On parameter estimation for neuron models

Membrane bound ion channels give rise to many of the electrical signal characteristics exhibited by neurons. Ion channel models of neural function such as that proposed by Hodgkin-Huxley can be represented as a set of differential equations. Solving these differential equations for a given neuron involves finding optimal values for the parameters that define the Hodgkin-Huxley equations. Most often, these parameters are evaluated using an optimization algorithm that takes as input ion channel current data recorded from a neuron using the voltage clamp technique. Real-valued optimization algorithms often fail to find a global optimum for the parameters of the Hodgkin-Huxley differential equations. Here, the authors show that interval analysis based optimization algorithm, a branch and bound algorithm, provides an accurate solution for the Hodgkin-Huxley model.