TY - JOUR

T1 - Stochastic analysis of Chemical Reaction Networks using Linear Noise Approximation

AU - Cardelli, Luca

AU - Kwiatkowska, Marta

AU - Laurenti, Luca

PY - 2016

Y1 - 2016

N2 - Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analyzed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approximate model checking algorithm based on the Linear Noise Approximation (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order polynomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on four case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deterministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN.

AB - Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analyzed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approximate model checking algorithm based on the Linear Noise Approximation (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order polynomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on four case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deterministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN.

KW - Applied Mathematics

KW - Biochemistry, Genetics and Molecular Biology (all)

KW - Chemical Reaction Networks

KW - Linear Noise Approximation

KW - Model checking

KW - Modeling and Simulation

KW - Probabilistic logic

KW - Statistics and Probability

KW - Applied Mathematics

KW - Biochemistry, Genetics and Molecular Biology (all)

KW - Chemical Reaction Networks

KW - Linear Noise Approximation

KW - Model checking

KW - Modeling and Simulation

KW - Probabilistic logic

KW - Statistics and Probability

UR - http://hdl.handle.net/10807/94546

UR - http://www.elsevier.com/locate/biosystems

U2 - 10.1016/j.biosystems.2016.09.004

DO - 10.1016/j.biosystems.2016.09.004

M3 - Article

SN - 0303-2647

VL - 149

SP - 26

EP - 33

JO - BioSystems

JF - BioSystems

ER -