Neural Manifolds for the Control of Movement
2017; Cell Press; Volume: 94; Issue: 5 Linguagem: Inglês
10.1016/j.neuron.2017.05.025
ISSN1097-4199
AutoresJuan A. Gallego, Matthew G. Perich, Lee E. Miller, Sara A. Solla,
Tópico(s)Motor Control and Adaptation
ResumoThe analysis of neural dynamics in several brain cortices has consistently uncovered low-dimensional manifolds that capture a significant fraction of neural variability. These neural manifolds are spanned by specific patterns of correlated neural activity, the “neural modes.” We discuss a model for neural control of movement in which the time-dependent activation of these neural modes is the generator of motor behavior. This manifold-based view of motor cortex may lead to a better understanding of how the brain controls movement. The analysis of neural dynamics in several brain cortices has consistently uncovered low-dimensional manifolds that capture a significant fraction of neural variability. These neural manifolds are spanned by specific patterns of correlated neural activity, the “neural modes.” We discuss a model for neural control of movement in which the time-dependent activation of these neural modes is the generator of motor behavior. This manifold-based view of motor cortex may lead to a better understanding of how the brain controls movement. Since the work of Herbert Jasper (Jasper et al., 1958Jasper H. Ricci G.F. Doane B. Patterns of cortical neuronal discharge during conditioned responses in monkeys.in: Wolstenholme G. O’Connor C. Ciba Foundation Symposium - Neurological Basis of Behaviour. John Wiley & Sons, 1958: 277-294Crossref Google Scholar) and Ed Evarts (Evarts, 1968Evarts E.V. Relation of pyramidal tract activity to force exerted during voluntary movement.J. Neurophysiol. 1968; 31: 14-27Crossref PubMed Scopus (745) Google Scholar), cortical function has been studied by recording single-neuron activity while animals perform a variety of behaviors, including decision making (Newsome et al., 1989Newsome W.T. Britten K.H. Movshon J.A. Neuronal correlates of a perceptual decision.Nature. 1989; 341: 52-54Crossref PubMed Scopus (801) Google Scholar), sensation (Wurtz, 1969Wurtz R.H. Visual receptive fields of striate cortex neurons in awake monkeys.J. Neurophysiol. 1969; 32: 727-742Crossref PubMed Scopus (245) Google Scholar), and movement (Georgopoulos et al., 1982Georgopoulos A.P. Kalaska J.F. Caminiti R. Massey J.T. On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex.J. Neurosci. 1982; 2: 1527-1537Crossref PubMed Google Scholar, Humphrey et al., 1970Humphrey D.R. Schmidt E.M. Thompson W.D. Predicting measures of motor performance from multiple cortical spike trains.Science. 1970; 170: 758-762Crossref PubMed Scopus (230) Google Scholar). In the motor system, the main focus of this article, single neuron studies typically involved recordings during repeated, stereotypical movements. Many of these experiments sought explicit representations that relate single-neuron activity to specific movement covariates, including but not limited to target position, endpoint and joint kinematics, endpoint forces, and muscle activity (Evarts, 1968Evarts E.V. Relation of pyramidal tract activity to force exerted during voluntary movement.J. Neurophysiol. 1968; 31: 14-27Crossref PubMed Scopus (745) Google Scholar, Georgopoulos et al., 1982Georgopoulos A.P. Kalaska J.F. Caminiti R. Massey J.T. On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex.J. Neurosci. 1982; 2: 1527-1537Crossref PubMed Google Scholar, Humphrey et al., 1970Humphrey D.R. Schmidt E.M. Thompson W.D. Predicting measures of motor performance from multiple cortical spike trains.Science. 1970; 170: 758-762Crossref PubMed Scopus (230) Google Scholar, Morrow et al., 2007Morrow M.M. Jordan L.R. Miller L.E. Direct comparison of the task-dependent discharge of M1 in hand space and muscle space.J. Neurophysiol. 2007; 97: 1786-1798Crossref PubMed Scopus (51) Google Scholar, Thach, 1978Thach W.T. Correlation of neural discharge with pattern and force of muscular activity, joint position, and direction of intended next movement in motor cortex and cerebellum.J. Neurophysiol. 