Center for the Study of Systems Biology, School of Biology, Georgia Institute of Technology, 250 14th Street NW, Atlanta, Georgia 30318-5304, USA.
J Chem Phys. 2013 Sep 28;139(12):121922. doi: 10.1063/1.4817660.
Hydrodynamic interactions exert a critical effect on the dynamics of macromolecules. As the concentration of macromolecules increases, by analogy to the behavior of semidilute polymer solutions or the flow in porous media, one might expect hydrodynamic screening to occur. Hydrodynamic screening would have implications both for the understanding of macromolecular dynamics as well as practical implications for the simulation of concentrated macromolecular solutions, e.g., in cells. Stokesian dynamics (SD) is one of the most accurate methods for simulating the motions of N particles suspended in a viscous fluid at low Reynolds number, in that it considers both far-field and near-field hydrodynamic interactions. This algorithm traditionally involves an O(N(3)) operation to compute Brownian forces at each time step, although asymptotically faster but more complex SD methods are now available. Motivated by the idea of hydrodynamic screening, the far-field part of the hydrodynamic matrix in SD may be approximated by a diagonal matrix, which is equivalent to assuming that long range hydrodynamic interactions are completely screened. This approximation allows sparse matrix methods to be used, which can reduce the apparent computational scaling to O(N). Previously there were several simulation studies using this approximation for monodisperse suspensions. Here, we employ newly designed preconditioned iterative methods for both the computation of Brownian forces and the solution of linear systems, and consider the validity of this approximation in polydisperse suspensions. We evaluate the accuracy of the diagonal approximation method using an intracellular-like suspension. The diffusivities of particles obtained with this approximation are close to those with the original method. However, this approximation underestimates intermolecular correlated motions, which is a trade-off between accuracy and computing efficiency. The new method makes it possible to perform large-scale and long-time simulation with an approximate accounting of hydrodynamic interactions.
流体动力相互作用对大分子的动力学具有关键影响。随着大分子浓度的增加，根据半浓聚合物溶液或多孔介质中流动的行为，可以预期会发生流体动力屏蔽。流体动力屏蔽不仅对理解大分子动力学具有重要意义，而且对模拟浓缩大分子溶液（例如在细胞中）也具有实际意义。Stokesian dynamics（SD）是模拟低雷诺数下悬浮在粘性流体中的 N 个粒子运动的最精确方法之一，因为它同时考虑了远场和近场流体动力相互作用。该算法传统上涉及 O（N(3)）的操作来计算每个时间步的布朗力，尽管现在可以使用渐近更快但更复杂的 SD 方法。受流体动力屏蔽思想的启发，SD 中流体动力矩阵的远场部分可以用对角矩阵近似，这相当于假设长程流体动力相互作用完全被屏蔽。这种近似允许使用稀疏矩阵方法，这可以将表观计算规模降低到 O（N）。以前有几项使用此近似值的单分散悬浮液模拟研究。在这里，我们为布朗力的计算和线性系统的求解使用新设计的预处理迭代方法，并考虑该近似值在多分散悬浮液中的有效性。我们使用类似于细胞内的悬浮液来评估对角近似方法的准确性。用该近似值获得的粒子扩散系数与原始方法的扩散系数接近。然而，这种近似值低估了分子间相关运动，这是准确性和计算效率之间的权衡。新方法使得可以使用近似的流体动力相互作用进行大规模和长时间的模拟。
