Simulation and parameter estimation study of a simple neuronal model of rhythm generation: role of NMDA and non-NMDA receptors.

Simple neural network models of the Xenopus embryo swimming CPG, based on the one originally developed by Roberts and Tunstall (1990), were used to investigate the role of the voltage-dependent N-methyl-D-aspartate (NMDA) receptor channels, in conjunction with faster non-NMDA components of synaptic excitation, in rhythm generation. The voltage-dependent NMDA current "follows" the membrane potential, leading to a postinhibitory rebound that is more efficient than one without voltage dependency and allows neurons to fire more than one action potential per cycle. Furthermore, the model demonstrated limited rhythmic activity in the absence of synaptic inhibition, supporting the hypothesis that the NMDA channels provide a basic mechanism for rhythmicity. However, the rhythmic properties induced by the NMDA current were observed only when there was moderate activation of the non-NMDA synaptic channels, suggesting a modulatory role for this component. The simulations also show that the voltage dependency of the NMDA conductance, as well as the fast non-NMDA current, stabilizes the alternation pattern versus synchrony. To verify that these effects and their implications on the mechanism of swimming and transition to other types of activity take place in the real preparation, constraints on parameter values have to be specified. A method to estimate synaptic parameters was tested with generated data. It is shown that a global analysis, based on multiple iterations of the optimization process (Foster et al., 1993), gives a better understanding of the parameter subspace describing network activity than a standard fit with a sensitivity analysis for an individual solution.