Computer simulations of random walk on the Sierpiński gasket and percolation clusters demonstrate that the short, initial condition-dependent stage of protein involving reactions can dominate the progress of the reaction over the main stage described by the standard kinetics. This phenomenon takes place if the intramolecular conformational transition dynamics modeled by the stochastic process is slow enough and the initial conformational substate of the protein already belongs to the transition state of the reaction. Both conditions are realized in two kinds of experiments: small ligand rebinding to protein after laser f lash photolysis and direct recording of single protein channel activity. The model considered suggests simple analytical formulae that can explain the time behavior of the processes observed and its variation with temperature. The initial condition-dependent stage, and not the stage described by the standard kinetics, is expected as responsible for the coupling of component reactions in the complete catalytic cycles and more complex processes of biological free energy transduction.Formulation of an advanced statistical theory of biochemical processes needs simple but realistic models of phenomena underlying microscopic dynamics of proteins. Many experiments performed since the mid-70s have indicated the existence of a slow activated dynamics of conformational transitions in the protein native phase apart from the usual much faster vibrations (1-6). The spectrum of relaxation times characterizing the conformational transition dynamics spreads over many orders of magnitude from 10 Ϫ11
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