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• W1866012920 abstract "•Purkinje cell activity in locomotion is rhythmic but highly variable across steps•Step-to-step variability expresses a range of characteristic patterns•Variability is related to behavioral factors and correlated for pairs of cells•Parallel and climbing fibers carry qualitatively distinct signals during stepping 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 also is shaped by behavior across steps, facilitating control of movement under dynamic conditions. 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 also is shaped by behavior across steps, facilitating control of movement under dynamic conditions. 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., 2010Churchland M.M. Yu B.M. Cunningham J.P. Sugrue L.P. Cohen M.R. Corrado G.S. Newsome W.T. Clark A.M. Hosseini P. Scott B.B. et al.Stimulus onset quenches neural variability: a widespread cortical phenomenon.Nat. Neurosci. 2010; 13: 369-378Crossref PubMed Scopus (640) Google Scholar, Monier et al., 2003Monier C. Chavane F. Baudot P. Graham L.J. Frégnac Y. Orientation and direction selectivity of synaptic inputs in visual cortical neurons: a diversity of combinations produces spike tuning.Neuron. 2003; 37: 663-680Abstract Full Text Full Text PDF PubMed Scopus (296) Google Scholar), depends strongly on network architecture (Litwin-Kumar and Doiron, 2012Litwin-Kumar A. Doiron B. Slow dynamics and high variability in balanced cortical networks with clustered connections.Nat. Neurosci. 2012; 15: 1498-1505Crossref PubMed Scopus (322) Google Scholar), and is altered by successive stages of sensory processing (Kara et al., 2000Kara P. Reinagel P. Reid R.C. Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons.Neuron. 2000; 27: 635-646Abstract Full Text Full Text PDF PubMed Scopus (272) Google Scholar). Furthermore, trial-to-trial correlations between neurons influence the accuracy of neural codes (Averbeck et al., 2006Averbeck B.B. Latham P.E. Pouget A. Neural correlations, population coding and computation.Nat. Rev. Neurosci. 2006; 7: 358-366Crossref PubMed Scopus (1034) Google Scholar, Moreno-Bote et al., 2014Moreno-Bote R. Beck J. Kanitscheider I. Pitkow X. Latham P. Pouget A. Information-limiting correlations.Nat. Neurosci. 2014; 17: 1410-1417Crossref PubMed Scopus (284) Google Scholar) and are highly dependent on global changes in brain state (Ecker et al., 2014Ecker A.S. Berens P. Cotton R.J. Subramaniyan M. Denfield G.H. Cadwell C.R. Smirnakis S.M. Bethge M. Tolias A.S. State dependence of noise correlations in macaque primary visual cortex.Neuron. 2014; 82: 235-248Abstract Full Text Full Text PDF PubMed Scopus (215) Google Scholar). 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., 2013Shenoy K.V. Sahani M. Churchland M.M. Cortical control of arm movements: a dynamical systems perspective.Annu. Rev. Neurosci. 2013; 36: 337-359Crossref PubMed Scopus (398) Google Scholar, Todorov and Jordan, 2002Todorov E. Jordan M.I. Optimal feedback control as a theory of motor coordination.Nat. Neurosci. 2002; 5: 1226-1235Crossref PubMed Scopus (1998) Google Scholar), the capacity of motor codes (Averbeck and Lee, 2003Averbeck B.B. Lee D. Neural noise and movement-related codes in the macaque supplementary motor area.J. Neurosci. 2003; 23: 7630-7641PubMed Google Scholar, Lee et al., 1998Lee D. Port N.L. Kruse W. Georgopoulos A.P. Variability and correlated noise in the discharge of neurons in motor and parietal areas of the primate cortex.J. Neurosci. 1998; 18: 1161-1170PubMed Google Scholar, Maynard et al., 1999Maynard E.M. Hatsopoulos N.G. Ojakangas C.L. Acuna B.D. Sanes J.N. Normann R.A. Donoghue J.P. Neuronal interactions improve cortical population coding of movement direction.J. Neurosci. 1999; 19: 8083-8093PubMed Google Scholar), and learning (Chaisanguanthum et al., 2014Chaisanguanthum K.S. Shen H.H. Sabes P.N. Motor variability arises from a slow random walk in neural state.J. Neurosci. 