A latent low-dimensional common input drives a pool of motor neurons: a probabilistic latent state-space model

Motor neurons appear to be activated with a common input signal that modulates the discharge activity of all neurons in the motor nucleus. It has proven difficult for neurophysiologists to quantify the variability in a common input signal, but characterization of this signal may improve our understanding of how the activation signal varies across motor tasks. Contemporary methods of quantifying the common input to motor neurons relies on compiling discrete action potentials into continuous signals, assuming the motor pool acts as a linear filter, and requiring signals to be of sufficient duration. We introduce a space-state model in which the discharge activity of motor neurons is modeled as inhomogeneous Poisson processes and propose a method to quantify a latent trajectory that represents the common input received by motor neurons. The approach also approximates the synaptic noise in the common input signal. The model is validated with four datasets: a simulation of 120 motor units, a pair of integrate-and-fire neurons with a Renshaw cell providing inhibitory feedback, the discharge activity of 10 integrate-and-fire neurons, and the discharge times of concurrently active motor units during an isometric voluntary contraction. The simulations revealed that a latent state-space model can quantify the trajectory and variability of the common input signal across all four conditions. When compared with the cumulative spike train method, the state-space approach was more sensitive and was less influenced by the duration of the signal. The state-space approach appears capable of detecting rather modest changes in common input signals across conditions.

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