The Neuromuscular Transform: The Dynamic, Nonlinear Link Between Motor Neuron Firing Patterns and Muscle Contraction in Rhythmic Behaviors

Abstract

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 neuron-muscle link comprises multiple steps of presynaptic and postsynaptic Ca(2+) 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.

Modulation of an Integrated Central Pattern Generator–Effector System: Dopaminergic Regulation of Cardiac Activity in the Blue CrabCallinectes sapidus

“…Regenerative membrane responses were not detected in the lobster myocardium, but they have been observed in other crustacean hearts (compiled in Anderson and Cooke 1971). Precisely to bridge such complexities of contraction-excitation coupling, a general analytical approach, termed the neuromuscular transform, was recently developed (Brezina et al 2000a(Brezina et al ,b, 2003a. This approach simply considers the inputoutput relation between the motor neuron firing pattern and the muscle contraction.…”

Co-Contraction and Passive Forces Facilitate Load Compensation of Aimed Limb Movements

“…In frogs, the muscles stabilize wiping movements without neuronal activity (Richardson et al, 2005). Brezina et al (2000b) transformed a neural input signal into rhythmic movements of Aplysia feeding behavior using a neuromuscular model, which was also analyzed to determine optimal neural patterns (Brezina et al, 2000a).…”

Muscles innervated by a single motor neuron exhibit divergent synaptic properties on multiple time scales

“…Contractile properties are also commonly non-linear, and can have distinct dynamics relative to motor neuron spike timing (Brezina et al, 2000;Enoka and Fuglevand, 2001;Hooper and Weaver, 2000;JorgeRivera et al, 1998). Further, from presynaptic transmitter release to the regulation of contraction machinery, all aspects of the neuromuscular transform are subject to neuromodulation and thus can differ according to the behavioral state of the organism (Brezina, 2010;Brezina et al, 2000;Hooper and Weaver, 2000;Williams et al, 2013;Worden, 1998).…”

“…Motor neurons relay these changes to muscles, which generate the behaviors. However, the motor neuron to muscle transformation is often non-linear and flexible (Brezina et al, 2000;Hooper and Weaver, 2000;Hooper et al, 1999;Morris and Hooper, 1997). Thus, to fully understand how behaviors are altered by modulation of circuit activity, it is necessary to determine how muscle responses are regulated and how this may vary across a physiological range of motor neuron activity.…”