The space-clamped Hodgkin-Huxley system with random synaptic input: inhibition of spiking by weak noise and analysis with moment equations

TL;DR

This paper investigates how weak noise can inhibit spiking in a Hodgkin-Huxley neuron model with stochastic synaptic input, using moment equations and numerical simulations to analyze the effects near critical conductance levels.

Contribution

It introduces a moment equation approach to analyze stochastic Hodgkin-Huxley models with Ornstein-Uhlenbeck synaptic inputs, revealing noise-induced inhibition and inverse stochastic resonance phenomena.

Findings

Weak noise inhibits spiking near critical conductance levels.

Noise can powerfully inhibit spiking in both excitatory and inhibitory inputs.

Inverse stochastic resonance observed with inhibitory-only noise.

Abstract

We consider a classical space-clamped Hodgkin-Huxley model neuron stimulated by synaptic excitation and inhibition with conductances represented by Ornstein-Uhlenbeck processes. Using numerical solutions of the stochastic model system obtained by an Euler method, it is found that with excitation only there is a critical value of the steady state excitatory conductance for repetitive spiking without noise and for values of the conductance near the critical value small noise has a powerfully inhibitory effect. For a given level of inhibition there is also a critical value of the steady state excitatory conductance for repetitive firing and it is demonstrated that noise either in the excitatory or inhibitory processes or both can powerfully inhibit spiking. Furthermore, near the critical value, inverse stochastic resonance was observed when noise was present only in the inhibitory input process. The system of 27 coupled deterministic differential equations for the approximate first and second order moments of the 6-dimensional model is derived. The moment differential equations are solved using Runge-Kutta methods and the solutions are compared with the results obtained by simulation for various sets of parameters including some with conductances obtained by experiment on pyramidal cells of rat prefrontal cortex. The mean and variance obtained from simulation are in good agreement when there is spiking induced by strong stimulation and relatively small noise or when the voltage is fluctuating at subthreshold levels. In the occasional spike mode sometimes exhibited by spinal motoneurons and cortical pyramidal cells the assunptions underlying the moment equation approach are not satisfied.