Motion of a Disordered Polypeptide Chain as Studied by Paramagnetic Relaxation Enhancements, ¹⁵N Relaxation, and Molecular Dynamics Simulations: How Fast Is Segmental Diffusion in Denatured Ubiquitin?

Molecular dynamics (MD) simulations have been widely used to analyze dynamic conformational equilibria of folded proteins, especially in relation to NMR observables. However, this approach found little use in the studies of disordered proteins, where the sampling of vast conformational space presents a serious problem. In this paper, we demonstrate that the latest advances in computation technology make it possible to overcome this limitation. The experimentally validated (calibrated) MD models allow for new insights into structure/dynamics of disordered proteins. As a test system, we have chosen denatured ubiquitin in solution with 8 M urea at pH 2. High-temperature MD simulations in implicit solvent have been carried out for the wild-type ubiquitin as well as MTSL-tagged Q2C, D32C, and R74C mutants. To recalibrate the MD data (500 K) in relation to the experimental conditions (278 K, 8 M urea), the time axes of the MD trajectories were rescaled. The scaling factor was adjusted such as to maximize the agreement between the simulated and experimental 15N relaxation rates. The resulting effective length of the trajectories, 311 μs, ensures good convergence properties of the MD model. The constructed MD model was validated against the array of experimental data, including additional 15N relaxation parameters, multiple sets of paramagnetic relaxation enhancements (PREs), and the radius of gyration. In each case, a near-quantitative agreement has been obtained, suggesting that the model is successful. Of note, the MD-based approach rigorously predicts the quantities that are inherently dynamic, i.e., dependent on the motional correlation times. This cannot be accomplished, other than in empirical fashion, on the basis of static structural models (conformational ensembles). The MD model was further used to investigate the relative translational motion of the MTSL label and the individual HN atoms. The derived segmental diffusion coefficients proved to be nearly uniform along the peptide chain, averaging to D = 0.49–0.55 × 10–6 cm2/s. This result was verified by direct analysis of the experimental PRE data using the recently proposed Ullman-Podkorytov model. In this model, MTSL and HN moieties are treated as two tethered spheres undergoing mutual diffusion in a harmonic potential. The fitting of the experimental data involving D as a single adjustable parameter leads to D = 0.45 × 10–6 cm2/s, in good agreement with the MD-based analyses. This result can be compared with the range of estimates obtained from the resonance energy transfer experiments, D = 0.2–6.0 × 10–6 cm2/s.分子动力学（MD）模拟已被广泛用于分析折叠蛋白质的动态构象平衡，尤其与核磁共振（NMR）可观测参数相关。然而，该方法在无序蛋白质研究中的应用却十分有限，因为这类蛋白需要采样广阔的构象空间，这一问题尤为突出。本文证明，计算技术的最新进展使得克服这一局限成为可能。经实验验证（校准）的MD模型能够为无序蛋白质的结构与动态特性提供新的认知。我们选取溶液中8 M尿素、pH 2条件下的变性泛素作为测试体系。针对野生型泛素以及MTSL标记的Q2C、D32C、R74C突变体，开展了隐式溶剂环境下的高温MD模拟。为了将500 K的MD模拟数据校准至实验条件（278 K、8 M尿素），我们对MD轨迹的时间轴进行了重缩放。缩放因子的调整原则为最大化模拟与实验15N弛豫速率之间的吻合度。最终轨迹的有效时长为311 μs，确保了MD模型具备良好的收敛性。我们构建的MD模型通过多组实验数据进行了验证，包括额外的15N弛豫参数、多套顺磁弛豫增强（PRE）数据以及回转半径。在所有案例中，模拟结果与实验数据均实现了近乎定量的吻合，表明该模型取得了成功。值得注意的是，基于MD的方法能够精准预测本质上依赖于运动关联时间的动态量，而这类参数仅靠经验方法无法基于静态结构模型（构象系综）实现准确预测。我们进一步利用该MD模型研究了MTSL标记基团与单个HN原子之间的相对平动运动。推导得到的片段扩散系数沿肽链几乎均一，平均值为D = 0.49–0.55 × 10–6 cm²/s。通过采用近期提出的Ullman-Podkorytov模型直接分析实验PRE数据，我们验证了这一结果。在该模型中，MTSL与HN基团被视为两个受谐势约束的球体，可发生相互扩散。以扩散系数D作为唯一可调参数拟合实验数据，得到D = 0.45 × 10–6 cm²/s，与基于MD分析得到的结果吻合良好。该结果可与共振能量转移实验得到的估算范围（D = 0.2–6.0 × 10–6 cm²/s）进行对比。