Absorption by a moving spherical organelle in a heterogeneous cytoplasm: Implications for the role of trafficking in a symplast

An organelle which absorbs (or secretes) a particular factor will find its mass transfer rate diffusion-limited if it is stationary with respect to its ambient cytoplasm; but organellar motion will raise that limit as a non-decreasing function of the Peclet number P. It is shown analytically that (i) no Whitehead paradox need be encountered in the creeping flow regime and (ii) the flux of the factor will be an even function of the Peclet number, P. By a novel analytic solution method, the flux is shown numerically to increase as P2 for P≲1. For P≳10, a quasi-planar approximating geometry yields analytically a flux which increases as P1/3. These two solutions overlap smoothly in the range 1≲P≲10. For P≈1, convection should increase the mass flux by roughly 100%.