Abstract
The study of the cortical control of movement experienced a conceptual shift over recent decades, as the basic currency of understanding shifted from single-neuron tuning towards population-level factors and their dynamics. This transition was informed by a maturing understanding of recurrent networks, where mechanism is often characterized in terms of population-level factors. By estimating factors from data, experimenters could test network-inspired hypotheses. Central to such hypotheses are ‘output-null’ factors that do not directly drive motor outputs yet are essential to the overall computation. In this Review, we highlight how the hypothesis of output-null factors was motivated by the venerable observation that motor-cortex neurons are active during movement preparation, well before movement begins. We discuss how output-null factors then became similarly central to understanding neural activity during movement. We discuss how this conceptual framework provided key analysis tools, making it possible for experimenters to address long-standing questions regarding motor control. We highlight an intriguing trend: as experimental and theoretical discoveries accumulate, the range of computational roles hypothesized to be subserved by output-null factors continues to expand.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$189.00 per year
only $15.75 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Tanji, J. & Evarts, E. V. Anticipatory activity of motor cortex neurons in relation to direction of an intended movement. J. Neurophysiol. 39, 1062–1068 (1976).
Weinrich, M., Wise, S. P. & Mauritz, K. H. A neurophysiological study of the premotor cortex in the rhesus monkey. Brain 107, 385–414 (1984).
Wise, S. P. The primate premotor cortex: past, present, and preparatory. Annu. Rev. Neurosci. 8, 1–19 (1985).
Churchland, M. M., Santhanam, G. & Shenoy, K. V. Preparatory activity in premotor and motor cortex reflects the speed of the upcoming reach. J. Neurophysiol. 96, 3130–3146 (2006).
Messier, J. & Kalaska, J. F. Covariation of primate dorsal premotor cell activity with direction and amplitude during a memorized-delay reaching task. J. Neurophysiol. 84, 152–165 (2000).
Churchland, 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 68, 387–400 (2010).
Churchland, M. M., Afshar, A. & Shenoy, K. V. A central source of movement variability. Neuron 52, 1085–1096 (2006).
Riehle, A. & Requin, J. The predictive value for performance speed of preparatory changes in neuronal activity of the monkey motor and premotor cortex. Behav. Brain Res. 53, 35–49 (1993).
Churchland, 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. 26, 3697–3712 (2006).
Churchland, M. M. & Shenoy, K. V. Delay of movement caused by disruption of cortical preparatory activity. J. Neurophysiol. 97, 348–359 (2007).
Li, N., Daie, K., Svoboda, K. & Druckmann, S. Robust neuronal dynamics in premotor cortex during motor planning. Nature 532, 459–464 (2016).
Svoboda, K. & Li, N. Neural mechanisms of movement planning: motor cortex and beyond. Curr. Opin. Neurobiol. 49, 33–41 (2018).
Vyas, S., Golub, M. D., Sussillo, D. & Shenoy, K. V. Computation through neural population dynamics. Annu. Rev. Neurosci. 43, 249–275 (2020).
Crammond, D. J. & Kalaska, J. F. Prior information in motor and premotor cortex: activity during the delay period and effect on pre-movement activity. J. Neurophysiol. 84, 986–1005 (2000).
Georgopoulos, 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. 2, 1527–1537 (1982).
Georgopoulos, A. P., Schwartz, A. B. & Kettner, R. E. Neuronal population coding of movement direction. Science 233, 1416–1419 (1986).
Churchland, M. M. & Lisberger, S. G. Shifts in the population response in the middle temporal visual area parallel perceptual and motor illusions produced by apparent motion. J. Neurosci. 21, 9387–9402 (2001).
Takemura, A., Inoue, Y., Kawano, K., Quaia, C. & Miles, F. A. Single-unit activity in cortical area MST associated with disparity-vergence eye movements: evidence for population coding. J. Neurophysiol. 85, 2245–2266 (2001).
Reimer, J. & Hatsopoulos, N. G. The problem of parametric neural coding in the motor system. Adv. Exp. Med. Biol. 629, 243–259 (2009).
Fetz, E. E. Are movement parameters recognizably coded in the activity of single neurons? Behav. Brain Sci. 15, 679–690 (1992).
Scott, S. H. Inconvenient truths about neural processing in primary motor cortex. J. Physiol. 586, 1217–1224 (2008).
Churchland, M. M. & Shenoy, K. V. Temporal complexity and heterogeneity of single-neuron activity in premotor and motor cortex. J. Neurophysiol. 97, 4235–4257 (2007).
Churchland, M. M. et al. Neural population dynamics during reaching. Nature 487, 51–56 (2012).
Sussillo, 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. 18, 1025–1033 (2015).
Mante, V., Sussillo, D., Shenoy, K. V. & Newsome, W. T. Context-dependent computation by recurrent dynamics in prefrontal cortex. Nature 503, 78–84 (2013).
Robinson, D. A. Implications of neural networks for how we think about brain function. Behav. Brain Sci. 15, 644–655 (1992).
Saxena, S. & Cunningham, J. P. Towards the neural population doctrine. Curr. Opin. Neurobiol. 55, 103–111 (2019).
Barack, D. L. & Krakauer, J. W. Two views on the cognitive brain. Nat. Rev. Neurosci. 22, 359–371 (2021).
Druckmann, S. & Chklovskii, D. B. Neuronal circuits underlying persistent representations despite time varying activity. Curr. Biol. 22, 2095–2103 (2012).
Kaufman, M. T., Churchland, M. M., Ryu, S. I. & Shenoy, K. V. Cortical activity in the null space: permitting preparation without movement. Nat. Neurosci. 17, 440–448 (2014).
Semedo, J. D., Zandvakili, A., Machens, C. K., Yu, B. M. & Kohn, A. Cortical areas interact through a communication subspace. Neuron 102, 249–259.e4 (2019).
Dum, R. P. & Strick, P. L. Spinal cord terminations of the medial wall motor areas in macaque monkeys. J. Neurosci. 16, 6513–6525 (1996).
Fetz, E. E. & Cheney, P. D. Postspike facilitation of forelimb muscle activity by primate corticomotoneuronal cells. J. Neurophysiol. 44, 751–772 (1980).
