SIMULATION OF THE BURSTING ACTIVITY OF NEURON-R15 IN APLYSIA - ROLE OF IONIC CURRENTS, CALCIUM BALANCE, AND MODULATORY TRANSMITTERS

1. An equivalent circuit model of the R15 bursting neuron in Aplysia has been combined with a fluid compartment model, resulting in a model that incorporates descriptions of most of the membrane ion channels that are known to exist in the somata of R15, as well as providing a Ca2+ balance on the cell. 2. A voltage-activated, calcium-inactivated Ca2+ current (denoted the slow inward current I(SI)) was sufficient to produce bursting activity without invoking any other calcium-dependent currents (such as a nonspecific cation current, I(NS), or a calcium-activated K+ current, I(K,Ca)). Furthermore, many characteristics of a typical R15 burst could be simulated, such as a parabolic variation in interspike interval, the depolarizing afterpotential (DAP), and the progressive decrease in the undershoots of spikes during a burst. 3. The dynamic activity of R15 was analyzed by separately characterizing two different temporal domains: the fast dynamics associated with action potentials and the slow dynamics associated with low-amplitude oscillations lasting tens of seconds ("slow waves"). The slow dynamics were isolated by setting the Na+ conductance (g(Na)BAR) to zero and then studied by the use of a system of equations reduced to two variables: intracellular concentration of Ca2+ and membrane potential. The fixed point of the system was located at the intersection of the nullclines for these two variables. A stability analysis of the fixed point was then used to determine whether a given set of parameters would produce slow-wave activity. 4. If the reduced model predicted slow-wave oscillations for a given set of parameters with g(Na)BAR set to zero, then bursting activity was observed for the same set of parameters in the full model with g(Na)BAR reset to its control value. However, for certain sets of parameters with g(Na)BAR at its usual value, the full model exhibited bursting activity because of a slow oscillation produced by the activation of I(NS) by action potentials. This oscillation resulted from an interaction between the fast and slow dynamics that the reduced model alone could not predict and was not observed when g(Na)BAR was subsequently set to zero. If g(NSBAR) was also set to zero, this discrepancy disappeared. 5. This model predicted a number of experimentally observed transitions in the dynamic activity, including the following: 1) the transition from a bursting mode to slow-wave activity induced by the Na+ channel blocker tetrodotoxin (TTX), 2) the transition from a bursting to a beating mode induced by the Na+-K+ pump blocker oubain, and 3) the entire range of transitions from a hyperpolarized mode through bursting modes to a beating mode produced by external current injection. 6. The model also simulated the effects of the modulatory agents serotonin (5-HT), dopamine, FMRFamide (Phe-Met-Arg-Phe-amide), and egg-laying hormone (ELH), and the second messenger guanosine 3',5'-cyclic monophosphate (cGMP). These agents modulate either I(SI) or the anomalous rectifier current (I(R)) or both. A critical distinction between the modulation of these two currents was that only I(SI) affected both the calcium nullcline and the potential nullcline. This distinction provided an alternative mechanism for the paradoxical effects of reducing I(SI). Specifically, depending on the new location of the fixed point, a reduction in I(SI) can either hyperpolarize the cell or induce slow beating