Time-dependent product-form Poisson distributions for reaction networks with higher order complexes

Autor: David Schnoerr, David F. Anderson, Chaojie Yuan
Rok vydání: 2019
Předmět:
Molecular Networks (q-bio.MN)
Poisson distribution
01 natural sciences
Quantitative Biology - Quantitative Methods
Models
Biological
010305 fluids & plasmas
03 medical and health sciences
symbols.namesake
0103 physical sciences
Master equation
FOS: Mathematics
Quantitative Biology - Molecular Networks
Gene Regulatory Networks
Statistical physics
Poisson Distribution
Representation (mathematics)
Quantitative Methods (q-bio.QM)
030304 developmental biology
Mathematics
0303 health sciences
Stochastic Processes
Stationary distribution
Stochastic process
Applied Mathematics
Systems Biology
Probability (math.PR)
Mathematical Concepts
Agricultural and Biological Sciences (miscellaneous)
Markov Chains
Term (time)
Kinetics
Models
Chemical
Nonlinear Dynamics
Modeling and Simulation
Product (mathematics)
FOS: Biological sciences
symbols
Linear Models
Distribution (differential geometry)
Mathematics - Probability
Metabolic Networks and Pathways
Signal Transduction
Zdroj: Journal of mathematical biology. 80(6)
ISSN: 1432-1416
Popis: It is well known that stochastically modeled reaction networks that are complex balanced admit a stationary distribution that is a product of Poisson distributions. In this paper, we consider the following related question: supposing that the initial distribution of a stochastically modeled reaction network is a product of Poissons, under what conditions will the distribution remain a product of Poissons for all time? By drawing inspiration from Crispin Gardiner's "Poisson representation" for the solution to the chemical master equation, we provide a necessary and sufficient condition for such a product-form distribution to hold for all time. Interestingly, the condition is a dynamical "complex-balancing" for only those complexes that have multiplicity greater than or equal to two (i.e. the higher order complexes that yield non-linear terms to the dynamics). We term this new condition the "dynamical and restricted complex balance" condition (DR for short).
Comment: Corrected an error in the proof of Lemma 2.1. Added examples and images from simulation results
Databáze: OpenAIRE
Externí odkaz: