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1Department of Biological Sciences, University at Buffalo, State University of New York, Buffalo, New York; and 2Department of Neurobiology, Harvard Medical School, Boston, Massachusetts
Submitted 20 December 2004; accepted in final form 16 June 2005
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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; Carr 1993; Dan et al. 1998; Heiligenberg 1991; Oertel 1999) and motor systems (Hahnloser et al. 2002; Yu and Margoliash 1996). Behavioral experiments have indicated that acuity can be more precise than the timing of spikes early in sensory processing. These findings are explained in part by several studies that have shown that variability in spike timing ("jitter") is reduced as sensory information is processed in the CNS (Carr 1993).
Jitter reduction has been thought to rely on the convergence of many subthreshold inputs (Burkitt and Clark 1999; Joris et al. 1994a; Mar
álek et al. 1997; Rothman and Young 1996; Rothman et al. 1993), which we explored in the accompanying paper (Xu-Friedman and Regehr 2005). However, many cells in the nervous system receive few synaptic inputs, either because there is a limited number of inputs or because only a limited subset of inputs is active at any given time. Furthermore, there may be advantages to minimizing the number of converging inputs. For example, limited convergence would preserve separate information carried by individual inputs, which could encode stimulus features other than timing with high resolution. The mechanisms of jitter reduction for cells that receive few inputs are not well understood, particularly if the synaptic inputs are subthreshold.
Here we examine how a small number of synaptic inputs can reduce jitter in their postsynaptic target. The best improvement occurred either with suprathreshold inputs or with subthreshold inputs that sum to just above spike threshold. However, the effectiveness of subthreshold inputs was highly sensitive to variability in both the number of inputs and the strength of those inputs. By contrast, convergence of suprathreshold inputs led to jitter reduction that was much less sensitive to changes in synaptic strength and variations in the number of inputs. Although the use of suprathreshold inputs to reduce jitter is conceptually simple, it has not been considered previously. It provides a surprisingly powerful and flexible means of jitter reduction despite its simplicity. We went on to characterize jitter reduction with suprathreshold inputs and identified the conditions necessary for them to contribute to temporal refinement for cells that receive few inputs throughout the nervous system. There were numerous differences between the properties of jitter reduction for few versus many inputs, as described in the accompanying paper (Xu-Friedman and Regehr 2005).
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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). In the experiments in Figs. 3, 6, and 7, each input had a peak conductance of 14 nS. For the experiments in Figs. 2 and 4, the peak conductance for each input was scaled relative to the threshold of the cell. We converted reported vector strength values to SD using the method of Paolini et al. (2001) to facilitate comparison.
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is the relative location of its peak. To generate triangle-distributed random numbers, we chose a uniform random number u, over the interval (0, 1), and transformed it to spike time t
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= 0, 0.25, 0.5, 0.75, and 1. The triangle distribution has SD 
in = w
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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; Sharp et al. 1993) at the synapse made by auditory nerve (AN) fibers onto bushy cells (BCs) in the mouse anteroventral cochlear nucleus (AVCN). In dynamic clamp, synaptic inputs are mimicked by injecting appropriate currents in the soma (Prinz et al. 2004). This approach is appropriate for the synapse made by AN fibers onto BCs because these synapses are axosomatic (Lorente de Nó 1981), so the current injected by dynamic clamp will have the same spatial effect as normal synaptic current. Furthermore, dynamic clamp enabled us to specify multiple synaptic inputs of any amplitude and timing. By contrast, in conventional current-clamp recordings, it is difficult to isolate and stimulate many individual synaptic inputs and impractical to regulate their amplitude.
An additional advantage of this synapse is that in vivo experiments in cats and rats have shown that BCs can have lower jitter than that of their AN inputs when presented with low-frequency tones (Joris et al. 1994a,b; Paolini et al. 2001). This appears to be true even for spherical BCs, despite the fact that they receive few (up to four) AN inputs (Liberman 1991; Sento and Ryugo 1989). BCs have powerful K-currents that tend to limit the extent of firing after an initial spike, and this may be an important feature in the ability of these cells to improve temporal precision (Manis and Marx 1991; Oertel 1983). Thus several characteristics make the AN to BC synapse an appropriate choice for these studies.
