Many physiological systems are regulated by complex networks of modulatory actions. Here we use mathematical modeling and complementary experiments to study the dynamic behavior of such a network in the accessory radula closer (ARC) neuromuscular system of Aplysia. The ARC muscle participates in several types of rhythmic consummatory feeding behavior. The muscle's motor neurons release acetylcholine to produce basal contractions, but also modulatory peptide cotransmitters that, through multiple cellular effects, shape the contractions to meet behavioral demands. We construct a dynamic model of the modulatory network and examine its operation as the motor neurons fire in realistic patterns that change gradually over an hour-long meal and abruptly with switches between the different feeding behaviors. The modulatory effects have very disparate dynamical time scales. Some react to the motor neuron firing only over many cycles of the behavior, but one key effect is fast enough to respond to each individual cycle. Switches between the behaviors are therefore followed by rapid relaxations along some modulatory dimensions but not others. The trajectory of the modulatory state is a transient throughout the meal, ranging widely over regions of the modulatory space not accessible in the steady state. There is a pronounced history-dependency: the modulatory state associated with a cycle of a particular behavior depends on when that cycle occurs and what behaviors preceded it. On average, nevertheless, each behavior is associated with a different modulatory state. In the following companion study, we add a model of the neuromuscular transform to reconstruct and evaluate the actual modulated contraction shapes.
Mathematical Modeling of Physiological Systems
