Current Stimuli That Provide Membrane Voltage Tracking in a Six Dimensional Neuron Model

Abstract

Optimization techniques have been applied to neuron models for a variety of purposes, including control of neuron firing rates and minimizing input stimulus current magnitudes. Optimal control is used to minimize a quantity of interest; often, the time or energy needed to complete an objective. Rather than attempting to control or modify neuron dynamics, this paper demonstrates that optimal control can be used to obtain an optimal input stimulus current i*(t) which causes a six dimensional Hodgkin–Huxley type neuron model to approximate a specified reference membrane voltage. The reference voltages considered in this paper consist of one or more action potentials as evoked by an input current i(t). In the described method, the user prescribes a balance of low squared integral of input stimulus current (input stimulus “energy”) and accurate tracking of the original reference voltage. In a previous work, the authors applied this approach to a reduced order neuron model. This paper demonstrates the applicability of this technique to biologically plausible higher dimensional conductance based neuron models. For each investigated neuron response, the method discovered optimal input stimuli current i*(t) having a lower energy than the original i(t), while still providing accurate tracking of the reference voltage.