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Previous Article | Next Article
The Journal of Neuroscience, December 15, 2002, 22(24):10790-10800
Highly Variable Spike Trains Underlie Reproducible Sensorimotor Responses in the Medicinal Leech
Davide Zoccolan, Giulietta Pinato, and Vincent Torre Scuola Internazionale Superiore di Studi Avanzati and Istituto Nazionale di Fisica della Materia, 34014 Trieste, Italy
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
The nervous system of the leech is a particularly suitable model to investigate neural coding of sensorimotor responses because it allows both observation of behavior and the simultaneous measurement of a large fraction of its underlying neuronal activity. In this study, we used a combination of multielectrode recordings, videomicroscopy, and computation of the optical flow to investigate the reproducibility of the motor response caused by local mechanical stimulation of the leech skin. We analyzed variability at different levels of processing: mechanosensory neurons, motoneurons, muscle activation, and behavior. Spike trains in mechanosensory neurons were very reproducible, unlike those in motoneurons. The motor response, however, was reproducible because of two distinct biophysical mechanisms. First, leech muscles contract slowly and therefore are poorly sensitive to the jitter of motoneuron spikes. Second, the motor response results from the coactivation of a population of motoneurons firing in a statistically independent way, which reduces the variability of the population firing. These data show that reproducible spike trains are not required to sustain reproducible behaviors and illustrate how the nervous system can cope with unreliable components to produce reliable action.
Key words: sensorimotor responses; optical flow; statistical independence; pooling variability; population coding; reproducibility of muscle contraction
INTRODUCTION
Understanding the neural code by identifying the relevant features of the neural activity that are reproducible from trial to trial during the execution of a repeated behavior (Bialek and Rieke, 1992
; Mainen and Sejnowski, 1995
The CNS of the leech Hirudo medicinalis is composed of a chain of 21 segmental ganglia, each consisting of ~400 neurons (Nicholls and Baylor, 1968
When the skin of the leech is touched, the animal bends its body to withdraw from the stimulus (Kristan, 1982
The local bending was quantitatively characterized by computing the optical flow, whose usefulness in neurobiology we have demonstrated recently (Zoccolan et al., 2001
Our results show that the firing pattern of individual motoneurons is highly variable from trial to trial and that local bending is mediated by the coactivation of a population of motoneurons firing in a statistically independent way. Because of statistical independence, the electrical activity of the motoneuron population becomes less variable. In addition, the time course of muscle contraction primarily depends on the number of incoming motoneuron spikes and not on their exact timing. These mechanisms are the basis of motor output reproducibility in leech local bending.
We show here that reproducible motor output does not require reproducible firing of individual motoneurons and illustrate the biophysical mechanisms that allow a reproducible motor output to be driven by highly variable spike trains. Similar properties are likely to be general features of neural computation and widely present across nervous systems.
MATERIALS AND METHODS
Preparation and electrical recordings. Two preparations were used: the first to quantify skin deformation and the second to analyze motoneuron firing during local bending. Both preparations were kept in a Sylgard-coated dish at room temperature (20-24°C) and bathed in Ringer's solution (in mM: 115 NaCl, 1.8 CaCl2, 4 KCl, 12 glucose, and 10 Tris maleate buffered to pH 7.4 with NaOH) (Muller et al., 1981
The first preparation consisted of a hemisection of leech skin approximately three segments in length, isolated from the rest of the body (Zoccolan et al., 2001
The second preparation was an isolated leech segmental ganglion with exposed nerve roots. Five suction pipettes were used to perform parallel extracellular recordings from the anterior-anterior (AA), anterior-medial (MA), and posterior-posterior (PP) roots and from the two bifurcations of the dorsal posterior root (DP:B1 and DP:B2) (Stent et al., 1978
; filled with 4 M potassium acetate), as described previously (Pinato et al., 2000
In both preparations, local bending was initiated by intracellular stimulation of mechanosensory dorsal or ventral P cells, ipsilateral to the recorded roots. In some experiments, a mechanical stimulus was delivered to the first preparation by rapidly pressing a nylon filament driven by a solenoid on the skin, as described previously (Pinato and Torre, 2000
Stimulation of individual motoneurons. Simultaneous extracellular recordings from the roots were also used to verify that electrical coupling between pairs of motoneurons (Ort et al., 1974
Imaging and behavior analysis. Skin deformations were quantified by computing the optical flows (see Fig. 1B) from image sequences of the contracting leech skin. Images were acquired at 5 or 8.3 Hz by a standard CCD camera mounted on a dissecting microscope and were then digitized and stored on a personal computer. The method for computing the optical flow is based on finding the best correlation between patches of successive images and is fully described in a previous work (Zoccolan et al., 2001
Spike train analysis. The variability of spikes fired by individual motoneurons was characterized by computing the CV of their firing rate over the number of trials of a repeated stimulation, in a given time window
t.
