A stochastic model for the membrane potential of a stimulated neuron

We present a simple model describing the transition between the prefiring, firing and postfiring phases of a single neuron in a large neural net. Using typical values for the physiological parameters that enter the model, we find average interspike times that are close to those reported in experimental measurements.     

Computation of spiking activity for a stochastic spatial neuron model: effects of spatial distribution of input on bimodality and CV of the ISI distribution

We obtain computational results for a new extended spatial neuron model in which the neuronal electrical depolarization from resting level satisfies a cable partial differential equation and the synaptic input current is also a function of space and time, obeying a first order linear partial differential equation driven by a two-parameter random process. The model is first described explicitly with the inclusion of all biophysical parameters. Simplified equations are obtained with dimensionless space and time variables. A standard parameter set is described, based mainly on values appropriate for cortical pyramidal cells. When the noise is small and the mean voltage crosses threshold, a formula is derived for the expected time to spike. A simulation algorithm, involving one-dimensional random processes is given and used to obtain moments and distributions of the interspike interval (ISI). The parameters used are those for a near balanced state and there is great sensitivity of the firing rate around the balance point. This sensitivity may be related to genetically induced pathological brain properties (Rett's syndrome). The simulation procedure is employed to find the ISI distribution for some simple patterns of synaptic input with various relative strengths for excitation and inhibition. With excitation only, the ISI distribution is unimodal of exponential type and with a large coefficient of variation. As inhibition near the soma grows, two striking effects emerge. The ISI distribution shifts first to bimodal and then to unimodal with an approximately Gaussian shape with a concentration at large intervals. At the same time the coefficient of variation of the ISI drops dramatically to less than 1/5 of its value without inhibition.     

Collective Equilibrium Behaviour of Ion Channel Gating in Cell Membranes: An Ising Model Formulation

A statistical mechanical model for voltage-gated ion channels in cell membranes is proposed using the transfer matrix method. Equilibrium behavior of the system is studied. Representing the distribution of channels over the cellular membrane on a one-dimensional array with each channel having two states (open and closed) and incorporating channel–channel cooperative interactions, we calculate the fraction of channels in the open state at equilibrium. Experimental data obtained from batrachotoxin-modified sodium channels in the squid giant axon, using the cut-open axon technique, is best fit by the model when there is no interaction between the channels.