2014; 34: 12071-12080Crossref PubMed Scopus (48) Google Scholar, Mandelblat-Cerf et al., 2009Mandelblat-Cerf Y. Paz R. Vaadia E. Trial-to-trial variability of single cells in motor cortices is dynamically modified during visuomotor adaptation.J. Neurosci. 2009; 29: 15053-15062Crossref PubMed Scopus (60) Google Scholar). 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., 1999Orlovsky G.N. Deliagina T.G. Grillner S. Neuronal control of locomotion: from mollusc to man. Oxford University Press, 1999Crossref Google Scholar, Shik and Orlovsky, 1976Shik M.L. Orlovsky G.N. Neurophysiology of locomotor automatism.Physiol. Rev. 1976; 56: 465-501PubMed Google Scholar), 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, 1988Armstrong D.M. The supraspinal control of mammalian locomotion.J. Physiol. 1988; 405: 1-37Crossref PubMed Scopus (281) Google Scholar, Arshavsky et al., 1986Arshavsky Y.I. Gelfand I.M. Orlovsky G.N. Cerebellum and rhythmical movements. Springer-Verlag, 1986Crossref Google Scholar, Shik and Orlovsky, 1976Shik M.L. Orlovsky G.N. Neurophysiology of locomotor automatism.Physiol. Rev. 1976; 56: 465-501PubMed Google Scholar), and damage to the cerebellar vermis severely impairs the control of limbs and posture in animal models and in human patients (Dow and Moruzzi, 1958Dow R.S. Moruzzi G. The physiology and pathology of the cerebellum. University of Minnesota Press, 1958Google Scholar, Martino et al., 2014Martino G. Ivanenko Y.P. Serrao M. Ranavolo A. d’Avella A. Draicchio F. Conte C. Casali C. Lacquaniti F. Locomotor patterns in cerebellar ataxia.J. Neurophysiol. 2014; 112: 2810-2821Crossref PubMed Scopus (82) Google Scholar, Morton and Bastian, 2004Morton S.M. Bastian A.J. Cerebellar control of balance and locomotion.Neuroscientist. 2004; 10: 247-259Crossref PubMed Scopus (313) Google Scholar). 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., 2014Vinueza Veloz M.F. Zhou K. Bosman L.W. Potters J.W. Negrello M. Seepers R.M. Strydis C. Koekkoek S.K. De Zeeuw C.I. Cerebellar control of gait and interlimb coordination.Brain Struct. Funct. 2014; (Published online August 20, 2014)Crossref PubMed Scopus (78) Google Scholar). During stepping, pathways from the spinal cord carry proprioceptive, cutaneous, and rhythmogenic signals to the cerebellar cortex (Arshavsky et al., 1986Arshavsky Y.I. Gelfand I.M. Orlovsky G.N. Cerebellum and rhythmical movements. Springer-Verlag, 1986Crossref Google Scholar, Bosco and Poppele, 2001Bosco G. Poppele R.E. Proprioception from a spinocerebellar perspective.Physiol. Rev. 2001; 81: 539-568PubMed Google Scholar, Oscarsson, 1965Oscarsson O. Functional Organization of the Spino- and Cuneocerebellar Tracts.Physiol. Rev. 1965; 45: 495-522PubMed Google Scholar). Mossy fibers related to the forelimbs, hindlimbs, and head have different distributions over cerebellar lobules but largely overlap (Adrian, 1943Adrian E. Afferent Areas in the Cerebellum Connected with the Limbs.Brain. 1943; 66: 289-315Crossref Scopus (129) Google Scholar, Anderson, 1943Anderson R.F. Cerebellar Distribution of the Dorsal and Ventral Spino-Cerebellar Tracts in the White Rat.J. Comp. Neurol. 1943; 79: 415-423Crossref Scopus (17) Google Scholar, Dow and Moruzzi, 1958Dow R.S. Moruzzi G. The physiology and pathology of the cerebellum. University of Minnesota Press, 1958Google Scholar, Matsushita and Hosoya, 1979Matsushita M. Hosoya Y. Cells of origin of the spinocerebellar tract in the rat, studied with the method of retrograde transport of horseradish peroxidase.Brain Res. 1979; 173: 185-200Crossref PubMed Scopus (135) Google Scholar, Snyder et al., 1978Snyder R.L. Faull R.L. Mehler W.R. A comparative study of the neurons of origin of the spinocerebellar afferents in the rat, cat and squirrel monkey based on the retrograde transport of horseradish peroxidase.J. Comp. Neurol. 1978; 181: 833-852Crossref PubMed Scopus (133) Google Scholar, Tolbert and Gutting, 1997Tolbert D.L. Gutting J.C. Quantitative analysis of cuneocerebellar projections in rats: differential topography in the anterior and posterior lobes.Neuroscience. 