Protein Folding Dynamics as Diffusion on a Free Energy Surface: Rate Equation Terms, Transition Paths, and Analysis of Single-Molecule Photon Trajectories
Protein Folding Dynamics as Diffusion on a Free Energy Surface: Rate Equation Terms, Transition Paths, and Analysis of Single-Molecule Photon Trajectories
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DOI：
10.1021/acs.jpcb.1c05401
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发表时间：
2021-11-18
影响因子：
3.3
通讯作者：
Munoz, Victor
中科院分区：
文献类型：
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作者：
Mothi, Nivin;Munoz, Victor
蛋白质折叠的速率通常被描述为多维能量景观投影到几个（理想情况下是一个）阶参数上的扩散。通过实验测试这样的近似需要解决单个分子的反应跃迁路径，这现在通过先进的单分子光谱技术变得可行。这也激发了理论家们对更好地理解反应性转变路径的兴趣。在这里，我们专注于这些问题，旨在建立（i）的过渡路径时间（TPT）和（ii）的方法，以提取自由能表面和蛋白质动力学的光子轨迹的最大似然分析（MLA-PT）的机械解释的实用指南。我们代表（联合国）折叠率作为扩散的1D自由能表面与FRET效率作为反应坐标代理。然后，我们进行扩散动力学模拟表面上有两个极小值和一个障碍，但具有不同的形状（曲率，势垒高度和对称性），再加上随机模拟的光子发射，重现目前的SM-FRET实验。从过渡路径的分析，我们发现，TPT是成反比的势垒高度（最小和障碍顶部之间的自由能差）为任何给定的表面形状，并划分成攀登和下降段的TPT提供了关键信息的障碍的对称性。我们还发现，用于从实验中确定TPT的原始MLA-PT程序低估了其值，特别是对于具有较小屏障的情况（例如，快速文件夹），我们建议一个简单的策略来纠正这种偏见。重要的是，我们还证明了光子轨迹包含足够的信息来提取1D自由能表面的形状和动力学（如果TPT比光子间时间长>4-5倍），使用MLA-PT直接实现扩散自由能表面模型。在处理真实的（未知的）实验数据时，自由能面与离散动力学三态模型的似然性之间的比较可以用来评价所估计的自由能面的统计显著性。
The rates of protein (un)folding are often described as diffusion on the projection of a hyperdimensional energy landscape onto a few (ideally one) order parameters. Testing such an approximation by experiment requires resolving the reactive transition paths of individual molecules, which is now becoming feasible with advanced single-molecule spectroscopic techniques. This has also sparked the interest of theorists in better understanding reactive transition paths. Here we focus on these issues aiming to establish (i) practical guidelines for the mechanistic interpretation of transition path times (TPT) and (ii) methods to extract the free energy surface and protein dynamics from the maximum likelihood analysis of photon trajectories (MLA-PT). We represent the (un)folding rates as diffusion on a 1D free energy surface with the FRET efficiency as a reaction coordinate proxy. We then perform diffusive kinetic simulations on surfaces with two minima and a barrier, but with different shapes (curvatures, barrier height, and symmetry), coupled to stochastic simulations of photon emissions that reproduce current SM-FRET experiments. From the analysis of transition paths, we find that the TPT is inversely proportional to the barrier height (difference in free energy between minimum and barrier top) for any given surface shape, and that dividing the TPT into climb and descent segments provides key information about the barrier's symmetry. We also find that the original MLA-PT procedure used to determine the TPT from experiments underestimates its value, particularly for the cases with smaller barriers (e.g., fast folders), and we suggest a simple strategy to correct for this bias. Importantly, we also demonstrate that photon trajectories contain enough information to extract the 1D free energy surface's shape and dynamics (if TPT is >4-5-fold longer than the interphoton time) using the MLA-PT directly implemented with a diffusive free energy surface model. When dealing with real (unknown) experimental data, the comparison between the likelihoods of the free energy surface and discrete kinetic three-state models can be used to evaluate the statistical significance of the estimated free energy surface.