1978; 41: 654-676Crossref PubMed Scopus (330) Google Scholar). Although some of these efforts involved the decoding of population activity (Georgopoulos et al., 1982Georgopoulos A.P. Kalaska J.F. Caminiti R. Massey J.T. On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex.J. Neurosci. 1982; 2: 1527-1537Crossref PubMed Google Scholar), they were restricted to models of non-interacting neurons whose individual activity was associated with specific movement covariates. However, some of these studies also identified single neurons whose activity did not represent movement parameters (Churchland and Shenoy, 2007Churchland M.M. Shenoy K.V. Temporal complexity and heterogeneity of single-neuron activity in premotor and motor cortex.J. Neurophysiol. 2007; 97: 4235-4257Crossref PubMed Scopus (185) Google Scholar, Fetz, 1992Fetz E.E. Are movement parameters recognizably coded in the activity of single neurons?.Behav. Brain Sci. 1992; 15: 679-690Google Scholar, Scott, 2008Scott S.H. Inconvenient truths about neural processing in primary motor cortex.J. Physiol. 2008; 586: 1217-1224Crossref PubMed Scopus (114) Google Scholar). If neurons in primary motor cortex (M1) were to represent movement parameters, those representations ought to be most evident in corticomotoneuronal (CM) cells, which make direct connections onto spinal motoneurons (Fetz, 1992Fetz E.E. Are movement parameters recognizably coded in the activity of single neurons?.Behav. Brain Sci. 1992; 15: 679-690Google Scholar). Yet, many of these CM cells do not represent any specific movement covariate (Fetz et al., 1989Fetz E.E. Cheney P.D. Mewes K. Palmer S. Control of forelimb muscle activity by populations of corticomotoneuronal and rubromotoneuronal cells.Prog. Brain Res. 1989; 80 (discussion 427–430): 437-449Crossref PubMed Scopus (119) Google Scholar). The ultimate role of M1 is to generate movement, not to represent it (Churchland et al., 2012Churchland M.M. Cunningham J.P. Kaufman M.T. Foster J.D. Nuyujukian P. Ryu S.I. Shenoy K.V. Neural population dynamics during reaching.Nature. 2012; 487: 51-56Crossref PubMed Scopus (744) Google Scholar, Cisek, 2006Cisek P. Preparing for speed. Focus on “Preparatory activity in premotor and motor cortex reflects the speed of the upcoming reach”.J. Neurophysiol. 2006; 96: 2842-2843Crossref PubMed Scopus (21) Google Scholar, Scott, 2004Scott S.H. Optimal feedback control and the neural basis of volitional motor control.Nat. Rev. Neurosci. 2004; 5: 532-546Crossref PubMed Scopus (615) Google Scholar); thus, it is not surprising that many M1 neurons do not relate to any single movement covariate. The search for representations at the single-neuron level might actually divert us from understanding the neural control of movement. Early neural network simulations indicated that individual neurons need not explicitly encode movement covariates when the goal of M1 population activity is to generate realistic muscle activation patterns (Fetz, 1992Fetz E.E. Are movement parameters recognizably coded in the activity of single neurons?.Behav. Brain Sci. 1992; 15: 679-690Google Scholar). The role of neurons that do not explicitly represent any movement covariate can be explained by recent work based on optimal feedback control theory, which postulates that the goal of motor cortex is to produce a desired movement and force, taking into account the state of the muscles. This hypothesis avoids the need for explicit representation of movement covariates by single neurons, though some neurons may still represent movement covariates or high-level task characteristics as a byproduct of the necessary control signals (Scott, 2008Scott S.H. Inconvenient truths about neural processing in primary motor cortex.J. Physiol. 2008; 586: 1217-1224Crossref PubMed Scopus (114) Google Scholar, Todorov, 2000Todorov E. Direct cortical control of muscle activation in voluntary arm movements: a model.Nat. Neurosci. 2000; 3: 391-398Crossref PubMed Scopus (308) Google Scholar). Recent and accelerating technical developments provide the experimental tools for monitoring the activity of large numbers of neurons, as well as the statistical and modeling tools for analyzing how these neural populations perform the computations necessary to plan and execute movement (Gao and Ganguli, 2015Gao P. Ganguli S. On simplicity and complexity in the brave new world of large-scale neuroscience.Curr. Opin. Neurobiol. 