title: Transformations that preserve detailed balance in Markov models.
abstract: Aggregated Markov processes related by similarity transformation are equivalent in that they cannot be distinguished by steady-state experiments. We derive an explicit formula for the set of all detailed-balance preserving similarity transformations between such continuous time Markov chains with N states. The matrices that define the allowed similarity transformations are found to be a simple non-linear function applied to almost any element of the special orthogonal group in N dimensions. Since a model is identifiable only if there is no similarity transformations to an equivalent model, we expect this result to prove useful in the theory of identification of aggregated Markov chains, an enterprise of growing importance as more and more single molecules yield to observation.
authors.affiliation: Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA.
authors.forename: William J
authors.initials: WJ
authors.lastname: Bruno
authors.forename: John E
authors.initials: JE
authors.lastname: Pearson
mesh_terms: D001699:Biometry; D015640:Ion Channel Gating; D007473:Ion Channels / Q000378:metabolism; D007700:Kinetics; D008390:Markov Chains; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics
chemical_list: D007473:Ion Channels