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Biophys. J. BioFAST: First Published February 3, 2006. doi:10.1529/biophysj.105.075135
© 2006 by the Biophysical Society.

A more recent version of this article appeared on May 15, 2006.
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CHANNELS, RECEPTORS, AND ELECTRICAL SIGNALING

Statistical evaluation of ion-channel gating models based on distributions of LogLikelihood Ratios

Laszlo Csanady 1*

1 Semmelweis University

* To whom correspondence should be addressed. E-mail: csanady{at}puskin.sote.hu.

Submitted on September 28, 2005
Revised on November 16, 2005
Accepted on 12 January 2006


  Abstract
The distributions of LogLikelihood Ratios ({Delta}LL) obtained from fitting ion-channel dwell-time distributions with nested pairs of gating models ({Xi}, full model; {Xi}R, submodel) were studied both theoretically and using simulated data. When {Xi} is true {Delta}LL is asymptotically Normally distributed with predictable mean and variance which increase linearly with data length n). When {Xi}R is true and corresponds to a distinct point in full parameter space {Delta}LL is gamma-distributed (2{Delta}LL is chi-square). However, when data generated by an l-component multiexponential distribution are fitted by l+1 components, {Xi}R corresponds to an infinite set of points in parameter space. The distribution of {Delta}LL is a mixture of two components, one identically zero, the other approximated by a gamma distribution. This empirical distribution of {Delta}LL, assuming {Xi}R, allows construction of a valid LogLikelihood Ratio test. The LogLikelihood Ratio test, the Akaike Information Criterion, and the Schwarz Criterion all produce asymmetrical Type I and II errors and inefficiently recognize {Xi}, when true, from short datasets. A new decision strategy, which considers both the parameter estimates and {Delta}LL, yields more symmetrical errors and a larger discrimination power for small n. These observations are explained by the distributions of {Delta}LL when {Xi} or {Xi}R is true.

Key Words: Normal distribution, Type I and II errors, chi-square, convergence in probability, dwell time, nested Markov models




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Copyright © 2006 by the Biophysical Society.