Chemical model of reaction cascades induced by activated enzymes or catalysts. Two-step cascades in visual transduction.

A dissipative system is approximated by a nonlinear rate equation: Z congruent to K1Z - K2Z3 (K2 greater than 0), in which the right side is derived from -delta G/delta Z of Taylor's series of the thermodynamic potential given by Gibbs' function G(Tc, Pc) (Z) at about the critical point C(Tc, Pc) of the control variables (parameters) T and P. The stability or instability of the system is treated by the changes in the control parameters. In the case that T not equal to P not equal to 0 in the steady state, Z = 0, and T and P pass the point C, K1 becomes negative. By this change, the G function is convex at Z = 0 and each product is created rapidly with concentration or number of the molecules Z = ([K1]/K2)1/2. This dynamic theory is applied to enzyme cascades. Based on cyclic GMP (cGMP) hypothesis in visual transduction, the cascade hydrolysis of cGMP of vertebrates is analyzed by dividing it into two-step reaction cascades: The initial process is that metarhodopsin II catalyzes the exchange of GDP for GTP by transducin (Gtd) and that GTP-Gtd complex is hydrolyzed to GDP-Gtd complex. In the following cascade cGMP is hydrolyzed with amplification of phosphodiesterase (PDE) activated by the removal of the small inhibitory subunit. The quantity of the hydrolysis of cGMP is estimated as approximately 5 x 10(4-5) molecules per photolyzed rhodopsin semiempirically, and this coincides well with experiments.