MODELING THE GASTRIC MILL CENTRAL PATTERN GENERATOR OF THE LOBSTER WITH A RELAXATION-OSCILLATOR NETWORK

1. The gastric mill central pattern generator (CPG) controls the chewi ng movements of teeth in the gastric mill of the lobster. This CPG has been extensively studied, but the precise mechanism underlying patter n generation is not well understood. The goal of this research was to develop a simplified model that captures the principle, biologically s ignificant features of this CPG. We introduce a simplified neuron mode l that embodies approximations of well-known membrane currents, and is able to reproduce several global characteristics of gastric mill neur ons. A network built with these neurons, using graded synaptic transmi ssion and having the synaptic connections of the biological circuit, i s sufficient to explain much of the network's behavior. 2. The cell mo del is a generalization and extension of the Van der Pol relaxation os cillator equations. It is described by two differential equations, one for current conservation and one for slow current activation. The mod el has a fast current that may, by adjusting one parameter, have a reg ion of negative resistance in its current-voltage (I-V) curve. It also has a slow current with a single gain parameter that can be regarded as the combination of slow inward and outward currents. 3. For suitabl e values of the fast current parameter and the slow current parameter, the isolated model neuron exhibits several different behaviors: plate au potentials, postinhibitory rebound, post-burst hyperpolarization, a nd endogenous oscillations. When the slow current is separated into in ward and outward fractions with separately adjustable gain parameters, the model neuron can fire tonically, be quiescent, or generate sponta neous voltage oscillations with varying amounts of depolarization or h yperpolarization. 4. The most common form of synaptic interaction in t he gastric CPG is reciprocal inhibition. A pair of identical model cel ls, connected with reciprocal inhibition, oscillates in antiphase if e ither the isolated cells are endogenous oscillators, or they are quies cent without plateau potentials, or they have plateau potentials but t he synaptic strengths are below a critical level. If the isolated cell s have widely differing frequencies (or would have if the cells were m ade to oscillate by adjusting the fast currents), reciprocal inhibitio n entrains the cells to oscillate with the same frequency but with pha ses that are advanced or retarded relative to the phases seen when the cells have the same frequency. The frequency of the entrained pair of cells lies between the frequencies of the original cells. The relativ e phases can also be modified by using very unequal synaptic strengths . 5. A reduced network model was used to study the coordination betwee n the lateral and medial subsets and the effect of deleting a cell fro m the circuit. The results of killing Int 1 in the model had effects s imilar to killing Int 1 in the biological circuit. This suggests that Int 1 accomplishes the coordination of the two subsets by indirectly a ltering the effective strengths of synapses between them. 6. A network of cells with all the known connections was also studied. It was foun d that the network would oscillate and produce an approximately biolog ically correct output pattern over a wide range of synaptic strengths. This remained true when the individual cells were adjusted to be osci llators or to be quiescent. Random changes in parameter values of up t o 40% had little effect on the overall pattern. The pattern of phase r elationships remained approximately constant when the model frequency was varied. The phase lag between the lateral and medial subsets of th e gastric network could be obtained by incorporating known slow synaps es and by adjusting a slow current parameter. If cells are killed sequ entially in the model, the network continues to generate a pattern so long as at least one pair of reciprocal inhibitory cells remains. Chan ges in the relative phases of slow-wave activity can be obtained by ch anging the gains of the slow currents. 7. A cell model that has a fast current with an N-shaped I-V curve, and slow inward and outward curre nts with linear steady-state I-V curves, captures important characteri stic properties of gastric neurons, and a network model built by conne cting these cells with instantaneous graded synaptic transmission capt ures important features of small CPGs. This simple cell model is an ab straction that delineates a basic mechanism common to all gastric cell s and provides a foundation on which to build more comprehensive model s of the gastric mill network.