Influence of fractal kinetics on molecular recognition

Abstract

Molecular recognition is a central issue for nearly every biological mechanism. The analysis of molecular recognition to has been conducted within the framework of classical chemical kinetics, in which the kinetic orders of a reaction have positive integer values. However, recent theoretical and experimental advances have shown that the assumption inherent in this classical framework are invalid under a variety of conditions in shown that the assumptions inherent in this classical framework are invalid under a variety of condition in which the reaction environment may be considered nonideal. A good example is provided by reactions that are spatially constrainal and diffusion limited. Bio molecular reactions confined within two-dimensional membranes, one-dimensional channels or fractal surfaces in general exhibit kinetic orders that are noninteger. An appropriate framework for the study of these nonideal phenomena is provided by the Power-Law formalism, which includes as special cases the Mass-Action formalism of chemical kinetics and the Michaelis–Menten formalism of enzyme kinetics. The Power-Law formalism is an appropriate representation not only for fractal kinetics per se , but also for other nonideal kinetic phenomena, provided the range of variation in concentration is not too large. After defining some elementary concepts of molecular recognition, and showing how these are manifested in classical kinetic terms, this paper contrasts the implications of classical and fractal kinetics in a few simple cases. The principal distinction lies in the ability of fractal kinetics to nonlinearly transform, rather than proportionally transmit, the input S/N ratio. As a consequence, fractal kinetics create a threshold for the input signal below which no recognition occurs and above which amplified recognition takes place. Thus, fractal kinetics implies an intimate relationship between design of the physiological mechanisms regulating the environment of the process and design of the molecular process itself. These results also suggest that recognition in the presence of a favorable input ration would emphasize rapid reactions, while recognition in the presence of an unfavorable input ratio would emphasize slow reactions.