How do biomolecular systems speed up and regulate rates?

Abstract

The viability of a biological system depends upon careful regulation of the rates of various processes. These rates have limits imposed by intrinsic chemical or physical steps (e.g., diffusion). These limits can be expanded by interactions and dynamics of the biomolecules. For example, (a) a chemical reaction is catalyzed when its transition state is preferentially bound to an enzyme; (b) the folding of a protein molecule is speeded up by specific interactions within the transition-state ensemble and may be assisted by molecular chaperones; (c) the rate of specific binding of a protein molecule to a cellular target can be enhanced by mechanisms such as long-range electrostatic interactions, nonspecific binding and folding upon binding; (d) directional movement of motor proteins is generated by capturing favorable Brownian motion through intermolecular binding energy; and (e) conduction and selectivity of ions through membrane channels are controlled by interactions and the dynamics of channel proteins. Simple physical models are presented here to illustrate these processes and provide a unifying framework for understanding speed attainment and regulation in biomolecular systems.

A minimum-reaction-flux solution to master-equation models of protein folding

“…As noted previously, 15 Eq. ͑22a͒ and ͑22b͒ is what is predicted by transition-state theory if the unfolded state is as specified by Zwanzig.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] In such models, the conformational space of a protein is reduced to a discrete collection of macrostates, and transitions between the macrostates are described as rate processes. With the increase in the number of macrostates, the folding problem can be modeled more and more realistically.…”

“…15 It was recognized that an approximate solution, proposed by Zwanzig 2 based on a local thermodynamic equilibrium assumption for his master-equation model can be obtained from a transition-state theory. Zwanzig's model is one dimensional, i.e., the macrostates are specified by a single discrete variable, which is the number of ordered residues in a protein.…”

“…In a transition-state theory for calculating the folding rate constant k f , 15 the unfolded set of macrostates is assumed to take an equilibrium distribution ͑and the folded state unoccupied͒. One then obtains…”

Facilitated Protein-DNA Binding: Theory and Monte Carlo Simulation

“…The protein can find its target much faster than simple diffusion-reaction theories predict. Numerous experimental and theoretical studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] make us believe that diffusive sliding along DNA greatly facilitates the binding process between DNA and protein.…”