Population Reconstruction of the Locomotor Cycle From Interneuron Activity in the Mammalian Spinal Cord

Matthew C. Tresch and Ole Kiehn

Department of Physiology, Section of Neurophysiology, The Panum Institute, 2200 Copenhagen N, Denmark


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Tresch, Matthew C. and Ole Kiehn. Population Reconstruction of the Locomotor Cycle From Interneuron Activity in the Mammalian Spinal Cord. J. Neurophysiol. 83: 1972-1978, 2000. Lesion studies have shown that neuronal networks in the ventromedial regions of the neonatal rat spinal cord are critical for the production of locomotion. We examined whether the locomotor cycle could be accurately predicted based on the activity recorded in a population of spinal interneurons located in these regions during pharmacologically induced locomotion. We used a Bayesian probabilistic reconstruction procedure to predict the most likely phase of locomotion given the observed activity in the neuronal population. The population reconstruction was able to predict the correct locomotor phase with high accuracy using a relatively small number of neurons. This result demonstrates that although the spike activity of individual spinal interneurons in the ventromedial region is weak and varies from cycle to cycle, the locomotor phase can be accurately predicted when information from the population is combined. This result is consistent with the proposed involvement of interneurons within these regions of the spinal cord in the production of locomotion.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Several studies have examined the coding of behavioral variables by neuronal populations. These analyses all seek to translate the activity of a population of neurons into a prediction of the value of some external variable, such as the direction of hand movement (Georgopoulos et al. 1986, 1988; Sanger 1996; Tanaka 1994), the position of the animal in space (Wilson and McNaughton 1995; Zhang et al. 1998), or features of a sensory stimulus (Lewis and Kristan 1998a,b; Oram et al. 1998; Rolls et al. 1997; Warland et al. 1997). Such procedures of population reconstruction have been used as a means to estimate the amount of information about some behavioral variable encoded by a neuronal population. Another reason for performing such analyses is that in some cases, the properties of the neuronal population are not always simply reflected in the properties of individual neurons.

In this study we use these analyses to examine the coding of the locomotor cycle by neuronal populations in the ventromedial regions of the neonatal rat spinal cord. Neuronal populations in these regions of the spinal cord have been shown to be critical for the production of stable locomotion (Kjaerulff and Kiehn 1996). However, although there is a statistically significant modulation of the spike activity of interneurons in these regions during the production of locomotion when examined over many cycles, relatively few action potentials comprise the difference between the activity of a neuron during its preferred and nonpreferred phase of locomotion (see Kiehn et al. 1996; MacLean et al. 1995; Raastad and Kiehn 2000; Tresch and Kiehn 1999b). Based on this weak modulation of spike activity, it is not clear whether the activity of these neurons is capable of playing an important role in the production of locomotion. The primary goal of this study is to assess whether the weak modulation observed in these interneurons located in ventromedial regions is capable of accurately predicting the locomotor cycle when this activity is combined across a population of neurons. If such a capability could be demonstrated, it would give additional support to the potential role of these neurons in the production of locomotion. Parts of these results have been published in abstract form (Tresch and Kiehn 1999a).


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Preparation and interneuronal recordings

