Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows.
Concluding Remarks The control of infective viruses released by terrorists, and the prevention of viral epidemics and pandemics, such as HIV, SARS, H1N1, and bird flu are of tremendous importance. The understanding of viral surface formation, evolution, viral attachment and penetration of host cells are prerequisites to viral disease prevention and control. This problem, as well as many other similar problems in molecular biology, poses pressing challenges to the theoretical community due to their large number of degrees of freedom. The main purpose of the present work is to introduce a differential geometry-based multiscale framework to handle complex biological systems. The present multiscale model couples macroscopic fluid dynamics, microscopic molecular dynamics, and surface dynamics in a unified framework. The differential geometry theory of surfaces is utilized to put continuum description and discrete description in an equal footing. The present work constructs a generalized action functional to self-consistently couple different scales. Governing equations for the fluid dynamics, that is, the generalized Navier-Stokes equation, and molecular dynamics, that is, the Newton's equation, are derived by minimizing the action functional. Additionally, we make use of viral symmetry to dramatically reduce viral data sizes and improve viral visualization. Finally, some of the proposed approaches are demonstrated by the generation of a few virus surfaces.
The proposed differential geometry-based multiscale model can be easily generalized to complex systems with multiple interfaces or many biomolecules. Additionally, the incorporation of continuum solid description into the present model will be published elsewhere. Finally, the inclusion of a quantum mechanical description can also be pursued in a similar way and will be published elsewhere. Numerical experiments that further demonstrate the proposed ideas are under our consideration.
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