Bounds on stochastic chemical kinetic systems at steady state

The Journal of Chemical Physics
Garrett R Dowdy, Paul I Barton

Abstract

The method of moments has been proposed as a potential means to reduce the dimensionality of the chemical master equation (CME) appearing in stochastic chemical kinetics. However, attempts to apply the method of moments to the CME usually result in the so-called closure problem. Several authors have proposed moment closure schemes, which allow them to obtain approximations of quantities of interest, such as the mean molecular count for each species. However, these approximations have the dissatisfying feature that they come with no error bounds. This paper presents a fundamentally different approach to the closure problem in stochastic chemical kinetics. Instead of making an approximation to compute a single number for the quantity of interest, we calculate mathematically rigorous bounds on this quantity by solving semidefinite programs. These bounds provide a check on the validity of the moment closure approximations and are in some cases so tight that they effectively provide the desired quantity. In this paper, the bounded quantities of interest are the mean molecular count for each species, the variance in this count, and the probability that the count lies in an arbitrary interval. At present, we consider only steady-state...Continue Reading

References

Oct 14, 2006·Annual Review of Physical Chemistry·Daniel T Gillespie
Jan 22, 2009·IET Systems Biology·C S Gillespie
Sep 29, 2011·Chemical Engineering Science·Vassilios Sotiropoulos, Yiannis N Kaznessis
Aug 14, 2013·Proceedings of the National Academy of Sciences of the United States of America·Patrick Smadbeck, Yiannis N Kaznessis
Jul 1, 2017·Physical Biology·Khem Raj GhusingaAbhyudai Singh

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Citations

Aug 24, 2018·The Journal of Chemical Physics·Garrett R Dowdy, Paul I Barton
Jul 22, 2019·The Journal of Chemical Physics·Juan KuntzMauricio Barahona

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