2015; 32: 148-155Crossref PubMed Scopus (164) Google Scholar). The challenge of understanding the neural control of movement by analyzing neural population activity is formidable, as population activity in any specific area not only reflects its intrinsic dynamics, but must also respond to its inputs and generate output projections based on the computations being performed (Sussillo et al., 2015Sussillo D. Churchland M.M. Kaufman M.T. Shenoy K.V. A neural network that finds a naturalistic solution for the production of muscle activity.Nat. Neurosci. 2015; 18: 1025-1033Crossref PubMed Scopus (229) Google Scholar). A simplification arises from the fact that neural computations are based on the joint activity of interconnected neurons (Fetz, 1992Fetz E.E. Are movement parameters recognizably coded in the activity of single neurons?.Behav. Brain Sci. 1992; 15: 679-690Google Scholar, Hatsopoulos et al., 1998Hatsopoulos N.G. Ojakangas C.L. Paninski L. Donoghue J.P. Information about movement direction obtained from synchronous activity of motor cortical neurons.Proc. Natl. Acad. Sci. USA. 1998; 95: 15706-15711Crossref PubMed Scopus (194) Google Scholar, 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 (394) Google Scholar); the resulting population activity is thus likely constrained by the connectivity of the underlying network. Here we argue that the underlying network connectivity constrains these possible patterns of population activity (Okun et al., 2015Okun M. Steinmetz N.A. Cossell L. Iacaruso M.F. Ko H. Barthó P. Moore T. Hofer S.B. Mrsic-Flogel T.D. Carandini M. Harris K.D. Diverse coupling of neurons to populations in sensory cortex.Nature. 2015; 521: 511-515Crossref PubMed Scopus (234) Google Scholar, Sadtler et al., 2014Sadtler P.T. Quick K.M. Golub M.D. Chase S.M. Ryu S.I. Tyler-Kabara E.C. Yu B.M. Batista A.P. Neural constraints on learning.Nature. 2014; 512: 423-426Crossref PubMed Scopus (325) Google Scholar, Tsodyks et al., 1999Tsodyks M. Kenet T. Grinvald A. Arieli A. Linking spontaneous activity of single cortical neurons and the underlying functional architecture.Science. 1999; 286: 1943-1946Crossref PubMed Scopus (537) Google Scholar) and that the possible patterns are confined to a low-dimensional manifold (Stopfer et al., 2003Stopfer M. Jayaraman V. Laurent G. Intensity versus identity coding in an olfactory system.Neuron. 2003; 39: 991-1004Abstract Full Text Full Text PDF PubMed Scopus (418) Google Scholar, Yu et al., 2009Yu B.M. Cunningham J.P. Santhanam G. Ryu S.I. Shenoy K.V. Sahani M. Gaussian-process factor analysis for low-dimensional single-trial analysis of neural population activity.J. Neurophysiol. 2009; 102: 614-635Crossref PubMed Scopus (290) Google Scholar) spanned by a few independent patterns that we call “neural modes.” These neural modes capture a significant fraction of population covariance. It is the activation of these neural modes, rather than the activity of single neurons, that provides the basic building blocks of neural dynamics and function (Luczak et al., 2015Luczak A. McNaughton B.L. Harris K.D. Packet-based communication in the cortex.Nat. Rev. Neurosci. 2015; 16: 745-755Crossref PubMed Scopus (112) Google Scholar, Sadtler et al., 2014Sadtler P.T. Quick K.M. Golub M.D. Chase S.M. Ryu S.I. Tyler-Kabara E.C. Yu B.M. Batista A.P. Neural constraints on learning.Nature. 