2008/07/28 by Radek Erban, S. Jonathan Chapman, Erban, Radek +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Chemistry · Physics and Astronomy · #Chemical Physics (physics.chem-ph) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Gene Regulatory Network Analysis #stochastic dynamics and bifurcation #thermodynamics and calorimetric analyses
paper · pdf · doi:10.48550/arxiv.0807.4498
openalex publication_date 2008/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs for example in the modelling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) is studied. Our approach is based on the chemical Fokker-Planck equation. To get some insights into advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, before the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size.