Griffin, D. M., Hudson, H. M., Belhaj-Saif, A., McKiernan, B. J. & Cheney, P. D. Do corticomotoneuronal cells predict target muscle EMG activity? J. Neurophysiol. 99, 1169–1986 (2008).
Leyton, S. S. F. & Sherrington, C. S. Observations on the excitable cortex of the chimpanzee, orang-utan and gorilla. Exp. Physiol. 11, 135–222 (1917).
Penfield, W. & Boldrey, E. Somatic motor and sensory representation in the cerebral cortex of man as studied by electrical stimulation. Brain 60, 389–443 (1937).
Asanuma, H. & Sakata, H. Functional organization of a cortical efferent system examined with focal depth stimulation in cats. J. Neurophysiol. 30, 35–54 (1967).
Russo, A. A. et al. Motor cortex embeds muscle-like commands in an untangled population response. Neuron 97, 953–966.e8 (2018).
Marshall, N. J. et al. Flexible neural control of motor units. Nat. Neurosci. 25, 1492–1504 (2022).
Erlhagen, W. & Schoner, G. Dynamic field theory of movement preparation. Psychol. Rev. 109, 545–572 (2002).
Bastian, A., Schoner, G. & Riehle, A. Preshaping and continuous evolution of motor cortical representations during movement preparation. Eur. J. Neurosci. 18, 2047–2058 (2003).
Cisek, P. Integrated neural processes for defining potential actions and deciding between them: a computational model. J. Neurosci. 26, 9761–9770 (2006).
Lee, C., Rohrer, W. H. & Sparks, D. L. Population coding of saccadic eye movements by neurons in the superior colliculus. Nature 332, 357–360 (1988).
Glimcher, P. W. & Sparks, D. L. Effects of low-frequency stimulation of the superior colliculus on spontaneous and visually guided saccades. J. Neurophysiol. 69, 953–964 (1993).
Schieber, M. H. & Rivlis, G. Partial reconstruction of muscle activity from a pruned network of diverse motor cortex neurons. J. Neurophysiol. 97, 70–82 (2007).
Omrani, M., Kaufman, M. T., Hatsopoulos, N. G. & Cheney, P. D. Perspectives on classical controversies about the motor cortex. J. Neurophysiol. 118, 1828–1848 (2017).
Morrow, 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. 97, 1786–1798 (2007).
Sergio, L. E., Hamel-Paquet, C. & Kalaska, J. F. Motor cortex neural correlates of output kinematics and kinetics during isometric-force and arm-reaching tasks. J. Neurophysiol. 94, 2353–2378 (2005).
Todorov, E. Direct cortical control of muscle activation in voluntary arm movements: a model. Nat. Neurosci. 3, 391–398 (2000).
Scott, S. H., Gribble, P. L., Graham, K. M. & Cabel, D. W. Dissociation between hand motion and population vectors from neural activity in motor cortex. Nature 413, 161–165 (2001).
Lillicrap, T. P. & Scott, S. H. Preference distributions of primary motor cortex neurons reflect control solutions optimized for limb biomechanics. Neuron 77, 168–179 (2013).
Morrow, M. M., Pohlmeyer, E. A. & Miller, L. E. Control of muscle synergies by cortical ensembles. Adv. Exp. Meb. Biol. 629, 179–199 (2009).
Oby, E. R., Ethier, C. & Miller, L. E. Movement representation in the primary motor cortex and its contribution to generalizable EMG predictions. J. Neurophysiol. 109, 666–678 (2013).
Heming, E. A. et al. Primary motor cortex neurons classified in a postural task predict muscle activation patterns in a reaching task. J. Neurophysiol. 115, 2021–2032 (2016).
Kwan, H. C., Yeap, T. H., Jiang, B. C. & Borrett, D. Neural network control of simple limb movements. Can. J. Physiol. Pharmacol. 68, 126–130 (1990).
Fetz, E. E. in The Neurobiology of Neural Networks (ed. Gardner, D.) 165–190 (MIT Press, 1993).
Maass, W., Natschlager, T. & Markram, H. Real-time computing without stable states: a new framework for neural computation based on perturbations. Neural Comput. 14, 2531–2560 (2002).
Jaeger, H. & Haas, H. Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication. Science 304, 78–80 (2004).
van Vreeswijk, C. & Sompolinsky, H. Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274, 1724–1726 (1996).
Churchland, M. M. et al. Stimulus onset quenches neural variability: a widespread cortical phenomenon. Nat. Neurosci. 13, 369–378 (2010).
Rajan, K., Abbott, L. & Sompolinsky, H. Stimulus-dependent suppression of chaos in recurrent neural networks. Phys. Rev. E 82, 011903 (2010).
Schaffer, E. S., Rajan, K., Churchland, M. M., Shenoy, K. V. & Abbott, L. F. Generating complex repeatable patterns of activity by gain modulating network neurons. In Soc. Neurosci. Annual Meeting 448.3 (2006).
Laje, R. & Buonomano, D. V. Robust timing and motor patterns by taming chaos in recurrent neural networks. Nat. Neurosci. 16, 925–933 (2013).
Sussillo, D. & Abbott, L. F. Generating coherent patterns of activity from chaotic neural networks. Neuron 63, 544–557 (2009).
Sussillo, D. & Barak, O. Opening the black box: low-dimensional dynamics in high-dimensional recurrent neural networks. Neural Comput. 25, 626–649 (2013).
Rokni, U. & Sompolinsky, H. How the brain generates movement. In Cosyne 222 (2005).
Martens, J. & Sutskever, I. Learning recurrent neural networks with hessian-free optimization. In Proc. 28th Int. Conf. Machine Learning 1033–1040 (2009).
Shenoy, K. V., Kaufman, M. T., Sahani, M. & Churchland, M. M. in Progress in Brain Research: Enhancing Performance for Action and Perception (eds Green, A., Chapman, E., Kalaska, J. F. & Lepore, F.) 33–58 (Elsevier, 2011).
Shenoy, K. V., Sahani, M. & Churchland, M. M. Cortical control of arm movements: a dynamical systems perspective. Annu. Rev. Neurosci. 36, 337–359 (2013).
Truccolo, W., Hochberg, L. R. & Donoghue, J. P. Collective dynamics in human and monkey sensorimotor cortex: predicting single neuron spikes. Nat. Neurosci. 13, 105–111 (2010).
