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Mathematical Biology Seminar: Modes of Motion of a Coronavirus

Author: Lona

Speaker: Professor Goong Chen from the Department of Mathematics and Institute for Quantum Science and Engineering, Texas A&M University


In this talk, we study coronavirus from a structural molecular biology point of view, with certain emphasis on how the mechanical motions of the  coronavirus may play in the invasion process of healthy cells. We first give a brief introduction and survey of the biological properties of a  coronavirus concerning how it moves and how it invades healthy cells.  The existing models of a coronavirus are mostly built atom-by-atom by  microbiologists, to the best of our knowledge. A major finding by those
researchers is the “wiggling” motion by the spikes of the virus. Such wiggling  motion has been identified to play the important functions of browsing,  surfing, and exploring activities in the virus’ search and roaming tofind healthy cells to invade.

A single coronavirus contains hundreds of millions or even billions of atoms.  Therefore, we can build our model by continuum mechanics in lieu of a  mass-spring-dashpot atom-by-atom model. A speherical shell with many spikes  mimicking the shape of coronavirus has been chosen as the elasto-plastic  continuum. For this small continuum, we can analyze its eigenmodes of vibration  by Modal Analysis. We have found the null space of six zero-frequency modes as  translations (along three coordinate axes) and rotations (pitch, roll and yaw)  and then, in addition, several thousands more nontrivial modes. They include  the wiggling motion, and many other more peculiar modal shapes
such as twisting, compression, embracing, locking, punching, and  shaking-off actions.

We also include the modal analysis of an IgG antibody. We make some  hypothetical opinions regarding how a coronavirus may interact with an antibody  based on their modal analysis. Many animation videos from supercomputer computations and simulations will be shown to illustrate the motions of a coronavirus.