2014; 512: 423-426Crossref PubMed Scopus (325) Google Scholar, 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 (394) Google Scholar). We thus propose a generative model of the activity of individual neurons based on the activation of neural modes, and explain how the parameters of the model can be identified using dimensionality reduction methods. We then review work showing that these neural modes span task-specific neural manifolds in premotor and motor cortices. We propose that neural manifolds spanned by a surprisingly small number of neural modes are likely to simplify the neural control of movement and speculate on the potential learning mechanisms underlying the emergence of this low-dimensional organization. Current multi-electrode arrays (MEAs) allow for the simultaneous recording of about a hundred neurons. This is much more than the small numbers recorded with single electrodes but still a tiny fraction of the total number of neurons involved in movement generation. Despite this limitation, brain-machine interfaces (BMIs) based on these MEAs are able to predict reasonably well many behavioral variables (Carmena et al., 2003Carmena J.M. Lebedev M.A. Crist R.E. O’Doherty J.E. Santucci D.M. Dimitrov D.F. Patil P.G. Henriquez C.S. Nicolelis M.A.L. Learning to control a brain-machine interface for reaching and grasping by primates.PLoS Biol. 2003; 1: E42Crossref PubMed Scopus (1313) Google Scholar, Ethier et al., 2012Ethier C. Oby E.R. Bauman M.J. Miller L.E. Restoration of grasp following paralysis through brain-controlled stimulation of muscles.Nature. 2012; 485: 368-371Crossref PubMed Scopus (340) Google Scholar, Serruya et al., 2002Serruya M.D. Hatsopoulos N.G. Paninski L. Fellows M.R. Donoghue J.P. Instant neural control of a movement signal.Nature. 2002; 416: 141-142Crossref PubMed Scopus (1082) Google Scholar). What is the underlying reason for this success? Intuitively, it is the high degree of correlation and redundancy across individual neural activity. This intuition has been recently made precise in elegant arguments on the low dimensionality of the stereotypical motor behaviors used in most motor control studies (Gao and Ganguli, 2015Gao P. Ganguli S. On simplicity and complexity in the brave new world of large-scale neuroscience.Curr. Opin. Neurobiol. 2015; 32: 148-155Crossref PubMed Scopus (164) Google Scholar). The relatively small number of independent signals needed to control behavior during the execution of such tasks only requires a small number of independent neural signals. These neural signals are the “latent variables” (Cunningham and Yu, 2014Cunningham J.P. Yu B.M. Dimensionality reduction for large-scale neural recordings.Nat. Neurosci. 2014; 17: 1500-1509Crossref PubMed Scopus (525) Google Scholar) that describe the dynamics of the “neural modes.” The participation of individual neurons in neural modes is illustrated in Figure 1A. Note that each neural mode includes a large fraction of the neurons in the population and that a given neuron can participate in several neural modes. In this view, the time-dependent activity of individual neurons is simply a reflection of the latent variables (Figure 1B) (Kaufman et al., 2016Kaufman M.T. Seely J.S. Sussillo D. Ryu S.I. Shenoy K.V. Churchland M.M. The largest response component in the motor cortex reflects movement timing but not movement type.eNeuro. 2016; 3 (ENEURO.0085-16.2016)Crossref PubMed Scopus (94) Google Scholar, Kobak et al., 2016Kobak D. Brendel W. Constantinidis C. Feierstein C.E. Kepecs A. Mainen Z.F. Qi X.L. Romo R. Uchida N. Machens C.K. Demixed principal component analysis of neural population data.eLife. 2016; 5: 1-36Crossref Scopus (216) Google Scholar, Macke et al., 2011Macke J.H. Buesing L. Cunningham J.P. Yu B.M. Shenoy K.V. Sahani M. Empirical models of spiking in neuronal populations.Adv. Neural Inf. Process. Syst. 2011; 24: 1-9Google Scholar). Consider the “neural space” in Figure 1C; each axis represents the activity of one of the N recorded neurons (here, N = 3). Assuming that network connectivity constrains the possible patterns of population activity (Okun et al., 2015Okun M. Steinmetz N.A. Cossell L. Iacaruso M.F. Ko H. Barthó P. Moore T. Hofer S.B. Mrsic-Flogel T.D. Carandini M. Harris K.D. Diverse coupling of neurons to populations in sensory cortex.Nature. 2015; 521: 511-515Crossref PubMed Scopus (234) Google Scholar, Sadtler et al., 2014Sadtler P.T. Quick K.M. Golub M.D. Chase S.M. Ryu S.I. Tyler-Kabara E.C. Yu B.M. Batista A.P. Neural constraints on learning.Nature. 2014; 512: 423-426Crossref PubMed Scopus (325) Google Scholar, Tsodyks et al., 1999Tsodyks M. Kenet T. Grinvald A. Arieli A. Linking spontaneous activity of single cortical neurons and the underlying functional architecture.Science. 