Statistical independence in motoneuron firing was measured by computing, for each pair of coactivated motoneurons i and j, the following quantities: (1) the probability, pi, that motoneuron i fires at least one spike in a given time interval
mP
log2P , where P is the probability that motoneuron i fires m spikes in log2P , where P gives the probability that motoneuron i fires m spikes and motoneuron j fires n spikes in
RESULTS
Reproducibility of the local bending
The firing pattern of mechanosensory neurons and the reproducibility of the local bending were studied using a leech skin preparation, in which a leech body wall segment was flattened over a piece of Sylgard while ganglion innervation was maintained (Nicholls and Baylor, 1968
Figure 1A shows the typical firing pattern of a dorsal P cell (Pd) after mechanical stimulation of the dorsal body wall. When the skin was touched with a nylon filament, the cell Pd quickly responded with highly reproducible firing. In fact, both the number of spikes and their timing were highly reproducible, with a jitter ranging from <100 µsec to <4 msec for the first four spikes fired by the neuron (Pinato and Torre, 2000
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Figure 1. Reproducibility of local bending. A, Four superimposed intracellular recordings from a dorsal P cell after identical mechanical stimulation (20 mN) of the dorsal leech skin. The thick bar indicates the stimulus duration (200 msec). The number above each action potential is the jitter (i.e., the SD of latency from the stimulus onset) of that action potential in milliseconds. B, Optical flow describing the maximal skin deformation induced by evoking two action potentials in a dorsal P cell. The optical flow is computed on a grid of 30 × 20 points. The gray background shows the annular margins of the leech skin preparation. The central annulus of the innervated segment is indicated by the white arrow. The × indicates the stationary point, i.e., the point that stays at rest during the contraction. The region framed by the box was used to compute the linear approximation of the optical flow, from which the elementary deformations shown in C were computed. To make the direction of the movement more clear, the field is drawn with a magnification of 3×. C, Decomposition of the optical flow in the box of B into the four elementary deformations: E, , S1, and S2. The mean values of the elementary deformations over 12 trials of the same stimulation are drawn. Their CV is shown at the bottom. D, Time evolution of the displacement (solid line) and the corresponding CV (dotted line) of a representative point on the leech skin during the same trials of C.
The firing of mechanosensory neurons made muscle fibers contract and initiate local bending. The intensity and shape of local bending are almost completely determined by the P cells (Kristan, 1982
Figure 1B shows the optical flow induced on the leech skin by evoking two spikes in the cell Pd. The flow is drawn on a gray background, showing the annular margins of the imaged skin preparation. The local structure of the optical flow can be analyzed by computing its best linear approximation in a region (Fig. 1B, box) around its stationary point (Fig. 1B, ×). The linear approximation is completely characterized by six parameters: the coordinates of the stationary point and the four elementary deformations: rotation (
Timing of motoneuron spike trains and low-pass filter properties of muscle fibers
Having assessed the reproducibility of the local bending (Fig. 1C,D) and of its coding at the level of mechanosensory neurons (Fig. 1A) (Pinato and Torre, 2000
The firing pattern of motoneurons after P cell stimulation was studied in the isolated leech ganglion. By using extracellular suction pipettes, it was possible to record voltage signals from fine roots ipsilateral to the stimulated P cell and to precisely characterize the variability of motoneuron spike trains involved in local bending (see Materials and Methods).
