We study effects of convective transport on a chemical front wave representing a signal propagation at a simple (single layer) epithelium by means of mathematical modeling. Plug flow and laminar flow regimes were considered. We observed a nonmonotonous dependence of the propagation velocity on the ligand receptor binding constant under influence of the convective transport. If the signal propagates downstream, the region of high velocities becomes much broader and spreads over several orders of magnitude of the binding constant. When the convective transport is oriented against the propagating signal, either velocity of the traveling front wave is slowed down or the traveling front wave can stop or reverse the direction of propagation. More importantly, chemical signal in epithelial systems influenced by the convective transport can propagate almost independently of the ligand-receptor binding constant in a broad range of this parameter. Furthermore, we found that the effects of the convective transport becomes more significant in systems where either the characteristic dimension of the extracellular space is larger/comparable with the spatial extent of the ligand diffusion trafficking or the ligand-receptor binding/ligand diffusion rate ratio is high.

Department of Chemical Engineering Institute of Chemical Technology Prague Czech Republic

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Heldin C.H. Academic Press; San Diego, CA: 2011. Functioning of transmembrane receptors in cell signaling.

Mandell J.W., Gocan N.C., Vandenberg S.R. Mechanical trauma induces rapid astroglial activation of ERK/MAP kinase: evidence for a paracrine signal. Glia. 2001;34:283–295. PubMed

Kim H.G., Kassis J., Wells A. EGF receptor signaling in prostate morphogenesis and tumorigenesis. Histol. Histopathol. 1999;14:1175–1182. PubMed

Swartz M.A. Signaling in morphogenesis: transport cues in morphogenesis. Curr. Opin. Biotechnol. 2003;14:547–550. PubMed

Cartwright J.H.E., Piro O., Tuval I. Fluid-dynamical basis of the embryonic development of left-right asymmetry in vertebrates. Proc. Natl. Acad. Sci. USA. 2004;101:7234–7239. PubMed PMC

Okada Y., Takeda S., Hirokawa N. Mechanism of nodal flow: a conserved symmetry breaking event in left-right axis determination. Cell. 2005;121:633–644. PubMed

Rutkowski J.M., Swartz M.A. A driving force for change: interstitial flow as a morphoregulator. Trends Cell Biol. 2007;17:44–50. PubMed

Lee D.Y., Li Y.S.J., Chien S. Oscillatory flow-induced proliferation of osteoblast-like cells is mediated by alpha(v)beta(3) and beta(1) integrins through synergistic interactions of focal adhesion kinase and Shc with phosphatidylinositol 3-kinase and the Akt/mTOR/p70S6K pathway. J. Biol. Chem. 2010;285:30–42. PubMed PMC

Shi Z.D., Ji X.Y., Tarbell J.M. Interstitial flow promotes vascular fibroblast, myofibroblast, and smooth muscle cell motility in 3-D collagen I via upregulation of MMP-1. Am. J. Physiol. Heart Circ. Physiol. 2009;297:H1225–H1234. PubMed PMC

Shi Z.D., Ji X.Y., Tarbell J.M. Interstitial flow induces MMP-1 expression and vascular SMC migration in collagen I gels via an ERK1/2-dependent and c-Jun-mediated mechanism. Am. J. Physiol. Heart Circ. Physiol. 2010;298:H127–H135. PubMed PMC

Boardman K.C., Swartz M.A. Interstitial flow as a guide for lymphangiogenesis. Circ. Res. 2003;92:801–808. PubMed

Helm C.L.E., Fleury M.E., Swartz M.A. Synergy between interstitial flow and VEGF directs capillary morphogenesis in vitro through a gradient amplification mechanism. Proc. Natl. Acad. Sci. USA. 2005;102:15779–15784. PubMed PMC

Semino C.E., Kamm R.D., Lauffenburger D.A. Autocrine EGF receptor activation mediates endothelial cell migration and vascular morphogenesis induced by VEGF under interstitial flow. Exp. Cell Res. 2006;312:289–298. PubMed

Hernández Vera R., Genové E., Semino C.E. Interstitial fluid flow intensity modulates endothelial sprouting in restricted Src-activated cell clusters during capillary morphogenesis. Tissue Eng. Part A. 2009;15:175–185. PubMed PMC

Pozrikidis C. Numerical simulation of blood and interstitial flow through a solid tumor. J. Math. Biol. 2010;60:75–94. PubMed

Song J.W., Munn L.L. Fluid forces control endothelial sprouting. Proc. Natl. Acad. Sci. USA. 2011;108:15342–15347. PubMed PMC

Shieh A.C., Swartz M.A. Regulation of tumor invasion by interstitial fluid flow. Phys. Biol. 2011;8:015012. PubMed

Bobo R.H., Laske D.W., Oldfield E.H. Convection-enhanced delivery of macromolecules in the brain. Proc. Natl. Acad. Sci. USA. 1994;91:2076–2080. PubMed PMC

Chen D., Norris D., Ventikos Y. The active and passive ciliary motion in the embryo node: a computational fluid dynamics model. J. Biomech. 2009;42:210–216. PubMed

Nguyen T.H., Eichmann A., Fleury V. Dynamics of vascular branching morphogenesis: the effect of blood and tissue flow. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2006;73:061907. PubMed

Fleury M.E., Boardman K.C., Swartz M.A. Autologous morphogen gradients by subtle interstitial flow and matrix interactions. Biophys. J. 2006;91:113–121. PubMed PMC

Luss D., Sheintuch M. Spatiotemporal patterns in catalytic systems. Catal. Today. 2005;105:254–274.

