Stochastic analysis of Chemical Reaction Networks using Linear Noise Approximation.
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.
Department of Computer Science, University of Oxford, United Kingdom; Microsoft Research, Cambridge, United Kingdom. Electronic address: luca@microsoft.com.
Luca
L
Cardelli
Department of Computer Science, University of Oxford, United Kingdom. Electronic address: marta.kwiatkowska@cs.ox.ac.uk.
Marta
M
Kwiatkowska
Department of Computer Science, University of Oxford, United Kingdom. Electronic address: luca.laurenti@cs.ox.ac.uk.
Luca
L
Laurenti
D000465:Algorithms; D000818:Animals; D006801:Humans; D016014:Linear Models; D008956:Models, Chemical; D011336:Probability; D013269:Stochastic Processes
Chemical Reaction Networks; Linear Noise Approximation; Model checking; Probabilistic logic