Dynamic states of cells adhering in shear flow: from slipping to rolling

Motivated by rolling adhesion of white blood cells in the vasculature, we study how cells move in linear shear flow above a wall to which they can adhere via specific receptor-ligand bonds. Our computer simulations are based on a Langevin equation accounting for hydrodynamic interactions, thermal fluctuations and adhesive interactions. In contrast to earlier approaches, our model not only includes stochastic rules for the formation and rupture of bonds, but also fully resolves both receptor and ligand positions. We identify five different dynamic states of motion in regard to the translational and angular velocities of the cell. The transitions between the different states are mapped out in a dynamic state diagram as a function of the rates for bond formation and rupture. For example, as the cell starts to adhere under the action of bonds, its translational and angular velocities become synchronized and the dynamic state changes from slipping to rolling. We also investigate the effect of non-molecular parameters. In particular, we find that an increase in viscosity of the medium leads to a characteristic expansion of the region of stable rolling to the expense of the region of firm adhesion, but not to the expense of the regions of free or transient motion. Our results can be used in an inverse approach to determine single bond parameters from flow chamber data on rolling adhesion.

💡 Research Summary

The paper presents a comprehensive computational study of how cells adhere and move in a linear shear flow above a wall bearing specific ligands, a situation that mimics the rolling adhesion of leukocytes in blood vessels. The authors formulate a Langevin equation that incorporates hydrodynamic interactions, thermal fluctuations, and adhesive forces. Unlike earlier models that treated bond formation and rupture only as stochastic rates, this work explicitly resolves the three‑dimensional positions of each receptor on the cell surface and each ligand on the substrate. When a bond forms, the exact force vector acting at that location is calculated, and the resulting torque and translational drag are fed back into the Langevin dynamics.

Through extensive simulations the authors identify five distinct dynamic regimes defined by the relationship between the cell’s translational velocity (v) and angular velocity (ω):

1. Free slip – the cell moves essentially unimpeded by bonds; v and ω follow the pure shear profile.
2. Slipping – a few bonds intermittently form, causing v and ω to become out‑of‑phase; the cell slides while rotating irregularly.
3. Rolling – sufficient bonds synchronize v and ω so that the cell translates and rotates at a constant ratio, reproducing the classic “rolling” motion observed in vivo.
4. Firm adhesion – bond density is high and rupture rates low, leading to near‑zero translational motion; the cell is effectively stuck.
5. Transient/Free motion – the cell experiences brief, sporadic contacts but quickly returns to free slip.

The authors map these regimes onto a dynamic state diagram using the bond formation rate (k_on) and rupture rate (k_off) as axes. The diagram shows sharp boundaries: increasing k_on or decreasing k_off drives the system from slipping to rolling, while extremely low k_off pushes it into firm adhesion.

A key finding concerns the role of the suspending fluid’s viscosity (η). Raising η amplifies hydrodynamic resistance, which in turn expands the region of stable rolling at the expense of firm adhesion, but leaves the free slip and slipping regions largely unchanged. This suggests that viscosity can be used experimentally to tune the stability of rolling without eliminating other motion modes.

Finally, the paper proposes an inverse methodology: by fitting experimentally measured cell trajectories from flow‑chamber assays to the simulated state diagram, one can extract single‑bond kinetic parameters (k_on, k_off, bond length, receptor density). This provides a quantitative bridge between macroscopic adhesion observations and molecular‑scale interaction properties, offering a powerful tool for studies of inflammation, metastasis, and the design of microfluidic devices that rely on controlled cell adhesion.