1997; 80: 359-371Crossref PubMed Scopus (29) Google Scholar), and vestibular pathways terminate in the same areas (Barmack et al., 1992Barmack N.H. Baughman R.W. Eckenstein F.P. Shojaku H. Secondary vestibular cholinergic projection to the cerebellum of rabbit and rat as revealed by choline acetyltransferase immunohistochemistry, retrograde and orthograde tracers.J. Comp. Neurol. 1992; 317: 250-270Crossref PubMed Scopus (127) Google Scholar, Barmack et al., 1993Barmack N.H. Baughman R.W. Errico P. Shojaku H. Vestibular primary afferent projection to the cerebellum of the rabbit.J. Comp. Neurol. 1993; 327: 521-534Crossref PubMed Scopus (100) Google Scholar, Denoth et al., 1979Denoth F. Magherini P.C. Pompeiano O. Stanojević M. Responses of Purkinje cells of the cerebellar vermis to neck and macular vestibular inputs.Pflugers Arch. 1979; 381: 87-98Crossref PubMed Scopus (67) Google Scholar, Jensen, 1985Jensen D.W. Posture-correlated responses to vestibular polarization in vermal versus intermediate posterior cerebellar cortex.Exp. Neurol. 1985; 88: 629-639Crossref PubMed Scopus (2) Google Scholar, Kotchabhakdi and Walberg, 1978Kotchabhakdi N. Walberg F. Cerebellar afferent projections from the vestibular nuclei in the cat: an experimental study with the method of retrograde axonal transport of horseradish peroxidase.Exp. Brain Res. 1978; 31: 591-604PubMed Google Scholar, Manzoni et al., 1999Manzoni D. Pompeiano O. Bruschini L. Andre P. Neck input modifies the reference frame for coding labyrinthine signals in the cerebellar vermis: a cellular analysis.Neuroscience. 1999; 93: 1095-1107Crossref PubMed Scopus (44) Google Scholar, Matsushita and Wang, 1987Matsushita M. Wang C.L. Projection pattern of vestibulocerebellar fibers in the anterior vermis of the cat: an anterograde wheat germ agglutinin-horseradish peroxidase study.Neurosci. Lett. 1987; 74: 25-30Crossref PubMed Scopus (19) Google Scholar, Precht et al., 1977Precht W. Volkind R. Blanks R.H. Functional organization of the vestibular input to the anterior and posterior cerebellar vermis of cat.Exp. Brain Res. 1977; 27: 143-160Crossref PubMed Scopus (51) Google Scholar). 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, 1984Armstrong D.M. Edgley S.A. Discharges of Purkinje cells in the paravermal part of the cerebellar anterior lobe during locomotion in the cat.J. Physiol. 1984; 352: 403-424Crossref PubMed Scopus (68) Google Scholar, Armstrong and Edgley, 1988Armstrong D.M. Edgley S.A. Discharges of interpositus and Purkinje cells of the cat cerebellum during locomotion under different conditions.J. Physiol. 1988; 400: 425-445Crossref PubMed Scopus (49) Google Scholar, Edgley and Lidierth, 1988Edgley S.A. Lidierth M. Step-related discharges of Purkinje cells in the paravermal cortex of the cerebellar anterior lobe in the cat.J. Physiol. 1988; 401: 399-415Crossref PubMed Scopus (36) Google Scholar, Orlovskiĭ, 1972Orlovskiĭ G.N. [Activity of Purkinje cells during locomotion].Biofizika. 1972; 17: 891-896PubMed Google Scholar, Udo et al., 1981Udo M. Matsukawa K. Kamei H. Minoda K. Oda Y. Simple and complex spike activities of Purkinje cells during locomotion in the cerebellar vermal zones of decerebrate cats.Exp. Brain Res. 1981; 41: 292-300PubMed Google Scholar) and impose their rhythm on routes descending back to the spinal cord (Arshavsky et al., 1986Arshavsky Y.I. Gelfand I.M. Orlovsky G.N. Cerebellum and rhythmical movements. Springer-Verlag, 1986Crossref Google Scholar). 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., 1999Orlovsky G.N. Deliagina T.G. Grillner S. Neuronal control of locomotion: from mollusc to man. Oxford University Press, 1999Crossref Google Scholar). 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., 1986Arshavsky Y.I. Gelfand I.M. Orlovsky G.N. Cerebellum and rhythmical movements. Springer-Verlag, 1986Crossref Google Scholar, Orlovskiĭ, 1972Orlovskiĭ G.N. [Activity of Purkinje cells during locomotion].Biofizika. 