Structured variability in Purkinje cell activity during locomotion
Britton A. Sauerbrei
,
Evgueniy V. Lubenov
, and
Athanassios G. Siapas
Computation and Neural Systems Program, Division of Biology and Biological Engineering, and
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA
91125
Athanassios G. Siapas: thanos@caltech.edu
Summary
The cerebellum is a prominent vertebrate brain structure that is critically involved in sensorimotor
function. During locomotion, cerebellar Purkinje cells are rhythmically active, shaping descending
signals and coordinating commands from higher brain areas with the step cycle. However, the
variation in this activity across steps has not been studied, and its statistical structure, afferent
mechanisms, and relationship to behavior remain unknown. Here, using multi-electrode recordings
in freely moving rats, we show that behavioral variables systematically influence the shape of the
step-locked firing rate. This effect depends strongly on the phase of the step cycle and reveals a
functional clustering of Purkinje cells. Furthermore, we find a pronounced disassociation between
patterns of variability driven by the parallel and climbing fibers. These results suggest that
Purkinje cell activity not only represents step phase within each cycle, but is also shaped by
behavior across steps, facilitating control of movement under dynamic conditions.
Introduction
Trial-to-trial variability is a widespread and fundamental feature of neural activity, evident
from the periphery through higher brain areas. Responses to sensory stimuli vary over
repeated presentations, and this variability is modulated by stimulus onset (
Churchland et
al., 2010
;
Monier et al., 2003
), depends strongly on network architecture (
Litwin-Kumar and
Doiron, 2012
), and is altered by successive stages of sensory processing (
Kara et al., 2000
).
Furthermore, trial-to-trial correlations between neurons influence the accuracy of neural
codes (
Averbeck et al., 2006
;
Moreno-Bote et al., 2014
), and are highly dependent on global
changes in brain state (
Ecker et al., 2014
). During the preparation and execution of
movement, neural activity often varies considerably across repetitions, even when the
movement is highly stereotyped. Such variability is thought to impose critical constraints on
motor performance (
Shenoy et al., 2013
;
Todorov and Jordan, 2002
), the capacity of motor
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Contributions
BAS and AGS designed the experiments. BAS performed the experiments. BAS, EVL, and AGS analyzed the data. BAS generated
the figures. BAS, EVL, and AGS wrote the manuscript.
HHS Public Access
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Neuron
. 2015 August 19; 87(4): 840–852. doi:10.1016/j.neuron.2015.08.003.
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codes (
Averbeck and Lee, 2003
;
Lee et al., 1998
;
Maynard et al., 1999
), and learning
(
Chaisanguanthum et al., 2014
;
Mandelblat-Cerf et al., 2009
).
Several features make locomotion a powerful framework for studying neural variability in
motor systems. First, locomotion is an ethologically relevant, nearly universal characteristic
of animal life. Many aspects of legged overground movement are remarkably consistent
across a wide range of species, from stick insects to humans (
Orlovsky et al., 1999
;
Shik and
Orlovsky, 1976
), and the insights obtained from its study will likely generalize beyond the
model organism chosen. Second, locomotion and other periodic behaviors are paradigmatic
cases of motor repetition, with centrally generated rhythms shaped by modulatory
influences. Third, studying locomotion eliminates the need for delays between experimental
trials, allowing efficient acquisition of data from a large number of cycles and improving the
statistical detection of patterns.
The cerebellum plays a critical role in the coordination of locomotion (
Armstrong, 1988
;
Arshavsky et al., 1986
;
Shik and Orlovsky, 1976
), and damage to the cerebellar vermis
severely impairs the control of limbs and posture in animal models and in human patients
(
Dow and Moruzzi, 1958
;
Martino et al., 2014
;
Morton and Bastian, 2004
). Furthermore,
mouse mutant lines with cell-type-specific abnormalities in the cerebellar cortex exhibit
locomotor deficits in speed, accuracy, consistency, and multi-joint coordination (
Vinueza
Veloz et al., 2014
). During stepping, pathways from the spinal cord carry proprioceptive,
cutaneous, and rhythmogenic signals to the cerebellar cortex (
Arshavsky et al., 1986
;
Bosco
and Poppele, 2001
;
Oscarsson, 1965
). Mossy fibers related to the forelimbs, hindlimbs, and
head have different distributions over cerebellar lobules but largely overlap (
Adrian, 1943
;
Anderson, 1943
;
Dow and Moruzzi, 1958
;
Matsushita and Hosoya, 1979
;
Snyder et al.,
1978
;
Tolbert and Gutting, 1997
), and vestibular pathways terminate in the same areas
(
Barmack et al., 1992
;
Barmack et al., 1993
;
Denoth et al., 1979
;
Jensen, 1985
;
Kotchabhakdi and Walberg, 1978
;
Manzoni et al., 1999
;
Matsushita and Wang, 1987
;
Precht
et al., 1977
). Signals from these pathways are relayed through the parallel fibers to Purkinje
cells in the vermal and intermediate cortex, which discharge periodically during stepping
(
Armstrong and Edgley, 1984
,
1988
;
Edgley and Lidierth, 1988
;
Orlovsky, 1972
;
Udo et al.,
1981
) and impose their rhythm on routes descending back to the spinal cord (
Arshavsky et
al., 1986
). This rhythmic discharge provides direct signals to the spinal limb controllers, and
also gates motor commands from higher brain centers, ensuring that these commands are
coordinated with the ongoing locomotor pattern (
Orlovsky et al., 1999
).
