Department of Chemical and Life Science Engineering, Virginia Commonwealth University, Richmond, Virginia 23284, USA.
J Chem Phys. 2011 Jan 14;134(2):025105. doi: 10.1063/1.3525381.
The transport of flexible biological macromolecules in confined geometries is found in a variety of important biophysical systems including biomolecular movements through pores in cell walls, vesicle walls, and synthetic nanopores for sequencing methods. In this study, we extend our previous analysis of the Fokker-Planck and Langevin dynamics for describing the coupled translational and rotational motions of single structured macromolecules near structured external surfaces or walls [M. H. Peters, J. Chem. Phys. 110, 528 (1999); 112, 5488 (2000)] to the problem of many interacting macromolecules in the presence of structured external surfaces representing the confining geometry. Overall macromolecular flexibility is modeled through specified interaction potentials between the structured Brownian subunits (B-particles), as already demonstrated for protein and DNA molecules briefly reviewed here. We derive the Fokker-Planck equation using a formal multiple time scale perturbation expansion of the Liouville equation for the entire system, i.e., solvent, macromolecules, and external surface. A configurational-orientational Langevin displacement equation is also obtained for use in Brownian dynamics applications. We demonstrate important effects of the external surface on implicit solvent forces through formal descriptions of the grand friction tensor and equilibrium average force of the solvent on the B-particles. The formal analysis provides both transparency of all terms of the Langevin displacement equation as well as a prescription for their determination. As an example, application of the methods developed, the real-time movement of an α-helix protein through a carbon nanotube is simulated.
柔性生物大分子在受限几何形状中的输运存在于各种重要的生物物理系统中，包括生物分子通过细胞壁、囊泡壁和用于测序方法的合成纳米孔中的运动。在这项研究中，我们扩展了以前对福克-普朗克和朗之万动力学的分析，以描述单结构大分子在结构外部表面或壁附近的耦合平移和旋转运动[M. H. Peters, J. Chem. Phys. 110, 528 (1999); 112, 5488 (2000)]，以解决存在结构外部表面的许多相互作用大分子的问题，这些表面代表了受限的几何形状。通过已经在这里简要回顾的蛋白质和 DNA 分子的指定相互作用势来模拟整体大分子的灵活性。我们使用整个系统（溶剂、大分子和外部表面）的刘维尔方程的正式多时间尺度微扰展开来推导出福克-普朗克方程。我们还为布朗动力学应用获得了构象-取向朗之万位移方程。我们通过正式描述巨摩擦张量和溶剂对 B 粒子的平衡平均力，证明了外部表面对隐溶剂力的重要影响。正式分析提供了朗之万位移方程所有项的透明度以及确定它们的处方。作为一个例子，应用所开发的方法，模拟了α-螺旋蛋白通过碳纳米管的实时运动。
