A stochastic model for cell adhesion to the vascular wall
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Cell dynamics in the vicinity of the vascular wall involves several factors of mechanical or biochemical origins. It is driven by the competition between the drag force of the blood flow and the resistive force generated by the bonds created between the circulating cell and the endothelial wall. Here, we propose a minimal mathematical model for the adhesive interaction between a circulating cell and the blood vessel wall in shear flow when the cell shape is neglected. The bond dynamics in cell adhesion is modeled as a nonlinear Markovian Jump process that takes into account the growth of adhesion complexes. Performing scaling limits in the spirit of Joffe and Metivier (Adv Appl Probab 18(1):20, 1986), Ethier and Kurtz (Markov processes: characterization and convergence, Wiley, New York, 2009), we obtain deterministic and stochastic continuous models, whose analysis allow to identify a threshold shear velocity associated with the transition from cell rolling and firm adhesion. We also give an estimation of the mean stopping time of the cell resulting from this dynamics. We believe these results can have strong implications for the understanding of major biological phenomena such as cell immunity and metastatic development.
KeywordsCell adhesion Metastatic development Immune response Atherosclerosis Stochastic process
Mathematics Subject Classification60J70 92C17
The authors are very grateful to V.C. Tran and R. Voituriez for very helpful discussions and suggestions.
- Dessalles R, D’Orsogna M, Chou T (2018) Exact steady-state distributions of multispecies birth-death-immigration processes: effects of mutations and carrying capacity on diversity. arXiv preprint arXiv:1806.00105
- Follain G, Osmani N, Azevedo S, Allio G, Mercier L, Karreman M, Solecki G, Fekonja N, Hille C, Chabannes V, Dolle G, Metivet T, Prudhomme C, Ruthensteiner B, Kemmling A, Siemonsen S, Schneider T, Fiehler J, Glatzel M, Winkler F, Schwab Y, Pantel K, Harlepp S, Goetz JG (2017) Hemodynamic forces tune the arrest, adhesion and extravasation of circulating tumor cells. bioRxiv . https://doi.org/10.1101/183046
- Granger DN, Senchenkova E (2010) Inflammation and the microcirculation. Colloquium series on integrated systems physiology: from molecule to function, vol 2. Morgan & Claypool Life Sciences, San Rafael, pp 1–87Google Scholar
- Korn C (2007) Stochastic dynamics of cell adhesion in hydrodynamic flow. Ph.D. thesis, Universität Potsdam, PotsdamGoogle Scholar
- Preziosi L, Vitale G (2011) Mechanics of tumor growth: multiphase models, adhesion, and evolving configurations, vol 92. New trends in the physics and mechanics of biological systems: Lecture Notes of the Les Houches Summer School. Oxford University Press, Oxford, p 177Google Scholar