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J Theor Biol. 2014 Feb 21;343:102-12. doi: 10.1016/j.jtbi.2013.11.010. Epub 2013 Nov 21.

Mesoscopic behavior from microscopic Markov dynamics and its application to calcium release channels.

Author information

  • 1University of Aberdeen, Department of Physics, Meston Walk, Aberdeen AB24 3UE, UK; University Luxembourg, Luxembourg Centre for Systems Biomedicine, 7, Avenue des Hauts-Fourneaux, L-4362 Esch-sur-Alzette, Luxembourg. Electronic address: nils.christian@uni.lu.
  • 2University Luxembourg, Luxembourg Centre for Systems Biomedicine, 7, Avenue des Hauts-Fourneaux, L-4362 Esch-sur-Alzette, Luxembourg; Institute for Systems Biology, 401 Terry Ave N, Seattle, WA 98109, USA.
  • 3Università di Roma Tor Vergata and INFN, Sezione di Roma 2, Via della Ricerca Scientifica, I-00133 Roma, Italy.
  • 4NIC/DESY Zeuthen, Platanenallee 6, D-15738 Zeuthen, Germany.
  • 5University of Aberdeen, Department of Physics, Meston Walk, Aberdeen AB24 3UE, UK; Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, 14473 Potsdam, Germany; Cluster of Excellence on Plant Sciences (CEPLAS), Heinrich-Heine-University, Universitätsstraße 1, D-40225 Düsseldorf, Germany. Electronic address: ebenhoeh@abdn.ac.uk.

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.

KEYWORDS:

Calcium signaling; Emergent properties of mesostates; Gillespie algorithm; receptor

PMID:
24270093
DOI:
10.1016/j.jtbi.2013.11.010
[PubMed - indexed for MEDLINE]
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