Integrin clustering is driven by mechanical resistance from the glycocalyx and the substrate

From Soft-Matter
Jump to: navigation, search

Entry by Angelo Mao, AP 225, Fall 2010

Title: Integrin clustering is driven by mechanical resistance from the glycocalyx and the substrate

Authors: Paszek M, et al

Journal: PloS Computational Biology

Volume: Vol 5(12)

Pages: e1000604


Summary

The authors create a model for integrin-ligand binding dynamics out of only several elements: the substrate, the cell surface, the intervening glycocalyx layer, integrins, and ligands. Due to the fact that an integrin-ligand bond deforms the surface of the cell and substrate to increase proximity between free ligands and integrins, the model demonstrates that integrin-ligand binding is a cooperative event, leading to integrin clustering. This model matches experimental observations relating ligand density, substrate stiffness, and other factors to integrin-ligand binding.

soft matter keywords: extracellular matrix, substrate, Hill coefficient

Model

Figure 1. Schematic of the model.

The authors used a lattice spring model (LSM) to model the stress and strain of the deformable cell membrane and substrate surface. In this model, the materials were treated as having nodes attached by springs. The integrin-ligand bonds themselves were treated as Hooke-ian springs, and the kinetics of the bond formation as a function of distance followed Bell's model. More specifically, within a certain distance, integrin and ligands attracted each other, and this affinity followed Boltzmann's distribution. The glycocalyx layer between the cell and its substrate was also modeled as a spring. As part of this model, the integrins were allowed to diffuse through the cell layer, and this was modeled by Monte Carlo simulation; the progression of the system as a whole was also simulated by Monte Carlo. Moreover, the movement of unbound integrins was different from that of bound integrins, and subject to a "hop" reaction.

To quantitatively analyze clustering of integrins on the cell surface, Ripley's K-functions were maximized. (The Ripley's K-function is a way of analyzing how dot clustering deviates from a Poisson distribution.)

Figure 2. Integrin clustering.
Figure 3. Heat map showing deformation of cell membrane.

Figure 3 is a good pictoral representation, derived from the researchers' model, explaining why cooperative integrin binding occurs. The first bond deforms the membrane so that the membrane is closer to the substrate at that point than others. Integrins near that first bond would be closer to ligands on the substrate, and the affinity between integrin and ligand would lead to integrin translation across the surface of the cell membrane, clustering, and patch of integrin-ligand bonds. One can imagine that the initial dark blue points in the earlier time points of Figure 2 led to deformation of the cell membrane as shown in figure 3, and subsequent clustering.

Figure 4. Varying parameters (explained below)

The authors varied parameters such as ligand density, substrate stiffness, and glycocalyx stiffness. Figure 4 shows the model's results of how bond number and Hill coefficient (which is indicative of cooperative binding) change with substrate stiffness and ligand density; the Y in figure 3A indicates the Young's modulus of the substrate. The logarithmic shape of figure A is indicative of cooperative binding, and the Hill coefficients are shown in B. Cooperativity is minor on soft substrates, the authors posit, because the substrate is so soft that cooperativity is unimportant. Cooperativity increases linearly (aka from the Hill coefficient) up to a certain stiffness.

Discussion

Various models had been proposed to explain integrin-ligand formation, which is characterized by clustering and variations based on substrate and ligand density variation. This model shows that the observed changes may occur solely from the energetics involved in integrin-ligand bonds, and the ability of integrins to migrate through the cell membrane. Previous studies do show, however, that there are intracellular components that affect integrin-ligand bonds, so this model only encapsulates a part of all integrin-ligand binding events. This model also has implications to the creation of soft materials for cell behavior, since it clearly shows that properties of the substrate strongly regulate binding. One of the more interesting predictions of the model is the time scale, which shows that most integrin-ligand bonds form and most clustering occurs within the first minute (figure 2). Comparing this time scale against that of the downstream biological effects of the bond formation would be interesting. Lastly, this model is philosophically interesting because it suggests that complex biological phenomena can be explained by the energies of physical interactions.

This model has limitations, however. The most significant one, probably, is that it assumes that the cell is resting peacefully on the glycocalyx layer on the substrate, an assumption that would be false in situations of fluid shear stress or other mechanical strain, as occurs in many physiological environments.