Generalized Fourier series solution of equations governing molecular-motor-assisted transport of adenoviral vectors in a spherical cell

This paper presents an analytical solution of one-dimensional transient molecular-motor-assisted transport equations that describe transport of adenoviruses in a spherical cell. The model of intracellular trafficking of adenoviruses is based on molecular-motor-assisted transport equations suggested by Smith and Simmons [D.A. Smith, R.M. Simmons, Models of motor-assisted transport of intracellular particles, Biophysical Journal 80 (2001) 45–68.]. These equations are presented in spherical coordinates and extended by accounting for the random component of motion of viral particles bound to filaments. This random component is associated with the stochastic nature of molecular motors responsible for the locomotion of viral particles bound to filaments. Utilizing the method of separation of variables, a generalized Fourier series solution for this problem is obtained. The solution uses two different orthogonal sets of eigenfunctions to represent the concentration of free viral particles transported by diffusion and the concentration of microtubule-bound viral particles transported by kinesin-family molecular motors away from the cell nucleus. Binding/detachment kinetic processes between the viral particles and microtubules are specified by first rate reaction constants; these lead to coupling between the two viral concentrations. The obtained solution simulates viral transport between the cell membrane and cell nucleus during initial stages of viral infection.