(264f) Impacts of Low Peclet Number Flow and Oscillatory Flow on Autocrine Signaling

Convective flow can occur even in relatively compact tissues, such as epithelium, and can significantly alter the character of autocrine signaling. We developed a mathematical model of cellular communication based on reaction-transport equations. We assume a combined convective-diffusive transport of a morphogen in the extracellular space. Morphogen-membrane receptor interactions, release of new morphogen and receptor molecules as well as membrane-bound proteins endocytosis are considered. The intracellular response to the morphogen binding is represented by a sigmoidal or the Heaviside function. The Peclet number for the morphogen is used as a measure of convective flux in the cellular system.

In our study, the autocrine communication is represented by a traveling front wave of the morphogen concentration above a uniform cellular layer. We studied dependence of the propagation velocity on various model parameters such as the Peclet number, size of the extracellular domain or morphogen-receptor binding strength. A model was proposed and numerical simulations were carried out. In addition, an exact solution of the model equations in an asymptotic regime was found.

We found that if the signal propagates downstream, the parameter region of high propagation velocities becomes much broader and extends over several orders of magnitude of the morphogen-receptor binding constant. When the convective transport is oriented against the propagating signal, either the traveling front wave is slowed down or becomes suspended or even reverses its direction of propagation. The effect of the convective transport becomes more significant in systems where the characteristic dimension of the extracellular space is larger than the spatial extent of the ligand diffusion trafficking.

 We also studied effects of oscillatory convective flow on the propagation velocity. We found that the time-averaged propagation velocity under oscillatory flow is smaller than the velocity under steady laminar flow regime at the corresponding value of the Peclet number, but significantly larger than under no-flow conditions. We derive asymptotic values of the propagation velocity and asymptotic characteristics of the corresponding concentration fronts in high- and low-frequency regimes and show that the observed velocity increase under the oscillatory flow originates in a convex dependence of the propagation velocity on the Peclet number. Our findings suggest that the specific response of cellular cultures to different flow conditions in the extracellular space is a consequence of nonlinear coupling between the extracellular transport and intracellular reaction cascades leading to a positive feedback loop of the autocrine signaling.

 Nebyla, M., Pribyl, M., Schreiber, I.: Oscillatory Flow Accelerates Autocrine Signaling due to Nonlinear Effect of Convection on Receptor-Related Actions. Biophysical Journal 105(3): 818-828, 2013.

Nebyla, M., Pribyl, M., Schreiber, I.: Effects of Convective Transport on Chemical Signal Propagation in Epithelia. Biophysical Journal 102(5): 990-1000, 2012.