BioRxiv
bioRxiv Subject Collection: Systems Biology
This feed contains articles for bioRxiv Subject Collection "Systems Biology"
The impossible challenge of estimating non-existent moments of the Chemical Master Equation
Motivation: The Chemical Master Equation is a set of linear differential equations that describes the evolution of the probability distribution on all possible configurations of a (bio-)chemical reaction system. Since the number of configurations and therefore the dimension of the CME rapidly increases with the number of molecules, its applicability is restricted to small systems. A widely applied remedy for this challenge are moment-based approaches which consider the evolution of the first few moments of the distribution as summary statistics for the complete distribution. Here, we investigate the performance of two moment-estimation methods for reaction systems whose equilibrium distributions encounter heavy-tailedness and hence do not possess statistical moments. Results: We show that estimation via Stochastic Simulation Algorithm trajectories lose consistency over time and estimated moment values span a wide range of values even for large sample sizes. In comparison, the Method of Moments returns smooth moment estimates but is not able to indicate the non-existence of the allegedly predicted moments. We furthermore analyze the negative effect of a CME solution’s heavy-tailedness on SSA run times and explain inherent difficulties. While moment estimation techniques are a commonly applied tool in the simulation of (bio-)chemical reaction networks, we conclude that they should be used with care, as neither the system definition nor the moment estimation techniques themselves reliably indicate the potential heavy-tailedness of the CME’s solution.
Wagner, V., Radde, N.
February 10, 2023
http://biorxiv.org/cgi/content/short/2023.02.08.527667v1?rss=1