Theoretical Studies On The Dynamic Aspects Of Macromolecular Function

为了理解多肽链如何折叠成定义明确的三维结构，必须能够表征这种单分子反应的过渡态系综的性质。理论上，该系综被定义为pfold等于一半的构象的集合。构象的pfold是蛋白质从该构象开始在其展开之前折叠的概率。在实验上，这个合奏是探讨的φ值分析。测量的phi值是当系统被氨基酸突变扰动时，折叠速率和平衡常数的比值变化的比率。pH值分析是实验研究蛋白质折叠机理的重要手段。我们最近发现了这些量之间一种意想不到的定量关系。除了奠定理论基础的φ值分析，我们的结果应该证明有用的微观模型的框架内进行这样的分析，大量的构象状态。 最近，我们在研究单个大分子行为的能力上取得了巨大的进步。 这些新的实验需要复杂的尖端技术和新的理论方法来解释它们。正如去年所报道的，我们已经开发了一种新的理论，从使用光镊和原子力显微镜进行的单分子拉伸实验中提取动力学信息（特别是激活的固有速率和自由能）。今年，与Amit Meller的实验小组合作，我们发表了我们认为将成为一篇有影响力的文章，将这一理论应用于单个DNA发夹的纳米孔解压缩。 在这些实验中，单个DNA分子通过将其穿过纳米孔而变性，所述纳米孔通过在脂质双层中重构通道蛋白而形成。分析了两种类型的测量：在恒定电压下的解压缩和在恒定电压斜坡速度下的解压缩。一个理论表达式，涉及这两种不同的实验进行了测试，发现是非常准确的。这以一种无模型的方式确立了这样一个事实，即这两个协议产生了关于破裂过程性质的相同信息。微观方法的基础上的Kramers理论的扩散势垒交叉使我们能够获得不仅是本征速率和过渡态的位置，但也活化的自由能。这是一个显着的进步，通常使用的现象学方法。因此，我们相信，我们的程序将成为事实上的标准方式解释实验数据在这个迅速崛起的领域。

To understand how polypeptide chains can fold into well-defined three-dimensional structures, one must be able to characterize the nature of the transition state ensemble of this unimolecular reaction.. Theoretically, this ensemble is defined as the set of conformations with pfold equal to a half. The pfold of a conformation is the probability that starting from this conformation the protein folds before it unfolds. Experimentally, this ensemble is probed by phi-value analysis. The measured phi value is the ratio of the changes in the logarithms of the folding rate and the equilibrium constant when the system is perturbed by an amino-acid mutation. Phi-value analysis is the most important way the mechanism of protein folding is studied experimentally. We have recently discovered an unexpected quantative relation between these quantaties. In addition to laying the theoretical foundation of phi-value analysis, our results should prove usefull in performing such analyses within the framework of microscopic models with a large number of conformational states. Dramatic advances have been made recently in our ability to study the behavior of single macromolecules. These new experiments require sopisticated cutting-edge technologies and the development of new theoretical approaches to interpret them. As reported last year, we have developped a novel theory to extract kinetic information ( specifically the intrinsic rates and free energies of activation) from single molecule pulling experiments performed using optical tweezers and atomic force microscopes. This year, in collaboration with the experimental group of Amit Meller, we published, what we believe will become an influential article, that applies this theory to the nanopore unzipping of individual DNA hairpins. In these experiments, a single DNA molecule is denatured by threading it through a nanopore which is formed by reconstituting a channel protein in a lipid bilayer. Two types of measurements were analyzed: unzipping at constant voltage and unzipping at constant voltage ramp speeds. A theoretical expression that relates these two different kinds of experiments was tested and found to be remarkably accurate. This established, in a model-free way, the fact that these two protocals yield the same information about the nature of the rupture process. Microscopic approaches based on the Kramers theory of diffusive barrier crosssing allowed us to obtain not only the intrinsic rates and transition state locations but also the free energies of activation. This represents a significant advance over the commonly used phenomenological approach. Consequently we believe that our procedure will become the de facto standard way of interpreting experimental data in this rapidly emerging area.