Sensitivity of a model oscillator to shifts in the voltage-dependence of one or more ionic currents.

The voltage dependences of ion channels are subject to change as a function of activity and neuromodulatory influences. We study the effects of alterations of the activation and inactivation curves in each of seven voltage-dependence currents in a bursting computational model, in control conditions and in simulated high potassium conditions. We find that modifications of the voltage-dependence of one current can result in changes of the contribution of many or all of the currents in the model neuron to its behavior. We construct two-dimensional maps of the regions of bursting, tonic spiking, or silence as a function of the voltage-dependence of participating currents, in both control and simulated high potassium. Consistent with experimental findings, the position of bursting regimes under the two conditions shows that most bursting neurons lose their bursting behavior in high potassium. The maps show that, in most but not all models, bursting can be recovered in high potassium conditions by shifts in the voltage-dependence of one or more of the neuron's currents. Surprisingly, in many models, shifts in the activation curves of several different currents can recover bursting behavior. Moreover, multiple degenerate bursting models with different maximal conductances can recover function in response to changes in the same ionic current. In some models, coordinated shifts in the voltage-dependence of two or more currents are necessary for recovery of bursting activity. These studies demonstrate that modulation of voltage-dependence can both alter a neuron's activity and contribute to resilience subsequent to perturbation.