The description of the acquisition and analysis of the interneuronal database used in these analyses is presented in detail elsewhere (Tresch and Kiehn 1999b). Briefly, the spinal cord of neonatal (P0-P4) rats (n = 20) was removed and placed in a chamber continuously perfused with oxygenated Ringer solution. The addition of serotonin (5-HT, 1-10 µM) and N-methyl-D-aspartate (NMDA, 3-10 µM) to the perfusion medium induced a rhythmic motor output in the spinal cord, which was monitored by recording the activity in the L2 and L5 ventral roots. The activity in these two ventral roots corresponds to the activation of flexor and extensor muscles, respectively (Kiehn and Kjaerulff 1996). The spike activity of spinal interneurons located within the ventromedial region of the spinal cord was recorded either intracellularly using tight-seal whole cell electrodes or extracellularly using tetrodes. This activity was related to the locomotor cycle. Each locomotor cycle was divided into two portions, one during the L2 burst and one during the L5 burst, and each portion was scaled to take up one-half of the locomotor cycle. The locomotor phase was expressed in angular coordinates (Berkowitz and Stein 1994; Drew and Doucet 1981) with the L2 burst lasting from 0 to 180° and the L5 burst lasting from 180 to 360°. In the present analysis each locomotor cycle was divided into 200 bins, 100 in each half of the cycle, and the number of spikes within each bin was counted. Because the average duration of a locomotor cycle was 1.97 ± 0.59 (SD) s, each of the bins was on average 10 ms long. An average 65 ± 29 locomotor cycles were collected for each neuron (minimum of 10 cycles).

An example of the locomotor-related activity of a spinal interneuron is illustrated in Fig. 1. Although the spike activity of the neuron over the individual cycles shown in Fig. 1A does not appear to be strongly related to the ventral root activity, when the activity of the neuron was examined over many cycles in Fig. 1B, a clear relationship could be observed. The slow drift in mean firing rate over the period of data collection seen in Fig. 1B was commonly observed in these experiments and could generally be related to changes in the intensity of the root discharge.



View larger version (23K):
[in this window]
[in a new window]
 
Fig. 1. Locomotor-related spike activity of spinal interneurons. A: spike activity of an interneuron recorded in the ventromedial spinal cord (top) along with alternating L2 and L5 ventral root activity (bottom) evoked by application of 5-HT (6 µM) and NMDA (6 µM). Ventral root recordings are shown rectified. B: raster plot of spike activity of neuron in A during locomotion. The x-axis indicates the progression of locomotor cycle from flexor-related L2 ventral root burst (0-180°) to extensor-related L5 ventral root burst (180-360°). The y-axis indicates each consecutive locomotor cycle over which activity of this cell was recorded. Each dot represents 1 spike produced by the neuron. C: modulation of mean firing rate for neuron illustrated in A using a combination of von Mises distributions as described in text.

Characterization of locomotor dependence of firing rate

The neural reconstruction procedures used here follow those described in Sanger (Oram et al. 1998; Sanger 1996; see also Zhang et al. 1998). The first step in these reconstruction procedures was to describe the modulation of neural mean firing rate by the locomotor cycle. The mean firing rate of each neuron was described as a mixture of von Mises distributions (Mardia 1972). A von Mises distribution is a probability distribution for data that depends on a circular variable such as the locomotor phase. The firing rate of each cell was fit to the following model
<IT>f</IT>(<IT>&thgr;</IT>)<IT>=</IT><LIM><OP>∑</OP><LL><IT>i</IT><IT>=1</IT></LL><UL><IT>N</IT></UL></LIM><IT> &pgr;</IT><SUB><IT>i</IT></SUB><IT>VM</IT>(<IT>&mgr;</IT><SUB><IT>i</IT></SUB><IT>, &kgr;</IT><SUB><IT>i</IT></SUB>)
where f(theta ) is the mean firing rate of each neuron as a function of the locomotor phase theta , VMi,kappa i) is a von Mises distribution with mean phase µi and concentration (variability measure) kappa i, pi i is the weight for each distribution, and N is the number of distributions used in the fit. Three distributions were used. The parameters for each fit were found using the expectation maximization algorithm (Dempster et al. 1977). This function gives a continuous estimate of the mean firing frequency of a neuron across the locomotor cycle. The combination of von Mises distributions could describe locomotor-related activity patterns which were asymmetric or had mulitple peaks (see Fig. 3A). Figure 1C shows the modulation of mean firing rate for the cell shown in Fig. 1, A and B, using a combination of von Mises distributions. The firing rate modulation of each neuron was calculated using all but one cycle of locomotion. This withheld locomotor cycle was used to assess the prediction error of the population reconstruction (see Predicting the locomotor phase from observed spike activity). We also used a kernel density based on individual spike arrival times to estimate the locomotor-related modulation of neurons but found that the combination of von Mises perfomed better in the reconstruction procedures described here.

