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Use of the Covariance Matrix in Directly Fitting Kinetic Parameters: Application to GABA_A Receptors

James J. Celentano ^* and Alan G. Hawkes 

^* Department of Physiology and Pharmacology, State University of New York Downstate Medical Center, Brooklyn, New York 11203; and University of Wales, Singleton Park, Swansea SA2 8PP, United Kingdom

Correspondence: Address reprint requests to James J. Celentano, E-mail: jimc10{at}aol.com.

A new method of analysis is described that begins to explore the relationship between the phases of ion channel desensitization and the underlying states of the channel. The method, referred to as covariance fitting (CVF), couples Q-matrix calculations with a maximum likelihood algorithm to fit macroscopic desensitization data directly to kinetic models. Unlike conventional sum-of-squares minimization, CVF fits both the magnitude of the recorded current and the strength of the correlations between different time points. When applied to simulated data generated using various kinetic models with up to 11 free parameters, CVF leads to reasonable parameter estimates. Coupled with the likelihood ratio test, it accurately discriminates between models with different numbers of states, discriminates between most models with the same number but a different arrangement of states, and extracts meaningful information on the relationship between the desensitized states and the phases of macroscopic desensitization. When applied to GABA_A receptor traces (outside out patches, 1ß22S, 1 mM GABA, >2.5 s), a model with two open states and three desensitized states is favored. When applied to simulated data generated using a consensus model, CVF leads to reasonable parameter estimates and accurately discriminates between this and other models.

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