Numerical investigation of adhesion dynamics of a deformable cell pair on an adhesive substrate in shear flow

Adhesion dynamics of cells is of great value to biological systems and adhesion-based biomedical applications. Although adhesion of a single cell or capsule has been widely studied, physical insights into the adhesion dynamics of aggregates containing two or more cells remain elusive. In this paper, we numerically investigate the dynamic adhesion of a deformable cell pair to a flat substrate under shear flow. Specifically, the immersed boundary–lattice Boltzmann method is utilized as the flow solver, and the stochastic receptor-ligand kinetics model is implemented to recover cell-substrate and cell-cell adhesive interactions. Special attention is paid to the roles of the cell deformability and adhesion strengths in cellular motion. Four distinct adhesion states, namely, rolling, tumbling, firm adhesion, and detachment, are identified and presented in phase diagrams as a function of the adhesion strengths for cell pairs with different deformabilities. The simulation results suggest that both the cell-cell and cell-substrate adhesion strengths act as the resistance to the rolling motion, and dominate the transition among various adhesion states. The cell deformability not only enhances the resistance effect, but also contributes to detachment or fast tumbling of the cell pair. These findings enrich the understanding of adhesion dynamics of cell aggregates, which could shed light on complex adhesion processes and provide instructions in developing adhesion-based applications.

Figure 1

Schematic illustration of the adhesion of a cell pair in shear flow. The deformable cells are initially in the shape of a sphere with the radius R, in tandem arrangement along the flow direction. The linear shear flow (shear rate $\dot{\gamma }$) is generated by assigning the top wall with a constant velocity of $u_w$. Cell-cell and cell-substrate adhesive interactions are mediated by the binding of adhesion bonds with the probabilistic rule.

Figure 2

Simulation snapshots of a cell pair presenting the rolling adhesion state at $\mathrm{Ca}=0.002$, ${\mathrm{\Gamma }}_s=50$, and ${\mathrm{\Gamma }}_c=50$. The left column is the side view. A triangular element of each cell is marked as the tracker of the cell motion, red for the rear cell and green (light gray) for the front cell. The right column shows the bottom shape and bond forces (in lattice units) acting on the membrane, and the linked protrusions are marked with white nodes.

Figure 3

Simulation snapshots of a cell pair presenting the tumbling adhesion state at $\mathrm{Ca}=0.002$, ${\mathrm{\Gamma }}_s=50$, and ${\mathrm{\Gamma }}_c=150$.

Figure 4

Simulation snapshots of a cell pair presenting the firm-adhesion state at $\mathrm{Ca}=0.002$, ${\mathrm{\Gamma }}_s=100$, and ${\mathrm{\Gamma }}_c=150$.

Figure 5

Simulation snapshots of a cell pair presenting the detachment state at $\mathrm{Ca}=0.008$, ${\mathrm{\Gamma }}_s=50$, and ${\mathrm{\Gamma }}_c=150$.

Figure 6

Time histories of (a) the translational velocity of the front cell and (b) the number of linked bonds on its bottom, for the four distinct cases shown in Figs. 2–5.

Figure 7

Adhesion phase diagrams of the cell pair as a function of cell-cell and cell-substrate adhesion strengths with various capillary numbers ($\mathrm{Ca}=0.001–0.008$). Stop-and-go adhesion is defined as a transition state, marked with the upper triangular.

Figure 8

(a) Average translational velocity of the front cell and (b) average number of the linked bonds between the two cells. The mean value and standard error are collected from six independent simulation runs for each case.

Figure 9

Average number of linked bonds on the bottom of (a) the rear cell and (b) the front cell (mean±SE; $n=6$).

Figure 10

Average deformation of (a) the rear cell and (b) the front cell (mean±SE; $n=6$).

Figure 11

Average period of a tumbling motion (mean±SE; $n=6$).

Figure 12

Minimum and maximum numbers of linked bonds between the two cells during the tumbling motion (mean±SE; $n=6$).