On a theory of stability for nonlinear stochastic chemical reaction networks

• Published in: The Journal of chemical physics Vol. 142; no. 18; p. 184101
• Main Authors: Smadbeck, Patrick, Kaznessis, Yiannis N.
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 14.05.2015; AIP Publishing LLC
• Subjects: Algorithms; Autocorrelation functions; CHEMICAL REACTIONS; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Computation; COMPUTERIZED SIMULATION; CORRELATION FUNCTIONS; DISTURBANCES; EIGENVALUES; EQUATIONS; FLUCTUATIONS; Jacobi matrix method; Jacobian matrix; Mathematical models; MATRICES; Networks; Nonlinear Dynamics; Nonlinear equations; NONLINEAR PROBLEMS; Nonlinear systems; Organic chemistry; Physics; PROBABILITY; RELAXATION; RESPONSE FUNCTIONS; Stability; Steady state; STEADY-STATE CONDITIONS; STOCHASTIC PROCESSES; Thermodynamics; Variation
• ISSN: 0021-9606; 1089-7690; 1520-9032; 1089-7690
• DOI: 10.1063/1.4919834

We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms.