Random walk of motor planning in task-irrelevant dimensions.

The movements that we make are variable. It is well established that at least a part of this variability is caused by noise in central motor planning. Here, we studied how the random effects of planning noise translate into changes in motor planning. Are the random effects independently added to a constant mean end point, or do they accumulate over movements? To distinguish between these possibilities, we examined repeated, discrete movements in various tasks in which the motor output could be decomposed into a task-relevant and a task-irrelevant component. We found in all tasks that the task-irrelevant component had a positive lag 1 autocorrelation, suggesting that the random effects of planning noise accumulate over movements. In contrast, the task-relevant component always had a lag 1 autocorrelation close to zero, which can be explained by effective trial-by-trial correction of motor planning on the basis of observed motor errors. Accumulation of the effects of planning noise is consistent with current insights into the stochastic nature of synaptic plasticity. It leads to motor exploration, which may subserve motor learning and performance optimization.

[1]  Kelvin E. Jones,et al.  Sources of signal-dependent noise during isometric force production. , 2002, Journal of neurophysiology.

[2]  E. Bizzi,et al.  Motor Learning with Unstable Neural Representations , 2007, Neuron.

[3]  Philip N. Sabes,et al.  Calibration of visually guided reaching is driven by error-corrective learning and internal dynamics. , 2007, Journal of neurophysiology.

[4]  Daniel M. Wolpert,et al.  Signal-dependent noise determines motor planning , 1998, Nature.

[5]  David V. Hinkley,et al.  Inference about the change-point in a sequence of binomial variables , 1970 .

[6]  Maurice G. Kendall,et al.  NOTE ON BIAS IN THE ESTIMATION OF AUTOCORRELATION , 1954 .

[7]  Gregor Schöner,et al.  Toward a new theory of motor synergies. , 2007, Motor control.

[8]  J. Kalaska,et al.  Comparison of variability of initial kinematics and endpoints of reaching movements , 1999, Experimental Brain Research.

[9]  Adonis K Moschovakis,et al.  Optimal Control of Gaze Shifts , 2009, The Journal of Neuroscience.

[10]  K. Shenoy,et al.  A Central Source of Movement Variability , 2006, Neuron.

[11]  James D. Hamilton Time Series Analysis , 1994 .

[12]  E. Todorov Optimality principles in sensorimotor control , 2004, Nature Neuroscience.

[13]  J. Foley The co-ordination and regulation of movements , 1968 .

[14]  F. H. C. Marriott,et al.  BIAS IN THE ESTIMATION OF AUTOCORRELATIONS , 1954 .

[15]  W. T. Thach,et al.  Purkinje cell activity during motor learning , 1977, Brain Research.

[16]  R. V. van Beers Saccadic Eye Movements Minimize the Consequences of Motor Noise , 2008, PloS one.

[17]  William W. S. Wei,et al.  Time series analysis - univariate and multivariate methods , 1989 .

[18]  A. Triller,et al.  From the stochasticity of molecular processes to the variability of synaptic transmission , 2011, Nature Reviews Neuroscience.

[19]  Michael I. Jordan,et al.  Optimal feedback control as a theory of motor coordination , 2002, Nature Neuroscience.

[20]  S. Panchapakesan,et al.  Inference about the Change-Point in a Sequence of Random Variables: A Selection Approach , 1988 .

[21]  Dagmar Sternad,et al.  Coordinate Dependence of Variability Analysis , 2010, PLoS Comput. Biol..

[22]  A. Kristofferson,et al.  Response delays and the timing of discrete motor responses , 1973 .

[23]  S. Glasauer,et al.  Optimal Control of Natural Eye-Head Movements Minimizes the Impact of Noise , 2011, The Journal of Neuroscience.

[24]  T. Sejnowski Statistical constraints on synaptic plasticity. , 1977, Journal of theoretical biology.

[25]  Cavina-Pratesi Cristiana,et al.  Results of Experiment 2. , 2013 .

[26]  R. J. van Beers,et al.  The Sources of Variability in Saccadic Eye Movements , 2007, The Journal of Neuroscience.

[27]  M. Latash,et al.  Motor Control Strategies Revealed in the Structure of Motor Variability , 2002, Exercise and sport sciences reviews.

[28]  M. Mauk,et al.  Simulations of Cerebellar Motor Learning: Computational Analysis of Plasticity at the Mossy Fiber to Deep Nucleus Synapse , 1999, The Journal of Neuroscience.

[29]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[30]  R. J. Marshall Autocorrelation estimation of time series with randomly missing observations , 1980 .

[31]  R. J. Beers The Sources of Variability in Saccadic Eye Movements , 2007 .

