Differential geometry approach for virus surface formation, evolution and visualization

病毒是传染媒介，可引起流行病和大流行病。防控病毒性疫情和大流行病对国土安全和日常生活的重要性怎么强调都不为过。病毒不能在宿主细胞外生长和/或繁殖。它们的感染开始于病毒在宿主细胞表面上的附着，伴随着病毒衣壳表面和宿主细胞膜的可能融合，随后是病毒渗透到宿主细胞中。这些过程主要涉及病毒衣壳表面与水生环境以及宿主表面膜或受体之间的非键合相互作用。因此，了解病毒在宿主细胞上的粘附分子机制、病毒与细胞膜融合的运动以及病毒侵入宿主细胞的动力学是非常必要的。这些研究的先决条件是有效的数学和计算技术的病毒表面的建设，进化和可视化，并分析病毒的非键相互作用与其宿主细胞。不幸的是，一个普通的病毒由数百万个原子组成，由于其环境和宿主细胞，病毒动力学涉及额外的自由度。病毒系统中异常庞大的数据集对全原子尺度的病毒表面形成、可视化和病毒相互作用分析提出了严峻的挑战。因此，水环境中病毒附着、融合和渗透的真实的时间动态模拟需要微秒或毫秒级的模拟时间，目前全原子模型在技术上是难以解决的。本项目通过开发一个多尺度框架来解决这些挑战，该框架通过对水环境的宏观连续描述来降低问题的维度，和病毒原子的微观离散描述。为了进一步减少过大病毒的病毒数据的大小，一个基于氨基酸残基的粗粒度粒子描述内置到我们的多尺度框架。引入总自由能泛函，将宏观表面张力和微观势能相互作用统一起来。 曲面微分几何理论是为了描述宏观域与微观域之间的界面而自然产生的。势驱动的几何流构造，以最小化总自由能泛函。基于几何测度理论，提出了一种混合欧拉-拉格朗日方法，以加速涉及拓扑变化的曲面构造。 除了有希望的初步结果说明这种方法的力量，提出了广泛的验证和应用，以确保这种方法产生强大的和强大的工具，病毒表面的建设，可视化，进化和动态。

Viruses are contagious agents and can cause epidemics and pandemics. The importance of the prevention and control of viral epidemics and pandemics to homeland security and daily life cannot be overemphasized. Viruses cannot grow and/or reproduce outside host cells. Their infection starts with the attachment of a virus on the host cell surface, with possible fusion of viral capsid surface and the host cellular membrane, followed by virus penetration into the host cell. These processes involve mostly non-bonding interactions between the virus capsid surface and the aquatic environment, as well as the host surface membrane or receptor. It is imperative to understand the molecular mechanism of virus attachment on its host cell, the movement of virus fusion with cellular membrane, and the dynamics of virus penetration into its host cell. The prerequisites to these studies are efficient mathematical and computational techniques for virus surface construction, evolution and visualization, and analysis of the virus's non-bonding interactions with its host cell. Unfortunately, an average virus comprises millions of atoms, and virus dynamics involves an additional number of degrees of freedom due to its environment and host cell. The exceptionally massive data sets in virus systems pose severe challenges to full-atomic scale virus surface formation, visualization and virus interaction analysis. Therefore, the real time dynamic simulation of viral attachment, fusion and penetration of a host cell in the aquatic environment requires microsecond or millisecond simulation time and is technically intractable with full-atom models at present.The proposed project addresses these challenges by developing a multiscale framework which reduces the problem dimensionality by a macroscopic continuum description of the aquatic environment, and a microscopic discrete description of virus atoms. To further reduce the size of virus data for excessively large viruses, a coarse-grain particle description based on amino acid residues is built into our multiscale framework. A total free energy functional is introduced to bring the macroscopic surface tension and microscopic potential interactions into the same footing. The differential geometry theory of surfaces raises naturally for the description of the interface between macroscopic and microscopic domains. Potential driven geometric flows are constructed to minimize the total free energy functional. A hybrid Eulerian-Lagrangian method is developed based on the geometric measure theory to accelerate the surface construction involving topological changes. In addition to promising preliminary results illustrating the power of this approach, extensive validation and applications are proposed to ensure that this methodology yields robust and powerful tools for virus surface construction, visualization, evolution, and dynamics.