1972; 17: 891-896PubMed Google Scholar, Udo et al., 1981Udo M. Matsukawa K. Kamei H. Minoda K. Oda Y. Simple and complex spike activities of Purkinje cells during locomotion in the cerebellar vermal zones of decerebrate cats.Exp. Brain Res. 1981; 41: 292-300PubMed Google Scholar) and awake (Armstrong and Edgley, 1984Armstrong D.M. Edgley S.A. Discharges of Purkinje cells in the paravermal part of the cerebellar anterior lobe during locomotion in the cat.J. Physiol. 1984; 352: 403-424Crossref PubMed Scopus (68) Google Scholar, Armstrong and Edgley, 1988Armstrong D.M. Edgley S.A. Discharges of interpositus and Purkinje cells of the cat cerebellum during locomotion under different conditions.J. Physiol. 1988; 400: 425-445Crossref PubMed Scopus (49) Google Scholar, Edgley and Lidierth, 1988Edgley S.A. Lidierth M. Step-related discharges of Purkinje cells in the paravermal cortex of the cerebellar anterior lobe in the cat.J. Physiol. 1988; 401: 399-415Crossref PubMed Scopus (36) Google Scholar) 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., 2014De Gruijl J.R. Hoogland T.M. De Zeeuw C.I. Behavioral correlates of complex spike synchrony in cerebellar microzones.J. Neurosci. 2014; 34: 8937-8947Crossref PubMed Scopus (43) Google Scholar, Flusberg et al., 2008Flusberg B.A. Nimmerjahn A. Cocker E.D. Mukamel E.A. Barretto R.P. Ko T.H. Burns L.D. Jung J.C. Schnitzer M.J. High-speed, miniaturized fluorescence microscopy in freely moving mice.Nat. Methods. 2008; 5: 935-938Crossref PubMed Scopus (306) Google Scholar, Ghosh et al., 2011Ghosh K.K. Burns L.D. Cocker E.D. Nimmerjahn A. Ziv Y. Gamal A.E. Schnitzer M.J. Miniaturized integration of a fluorescence microscope.Nat. Methods. 2011; 8: 871-878Crossref PubMed Scopus (701) Google Scholar, Hoogland et al., 2015Hoogland T.M. De Gruijl J.R. Witter L. Canto C.B. De Zeeuw C.I. Role of Synchronous Activation of Cerebellar Purkinje Cell Ensembles in Multi-joint Movement Control.Curr. Biol. 2015; 25: 1157-1165Abstract Full Text Full Text PDF PubMed Scopus (64) Google Scholar, Ozden et al., 2012Ozden I. Dombeck D.A. Hoogland T.M. Tank D.W. Wang S.S.-H. Widespread state-dependent shifts in cerebellar activity in locomoting mice.PLoS ONE. 2012; 7: e42650Crossref PubMed Scopus (75) Google Scholar). 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, 1995Smith S.S. Sensorimotor-correlated discharge recorded from ensembles of cerebellar Purkinje cells varies across the estrous cycle of the rat.J. Neurophysiol. 1995; 74: 1095-1108PubMed Google Scholar), 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, 1984Armstrong D.M. Edgley S.A. Discharges of Purkinje cells in the paravermal part of the cerebellar anterior lobe during locomotion in the cat.J. Physiol. 1984; 352: 403-424Crossref PubMed Scopus (68) Google Scholar), 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, 1988Armstrong D.M. Edgley S.A. Discharges of interpositus and Purkinje cells of the cat cerebellum during locomotion under different conditions.J. Physiol. 1988; 400: 425-445Crossref PubMed Scopus (49) Google Scholar). 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 timescale 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., 1966Eccles J.C. Llinás R. Sasaki K. The excitatory synaptic action of climbing fibres on the Purkinje cells of the cerebellum.J. Physiol. 1966; 182: 268-296Crossref PubMed Scopus (599) Google Scholar). 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. 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., 1966Eccles J.C. Llinás R. Sasaki K. The excitatory synaptic action of climbing fibres on the Purkinje cells of the cerebellum.J. Physiol. 