The mean firing rate for each cell was used to parameterize a Poisson model of spike count distributions. Poisson models have been used extensively to describe the activity of neurons throughout the nervous system and are fully described by only the single parameter of mean firing rate (see Rieke et al. 1997). The validity of this model for the spike activity of locomotor-related spinal interneurons is assessed in Fig. 2. Figure 2A is derived from the cell illustrated in Fig. 1. The connected crosses show the probability of a particular spike count being observed in the actual data when the locomotor cycle was divided into 10 bins, each lasting on average 200 ms. This probability was estimated as the fraction of cycles for which the cell produced the given spike count. As would be expected from Fig. 1, the cell had a high probability of producing no spikes in the middle of the cycle whereas the highest probability of it producing one spike was in the latter part of the cycle. Because of its low firing rate this neuron never produced more than one spike at any bin when the cycle was divided into 10 bins. The smooth lines on the same plot indicate the probability of producing different spike counts using a Poisson model with the mean firing rate shown in Fig. 1C over the same interval of time. The model captured the main features of the observed activity but deviated in the region of the cycle at which the neuron was most active. In this region of the cycle the model predicted a wider distribution of spike counts than that observed with there being a small probability of observing spike counts of two and three. This overestimate of spike count variability by Poisson models, illustrated in Fig. 2A, was generally the case for the neurons observed in this study. Figure 2B shows a plot of mean spike count versus spike count variance for each neuron recorded in this study. For this plot, the locomotor cycle was divided into 10 bins and the mean spike count and its variance in each of the bins was calculated. Each cell therefore contributes 10 points to this figure. The straight line in the plot indicates the predicted behavior for a Poisson distribution: spike count variance equals mean spike count. The curved line on the bottom of the plot indicates the minimum possible variance of a neuron due only to counting statistics (de Ruyter van Stevenick et al. 1997). The plot shows that the tendency of the neural activity in this preparation was to be more reliable than would be expected from a Poisson process. However, because of the very low firing rates of neurons in this preparation, the large majority of neurons had mean spike counts of 0.5 or less per bin. In this region of the plot, the variability expected from a Poisson process is similar to that expected from a completely reliable neuron. Because of this small deviation, along with the ease of using Poisson models for the iterative computations in this study, we have used Poisson models of spike count statistics throughout this study (see DISCUSSION).



View larger version (18K):
[in this window]
[in a new window]
 
Fig. 2. Comparison of firing properties of spinal interneurons to a Poisson model of spike generation. A: probability of producing different numbers of spikes over locomotor cycle for neuron shown in Fig. 1. Line connecting crosses shows probability of the cell producing different spike counts estimated from observed activity of cell. Continuous lines show probability of different spike counts using a Poisson model of spike generation. At higher firing rates (2-3 spikes/bin), the Poisson model predicted a wider range of spike counts than was actually observed for this cell. B: relationship between mean spike count and spike count variance for all neurons with locomotor cycle divided into 10 bins. Solid diagonal line indicates relationship expected for a Poisson process whereas curved line indicates minimal variance expected based on counting statistics. Majority of neurons appeared to be more reliable than a Poisson process, although at low firing rates the difference between a variable Poisson process and a perfectly reliable neuron is minimal.

