Maximum likelihood estimation of ion channel kinetics from macroscopic currents

¹ NINDS, NIH, Bethesda
² Wash. U. St. Louis
³ SUNY - Buffalo

^* To whom correspondence should be addressed. E-mail: sachs{at}buffalo.edu.

Submitted on September 18, 2004
Revised on October 15, 2004
Accepted on 20 January 2005

	Abstract

We describe a maximum likelihood method for direct estimation of rate constants from macroscopic ion channel data for kinetic models of arbitrary size and topology. The number of channels in the preparation, and the mean and standard deviation of the unitary current can be estimated, and, most importantly, a priori constraints can be imposed on rate constants. The method allows for arbitrary stimulation protocols, including stimuli with finite rise time, trains of ligand or voltage steps, and global fitting across different experimental conditions. The initial state occupancies can be optimized from the fitted kinetics. Utilizing arbitrary stimulation protocols and using the mean and the variance of the current reduce or eliminate problems of model identifiability (Kienker, 1989). The algorithm is faster than a recent method that uses the full autocovariance matrix (Celentano and Hawkes, 2004), in part due to the analytical calculation of the likelihood gradients. We tested the method with simulated data and with real macroscopic currents from acetylcholine receptors, elicited in response to brief pulses of carbachol. Given appropriate stimulation protocols, our method chose a reasonable model size and topology.

Key Words: Markov model, algorithm, modeling, optimization, whole cell

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