The Encoding of Input Currents by Motoneurones in Relation to Neuronal Modelling

Introduction Several coding stages occur in the nervous system when an internal decision is reached to enact a certain movement. The desired movement is coded into spike trains of a large number of neurons in prefrontal, premotor and suplementary motor cortices as well as in other areas such as the basal ganglia and cerebellum. These spike trains can be assembled in a column vector x(t), each element representing one neuron’s spike train. Another coding stage translates all those spike trains into the spike trains of neurons in the primary motor cortex, which we assemble in vector y(t). This vector is next encoded (through direct and indirect pathways) as vector z(t) containing the spike trains of motoneurons from several (K) motoneuron pools in the spinal cord that will activate axial and limb muscles involved in the desired movement. This vector z(t) can be partitioned as z(t)=[z1(t) z2(t) ... zK-1(t) zK(t)] , where each zi(t) is associated with a given motoneuron pool. Observing only zi(t) will only give us a partial view of the coding from y(t) on z(t). Needless to say, if we only examine the spike train of one motoneuron from a given motoneuron pool even less understanding can be obtained about the general coding strategy associated with the desired movement. Nevertheless, there is an interest in studying the spike trains from single motoneurons and from the ensemble of motoneurons from a given motoneuron pool because they perform the final encoding prior to the final stage which is the decoding of the spike trains into muscle contraction. Experiments have indicated that there is a degree of matching between motoneuron and muscle fibre characteristics [e.g., Kernell, 1990]. These are interesting to analyse both in terms of theoretical studies of information transmission or dynamical systems in neuromuscular structures as well as in terms of neuronal modelling. The degree of matching of motoneuronal spike trains and muscle response found in nature has to be mimicked by any “good” models of motoneurons and muscle. In this work we briefly review a few findings from the literature that point to an “optimal” matching between spike trains/motoneuronal dynamics and muscle contraction. From these data we extract relations between motoneurone spike trains and resulting muscle fibre contraction in different types of movement. These should serve as standards in the validation of motoneuron and muscle models. Spike trains from an improved motoneuron model developed by the authors are analysed in terms of the matching with muscle mechanical behaviour.