Scientific Understanding of Consciousness
Consciousness as an Emergent Property of Thalamocortical Activity

Neural Population Dynamics



Nature 487, 51–56  (05 July 2012)

Neural population dynamics during reaching

Department of Neuroscience, Kavli Institute for Brain Science, David Mahoney Center, Columbia University Medical Center, New York, New York 10032, USA

Mark M. Churchland

Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA

Mark M. Churchland, Matthew T. Kaufman, Justin D. Foster, Stephen I. Ryu & Krishna V. Shenoy

Neurosciences Program, Stanford University, Stanford, California 94305, USA

Mark M. Churchland, Matthew T. Kaufman & Krishna V. Shenoy

Department of Biomedical Engineering, Washington University in St Louis, St Louis, Missouri 63130, USA

John P. Cunningham

Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK

John P. Cunningham

Department of Bioengineering, Stanford University, Stanford, California 94705, USA

Paul Nuyujukian & Krishna V. Shenoy

Stanford University School of Medicine, Stanford, California 94305, USA

Paul Nuyujukian

Department of Neurosurgery, Palo Alto Medical Foundation, Palo Alto, California 94301, USA

Stephen I. Ryu

Department of Neurobiology, Stanford University School of Medicine, Stanford, California 94305, USA

Krishna V. Shenoy


Most theories of motor cortex have assumed that neural activity represents movement parameters. This view derives from what is known about primary visual cortex, where neural activity represents patterns of light. Yet it is unclear how well the analogy between motor and visual cortex holds. Single-neuron responses in motor cortex are complex, and there is marked disagreement regarding which movement parameters are represented. A better analogy might be with other motor systems, where a common principle is rhythmic neural activity. Here we find that motor cortex responses during reaching contain a brief but strong oscillatory component, something quite unexpected for a non-periodic behaviour. Oscillation amplitude and phase followed naturally from the preparatory state, suggesting a mechanistic role for preparatory neural activity. These results demonstrate an unexpected yet surprisingly simple structure in the population response. This underlying structure explains many of the confusing features of individual neural responses.

Motor and premotor cortex were among the first cortical areas to be extensively studied. Yet their basic response properties are poorly understood, and it remains controversial whether neural activity relates to muscles or to abstract movement features. At the heart of this debate is the complexity of individual neural responses, which exhibit a great variety of multiphasic patterns. One explanation is that responses represent many movement parameters.

Alternatively, motor cortex may constitute a dynamical system that generates and controls movement. In this conception, neural responses reflect underlying dynamics and display ‘tuning’ only incidentally. If so, then dynamical features should be present in the population response. In looking for dynamical structure, we focused on a common principle for movement generation across the animal kingdom: the production of rhythmic, oscillatory activity.

We first examined neural responses in a context where rhythmic pattern generation is known to occur. The medicinal leech generates rhythmic muscle contractions at ~1.5Hz during swimming and many single neurons display firing rate oscillations at that frequency. Rhythmic structure was also present for cortical responses in the walking monkey: ~1Hz oscillations matching the ~1Hz movement of the arm. If single-neuron oscillations are generated by population-level dynamics, then the population response (the neural state) should rotate with time. We projected the population response onto a two-dimensional state space and found rotations of the neural state for both the swimming leech and the walking monkey. These observations, although not trivial, are largely expected for a neural dynamical system that generates rhythmic output.

The central finding of this study is that quasi-oscillatory neural responses are present during reaches. This is illustrated by the average firing rate of an example motor cortex neuron and the corresponding population-level projection. The rotation of the neural state is short lived (~1 cycle) but otherwise resembles rotations seen during rhythmic movement.

Most neurons exhibited preparatory and movement-related responses. Responses were typically complex, multiphasic and heterogeneous. Yet there appear to be oscillations in many single-neuron responses, beginning just before movement onset and lasting for ~1–1.5 cycles.

If the initial population-level preparatory state is known, subsequent states are reasonably predictable. Such predictability is absent at the individual-neuron level: the correlation between preparatory and movement tuning averages nearly zero Nevertheless, the ordered state-space rotations relate directly to the seemingly disordered single-neuron responses. Each axis of the jPCA projection captures a time-varying pattern that resembles a single-neuron response. Single neurons strongly reflect combinations of these underlying patterns. However, that underlying structure is not readily apparent when plotting each pattern alone, or each neuron individually. Furthermore, the rotations during reaching are quasi-oscillatory, lasting only 1–1.5 cycles. Their brevity and high frequency (up to ~2.5Hz) makes them easy to miss unless trial counts are high (data sets averaged 810 trials per neuron) and data are precisely aligned on movement onset.

The central result of this study is the presence of the rotational patterns. Those projections captured an average of 28% of the total data variance, and thus reveal patterns that are strongly present in the data.

Rotations of the population state are a prominent feature of the cortical response during reaching. Rotations follow naturally from the preparatory state and are consistent in direction and angular velocity across the different reaches that each monkey performed. The rotational structure is much stronger and more consistent than expected from chance or previous models. These population-level rotations are a relatively simple dynamical feature yet explain seemingly complex features of individual-neuron responses, including frequent reversals of preferred direction and the lack of correlation between preparatory and movement-period tuning. State-space rotations produce briefly oscillatory temporal patterns that provide an effective basis for producing multiphasic muscle activity, suggesting that non-periodic movements may be generated via neural mechanisms resembling those that generate rhythmic movement.

Recent results suggest that preparatory activity sets the initial state of a dynamical system, whose subsequent evolution produces movement activity.

Many of the neural response features that seem most baffling from a representational perspective are natural and straightforward from a population-level dynamical systems perspective.

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