Department of Chemical Sciences, Tata Institute of Fundamental Research, Mumbai, 400 005, India.
J Chem Theory Comput. 2021 May 11;17(5):3103-3118. doi: 10.1021/acs.jctc.0c01070. Epub 2021 Apr 5.
The directional flexibility of proteins is an equilibrium molecular property which is accessible to both experiment and computation. Single molecule force spectroscopy (SMFS) experiments report effective directional spring constants to describe the collective anisotropic response of a protein structure to mechanical pulling forces applied along selected axes. On the other hand, computational methods have thus far employed either indirect force based nonequilibrium simulations or coarse-grained elastic network models (ENM) to predict protein directional spring constants. Here, we examine the ability of equilibrium atomistic Molecular Dynamics (MD) simulations to estimate the directional flexibility and mechanical anisotropy of proteins. MD-derived effective directional spring constants are found to correlate well with SMFS spring constants (ρ = 0.97-0.99; Adj = 0.92-0.99) and unfolding forces (ρ = 0.85-0.97; Adj = 0.63-0.91) for five different globular proteins. Specifically, the computed spring constants reproduce the mechanical anisotropy reported by SMFS along five different directions of green fluorescence protein (GFP) and six directions of the immunoglobulin-binding B1 domain of streptococcal protein G (GB1). Further, protein dynamics as captured in MD can be translated into spring constants which can distinguish the N-C directional flexibility of ubiquitin (Ub) from two structurally homologous small ubiquitin-like modifier (SUMO1 and SUMO2) isoforms. We apply our computational framework to study the mechanical anisotropy of Ub along the seven lysine-C-term directions which are functionally relevant. We show that Ub possesses two distinct flexibility scales along these directions which roughly differ by an order of magnitude. Further, our studies reveal that the mechanical anisotropy of Ub is modified in contrasting ways by the binding of two partner proteins (UBCH5A and UEV) which attach and recognize these biomolecular tag proteins. On the basis of equilibrium MD benchmarks for flexibility along 2485 bond vectors in Ub, we propose and validate a new covariance-propagation scheme to extract spring constants from ENM normal modes. We also critically examine the ability of ENM to predict directional flexibility of proteins and suggest modifications to improve these intuitive and scalable descriptions.
蛋白质的定向柔韧性是一种平衡的分子特性，既可以通过实验也可以通过计算来获得。单分子力谱（SMFS）实验报告有效的定向弹簧常数，以描述蛋白质结构对沿选定轴施加的机械拉力的集体各向异性响应。另一方面，计算方法迄今为止要么使用基于间接力的非平衡模拟，要么使用粗粒弹性网络模型（ENM）来预测蛋白质的定向弹簧常数。在这里，我们研究了平衡原子分子动力学（MD）模拟估计蛋白质定向柔韧性和机械各向异性的能力。发现 MD 衍生的有效定向弹簧常数与 SMFS 弹簧常数（ρ=0.97-0.99；Adj=0.92-0.99）和展开力（ρ=0.85-0.97；Adj=0.63-0.91）高度相关，适用于五种不同的球状蛋白质。具体而言，所计算的弹簧常数再现了 SMFS 沿绿色荧光蛋白（GFP）的五个不同方向和链球菌蛋白 G（GB1）的六个方向报告的机械各向异性。此外，MD 中捕获的蛋白质动力学可以转化为弹簧常数，这些常数可以区分泛素（Ub）的 N-C 定向柔韧性与其两种结构同源的小泛素样修饰物（SUMO1 和 SUMO2）同工型。我们应用我们的计算框架来研究 Ub 沿七个赖氨酸-C 末端方向的机械各向异性，这些方向在功能上是相关的。我们表明，Ub 沿这些方向具有两种不同的柔韧性尺度，大致相差一个数量级。此外，我们的研究表明，Ub 的机械各向异性通过两种伴侣蛋白（UBCH5A 和 UEV）的结合以不同的方式被修饰，这些伴侣蛋白附着并识别这些生物分子标签蛋白。基于 Ub 中 2485 个键向量的灵活性的平衡 MD 基准，我们提出并验证了一种新的协方差传播方案，以从 ENM 正常模式中提取弹簧常数。我们还批判性地检查了 ENM 预测蛋白质定向柔韧性的能力，并提出了改进这些直观和可扩展描述的建议。
