We study effects of oscillatory convective flow in extracellular space on the velocity of chemical signal propagation having a form of a front wave above a cellular layer. We found that the time-averaged propagation velocity under oscillatory flow for a particular Péclet number amplitude is slower than the velocity under steady laminar flow regime for the same value of the Péclet number, but significantly faster 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 reason for the observed velocity increase under the oscillatory flow stems from a nonlinear dependence of the propagation velocity on the Péclet number, particularly from the convex character of the dependence. Our findings suggest that the specific responses of cellular cultures to different flow conditions in the extracellular space (for example, expression of atherosclerosis protective genes under steady laminar flow but not under oscillatory flow) is a consequence of a nonlinear coupling between the extracellular transport and complex intracellular reaction cascades forming a positive feedback loop of the autocrine signaling. This mechanism can operate independently of, or in conjunction with, a direct stress-sensing due to mechanotransduction.

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