Molecular dynamics with the united-residue model of polypeptide chains. I. Lagrange equations of motion and tests of numerical stability in the microcanonical mode
Molecular dynamics with the united-residue model of polypeptide chains. I. Lagrange equations of motion and tests of numerical stability in the microcanonical mode
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DOI：
10.1021/jp058008o
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发表时间：
2005-07-21
影响因子：
3.3
通讯作者：
Scheraga, HA
中科院分区：
文献类型：
--
作者：
Khalili, M;Liwo, A;Scheraga, HA
采用拉格朗日方法推导了本实验室建立的基于物理的联合剩余力场的运动方程。选择C-α中心点C-α和C-α中心点SC（SC表示侧链中心）虚拟键矢量作为变量。采用速度Verlet算法对运动方程进行积分。对未封闭的Ala（10）多肽的测试表明，该算法在高达1.467 fs的时间步长的短时间段内是稳定的;然而，即使在0.489 fs的较短时间步长下，由于加速度的瞬时跳跃，总能量也会发生一些漂移。这些跳跃是由数值不稳定性的力量所产生的U-rot组件的UNRES描述的侧链旋转异构态的能量。Gly（10）序列的检测运行（其中U-rot不存在）和用简单数值稳定的调和势代替U-rot的Ala（10）序列证实了这一观察;仅在7.335fs的时间步长内观察到总能量的振荡，并且仅对于9.78fs的时间步长，总能量的某些漂移或轨迹的不稳定性开始出现在长时间（2ns和更长）轨迹中。这些结果表明，目前的U-rot组件（这是来自蛋白质数据库的统计潜力）必须用更数值稳定的功能，这项工作正在进行中，在我们的实验室。为了减少规则多肽序列的能量漂移，我们引入了一种非辛变时间步长算法。如果加速度的最大变化超过选定的截止值，则该算法在轨迹的给定点处按比例缩小时间步长。使用该算法，总能量合理地保存到2.445 fs的时间步长，如在未封闭的Ala（10）多肽上测试的。我们还尝试了一个辛多时间步可逆的ARMA算法，并取得了令人满意的能量守恒的时间步长高达7.335 fs。然而，目前看来，可逆RESPA算法比可变时间步长算法贵几倍，因为需要执行额外的矩阵乘法。我们还观察到，由于Ala（10）在微正则模式下在皮秒内折叠和展开，这表明UNRES动力学中的有效（基于事件的）时间单位比全原子动力学大得多，因为在推导UNRES势时对快速移动的自由度进行了平均。
The Lagrange formalism was implemented to derive the equations of motion for the physics-based united-residue (UNRES) force field developed in our laboratory. The C-alpha center dot center dot center dot C-alpha and C-alpha center dot center dot center dot SC (SC denoting a side-chain center) virtual-bond vectors were chosen as variables. The velocity Verlet algorithm was adopted to integrate the equations of motion. Tests on the unblocked Ala(10) polypeptide showed that the algorithm is stable in short periods of time up to the time step of 1.467 fs; however, even with the shorter time step of 0.489 fs, some drift of the total energy occurs because of momentary jumps of the acceleration. These jumps are caused by numerical instability of the forces arising from the U-rot component of UNRES that describes the energetics of side-chain-rotameric states. Test runs on the Gly(10) sequence (in which U-rot is not present) and on the Ala(10) sequence with U-rot replaced by a simple numerically stable harmonic potential confirmed this observation; oscillations of the total energy were observed only up to the time step of 7.335 fs, and some drift in the total energy or instability of the trajectories started to appear in long-time (2 ns and longer) trajectories only for the time step of 9.78 fs. These results demonstrate that the present U-rot components (which are statistical potentials derived from the Protein Data Bank) must be replaced with more numerically stable functions; this work is under way in our laboratory. For the purpose of our present work, a nonsymplectic variable-time-step algorithm was introduced to reduce the energy drift for regular polypeptide sequences. The algorithm scales down the time step at a given point of a trajectory if the maximum change of acceleration exceeds a selected cutoff value. With this algorithm, the total energy is reasonably conserved up to a time step of 2.445 fs, as tested on the unblocked Ala(10) polypeptide. We also tried a symplectic multiple-time-step reversible RESPA algorithm and achieved satisfactory energy conservation for time steps up to 7.335 fs. However, at present, it appears that the reversible RESPA algorithm is several times more expensive than the variable-time-step algorithm because of the necessity to perform additional matrix multiplications. We also observed that, because Ala(10) folds and unfolds within picoseconds in the microcanonical mode, this suggests that the effective (event-based) time unit in UNRES dynamics is much larger than that of all-atom dynamics because of averaging over the fast-moving degrees of freedom in deriving the UNRES potential.