Universität zu Köln

Christian, Nils, Skupin, Alexander, Morante, Silvia ORCID: 0000-0002-3913-5733, Jansen, Karl, Rossi, Giancarlo ORCID: 0000-0001-9688-9454 and Ebenhoeh, Oliver ORCID: 0000-0002-7229-7398 (2014). Mesoscopic behavior from microscopic Markov dynamics and its application to calcium release channels. J. Theor. Biol., 343. S. 102 - 113. LONDON: ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD. ISSN 1095-8541

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Abstract

A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical framework that allows the calculation of mesoscopic properties from the knowledge of microscopic Markovian transition probabilities. We show how exact analytic formulae for the first and second moments of resident time distributions in mesostates can be derived from microscopic resident times and transition probabilities even for systems with a large number of microstates. We apply our formalism to models of the inositol trisphosphate receptor, which plays a key role in generating calcium signals triggering a wide variety of cellular responses. We demonstrate how experimentally accessible quantities, such as opening and closing times and the coefficient of variation of inter-spike intervals, and other, more elaborated, quantities can be analytically calculated from the underlying microscopic Markovian dynamics. A virtue of our approach is that we do not need to follow the detailed time evolution of the whole system, as we derive the relevant properties of its steady state without having to take into account the often extremely complicated transient features. We emphasize that our formulae fully agree with results obtained by stochastic simulations and approaches based on a full determination of the microscopic system's time evolution. We also illustrate how experiments can be devised to discriminate between alternative molecular models of the inositol trisphosphate receptor. The developed approach is applicable to any system described by a Markov process and, owing to the analytic nature of the resulting formulae, provides an easy way to characterize also rare events that are of particular importance to understand the intermittency properties of complex dynamic systems. (C) 2013 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Christian, Nils UNSPECIFIED UNSPECIFIED UNSPECIFIED Skupin, Alexander UNSPECIFIED UNSPECIFIED UNSPECIFIED Morante, Silvia UNSPECIFIED orcid.org/0000-0002-3913-5733 UNSPECIFIED Jansen, Karl UNSPECIFIED UNSPECIFIED UNSPECIFIED Rossi, Giancarlo UNSPECIFIED orcid.org/0000-0001-9688-9454 UNSPECIFIED Ebenhoeh, Oliver UNSPECIFIED orcid.org/0000-0002-7229-7398 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-445731
DOI:	10.1016/j.jtbi.2013.11.010
Journal or Publication Title:	J. Theor. Biol.
Volume:	343
Page Range:	S. 102 - 113
Date:	2014
Publisher:	ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Place of Publication:	LONDON
ISSN:	1095-8541
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language INOSITOL 1,4,5-TRISPHOSPHATE RECEPTOR; KINETIC-MODEL; SINGLE; ION; SIMULATIONS; RETICULUM; TRANSPORT; CLUSTERS Multiple languages Biology; Mathematical & Computational Biology Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/44573