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 chewing movements of teeth in the gastric mill of the lobster. This CPG has been extensively studied, but the precise mechanism underlying pattern generation is not well understood. The goal of this research was to develop a simplified model that captures the principle, biologically significant features of this CPG. We introduce a simplified neuron model that embodies approximations of well-known membrane currents, and is able to reproduce several global characteristics of gastric mill neurons. A network built with these neurons, using graded synaptic transmission and having the synaptic connections of the biological circuit, is sufficient to explain much of the network's behavior. 2. The cell model is a generalization and extension of the Van der Pol relaxation oscillator equations. It is described by two differential equations, one for current conservation and one for slow current activation. The model has a fast current that may, by adjusting one parameter, have a region 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 suitable values of the fast current parameter and the slow current parameter, the isolated model neuron exhibits several different behaviors: plateau potentials, postinhibitory rebound, post-burst hyperpolarization, and endogenous oscillations. When the slow current is separated into inward and outward fractions with separately adjustable gain parameters, the model neuron can fire tonically, be quiescent, or generate spontaneous voltage oscillations with varying amounts of depolarization or hyperpolarization. 4. The most common form of synaptic interaction in the gastric CPG is reciprocal inhibition. A pair of identical model cells, connected with reciprocal inhibition, oscillates in antiphase if either the isolated cells are endogenous oscillators, or they are quiescent without plateau potentials, or they have plateau potentials but the synaptic strengths are below a critical level. If the isolated cells have widely differing frequencies (or would have if the cells were made to oscillate by adjusting the fast currents), reciprocal inhibition entrains the cells to oscillate with the same frequency but with phases 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 relative phases can also be modified by using very unequal synaptic strengths. 5. A reduced network model was used to study the coordination between the lateral and medial subsets and the effect of deleting a cell from the circuit. The results of killing Int 1 in the model had effects similar to killing Int 1 in the biological circuit. This suggests that Int 1 accomplishes the coordination of the two subsets by indirectly altering the effective strengths of synapses between them. 6. A network of cells with all the known connections was also studied. It was found that the network would oscillate and produce an approximately biologically correct output pattern over a wide range of synaptic strengths. This remained true when the individual cells were adjusted to be oscillators or to be quiescent. Random changes in parameter values of up to 40% had little effect on the overall pattern. The pattern of phase relationships remained approximately constant when the model frequency was varied. The phase lag between the lateral and medial subsets of the gastric network could be obtained by incorporating known slow synapses and by adjusting a slow current parameter. If cells are killed sequentially in the model, the network continues to generate a pattern so long as at least one pair of reciprocal inhibitory cells remains. Changes in the relative phases of slow-wave activity can be obtained by changing 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 currents with linear steady-state I-V curves, captures important characteristic properties of gastric neurons, and a network model built by connecting these cells with instantaneous graded synaptic transmission captures important features of small CPGs. This simple cell model is an abstraction that delineates a basic mechanism common to all gastric cells and provides a foundation on which to build more comprehensive models of the gastric mill network.