Continuous Time Markov Chain Models of Voltage Gating of Gap Junction Channels

Abstract

The major goal of this study was to create a continuous time Markov chain (CTMC) models of voltage gating of gap junction (GJ) channels formed of connexin protein. This goal was achieved by using the Piece Linear Aggregate (PLA) formalism to describe the function of GJs and transforming PLA into Markov process. Infinitesimal generator of CTMC was used to automate construction of Markov chain model from description of the system using PLA formalism. Developed Markov chain models were used to simulate gap junctional conductance dependence on transjunctional voltage. The proposed method was implemented to create models of voltage gating of GJ channels containing 4 and 12 gates. CTMC modeling results were compared with the results obtained using a discrete time Markov chain (DTMC) model. It was shown that CTMC modeling requires less CPU time than an analogous DTMC model.

Application of Stochastic Automata Networks for Creation of Continuous Time Markov Chain Models of Voltage Gating of Gap Junction Channels

“…We used SAN to create equivalent CTMC model due to the complexity of estimation of functional transition rates. Unlike a PLA approach, which we have used earlier for CTMC modelling of GJs [ 8 ], SAN and Kronecker algebra operations help to get more insight into the structure of infinitesimal generator matrix.…”

“…Thus, it is evident that modeling requires fast construction of the matrix of transition probabilities (transition rates) and fast solution of the steady-state probabilities because the amount of central processing unit (CPU) time is high even at relatively small number of states. In our prior studies [ 8 ], we already used continuous time Markov chain (CTMC) model of GJs gating. A transformation of the transition probabilities into transition rates is necessary to generate CTMC model with the same steady-state probabilities, but infinitesimal generator matrix of CTMC model is sparse.…”

“…A transformation of the transition probabilities into transition rates is necessary to generate CTMC model with the same steady-state probabilities, but infinitesimal generator matrix of CTMC model is sparse. For example, infinitesimal generator of GJ model presented in [ 8 ] was a tridiagonal matrix. Therefore, generation of matrix and modeling of GJs under steady-states conditions using the CTMC model require smaller amount of CPU time compared to using the DTMC model.…”

“…In previous study [ 8 ] we used piece linear aggregate (PLA) formalism for CTMC model creation. PLA formalism allows building and storing infinitesimal generator of Markov chain model automatically, but matrix structure cannot be easily deduced, especially in more complex models.…”

A marginal contribution coefficient for sequences of nonstationary continuous Markov chains

“…Time series data are widely used in many different areas such as stock market, medical and biological, natural languages, neural networks, etc (See, for example, previous studies). As a consequence, much effort has been devoted to introducing new methodologies for classification, clustering, and approximation of time series .…”