Adhesive dynamics of lubricated films

Universal self-similar attractor in the bending-driven levelling of thin viscous films

We study theoretically and numerically the bending-driven levelling of thin viscous films within the lubrication approximation. We derive Green’s function of the linearized thin-film equation and further show that it represents a universal self-similar attractor at long times. As such, the rescaled perturbation of the film profile converges in time towards the rescaled Green’s function, for any summable initial perturbation profile. In addition, for stepped axisymmetric initial conditions, we demonstrate the existence of another, short-term and one-dimensional-like self-similar regime. We also characterize the convergence time towards the long-term universal attractor in terms of the relevant physical and geometrical parameters, and provide the local hydrodynamic fields and global elastic energy in the universal regime as functions of time. Finally, we extend our analysis to the nonlinear thin-film equation through numerical simulations.

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.

Elastohydrodynamics and Kinetics of Protein Patterning in the Immunological Synapse

We propose a minimal mathematical model for the physical basis of membrane protein patterning in the immunological synapse (IS), which encompass membrane mechanics, protein binding kinetics and motion, and fluid flow in the synaptic cleft. Our theory leads to simple predictions for the spatial and temporal scales of protein cluster formation, growth and arrest as a function of membrane stiffness, rigidity and kinetics of the adhesive proteins, and the fluid flow in the synaptic cleft. Numerical simulations complement these scaling laws by quantifying the nucleation, growth and stabilization of proteins domains on the size of the cell. Direct comparison with experiment shows that passive elastohydrodynamics and kinetics of protein binding in the synaptic cleft can describe the short-time formation and organization of protein clusters, without evoking any active processes in the cytoskeleton. Despite the apparent complexity of the process, our analysis shows that just two dimensionless parameters characterize the spatial and temporal evolution of the protein pattern: a ratio of membrane elasticity to protein stiffness, and the ratio of a hydrodynamic time scale for fluid flow relative to the protein binding rate. A simple phase diagram encompasses the variety of patterns that can arise.