Implementation and analysis of neuromodulatory mechanisms in a mathematical model of neuron R15 in Aplysia

An existing model of the bursting neuron R15 in Aplysia has been modified to incorporate the effects of the neuromodulatory agents serotonin and dopamine upon the conductances of the subthreshold currents $I\sb{R}$ and $I\sb{SI}$. The model duplicates the various forms of behavior exhibited by R15 in vitro in the presence of serotonin or dopamine, implying that the modeled mechanisms are sufficient to evoke the varied behavioral patterns exhibited by R15. The response of the model to extrinsic stimuli is examined. Serotonin enhances the cell's response to current stimuli of either polarity, while dopamine reduces the cell's response. The model demonstrates bistable behavior, indicating that the model's current state of behavior is dependent upon past behavior and/or stimuli. A nullcline and bifurcation analysis upon reduced models explains the mechanism of bursting and the effects of serotonin and dopamine through the existence of saddle-node and Hopf bifurcations