Theoretical Studies On The Dynamic Aspects Of Macromolec

在本报告所述期间，发表了关于下列主题的论文：（1）通过NMR弛豫在多个场探测钙调素的畴运动（2）分析非平衡单分子拉伸实验以获得动力学信息（3）分析单大分子荧光共振能量转移实验以获得蛋白质折叠的自由能分布（4）单分子动力学中跃迁的统计。第一篇论文涉及的问题，分析核磁共振弛豫数据产生的信息的幅度和时间尺度的域间运动的蛋白质，是一个合作与实验组尼科Tjandra。这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，介绍了一种从实验中提取动力学信息的新方法，在实验中，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的罕见跃迁，例如蛋白质的解折叠或配体的解离。我们的程序是基于一个简单的微观模型的严格分析，并已对计算机模拟的结果进行了测试。这是比传统的方法，并有望取代it. The最后两个文件处理的理论解释福斯特共振能量转移实验蛋白质折叠。在这些实验中，由施主和受主发射的光子数被监测。这些包含结构信息，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。给出了一个任意的动力学方案，我们展示了如何计算固定时间窗口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种状态的折叠-展开动力学的分布，并确定了从这种分布中提取的自由能分布如何取决于时间窗口的大小。这种分析对于有意义地解释实验是必不可少的。

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.