Dissecting mechanisms behind force control in humans by a mixture of experimentation, mathematical analysis and computer simulations of neuronal models

A great deal of knowledge about the physiology of motor neurons (MNs) and spinal interneurons has been obtained thanks to extensive studies in cats (anaesthetized or behaving). Due to obvious ethical and technical limitations the related studies in humans have a much more limited scope. Yet, much knowledge has been obtained on the behaviours of human motor units (MUs), for example by recording the extracellular motor unit action potentials (MUAPs) through flexible fine wire electrodes inserted into a muscle. Each electrode may record MUAP trains from a few neighbouring MUs. Each of these trains may be discriminated by a spike sorting software, thus providing a peephole to observe and quantify the spiking activity of a fraction of the spinal cord MNs. If muscle force, muscle electrical activity (EMG) and/or some biomechanical variable is measured concomitantly, then one can correlate what happens at the MN level with a macroscopic outcome of the motor system. However, when the questions involve the inputs to a human MN pool (descending commands, activity from interneurons and from peripheral nerves) then much ingenuity is needed to obtain inferences on how these structures are acting. Recently, an additional tool has been employed to help improve our understanding of the neurophysiological basis of muscle force control: mathematical modelling and computer simulations of large-scale neuromuscular models.

In this issue of The Journal of Physiology, Farina et al. (2014) address the question of the input–output mapping of a MN pool in humans. Due to the challenge posed by such a question, a full set of approaches was employed: experimental, theoretical and computer simulations of mathematical models of a MN pool. They conceptualized a common input to all MNs (De Luca et al. 1982) plus uncorrelated inputs to each MN of the pool. The main hypothesis was that the MN pool was only sensitive to the common inputs and averaged out the other inputs which were not common to all the pool. The experimental approach investigated the spiking activity of MUs recorded by fine wire electrodes inserted into the abductor digiti minimi of healthy subjects exerting weak voluntary contractions of this muscle. The main finding was that when the spike trains from each of two subsets of MUs were superposed, the coherence function between the two superposed spike trains tended to 1 (from 0 Hz to the minimum firing rate of the MUs) when the number of MUs per subset was increased. This result is consistent with and reinforces the main hypothesis of their paper. The simulation approach relied mainly on biophysically based MN models whose inputs (the somatic currents) were equivalent to a sum of sinusoids common to all MNs, summed with a combination of sinusoids with frequencies and phases chosen randomly for each MN of the pool (these represented the uncorrelated inputs to each MN). The result was that the MN pool output (i.e. the drive to the muscle) was strongly dominated by the frequency of the common input. For the theoretical approach, the authors started from the mathematical expression of the spectrum of the output of a perfect integrate-and-fire neuron model to an input equal to a sum of sinusoids of different frequencies. From a mathematical analysis, the authors concluded that a set of such neurons would amplify the common input from a frequency of 0 Hz to the minimum discharge rate of the active MUs, i.e. from 0 to about 6–10 Hz. In other words the MN pool increases the signal to noise ratio (reminiscent of signal averaging procedures), where the signal is the common input to the pool and the noise is made of the non-common (uncorrelated) inputs. In synthesis, the common inputs, which include cortical commands, would be reflected with little distortion in the drive to the muscle for a range of low frequencies (from 0 to about 6–10 Hz). This conclusion that the functional output of the MN pool reflects the common inputs to the MNs is very relevant information for studies of the neural bases of force control.

In a related study, also combining human experiments with large-scale modelling approaches (Watanabe et al. 2013), the presynaptic inputs acting on a given MN pool were represented by gamma point processes with appropriate parameters. The MNs (more than a thousand) and muscle fibres were modelled from biophysical and biomechanical standpoints. The outputs were muscle force and EMG (mean level and variability) and the inputs were the spike trains of the set of presynaptic axons to the MN pool. One of the objectives was to verify how the mean force level and the force standard deviation generated by this large-scale model could reproduce experimental data obtained from humans (plantarflexion torque generation and muscle electrical activity). One of the conclusions was that the inputs to the MN pool should have a higher variability for higher force levels (which have higher variability than lower force levels), which is consistent with the conceptual conclusions of Farina et al. (2014).

This issue's article by Farina and collaborators is paradigmatic of the power of combining experimental, modelling and theoretical approaches to questions in neuroscience.