title: Linear summation of outputs in a balanced network model of motor cortex.
abstract: Given the non-linearities of the neural circuitry's elements, we would expect cortical circuits to respond non-linearly when activated. Surprisingly, when two points in the motor cortex are activated simultaneously, the EMG responses are the linear sum of the responses evoked by each of the points activated separately. Additionally, the corticospinal transfer function is close to linear, implying that the synaptic interactions in motor cortex must be effectively linear. To account for this, here we develop a model of motor cortex composed of multiple interconnected points, each comprised of reciprocally connected excitatory and inhibitory neurons. We show how non-linearities in neuronal transfer functions are eschewed by strong synaptic interactions within each point. Consequently, the simultaneous activation of multiple points results in a linear summation of their respective outputs. We also consider the effects of reduction of inhibition at a cortical point when one or more surrounding points are active. The network response in this condition is linear over an approximately two- to three-fold decrease of inhibitory feedback strength. This result supports the idea that focal disinhibition allows linear coupling of motor cortical points to generate movement related muscle activation patterns; albeit with a limitation on gain control. The model also explains why neural activity does not spread as far out as the axonal connectivity allows, whilst also explaining why distant cortical points can be, nonetheless, functionally coupled by focal disinhibition. Finally, we discuss the advantages that linear interactions at the cortical level afford to motor command synthesis.
authors.affiliation: Center for Neurophysics, Physiology and Pathology, Centre National de la Recherche Scientifique UMR 8119, Université Paris-Descartes Paris, France ; Department of Neurorehabilitation Engineering, University Medical Center Göttingen, Georg-August University Germany.
authors.forename: Charles
authors.initials: C
authors.lastname: Capaday
authors.affiliation: Center for Neurophysics, Physiology and Pathology, Centre National de la Recherche Scientifique UMR 8119, Université Paris-Descartes Paris, France.
authors.forename: Carl
authors.initials: C
authors.lastname: van Vreeswijk
keywords: balanced networks; linear summation; motor cortex; neural transfer functions; rate models; spiking models