Dynamical estimation of neuron and network properties II: Path integral Monte Carlo methods.

Hodgkin-Huxley (HH) models of neuronal membrane dynamics consist of a set of nonlinear differential equations that describe the time-varying conductance of various ion channels. Using observations of voltage alone we show how to estimate the unknown parameters and unobserved state variables of an HH model in the expected circumstance that the measurements are noisy, the model has errors, and the state of the neuron is not known when observations commence. The joint probability distribution of the observed membrane voltage and the unobserved state variables and parameters of these models is a path integral through the model state space.

Dynamical estimation of neuron and network properties I: variational methods.

We present a method for using measurements of membrane voltage in individual neurons to estimate the parameters and states of the voltage-gated ion channels underlying the dynamics of the neuron's behavior. Short injections of a complex time-varying current provide sufficient data to determine the reversal potentials, maximal conductances, and kinetic parameters of a diverse range of channels, representing tens of unknown parameters and many gating variables in a model of the neuron's behavior. These estimates are used to predict the response of the model at times beyond the observation window.