Stevenson, I. H. et al. Functional connectivity and tuning curves in populations of simultaneously recorded neurons. PLoS Comput. Biol. 8, e1002775 (2012).
Mastrogiuseppe, F. & Ostojic, S. Linking connectivity, dynamics, and computations in low-rank recurrent neural networks. Neuron 99, 609–623.e29 (2018).
Murphy, B. K. & Miller, K. D. Balanced amplification: a new mechanism of selective amplification of neural activity patterns. Neuron 61, 635–648 (2009).
Pandarinath, C. et al. Inferring single-trial neural population dynamics using sequential auto-encoders. Nat. Methods 15, 805–815 (2018).
Yu, B. M. et al. Gaussian-process factor analysis for low-dimensional single-trial analysis of neural population activity. J. Neurophysiol. 102, 614–635 (2009).
Seely, J. S. et al. Tensor analysis reveals distinct population structure that parallels the different computational roles of areas M1 and V1. PLoS Comput. Biol. 12, e1005164 (2016).
DePasquale, B., Sussillo, D., Abbott, L. F. & Churchland, M. M. The centrality of population-level factors to network computation is demonstrated by a versatile approach for training spiking networks. Neuron 111, 631–649.e10 (2023).
Cunningham, J. P. & Yu, B. M. Dimensionality reduction for large-scale neural recordings. Nat. Neurosci. 17, 1500–1509 (2014).
Williamson, R. C., Doiron, B., Smith, M. A. & Yu, B. M. Bridging large-scale neuronal recordings and large-scale network models using dimensionality reduction. Curr. Opin. Neurobiol. 55, 40–47 (2019).
Churchland, M. M., Yu, B. M., Sahani, M. & Shenoy, K. V. Techniques for extracting single-trial activity patterns from large-scale neural recordings. Curr. Opin. Neurobiol. 17, 609–618 (2007).
Zimnik, A. J. & Churchland, M. M. Independent generation of sequence elements by motor cortex. Nat. Neurosci. 24, 412–424 (2021).
O’Shea, D. J. et al. Direct neural perturbations reveal a dynamical mechanism for robust computation. Preprint at bioRrxiv https://doi.org/10.1101/2022.12.16.520768 (2022).
Kalaska, J. F. Emerging ideas and tools to study the emergent properties of the cortical neural circuits for voluntary motor control in non-human primates. F1000Research 8, https://doi.org/10.12688/f1000research.17161.1 (2019).
Brown, T. G. On the nature of the fundamental activity of the nervous centres; together with an analysis of the conditioning of rhythmic activity in progression, and a theory of the evolution of function in the nervous system. J. Physiol. 48, 18–46 (1914).
Yuste, R., MacLean, J. N., Smith, J. & Lansner, A. The cortex as a central pattern generator. Nat. Rev. Neurosci. 6, 477–483 (2005).
Goldreich, D., Krauzlis, R. J. & Lisberger, S. G. Effect of changing feedback delay on spontaneous oscillations in smooth pursuit eye movements of monkeys. J. Neurophysiol. 67, 625–638 (1992).
Lisberger, S. G. & Sejnowski, T. J. Motor learning in a recurrent network model based on the vestibulo-ocular reflex. Nature 360, 159–161 (1992).
Churchland, M. M. & Lisberger, S. G. Experimental and computational analysis of monkey smooth pursuit eye movements. J. Neurophysiol. 86, 741–759 (2001).
Kelso, J. A. Multistability and metastability: understanding dynamic coordination in the brain. Philos. Trans. R. Soc. Lond. B Biol. Sci. 367, 906–918 (2012).
van Gelder, T. The dynamical hypothesis in cognitive science. Behav. Brain Sci. 21, 615–665 (1998).
Ajemian, R. et al. Assessing the function of motor cortex: single-neuron models of how neural response is modulated by limb biomechanics. Neuron 58, 414–428 (2008).
Scott, S. H. Optimal feedback control and the neural basis of volitional motor control. Nat. Rev. Neurosci. 5, 532–546 (2004).
Todorov, E. Cosine tuning minimizes motor errors. Neural Comput. 14, 1233–1260 (2002).
Cisek, P. Preparing for speed. Focus on: “Preparatory activity in premotor and motor cortex reflects the speed of the upcoming reach”. J. Neurophysiol. 96, 2842–2843 (2006).
Bizzi, E. & Ajemian, R. From motor planning to execution: a sensorimotor loop perspective. J. Neurophysiol. 124, 1815–1823 (2020).
Middleton, F. A. & Strick, P. L. Basal ganglia and cerebellar loops: motor and cognitive circuits. Brain Res. Brain Res. Rev. 31, 236–250 (2000).
Sauerbrei, B. A. et al. Cortical pattern generation during dexterous movement is input-driven. Nature 577, 386–391 (2019).
Pruszynski, J. A. et al. Primary motor cortex underlies multi-joint integration for fast feedback control. Nature 478, 387–390 (2011).
Requin, J., Riehle, A. & Seal, J. Neuronal activity and information processing in motor control: from stages to continuous flow. Biol. Psychol. 26, 179–198 (1988).
Crammond, D. J. & Kalaska, J. F. Modulation of preparatory neuronal activity in dorsal premotor cortex due to stimulus-response compatibility. J. Neurophysiol. 71, 1281–1284 (1994).
Pruszynski, J. A. & Scott, S. H. Optimal feedback control and the long-latency stretch response. Exp. Brain Res. 218, 341–359 (2012).
Prut, Y. & Fetz, E. E. Primate spinal interneurons show pre-movement instructed delay activity. Nature 401, 590–594 (1999).
Kaufman, M. T. et al. Roles of monkey premotor neuron classes in movement preparation and execution. J. Neurophysiol. 104, 799–810 (2010).
Girard, B. & Berthoz, A. From brainstem to cortex: computational models of saccade generation circuitry. Prog. Neurobiol. 77, 215–251 (2005).
Vogels, T. P., Rajan, K. & Abbott, L. F. Neural network dynamics. Annu. Rev. Neurosci. 28, 357–376 (2005).