We conducted our experiments using mouse brain slices. BCs in mice are thought to have intrinsic properties similar to those in other species and appear to receive few AN inputs (Nicol and Walmsley 2002; Oertel 1985). Therefore mice make a good model system to examine how jitter reduction might be accomplished with few inputs. To mimic synaptic conductances accurately, we made voltage-clamp recordings from BCs to measure the excitatory postsynaptic current (EPSC) time course (see Xu-Friedman and Regehr 2005).
We wanted to understand how the amplitude of synaptic inputs could affect postsynaptic responses separate from the obvious complication of different firing thresholds between cells. Therefore we first measured the firing threshold of cells by applying synaptic conductances in dynamic clamp with a range of peak amplitudes (Fig. 1A). BC firing showed a steep dependency on input amplitude, so threshold was taken as the lowest peak conductance that triggered a spike. Threshold ranged from 10 to 20 nS in different cells (13.7 ± 3.5 nS, mean ± SD, n = 113, Fig. 1B).
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; Joris et al. 1994a; Kiang 1965). We therefore stochastically varied the timing of each input according to both alpha and Gaussian distributions with SD values of 0.5 ms. We considered inputs with a range of amplitudes. To facilitate comparisons between cells, the total conductance for all inputs Gtot was set relative to the threshold conductance of a given cell. An experiment testing the effects of three converging inputs on jitter reduction is illustrated in Fig. 2A. For Gtot = 0.9 times threshold, the cell failed to fire a spike (Fig. 2, A, left, and B). When Gtot was 1.8 times threshold, the BC always responded, but the time of response was more variable (Fig. 2, A, middle, and B). When Gtot was 3.6 times threshold (i.e., each input was suprathreshold), the BC always responded (Fig. 2, A, right, and B). There was rarely any response to later inputs, presumably because they were suppressed by K-channel activation (Manis and Marx 1991) or Na-channel inactivation during the cell's refractory period (Fig. 2B). However, if Gtot was further increased above threshold, later spikes could be elicited (Fig. 2B, gray dots). When different input timing distributions were used, some features of the BC response remained the same, but there were also some major changes. Both alpha and Gaussian distributions showed an increase in the number of spikes per trial as Gtot increased (Fig. 2B). In addition, the response shifted in latency to earlier times with both distributions. However, alpha-distributed inputs led to much greater reductions in first spike jitter (Fig. 2B, left, black dots) compared with Gaussian-distributed inputs (Fig. 2B, right, black dots). In fact, there was very little change in jitter over the whole range of Gtot for Gaussian-distributed inputs.
We observed similar results for six cells (Fig. 2C). For small inputs (Gtot 
1.05 times threshold), the BC responded only rarely, but with high precision. For somewhat larger inputs (Gtot = 1.2 to 2.4), the average number of spikes per trial increased, the latency to response decreased, and jitter increased. For larger, suprathreshold inputs (Gtot 
3.6), the response probability was high and jitter was greatly reduced with alpha-distributed inputs. By contrast, for Gaussian-distributed inputs, jitter was not substantially reduced. At higher amplitudes, secondary spikes could be elicited with both distributions, which compromise jitter reduction (Fig. 2C, gray traces) (see also Rothman et al. 1993). Multiple spikes are not normally observed over one cycle of a tone stimulus in BCs in vivo (Joris et al. 1994a) because they are suppressed both by the refractory period and by short latency inhibition that occurs in the intact AVCN (0.6–4 ms; Oertel 1983; Paolini and Clark 1998; Wickesberg and Oertel 1990; Wu and Oertel 1986). Jitter reduction was consistently better when only the first spike was considered (black traces). Thus very small inputs and suprathreshold inputs provide optimal jitter reduction.