[32]  Olivier White,et al.  Use-Dependent and Error-Based Learning of Motor Behaviors , 2010, The Journal of Neuroscience.

[33]  Eilon Vaadia,et al.  Trial-to-Trial Variability of Single Cells in Motor Cortices Is Dynamically Modified during Visuomotor Adaptation , 2009, The Journal of Neuroscience.

[34]  H. Seung,et al.  Learning in Spiking Neural Networks by Reinforcement of Stochastic Synaptic Transmission , 2003, Neuron.

[35]  Robert J. van Beers,et al.  How Does Our Motor System Determine Its Learning Rate? , 2012, PloS one.

[36]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[37]  M. Brainard,et al.  Performance variability enables adaptive plasticity of ‘crystallized’ adult birdsong , 2007, Nature.

[38]  Daniel M. Wolpert,et al.  The Main Sequence of Saccades Optimizes Speed-accuracy Trade-off , 2006, Biological Cybernetics.

[39]  Eli Brenner,et al.  Quickly ‘learning’ to move optimally , 2011, Experimental Brain Research.

[40]  J. Smeets,et al.  Nature of variability in saccades. , 2003, Journal of neurophysiology.

[41]  R. J. Beers,et al.  Motor Learning Is Optimally Tuned to the Properties of Motor Noise , 2009, Neuron.

[42]  R. J. van Beers,et al.  The role of execution noise in movement variability. , 2004, Journal of neurophysiology.

[43]  James Gordon,et al.  Accuracy of planar reaching movements , 1994, Experimental Brain Research.

[44]  Zoubin Ghahramani,et al.  Computational principles of movement neuroscience , 2000, Nature Neuroscience.

[45]  Shigeru Kitazawa,et al.  Optimization of goal-directed movements in the cerebellum: a random walk hypothesis , 2002, Neuroscience Research.

[46]  Stephen G. Lisberger,et al.  Links from complex spikes to local plasticity and motor learning in the cerebellum of awake-behaving monkeys , 2008, Nature Neuroscience.

[47]  Michael S. Brainard,et al.  Central Contributions to Acoustic Variation in Birdsong , 2008, The Journal of Neuroscience.

[48]  Maria Huhtala,et al.  Random Variables and Stochastic Processes , 2021, Matrix and Tensor Decompositions in Signal Processing.

[49]  Jonathan B. Dingwell,et al.  Do Humans Optimally Exploit Redundancy to Control Step Variability in Walking? , 2010, PLoS Comput. Biol..

[50]  H Collewijn,et al.  Modulation of the human vestibuloocular reflex during saccades: probing by high-frequency oscillation and torque pulses of the head. , 1996, Journal of neurophysiology.

[51]  Joshua I. Gold,et al.  Bayesian Online Learning of the Hazard Rate in Change-Point Problems , 2010, Neural Computation.

[52]  Robert J. van Beers,et al.  How does our motor system determine its learning rate , 2012 .

[53]  Paola Cesari,et al.  Body-goal Variability Mapping in an Aiming Task , 2006, Biological Cybernetics.

[54]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[55]  Links from complex spikes to local plasticity and motor learning in the cerebellum of awake-behaving monkeys. , 2008, Nature neuroscience.

[56]  R. J. Beers Correction: Saccadic Eye Movements Minimize the Consequences of Motor Noise , 2008 .

[57]  Gregor Schöner,et al.  The uncontrolled manifold concept: identifying control variables for a functional task , 1999, Experimental Brain Research.

[58]  Dagmar Sternad,et al.  Neuromotor Noise, Error Tolerance and Velocity-Dependent Costs in Skilled Performance , 2011, PLoS Comput. Biol..

[59]  Chris Chatfield,et al.  The Analysis of Time Series , 1990 .

[60]  Chris Chatfield,et al.  The Analysis of Time Series: An Introduction , 1981 .

[61]  J. Gordon,et al.  Accuracy of planar reaching movements , 1994, Experimental Brain Research.

[62]  Eli Brenner,et al.  Sensory integration does not lead to sensory calibration , 2006, Proceedings of the National Academy of Sciences.

[63]  K.-R. Muller,et al.  BCI meeting 2005-workshop on BCI signal processing: feature extraction and translation , 2006, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[64]  N. A. Bernshteĭn The co-ordination and regulation of movements , 1967 .

[65]  Ryan P. Adams,et al.  Bayesian Online Changepoint Detection , 2007, 0710.3742.

[66]  H. Zelaznik,et al.  Motor-output variability: a theory for the accuracy of rapid motor acts. , 1979, Psychological review.