Product-Form Stationary Distributions for Deficiency Zero Networks with Non-mass Action Kinetics

In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous-time Markov chains. Here we present a class of models that appears naturally in certain averaging approaches whose stationary...

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Bibliographic Details
Published in:Bulletin of mathematical biology 2016-12, Vol.78 (12), p.2390-2407
Main Authors: Anderson, David F., Cotter, Simon L.
Format: Article
Language:English
Subjects:
Algorithms
Biochemical Phenomena
Cell Biology
Kinetics
Life Sciences
Markov Chains
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Models, Biological
Original
Original Article
Protein Multimerization
Stochastic Processes
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Summary:In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous-time Markov chains. Here we present a class of models that appears naturally in certain averaging approaches whose stationary distributions can be computed explicitly. In particular, we study continuous-time Markov chain models for biochemical interaction systems with non-mass action kinetics whose network satisfies a certain constraint. Analogous with previous related results, the distributions can be written in product form.
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-016-0220-y