Figure 2A shows three extracellular recordings from the DP:B2 bifurcation, obtained during identical repeated stimulation of the dorsal P cell (intracellular recording from P cell shown in Fig. 2A, bottom). Spikes fired by three identified motoneurons are indicated by rows of dots of different colors (green, motoneuron 6; blue, motoneuron L; red, motoneuron 3). These are all excitatory motoneurons innervating longitudinal muscle fiber, responsible for the shortening of the leech body during local bending. These motoneurons fired in a rather irregular way among different trials, and this result is emphasized by the comparison with the precise timing of the spikes fired by P cell (black dots). Figure 2B shows the jitter of the first spike evoked in these motoneurons and in other five longitudinal excitatory motoneurons (blue circles), simultaneously recorded from the other roots. Data from similar experiments performed on two other preparations are also shown (red squares, green triangles). In every experiment, the firing pattern of all coactivated motoneurons was much more variable than the firing activity of mechanosensory neurons (compare Fig. 1A). The first spikes occurred with a jitter usually higher than 10 msec (second experiment: motoneuron 5, ~6 msec; motoneuron 107, ~8 msec; first and second experiments: motoneuron 3, ~19 msec; motoneuron 6, ~12 msec) and often of the order of 50-100 msec. For some motoneurons, the jitter was >200 msec (first experiment: motoneurons 4 and 8, data not shown). The second spikes had a still higher jitter, whereas the third, fourth, and fifth spikes had jitters ranging from several hundred milliseconds to >1000 msec (data not shown).
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Figure 2. Variability of motoneuron spike trains during local bending. A, Three extracellular voltage recordings from the DP:B2 root during identical intracellular stimulation of a P cell with two spikes (bottom trace). In the extracellular recordings, the spikes from a P cell and from motoneurons 3, L, and 6 are indicated by black, red, blue, and green dots, respectively. B, Blue circles, Jitter of the first spike of the motoneurons shown in A and five other motoneurons simultaneously recorded from the AA, MA, PP, and DP:B1 roots. Red squares, green triangles, Similar data obtained from identical experiments repeated in two other preparations. In all three experiments considered, spike discharges in motoneurons were evoked by intracellular stimulation of a dorsal P cell with two spikes. Jitter was computed from 76, 85, and 44 repetitions of the same stimulation for experiments 1 (blue circles), 2 (red squares), and 3 (green triangles), respectively. Motoneurons 4, 5, 8, L, 3, 6, 107, and 108 are all excitors of longitudinal muscles.
These experiments were repeated in five different preparations (data from three shown in Fig. 2B), in which the dorsal and the ventral P cells were alternatively stimulated. As shown in Figure 2B, for some motoneurons the value of the jitter of the first and consecutive spikes had a large variability from preparation to preparation. In summary, all these experiments clearly showed that the precise time coding of the stimulus in mechanosensory neurons is not preserved at the level of the motoneurons. Nevertheless, the motor response elicited by local mechanical stimulation of the leech skin is significantly reproducible (Fig. 1C,D). One of the biophysical mechanisms that can account for the reproducibility of the local bending is the low-pass-filtering property of the muscles. Leech muscles (Mason and Kristan, 1982
This integration property of the leech muscles was verified in a series of experiments in which the spike timing of a single motoneuron was changed by applying depolarizing current steps of different durations and intensities but that all evoked the same total number of action potentials. Figure 3A shows the time course of the displacement of a selected point on the leech skin, when spike trains of different durations and frequencies were evoked in motoneuron 3, an excitor of longitudinal muscles. The displacements indicated in Figure 3A (dotted traces, solid traces) were induced by the spike discharges shown respectively in the top (first stimulation protocol) and the bottom (second stimulation protocol) of Figure 3B. The total number of spikes evoked by these two intracellular stimuli was the same (37), but their time distributions were completely different. Nevertheless, the resulting displacements were almost identical. Note that muscle contraction has an intrinsic high variability, so that, when a spike train identical to that shown in Figure 3B, top, was again evoked, the corresponding displacement (Fig. 3A, dashed line) differed from the dotted trace more than the solid trace did (this property will be discussed in the next section). Data presented in Figure 3 show that contractions induced by the second protocols do not differ from contractions induced by the first more than what would be expected from the natural variability of muscle contraction evoked by a fixed number of spikes (see Fig. 5). Similar stimulation protocols, applied to five different motoneurons in three different preparations, confirmed the results shown in Figure 3. In all experiments, skin displacements evoked by the second protocol were always statistically indistinguishable by those evoked by the first one: (1) the second protocol produced displacements that were always within 1 SD from the mean displacement induced by the first stimulation protocol; and (2) including data from the second protocol in the computation of mean and SD for the first did not significantly change the value of the mean or increase the SD.
