Fig 1.
Overview of the processes modelled in this study.
(A)—Integrins bind to talin and vinculin in a precomplexation step, then form a small cluster, termed ‘seed’. Seeds can dimerise to form larger clusters, termed ‘clusts’. Actin filaments pull on talin and vinculin causing cryptic vinculin-binding sites on talin to be exposed, promoting more vinculin recruitment. This chain can then break at the integrin–ligand catch-slip bond or the talin–actin slip bond (black boxes). See Table 1 for a detailed description of the terminology. (B)—Overview of reactions in the model. Int, tal, and vinc refer to concentrations of integrins, talin and vinculin respectively. Black rectangle encloses the reinforcement reactions (expanded further in Fig 1C). Grey arrows represent clust formation reactions. Red arrows represent actin binding reactions. Dotted arrows represent force-dependent reactions—blue dotted: reinforcement, black dotted: actin unbinding. Dashed arrows represent adhesion disassembly reactions, black dashed: talin refolding, purple dashed: cluster breakdown. Yellow lightning bolts indicate rates that undergo signal-dependent rate modification (SDRM), dark green solid hourglasses represent rates that undergo time-dependent rate modification (TDRM). The rate constants undergoing signal-dependent modifications are driven to zero after ∼158 s leaving active only the lower part of the model, enclosed in the blue box, representing adhesions that will undergo further maturation. (C)—Talin and vinculin are modelled as Hookean springs (also see Fig A in S1 Appendix). In this model, to capture the process of reinforcement, a maximum of three vinculin binding events occur sequentially (blue arrows) at different points along the talin rod, thereby increasing the stiffness of individual integrin–talin–vinculin spring systems. Clustering is modelled as an increase in the number of integrin–talin–vinculin spring systems in parallel (grey arrows). This figure was created using BioRender.com.
Table 1.
Terminology used in this manuscript.
Fig 2.
Schematic showing the flowchart for simulation and force quantification.
Fig 3.
While NA formation is substrate stiffness independent, maturation is influenced considerably by stiffness.
(A)—Concentration over time of species in the model that represent NAs (S1 and C1). The curves for all tested substrate rigidities overlap and hence appear as a single (blue) line. The vertical dotted line marks the time point when the signal threshold is crossed and hence new NA formation reduces. (B)—Concentrations over time of all the actin-bound species. Species representing NAs (S1a, C1a) increase initially before being driven to 0 after the signal concentration drops below the threshold. The highest levels of maturation occur on substrate of moderate stiffness (ksub = 1 pN/nm).
Table 2.
Mean periods in s of different actin-bound clutches for different substrate stiffnesses.
Fig 4.
Model predictions of mean actin retrograde velocity and maturation fraction for the baseline model.
(A) shows the predicted velocity vs substrate stiffness compared to previous studies, (B) shows the predicted velocity (blue) and mean force exerted by all adhesions (red) in this model, and (C) shows the NA maturation fraction vs substrate stiffness.
Fig 5.
(A)—Maturation fraction vs stiffness (outcome 1) and (B)—Mean retrograde velocity vs stiffness for a local variation in parameter values of different parameters. Black arrows in (B) point in the direction of increasing parameter value and track the optimal stiffness (outcome 2).
Fig 6.
Vinculin concentration can influence maturation fraction.
(A) and (B) are cell types or biological contexts where vinculin availability is low and high respectively. In A, the likelihood of vinculin binding to the exposed vinculin-binding sites on talin is low leading to a low maturation fraction. However, in B, due to a relatively higher vinculin availability, the integrin-actin link is highly likely to be reinforced by vinculin, increasing the maturation fraction. This figure was created using BioRender.com.