Stochastic dynamics of adhesion clusters under shared constant force and with rebinding

Abstract

Single receptor-ligand bonds have finite lifetimes, so that biological systems can dynamically react to changes in their environment. In cell adhesion, adhesion bonds usually act cooperatively in adhesion clusters. Outside the cellular context, adhesion clusters can be probed quantitatively by attaching receptors and ligands to opposing surfaces. Here we present a detailed theoretical analysis of the stochastic dynamics of a cluster of parallel bonds under shared constant loading and with rebinding. Analytical solutions for the appropriate one-step master equation are presented for special cases, while the general case is treated with exact stochastic simulations. If the completely dissociated state is modeled as an absorbing boundary, mean cluster lifetime is finite and can be calculated exactly. We also present a detailed analysis of fluctuation effects and discuss various approximations to the full stochastic description.

Probing mechanical principles of focal contacts in cell–matrix adhesion with a coupled stochastic–elastic modelling framework

“…Based on this assumption, the deterministic equation of Bell's framework [30] predicted that molecular clusters remain stable and have infinite lifetime up to a critical load; in contrast, more recent work by Erdmann & Schwarz [36,37] indicated that the cluster lifetime is always finite and increases monotonically as the cluster size grows: the larger the cluster, the longer the cluster lifetime.…”

“…For time-independent loading, both theories and experiments have indicated that the dissociation rate k off of a closed bond increases exponentially with a force F acting on the bond as [30]: For failure of a multiple-bond adhesion, such as those in FAs, one must take into account the fact that individual bonds can rebind after they break until the whole adhesion is detached. The analysis of single bond force spectroscopy [53] did not consider such rebinding, but theoretical considerations by Erdmann & Schwarz [36,37] indicated that bond rebinding can greatly enhance the adhesion lifetime.…”

“…More recent progresses have been made in modelling curved biological membranes spreading on a flat substrate mediated by binder diffusion [33,34], as well as receptor-mediated cellular uptake and release of viruses or nanoparticles [35]. Erdmann & Schwarz [36,37] Focal adhesions can be exposed to cytoskeletally generated contractile forces in actin bundles, as well as externally applied loads outside of the cell.…”

Dynamic force spectroscopy on multiple bonds: Experiments and model

“…Here the simplest possible case is the irreversible rupture of a small number of equivalent bonds, which can be described in the mathematical framework of a one-step master equation [9]. Multiple bonds also allow rebinding of broken bonds, which can be described in the same framework [11,12]. It has also been applied before to the case of linear loading commonly used in DFS [13].…”

Forced desorption of semiflexible polymers, adsorbed and driven by molecular motors

“…Such peeling experiments have been shown to be important in quantifying the strengths of actomyosin rigor bonds, in absence of ATP driven activity, measured by pulling F-actins off myosin coated substrate using optical tweezers [40]. Rupture of multiple bonds have also been studied in the context of cell adhesion [41][42][43][44][45] and the unzipping of DNA [46][47][48]. Semiflexible polymers themselves are known to show interesting mechanical and dynamic properties [49][50][51][52][53][54][55].…”