Numerical simulation of the viral entry into a cell driven by the receptor diffusion
This study focuses on the receptor driven endocytosis typical of viral entry into a cell. A locally increased density of receptors at the time of contact between the cell and the virus is necessary in this case. The virus is considered as a substrate with fixed receptors on its surface, while the receptors of the host cell are free to move over its membrane, allowing a local change in their concentration. In the contact zone the membrane inflects and forms an envelope around the virus. The created vesicle imports its cargo into the cell. The described process is simulated by the diffusion equation accompanied by two boundary conditions. The first boundary condition states that the conservation of binders expressed as the local rate of change of density has to be equal to the negative of the local flux divergence. The second boundary condition represents the energy balance condition with contributions due to the binding of receptors, the free energy of the membrane, its curvature and the kinetic energy due to the motion of the front. The described moving boundary problem in terms of the binder density and the velocity of the adhesion front is well posed and relies on biomechanically motivated assumptions. The problem is numerically solved by using the finite difference method, and the illustrative examples have been chosen to show the influence of the mobility of the receptors and of their initial densities on the velocity of the process.\n\nSIGNIFICANCEThe receptor driven endocytosis represents one of the most important mechanisms for the viral entry into a cell. However, the high velocities and small characteristic length scale cause many difficulties during the experimental investigation of such a process. This calls upon the application of virtual computer simulations investigating the process parameters and identifying factors inhibiting or completely ceasing the viral entry into cells. The development of methods for the optimization of the cell immunity system is aimed to as the final goal.