Exploring optimal current stimuli that provide membrane voltage tracking in a neuron model

Abstract

Studying neurons from an energy efficiency perspective has produced results in the research literature. This paper presents a method that enables computation of low energy input current stimuli that are able to drive a reduced Hodgkin-Huxley neuron model to approximate a prescribed time-varying reference membrane voltage. An optimal control technique is used to discover an input current that optimally minimizes a user selected balance between the square of the input stimulus current (input current 'energy') and the difference between the reference voltage and the membrane voltage (tracking error) over a stimulation period. Selecting reference signals to be membrane voltages produced by the neuron model in response to common types of input currents i(t) enables a comparison between i(t) and the determined optimal current stimulus i*(t). The intent is not to modify neuron dynamics, but through comparison of i(t) and i*(t) provide insight into neuron dynamics. Simulation results for four different bifurcation types demonstrate that this method consistently finds lower energy stimulus currents i*(t) that are able to approximate membrane voltages as produced by higher energy input currents i(t) in this neuron model.

Evolution of extrema features reveals optimal stimuli for biological state transitions

“…Analytical methods for deriving optimal control signals traditionally use calculus of variations 24 – 26 ; broad application of these techniques to biology is limited because validated mathematical models are available in only a few systems, and variational solutions to complex models can be elusive 27 , 28 . To deal with complex models, researchers have used phase reduction models 28 – 32 , parameterized stimuli 33 , or simpler conceptual models 24 , 25 . The majority of biological systems however, do not have models readily available, and as such empirical approaches have explored the system’s responses to simple stimulus waveforms (e.g., rectangular, sinusoidal) 34 – 37 .…”

A new approach to optimal control of conductance-based spiking neurons

“…An event-based energy-optimal desynchronizing control for coupled reduced Hodgkin-Huxley neurons was established in [14] by means of the Hamilton-Jacobi-Bellman approach. In [15], the tracking control with low energy input current stimuli of a reference membrane voltage in the reduced Hodgkin-Huxley neuron model was addressed to support investigations of neuron dynamics and energy efficiency. In [18], a low energy extracellular electric field input was designed for a reduced two-compartment model based on Pinsky-Rinzel model, and applied to drive the neuron to closely track a prescriptive spike train.…”