Small inputs appear to be effective at reducing jitter because they must all arrive very close in time to trigger a spike, because of the fast time constant of BCs (Oertel 1983). This high degree of coincidence is likely to happen only when they are all well locked to a stimulus. This happens in a small subset of trials, resulting in a low probability of postsynaptic spiking. When Gtot = 0.9 times threshold, the probability of firing was 13 ± 3% for alpha-distributed inputs (n = 11 cells) and 13 ± 4% for Gaussian-distributed inputs (n = 5 cells).
Suprathreshold inputs are similar to small ones in that they are also effective at reducing jitter. However, the probability of firing is much higher and more consistent with suprathreshold inputs (Fig. 2C). Thus jitter reduction using suprathreshold inputs is more robust than using small inputs.
We wanted to further explore the effectiveness of suprathreshold, alpha-distributed inputs at reducing jitter. Most models of convergence have emphasized the interaction of multiple subthreshold inputs, whereas suprathreshold inputs have received less attention (Joris et al. 1994a; Marálek et al. 1997; Rothman and Young 1996; Rothman et al. 1993). First, we tested the sensitivity of jitter reduction to the number of suprathreshold inputs, using alpha-distributed inputs (in = 1 ms) with peak conductance of 14 nS, which was suprathreshold for the cells tested here. Sample trials are illustrated for one and four inputs in Fig. 3A. The resulting latency from the starting time to the first BC spike is shown for a sample experiment for one to four inputs (Fig. 3B). The amount of jitter in the BC spike matched the jitter for one input (Fig. 3B, top, red). There were two main effects of increasing the number of inputs: the spike latency shortened and the jitter got progressively smaller for two (green) and three (cyan) inputs, and was least for four inputs (Fig. 3B, bottom, blue). Eight experiments gave similar results. Average histograms of first spike times show that the distribution is much broader for one input and is progressively sharper with multiple inputs (Fig. 3C). Normalizing these spike-latency histograms more clearly shows the improvement in jitter (Fig. 3D). The spike latency shifted by nearly 1 ms as the number of inputs increased to four (Fig. 3E), whereas the SD of BC spike latency was reduced considerably with two to four inputs compared with one (Fig. 3F). The SD was <0.5 ms for three and four inputs.
In the experiments described so far, each trial was well separated in time to minimize activity-dependent effects. However, neurons usually fire in trains of activity. High rates of postsynaptic spiking could change threshold by activating or inactivating conductances that influence spike generation. We therefore examined the ability of a small number of inputs to reduce jitter during trains. We applied trains in dynamic clamp with three inputs during each of 20 cycles. The timing of each input followed an alpha distribution with SD of 0.5 ms. To investigate the effects of postsynaptic changes in excitability during trains without confounding presynaptic changes, the amplitude of each input was held constant throughout the train at 2.5 times threshold (i.e., Gtot = 7.5). Threshold was determined as in Fig. 1. Responses of a typical cell to 100- and 333-Hz trains are shown in Fig. 4, A and B. In both cases, the BC fired a spike on every cycle of the train, which was triggered by the first excitatory postsynaptic potential (EPSP) in each cycle. There were occasional secondary spikes (asterisk in Fig. 4A), which were few in number and followed the first spike in a cycle with a long latency. This indicates that jitter reduction of first spikes could continue throughout trains of high frequency.
Similar experiments were conducted in six cells, the average results of which are shown in Fig. 4C. The number of spikes elicited per cycle was greater than one during the first cycle of the train, consistent with the findings for isolated stimuli presented in Fig. 2C. The frequency of secondary spikes decreased over the course of the train, particularly at high frequencies (Fig. 4C, top). There were also small changes in latency to first spike after the second cycle (Fig. 4C, middle). Spikes continued to be triggered off the first EPSP in each cycle, but the time required to reach threshold was greater after the second cycle. The jitter of first spikes in each cycle was constant throughout the train and was reduced compared with the inputs (Fig. 4C, bottom). Thus convergence of few suprathreshold inputs can contribute to significant jitter reduction during high levels of activity.