1999; 286: 1943-1946Crossref PubMed Scopus (537) Google Scholar), the population dynamics will not explore the full high-dimensional neural space but will instead remain confined to a low-dimensional surface within the full space, the “neural manifold.” In the simplest linear case, the neural manifold is flat, as is the hyperplane in Figure 1C, spanned by the two neural modes, u1 and u2. This geometrical picture illustrates a possible generative model for the dynamics of individual neurons: the activity ni(t) of the ith neuron, 1≤i≤N, results from a linear combination of latent variables Lj(t) plus additive noise εi:ni(t)=∑juij Lj(t)+εi.Equation 1 Here, Lj(t) is the jth latent variable, the time-dependent activation of the jth neural mode. Each latent variable results from projecting the neural population activity onto the corresponding neural mode. The coefficient uij in the linear combination quantifies the contribution of the jth latent variable to the activity of the ith neuron. These “participation weights” relate to the internal connectivity of the network (Okun et al., 2015Okun M. Steinmetz N.A. Cossell L. Iacaruso M.F. Ko H. Barthó P. Moore T. Hofer S.B. Mrsic-Flogel T.D. Carandini M. Harris K.D. Diverse coupling of neurons to populations in sensory cortex.Nature. 2015; 521: 511-515Crossref PubMed Scopus (234) Google Scholar). The noise term εi represents intrinsic neural noise, and potentially other processes not accounted for in the model. By construction, neural population activity remains within the neural manifold except for small fluctuations (see how close the actual black trajectory is to the gray trajectory projected into the manifold in Figure 1C). Dimensionality reduction techniques allow us to study neural population dynamics by finding a set of neural modes that span the neural manifold and identify relevant population features (Cunningham and Yu, 2014Cunningham J.P. Yu B.M. Dimensionality reduction for large-scale neural recordings.Nat. Neurosci. 2014; 17: 1500-1509Crossref PubMed Scopus (525) Google Scholar). Common linear techniques for dimensionality reduction, such as principal component analysis (PCA) and factor analysis (FA), identify neural modes as dominant patterns of covariation across neurons and yield the parameters of the generative model (Equation 1; Figure 1B). As an illustration, we show that neural data recorded during an isometric wrist task (Figures 2A and 2B ) is largely accounted for by the latent variables in Figure 2C. The low dimensionality of the neural manifold follows from the rapid increase of the explained variance with the number of neural modes (Figure 2D). The concept of the neural manifold and its associated latent variables has been used in a series of recent studies that abandon the search for movement representation by single neurons to consider instead movement planning and execution based on the activation of a few neural modes (Ahrens et al., 2012Ahrens M.B. Li J.M. Orger M.B. Robson D.N. Schier A.F. Engert F. Portugues R. Brain-wide neuronal dynamics during motor adaptation in zebrafish.Nature. 2012; 485: 471-477Crossref PubMed Scopus (432) Google Scholar, Bruno et al., 2015Bruno A.M. Frost W.N. Humphries M.D. Modular deconstruction reveals the dynamical and physical building blocks of a locomotion motor program.Neuron. 2015; 86: 304-318Abstract Full Text Full Text PDF PubMed Scopus (39) Google Scholar, Churchland et al., 2010aChurchland M.M. Cunningham J.P. Kaufman M.T. Ryu S.I. Shenoy K.V. Cortical preparatory activity: representation of movement or first cog in a dynamical machine?.Neuron. 2010; 68: 387-400Abstract Full Text Full Text PDF PubMed Scopus (260) Google Scholar, Churchland et al., 2010bChurchland 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 (636) Google Scholar, Churchland et al., 2012Churchland M.M. Cunningham J.P. Kaufman M.T. Foster J.D. Nuyujukian P. Ryu S.I. Shenoy K.V. Neural population dynamics during reaching.Nature. 2012; 487: 51-56Crossref PubMed Scopus (744) Google Scholar, Churchland and Shenoy, 2007Churchland M.M. Shenoy K.V. Temporal complexity and heterogeneity of single-neuron activity in premotor and motor cortex.J. Neurophysiol. 