Sheintuch M., Nekhamkina O. Thermal patterns in simple models of cylindrical reactors. Chem. Eng. Sci. 2003;58:1441–1451.

Nekhamkina O., Sheintuch M. Transversal moving-front patterns: criteria and simulations for two bed and cylindrical shell packed-bed reactors. Chem. Eng. Sci. 2008;63:3716–3726.

Dixon J.B., Raghunathan S., Swartz M.A. A tissue-engineered model of the intestinal lacteal for evaluating lipid transport by lymphatics. Biotechnol. Bioeng. 2009;103:1224–1235. PubMed PMC

Dobens L.L., Raftery L.A. Integration of epithelial patterning and morphogenesis in Drosophila ovarian follicle cells. Dev. Dyn. 2000;218:80–93. PubMed

Pribyl M., Muratov C.B., Shvartsman S.Y. Long-range signal transmission in autocrine relays. Biophys. J. 2003;84:883–896. PubMed PMC

Muratov C.B., Posta F., Shvartsman S.Y. Autocrine signal transmission with extracellular ligand degradation. Phys. Biol. 2009;6:016006. PubMed

Ng C.P., Helm C.L.E., Swartz M.A. Interstitial flow differentially stimulates blood and lymphatic endothelial cell morphogenesis in vitro. Microvasc. Res. 2004;68:258–264. PubMed

Tomei A.A., Siegert S., Swartz M.A. Fluid flow regulates stromal cell organization and CCL21 expressions in a tissue-engineered lymph node microenvironment. J. Immunol. 2009;183:4273–4283. PubMed

Haessler U., Kalinin Y., Wu M. An agarose-based microfluidic platform with a gradient buffer for 3D chemotaxis studies. Biomed. Microdevices. 2009;11:827–835. PubMed

Chang S.F., Chang C.A., Chiu J.J. Tumor cell cycle arrest induced by shear stress: roles of integrins and Smad. Proc. Natl. Acad. Sci. USA. 2008;105:3927–3932. PubMed PMC

Shamloo A., Ma N., Heilshorn S.C. Endothelial cell polarization and chemotaxis in a microfluidic device. Lab Chip. 2008;8:1292–1299. PubMed

Park J.Y., Yoo S.J., Lee S.H. Simultaneous generation of chemical concentration and mechanical shear stress gradients using microfluidic osmotic flow comparable to interstitial flow. Lab Chip. 2009;9:2194–2202. PubMed

Shin H.S., Kim H.J., Jeon N.L. Shear stress effect on transfection of neurons cultured in microfluidic devices. J. Nanosci. Nanotechnol. 2009;9:7330–7335. PubMed

Deen W.M. Oxford University Press; New York: 1998. Analysis of Transport Phenomena.

Bird R.B., Stewart W.E., Lightfoot E.N. John Wiley & Sons; New York: 2002. Transport Phenomena.

White F.M. McGraw-Hill; New York: 1994. Fluid Mechanics.

Qiao L., Nachbar R.B., Shvartsman S.Y. Bistability and oscillations in the Huang-Ferrell model of MAPK signaling. PLOS Comput. Biol. 2007;3:1819–1826. PubMed PMC

Shvartsman S.Y., Hagan M.P., Lauffenburger D.A. Autocrine loops with positive feedback enable context-dependent cell signaling. Am. J. Physiol. Cell Physiol. 2002;282:C545–C559. PubMed

Ferrell J.E., Jr., Machleder E.M. The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. Science. 1998;280:895–898. PubMed

Pribyl M., Muratov C.B., Shvartsman S.Y. Discrete models of autocrine cell communication in epithelial layers. Biophys. J. 2003;84:3624–3635. PubMed PMC

Shvartsman S.Y., Wiley H.S., Lauffenburger D.A. Spatial range of autocrine signaling: modeling and computational analysis. Biophys. J. 2001;81:1854–1867. PubMed PMC

Doedel E.J., Oldeman B.E. Concordia University; Montreal, Canada: 2009. AUTO-07P: Continuation and bifurcation software for ordinary differential equations.

Aris R. On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A Math. Phys. Sci. 1956;235:67–77.

Kolev S.D., van der Linden W.E. Laminar dispersion in parallel plate sections of flow systems used in analytical chemistry and chemical engineering. Anal. Chim. Acta. 1991;247:51–60.

Grayson W.L., Fröhlich M., Vunjak-Novakovic G. Engineering anatomically shaped human bone grafts. Proc. Natl. Acad. Sci. USA. 2010;107:3299–3304. PubMed PMC

Chung S., Sudo R., Kamm R.D. Microfluidic platforms for studies of angiogenesis, cell migration, and cell-cell interactions. Ann. Biomed. Eng. 2010;38:1164–1177. PubMed

Galie P.A., Stegemann J.P. Simultaneous application of interstitial flow and cyclic mechanical strain to a three-dimensional cell-seeded hydrogel. Tissue Eng. Part C Methods. 2011;17:527–536. PubMed PMC

Krakstad C., Chekenya M. Survival signalling and apoptosis resistance in glioblastomas: opportunities for targeted therapeutics. Mol. Cancer. 2010;9:135. PubMed PMC

Varma A., Morbidelli M. Oxford University Press; New York: 1997. Mathematical Methods in Chemical Engineering.

Minimal oscillating subnetwork in the Huang-Ferrell model of the MAPK cascade

Oscillatory flow accelerates autocrine signaling due to nonlinear effect of convection on receptor-related actions