Fig 1.
Composition and organization of an AC.
(a) the main cell components of the AC: fibronectin, transmembrane integrins, talin, vinculin, and an actomyosin network made of F-actin, myosin motors, and α-actinin. (b) Organization of these adhesion complex components in the AC. Fibronectin, laminin, or collagen serve as anchoring points for the transmembrane integrins to attach to the extracellular space. Integrins bind to the talin rod, which is also connected to the actin network through specific actin binding sites. Actin filaments bundle together mediated by α-actinin to form stress fibers and exert forces on the adhesion chain by the active pulling forces of myosin motors.
Fig 2.
Lifetime of the weakest link for slip (red) and catch bonds with CMR (solid blue). Experimental data of integrin α5β1 are shown in dots (black) [73]. The inset shows a zoom of the lifetime for small forces: catch case with CMR (solid blue) and without CMR (dashed blue).
Fig 3.
Composition of a single molecular chain and role of the ECM rigidity on an adhesion chain.
(a) From bottom to top, a single adhesion chain made of a substrate (green), represented as a spring, with one end attached to a fixed surface and the other bound to talin (yellow). The talin’s rod is made of 13 domains and its tail is attached to an actin fiber (red), which is connected to a number of myosin motors (blue), anchored to a fixed surface. Each talin’s domain behaves as a WLC or an FJC in their unfolded and folded states, respectively. (b-f) Model variables Fsub, P, v, xsub and xtalin for a molecular chain kept bound while varying Young’s modulus E of the substrate in the range 0.1–100 kPa. (g) The color map shows the average folded (red) or unfolded (blue) state for each Young’s modulus and domain of the talin rod. (h) An extension-force relation of the talin rod for a force-driven test at a rate of 3.8 pN / s. These results are reproduced from a previous publication [24]. (i) An force-extension relation of the talin rod in our model. The Young’s modulus of the substrate is 100 kPa, so it can be compared to data by Yao et al. [24]. Each peak corresponds with the unfold of a talin domain (11 in total).
Table 1.
Model parameters for an AC with α5β1 and αVβ3 integrins.
For Young’s modulus of the substrate, we take again the range E = 0.1–100 kPa. For the radius of the FA, we take a fixed value of a = 708 nm [50] with equispaced ligands at a distance of d = 100 nm. The number of equispaced ligands nc is then computed given the radius of the circular AC and the distance d, and we get nc = 158 binders (see Fig A5 in S1 Text). For the stiffness of the linear spring that models the integrin, we take κc = 10 pN/nm [40, 73]. For the initial density of integrins, we choose int/μm2 [8, 69]. The stall force of a single myosin motor is Fm = 2 pN [78] and we take several myosin motors equal to the number of ligands, following previous models [43, 69]. As for the unloaded actin velocity vu, we choose vu = 110 nm/s, similar to velocities measured in previous experimental data [79–81].
Fig 4.
Lifetime for α5β1 integrins with CMR and for αVβ3 integrins.
The parameters obtained for are reported in Table 1.
Fig 5.
Experimental and computational comparison of AC with α5β1 and αVβ3 integrins.
The computational results of tractions and retrograde flow velocities are averaged over 10 Gillespie simulations and plotted against Young’s modulus of the substrate E. The model results are compared against previous experimental data [8], represented with red dots.
Fig 6.
Computational results in an AC with α5β1 and αVβ3 integrins.
Results are averaged over 10 Gillespie simulations. We plot Pb, Bin. w/ Vinc., folding/unfolding states, xintmax and xtalinmax and Fcmax against Young’s modulus of the substrate E for ACs crowded with α5β1 (a) and αVβ3 (b). The color plot shows the folded/unfolded state of talin domains and it is obtained for one Gillespie simulation, averaging over the bound binders.
Fig 7.
Time behavior of AC with α5β1 and αVβ3 integrins.
Results are for one Gillespie simulation, fixing Young’s modulus of the substrate to E = 2.51 kPa. The figure shows the time evolution for Pb, Bin. w/ Vinc., folding/unfolding states, xintmax and xtalinmax and Fcmax for ACs crowded with α5β1 (a) and αVβ3 (b).
Fig 8.
Values of the model parameters and bond behavior.
(a) Default values and ranges for the parameters in the binding and unbinding rates of integrins for the multiscale clutch model. * indicates well-characterized parameters for which we only analyze a small range of values. For koff,slip and koff,catch we adopt an exponential distribution to cover several orders of magnitude. We use a linear distribution for the other parameters. We use previous experimental data on αIIbβ3 integrins to define the binding rate [85]. As for the range of the unbinding rate , we take into account the experimental data for the lifetime of α5β1, αVβ3 and αLβ2 integrins [86]. (b) Integrin lifetimes obtained with the extremes of the ranges for Fb,slip = Fb,catch, koff,catch and koff,slip, together with experimental data for α5β1 [40] and αVβ3 [8].
Fig 9.
Sensitivity analysis of the parameters integrin-fibronectin bond model.
Sensitivity analysis for the model parameters kont, koff,slip, koff,catch and Fb,slip = Fb,catch (a-d). We plot the variables Pb, the number of binders with vinculin (Bin. w/vinc), , and P against Young’s modulus of the substrate E in columns. The results are obtained averaging over 10 Gillespie simulations.
Fig 10.
Cell adhesion size as a function of the distance between ligands.
(a) Size of the ACs [50] and fit of the data to a Gaussian hill for ligand spacing of 50 nm (red), 100 nm (black), and 200 nm (blue). (b) The number of ligands nc and radius of the adhesion a for the variation of ligand spacing in α5β1 integrins.
Fig 11.
Results for variation of ligands spacing for α5β1 integrins.
(a-f) Results show Pb, xsub, ,
, Bin.w/ vinc. and P for distance between ligands of d 50 nm (in red), d = 100 nm (in black) and d = 200 nm (in blue).
Fig 12.
Experimental and computational comparison of forces and extension of the molecular chains.
Experimental data is presented in circles (see the introduction for references), computational results from previous clutch models in diamonds, and current computational results in squares. Forces are represented by the symbols in black and displacement in blue. Displacements are separated for talin and integrins.