2007; 97: 4235-4257Crossref PubMed Scopus (185) Google Scholar, Elsayed et al., 2016Elsayed G.F. Lara A.H. Kaufman M.T. Churchland M.M. Cunningham J.P. Reorganization between preparatory and movement population responses in motor cortex.Nat. Commun. 2016; 7: 13239Crossref PubMed Scopus (153) Google Scholar, Kaufman et al., 2014Kaufman M.T. Churchland M.M. Ryu S.I. Shenoy K.V. Cortical activity in the null space: permitting preparation without movement.Nat. Neurosci. 2014; 17: 440-448Crossref PubMed Scopus (331) Google Scholar, Kaufman et al., 2016Kaufman M.T. Seely J.S. Sussillo D. Ryu S.I. Shenoy K.V. Churchland M.M. The largest response component in the motor cortex reflects movement timing but not movement type.eNeuro. 2016; 3 (ENEURO.0085-16.2016)Crossref PubMed Scopus (94) Google Scholar, Michaels et al., 2016Michaels J.A. Dann B. Scherberger H. Neural population dynamics during reaching are better explained by a dynamical system than representational tuning.PLoS Comput. Biol. 2016; 12: e1005175Crossref PubMed Scopus (70) Google Scholar, Overduin et al., 2015Overduin S.A. d’Avella A. Roh J. Carmena J.M. Bizzi E. Representation of muscle synergies in the primate brain.J. Neurosci. 2015; 35: 12615-12624Crossref PubMed Scopus (114) Google Scholar, Sadtler et al., 2014Sadtler P.T. Quick K.M. Golub M.D. Chase S.M. Ryu S.I. Tyler-Kabara E.C. Yu B.M. Batista A.P. Neural constraints on learning.Nature. 2014; 512: 423-426Crossref PubMed Scopus (325) Google Scholar, Santhanam et al., 2009Santhanam G. Yu B.M. Gilja V. Ryu S.I. Afshar A. Sahani M. Shenoy K.V. Factor-analysis methods for higher-performance neural prostheses.J. Neurophysiol. 2009; 102: 1315-1330Crossref PubMed Scopus (68) Google Scholar, Sussillo et al., 2015Sussillo D. Churchland M.M. Kaufman M.T. Shenoy K.V. A neural network that finds a naturalistic solution for the production of muscle activity.Nat. Neurosci. 2015; 18: 1025-1033Crossref PubMed Scopus (229) Google Scholar). One of the earliest findings of a neural manifold for movement control comes from Shenoy and colleagues (Santhanam et al., 2009Santhanam G. Yu B.M. Gilja V. Ryu S.I. Afshar A. Sahani M. Shenoy K.V. Factor-analysis methods for higher-performance neural prostheses.J. Neurophysiol. 2009; 102: 1315-1330Crossref PubMed Scopus (68) Google Scholar), who analyzed population activity recorded with an MEA implanted in the arm area of dorsal premotor cortex (PMd) during a delayed center-out reach task. Single-neuron activity in PMd correlates with the direction toward the end point of an upcoming reach movement (Riehle and Requin, 1989Riehle A. Requin J. Monkey primary motor and premotor cortex: single-cell activity related to prior information about direction and extent of an intended movement.J. Neurophysiol. 1989; 61: 534-549Crossref PubMed Scopus (342) Google Scholar, Shen and Alexander, 1997Shen L. Alexander G.E. Preferential representation of instructed target location versus limb trajectory in dorsal premotor area.J. Neurophysiol. 1997; 77: 1195-1212Crossref PubMed Scopus (190) Google Scholar). Shenoy and colleagues used FA to obtain neural modes that accounted for the observed shared variance of individual neurons. They found that a three-dimensional manifold sufficed to identify target-specific clusters of latent activity during the delay period (Figure 3A). A subsequent study (Churchland et al., 2010bChurchland 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 (636) Google Scholar) showed a systematic decrease in the trial-to-trial variability in the neural dynamics of both PMd and primary visual cortex (V1) following stimulus onset, as demonstrated in two-dimensional visualizations of the latent variables (Figure 3B). The low-dimensional manifold was characterized using Gaussian process factor analysis (GPFA), a method that combines FA with temporal smoothing through a Gaussian kernel, to extract the low-dimensional trajectories defined by the latent variables during individual trials. The method was proposed and compared to static methods like PCA and FA in an earlier paper (Yu et al., 2009Yu B.M. Cunningham J.P. Santhanam G. Ryu S.I. Shenoy K.V. Sahani M. Gaussian-process factor analysis for low-dimensional single-trial analysis of neural population activity.J. Neurophysiol. 