter for real fiber stimulation match dynamic-clamp experiments. A, Measuring EPSP amplitudes. Traces are raw membrane potential (V, top) and first (V′, middle) and second (V″, bottom) derivatives. Broad-dashed lines indicate fiber stimulation times (stimulus artifact was small in this example). Fine-dashed lines indicate times of EPSPs and spikes as used for subsequent analyses. All traces are filtered at 5 kHz. B, Dynamic range. Average Pspike was calculated for individual pulses in trains of 100, 200, and 333 Hz stimulation rates and plotted against the average EPSP amplitude (open circles). This relationship was fit to Equation 1 to estimate the dynamic range (open dumbbells above the plot). To estimate the deterministic dynamic range, we sorted EPSPs by amplitude before calculating Pspike and average EPSP (closed circles). C, Average dynamic ranges from six similar experiments averaging by EPSP amplitude (closed circles, solid bar) or train pulse (open circles, open bar). The increase is statistically significant (p < 0.001, t test). D, Same data as C, but normalized to spike threshold (EPSP1/2), to facilitate comparison with dynamic-clamp experiments. E, BC spike jitter in the same cell as A and B. All successful spikes are overlaid for pulses 11–20 in 200 Hz trains (86), which cover a wide range of EPSP amplitudes. The EPSP latency is quite constant, whereas spikes are extremely variable. The arrow indicates the stimulus time. F, Spike latency for the same cell as A, B, and E. Latency was measured from the stimulus (upper circles) or the EPSP (lower squares). All spike times are shown for 100 (blue), 200 (green), and 333 (red) Hz stimulation. Both methods indicate that latency is highly inversely dependent on EPSP amplitude. G, Average spike jitter in six experiments for pulses 11–20 of 100, 200, and 333 Hz trains. In two cells, spike probability was too low to measure jitter at 333 Hz stimulation.

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