Although the cerebellar contribution to the control of locomotion has been studied
extensively, a number of experimental challenges remain. Previous studies have used
decerebrate (
Arshavsky et al., 1986
;
Orlovsky, 1972
;
Udo et al., 1981
) and awake
(
Armstrong and Edgley, 1984
,
1988
;
Edgley and Lidierth, 1988
) cats restricted on a
treadmill, but none have examined step-locked simple and complex spikes in freely
behaving rodents. Furthermore, treadmill studies of constant-speed stepping have dominated
the study of cerebellar activity, but are limited in their ability to reveal the neuronal
dynamics that occur in freely moving animals that spontaneously initiate, maintain, and
terminate locomotion. Several studies have imaged calcium transients in Purkinje cell
ensembles, revealing olivo-cerebellar interactions during locomotion (
De Gruijl et al., 2014
;
Sauerbrei et al.
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Flusberg et al., 2008
;
Ghosh et al., 2011
;
Hoogland et al., 2015
;
Ozden et al., 2012
). These
transients, however, reflect complex spikes, which constitute only a small fraction of the
spiking output. Few simultaneous recordings of simple spikes from multiple Purkinje cells
have been made during locomotion (
Smith, 1995
), and correlations between pairs of neurons
across steps have not been studied. Finally, Purkinje cell activity has been reported to vary
extensively across steps (
Armstrong and Edgley, 1984
), but there has been no systematic
study of this variation and its relationship to behavior, though some evidence suggests that
animal speed can influence activity averaged over many steps (
Armstrong and Edgley,
1988
).
Here, we use chronically implanted multi-tetrode arrays in conjunction with
electromyography and behavioral measurements in freely moving rats to address several
open questions. First, is the step-locked firing pattern for a Purkinje cell highly stereotyped,
or does it change extensively across steps? Furthermore, if this pattern is flexible, what are
its major modes of variation? Second, how is neuronal variability related to behavior?
Correlations between neuronal activity and behavioral factors would suggest that step-to-
step variation plays a functional role in motor control, while the absence of correlations
might indicate that such variation is noise. In addition, if such correlations are present, do
they influence only the mean firing rate within a step cycle, or does interaction between
behavior and spiking occur on a finer time scale through step-phase-dependent effects?
Third, is the activity of multiple Purkinje cells correlated across steps? Uncorrelated activity
would suggest that variation reflects intrinsic noise at the level of individual neurons, while
pairwise correlations would be consistent with coordinated inputs. Fourth, how is Purkinje
cell output shaped across steps by its two afferent systems, the parallel and climbing fibers?
The contributions of these two pathways can be distinguished using extracellular recording:
the parallel fibers control the rate of simple spikes, while the climbing fibers produce
complex spikes (
Eccles et al., 1966
). One possibility is that both pathways use an analog rate
code for sensorimotor variables both within steps (representing step phase) and across steps
(representing behavioral factors such as speed). Alternatively, the two pathways might
encode distinct features using qualitatively different coding schemes.
Results
Tetrode recordings from freely moving rats reveal high step-to-step variability
Using chronically implanted multi-tetrode arrays, we recorded spiking activity from 120
Purkinje cells in the medial cerebellar vermis of freely behaving rats (n=3; Figure 1A). Most
cells were located in lobule V (n=74) and VI (n=42), with a small number in lobule IV (n=4)
(Figure S3). All recorded neurons were identified as Purkinje cells by the presence of
complex spiking (
Eccles et al., 1966
), and in many of these cells (n=65), it was possible to
reliably distinguish between simple and complex spikes throughout the session (Figure 1B).
The animals were trained to walk freely on a linear track for water reward at ports
positioned at the ends of the track, while we recorded head location, head attitude, an EMG
of acromiotrapezius activity, and the timing of licks at the water ports (Figure 1A, Figure
S1). For most cells, firing rates were elevated during locomotion, relative to inactivity and
licking (Figure S4C, p < 10
−7
and p < 10
−6
, respectively, paired t-tests), and complex spikes
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also exhibited rate increases for the same states (Figure S4D, p = .0011 and p = .015, paired
t-tests). Phasic increases in firing occurred at the onset of locomotion, and phasic increases
or decreases were common during movement termination (Figure S4A). Lick times were
recorded for 114 cells, and 101 of these were significantly modulated by licking (Figure
S4B, Kuiper’s test, false discovery rate set at q = .05).
