Theoretical Studies On The Dynamic Aspects Of Macromolecular Function

允许代谢物在细胞或不同细胞间交换的膜通道是具有充满水的孔洞的蛋白质结构。传统上，这样的通道被认为是分子筛，它只根据大小区分不同的溶质。换句话说，它们被认为是低选择性结构，允许溶质通过，而不与通道孔有任何显著的相互作用。我们已经展示了自然界如何在原则上利用和调整溶质-孔相互作用，以这种方式最大化溶质通量(即每秒转移的分子数量)，从而提高通道的效率。基本思想是，当通道中只能有一种溶质时，通量必须作为溶质-通道相互作用的函数具有最大值。物理上的原因如下：如果相互作用太吸引，溶质永远不会离开通道，从而阻止其他分子通过。如果太过排斥，溶质分子就永远不会进入通道。由于通量在这两个极限中都为零，因此一定存在输运最快的最佳相互作用。我们为这一过程建立了一个定量的数学模型，并利用变分法确定了使通量最大化的最优通道内相互作用势。结果表明，该最佳电势向浓度较低的一侧倾斜。这导致了一种违反直觉的预测，即溶质在通道的“出口”附近比在“入口”附近更好地“结合”。此外，我们还发现，最佳相互作用势的大小取决于通道外的溶质浓度。这表明，在给定的生物体中，设计用于运输同一分子的通道蛋白可能具有不同的氨基酸序列。一个基因可能编码在高溶质浓度下起作用的通道蛋白，而另一个基因可能编码在低浓度下起作用的通道蛋白。 最近，我们在研究单个大分子的行为方面取得了巨大的进步。机械力的受控作用为研究单分子的结构、功能和动力学提供了有力的工具。这些新的实验需要理想化的尖端技术和新的理论方法来解释它们。动态力光谱探测动力学和热力学，本实验室的长期兴趣是发展分析此类实验所需的理论。为了使我们多年来取得的进展能够为广大潜在用户所用，我们在今年出版的一本书中写了一章，题为《单分子力谱的热力学和动力学》，该书汇集了来自世界各地的所有领先研究小组的贡献。 我们今年的主要贡献是开发了一种新颖而简单的程序，可以从使用光钳和原子力显微镜进行的单分子拉动实验中提取动力学信息(特别是本征活化速率和自由能)。我们方法的基石是将在不同加载速率下获得的破裂力直方图转换为在恒力实验中可测量的力相关寿命。为了解释这些与力有关的寿命，我们推导了广泛使用的贝尔公式的一个推广，该公式在Kramers扩散势垒穿越理论的框架内是准确的。我们已经通过分析DNA发夹的纳米孔解压缩和通过柔性连接物连接到原子力显微镜上的蛋白质的展开来说明我们的过程。我们已经证明，即使当分子伸缩是一个较差的反应坐标，并且必须考虑高维自由能表面时，我们的方法仍然有效。我们相信，在这个迅速崛起的领域，我们的程序将成为解释实验数据的事实上的标准方法。

Membrane channels that allow metabolites to exchange between cells or different cellular compartments are protein structures with water-filled pores. Traditionally such channels were thought to be molecular sieves which discriminate between different solutes based only on size. In other words, they were regarded as low-selectivity structures that allow passage of the solute without any significant interaction with the channel pore. We have shown how nature can in principle exploit and tune the solute-pore interaction in such a way to maximize the solute flux(i.e., the number of molecules translocated per second) and therefore increase the efficiency of the channel. The basic idea is that when only one solute can be in the channel, the flux must have a maximum as a function of the solute-channel interaction. Physically the reason is the following.If the interaction is too attractive, the solute will never leave the channel thus blocking it for the passage of other molecules. If it is too repulsive, the solute molecule will never enter the channel. Since the flux vanishes in both these limits, there must exist an optimum interaction for which the transport is the fastest. We have constructed a quantitative mathematical model for this process and using the calculus of variations determined the optimal intrachannel interaction potential that maximizes the flux. This optimum potential turns out to be tilted towards the side with lower concentration. This makes the counterintuitive prediction that it is better for the solute to "bind" more strongly near the "exit" of the channels rather than near the "entrance". In addtion we found that the value of the optimum interaction potential depends on the concentration od solute outside the channel. This suggests that in a given organism, channel proteins designed to transport the same molecule may have different amino acid sequences. One gene might code for a channel protein that functions at high solute concentrations, while another for one that works at low concentrations. Dramatic advances have been made recently in our ability to study the behavior of single macromolecules. The controlled application of mechanical forces on single molecules has provided a powerful tool to study their structure, function and dynamics. These new experiments require sopisticated cutting-edge technologies and the development of new theoretical approaches to interpret them. Dynamic force spectroscopy probes both kinetics and thermodynamics and a long term interest of this laboratory has been the development of the theory required to analyze such experiments. In order to make the advances we made over the years accessible to a wide audience of potential users, we have written a chapter entitled "Thermodynamics and Kinetics from Single-Molecule Force Spectroscopy" in a book published this year that contains contributions from all the leading research groups throuhout the world. The major contribution we made this year was the development of a novel and simple procedure 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. The cornerstone of our method is a transformation ot the rupture-force histograms obtained at different force-loading rates into the force dependent lifetimes measurable in contant-force experiments. To interpret these force dependent lifetimes we derived a generalization ot the widely-used Bell's formula that is exact within the framework of Kramers theory of diffusive barrier crossing. We have illustrated our procedure by analyzing the nanopore unzipping of DNA hairpins and the unfolding of a protein attached by flexible linkers to an atomic force miscroscope. We have shown that our approach remains valid even when the molecular extension is a poor reaction coordinate and higher dimensional free energy surfaces must be considered. We believe that our procedure will become the de facto standard way of interpreting experimental data in this rapidly emerging area.