Switching Dynamics in Reaction Networks Induced by Molecular Discreteness
arXiv:physics/0612060 · doi:10.1088/0953-8984/19/6/065150
Abstract
To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however, the discreteness in the number of molecules cannot be neglected since the number of molecules must be an integer. This discreteness can be important in biochemical reactions, where the total number of molecules is not significantly larger than the number of chemical species. To elucidate the effects of such discreteness, we study autocatalytic reaction systems comprising several chemical species through stochastic particle simulations. The generation of novel states is observed; it is caused by the extinction of some molecular species due to the discreteness in their number. We demonstrate that the reaction dynamics are switched by a single molecule, which leads to the reconstruction of the acting network structure. We also show the strong dependence of the chemical concentrations on the system size, which is caused by transitions to discreteness-induced novel states.
11 pages, 5 figures
References in corpus (7)
- The Importance of Being Discrete - Life Always Wins on the Surface
- Transitions Induced by the Discreteness of Molecules in a Small Autocatalytic System
- Molecular Discreteness in Reaction-Diffusion Systems Yields Steady States Not Seen in the Continuum Limit
- Adaptation of Autocatalytic Fluctuations to Diffusive Noise
- Alteration of Chemical Concentrations through Discreteness-Induced Transitions in Small Autocatalytic Systems
- "Quantum phase transitions" in classical nonequilibrium processes
- Discreteness-induced Stochastic Steady State in Reaction Diffusion Systems: Self-consistent Analysis and Stochastic Simulations