Non-Equilibrium Phase Transitions in Enzyme Reaction Systems

The reaction-diffusion equation for an enzyme-controlled reaction is studied. It is shown that in the presence of a substrate inhibition of second (fourth) order two (three) uniform and stable stationary states exist. Following the method of Schlögl (1972) the posssibility of a spatial separation of these substrate phases is investigated. For plane and spherical boundary layers between the different phases the coexistence values of the reaction parameters (substrate input, decay rate, inhibition rate etc.) are found by a method analogous to the Maxwellian construction for the coexistence-line of a van der Waals gas. For deviations from the coexistence values the transition region between the phases is not at rest but moves with constant velocity and finally the system turns to a uniform stable state. Several aspects of the stochastic theory of the given reaction are discussed.

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