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Figure 3. Low-pass filter properties of muscle fibers. A, Time course of the displacement of a selected point on the leech skin, when motoneuron 3 was forced to fire a controlled number of spikes (37) in three different stimulations. The displacements indicated by the dotted and solid traces were induced by the spike discharges shown respectively at the top and bottom of B. The displacement indicated by the dashed trace was evoked by a spike discharge similar to that shown in the top of B. B, Top, Spike train evoked in motoneuron 3 by a single depolarizing current step of 0.7 nA lasting 1 sec (total number of evoked spikes, 37). Bottom, Spike train evoked in motoneuron 3 by two consecutive depolarizing current steps of 1 nA lasting 350 msec each (total number of evoked spikes, 37).
Reproducibility of motoneuron firing
Having assessed that muscle contraction primarily depends on the number of spikes fired by activated motoneurons, the reproducibility of motoneuron firing after mechanical stimulation was investigated. As shown in Figure 3, the contraction of leech muscles is not sensitive to the jitter of the motoneuron spikes, but muscle contraction may be sensitive to the number of the incoming spikes in the time window over which spikes are integrated. In fact, Figure 2A shows that not only is the spike timing of coactivated motoneurons significantly variable, but the spike number is, too.
The statistical properties of motoneuron firing were quantified by computing the average firing rate (AFR) and its CV for all identified motoneurons coactivated during local bending. A 200 msec time bin was used, because this is large enough to observe a noticeable skin contraction when single motoneurons are induced to fire at a physiological rate (Arisi et al., 2001
Figure 4 shows the AFR (solid line) and the CV (dashed line) for all identified motoneurons from the experiment already shown in Figure 2, A and B (blue circles). In the experiment, two spikes were evoked in the cell Pd. All motoneuron bursts were recorded from roots ipsilateral to the stimulated cell Pd. This means that the innervation fields of the recorded motoneurons were all ipsilateral to the receptive field of the cell Pd (contralateral motoneurons were not recorded in the present study). As expected (Lockery and Kristan, 1990a
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Figure 4. First-order statistics of motoneuron spike trains. Average firing rate (solid lines) and coefficient of variation (dashed lines) of the activity of 12 coactivated motoneurons during local bending are shown. Motoneurons are from the same experiment analyzed in Figure 2, A and B (blue circles). Local bending was elicited by inducing a dorsal P cell to fire two spikes. Data were obtained from 76 different trials. Bin width, 200 msec.
This pattern of activation of motoneurons is consistent with the classical description of dorsal local bending: activation of all DEs and cell L, activation of VI, and inhibition of DI and VE (Lockery and Kristan, 1990a
Figure 4 shows that the CV of the firing activity of individual motoneurons coactivated during local bending is rather high. All activated motoneurons have a CV between 0.4 and 1 at the peak of the response, with the only exception being cell 6 (CV ~0.3). Similar results were obtained in all five tested preparations, in which the dorsal and ventral P cells were alternatively stimulated. In every experiment, between 8 and 12 motoneurons were simultaneously recorded and identified, and their AFR and CV were computed. Almost all recorded motoneurons had a CV between 0.4 and 1 at the peak of the AFR. No more than one dorsal or ventral excitor per experiment had a CV of ~0.3 after stimulation, respectively, of the dorsal or ventral P cell. To test whether such variable firing rates in individual motoneurons can sustain the reproducible motor responses observed during local bending (Fig. 1C,D), we investigated the reproducibility of the contractions induced by single-motoneuron firing.
