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Differential geometry approach for virus surface formation, evolution and visualization
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.