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. ### Competing Interest Statement The authors have declared no competing interest.