Author: ["O. Bénichou","C. Chevalier","J. Klafter","B. Meyer","R. Voituriez"]
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Abstract
It has long been appreciated that the transport properties of molecules can control reaction kinetics. This effect can be characterized by the time it takes a diffusing molecule to reach a target—the first-passage time (FPT). Determining the FPT distribution in realistic confined geometries has until now, however, seemed intractable. Here, we calculate this FPT distribution analytically and show that transport processes as varied as regular diffusion, anomalous diffusion, and diffusion in disordered media and fractals, fall into the same universality classes. Beyond the theoretical aspect, this result changes our views on standard reaction kinetics and we introduce the concept of ‘geometry-controlled kinetics’. More precisely, we argue that geometry—and in particular the initial distance between reactants in ‘compact’ systems—can become a key parameter. These findings could help explain the crucial role that the spatial organization of genes has in transcription kinetics, and more generally the impact of geometry on diffusion-limited reactions. The time taken for a reactant to reach a target is best represented theoretically by a distribution of times. This distribution has now been calculated analytically and shows quantitatively that in the case of uncrowded environments, a reactant's starting point — in relation to the target — does not influence the search time. It does, however, have an effect in the case of crowded systems — leading to ‘geometry-controlled kinetics’. Cite this article
Bénichou, O., Chevalier, C., Klafter, J. et al. Geometry-controlled kinetics. Nature Chem 2, 472–477 (2010). https://doi.org/10.1038/nchem.622 