Variability of muscle contraction
The variability of the motor response depends on the variability of the motoneuron firing pattern as well as on the variability of the muscle contraction (see Discussion; Stuart, 1970
0.3 cannot induce skin deformations with a CV of <0.5.
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Figure 5. Variability of muscle contraction. A, Displacement of a selected point on the leech skin during the repetitive stimulation of motoneuron 107 with depolarizing current steps of increasing size, lasting 400 msec and evoking a controlled number of spikes in the neuron. Eleven trials (black lines) with 14 spikes, 12 trials (red lines) with 17 spikes, and 11 trials (blue lines) with 20 spikes were recorded. B, Mean CV of the maximal displacement of 6 selected points, when a fixed number of spikes were evoked in motoneuron 107 in different repetitions. Eleven, 12, and 11 repetitions with 14, 17, and 20 spikes, respectively, were considered. C, Relationship between the mean CV of the maximal displacement of 6 selected points and the CV of the spike number for motoneurons 107 (black diamonds), 5 (red squares), 8 (green circles), and CiV (blue triangles) impaled in four different preparations.
Figure 4 suggests that the CV of the firing rate of coactivated motoneurons, at the peak of the response, is too high to account for the reproducibility of local bending. However, for slow-contracting, nonspiking muscles, such as those of the leech, the contraction amplitude primarily depends on the number of spikes in the motoneuron burst induced by mechanosensory stimulation rather than on the firing frequency of motoneurons (Morris and Hooper, 1997
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Figure 6. Variability of spike number in motoneuron bursts. Coefficients of variation of the spike number, in time bins of increasing size after Pd firing, are shown for motoneurons 6 (circles), 3 (asterisks), L (×), 5 (squares), 4 (diamonds), 108 (+), 107 ( ) and 8 (triangles) (same data as in Fig. 4).
Data presented in Figures 4-6 clearly show that the reproducibility of the local bending cannot be exclusively explained by the low-pass-filtering properties of the leech muscles (Fig. 3). Although muscle fibers are not sensitive to the timing of the incoming spikes, muscle contractions are rather sensitive to variations in the spike number (Fig. 5C). The AFR of individual motoneurons, coactivated during local bending (Fig. 4), is definitely too variable to account for this reproducible behavior. Moreover, the number of spikes in motoneuron bursts lasting up to 1 sec, is also too variable to explain the reproducibility of the local bending (Fig. 6). Some other mechanism should take place to reduce variability of the motor output.
Distributed organization of the motor output
A biophysical mechanism that can explain such a low variability of the local bending is the distributed organization of the firing activity sustaining it at the level of the motoneurons. Figure 7 shows the analysis of statistical independence for the activity of some motoneurons whose AFR and CV were reported in Figure 4. The statistical independence of motoneuron firing was characterized by computing, for each pair of coactivated motoneurons, the joint probability, pij that both motoneurons fire one spike, and Hij, the joint entropy of their firing activity (Pinato et al., 2000
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Figure 7. Statistical independence of motoneuron firing. Joint probabilities and joint entropies are shown for all possible pair-wise combinations of motoneurons 6, 5, 3, 107, and 4, whose AFR and CV are shown in Figure 4. Top right panels, For each pair of motoneurons i and j, the joint probability of firing pij (red line) is compared with the product of individual probabilities pi/pj (black dashed line). Bottom left panels, The joint entropy Hij (red line) is compared with the sum of individual entropies Hi + Hj (black dashed line). Bin width, 20 msec.