There are also presynaptic changes during trains that could affect jitter reduction. AN endbulbs show activity-dependent changes in synaptic strength during trains. We recorded from BCs in voltage clamp and placed a stimulus electrode in the AVCN that could elicit an EPSC at low stimulus intensities. These were verified to be single inputs by decreasing the stimulus amplitude slightly, where an EPSC that entirely disappeared clearly arose from a single fiber. If the stimulus amplitude was increased to recruit more AN fibers, two to three inputs per cell could be distinguished (mean = 2.7, n = 6 cells), which represents a lower bound on the total number of inputs. Stimulation of single, well-isolated AN inputs with trains of 20 pulses at 100 Hz caused significant depression, which was greater with 200- and 333-Hz trains (Fig. 5A). The EPSC amplitude is expressed as the peak conductance in Fig. 5B for eight cells examined (Fig. 5B). The first synaptic conductance in a train was very large (76 ± 15 nS), and depressed to 24 ± 4 nS at 100-Hz stimulation, 12 ± 3 nS at 200 Hz, and 7 ± 2 nS at 333 Hz. The average spike threshold for isolated inputs from Fig. 1 is shown for comparison (black arrow, Fig. 5B). Activity during a 20-pulse train leads to changes in spike threshold (Xu-Friedman and Regehr 2005). Taking into account these effects, an estimate of average spike threshold at the end of a train is indicated by the colored arrows in Fig. 5B. Thus single AN synapses are expected to remain suprathreshold throughout a 20-pulse, 100-Hz train (green trace and green arrow). In higher-frequency trains, AN synapses start out suprathreshold but depress sufficiently to become subthreshold. We estimate that the average AN input becomes subthreshold at pulse 10 for 200-Hz trains (blue), and pulse 5 for 333-Hz trains (red). There was considerable variability in EPSC size during a train (Fig. 5B), so the point at which an individual AN input becomes subthreshold would depend on its initial amplitude and the individual BC threshold. However, the kinetics of use-dependent plasticity were consistent between AN fibers, as shown by first normalizing to the initial EPSC amplitude (Fig. 5C).
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t–
fin(
)d. To derive an expression for the postsynaptic spike distribution, we first calculate the cumulative density function for the postsynaptic cell
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Finally, to examine jitter reduction at different timescales, we assessed the firing of BCs in response to synaptic inputs that followed alpha distributions with a range of SDs (Fig. 7A). In these experiments (Fig. 7B; n = 5 to 6), first spikes are indicated by black lines and later spikes with gray lines. There were few secondary spikes triggered (Fig. 7B). For SDin < 1 ms, the number of spikes per trial was very close to one, and for SDin = 0.2 ms, secondary spikes were completely absent. This indicates that the action potential refractory period was sufficient to eliminate most later spikes, allowing good jitter reduction. For SDin = 5 ms, however, the number of spikes per trial approached two (Fig. 7C). These secondary spikes can have a substantial impact on jitter. Just considering first spikes, jitter reduction is similar for SDin = 0.2–5 ms (Fig. 7D, four traces with black symbols). However, when considering all spikes (Fig. 7D, four traces with gray symbols), jitter was greatest for SDin = 5 ms (Fig. 7D, open gray squares) and decreased as SDin decreased. At SDin = 0.2 ms, there were no secondary spikes, so the two traces are identical. Thus to reduce jitter for inputs with high SDin, an additional mechanism besides refractory period would be necessary to eliminate late spikes, such as time-locked inhibition. In the presence of such a mechanism, jitter reduction with suprathreshold inputs is scale invariant.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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). The extent of use-dependent plasticity depends on the stimulus frequency, and it appears to be an inevitable consequence of activity. For the subthreshold inputs that optimally improve spike timing, even a slight enhancement of synaptic strength degrades jitter reduction (Fig. 2). Slight depression causes the summed inputs to be below spike threshold such that they would be unable to trigger a postsynaptic spike. Thus the highly precise amplitude requirements for few, very small inputs make them unreliable for reducing jitter. By contrast, for suprathreshold inputs, even substantial changes in synaptic strength during normal activity have only a negligible effect on the amount of jitter reduction. This makes suprathreshold inputs particularly robust at reducing jitter. A second factor in vivo is the sensitivity of jitter reduction to variability in the number of active presynaptic inputs. Any reduction of active inputs would be a particularly severe problem with small numbers of subthreshold inputs because it may prevent spike initiation in the postsynaptic cell. This is undesirable because it reduces information transfer and degrades performance. Spike-timing refinement by suprathreshold inputs is much less sensitive to variations in the number of active inputs. Information transmission takes place as long as at least one of the inputs is active because only one input is required to produce a response in the postsynaptic cell. Furthermore, substantial jitter reduction (about 40%) takes place with just two inputs.