All cells discharged rhythmically during locomotion (Figure 1C, Figure 2A, B; q = .05,
Kuiper’s test), consistent with previous studies of paravermal lobule V in awake cats on a
treadmill (
Armstrong and Edgley, 1984
,
1988
;
Edgley and Lidierth, 1988
). Cells exhibited
one (n=26), two (n=69), or three (n=25) peaks in the step cycle, and the location of these
peaks was widely dispersed across cells (Figure 2B). However, although the average activity
of each cell exhibited clear tuning to step phase, an inspection of spiking patterns across
individual steps revealed a high degree of variability. The firing rate of the Purkinje cell in
Figure 1C, for instance, shows large fluctuations within each step cycle, but even more
striking are the changes in its amplitude and shape across steps. This extensive step-to-step
variability was typically observable in the step-locked spike rasters (Figure 2A,
lower
panel
) and firing rate curves (Figure 2C).
In order to quantify this variability, we computed the variance-to-mean ratio, or Fano factor,
for the spike counts within a window starting at the EMG peak for each step cycle (Figure
2D, above). For a Poisson process, the count variance equals the count mean, and the Fano
factor is one. By contrast, Purkinje cell spike counts typically had higher variances than
means (Figure 2E, left panel), with a mean Fano Factor of 1.58 for a window duration of
350ms. These values indicate that spiking is more variable than expected for a Poisson
process, and more variable than previously reported for macaque neocortical neurons during
visually-guided reaching (e.g. supplementary motor area (
Averbeck and Lee, 2003
;
Mandelblat-Cerf et al., 2009
), motor cortex (
Mandelblat-Cerf et al., 2009
), premotor cortex
(
Churchland et al., 2010
;
Churchland et al., 2006
), and the parietal reach region (
Churchland
et al., 2010
)). Interestingly, we observed a strong disassociation between patterns of
variability for simple spikes, which were over-dispersed relative to a Poisson process, and
for complex spikes, which were under-dispersed (Figure 2D, below, 2E, center and right).
Patterns of variability in step-locked firing rates
If firing patterns differ across steps, what are the major modes of variation? In order to
address this question, we performed principal component analysis on the step-locked firing
rates for each cell. This produced an effective reduction of the data, with the first three
components accounting for an average of 75% of the variance (Figure 3B,
left
). Sorting
cycles by principal component scores (Figure S5) or visualizing the effects of the
coefficients as perturbations of the mean firing rate curve (Figure 3A) revealed several
common patterns: “bias” (an additive shift in the curve with little change in its shape),
“amplitude” (multiplicative scaling of the curve), and “phase” (a horizontal shift of the
curve forward or backward in time). These same three patterns have been independently
identified in kinematic data from humans during locomotion (
Ramsay and Silverman, 2005
).
While many cells had components that directly reflected one of these modes, more complex
patterns were observed, as well. For instance, some cells with multiple peaks exhibited
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components that shifted the firing rate around one of the peaks, while imposing little change
on the rest of the curve (e.g. component 1 for the cell marked with red arrow in Figure 3A,
corresponding to the neuron from Figure 1C).
To quantify the extent to which a component represented a change in bias, amplitude, or
phase, we computed three scores corresponding to these patterns: S
bias
, S
amp
, and S
phase
(see
methods section). Across the sample of Purkinje cells, the first principal component had
much higher bias scores than the second (p < 10
−9
, Kolmogorov-Smirnov test) and third (p <
10
−23
) components (Figure 3B), and the second component had higher bias scores than the
third (p < 10
−4
), indicating that differences across steps were due largely to shifts in the
mean firing rate. By contrast, the phase shift scores were much lower for the first principal
component than for the second (p < 10
−6
) and third (p < 10
−11
), and for the second than the
third (p = .0023). Furthermore, three-dimensional scatterplots revealed an aggregation of
neurons around a pure bias shift for the first component, and around a pure phase shift for
the third component (Figure 3C).
