The current contribution deals with the simulation of the viral entry into a cell. There are two dominant mechanisms typical of this process: the endocytosis and the fusion with the cellular membrane. However, we only focus on the first scenario. To this end, we consider a virus as a substrate with a constant concentration of receptors on the surface. Opposite to this, the concentration of receptors of the host cell varies and these receptors are free to move over the membrane. When the contact with the cell surface has been achieved, the receptors start to diffuse to the contact (adhesion) zone. The membrane in this zone inflects and forms an envelope around the surface of the virus. This is the way the newly formed vesicle imports its cargo into the cell. In order to simulate the process described, we assume that the differential equation typical of the heat transport is suitable to simulate the diffusion of receptors. We also formulate two boundary conditions: First, we consider the balance of fluxes on the front of the adhesion zone. Here, it is supposed that the velocity is proportional to the gradient of the chemical potential. The second subsidiary condition is the energy balance equation depending on four different contributions: the energy of binding receptors, the free energy of the membrane, the energy due to the curvature of the membrane and the kinetic energy due to the motion of the front. The differential equation itself along with two boundary conditions forms a well‐posed problem which can be solved by applying a direct method, for example the finite difference method. The contribution also includes numerical examples showing the distribution of receptors over the membrane as well as the motion of the front of the adhesion surface. The influence of the mobility of receptors has been studied in particular. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Proceedings in Applied Mathematics & Mechanics – Wiley
Published: Jan 1, 2017
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