Criteria for effective jitter reduction
Our dynamic-clamp experiments indicate that jitter reduction can take place at neurons that receive few, suprathreshold inputs. Recordings in voltage clamp suggest that this may occur at the mouse AN endbulb synapse. In addition, the avian homolog of AVCN BCs, the nucleus magnocellularis neurons, also appear to receive few, large AN inputs (Carr and Boudreau 1991; Jackson and Parks 1982), which can be suprathreshold during high rates of activity (Brenowitz and Trussell 2001). Suprathreshold inputs are also found in thalamic relay neurons (Chen and Regehr 2000; Cleland et al. 1971; Nicolelis et al. 1993) and inhibitory interneurons in cortex (Galarreta and Hestrin 2001; Swadlow and Gusev 2002), cerebellum (Carter and Regehr 2002), neostriatum (Bennett and Wilson 1998), and hippocampus (Fricker and Miles 2000). However, the presynaptic firing rate, the presence of neuromodulators, and the recent firing history of the postsynaptic cell may all affect whether the synaptic inputs are suprathreshold. Our results suggest that AN inputs remain suprathreshold for a period of time even when firing at rates 333 Hz (Fig. 5). Thus the degree of jitter reduction is likely to be context dependent. For BCs, jitter will depend on the frequency, intensity, and duration of the sound.
Suprathreshold inputs are most effective at reducing jitter when the distribution of input latencies has a sharp onset (Figs. 2 and 6). These experiments indicate that higher-order statistics of the input distribution have an important impact on postsynaptic spike timing. Distributions with rapid onset are reasonable in response to generator potentials in sensory cells or in response to EPSPs (Fetz and Gustafsson 1983). Rapid onset has been documented in AN fibers presented with low-frequency tones (Johnson 1980; Joris et al. 1994a; Kiang 1965) and in visual cortical neurons (Marálek et al. 1997). In addition, because the response of the postsynaptic cell also has a sharp rise time, this could contribute to further jitter reduction at later stages in the pathway.
The effectiveness of suprathreshold inputs is independent of the amount of jitter in the inputs. There was no difference in the relative improvement of temporal precision when the input jitter was large (5 ms) or small (0.2 ms), when considering the time of first spike latency in the postsynaptic cell (Fig. 7). This happens despite the large changes in rate of rise of the input distribution. This property of scale invariance means that suprathreshold inputs could help to reduce jitter at synapses other than the AN endbulb synapse considered here, where the amount of jitter in the inputs and the absolute requirements for temporal precision in the outputs may be specialized. For the BCs studied here, the refractory period was sufficient to block the response to very late inputs when the input jitter was small. However, for systems with a large input jitter (5 ms), it is clear that either the refractory period must be longer than that found in BCs or else late spikes must be eliminated by delayed inhibition. Such delayed inhibition does exist in the AVCN, although it may subserve different functions (Oertel 1983; Paolini and Clark 1998; Wickesberg and Oertel 1990; Wu and Oertel 1986).