Predicting the locomotor phase from observed spike activity

Using the procedures described above, the probability of a spike count over a given interval of the locomotor phase, P(N|theta ), can be calculated for each cell (as shown in Fig. 2A). We used this information to predict the most likely locomotor phase based on the observed activity of a neuron at a new time (Oram et al. 1998; Sanger 1996; Zhang et al. 1998). This calculation was done using Bayes rule
<IT>P</IT>(<IT>&thgr;‖</IT><IT>N</IT>)<IT>=</IT><FR><NU><IT>P</IT>(<IT>N</IT><IT>‖&thgr;</IT>)<IT>P</IT>(<IT>&thgr;</IT>)</NU><DE><IT>P</IT>(<IT>N</IT>)</DE></FR>
where P(theta |N) is the probability of the locomotor phase given the observed spike count, P(theta ) is the probability of observing each locomotor phase, taken from the relative durations of each phase bin. In the present experiments, the average duration of each locomotor phase was the same (Tresch and Kiehn 1999b): P(theta ) was therefore uniform. P(N) is the probability of observing the spike count and was treated as a normalizing constant, ensuring that the sum of probabilities over all locomotor phases was one (Sanger 1996). P(N|theta ) was calculated from the Poisson description of the spike count distributions as described above. Bayes rule was used to calculate for each neuron the probability of each phase of locomotion given a particular spike count over an interval.

This information about the most likely phase from multiple neurons was then combined. Assuming that the activity in different neurons is independent, probabilities from multiple neurons can be combined simply through multiplication
<IT>P</IT>(<IT>&thgr;‖</IT>{<IT>N</IT><SUB><IT>1</IT></SUB><IT>, </IT><IT>N</IT><SUB><IT>2</IT></SUB><IT>,…, </IT><IT>N<SUB>M</SUB></IT>})<IT>=</IT><FR><NU><IT>1</IT></NU><DE><IT>&eegr;</IT></DE></FR> <LIM><OP>∏</OP><LL><IT>j</IT><IT>=1</IT></LL><UL><IT>M</IT></UL></LIM> <IT>P</IT>(<IT>&thgr;‖</IT><IT>N<SUB>j</SUB></IT>)
where M is the number of neurons in the population, and eta  is a normalization coefficient ensuring that the total probability over all phases is one. This process of multiplication serves to increase the accuracy of the prediction of locomotor phase and to reduce the effects of variable activity in any particular neuron. Note that this multiplication assumes that there is no correlation in the spike activity of spinal interneurons, a possibility we have not examined here (see DISCUSSION). An illustration of this process in shown in Fig. 3. Figure 3A shows the mean firing rates of two neurons, both fit using the combination of von Mises described above. The cell in the top of Fig. 3A is the same as the cell shown in Fig. 1. Figure 3B shows the probability of different locomotor phases given that the cell in the top of Fig. 3A fired no spikes in an interval of 200 ms (one tenth of the locomotor cycle) and that the cell in the bottom of Fig. 3A fired one spike in the same interval of the locomotor cycle. As would be expected by the modulation of its mean frequency, when the cell in the top of Fig. 3A fired no spikes [P(theta |N1 = 0)], the most likely locomotor phase was anywhere between 90 and ~270°. Similarly, when the cell in the bottom of Fig. 3A fired one spike [P(theta |N2 = 1)], the most likely phase was somewhere between 135 and 315°. When the information from the two cells was combined [P(theta |N1 = 0, N2 = 1)], the distribution of phases became better defined, increasing the probability of the region of the locomotor cycle where their separate probability distributions overlapped. The locomotor phase with the maximum probability was taken as the predicted locomotor phase; in this case, a locomotor phase ~180° was most likely. The error between the locomotor phase predicted by this reconstruction procedure and the actual locomotor phase which gave rise to the neural activity was used to assess the quality of the reconstruction.



View larger version (17K):
[in this window]
[in a new window]
 
Fig. 3. Predicting the most likely locomotor phase based on neuronal activity. A: mean firing rates of 2 neurons through locomotor cycle. Based on these firing rates, probability of any locomotor phase given a particular spike count can be calculated using Bayes' rule. B: probability of each locomotor phase given that the cell in top of A fired no spikes [P(theta |N1 = 0)] and that the cell in bottom of A fired 1 spike [P(theta |N2 = 1)]. Probability of each locomotor phase given activity in both cells was combined by multiplication [P(theta |N1 = 0, N2 = 1)].

