Theoretical Studies On The Dynamic Aspects Of Macromolec

在本报告所述期间，发表了涉及以下主题的论文：(1)利用核磁共振弛豫技术探测钙调素在多个场中的结构域运动(2)非平衡单分子拉动实验产生动力学信息的分析(3)单大分子荧光共振能量转移实验产生蛋白质折叠的自由能谱的分析(4)单分子动力学跃迁的统计。第一篇论文是与Nico Tjandra的实验小组合作，研究分析核磁共振弛豫数据以获得关于蛋白质结构域间运动的幅度和时间尺度的信息的问题。这一领域一直是我们的长期利益之一。剩下的三篇论文涉及我们的主要新兴趣，即单分子实验的分析。第一个是与我的同事Gerhard Hummer合作完成的，提出了一种从实验中提取动力学信息的新方法，在这些实验中，激光镊子或原子力显微镜施加的机械力被用来驱动单个分子中罕见的转变，如蛋白质的展开或配体的解离。我们的程序基于对一个简单的微观模型的严格分析，并已与计算机模拟的结果进行了测试。它比传统的方法要好得多，有望取代它。最后两篇论文涉及解释蛋白质折叠上的Forster共振能量转移实验所需的理论。在这些实验中，对施主和受主发射的光子数量进行了监测。它们包含结构信息，因为供体和受体之间的能量转移效率取决于它们之间的距离。在给定任意动力学方案的情况下，我们说明了如何计算在固定时间窗下所获得的能量转移的概率分布。我们特别考虑了随机卷曲蛋白质和两态折叠-去折叠动力学的分布，并确定了从这些分布中提取的自由能分布如何依赖于时间窗口的大小。这种分析对于解释实验的意义是必不可少的。

In this reporting period, papers dealing with the following topics appeared in print: (1)The domain motions of calmodulin probed by NMR relaxation at multiple fields (2)The analysis of nonequilibrium single molecule pulling experiments to yield kinetic information (3) The analysis of single macromolecule fluorescence resonance energy transfer experiments to yield free-energy profiles of protein folding (4)The statistics of transitions in single molecule kinetics. The first paper deals with the problem of analyzing NMR relaxation data to yield information about the amplitude and time scale of interdomain motions in proteins and is a collaboration with the experimental group of Nico Tjandra. This area has been one of our long term interests. The remaining three papers deal with our main new interest, namely the analysis of single molecule experiments. The first of these,done in collaboration with my colleague Gerhard Hummer, intoduces a new approach to extract kinetic information from experiments in which mechanical forces exerted by laser tweezers or atomic force microscopes are used to drive rare transitions in single molecules such as unfolding of a protein or dissociation of a ligand. Our procedure is based on the rigorous analysis of a simple microscopic model and has been tested against the result of computer simulation. It is much better than the conventional approach and is expected to replace it. The last two papers deal with the theory required to interpret Forster resonance energy transfer experiments on protein folding. In these experiments the number of photons emitted by a donor and an acceptor are monitoried. These contain structural information because the efficiency of energy transfer between tne donor and acceptor depend on the distance between them. Given an arbitrary dynamical scheme we showed how to calculate the probability distribution of the energy transfer obtained for fixed time windows. We specifically considered the distributions for a random coil protein and for two state folding-unfolding kinetics and determined how the free energy profiles extracted from such distributions depend on the size of the time window. This kind of analysis is essential for the meanigful interpretation of experiments.