Dynamical singularities in ultradiffusion

A synthetic picture of intramolecular dynamics of proteins. Towards a contemporary statistical theory of biochemical processes

An increasing body of experimental evidence indicates the slow character of internal dynamics of native proteins. The important consequence of this is that theories of chemical reactions, used hitherto, appear inadequate for description of most biochemical reactions. Construction of a contemporary, truly advanced statistical theory of biochemical processes will need simple but realistic models of microscopic dynamics of biomolecules. In this review, intended to be a contribution towards this direction, three topics are considered. First, an intentionally simplified picture of dynamics of native proteins which emerges from recent investigations is presented. Fast vibrational modes of motion, of periods varying from 10(-14) to 10(-11) s, are contrasted with purely stochastic conformational transitions. Significant evidence is adduced that the relaxation time spectrum of the latter spreads in the whole range from 10(-11) to 10(5) s or longer, and up to 10(-7) s it is practically quasi-continuous. Next, the essential ideas of the theory of reaction rates based on stochastic models of intramolecular dynamics are outlined. Special attention is paid to reactions involving molecules in the initial conformational substrates confirmed to the transition state, which is realized in actual experimental situations. And finally, the two best experimentally justified classes of models of conformational transition dynamics, symbolically referred to as "protein glass" and "protein machine", are described and applied to the interpretation of a few simple biochemical processes, perhaps the most important result reported is the demonstration of the possibility of predominance of the short initial condition-dependent stage of protein involved reactions over the main stage described by the standard kinetics. This initial stage, and not the latter, is expected to be responsible for the coupling of component reactions in the complete enzymatic cycles as well as more complex processes of biological free energy transduction.

Analysis of fractal ion channel gating kinetics: kinetic rates, energy levels, and activation energies

Ion channels in the cell membranes of the corneal endothelium, hippocampal neurons, and fibroblasts, and gramicidin channels in lipid bilayers have open and closed times that can be fit, in whole or part, by power law distributions. That is, the gating is self-similar when viewed at different time scales. Hence, kinetic processes at slow and fast time scales are not independent but rather are interrelated. To study how such a relationship can arise we analyze a closed in equilibrium open channel with the fractal dimension for leaving the closed state DCO approximately 2 and the fractal dimension for leaving the open state DOC approximately 1. This special case can be analyzed because it can be represented by equivalent Markov processes. We show that it is equivalent to Markov chains with forward and backward kinetic rate constants approximately equal at each stage, and forming an approximate geometric progression along the different stages. These kinetic rates determine the energy levels and activation energy barriers separating those levels. We find that there are many conformational states (substates) separated by high activation energy barriers. This is similar to the energy structure found for globular proteins such as myoglobin. However, the novel feature reported here is that the activation energy barriers are not independent but are interrelated and form an arithmetic progression. Because of this relationship the fast processes across the low activation energy barriers are linked to slow processes across the high activation energy barriers.