These observations suggest that the motor response analyzed in Figure 1 has a distributed organization (Tsau et al., 1994
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Figure 8. Pooling variability of coactivated motoneurons. A, The CV of eight longitudinal motoneurons (cells 6, 5, 107, 3, L, 4, 108, and 8) coactivated during local bending (dashed lines) is compared with the CV (solid line) of their pooled activity. Motoneurons are from the same experiment analyzed in Figures 2, 4, and 6. B, The CV of the pooled activity of the same motoneurons is computed by removing individual motoneurons one at the time from the pool. The bottom trace (a) is the CV computed for the whole population of motoneurons (cells 6, 5, 107, 3, L, 4, 108, and 8) and corresponds to the solid line in A. The other traces are the CVs obtained by removing the following motoneurons from the starting population: cell 6 (b); cells 6 and 3 (c); cells 6, 3, and 5 (d); cells 6, 3, 5, and 4 (e); cells 6, 3, 5, 4, and L (f); and cells 6, 3, 5, 4, L, and 107 (g).
This distributed coding across a population of independent motoneurons not only assures reliability of the motor response but also allows graceful degradation of performance with damage to individual motoneurons. We tested the robustness of population coding by computing the CV of the pooled activity of the motoneuron population from which data of single motoneurons were removed one at the time. The result is shown in Figure 8B. The CV increased in little steps while individual motoneurons were removed from the pool. This guarantees a gradual decrease in the reliability of motor output in case of damage to individual motoneurons. Note in particular that even when we removed the motoneurons with more reproducible firing (cells 6 and 3) from pooling, the variability of the population firing did not significantly increase and still had a CV with a minimum of <0.25 (for details, see legend to Fig. 8).
Local bending is sustained by the coactivation of several motoneurons
Given that local bending is sustained by the coactivation of a population of motoneurons (Fig. 4), and that skin deformations induced by pairs of motoneurons superimpose linearly (Zoccolan and Torre, 2002
Figure 9 summarizes the results of one of these experiments. Figure 9A shows the optical flow induced by firing two spikes in a dorsal P cell. In the same preparation, motoneurons L, 3, 5, 112, and 107 were impaled. The corresponding optical flows are drawn in Figure 9B-E (optical flow of cell 107 not shown). These optical flows were obtained by inducing the impaled motoneurons to fire a burst of action potentials at 15-20 Hz for 400 msec to evoke firing patterns similar to those recorded during Pd stimulation (Fig. 4). Figure 9F shows the linear superposition of these optical flows induced by individual motoneurons. Because most excitors of longitudinal muscles were included in the sum, a marked similarity between the intensity and shape of the local bending (Fig. 9A) and those of the linear sum of the impaled motoneurons (Fig. 9F) is apparent. This was confirmed by calculating the elementary deformations of the two fields drawn in Figure 9, A and F. As shown in Figure 10, the main elementary deformations (E and S1) of these two optical flows differ for <5%. These results confirm that the local bending cannot be accounted for by the activation of just one motoneuron; it is necessary to consider the optical flows associated with a large number of motoneurons to obtain a good approximation of its shape and intensity. Specifically, Figure 9 shows that the coactivation of several motoneurons assures not only the reproducibility of the local bending (Fig. 8) but also its strength (note that the optical flows induced by motoneurons are shown with a magnification four times higher than the optical flow associated with the local bending). These results were confirmed in two other experiments in which a P cell and three or four motoneurons were impaled in the same preparation.
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Figure 9. Distributed motor output. A, Optical flow describing the maximal skin contraction evoked by the firing of two spikes by a dorsal P cell. B-E, Optical flows describing the maximal skin contractions induced by the firing of motoneurons L, 3, 5, and 112, respectively, at ~10-20 Hz in the same preparation. F, Linear superposition of the optical flows in B-E. The gain of the optical flow in A and F is 1; otherwise it is 4. The boxes in A and F are the linearization regions used to compute the stationary point position (×) and the elementary deformations shown in Figure 10.
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Figure 10. Accuracy of the linear superposition. Elementary deformations are shown for the optical flows shown in Figures 9, A (gray bars) and F (white bars).
