Dynamics of the Electron Transfer Reaction in Cytochrome b_5

电子转移是化学和生物学中最基本的过程之一。通过经典模型、半经典模型和量子模型建立了描述非绝热电子转移过程的理论框架。在所有这些理论中，基本假设是电子传递速率常数可以分为两个因子——电子耦合因子和弗兰克-康登因子。本文提出了一种新的方法来理解蛋白质模式与电子转移反应之间的关系，特别是与Frank-Condon因子的关系。我们提出了一个简化的自旋玻色子哈密顿模型，其中玻色子浴由调和蛋白正常模式或由主成分分析确定的集体模式表示。溶剂效应被纳入了坦福德-柯克伍德模型。自旋玻色子模型已经在前人的研究中应用于电子转移问题。然而，我们的工作带来了几个新的方面。我们的出发点是频域的正态分析。这使我们能够在结构上识别蛋白质和溶剂中的所有浴模式。如果要将蛋白质的特定结构波动与电子转移耦合联系起来，这是很重要的。因此，我们的模型具有自旋玻色子模型的所有优点，另外还有一个优点，即单个槽模式不再是空间匿名的。目前的分析不仅限于谐波正常模式，而是可以使用数据从分子动力学运行和通过主成分分析。

Electron transfer is one of the most fundamental process in chemistry and biology. Theoretical frameworks describing non-adiabatic electron transfer process is well established through classical, semiclassical and quantum models. In all these theories, the basic assumption is that the electron transfer rate constant can be partitioned into two factors-the electronic coupling factor and the Frank-Condon factor.A new aproach is proposed in order to understand the relation between the protein modes and the electron transfer reaction, especially the Frank-Condon factor. We have presented a reduced spin-boson hamiltonian model where the bosonic bath is represented by the harmonic protein normal modes or the collective modes determined by the principal component analysis. Solvent effect is incorporated by the Tanford-Kirkwood model.The spin-boson model have been applied to the problem of electron transfer by others in previous studies. However, there are several new aspects that our work brings out. Our starting point is the normal mode analysis in the frequency domain. This allowed us to structurally identify all the bath modes in protein and solvent. This is important if one ones to correlate specific structural fluctuations of the protein to electron transfer coupling. Thus our model has all the advantages of a spin-boson model, with the added advantage that the individual bath modes are no more spatially anonymous. The present analysis is not just restricted to harmonic normal modes, but instead one can use data from a molecular dynamics run and through a principal component analysis.