We assessed the quality of reconstruction using a bootstrap procedure. On each iteration of the procedure, a set of neurons was first chosen randomly from the set of all neurons (n = 123). The modulation of firing rate of each neuron was calculated as described above based on its activity in all but one cycle of locomotion. This excluded cycle was then divided into equal bins of locomotor phase (5-100 bins). Because the neurons described here were not recorded during the same bout of locomotion, the same sized bin of locomotor phase did not generally correspond to the same interval of time for each neuron. The number of spikes observed for a neuron in each bin of this excluded cycle was then counted. Based on the spike counts in each bin, the most likely locomotor phase was calculated first for each cell separately and then for the entire population of cells. The error between the most likely locomotor phase predicted from the population activity and the locomotor phase in the center of the bin of the cycle was then calculated. This procedure was then repeated using different numbers of neurons or dividing the locomotor cycle into different numbers of bins. To examine numbers of neurons greater than the number of neurons actually recorded in these experiments, we resampled the recorded population choosing neurons randomly with replacement.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

We found that populations of spinal interneurons were generally able to predict the locomotor phase well. An example of the locomotor phases predicted by a neuronal population of 100 cells for 1 locomotor cycle is shown in Fig. 4A. This figure shows the probability density over each locomotor phase given the neuronal population activity, P(theta |{Ni}) for one locomotor cycle divided into 10 bins. The 10 plots show this quantity calculated for each of the 10 bins of the locomotor cycle. The vertical lines represent the center of the phase bin over which the population activity was actually observed. It can be seen that the locomotor phase predicted by the population followed the actual phase of locomotion well, although the two did not always correspond perfectly. Figure 4B shows the distribution of prediction errors over 100 iterations using a population of 100 cells and the locomotor cycle divided into 10 bins. The average error of this distribution was 12.60° indicating that the population prediction was generally very accurate. Note that this error was calculated as the average difference between the most likely locomotor phase predicted by the reconstruction procedure and the center of the bin over which the population activity was collected to make the prediction (as indicated in Fig. 4A). We are therefore comparing a continuous variable, the predicted locomotor phase, with a discretization of a continuous variable, the center of the bin of locomotor phase. If we treat the prediction by the population as a categorical prediction of the one of the bins of locomotor phase instead of the particular phase angle, the quality of the reconstruction can be assessed by examining the percentage of correct categorizations. For the data shown in Fig. 4B, 77% of the predictions were in the correct bin (chance 10%), whereas 98% were either in the correct bin or in one of the two adjacent bins (chance 30%). The consistency of the population prediction across the locomotor cycle is shown in Fig. 5, showing that the average predicted locomotor phase was very close to the actual locomotor phase throughout the locomotor cycle.



View larger version (23K):
[in this window]
[in a new window]
 
Fig. 4. Prediction of locomotor phase by neuronal populations. A: example of prediction of locomotor phase by a population of 100 neurons. Each horizontal box indicates prediction of locomotor phase given activity in neuronal population during 1 of 10 bins of the cycle, progressing from beginning of cycle (top) to end of cycle (bottom). Vertical line in each box indicates center of bin over which neuronal activity was collected. Curved line represents probability density of each locomotor phase given observed population activity. B: distribution of errors for 100 iterations of reconstruction procedures using 100 neurons. Because locomotor cycle was divided into 10 bins, there are 1,000 data points in this figure. Error was calculated as angular difference between center of actual locomotor phase bin and maximum of probability density calculated by reconstruction procedures.



View larger version (12K):
[in this window]
[in a new window]
 
Fig. 5. Average predicted locomotor phase vs. actual locomotor phase using a population of 100 neurons with cycle divided into 10 bins. Predicted locomotor phase was very close to actual locomotor phase throughout locomotor cycle. Error bars represent ± SD.

