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BioMed Research International
Volume 2015 (2015), Article ID 936295, 13 pages
http://dx.doi.org/10.1155/2015/936295
Research Article

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

1Department of Mathematical Modelling, Kaunas University of Technology, Studentų Street 50, 51368 Kaunas, Lithuania
2Laboratory of Systems Control and Automation, Lithuanian Energy Institute, Breslaujos Street 3, 44403 Kaunas, Lithuania
3Department of Applied Informatics, Vytautas Magnus University, Vileikos Street 8-409, 44404 Kaunas, Lithuania
4Department of Business Informatics Research in Systems, Kaunas University of Technology, Studentų Street 56, 5142 Kaunas, Lithuania
5Department of Anesthesiology, Albert Einstein College of Medicine, 1300 Morris Park Avenue, Bronx, NY 10461, USA
6Department of Anesthesiology, New York Hospital Queens, 56-45 Main Street, Flushing, NY 11355, USA
7Institute of Cardiology, Lithuanian University of Health Sciences, Sukileliu Street 17, 50009 Kaunas, Lithuania
8Department of Neuroscience, Albert Einstein College of Medicine, 1300 Morris Park Avenue, Bronx, NY 10461, USA

Received 4 July 2014; Revised 7 December 2014; Accepted 8 December 2014

Academic Editor: Carlo Cattani

Copyright © 2015 Mindaugas Snipas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ∼20 times.