A self-organized chemical model and reaction cascade.

Some reaction cascades in biological systems are analyzed by a self-organized chemical model, an autocatalytic reaction. This model is described by the coupling of a primary system which stabilizes the initial stage of the reaction rapidly and a partial system which controls the primary system slowly. By the internal force caused by a trigger above the threshold, the coupled system in near-equilibrium is broken and changed into a new state. From the rate equation for the coupled system, a dimensionless nonlinear state equation, n = -n3 - un - v, is derived, where n is the concentration of intermediate, and u, v are dynamic variables of the system. This equation is similar to a nonequilibrium tri-molecular reaction. By using this chemical network theory, fibrin polymerization. F + F----fm----fp + X, where F is a fibrinogen molecule, fm is a fibrin monomer, fp is fibrin polymer, and X is small peptides released from fibrinogen, is discussed as an excellent example of the enzyme reaction cascade.