Heming, E. A., Cross, K. P., Takei, T., Cook, D. J. & Scott, S. H. Independent representations of ipsilateral and contralateral limbs in primary motor cortex. eLife 8, e48190 (2019).
Churchland, M. M. & Cunningham, J. P. A dynamical basis set for generating reaches. Cold Spring Harb. Symp. Quant. Biol. 79, 67–80 (2014).
Hennequin, G., Vogels, T. P. & Gerstner, W. Optimal control of transient dynamics in balanced networks supports generation of complex movements. Neuron 82, 1394–1406 (2014).
Kao, T. C., Sadabadi, M. S. & Hennequin, G. Optimal anticipatory control as a theory of motor preparation: a thalamo-cortical circuit model. Neuron 109, 1567–1581.e12 (2021).
Michaels, J. A., Dann, B. & Scherberger, H. Neural population dynamics during reaching are better explained by a dynamical system than representational tuning. PLoS Comput. Biol. 12, e1005175 (2016).
Morrow, M. M. & Miller, L. E. Prediction of muscle activity by populations of sequentially recorded primary motor cortex neurons. J. Neurophysiol. 89, 2279–2288 (2003).
Ames, K. C. & Churchland, M. M. Motor cortex signals for each arm are mixed across hemispheres and neurons yet partitioned within the population response. eLife 8, e46159 (2019).
Naufel, S., Glaser, J. I., Kording, K. P., Perreault, E. J. & Miller, L. E. A muscle-activity-dependent gain between motor cortex and EMG. J. Neurophysiol. 121, 61–73 (2019).
Elsayed, G. F. & Cunningham, J. P. Structure in neural population recordings: an expected byproduct of simpler phenomena? Nat. Neurosci. 20, 1310–1318 (2017).
Lara, A. H., Cunningham, J. P. & Churchland, M. M. Different population dynamics in the supplementary motor area and motor cortex during reaching. Nat. Commun. 9, 2754 (2018).
Evarts, E. V. Relation of pyramidal tract activity to force exerted during voluntary movement. J. Neurophysiol. 31, 14–27 (1968).
Ashe, J. & Georgopoulos, A. P. Movement parameters and neural activity in motor cortex and area 5. Cereb. Cortex 4, 590–600 (1994).
Sanger, T. D. Theoretical considerations for the analysis of population coding in motor cortex. Neural Comput. 6, 29–37 (1994).
Hatsopoulos, N. G., Xu, Q. & Amit, Y. Encoding of movement fragments in the motor cortex. J. Neurosci. 27, 5105–5114 (2007).
Rickert, J., Riehle, A., Aertsen, A., Rotter, S. & Nawrot, M. P. Dynamic encoding of movement direction in motor cortical neurons. J. Neurosci. 29, 13870–13882 (2009).
Kalidindi, H. T. et al. Rotational dynamics in motor cortex are consistent with a feedback controller. eLife 10, e67256 (2021).
Pandarinath, C. et al. Latent factors and dynamics in motor cortex and their application to brain–machine interfaces. J. Neurosci. 38, 9390–9401 (2018).
Saxena, S., Russo, A. A., Cunningham, J. & Churchland, M. M. Motor cortex activity across movement speeds is predicted by network-level strategies for generating muscle activity. eLife 11, e67620 (2022).
Foster, J. D. et al. A freely-moving monkey treadmill model. J. Neural Eng. 11, 046020 (2014).
Rush, E. R., Jayaram, K. & Humbert, J. S. From data-fitting to discovery: interpreting the neural dynamics of motor control through reinforcement learning. Preprint at arxiv https://doi.org/10.48550/arXiv.2305.11107 (2023).
Linden, H., Petersen, P. C., Vestergaard, M. & Berg, R. W. Movement is governed by rotational neural dynamics in spinal motor networks. Nature 610, 526–531 (2022).
Suresh, A. K. et al. Neural population dynamics in motor cortex are different for reach and grasp. eLife 9, e58848 (2020).
Yanai, Y., Adamit, N., Israel, Z., Harel, R. & Prut, Y. Coordinate transformation is first completed downstream of primary motor cortex. J. Neurosci. 28, 1728–1732 (2008).
Dacre, J. et al. A cerebellar–thalamocortical pathway drives behavioral context-dependent movement initiation. Neuron 109, 2326–2338.e8 (2021).
Gao, Z. et al. A cortico-cerebellar loop for motor planning. Nature 563, 113–116 (2018).
Machens, C. K., Romo, R. & Brody, C. D. Functional, but not anatomical, separation of “What” and “When” in prefrontal cortex. J. Neurosci. 30, 350–360 (2010).
Raposo, D., Kaufman, M. T. & Churchland, A. K. A category-free neural population supports evolving demands during decision-making. Nat. Neurosci. 17, 1784–1792 (2014).
Jun, J. K. et al. Heterogenous population coding of a short-term memory and decision task. J. Neurosci. 30, 916–929 (2010).
Elsayed, 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. 7, 13239 (2016).
Lara, A. H., Elsayed, G. F., Zimnik, A. J., Cunningham, J. P. & Churchland, M. M. Conservation of preparatory neural events in monkey motor cortex regardless of how movement is initiated. eLife 7, e31826 (2018).
Ames, K. C., Ryu, S. I. & Shenoy, K. V. Neural dynamics of reaching following incorrect or absent motor preparation. Neuron 81, 438–451 (2014).
Rosenbaum, D. A. Human movement initiation: specification of arm, direction, and extent. J. Exp. Psychol. Gen. 109, 444–474 (1980).
Riehle, 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. 61, 534–549 (1989).
Ghez, C. et al. Discrete and continuous planning of hand movements and isometric force trajectories. Exp. Brain Res. 115, 217–233 (1997).
Franks, I. M., Nagelkerke, P., Ketelaars, M. & Van Donkelaar, P. Response preparation and control of movement sequences. Can. J. Exp. Psychol. 52, 93–102 (1998).
Ames, K. C., Ryu, S. I. & Shenoy, K. V. Simultaneous motor preparation and execution in a last-moment reach correction task. Nat. Commun. 10, 2718 (2019).
Stavisky, S. D., Kao, J. C., Ryu, S. I. & Shenoy, K. V. Motor cortical visuomotor feedback activity is initially isolated from downstream targets in output-null neural state space dimensions. Neuron 95, 195–208.e9 (2017).