Neural variability exhibits step-phase-dependent correlations with behavior
Are these step-to-step fluctuations in neuronal spiking related to behavior? Examination of
the spiking activity of individual neurons over several laps often suggested systematic
changes in step-locked firing rates with behavioral variables, such as speed (Figure 4A). In
order to characterize this further, we first measured the animals’ average head speed,
acceleration, roll, pitch, and EMG amplitude within each step and examined their
relationship to the firing rates. For each neuron and behavioral variable, we divided the steps
into intervals according to the value of the variable and averaged the firing rate curves
within each interval (see methods section). This often produced a sequence of curves that
varied smoothly and systematically as the behavioral parameters changed (Figure 4B, C). In
order to quantify the effects of behavior on neuronal activity, we estimated a linear model
for each Purkinje cell, with speed, acceleration, roll, pitch, and EMG amplitude as
independent variables and the mean firing rate on each cycle as the dependent variable.
Speed, acceleration, and head attitude had significant effects for many cells. Out of 120 total
Purkinje cells, 81 were modulated by speed, 84 by acceleration, 70 by roll, and 54 by pitch
(Figure S6A). By contrast, only 27 neurons were significantly modulated by EMG
amplitude. For each independent variable, both positive and negative regression coefficients
were observed, but most significant values were positive for speed (p = .014, binomial test).
An examination of coefficients for pairs of variables failed to reveal any clustering of
Purkinje cell tuning properties: instead, a broad distribution of values was observed (Figure
S6B).
If behavior is correlated with Purkinje cell activity, what is the structure of its relationship to
the step-phase-dependent firing rate? This question is central, for two reasons. First, cycle-
to-cycle variability is not restricted to shifts in mean firing rate, but can express a variety of
patterns, as indicated by the analysis of principal component coefficients (Figure 3). Second,
the behavioral variables – particularly roll, pitch, and EMG amplitude – can fluctuate on a
faster time scale than that of a single step cycle (Figure S1). In order to address this
question, we estimated regression curves parameterized by step phase for each cell and
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behavioral variable. These curves capture how a given behavioral variable modulates the
shape of the step-locked firing rate for each cell. For many cells, the relationship between
behavior and neural activity varied in magnitude, and in some cases in sign, according to the
phase of the step cycle (Figure 4D). For example, the neuron on the left in Figure 4D shows
a decrease with speed during the first half of the step cycle, but an increase with speed
during the second half. Consequently, this neuron’s speed regression curve has a shape
similar to its average firing rate curve, and imposes a strong amplitude shift. To further
quantify the patterns of this behavioral modulation, we computed bias, amplitude, and phase
scores for these curves (see Supplemental Experimental Procedures). Three-dimensional
scatterplots of scores (S
bias
, S
amp
, and S
phase
) for the regression curves revealed large
differences between behavioral variables, as well as the presence of clusters (Figure 4E). We
performed a hierarchical cluster analysis on the (S
bias
, S
amp
, S
phase
) observations for cells
with significant tuning to each variable, and this analysis revealed several key features. First,
all variables except EMG amplitude exhibited a large aggregation of cells around a pure bias
shift. Second, speed and pitch exhibited clusters near a pure amplitude shift. Third, roll and
acceleration exhibited clusters near a pure phase shift. These results demonstrate a
functional segregation in Purkinje cell properties that is not observed after averaging
behavior and firing rates within each step cycle.
Purkinje cell pairs exhibit correlated activity across steps
In many sessions, it was possible to record simultaneously from multiple Purkinje cells, and
step-averaged firing rates for pairs often appeared to covary across steps (Figure 5A). Such
covariation may result in part from similar tuning to measured behavioral variables, so we
first removed the effects of these factors using the regression models and then examined
correlations between the residuals. Scatterplots of the residual firing rates for pairs recorded
on distinct tetrodes revealed clear associations in many cases (Figure 5B, above), and 40 out
of 89 pairs were significantly correlated (Figure 5B, below; q = .05, partial rank correlation),
with both positive and negative correlations observed. Further analysis of the residuals and
the rank-transformed variables indicated that the correlations were unlikely to be due to
nonlinear interactions between measured behavioral variables and firing rates (Figure S7).
These correlations suggest that step-to-step variability is not independent, intrinsic noise at
the level of individual Purkinje cells, but is rather driven by coordinated inputs. The relative
spatial location of recorded cells did not influence correlations: no significant differences
were observed between ipsilateral and contralateral pairs (p = .27, two-sample t-test),
between cells in the same lobule and in different lobules (p = .35, two-sample t-test), or
between cells at different mediolateral or rostrocaudal distances (p = .95, .92, respectively,
one-way ANOVA) (Figure 5C).
Parallel and climbing fiber inputs carry qualitatively distinct signals
Because the climbing fiber system plays an essential role in motor performance and
learning, we examined the relationship between complex spikes, which are driven by this
pathway, and step phase, speed, acceleration, head posture, and EMG. In contrast to simple
spikes, which were strongly modulated by the stepping rhythm for all Purkinje cells,
complex spikes were modulated in a minority of neurons (12/65; q = .05, Kuiper’s test;
Figure 6A, B). The depth of modulation was larger for simple than complex spikes (p <
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