DISCUSSION
The data presented here show that local bending (a simple sensorimotor response of the leech) is rather reproducible (Fig. 1), but the firing of the motoneurons that sustains it is much more variable (Figs. 2, 4). Because it was possible to record simultaneously from the majority of motoneurons involved in the motor response (Fig. 4), the existence of hidden motoneurons firing in a highly reproducible way is unlikely. We therefore conclude that highly reproducible spike trains are not necessary for highly reproducible motor responses.
Temporal averaging
Reliability of the behavior is obtained by temporal and ensemble averaging. Temporal averaging is guaranteed by the low-pass-filtering properties of the leech muscle fibers, which integrate motoneuron spikes within an effective time window of ~200 msec (Arisi et al., 2001
Muscle contractions produced by individual motoneurons show significant variability even when driven by perfectly reliable spike trains (Fig. 5B). When spike trains in a motoneuron have a CV of ~0.25, the resulting muscle contraction has a CV of approximately or >0.5, i.e., significantly higher than the CV of the movements observed during local bending (compare Figs. 1, 5). Therefore, the reliability of local bending cannot be accounted only by the low-pass properties of muscle contraction.
Ensemble averaging
The motor response is mediated by coactivation of an ensemble of distinct motoneurons (Figs. 4, 7, 8) that fire in an almost statistically independent way (Fig. 7). Statistical independence compensates for the fluctuations (Figs. 4, 6) in the firing of individual motoneurons; thus the ensemble firing of the motoneuron population becomes less variable (Fig. 8A). In addition, fluctuations of muscle contraction evoked by individual motoneurons (Fig. 5) will probably be compensated and averaged by statistical independence (Hoover et al., 2002
Figure 11 shows a simple scheme, indicating where, in the reflex pathway, variability is introduced and which biophysical mechanisms counteract it. The first spikes in the mechanosensory P cell are remarkably reproducible (Fig. 1A), often with a jitter of <100 µsec (Pinato and Torre, 2000
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Figure 11. Proposed scheme of the neuronal network mediating local bending reflex. Mechanosensory stimuli (S) are coded by precise firing of a pressure P cell (black unit). Then, neural signals cross some layers of interneurons (gray units) to reach motoneurons (white units) that, in turn, innervate muscle fibers. The typical jitter of the first spike for P cells and motoneurons is shown at the bottom together with the CV of P cell firing, the typical CV of individual motoneuron firing, and the CV of the amplitude of the motor response. Reliability of the motor response is achieved by integrating spikes over a population of some dozens of motoneurons and over a time window of several hundred milliseconds.
Comparison with previous studies
A number of studies focused on reliability of neural firing in invertebrate (Bialek and Rieke, 1992
The cat visual system
A similar attempt to track variability at different neural stages has been performed recently in the cat visual system by Kara et al. (2000)The stomatogastric neuromuscular system of the lobster
A recent article by Hoover et al. (2002)Conclusions
Averaging action potentials over an ensemble of neurons and over an appropriate time window is a likely mechanism for nervous systems to achieve high reproducibility despite using poorly reliable components such as neurons, synapses, and muscles. The extent of ensemble and time averaging, however, will be constrained by the task to be performed and by the biophysical properties of the specific neurons involved. The precision of spike occurrence depends on the requirements of the action or output: in the present case, a significant jitter (even of ~100 msec) and a CV of ~0.4 in individual motoneurons were tolerated. Several tasks performed by the auditory system (Heil, 1997
FOOTNOTES Received July 3, 2002; revised Sept. 13, 2002; accepted Sept. 18, 2002.
This work was funded by European Union Grant Parallel 960211. We thank Dr. Hugh Robinson for valuable scientific suggestions and helpful comments on this manuscript and Manuela Schipizza Lough and Dylan Dean for editing the text.
Correspondence should be addressed to Vincent Torre, Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2, 34014 Trieste, Italy. E-mail: torre{at}sissa.it.
G. Pinato's present address: Department of Medical Physiology, University of Copenhagen, DK-2200 Copenhagen, Denmark.
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