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| \justifying The endocytosis of 100nm targeted liposomes by endothelium cells in a shear flow is modeled by a set of master equations of the birth and death process. The relations between the shear rate and the parameters in the equations are established to analyze the effect of the shear flow on endocytosis. With the model, we show that the shear-induced variation of the bond formation rate does not influence the endocytosis and the insufficient binding strength of the non-specific attraction between lipid bilayers of liposomes and membranes of cells is the reason for the appreciable decrease in the number of endocytosed liposomes with the shear rate in former experiments. For the endocytosis of liposomes conjugated with PH1 peptide by human umbilical vein endothelial cells which expresses Tie2 receptors on their membranes, it is shown that the shear-elevated expression of Tie2 can evidently increase the number of endocytosed liposomes if the shear rate is larger than $100{\rm s}^{-1}$ and the duration of the experiment is longer than 30min. This result agrees with our experimental data. |
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| Keywords:biophysics, liposome, endocytosis, shear flow, receptor-ligand interaction, stochastic modeling |
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