Suprathreshold inputs in vivo
To understand the advantages of suprathreshold inputs in vivo, it is useful to consider one system that has been well characterized for jitter reduction: spherical BCs in cats. These cells are known to receive few AN inputs (Liberman 1991; Sento and Ryugo 1989), but it is not known whether the AN inputs are suprathreshold. Tone frequencies <3 kHz evoke rapid phase-locked firing in AN fibers (Johnson 1980; Kiang 1965). However, for nonsaturating sound amplitudes, or for tone frequencies higher than the maximal firing rate of AN fibers (200–300 Hz; Johnson 1980; Kiang 1965; Sachs and Abbas 1974), AN fibers do not fire on every cycle of the tone. Therefore there is variability in the number of active AN fibers for a given cycle, which our results indicate will lead to unreliable postsynaptic responses or poor jitter reduction if the inputs are subthreshold. Nonetheless jitter reduction in BCs in vivo is documented for tone frequencies 1 kHz (Joris et al. 1994a). AN fibers tuned to 500 Hz can achieve minimal SDs of 0.16–0.24 ms (Johnson 1980), whereas BCs reach 0.1–0.18 ms (Joris et al. 1994a). This represents a drop in SD of nearly 30%. Our results suggest that this amount of jitter reduction could be readily accounted for by the interaction of two active suprathreshold inputs. This example illustrates the potential utility of suprathreshold inputs in reducing jitter under conditions where the integration of subthreshold inputs would be adversely affected.
Comparison of jitter reduction achieved with small and large numbers of inputs
Jitter reduction is considerably different for a small number of suprathreshold synaptic inputs compared with many subthreshold inputs (Xu-Friedman and Regehr 2005). The first difference is that greater jitter reduction is possible with a large number of inputs, limited only by noise in the spike-generation process of the postsynaptic cell. We found that this limit is at most about 20 µs in BCs (Xu-Friedman and Regehr 2005). This degree of precision is not possible with few inputs, even when they are suprathreshold. In practice, however, the number of inputs may be limited that have similar receptive fields and are coactive. Thus systems that have only few inputs available would reduce jitter the most if those inputs are suprathreshold. Just two converging suprathreshold inputs can cut jitter nearly in half under ideal circumstances.
Second, suprathreshold inputs showed little jitter reduction when the timing distribution of the synaptic inputs had slow onset. This was similar to the case presented in the accompanying paper in which alpha-distributed, subthreshold inputs always outperformed Gaussian-distributed inputs. In that case, this limitation could be overcome by increasing the number of converging inputs. However, for systems limited to few inputs, alpha-distributed, suprathreshold inputs present more obvious advantages.
Third, suprathreshold inputs by definition always produce a response in the postsynaptic cell, even when the temporal distribution of inputs is much longer than the time constant of the cell. With many subthreshold inputs, this situation led to failure to respond (see Fig. 8 in Xu-Friedman and Regehr 2005). With suprathreshold inputs, however, timing information would not be lost. The first postsynaptic spike would convey useful, more precise information about timing.
Thus we have set out for the first time how cells with few synaptic inputs can reduce jitter using suprathreshold inputs, and the conditions that determine their effectiveness. This simple characteristic of suprathreshold inputs leads to robust improvement in temporal precision, whereas subthreshold synapses perform less reliably. Suprathreshold inputs provide a powerful means of reducing jitter, which is relatively insensitive to activity-dependent changes in synaptic strength, to variability in the number of active inputs, and to the amount of jitter in the inputs. These characteristics make suprathreshold synapses highly effective at reducing jitter in situations where the number of inputs is small. These findings indicate that to understand how convergence leads to jitter reduction in a number of systems will require a careful evaluation of the number, amplitude, and temporal distribution of inputs. Our results predict that systems that are adapted to reduce jitter will use different strategies, depending on the characteristics of their inputs.
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ACKNOWLEDGMENTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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FOOTNOTES |
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Address for reprint requests and other correspondence: M. Xu-Friedman, Department of Biological Sciences, 641 Cooke Hall, University at Buffalo, State University of New York, Buffalo, NY (E-mail: mx{at}buffalo.edu)
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REFERENCES |
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