Nascent Adhesion Clustering: Integrin-Integrin and Integrin-Substrate Interactions
Abstract
:1. Introduction
2. Nascent Adhesion Clusters: Background
Finer Points Regarding the Background on Nascent Clusters
3. Clustering Model: Outline
3.1. Specific Integrin Elastic Model
3.2. Simulation Model: General Set Up
3.3. Simulation Model: Force Mediated Diffusion
3.4. Ligation vs. Bond Rupture Kinetics
3.5. Scaffolding Proteins Affect Clustering: Talin
4. Results
4.1. Effects of Parameters
- Ligation distance, : As the force, f, within an integrin depends on , as does the integrin’s displacement field, we expect this parameter to have a first order effect on integrin migration and ligation binding lifetime. These effects are, however, complex due to the cooperative nature of integrin interaction as well as the stochastic nature of integrin migration and ligation and un-ligation behavior. We further note that the interaction forces are related to combinations of terms such as as in Equation (7), and as and , the interaction force between integrins may be expected to dominated by . However, as the internal force, f, depends on E, the rate of un-ligation will depend directly on stiffness E. Hence the effects of E, per se, are not easily anticipated a priori. For example, due to the attractive forces among the integrins we expect that increased mobilities will tend to reduce time scales for cluster formation and perhaps affect cluster size.
- Integrin diffusion coefficient, D: Both the rate of diffusion and viscous motion depend on the magnitude of D since the viscous mobility, , and D are related as . Hence we expect that D will have a first order effect in promoting clustering.
- Cell membrane-substrate stiffness, E: The effect of stiffness has already been noted and we expect that its main effect will be in determining whether clusters are stable or not; this is expected due to the effect of large integrin internal forces on the rate of un-ligation, i.e., . In terms of interaction force, the effect of E becomes more difficult to anticipate in such a stochastic process as diffusion-interaction driven clustering. Hence, we might say “we’ll see what happens and try to rationalize after”.
4.2. Simulation Results
4.2.1. Cluster-Cluster Interaction
5. Discussion
- We have demonstrated that nascent clusters should form on substrates of all rigidities, a claim made in the title of Changede and Sheetz [32,33]. This basis for their finding becomes clear upon the realization that a driving force for clustering stems from the energy reductions that follow clustering as illustrated by attractive pairwise force between integrins given in, e.g., Equation (7). As noted earlier, this force scales directly with terms such as where and , respectively, scale as E and , E being the system rigidity (stiffness). Hence, the this force does not depend strongly on system rigidity; the internal force within an integrin, however, does depend on system rigidity and that will affect ligation bond survival time. Of course, this basis may also be appreciated by the simulations of Reynar et al. [58,59] noted above; in those cases there was no substrate, but only the free energy of the deformed membrane.
- Our simulations reveal important quantitative and qualitative effects of integrin mobility, on clustering as illustrated in Figure 10, and by comparing Figure 10 with Figure 9, as examples. First, we observe that clusters tend to be larger when the mobility of unligated integrins is increased; in the specific case studies clusters were in the size range (in Figure 9) and with a factor of 5 increase in were more in the range of (in Figure 10) in diameter. Moreover, if ligated integrins were ascribed a somewhat increased mobility, clusters were observed to “drift” so that they aggregated. To visualize why this may happen, we noted that clusters that stand apart by some distance from each other appear as “large point forces” and hence attract with a force similar in kind to that described by Equation (7) for single integrin pairs; this is the thermodynamic force driving the drifting motion. The actual mechanism for this drifting involves integrin unligation and ligation at the juxtaposed peripheries of merging clusters as illustrated in the simulation frames shown for Case #2 of Figure 10. But the question arises: what accounts for this enhanced mobility of ligated integrins? In the cases studied by Changede and Sheetz [32], involving cells on supported bilipid layers (SBLs), they reported that the ligands on SBLs were mobile. For cells adhered to an ECM or an organic substrate this would remain an open question. Nonetheless, if clusters are observed to aggregate, this offers a potential mechanism. Clearly, this sort of observation, among others, suggests that integrin mobility is an important determinant for deciphering cluster dynamics and hence experimental studies of clustering will be deficient without such information.
- On the question of integrin mobility we note the study of Rossier et al. [93] as a noteworthy example. Their study was particularly concerned with understanding the role of, in particular and containing, integrins dynamics on FAs in fibroblasts on fibronectin substrates. We have used these studies to motivate our variations in diffusion coefficient as explained in our case studies above. Accordingly, we “immobilize” integrins upon ligation where we have assumed that the integrins bind talin, and possibly kindlins as well; this is done by assigning a nearly vanishingly small value of . Rossier et al. [93] defined integrin confinement within FAs in terms of a radius, , and with that specified diffusion coefficients accordingly. This sort of detail may be incorporated into a model such as ours for further refinement.
- Finally we add that our model helps explain the patterns of integrin clustering observed in the experiments we have cited, e.g., [32,33,34], that are some of the most comprehensive conducted to date. In particular, we find that the numbers of integrins that appear in clusters appears to lie in the range of 30–50 which is again typical to what is observed experimentally [32,33]; this in itself is a noteworthy and not obvious trend. However we also note that depending on factors such as the initial density of integrins and the magnitude of diffusion coefficients numbers outside this range are indeed possible. For this reason we have made special note that future studies of nascent clustering should document the mobility of integrins as well as their expressed numbers.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Lin, K.; Asaro, R.J. Nascent Adhesion Clustering: Integrin-Integrin and Integrin-Substrate Interactions. Biophysica 2022, 2, 34-58. https://doi.org/10.3390/biophysica2010004
Lin K, Asaro RJ. Nascent Adhesion Clustering: Integrin-Integrin and Integrin-Substrate Interactions. Biophysica. 2022; 2(1):34-58. https://doi.org/10.3390/biophysica2010004
Chicago/Turabian StyleLin, Kuanpo, and Robert J. Asaro. 2022. "Nascent Adhesion Clustering: Integrin-Integrin and Integrin-Substrate Interactions" Biophysica 2, no. 1: 34-58. https://doi.org/10.3390/biophysica2010004