Rizzolatti, G. et al. Functional organization of inferior area 6 in the macaque monkey. II. Area F5 and the control of distal movements. Exp. Brain Res. 71, 491–507 (1988).
Haith, A. M., Pakpoor, J. & Krakauer, J. W. Independence of movement preparation and movement initiation. J. Neurosci. 36, 3007–3015 (2016).
Haith, A. M., Huberdeau, D. M. & Krakauer, J. W. The influence of movement preparation time on the expression of visuomotor learning and savings. J. Neurosci. 35, 5109–5117 (2015).
Kaufman, M. T., Churchland, M. M., Ryu, S. I. & Shenoy, K. V. Vacillation, indecision and hesitation in moment-by-moment decoding of monkey motor cortex. eLife 4, e04677 (2015).
Mirabella, G., Pani, P. & Ferraina, S. Neural correlates of cognitive control of reaching movements in the dorsal premotor cortex of rhesus monkeys. J. Neurophysiol. 106, 1454–1466 (2011).
Kaufman, M. T. et al. The largest response component in the motor cortex reflects movement timing but not movement type. eNeuro 3, https://doi.org/10.1523/ENEURO.0085-16.2016 (2016).
Inagaki, H. K. et al. A midbrain–thalamus–cortex circuit reorganizes cortical dynamics to initiate movement. Cell 185, 1065–1081.e23 (2022).
Chabrol, F. P., Blot, A. & Mrsic-Flogel, T. D. Cerebellar contribution to preparatory activity in motor neocortex. Neuron 103, 506–519.e4 (2019).
Bastian, A., Riehle, A., Erlhagen, W. & Schoner, G. Prior information preshapes the population representation of movement direction in motor cortex. Neuroreport 9, 315–319 (1998).
Miri, A. et al. Behaviorally selective engagement of short-latency effector pathways by motor cortex. Neuron 95, 683–696.e11 (2017).
Warriner, C. L., Fageiry, S., Saxena, S., Costa, R. M. & Miri, A. Motor cortical influence relies on task-specific activity covariation. Cell Rep. 40, 111427 (2022).
Briggman, K. L. & Kristan, W. B. Multifunctional pattern-generating circuits. Annu. Rev. Neurosci. 31, 271–294 (2008).
Kurtzer, I., Herter, T. M. & Scott, S. H. Random change in cortical load representation suggests distinct control of posture and movement. Nat. Neurosci. 8, 498–504 (2005).
Donchin, O. et al. Single-unit activity related to bimanual arm movements in the primary and supplementary motor cortices. J. Neurophysiol. 88, 3498–3517 (2002).
Cisek, P., Crammond, D. J. & Kalaska, J. F. Neural activity in primary motor and dorsal premotor cortex in reaching tasks with the contralateral versus ipsilateral arm. J. Neurophysiol. 89, 922–942 (2003).
Cross, K. P., Heming, E. A., Cook, D. J. & Scott, S. H. Maintained representations of the ipsilateral and contralateral limbs during bimanual control in primary motor cortex. J. Neurosci. 40, 6732–6747 (2020).
Yang, G. R., Joglekar, M. R., Song, H. F., Newsome, W. T. & Wang, X. J. Task representations in neural networks trained to perform many cognitive tasks. Nat. Neurosci. 22, 297–306 (2019).
Driscoll, L., Shenoy, K. & Sussillo, D. Flexible multitask computation in recurrent networks utilizes shared dynamical motifs. Preprint at bioRxiv https://doi.org/10.1101/2022.08.15.503870 (2022).
Logiaco, L., Abbott, L. F. & Escola, S. Thalamic control of cortical dynamics in a model of flexible motor sequencing. Cell Rep. 35, 109090 (2021).
Sabatini, D. A. & Kaufman, M. T. Reach-dependent reorientation of rotational dynamics in motor cortex. Preprint at bioRxiv https://doi.org/10.1101/2021.09.09.459647 (2023).
Sadtler, P. T. et al. Neural constraints on learning. Nature 512, 423–426 (2014).
Gallego, J. A., Perich, M. G., Miller, L. E. & Solla, S. A. Neural manifolds for the control of movement. Neuron 94, 978–984 (2017).
Gallego, J. A., Perich, M. G., Chowdhury, R. H., Solla, S. A. & Miller, L. E. Long-term stability of cortical population dynamics underlying consistent behavior. Nat. Neurosci. 23, 260–270 (2020).
Gallego, J. A. et al. Cortical population activity within a preserved neural manifold underlies multiple motor behaviors. Nat. Commun. 9, 4233 (2018).
Gao, P. & Ganguli, S. On simplicity and complexity in the brave new world of large-scale neuroscience. Curr. Opin. Neurobiol. 32, 148–155 (2015).
Gao, P. et al. A theory of multineuronal dimensionality, dynamics and measurement. Preprint at bioRxiv https://doi.org/10.1101/214262 (2017).
Perkins, S. M., Cunningham, J. P., Wang, Q. & Churchland, M. M. Simple decoding of behavior from a complicated neural manifold. Preprint at bioRxiv https://doi.org/10.1101/2023.04.05.535396 (2023).
Schneider, S., Lee, J. H. & Mathis, M. W. Learnable latent embeddings for joint behavioural and neural analysis. Nature 617, 360–368 (2023).
Chaudhuri, R., Gercek, B., Pandey, B., Peyrache, A. & Fiete, I. The intrinsic attractor manifold and population dynamics of a canonical cognitive circuit across waking and sleep. Nat. Neurosci. 22, 1512–1520 (2019).
Gardner, R. J. et al. Toroidal topology of population activity in grid cells. Nature 602, 123–128 (2022).
Hatsopoulos, N. G. Encoding in the motor cortex: was evarts right after all? Focus on “motor cortex neural correlates of output kinematics and kinetics during isometric-force and arm-reaching tasks”. J. Neurophysiol. 94, 2261–2262 (2005).
Scott, S. H. Population vectors and motor cortex: neural coding or epiphenomenon? Nat. Neurosci. 3, 307–308 (2000).
Herter, T. M., Korbel, T. & Scott, S. H. Comparison of neural responses in primary motor cortex to transient and continuous loads during posture. J. Neurophysiol. 101, 150–163 (2009).
