(596bc) Effects of Oscillatory Convective Flow On Chemical Signal Propagation in Epithelia

Convective transport plays an important role in the development and morphogenesis of vascular system, formation of the left-right body axis, cartilage feeding etc. Recently, we have developed a mathematical model of autocrine chemical signaling at simple epithelia under the influence of the convective flow [1]. We have considered signaling mediated by epidermal growth factor receptors (EGFR) and their ligands. Even if the Peclet number is about one, we have shown that the convective transport in the extracellular medium can accelerate the velocity of chemical signal propagation by several orders of the magnitude. However, when the convection transport is oriented against the propagating signal, the signaling can stop or reverse the direction of propagation. Our findings are in good qualitative agreement with available experimental data.

The convective transport in tissues is induced by pressure gradients that result from body motion, heart action or some circadian rhythms. Hence, the typical convective flow at an epithelium is time dependent. In this contribution, we compare the velocity of signal propagation in systems with no convective transport and in systems with harmonically oscillating convective flow. We assume, the time-averaged convective velocity is equal to zero in the periodic regimes. There are two parameters related to the oscillating flow: the amplitude (amplitude of the Peclet number) and the period of the oscillations. In biologically reasonable regimes, we have found that the propagation velocity is higher in the oscillation regimes than in those without convection. This difference generally increases with the growing oscillation amplitude. The dependence of the propagation velocity on the period of harmonic flow is non-monotonous. In regimes with short periods, the propagation velocities are almost equal to the velocities in the systems without convection. For longer periods, the propagation velocity increases. At certain period value (typically ~10⁴ s), the velocity maximum is attained. The propagation velocity for very long periods can be obtained as the weighted velocity average given by the solution for constant Peclet numbers [1].

Our findings reveal that not only the convection transport but also its character can significantly accelerate or decelerate signal propagation mediated by growth factors in epithelia. We believe that our findings can be useful in tissue engineering or optimization of treatment therapies (convection enhanced delivery).

[1] M. Nebyla, M. Pribyl, and I. Schreiber, Effects of Convective Transport on Chemical Signal Propagation in Epithelia, Biophysical Journal 102, 2012