The neuromuscular transform: The dynamic, nonlinear link between motor neuron firing patterns and muscle contraction in rhythmic behaviors

The nervous system issues motor commands to muscles to generate behavior. All such commands must, however, pass through a filter that we call here the neuromuscular transform (NMT). The NMT transforms patterns of motor neuron firing to muscle contractions. This work is motivated by the fact that the NMT is far from being a straightforward, transparent link between motor neuron and muscle. The NMT is a dynamic, nonlinear, and modifiable filter. Consequently motor neuron firing translates to muscle contraction in a complex way. This complexity must be taken into account by the nervous system when issuing its motor commands, as well as by us when assessing their significance. This is the first of three papers in which we consider the properties and the functional role of the NMT. Physiologically, the motor neuronmuscle link comprises multiple steps of presynaptic and postsynaptic Ca²⁺ elevation, transmitter release, and activation of the contractile machinery. The NMT formalizes all these into an overall input-output relation between patterns of motor neuron firing and shapes of muscle contractions. We develop here an analytic framework, essentially an elementary dynamical systems approach, with which we can study the global properties of the transformation. We analyze the principles that determine how different firing patterns are transformed to contractions, and different parameters of the former to parameters of the latter. The key properties of the NMT are its nonlinearity and its time dependence, relative to the time scale of the firing pattern We then discuss issues of neuromuscular prediction, control, and coding. Does the firing pattern contain a code by means of which particular parameters of motor neuron firing control particular parameters of muscle contraction? What information must the motor neuron, and the nervous system generally, have about the periphery to be able to control it effectively? We focus here particularly on cyclical, rhythmic contractions which reveal the principles particularly clearly. Where possible, we illustrate the principles in an experimentally advantageous model system, the accessory radula closer (ARC)-opener neuromuscular system of Aplysia. In the following papers, we use the framework developed here to examine how the properties of the NMT govern functional performance in different rhythmic behaviors that the nervous system may command.