Many
experimental and theoretical studies have shown that the mechanical
properties of cells and the extracellular matrix can significantly
affect the lifetime and strength of the adhesion clusters of molecular
bonds. However, there are few studies on how the shape of the contact
surface affects the lifetime and strength of the adhesion clusters
of molecular bonds, especially theoretical studies in this area. An
idealized model of focal adhesion is adopted, in which two rigid media
are bonded together by an array of receptor–ligand bonds modeled
as Hookean springs on a complex surface topography, which is described
by three parameters: the surface shape factor β, the length
of a single identical surface shape L, and the amplitude
of surface shapes w. In this study, systematic Monte
Carlo simulations of this model are conducted to study the lifetime
of the molecular bond cluster under linear incremental force loading
and the strength of the molecular bond cluster under linear incremental
displacement loading. We find that both small surface shape amplitudes
and large surface shape factors will increase the lifetime and strength
of the adhesion cluster, whereas the length of a single surface shape
causes oscillations in the lifetime and strength of the cluster, and
this oscillation amplitude is affected by the surface shape amplitude
and the factor. At the same time, we also find that the pretension
in the cluster will play a dominant role in the adhesion strength
under large amplitudes and small factors of surface shapes. The physical
mechanisms behind these phenomena are that the changes of the length
of a single surface shape, the amplitude of surface shapes, and the
surface shape factor cause the changes of stress concentration in
the adhesion region, bond affinity, and the number of similar affinity
bonds.