UPMC Univ Paris 06, CNRS-UMR 7600 Laboratoire de Physique Théorique de la Matière Condensée, 4 Place Jussieu, F-75005 Paris, France.
Nat Chem. 2010 Jun;2(6):472-7. doi: 10.1038/nchem.622. Epub 2010 Apr 18.
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.
长期以来，人们一直认识到分子的输运性质可以控制反应动力学。这种效应可以用扩散分子到达目标所需的时间——首通时间（FPT）来描述。然而，直到现在，确定在现实受限几何形状中的 FPT 分布似乎还难以处理。在这里，我们通过分析计算出这个 FPT 分布，并表明从规则扩散到反常扩散，再到无序介质和分形中的扩散，各种输运过程都属于相同的普适类。除了理论方面，这一结果改变了我们对标准反应动力学的看法，并引入了“几何控制动力学”的概念。更确切地说，我们认为几何形状——特别是在“紧凑”系统中反应物之间的初始距离——可以成为一个关键参数。这些发现有助于解释基因空间组织在转录动力学中所起的关键作用，更普遍地说，解释了几何形状对扩散限制反应的影响。
