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Originally published as Biophys J. BioFAST on February 3, 2006.
doi:10.1529/biophysj.105.075135
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Biophysical Journal 90:3523-3545 (2006)
© 2006 The Biophysical Society

Statistical Evaluation of Ion-Channel Gating Models Based on Distributions of Log-Likelihood Ratios

László Csanády

Department of Medical Biochemistry, Semmelweis University, and Neurochemical Group of the Hungarian Academy of Sciences, Budapest, Hungary

Correspondence: Address reprint requests to László Csanády, Dept. of Medical Biochemistry, Semmelweis University, 1444 Budapest, Pf. 262, Hungary. Tel.: 36-1-266-2755, Ext. 4023; E-mail: csanady{at}puskin.sote.hu.

The distributions of log-likelihood 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 that 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 log-likelihood ratio test. The log-likelihood 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.




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