Robust activity of some networks, such as central pattern generators, suggests the existence of physiological mechanisms that maintain the most important characteristics, for example, the period and spike frequency of the pattern. Whatever these mechanisms are, they change the appropriate model parameters to or along the isomanifolds on which the characteristics of the pattern are constant, while their sensitivities to parameters may be different. Setting synaptic connections to zero at the points of isomanifolds allows for dissecting the maintenance mechanisms into components involving synaptic transmission and components involving intrinsic currents. The physiological meaning of the intrinsic current changes might be revealed by analysis of their impact on endogenous neuronal dynamics. Here, we sought answers to two questions: (1) Do parameter variations in insensitive directions (along isomanifolds) change endogenous dynamics of the network neurons? (2) Do sensitive and insensitive directions for network pattern characteristics depend on endogenous dynamics of the network neurons?

We considered a leech heartbeat half-center oscillator model network and analyzed isomanifolds on which the burst period or spike frequency of the model, or both, are constant. Based on our analysis, we hypothesize that the dependence on endogenous dynamics of the isolated neurons is the stronger the more characteristics of the pattern have to be maintained. We also found that in general, the network was more flexible when it consisted of endogenously tonically spiking rather than bursting or silent neurons. Finally, we discuss the physiological implications of our findings.

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