1966; 182: 268-296Crossref PubMed Scopus (599) Google Scholar), 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 (Figures 1A and 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 also exhibited rate increases for the same states (Figure S4D, p = 0.0011 and p = 0.015, 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 = 0.05). All cells discharged rhythmically during locomotion (Figures 1C, 2A , and 2B; q = 0.05, Kuiper’s test), consistent with previous studies of paravermal lobule V in awake cats on a treadmill (Armstrong and Edgley, 1984Armstrong D.M. Edgley S.A. Discharges of Purkinje cells in the paravermal part of the cerebellar anterior lobe during locomotion in the cat.J. Physiol. 1984; 352: 403-424Crossref PubMed Scopus (68) Google Scholar, Armstrong and Edgley, 1988Armstrong D.M. Edgley S.A. Discharges of interpositus and Purkinje cells of the cat cerebellum during locomotion under different conditions.J. Physiol. 1988; 400: 425-445Crossref PubMed Scopus (49) Google Scholar, Edgley and Lidierth, 1988Edgley S.A. Lidierth M. Step-related discharges of Purkinje cells in the paravermal cortex of the cerebellar anterior lobe in the cat.J. Physiol. 1988; 401: 399-415Crossref PubMed Scopus (36) Google Scholar). 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 350 ms. These values indicate that spiking is more variable than expected for a Poisson process, and more variable than typical for macaque neocortical neurons during visually guided reaching (e.g., supplementary motor area [Averbeck and Lee, 2003Averbeck B.B. Lee D. Neural noise and movement-related codes in the macaque supplementary motor area.J. Neurosci. 2003; 23: 7630-7641PubMed Google Scholar, Mandelblat-Cerf et al., 2009Mandelblat-Cerf Y. Paz R. Vaadia E. Trial-to-trial variability of single cells in motor cortices is dynamically modified during visuomotor adaptation.J. Neurosci. 2009; 29: 15053-15062Crossref PubMed Scopus (60) Google Scholar], motor cortex [Mandelblat-Cerf et al., 2009Mandelblat-Cerf Y. Paz R. Vaadia E. Trial-to-trial variability of single cells in motor cortices is dynamically modified during visuomotor adaptation.J. Neurosci. 2009; 29: 15053-15062Crossref PubMed Scopus (60) Google Scholar], premotor cortex [Churchland et al., 2010Churchland M.M. Yu B.M. Cunningham J.P. Sugrue L.P. Cohen M.R. Corrado G.S. Newsome W.T. Clark A.M. Hosseini P. Scott B.B. et al.Stimulus onset quenches neural variability: a widespread cortical phenomenon.Nat. Neurosci. 2010; 13: 369-378Crossref PubMed Scopus (640) Google Scholar, Churchland et al., 2006Churchland M.M. Yu B.M. Ryu S.I. Santhanam G. Shenoy K.V. Neural variability in premotor cortex provides a signature of motor preparation.J. Neurosci. 2006; 26: 3697-3712Crossref PubMed Scopus (291) Google Scholar], and the parietal reach region [Churchland et al., 2010Churchland M.M. Yu B.M. Cunningham J.P. Sugrue L.P. Cohen M.R. Corrado G.S. Newsome W.T. Clark A.M. Hosseini P. Scott B.B. et al.Stimulus onset quenches neural variability: a widespread cortical phenomenon.Nat. Neurosci. 2010; 13: 369-378Crossref PubMed Scopus (640) Google Scholar]). 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 (Figures 2D, below, and 2E, center and right). 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, 2005Ramsay J.O. Silverman B.W. Functional data analysis.Second Edition. Springer, 2005Crossref Google Scholar). 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 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: Sbias, Samp, and Sphase (see Experimental Procedures). 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 = 0.0023). Furthermore, 3D 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). Are these step-to-step fluctuations in neuronal spiking related to behavior? Examination of the spiking activity of" @default.
• W1866012920 created "2016-06-24" @default.
• W1866012920 creator A5025818097 @default.
• W1866012920 creator A5033281863 @default.
• W1866012920 creator A5048804210 @default.
• W1866012920 date "2015-08-01" @default.
• W1866012920 modified "2023-10-17" @default.
• W1866012920 title "Structured Variability in Purkinje Cell Activity during Locomotion" @default.
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