Griffin, D. M., Hoffman, D. S. & Strick, P. L. Corticomotoneuronal cells are “functionally tuned”. Science 350, 667–670 (2015).
Griffin, D. M. & Strick, P. L. The motor cortex uses active suppression to sculpt movement. Sci. Adv. 6, eabb8395 (2020).
Shalit, U., Zinger, N., Joshua, M. & Prut, Y. Descending systems translate transient cortical commands into a sustained muscle activation signal. Cereb. Cortex 22, 1904–1914 (2012).
Albert, S. T. et al. Postural control of arm and fingers through integration of movement commands. eLife 9, e52507 (2020).
Fink, A. J. et al. Presynaptic inhibition of spinal sensory feedback ensures smooth movement. Nature 509, 43–48 (2014).
Soechting, J. F. & Flanders, M. Moving in three-dimensional space: frames of reference, vectors, and coordinate systems. Annu. Rev. Neurosci. 15, 167–191 (1992).
Burnod, Y. et al. Visuomotor transformations underlying arm movements toward visual targets: a neural network model of cerebral cortical operations. J. Neurosci. 12, 1435–1453 (1992).
Wang, T., Chen, Y. & Cui, H. From parametric representation to dynamical system: shifting views of the motor cortex in motor control. Neurosci. Bull. 38, 796–808 (2022).
Fu, Q. G., Flament, D., Coltz, J. D. & Ebner, T. J. Temporal encoding of movement kinematics in the discharge of primate primary motor and premotor neurons. J. Neurophysiol. 73, 836–854 (1995).
Schwartz, A. B. Direct cortical representation of drawing. Science 265, 540–542 (1994).
Moran, D. W. & Schwartz, A. B. Motor cortical representation of speed and direction during reaching. J. Neurophysiol. 82, 2676–2692 (1999).
Schroeder, K. E., Perkins, S. M., Wang, Q. & Churchland, M. M. Cortical control of virtual self-motion using task-specific subspaces. J. Neurosci. 42, 220–239 (2022).
Yang, L., Michaels, J. A., Pruszynski, J. A. & Scott, S. H. Rapid motor responses quickly integrate visuospatial task constraints. Exp. Brain Res. 211, 231–242 (2011).
Russo, A. A. et al. Neural trajectories in the supplementary motor area and motor cortex exhibit distinct geometries, compatible with different classes of computation. Neuron 107, 745–758.e6 (2020).
Hennig, J. A. et al. Learning is shaped by abrupt changes in neural engagement. Nat. Neurosci. 24, 727–736 (2021).
Smoulder, A. L. et al. A neural basis of choking under pressure. Preprint at bioRxiv https://doi.org/10.1101/2023.04.16.537007 (2023).
Perich, M. G., Gallego, J. A. & Miller, L. E. A neural population mechanism for rapid learning. Neuron 100, 964–976.e7 (2018).
Vyas, S. et al. Neural population dynamics underlying motor learning transfer. Neuron 97, 1177–1186.e3 (2018).
Sun, X. et al. Cortical preparatory activity indexes learned motor memories. Nature 602, 274–279 (2022).
Vyas, S., O’Shea, D. J., Ryu, S. I. & Shenoy, K. V. Causal role of motor preparation during error-driven learning. Neuron 106, 329–339.e4 (2020).
Sheahan, H. R., Franklin, D. W. & Wolpert, D. M. Motor planning, not execution, separates motor memories. Neuron 92, 773–779 (2016).
Versteeg, C. & Miller, L. E. Dynamical feedback control: motor cortex as an optimal feedback controller based on neural dynamics. Preprint at https://doi.org/10.20944/preprints202201.0428.v1 (2022).
Serruya, M. D., Hatsopoulos, N. G., Paninski, L., Fellows, M. R. & Donoghue, J. P. Instant neural control of a movement signal. Nature 416, 141–142 (2002).
Taylor, D. M., Tillery, S. I. & Schwartz, A. B. Direct cortical control of 3D neuroprosthetic devices. Science 296, 1829–1832 (2002).
Carmena, J. M. et al. Learning to control a brain–machine interface for reaching and grasping by primates. PLoS Biol. 1, E42 (2003).
Georgopoulos, A. P. & Carpenter, A. F. Coding of movements in the motor cortex. Curr. Opin. Neurobiol. 33C, 34–39 (2015).
Musallam, S., Corneil, B. D., Greger, B., Scherberger, H. & Andersen, R. A. Cognitive control signals for neural prosthetics. Science 305, 258–262 (2004).
Santhanam, G., Ryu, S. I., Yu, B. M., Afshar, A. & Shenoy, K. V. A high-performance brain–computer interface. Nature 442, 195–198 (2006).
Yu, B., Ryu, S., Santhanam, G., Churchland, M. & Shenoy, K. Improving neural prosthetic system performance by combining plan and peri-movement activity. In IEEE EMBS 26th Annual Meeting 4516–4519 (2004).
Kao, J. C. et al. Single-trial dynamics of motor cortex and their applications to brain–machine interfaces. Nat. Commun. 6, 7759 (2015).
Jarosiewicz, B. et al. Functional network reorganization during learning in a brain–computer interface paradigm. Proc. Natl Acad. Sci. USA 105, 19486–19491 (2008).
Chase, S. M., Kass, R. E. & Schwartz, A. B. Behavioral and neural correlates of visuomotor adaptation observed through a brain–computer interface in primary motor cortex. J. Neurophysiol. 108, 624–644 (2012).
Golub, M. D. et al. Learning by neural reassociation. Nat. Neurosci. 21, 607–616 (2018).
Oby, E. R. et al. New neural activity patterns emerge with long-term learning. Proc. Natl Acad. Sci. USA 116, 15210–15215 (2019).
Peters, A. J., Chen, S. X. & Komiyama, T. Emergence of reproducible spatiotemporal activity during motor learning. Nature 510, 263–267 (2014).
Losey, D. M. et al. Learning alters neural activity to simultaneously support memory and action. Preprint at bioRxiv https://doi.org/10.1101/2022.07.05.498856 (2022).
Ethier, C., Oby, E. R., Bauman, M. J. & Miller, L. E. Restoration of grasp following paralysis through brain-controlled stimulation of muscles. Nature 485, 368–371 (2012).
