Chemical dynamic approach to synergetics and instability in biological systems

Based on Haken's theory, self-organization or synergetics is discussed using chemical dynamics to represent an autocatalytic reaction. In a simple case the changes in a self-organizing system are given by a set of two rate equations for a primary and a partial system. When these systems mutually form a feedback loop under the adiabatic condition, the rate equation of self-organization is described by a generalized Gibbs' free energy change delta U (delta x) followed by the reaction. The sign of the parameter k'3 (k0-kex; k0, kex: rate constants with or without an external stimulus) determines the instability of the coupled system in quasi-equilibrium (k'3 approximately greater than 0; k0 greater than kex). When the product exceeds the threshold (k'3 less than 0; k0 less than kex), the system transfers into a new state, or a phase transition appears. Considering the Boltzmann distribution, the transition parameter k'3 is evaluated by an average distribution of the states and the instability is discussed using the reaction velocities vqe and vqe in the quasi-equilibrium state. As an example of this model membrane excitation is discussed briefly.