Modelling virus contact mechanics under atomic force imaging conditions

Abstract

In this paper, we present a discrete model governing the deformation of a convex regular polygon subjected not to cross a given flat rigid surface, on which it initially lies in correspondence of one point only. First, we set up the model in the form of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable Euclidean space. Second, we show the existence and uniqueness of the solution. The model provides a simplified illustration of processes involved in virus imaging by atomic force microscopy: adhesion to a surface, distributed strain, relaxation to a shape that balances adhesion and elastic forces. The analysis of numerical simulations results based on this model opens a new way of estimating the contact area and elastic parameters in virus contact mechanics studies.

Keywords:

• Elliptic variational inequalities
• contact mechanics
• biological systems

2020 Mathematics Subject Classifications:

• 74M15
• 35Q92
• 35J86
• 92B05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

We gratefully acknowledge support by the Army Research Office, under award W911NF-17-1-0329 and by the National Science Foundation, under award CBET 1803440 and 1808027 (to BD). We acknowledge the Center for Bioanalytical Metrology (CBM), an NSF Industry-University Cooperative Research Center, for providing funding under grant NSF IIP 1916645. This work was partly supported by the Research Fund of Indiana University.