Willett, F. R., Avansino, D. T., Hochberg, L. R., Henderson, J. M. & Shenoy, K. V. High-performance brain-to-text communication via handwriting. Nature 593, 249–254 (2021).
Wong, A. L., Goldsmith, J., Forrence, A. D., Haith, A. M. & Krakauer, J. W. Reaction times can reflect habits rather than computations. eLife 6, e28075 (2017).
Wong, A. L., Haith, A. M. & Krakauer, J. W. Motor planning. Neuroscientist. https://doi.org/10.1177/1073858414541484 (2014).
Cisek, P. & Kalaska, J. F. Neural mechanisms for interacting with a world full of action choices. Annu. Rev. Neurosci. 33, 269–298 (2010).
Stringer, C. et al. Spontaneous behaviors drive multidimensional, brainwide activity. Science 364, 255 (2019).
Yoo, S. B. M. & Hayden, B. Y. The transition from evaluation to selection involves neural subspace reorganization in core reward regions. Neuron 105, 712–724.e4 (2020).
Herzfeld, D. J., Kojima, Y., Soetedjo, R. & Shadmehr, R. Encoding of action by the Purkinje cells of the cerebellum. Nature 526, 439–442 (2015).
Acknowledgements
The authors thank members of the Churchland laboratory for reviewing and editing this manuscript. M.M.C. thanks Y. Pavlova for laboratory management. K.V.S. thanks B. Davis for administrative support and S. Kosasih for laboratory management. M.M.C is supported by the Grossman Center for the Statistics of Mind, the Simons Foundation Collaboration on the Global Brain, the Kavli Institute for Brain Science and the Zuckerman Mind Brain Behaviour Institute. K.V.S. was supported by National Institute of Neurological Disorders and Stroke (NINDS) U01NS123101, U19NS112954 and R01NS116623; National Institute on Deafness and Other Communication Disorders (NIDCD) R01NS121097, R01DC014034, U01DC019430 and U01DC017844; National Institutes of Health (NIH) National Institute of Mental Health (NIMH) R01MH086373; the Simons Foundation Collaboration on the Global Brain; L. and P. Garlick; S. and B. Reeves; the Wu Tsai Neurosciences Institute; the Bio-X Institute at Stanford University; The Hong Seh and Vivian W. M. Lim Professorship at Stanford University; and the Howard Hughes Medical Institute (HHMI) at Stanford University.
Author information
Authors and Affiliations
Contributions
The authors contributed equally to all aspects of the article.
Corresponding author
Ethics declarations
Competing interests
M.M.C is an inventor of the MINT decoding approach, which has been licensed to Blackrock Neurotech. K.V.S. served on the Scientific Advisory Boards (SABs) of MIND-X Inc. (acquired by Blackrock Neurotech), Inscopix Inc. (merged with Brucker Nano) and Heal Inc.; served as a consultant/adviser for CTRL-Labs (on the founding SAB; acquired by Facebook Reality Labs in Fall 2019, which is now Meta Platform Reality Labs); and served as a consultant/adviser for and was a co-founder (2016–2023) of Neuralink.
Peer review
Peer review information
Nature Reviews Neuroscience thanks Rune Berg, Matthew Perich and the other, anonymous, reviewer for their contribution to the peer review of this work.
Additional information
I dedicate this review to my friend and colleague Krishna Shenoy, who died as we were completing the writing. That act of writing brought our long intellectual relationship full circle. Our final days together were spent much like our initial days: sitting in a room talking about preparatory activity. Pondering the nature of preparatory activity had sent us down the long path of trying to understand the chain of neural events that produces voluntary movement. We saw preparation as the ‘first cog’ in that causal chain. Preparatory activity must somehow have, wrapped up in it, the information necessary to generate time-varying patterns of muscle activity that will soon occur. Trying to figure out how that could work was the first cog in our personal journey — one whose various branches trace back to the initial question that consumed us: what does preparatory activity do? Our adoption and promotion of other ideas — dynamics, null spaces, factors — were a straightforward consequence of our desire to answer that question. We hope that this review brings readers on a similar journey.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Glossary
- Single-neuron response
-
The response of a real (or simulated) neuron is notated as \({r}_{n}(t)\), where t indicates time and n indicates we are considering the nth neuron.
- Population response
-
The responses of \(N\) neurons, constituting an \(N\)-dimensional vector \({\boldsymbol{r}}(t)\). Each vector element, \({r}_{n}(t)\), describes the activity of one neuron.
- Weight
-
A number indicating the degree to which one thing (for example, a neuron) influences something else (for example, another neuron). Weights come in many flavours and can summarize many things, including synaptic strengths and the impact of neural activity on muscle activity.
- Neural dimension
-
An N-dimensional vector containing one weight per neuron. Just like the weights themselves, neural dimensions come in multiple flavours.
- Weighted sum
-
Weighted sums of neural activity are central to many analyses that seek to understand network function (real or simulated). If the vector \({\boldsymbol{v}}\) is a neural dimension, one computes \(\mathop{\sum }\limits_{n=1}^{N}{{\boldsymbol{v}}}_{n}{{\boldsymbol{r}}}_{n}(t)\). Using vector notation, the weighted sum \(a(t)={{\boldsymbol{v}}}^{{\rm{T}}}{\boldsymbol{r}}(t)\) is referred to as ‘activity in dimension \({\boldsymbol{v}}\)’.
- Subspace
-
A set of one or more orthogonal neural dimensions. Dimensions are collected into columns of a matrix \({\boldsymbol{V}}\). The vector of weighted sums \({\boldsymbol{a}}(t)={{\boldsymbol{V}}}^{{\rm{T}}}{\boldsymbol{r}}(t)\) is referred to as ‘activity in the subspace of \({\boldsymbol{V}}\) ’.
- Activity subspace
-
A subspace that fully captures neural responses. Suppose we computed a(t) as above (see subspaces). If we can successfully invert this relationship using r(t) ≈ Va(t), then the dimensions in V span the activity subspace.
- Dimensionality reduction
-
A method, such as principal component analysis (PCA), for estimating dimensions that constitute the activity subspace.
