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。 单分子力谱理论。 在与Szabo博士（NIDDK，NIH）和Dudko教授（UC San Diego）的合作中，我们继续开发形式化，以从单分子力谱实验中提取准确的动力学信息（Dudko等人，Proc. Natl. Acad. Sci. USA 2008）。 我们开发并应用了一个简单的程序，提取动力学信息的牵引实验转化成力依赖于恒定力实验中可测量的寿命在不同的力加载速率下获得的断裂力直方图。为了解释由此产生的力依赖的寿命，我们推导出一个广义的贝尔公式，在Kramers理论的框架内是正式准确的。这一结果补充了分析表达式的寿命，我们以前推导出的一类模型潜力。 该程序被应用于DNA发夹的纳米孔解压缩和通过柔性连接器连接到原子力显微镜的蛋白质的展开。 我们可以表明，我们的程序，以转换到力依赖的寿命断裂力直方图仍然有效，即使当分子的延伸是一个穷人的反应坐标和高维自由能表面必须考虑。 蛋白质受力折叠：与Robert Best博士（英国剑桥大学）合作，我们在Rief小组最近的一项实验研究的评论中研究了力存在下钙调蛋白的偶联折叠、钙结合和靶肽结合（Best et al. Science 2009）。 蛋白质动力学的主方程描述。在与Berezhkovskii和Szabo博士（LCP，NIDDK）的合作中，我们通过主方程描述了双态蛋白质的折叠动力学，并表明折叠和未折叠状态之间的反应通量可以用瓶颈区域中微观状态的承诺或分裂概率表示（Berezhkovskii等人，J. Chem. Phys. 2009）。这个一般的形式主义，使人们能够确定有多少通过一个分割表面的每个微观过渡的整体反应通量的贡献。我们的研究结果的通量在网络中具有复杂的连通性，得到使用离散对应的Kramers理论的活化速率过程，表明反应性的过渡的数量通常是远远小于过渡的总数，在平衡时跨越一个分割面。

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. Theory of single molecule force spectroscopy. In collaboration with Dr. Szabo (NIDDK, NIH) and Prof. Dudko (UC San Diego), we have continued our development of formalisms to extract accurate kinetic information from single-molecule force spectroscopy experiments (Dudko et al., Proc. Natl. Acad. Sci. USA 2008). We developed and applied a simple procedure to extract kinetic information from pulling experiments by transforming the rupture-force histograms obtained at different force-loading rates into the force-dependent lifetimes measurable in constant-force experiments. To interpret the resulting force-dependent lifetimes, we derived a generalization of Bells formula that is formally exact within the framework of Kramers theory. This result complements the analytical expression for the lifetime that we derived previously for a class of model potentials. The procedure was applied to the nanopore unzipping of DNA hairpins and the unfolding of a protein attached by flexible linkers to an atomic force microscope. We could show that our procedure to transform rupture-force histograms into the force-dependent lifetimes remains valid even when the molecular extension is a poor reaction coordinate and higher-dimensional free-energy surfaces must be considered. Protein folding under force: In collaboration with Dr. Robert Best (University of Cambdrige, UK) we have examined the coupled folding, calcium binding, and target peptide binding of calmodulin in the presence of force (Best et al. Science 2009) in a commentary on a recent experimental study by the group of Rief. Master-equation descriptions of protein dynamics. In collaboration with Drs. Berezhkovskii and Szabo (LCP, NIDDK), we described the folding dynamics of a two-state protein by a master equation, and showed that the reactive flux between folded and unfolded states can be expressed in terms of the commitment or splitting probabilities of the microstates in the bottleneck region (Berezhkovskii et al, J. Chem. Phys. 2009). This general formalism allows one to determine how much each microscopic transition through a dividing surface contributes to the overall reactive flux. Our results for the flux in a network with complex connectivity, obtained using the discrete counterpart of Kramers theory of activated rate processes, show that the number of reactive transitions is typically much smaller than the total number of transitions that cross a dividing surface at equilibrium.