A graph-based approach to identify motor neuron synergies

Multiple studies have experimentally observed common fluctuations in the discharge rates of spinal motor neurons, which have been classically interpreted as generated by correlated synaptic inputs. However, so far it has not been possible to identify the number of inputs, nor their relative strength, received by each motor neuron. This information would reveal the distribution of inputs and dimensionality of the neural control of movement at the motor neuron level. Here, we propose a method that generates networks of correlation between motor neuron outputs to estimate the number of common inputs to motor neurons and their relative strengths. The method is based on force-directed graphs, the hierarchical clustering of motor neurons in the graphs, and the estimation of input strengths based on the graph structure. To evaluate the accuracy and robustness of the method, we simulated 100 motor neurons driven by a known number of inputs with fixed weights. The simulation results showed that 99.2 {+/-} 0.6%, 94.3 {+/-} 2.2 %, and 95.1 {+/-} 2.7 % of the motor neurons were accurately assigned to the input source with the highest weight for simulations with 2, 3, and 4 inputs, respectively. Moreover, the normalised weigths (range 0 to 1) with which each input was transmitted to individual motor neurons were estimated with a root-mean-squared error of 0.11, 0.18, and 0.28 for simulations with 2, 3, and 4 inputs, respectively. These results were robust to errors introduced in the discharge times (as they may occur due to errors by decomposition algorithms), with up to 5% of missing spikes or false positives. We finally applied this method on various experimental datasets to demonstrate typical case scenario when studying the neural control of movement. Overall, these results show that the proposed graph-based method accurately describes the distribution of inputs across motor neurons. Authors summaryAn important characteristics for our understanding of the neural control of natural behaviors if the dimensionality in neural control signals to the musculoskeletal system. This dimensionality in turn depends on the number of synaptic inputs transmitted to the elementary units of this control, i.e., the spinal motor neurons, and on their correlation. We propose a graph-based approach applied to the discharge times of motor neurons to estimate the number of inputs and associated strength transmitted to each motor neuron. For this purpose, we first calculated the correlation between motor neuron smoothed discharge rates, assuming that correlated discharge rates result from the reception of a correlated inputs. Then, we derived networks/graphs in which each node represented a motor neuron and where the nodes were positioned close to each or further apart, depending on the level of correlated activities of the corresponding motor neurons. Using simulations of motor neuron behaviour, we showed that the spatial information embedded in the proposed graphs can be used to accurately estimate the number and the relative strengths of the inputs received by each motor neurons. This method allows to reconstruct the distribution of synaptic inputs to motor neurons from the observed motor neuron activity.