Theory of single-molecule biophysics

在单分子实验中，力可以直接施加在单个分子上，并且它们的响应可以作为时间的函数。这些实验从根本上揭示了关于单个生物分子的结构、动力学和相互作用的新颖和独特的信息。 与Amit Meller（波士顿大学）的实验组合作，我们研究了跨膜纳米孔内单个DNA发夹的力诱导解压缩（Dudko等人，Biophys. J. 2007）。 这种实验方法的目的是对单个DNA分子进行测序。 我们开发了一个系统的程序，用于从这样的力谱实验中提取动力学信息，考虑两种类型的测量被认为是：在恒定电压（或力）下解压缩，以及在恒定电压斜坡速度（或力斜坡速度）下解压缩。 通过在低到中等斜坡速度下对实验数据进行全局最大似然分析，我们可以参数化不同的理论模型。为了验证模型，我们将它们的预测与两组独立的数据进行了比较，这两组数据是在高斜坡速度和恒定电压下收集的，通过使用两种测量之间的定量关系。微观方法的基础上Kramers理论的扩散势垒交叉使我们能够估计不仅固有的速率和过渡态的位置，但也活化自由能。我们的理论模型表明，纳米孔DNA解链过渡可以准确地描述为一个两态过程。 然而，定量分析还表明，DNA与纳米孔的相互作用可以对测量速率产生显著影响，这一观察结果与分子传感器件的开发有关。 通过在单分子水平上开发线粒体质子泵细胞色素c氧化酶的动力学模型，我们首次能够鉴定这种关键酶功能的最低要求（Kim et al.，Proc. Natla. Acad. Sci. USA 2007）。在有氧生活中，氧气还原为水驱动了线粒体（或细菌）内膜上电化学梯度的产生，为ATP的产生提供动力。细胞色素c氧化酶（CcO）是催化氧还原的酶，它从细胞膜外侧吸收四个电子，从细胞膜内侧吸收四个质子。此外，大约一半的氧化还原能量用于四个额外的质子跨膜转运。尽管已经提出了许多模型来解释这种质子泵，但核心问题仍然没有答案：如何利用氧化还原化学来使质子逆着化学梯度和电势梯度移动。 为了探索这种氧化还原耦合质子泵的基本机制，我们在单分子水平上开发了符合基本物理原理的动力学模型。我们证明，对电势泵可以实现纯粹通过静电耦合，给定的电荷中心的不对称排列，然而，非线性门是非常有效的真实的酶是必不可少的。这里确定的质子泵的基本要求突出了细胞色素c氧化酶泵可能的进化起源。所确定的一般设计原则也与其他分子机器相关，并建议未来在生物燃料电池中的应用。 值得注意的是，单分子力谱理论也与使用计算机模拟的自由能计算密切相关。 在一本书的章节（Hummer，2007）中，我们建立并探索了这种联系。 我们表明，非平衡过程的统计物理学的最新发展导致一个实用的理论，单分子拉实验。 特别地，可以使用由我们（Hummer和Szabo，Proc Natl Acad Sci USA，2001）基于Jarzynski恒等式导出的非平衡关系，从非平衡拉伸实验中严格地提取热力学性质。

In single-molecule experiments forces can be exerted directly on individual molecules and their response can be followed as a function of time. These experiments reveal fundamentally novel and unique information on the structure, dynamics, and interactions of individual biomolecules. In collaboration with the experimental group of Amit Meller (Boston University), we studied the force-induced unzipping of individual DNA hairpins inside membrane-spanning nanopores (Dudko et al., Biophys. J. 2007). This experimental method has been developed with the aim of sequencing individual DNA molecules. We developed a systematic procedure for extracting kinetic information from such force-spectroscopy experiments, considering two types of measurements are considered: unzipping at constant voltage (or force), and unzipping at constant voltage-ramp speeds (or force-ramp speeds). By performing a global maximum-likelihood analysis of the experimental data at low-to-intermediate ramp speeds, we could parametrize different theoretical models. To validate the models, we compared their predictions with two independent sets of data, collected at high ramp speeds and at constant voltage, by using a quantitative relation between the two types of measurements. Microscopic approaches based on Kramers theory of diffusive barrier crossing allowed us to estimate not only intrinsic rates and transition state locations, but also free energies of activation. Our theoretical model showed that the nanopore DNA unzipping transition can be described accurately as a two-state process. However, the quantitative analysis also showed that the interactions of the DNA with the nanopore can have a significant effects on the measured rates, an observation relevant for the development of molecular sensing devices. By developing a kinetic model of the mitochondrial proton pump cytochrome c oxidase at the single-molecule level, we were able for the first time to identify the minimal requirements for the function of this key enzyme (Kim et al., Proc. Natla. Acad. Sci. USA 2007). In aerobic life, the reduction of oxygen to water drives the generation of the electrochemical gradient across the inner mitochondrial (or bacterial) membrane that powers the production of ATP. Cytochrome c oxidase (CcO), the enzyme catalyzing oxygen reduction, takes up four electrons from the outside of the membrane and four protons from the inside. In addition, roughly half of the redox energy is used for translocation of four additional protons across the membrane. Even though many models have been proposed to explain this proton pumping, the central question had remained unanswered: how redox chemistry could be harnessed to move protons against both chemical and potential gradients. To explore the fundamental mechanisms of such redox coupled proton pumps, we developed kinetic models at the single-molecule level consistent with basic physical principles. We demonstrated that pumping against an electric potential can be achieved purely through electrostatic couplings, given an asymmetric arrangement of charge centers; however, nonlinear gates are essential for highly efficient real enzymes. The fundamental requirements for proton pumping identified here highlight a possible evolutionary origin of cytochrome c oxidase pumping. The general design principles identified are relevant also for other molecular machines and suggest future applications in biology-inspired fuel cells. Remarkably, the theory of single-molecule force spectroscopy is also closely related to free energy calculations using computer simulations. In a book chapter (Hummer, 2007), we establish and explore this connection. We show that recent developments in the statistical physics of nonequilibrium processes lead to a practically useful theory of single-molecule pulling experiments. In particular, one can use non-equilibrium relations derived by us (Hummer and Szabo, Proc Natl Acad Sci USA, 2001) on the basis of Jarzynski's identity to extract thermodynamic properties rigorously from nonequilibrium pulling experiments.