A mathematical model for the interaction of a virus with the plasma membrane of cell

Abstract

Understanding the interactions of viruses with cell membranes is important for the proposal of vaccines and treatments for diseases caused by this type of contamination. An example of this is the case of the pandemic caused by the new Covid-19, which in 2020 placed was responsible for a third of the world under virus quarantine, causing huge economic losses and thousand of deaths across the planet. In this context, this research proposes to build a mathematical model for the interaction of a virus with the plasma membrane in a mammalian cell, which leads to a mathematical problem with boundary conditions. Using Green’s functions, the model was able to answer what is the general expression for potential electrostatic energy of this interaction in terms of Bessel functions and Wigner coefficients. It is reasonable to speculate, based on the results presented by the model, that a virus has to present an effective charge resulting in a solution with a pH value of about 7 to approach the cell membrane, while an electrically neutral virus should not have the ability to interact and enter membranes. The values ?for the interaction energy and the force between the membrane and the cluster offer the order of magnitude of the distances over which such interaction is effective.