Theoretical Studies On The Dynamic Aspects Of Macromolecular Function

大分子功能动态方面的理论研究

• 批准号: 10697716
• 负责人: Attila Szabo
• 金额: $ 74.97万
• 依托单位: NATIONAL INSTITUTE OF DIABETES AND DIGESTIVE AND KIDNEY DISEASES
• 依托单位国家: 美国
• 资助国家: 美国
• 起止时间: 至
• 项目状态: 未结题
• 来源: https://reporter.nih.gov/project-details/10697716
• 关键词: Adoption; Algebra; Algorithmic Analysis; Amyloid beta-Protein; Behavior; Binding Proteins; Biological Process; Catalysis; Cells; Chemical Dynamics; Collaborations; Color; Computer Simulation; Data; Data Analyses; Derivation procedure; Development; Diffuse; Diffusion; Documentation; Dyes; Energy Transfer; Enzymes; Equilibrium; Fluorescence; Fluorescence Resonance Energy Transfer; Goals; Individual; Investigation; Kinetics; Knowledge; Label; Lasers; Lead; Learning; Likelihood Functions; Mainstreaming; Measurement; Methods; Microscopic; Molecular; Molecular Conformation; Nature; Nuclear Magnetic Resonance; Output; Paper; Peptides; Photons; Play; Positioning Attribute; Preparation; Probability; Procedures; Proteins; Publishing; Reaction; Relaxation; Reporting; Role; Sampling; Scanning Probe Microscopes; Selection Criteria; Signal Transduction; Specific qualifier value; Speed; Spottings; Statistical Mechanics; Structure; System; Techniques; Testing; Theoretical Studies; Time; Work; biological systems; chemical reaction; experimental study; fluorophore; insight; laser tweezer; light intensity; macromolecule; monomer; novel strategies; physical process; protein aggregation; protein folding; simulation; single molecule; single-molecule FRET; statistics; theories; time interval

Single-molecule FRET (smFRET) has become a mainstream technique for studying biomolecular structural dynamics. In these experiments, a molecule is illuminated by a laser, and the donor fluorophore is excited. The donor can emit a photon or transfer the excitation to an acceptor which then can emit a photon of a different color. The rate of transfer depends on the inter-dye distance and this is why there is information about conformational dynamics. The output of these experiments is a sequence of photons with recorded colors and arrival times. The distances between fluorescence labels attached to a molecule fluctuate due to conformational dynamics on a wide range of time scales. The rapid and wide adoption of smFRET experiments by an ever-increasing number of groups has generated significant progress in sample preparation, measurement procedures, data analysis, algorithms and documentation. The paper that describes the current state of the art from different perspectives that was described in the last report has now appeared in print (eLife 2021; 10:e60416, see below for DOI). This year we have been working on the analysis of single-molecule experiments to get molecule's diffusion coefficient and brightness. This work is being done in collaboration with Dr. Hoi Sung Chung from LCP, who studies oligomer formation in amyloid beta (A) aggregation on a single-molecule level. In these experiments, A-peptides are labeled by donor or acceptor fluorophores and mixed together. At the early stage of aggregation, oligomers start to form. The oligomers freely diffuse in solution and occasionally diffuse into the laser confocal spot. Inside the spot, the donor fluorophore is excited and can emit a donor photon or it can transfer the energy to the acceptor, which can emit an acceptor photon. Since the monomers can only emit donor photons, the bursts of donor and acceptor photons emitted by the oligomers can be differentiated by FRET efficiency. The number of oligomers is much smaller than that of the monomers. The question is what can we learn about oligomers from a small number of bursts of photons. Informative parameters would be the brightness and the diffusion coefficient of the molecules, which depend on the oligomer size. The standard FCS correlation function, which is commonly used to get the diffusion coefficient, is not helpful in this case, since the most intense signal comes from the monomers. Moreover, we would also like to use our knowledge of the molecules brightness, which is not included in the correlation function. To characterize the oligomers, we developed a new method that allows one to get both the diffusion coefficient and the photon count rate from a small number of selected bursts of photons. The selection criteria include thresholds for the inter-photon times, the number of photons in a burst, and the FRET efficiency. In this approach, we construct a likelihood function which accounts for these selection criteria and optimize it with respect to the parameters. To avoid complexity and to decrease the computational effort, the elongated laser spot is replaced by an effective isotropic spot with the size of the spot calculated from the condition of the best fit. We have been using the Maximum Likelihood method previously to get FRET efficiencies of single molecules, which are related to the distances between fluorophore labels, as well as the transition rates in protein folding and binding. However, including translational diffusion into analysis happened to be very challenging since burst selection modifies photon statistics and the likelihood function, and could not be circumvented. The new method has been tested by comparison with simulated photon trajectories in the elongated laser spot, and the results are promising. The diffusion coefficient and the count rate can be accurately determined from bursts with small numbers of photons. The work is still in progress, and we expect successful application of the new method to a number of important molecular systems, including protein folding and aggregation of A-peptides. In collaboration with Dr. A.M. Berezhkovskii, we published a paper which just appeared online (doi.org/10.1021/acs.jpcb.2c03757), in which we derive remarkable relations among the numbers of transitions between two boundaries (fluxes), the probability of reaching one boundary before the other (committors), and the time it takes to get from one boundary to the other (first passage times). These boundaries specify what is a reactant and a product in a chemical reaction, so the above-mentioned quantities play central role in describing the kinetics (how concentrations change with time) of reactions where one molecule is transformed to another. For example, the first passage time is just the inverse of the rate and transition states are those conformations for which the committor is equal to one-half. To appreciate the importance of our work, some background is needed. Statistical mechanics that allows us to understand transformations of matter in microscopic terms (i.e., on a molecular level) is more than a century old. Starting in the beginning of this century, a new approach has emerged stimulated largely by computer simulations of the dynamics of molecules, where a trajectory (i.e., the position of every atom in a molecule as a function of time) is obtained. The newly emerging statistical mechanics of trajectories, which focuses on analyzing trajectories, has lead to a number of new and unexpected theoretical results that surprisingly were not discovered before. The relations that are the focus of our paper are arguably the most striking of these. Our algebraic derivation of them provides new insight into their nature and opens the door to using them to speed up simulations in order to study chemical reactions that are too slow to be studied in a brute-force way.