2009; 102: 614-635Crossref PubMed Scopus (290) Google Scholar) that identified variability reduction following target presentation in PMd data. The notion of a neural manifold and its associated latent variables was subsequently used by Churchland, Shenoy, and colleagues (Churchland et al., 2010aChurchland M.M. Cunningham J.P. Kaufman M.T. Ryu S.I. Shenoy K.V. Cortical preparatory activity: representation of movement or first cog in a dynamical machine?.Neuron. 2010; 68: 387-400Abstract Full Text Full Text PDF PubMed Scopus (260) Google Scholar, Churchland et al., 2012Churchland M.M. Cunningham J.P. Kaufman M.T. Foster J.D. Nuyujukian P. Ryu S.I. Shenoy K.V. Neural population dynamics during reaching.Nature. 2012; 487: 51-56Crossref PubMed Scopus (744) Google Scholar) to explain how neural activity in both PMd and M1 during movement planning (Riehle and Requin, 1989Riehle A. Requin J. Monkey primary motor and premotor cortex: single-cell activity related to prior information about direction and extent of an intended movement.J. Neurophysiol. 1989; 61: 534-549Crossref PubMed Scopus (342) Google Scholar) does not generate movement during the delay preceding a go signal (Cisek and Kalaska, 2005Cisek P. Kalaska J.F. Neural correlates of reaching decisions in dorsal premotor cortex: specification of multiple direction choices and final selection of action.Neuron. 2005; 45: 801-814Abstract Full Text Full Text PDF PubMed Scopus (701) Google Scholar). To explain how M1 could prepare movement without causing it, the same group (Kaufman et al., 2014Kaufman M.T. Churchland M.M. Ryu S.I. Shenoy K.V. Cortical activity in the null space: permitting preparation without movement.Nat. Neurosci. 2014; 17: 440-448Crossref PubMed Scopus (331) Google Scholar) identified a six-dimensional neural manifold using PCA, then built a linear model that related these latent variables to three “muscle synergies” (d’Avella et al., 2003d’Avella A. Saltiel P. Bizzi E. Combinations of muscle synergies in the construction of a natural motor behavior.Nat. Neurosci. 2003; 6: 300-308Crossref PubMed Scopus (896) Google Scholar, Tresch and Jarc, 2009Tresch M.C. Jarc A. The case for and against muscle synergies.Curr. Opin. Neurobiol. 2009; 19: 601-607Crossref PubMed Scopus (379) Google Scholar), also identified by PCA. Based on this linear model, they divided the neural manifold into a “potent” space, whose activity controls muscle activity, and a “null” space, whose activity does not affect muscle activity (Kaufman et al., 2014Kaufman M.T. Churchland M.M. Ryu S.I. Shenoy K.V. Cortical activity in the null space: permitting preparation without movement.Nat. Neurosci. 2014; 17: 440-448Crossref PubMed Scopus (331) Google Scholar) (Figure 3C). They showed that preparatory activity lies in the null space; this condition-dependent activity provides an initialization from which the population dynamics evolve to generate the desired movement (Churchland et al., 2010aChurchland M.M. Cunningham J.P. Kaufman M.T. Ryu S.I. Shenoy K.V. Cortical preparatory activity: representation of movement or first cog in a dynamical machine?.Neuron. 2010; 68: 387-400Abstract Full Text Full Text PDF PubMed Scopus (260) Google Scholar, Churchland et al., 2012Churchland M.M. Cunningham J.P. Kaufman M.T. Foster J.D. Nuyujukian P. Ryu S.I. Shenoy K.V. Neural population dynamics during reaching.Nature. 2012; 487: 51-56Crossref PubMed Scopus (744) Google Scholar, Kaufman et al., 2014Kaufman M.T. Churchland M.M. Ryu S.I. Shenoy K.V. Cortical activity in the null space: permitting preparation without movement.Nat. Neurosci. 2014; 17: 440-448Crossref PubMed Scopus (331) Google Scholar, 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 (394) Google Scholar). In a recent follow-up study, the same group expanded this analysis to show that preparatory and movement activity lie in orthogonal spaces within the manifold and that population dynamics evolve from one to the other (Elsayed et al.
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