A three-dimensional discrete model for approximating the deformation of a viral capsid subjected to lying over a flat surface

TL;DR

This paper introduces a 3D discrete model for simulating the deformation of a viral capsid, modeled as an icosahedron, when it lies on a flat surface, combining variational inequalities with numerical validation.

Contribution

The paper develops a novel 3D discrete model using variational inequalities to analyze viral capsid deformation with proven existence and uniqueness of solutions.

Findings

Numerical results align with physical expectations.

Model effectively captures capsid deformation behavior.

Mathematical proof ensures model reliability.

Abstract

In this paper we present a three-dimensional discrete model governing the deformation of a viral capsid, modelled as a regular icosahedron and subjected not to cross a given flat rigid surface on which it initially lies in correspondence of one vertex 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 space. Secondly, we show the existence and uniqueness of the solution for the proposed model. Finally, we numerically test this model and we observe that the outputs of the numerical experiments comply with physics.