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，它们的响应可以作为时间的函数来跟踪。这些实验揭示了关于单个生物分子的结构、动力学和相互作用的基本新颖和独特的信息。 单分子力谱理论。然后，我们展示了这些联系如何导致从实验中提取热力学信息的新的、实用的有用方法，包括结合和展开自由能。 力作用下的蛋白质折叠：我们与英国坎布里奇大学的罗伯特·贝斯特博士合作，研究了蛋白质在机械张力下的折叠。尽管对蛋白质的机械去折叠进行了大量的研究，但在拉伸作用下成功地重新折叠蛋白质的尝试仍然相对较少。力对折叠动力学的影响可以用一维Kramers扩散势垒穿越理论来拟合，从而得到了具有物理意义的折叠活化势垒高度和位置参数。 力诱导蛋白质展开：我们与UCSD的Dudko博士和剑桥的Best博士合作，探索了一种描述在力存在下分子断裂的理论方法的有效性(与Dudko和Szabo博士合作开发；另见上文)。我们在粗粒蛋白质模型中对去折叠动力学进行了广泛的模拟。通过在广泛的拉伸力范围内和不同拉伸方向的模拟计算的展开速率，揭示了在低力时从力无关的过程到高力时的力依赖过程的翻转，类似于有时在使用化学变性剂的研究中看到的展开速率的翻转。虽然这样的利率变动在一个维度上是意想不到的，但我们证明了它可以在两个维度的动态中发生。我们的结果与蛋白质工程实验和模拟结果一致，这表明高力作用下的去折叠机制可能不同于内在机制。如果翻转发生在低力下，则可以解释实验中外推速率和内在率之间的明显相似性，这对于不同展开的障碍来说是意想不到的。

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.