Time course of reactions controlled and gated by intramolecular dynamics of proteins: Predictions of the model of random walk on fractal lattices

Abstract

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

Universal Proximity Effect in Target Search Kinetics in the Few-Encounter Limit

“…Our results have immediate consequences for the interpretation of single-molecule reaction or binding experiments (e.g. [20] and refs. therein), that nowadays allow one to directly visualize the few-encounter regime.…”

“…A case of particular relevance is cellular signaling by specific molecules [13][14][15][16][17][18][19][20][21]. The existence and impact of significant sample-to-sample fluctuations in the precise timing of cellular regulation, often at low-copy numbers of the signaling molecules, are by now well established both experimentally and theoretically [8,[18][19][20][22][23][24][25][26]. Remarkably, despite the highly heterogeneous character of the motion of signaling molecules in the nucleus and cell cytoplasm [27][28][29] the overall signaling kinetics appears to be universally stable, thus allowing cellular operation at a remarkable precision [30].…”

“…Based on Smoluchowski's concepts first passage time statistics characterize the diffusion limitation of molecular reactions [2][3][4][5][6][7][8][9][10][11][12][13]. A case of particular relevance is cellular signaling by specific molecules [13][14][15][16][17][18][19][20][21]. The existence and impact of significant sample-to-sample fluctuations in the precise timing of cellular regulation, often at low-copy numbers of the signaling molecules, are by now well established both experimentally and theoretically [8,[18][19][20][22][23][24][25][26].…”

Geometry-controlled kinetics

“…This has recently been calculated, and a linear scaling with the volume has been demonstrated [12][13][14][15]. However, as soon as several time scales are involved, the kinetics can not be determined by the mean of the FPT only, and the entire distribution is needed [16,17].Gene transcription provides an extremely important example -which we shall repeatedly invoke in what follows -of reactions involving a small copy number of (or even single) reactants confined within a small (micron-sized) domain, and whose kinetics must be precisely regulated to fulfill vital cell functions. Interest in the question of how geometrical parameters impact on the kinetics of such transcriptional reactions and could act as regulatory factors has recently increased, mainly because of new experimental tools that enable the observation of the real-time production of proteins at the single molecule level [4].…”

“…This has recently been calculated, and a linear scaling with the volume has been demonstrated [12][13][14][15]. However, as soon as several time scales are involved, the kinetics can not be determined by the mean of the FPT only, and the entire distribution is needed [16,17].…”