Modelling Virus Contact Mechanics under Atomic Force Imaging Conditions

TL;DR

This paper introduces a discrete variational inequality model for virus contact mechanics under atomic force microscopy, enabling better estimation of contact areas and elastic parameters in virus imaging studies.

Contribution

It presents a novel variational inequality framework for modeling virus deformation during atomic force microscopy, with proven existence and uniqueness of solutions.

Findings

Model effectively simulates virus deformation and contact mechanics.

Numerical results assist in estimating contact areas and elastic parameters.

Provides a new approach for analyzing virus imaging data.

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. Secondly, 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.