纳米组分自组装成复合结构：Langevin方程的推导与模拟
Self-Assembly of Nanocomponents into Composite Structures: Derivation and Simulation of Langevin Equations
摘要：
通过多尺度方法分析了纳米组分自组装成病毒、纳米胶囊或其他复合结构的动力学。其目的是实现可预测性，并保持关键的原子尺度的功能，形成和稳定的复合结构。我们从一个全原子的描述，刘维尔方程，和序参量表征纳米尺度的系统功能。从Liouville方程出发，利用多尺度扰动技术，导出了一个关于序参量的Smoluchowski型随机动力学方程.分析了具有内部原子结构的纳米组分的复合结构的自组装，并推导了生长速率。应用包括从衣壳组装病毒衣壳，从其主要亚基组装核糖体，以及从纤维和纳米颗粒组装复合材料。我们的方法克服了其他粗粒化方法中忽略纳米结构对原子涨落的影响的错误。我们考虑了序参量对原子涨落统计的影响，这些涨落对驱动序参量演化的熵和平均力有贡献。这种方法使计算机模拟自组装的有效算法，而其他方法严重限制的时间步长，由于分离的扩散和复杂的特征时间。鉴于我们的方法不需要对每个新应用进行重新校准，它提供了一种估计组装速率的方法，从而促进了自组装途径和动力学死端结构的发现。
英文摘要：
The kinetics of the self-assembly of nanocomponents into a virus, nanocapsule, or other composite structure is analyzed via a multiscale approach. The objective is to achieve predictability and to preserve key atomic-scale features that underlie the formation and stability of the composite structures. We start with an all-atom description, the Liouville equation, and the order parameters characterizing nanoscale features of the system. An equation of Smoluchowski type for the stochastic dynamics of the order parameters is derived from the Liouville equation via a multiscale perturbation technique. The self-assembly of composite structures from nanocomponents with internal atomic structure is analyzed and growth rates are derived. Applications include the assembly of a viral capsid from capsomers, a ribosome from its major subunits, and composite materials from fibers and nanoparticles. Our approach overcomes errors in other coarse-graining methods which neglect the influence of the nanoscale configuration on the atomistic fluctuations. We account for the effect of order parameters on the statistics of the atomistic fluctuations which contribute to the entropic and average forces driving order parameter evolution. This approach enables an efficient algorithm for computer simulation of self-assembly, whereas other methods severely limit the timestep due to the separation of diffusional and complexing characteristic times. Given that our approach does not require recalibration with each new application, it provides a way to estimate assembly rates and thereby facilitate the discovery of self-assembly pathways and kinetic dead-end structures.
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