The ability of the population reconstruction to predict the correct locomotor phase depends on both the number of neurons included in the population and the time interval over which the activity of the population is integrated (Lewis and Kristan 1998b; Zhang et al. 1996). The effects of these two factors on the prediction of the locomotor phase are summarized in Fig. 6. The intervals displayed on the x-axis are the amounts of time spent in one bin of the locomotor cycle averaged across all neurons. Given an average locomotor cycle of 2 s, an interval of 200 ms corresponds to dividing the locomotor cycle into 10 bins. As seen in the figure, the reconstruction accuracy improved as either the integration time interval or the number of cells was increased. With a population size of 1,000 cells, an interval as short as 20 ms could be used to predict the locomotor cycle with an accuracy of 15.39°. Thus a low prediction error could be achieved either by a large number of cells and a short integration time or by a small number of cells and a longer integration time.



View larger version (23K):
[in this window]
[in a new window]
 
Fig. 6. Interaction between number of neurons used in reconstruction procedure and length of interval time over which neuronal activity was integrated. The y-axis indicates prediction error of reconstruction procedure; x-axis indicates length of integration time used in reconstruction procedures. Connected lines show prediction error as a function of integration interval for different numbers of neurons in population, from 20 to 1,000 neurons. Each point reflects prediction error averaged over 50 iterations of reconstruction procedures.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The analyses show that the phase of locomotion can be accurately predicted from the activity observed in a sampled population of spinal interneurons. The procedures described here have been used in other systems to estimate the amount of information about specific behavioral variables encoded by a neuronal population (see Zhang et al. 1998 for a thorough discussion). The main point of the present analysis was to demonstrate that the activity in a population of spinal interneurons within the ventromedial spinal cord contains sufficient information to predict the actual locomotor phase using reasonably sized populations of neurons. Based on the relatively weak spike modulation of the individual interneurons located within the ventromedial spinal cord (Kiehn et al. 1996; McLean et al. 1995; Raastad and Kiehn 2000), it might have been argued that these neurons are not critically involved in the production of locomotor behavior because their spike activity appears to convey relatively little information about the locomotor cycle. However, the present results demonstrate that, as a population, these interneurons are in fact capable of specifying the locomotor cycle. Combined with other experiments showing that neurons in these regions of the spinal cord have intrinsic rhythmogenic properties (Hochman et al. 1994; Kiehn et al. 1996) and that lesions of these regions abolish the production of locomotion (Kjaerulff and Kiehn 1996), the present results suggest that interneurons in these regions play an important role in locomotion. Further experiments will be necessary to establish more precisely the exact nature of this role.

Assumptions of the reconstruction procedures

One of the assumptions we have made in the present analysis was that the spike trains of spinal interneurons could be described by a Poisson model of spike generation. This assumption was helpful because Poisson models are simple to use computationally. The results shown in Fig. 2 suggest that in general the spike activity of spinal interneurons during the production of locomotion is more reliable than would be expected based on a Poisson model of spike generation. This comparatively high reliability is somewhat surprising because there are clearly differences from one cycle to the next in the exact motor output produced by the spinal cord and possibly also in the synaptic activity impinging onto individual interneurons. Assuming that the activity of the neurons described in this study reflect in some way this cycle to cycle variability, it is likely that the reliability of these neurons is even greater than suggested by Fig. 2B. Part of the variablity in motor output is reflected in a slow drift in firing rate as can be seen for the neuron illustrated in Fig. 1B. A slow drift often corresponded to changes in the intensity of the ventral root discharge. However, in preliminary analyses in which we attempted to account for this slow drift by relating it to the magnitude of the root discharge, the variability was not decreased substantially. Despite this less than Poisson variability, it is clear from Fig. 2B that when the mean count of spiking was low the variability of the observed firing was close to that expected from a Poisson process. The reconstruction procedures described here using a Poisson model of spike activity would therefore appear to be an adequate approximation. It is possible, however, that other models of spike count statistics might better describe the activity of these neurons (e.g., Gershon et al. 1998; Oram et al. 1999) and consequently give a better prediction of the locomotor cycle.