- Readout
-
A signal that exits the neural population, such as a descending command for muscle activity (see Fig. 1c). Assuming linearity, the readout is a weighted sum of population responses: \(z(t)={{\boldsymbol{b}}}^{{\rm{T}}}{\boldsymbol{r}}(t)\) (see readout dimensions for how \({\boldsymbol{b}}\) is defined).
- Readout dimensions
-
Each readout has an associated neural dimension, \({\boldsymbol{b}}\), containing weights (one per neuron) used for the readout. Analysis and visualization often employ a lower-dimensional \({{\boldsymbol{b}}}^{{\rm{F}}{\rm{a}}{\rm{c}}}\), with one weight per factor.
- Output-potent space
-
The subspace, spanned by the readout dimensions, where neural activity impacts those readouts. Dimension \({\boldsymbol{v}}\) is ‘output-potent’ if it overlaps with a readout dimension: \({{\boldsymbol{b}}}^{{\rm{T}}}{\boldsymbol{v}}\ne 0\).
- Null-space
-
The subspace, orthogonal to the readout dimensions, where neural activity has no impact on those readouts. Dimension \({\boldsymbol{v}}\) is ‘output-null’ if it is orthogonal to each readout dimension: \({{\boldsymbol{b}}}^{{\rm{T}}}{\boldsymbol{v}}=0\).
- Factors
-
For many recurrent networks, computation can be summarized by considering K factors rather than N neurons (see Fig. 1c), with K \(\ll \) N. Each factor is a weighted sum of activity: xi(t) = \({{\boldsymbol{w}}}_{i}^{{\rm{T}}}\)r(t), where \({{\boldsymbol{w}}}_{i}\) is a neural dimension. Considering all factors: x(t) = WTr(t). \({\boldsymbol{W}}\) reflects network connectivity (see recurrent connectivity).
- Neural state
-
The value of the factors, \({\boldsymbol{x}}(t)\), at a particular moment t. ‘Neural state’ may also refer to the population response, \({\boldsymbol{r}}(t)\). Assuming factors are a valid summary of the population response, these definitions are equivalent.
- State space
-
A method for visualizing the neural state as a point in a space where each axis corresponds to a factor (or some other weighted sum of neural activity).
- Neural trajectory
-
The value of the factors, \({\boldsymbol{x}}(t)\), across a span of time. When plotted in state space, trajectories form traces that describe how activity changes with time (see Fig. 1c, inset).
- Manifold
-
The shape formed by the collection of neural trajectories, defining the possible locations of the neural state within the activity subspace. For example, when cycling at different speeds, the manifold has a tube-like shape (see Fig. 2d).
- Tuning
-
A description of how a neuron’s response reflects a specific quantity, such as a stimulus. In recurrent networks, factors can be the relevant quantities.
- Factor tuning
-
The weight un,i quantifies how the ith factor impacts the nth neuron. The neural dimension \({{\boldsymbol{u}}}_{i}\) quantifies the impact on all neurons. Given a matrix \({\boldsymbol{U}}\) of factor-tuning dimensions, population activity is \({\boldsymbol{r}}(t)\approx {\boldsymbol{U}}{\boldsymbol{x}}(t)\). The approximation reflects non-linearity and spiking variability. \({\boldsymbol{U}}\) reflects network connectivity (see recurrent connectivity), and defines the activity subspace.
- Output-potent factors
-
Factor \({x}_{i}(t)\) is output-potent (that is, impacts the readout) if its factor-tuning dimension, \({{\boldsymbol{u}}}_{i}\), is output-potent (overlaps with one or more readout dimensions).
- Output-null factors
-
Factor \({x}_{i}(t)\) is output-null (that is, does not impact the readout) if its factor-tuning dimension, \({{\boldsymbol{u}}}_{i}\), is output-null (lies within the null-space).
- Recurrent connectivity
-
Synaptic connections that cause activity to flow in ‘loops’. The causal flow is simplified by considering factors (Fig. 1c) and matrices \({\boldsymbol{W}}\) and \({\boldsymbol{U}}\) (see factors and factor tuning). Factors are weighted sums of neural responses: \({\boldsymbol{x}}(t)={{\boldsymbol{W}}}^{{\rm{T}}}{\boldsymbol{r}}(t)\). Responses reflect the factors, \({\boldsymbol{r}}(t)\approx {\boldsymbol{U}}{\boldsymbol{x}}(t)\), completing the loop. In some networks, \({\boldsymbol{W}}\) and \({\boldsymbol{U}}\) can be computed directly from synaptic connectivity.
- Factor-level dynamics
-
In recurrent networks, activity at the present moment drives activity at the next moment. Such dynamics are often best described at the factor level: \(\dot{{\boldsymbol{x}}}\) = f(x) + y. The function f defines a flow-field in state space (see Fig. 1c, inset). y captures inputs from outside the observed system.
- Rotational dynamics
-
Dynamics linking two factors, \({x}_{1}\) and \({x}_{2}\), such that neural states flow from one to the other while preserving their order (see Fig. 2a). Suppose that, for three conditions during preparation, factor \({x}_{{\rm{prep}}}\) takes values \(\{-1,1,2\}\) while factor \({x}_{{\rm{exec}}}\) takes values \(\{0,0,0\}\). After a 90° rotation, activity has left the preparatory subspace, \({x}_{{\rm{prep}}}=\{0,0,0\}\), and entered the execution subspace, \({x}_{{\rm{exec}}}=\{-1,1,2\}\). Depending on the network, rotations might continue or might end after ~90°.
- Factor estimation
-
To estimate factors from measurements of neural activity alone, without knowledge of connectivity, experimenters use dimensionality reduction to estimate the activity subspace and invert the relationship r(t) ≈ Ux(t). For example, one may use x(t) ≈ UTr(t), assuming the estimated U is orthonormal.
- Motor neurons
-
Neurons in the spinal cord that connect directly to a muscle. Each motor neuron spike produces one spike in the muscle fibres it innervates. Motor neurons receive direct (monosynaptic) and indirect (polysynaptic) inputs from motor-cortex neurons.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Churchland, M.M., Shenoy, K.V. Preparatory activity and the expansive null-space. Nat. Rev. Neurosci. 25, 213–236 (2024). https://doi.org/10.1038/s41583-024-00796-z
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41583-024-00796-z