Adhesive dynamics of lubricated films

Membrane waves have been observed near the leading edge of a motile cell. Such phenomenon is the result of the interplay between hydrodynamics and adhesive dynamics. Here we consider membrane dynamics on a thin fluid gap supported by adhesive bonds. Using coupled lubrication theory and adhesive dynamics, we derive an evolution equation to account for membrane tension, bending, adhesion, and viscous lubrication. Four adhesion scenarios are examined: no adhesion, uniform adhesion, clustered adhesion, and focal adhesion. Two contrasting traveling wave types are found, namely, tension and adhesion waves. Tension waves disperse with time and space, whereas adhesion waves show increased amplitudes and are highly persistent. We show that the transition from tension to adhesion waves depends on a necessary, but insufficient, criterion that the wave amplitude must exceed a critical gap height, which is dependent on adhesion binding probability. We also show that strong adhesion results in sharp tension-to-adhesion wave transitions. The present work could explain the strong persistence of the waves observed in adhered cells using differential inference contrast (DIC) microscopy and the observation that the wavelengths decrease shortly after leading edge retraction.