Department of Physiology, Section of Neurophysiology, The Panum Institute, 2200 Copenhagen N, Denmark
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ABSTRACT |
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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.
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INTRODUCTION |
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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
).
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METHODS |
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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.
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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
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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).
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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|), 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
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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
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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.
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RESULTS |
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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(|{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.
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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.
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DISCUSSION |
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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.
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ACKNOWLEDGMENTS |
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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.
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FOOTNOTES |
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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.
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REFERENCES |
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