单分子FRET（smFRET）已成为研究生物分子结构动力学的主流技术。在这些实验中，分子被激光照射，供体荧光团被激发。供体可以发射光子或将激发转移到受体，然后受体可以发射不同颜色的光子。转移速率取决于染料间的距离，这就是为什么有关于构象动力学的信息。这些实验的输出是一系列记录了颜色和到达时间的光子。由于大范围时间尺度上的构象动力学，附着在分子上的荧光标记之间的距离发生波动。 smFRET 实验被越来越多的团体迅速广泛采用，在样品制备、测量程序、数据分析、算法和文档方面取得了重大进展。 上一份报告中描述的从不同角度描述当前技术水平的论文现已出版（eLife 2021；10：e60416，DOI 见下文）。 今年我们一直致力于单分子实验的分析，得到分子的扩散系数和亮度。 这项工作是与 LCP 的 Hoi Sung Chung 博士合作完成的，他在单分子水平上研究淀粉样蛋白 β (A) 聚集中寡聚体的形成。 在这些实验中，A 肽被供体或受体荧光团标记并混合在一起。 在聚集的早期阶段，低聚物开始形成。 低聚物在溶液中自由扩散，偶尔扩散到激光共焦斑中。 在斑点内，供体荧光团被激发并可以发射供体光子，或者它可以将能量转移到受体，受体可以发射受体光子。 由于单体只能发射供体光子，因此低聚物发射的供体和受体光子的爆发可以通过 FRET 效率来区分。 低聚物的数量远小于单体的数量。 问题是我们可以从少量光子爆发中了解低聚物的什么信息。 信息参数是分子的亮度和扩散系数，这取决于低聚物的尺寸。 通常用于获取扩散系数的标准 FCS 相关函数在这种情况下没有帮助，因为最强烈的信号来自单体。 此外，我们还想利用我们对分子亮度的了解，这不包括在相关函数中。 为了表征低聚物，我们开发了一种新方法，可以从少量选定的光子突发中获得扩散系数和光子计数率。 选择标准包括光子间时间阈值、突发中的光子数量以及 FRET 效率。 在这种方法中，我们构建了一个考虑这些选择标准的似然函数，并根据参数对其进行优化。 为了避免复杂性并减少计算量，细长的激光光斑被有效的各向同性光斑取代，光斑的尺寸是根据最佳拟合条件计算的。 我们之前一直使用最大似然法来获得单分子的 FRET 效率，该效率与荧光团标记之间的距离以及蛋白质折叠和结合的转变率有关。 然而，将平移扩散纳入分析恰好非常具有挑战性，因为突发选择会修改光子统计数据和似然函数，并且无法规避。 通过与细长激光光斑中的模拟光子轨迹进行比较，对新方法进行了测试，结果令人鼓舞。 扩散系数和计数率可以从少量光子的突发中准确确定。 这项工作仍在进行中，我们期望新方法能够成功应用于许多重要的分子系统，包括蛋白质折叠和 A 肽聚集。 与 A.M. 博士合作Berezhkovskii，我们刚刚在网上发表了一篇论文 (doi.org/10.1021/acs.jpcb.2c03757)，其中我们得出了两个边界之间的转换次数（通量）、先于另一个边界（提交者）到达一个边界的概率以及从一个边界到达另一个边界所需的时间（第一次通过时间）之间的显着关系。 这些边界指定了化学反应中的反应物和产物，因此上述数量在描述一个分子转化为另一个分子的反应动力学（浓度如何随时间变化）方面发挥着核心作用。 例如，第一次通过时间只是速率的倒数，过渡态是提交者等于一半的构象。 为了理解我们工作的重要性，需要一些背景知识。 统计力学使我们能够从微观角度（即分子水平）理解物质的转变，已有一个多世纪的历史。 从本世纪初开始，出现了一种新方法，主要是通过对分子动力学的计算机模拟来获得轨迹（即分子中每个原子随时间变化的位置）。 新出现的轨迹统计力学专注于分析轨迹，它带来了许多新的、意想不到的理论结果，令人惊讶的是，这些结果以前从未被发现。 我们本文关注的关系可以说是其中最引人注目的。 我们对它们的代数推导提供了对其本质的新见解，并为使用它们加速模拟打开了大门，以便研究因速度太慢而无法以暴力方式研究的化学反应。