The probabilistic analysis used here also assumes that the firing rates of spinal interneurons are uncorrelated. Given that the majority of neurons used in these analyses were not recorded simultaneously but combined from separate experiments, the issue of whether such correlations exist in these neural populations would not be expected to affect our results. It is possible, however, that such correlations do in fact exist in these populations, and the reconstruction analysis described here would need to be expanded to account for such correlations (Oram et al. 1998).

Implications and applications of population reconstruction procedures

There are several potential implications of the analyses presented here. The most straightforward interpretation is the indication that it is possible to predict the ongoing phase of locomotor behavior based on the activity patterns of a relatively small population of spinal interneurons. Although this result arises directly from the modulation of neural spike activity in these interneurons, it was not clear before this analysis that the prediction of locomotor phase could be performed using a reasonable number of interneurons. However, we also note that one limitation of the present analysis is that our description of the motor output of locomotion is relatively simple, consisting of a single variable, namely the locomotor phase as determined by the ventral root activity. The ability of these same analyses to predict the detailed activation patterns of the full set of hindlimb muscles during locomotion or the variable timing of flexor and extensor phases during different ambulatory speeds has not been assessed.

Another implication of our results is the possible role of spike activity of neurons in the ventromedial regions of the spinal cord in the production of locomotion. As mentioned above, the activity patterns of individual neurons during locomotion are not always clearly modulated with the locomotor cycle when examined qualitatively, even though examining data from many cycles might demonstrate a significant modulation of a neuron's activity (Raastad and Kiehn 2000; Tresch and Kiehn 1999b). The present results demonstrate that such weak modulation, when combined with similar modulation from other neurons, is able to predict the locomotor cycle well. These results therefore demonstrate that even with weak and inconsistent spike activity, neurons located in the ventromedial area are able to play an important role in the timing of locomotion in this preparation.

It is important to note that the reconstruction procedures described here are not meant as a model of the production of the rhythmic motor output. Although it has been suggested that the probabilistic methods can be implemented by biological networks of neurons (Zhang et al. 1998), we have no evidence that this is the case in the spinal cord. Instead, these analyses can be seen as a method to examine the amount of information about a behavioral variable encoded by the spike activity in a particular neural population. In this context, these analyses might provide a tool with which to examine features of neural networks underlying the production of movements in general (Sanger 1996) and of locomotion in specific. For instance, the analysis might be applied to a set of identified neurons to examine their properties at a population level. Although a set of neurons might share particular anatomic and physiological criteria that identify it as a distinct class, there can be considerable differences among the characteristics of individual neurons within that class (e.g., Harrison and Jankowska 1985). The analyses described here might provide a method to examine the movement related activity in the overall population of such an identified class of neurons. Similarly, these analyses might be used to compare the ability of two different spinal interneuronal populations (for example Renshaw cells or commissural interneurons) to predict, and therefore potentially influence, the locomotor cycle. Future work will be required to assess the practical utility of these procedures in the investigation of the neural production of locomotion.


    ACKNOWLEDGMENTS

We thank S. Giszter for comments on an earlier version of this work.

This work was supported by the Danish Medical Research Council and the Novo Foundation. M. C. Tresch is supported by a fellowship from The Lundbeck Foundation.


    FOOTNOTES

Address for reprint requests: O. Kiehn, Section of Neurophysiology, Dept. of Physiology, The Panum Institute, Blegdamsvej 3, 2200 Copenhagen N, Denmark.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 15 July 1999; accepted in final form 5 November 1999.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

0022-3077/00 $5.00 Copyright © 2000 The American Physiological Society