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تسجيل مستخدم جديدSwitching Dynamics in Reaction Networks Induced by Molecular Discreteness
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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.
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To study the dynamics of chemical processes, we often adopt rate equations to observe the change in chemical concentrations. However, when the number of the molecules is small, the fluctuations cannot be neglected. We often study the effects of fluct
uations with the help of stochastic differential equations. Chemicals are composed of molecules on a microscopic level. In principle, the number of molecules must be an integer, which must only change discretely. However, in analysis using stochastic differential equations, the fluctuations are regarded as continuous changes. This approximation can only be valid if applied to fluctuations that involve a sufficiently large number of molecules. In the case of extremely rare chemical species, the actual discreteness of the molecules may critically affect the dynamics of the system. To elucidate the effects of the discreteness, we study an autocatalytic system consisting of several interacting chemical species with a small number of molecules through stochastic particle simulations. We found novel states, which were characterized as an extinction of molecule species, due to the discrete nature of the molecules. We also observed a strong dependence of the chemical concentrations on the size of the system, which was caused by transitions to the novel states.
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