Paquay Stefan, Kusters Remy
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, the Netherlands.
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, the Netherlands.
Biophys J. 2016 Mar 29;110(6):1226-33. doi: 10.1016/j.bpj.2016.02.017.
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in the field of diffusive transport have focused on solving the diffusion equation on curved surfaces, for which it is not tractable to incorporate particle interactions even though these play a crucial role in crowded systems. We show here that it is possible to take such interactions into account by combining standard constraint algorithms with the classical velocity Verlet scheme to perform molecular dynamics simulations of particles constrained to an arbitrarily curved surface. Furthermore, unlike Brownian dynamics schemes in local coordinates, our method is based on Cartesian coordinates, allowing for the reuse of many other standard tools without modifications, including parallelization through domain decomposition. We show that by applying the schemes to the Langevin equation for various surfaces, we obtain confined Brownian motion, which has direct applications to many biological and physical problems. Finally we present two practical examples that highlight the applicability of the method: 1) the influence of crowding and shape on the lateral diffusion of proteins in curved membranes; and 2) the self-assembly of a coarse-grained virus capsid protein model.
受约束粒子的动力学模拟能够极大地帮助我们理解生物过程的时空演化，比如沿着膜的侧向运输以及病毒的自组装。扩散输运领域的大多数理论研究都集中在求解曲面上的扩散方程，即便粒子间相互作用在拥挤系统中起着关键作用，但在求解该方程时纳入这种相互作用却难以处理。我们在此表明，通过将标准约束算法与经典速度Verlet格式相结合，能够考虑到此类相互作用，从而对约束在任意曲面上的粒子进行分子动力学模拟。此外，与局部坐标下的布朗动力学格式不同，我们的方法基于笛卡尔坐标，无需修改即可复用许多其他标准工具，包括通过区域分解实现并行化。我们表明，通过将这些格式应用于各种曲面的朗之万方程，可得到受限布朗运动，这直接适用于许多生物和物理问题。最后，我们给出两个实际例子以突出该方法的适用性：1）拥挤和形状对蛋白质在曲面膜中侧向扩散的影响；2）粗粒度病毒衣壳蛋白模型的自组装。
