Modeling stochasticity in biochemical reaction networks

Constantino, Pedro H.; Vlysidis, Michail; Smadbeck, Patrick; Kaznessis, Yiannis N.

doi:10.1088/0022-3727/49/9/093001

Cited by 13 publications

(17 citation statements)

References 84 publications

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“…Most of these involve some approximation that renders their results inexact and potentially misleading. Those that retain the exactness of Gillespie's algorithm remain fundamentally limited in that they must simulate every reaction 3 .…”

Section: Introductionmentioning

confidence: 99%

Dynamic bounds on stochastic chemical kinetic systems using semidefinite programming

Dowdy

Barton

2018

The Journal of Chemical Physics

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Applying the method of moments to the chemical master equation appearing in stochastic chemical kinetics often leads to the so-called closure problem. Recently, several authors showed that this problem can be partially overcome using moment-based semidefinite programs (SDPs). In particular, they showed that moment-based SDPs can be used to calculate rigorous bounds on various descriptions of the stochastic chemical kinetic system's stationary distribution(s)-for example, mean molecular counts, variances in these counts, and so on. In this paper, we show that these ideas can be extended to the corresponding dynamic problem, calculating time-varying bounds on the same descriptions.

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Section: Introductionmentioning

confidence: 99%

Dynamic bounds on stochastic chemical kinetic systems using semidefinite programming

Dowdy

Barton

2018

The Journal of Chemical Physics

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“…Although the approach has been validated for small networks of nonlinear chemical reactions with simple dynamics (Constantino et al, 2016; Smadbeck and Kaznessis, 2013), we present in this paper the first results for oscillatory systems.…”

Section: Theoretical Backgroundmentioning

confidence: 98%

Maximum entropy prediction of non-equilibrium stationary distributions for stochastic reaction networks with oscillatory dynamics

Constantino

Kaznessis

2017

Chemical Engineering Science

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Many chemical reaction networks in biological systems present complex oscillatory dynamics. In systems such as regulatory gene networks, cell cycle, and enzymatic processes, the number of molecules involved is often far from the thermodynamic limit. Although stochastic models based on the probabilistic approach of the Chemical Master Equation (CME) have been proposed, studies in the literature have been limited by the challenges of solving the CME and the lack of computational power to perform large-scale stochastic simulations. In this paper, we show that the infinite set of stationary moment equations describing the stochastic Brusselator and Schnakenberg oscillatory reactions networks can be truncated and solved using maximization of the entropy of the distributions. The results from our numerical experiments compare with the distributions obtained from well-established kinetic Monte Carlo methods and suggest that the accuracy of the prediction increases exponentially with the closure order chosen for the system. We conclude that maximum entropy models can be used as an efficient closure scheme alternative for moment equations to predict the non-equilibrium stationary distributions of stochastic chemical reactions with oscillatory dynamics. This prediction is accomplished without any prior knowledge of the system dynamics and without imposing any biased assumptions on the mathematical relations among species involved.

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“…In this section, we briefly discuss the elements of the ZI-closure scheme. More details on the method can be found in [ 14 , 35 , 36 ].…”

Section: Zero-information Closure Schemementioning

confidence: 99%

“…The dependence of the lower-order vector

on the higher-order one

is evident in this equation. This is the closure scheme challenge, which we have previously solved by developing the ZI-closure scheme [ 14 , 35 , 36 ].…”

Section: Zero-information Closure Schemementioning

confidence: 99%

On Differences between Deterministic and Stochastic Models of Chemical Reactions: Schlögl Solved with ZI-Closure

Vlysidis

Kaznessis

2018

Entropy

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Deterministic and stochastic models of chemical reaction kinetics can give starkly different results when the deterministic model exhibits more than one stable solution. For example, in the stochastic Schlögl model, the bimodal stationary probability distribution collapses to a unimodal distribution when the system size increases, even for kinetic constant values that result in two distinct stable solutions in the deterministic Schlögl model. Using zero-information (ZI) closure scheme, an algorithm for solving chemical master equations, we compute stationary probability distributions for varying system sizes of the Schlögl model. With ZI-closure, system sizes can be studied that have been previously unattainable by stochastic simulation algorithms. We observe and quantify paradoxical discrepancies between stochastic and deterministic models and explain this behavior by postulating that the entropy of non-equilibrium steady states (NESS) is maximum.

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Modeling stochasticity in biochemical reaction networks

Cited by 13 publications

References 84 publications

Dynamic bounds on stochastic chemical kinetic systems using semidefinite programming

Dynamic bounds on stochastic chemical kinetic systems using semidefinite programming

Maximum entropy prediction of non-equilibrium stationary distributions for stochastic reaction networks with oscillatory dynamics

On Differences between Deterministic and Stochastic Models of Chemical Reactions: Schlögl Solved with ZI-Closure

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