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。 与Szabo博士（NIDDK，NIH）合作，我们开发并分析了从单分子力谱实验中提取热力学和动力学信息的形式化。 在一本书的章节（Hummer和Szabo，2008）中，我们建立了非平衡过程统计物理学的最新发展与单分子拉伸实验之间的联系。 然后，我们将展示这些连接如何导致从实验中提取热力学信息的新的，实际有用的方法，包括结合和展开自由能。 在同一章中，我们还展示了如何从单分子拉伸实验中提取动力学信息，包括蛋白质和核酸的解折叠速率。 蛋白质受力折叠：与Robert Best博士（英国剑桥大学）合作，我们研究了机械张力下蛋白质的折叠。 尽管对蛋白质的机械解折叠进行了大量的研究，但在存在拉伸力的情况下对蛋白质进行重折叠的成功尝试仍然相对较少。我们探讨了蛋白质重折叠动力学下的力量，使用模拟的粗粒度模型的泛素。力对折叠动力学的影响可以通过扩散势垒交叉的一维Kramers理论来拟合，从而得到折叠活化势垒的高度和位置的物理上有意义的参数。通过比较从不同方向拉伸得到的参数，我们发现未折叠状态在复性动力学中起主导作用。我们的研究结果解释了为什么即使在适度的拉力下，重折叠也变得非常缓慢，并建议如何在更高的力下在实验中实际观察到。 力诱导的蛋白质解折叠：在与Dudko博士（UCSD）和Best博士（剑桥）的合作中，我们探索了一种理论方法（由Dudko博士和Szabo博士合作开发;也见上文）的有效性，该方法描述了存在力时的分子断裂。我们进行了广泛的模拟粗粒度蛋白质模型的展开动力学。展开率计算从模拟在一个广泛的拉伸力，并为不同的拉动方向，揭示了一个营业额从一个力独立的过程在低力的力依赖的过程在高力，类似于翻转展开率有时看到在使用化学变性剂的研究。虽然这样的周转率是出乎意料的，在一维，我们证明，它可以发生在只有两个维度的动态。我们的研究结果与蛋白质工程实验和模拟结果雅阁，表明在高作用力下的去折叠机制可能不同于内在机制。外推和内在率在实验中，意想不到的不同的展开障碍之间的明显相似性，可以解释，如果营业额发生在低力。

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), we have developed and analyzed formalisms to extract thermodynamic and kinetic information from single-molecule force spectroscopy experiments. In a book chapter (Hummer and Szabo, 2008),we establish the connection between recent developments in the statistical physics of nonequilibrium processes and single-molecule pulling experiments. We then show how these connections lead to novel, practically useful methods of extracting thermodynamic information from the experiments, including binding and unfolding free energies. In the same book chapter, we also showed how kinetic information, including protein and nucleic acids unfolding rates, can be extracted from single-molecule pulling experiments. Protein folding under force: In collaboration with Dr. Robert Best (University of Cambdrige, UK), we have studied the folding of proteins under mechanical tension. Despite a large number of studies on the mechanical unfolding of proteins, there are still relatively few successful attempts to refold proteins in the presence of a stretching force. We explored the protein refolding kinetics under force by using simulations of a coarse-grained model of ubiquitin. The effects of force on the folding kinetics could be fitted by a one-dimensional Kramers theory of diffusive barrier crossing, resulting in physically meaningful parameters for both the height and the location of the folding activation barrier. By comparing parameters obtained from pulling in different directions, we found that the unfolded state plays a dominant role in the refolding kinetics. Our findings explain why refolding becomes very slow at even moderate pulling forces and suggest how it could be practically observed in experiments at higher forces. Force-induced protein unfolding: In collaboration with Dr. Dudko (UCSD) and Dr. Best (Cambridge), we explored the validity of a theoretical approach (developed in collaboration with by Drs. Dudko and Szabo; see also above) describing molecular rupture in the presence of force. We performed extensive simulations of the unfolding kinetics in coarse-grained protein models. Unfolding rates calculated from simulations over a broad range of stretching forces, and for different pulling directions, reveal a turnover from a force-independent process at low force to a force dependent process at high force, akin to the roll-over in unfolding rates sometimes seen in studies using chemical denaturant. While such a turnover in rates is unexpected in one dimension, we demonstrated that it could occur for dynamics in just two dimensions. Our results were found to be in accord with protein engineering experiments and simulations which indicate that the unfolding mechanism at high force can differ from the intrinsic mechanism. The apparent similarity between extrapolated and intrinsic rates in experiments, unexpected for different unfolding barriers, can be explained if the turnover occurs at low forces.