title: Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.
abstract: Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature.
authors.affiliation: Simula Research Laboratory, Center for Biomedical Computing, P.O. Box 134, Lysaker 1325, Norway. Electronic address: aslak@simula.no.
authors.forename: Aslak
authors.initials: A
authors.lastname: Tveito
authors.affiliation: Simula Research Laboratory, Center for Biomedical Computing, P.O. Box 134, Lysaker 1325, Norway.
authors.forename: Glenn T
authors.initials: GT
authors.lastname: Lines
authors.affiliation: Simula Research Laboratory, Center for Biomedical Computing, P.O. Box 134, Lysaker 1325, Norway; Department of Biosciences, University of Oslo, Oslo, Norway.
authors.forename: Andrew G
authors.initials: AG
authors.lastname: Edwards
authors.affiliation: Department of Bioengineering, University of California, San Diego, USA.
authors.forename: Andrew
authors.initials: A
authors.lastname: McCulloch
mesh_terms: D000818:Animals; D006801:Humans; D007473:Ion Channels; D008390:Markov Chains; D015233:Models, Statistical
chemical_list: D007473:Ion Channels
keywords: Inversion; Ion channels; Markov models; Partial differential equations; Transmembrane potential