Figure 1.
Schematics of the chemo-mechanical model of integrin dynamics.
(A) Depiction of the cell-ECM interface. Mobile integrin receptors are distributed on the bottom surface of an elastic thin plate representing the cell membrane and associated actin cortex. ECM ligand sites are randomly incorporated on the top surface of an elastic substrate. Deviation from the equilibrium separation distance between the plate and substrate are resisted by a harmonic potential representing the cellular glycocalyx. During the simulation, integrin receptors switch between inactive and active conformations, and active integrins can bind ECM ligands. Free integrins not bound to the matrix can also diffuse along the cell surface. Formation of integrin-ligand bonds can induce mechanical deformations in the plate and substrate. (B) Depiction of the lattice spring model (LSM) used to numerically calculate the stress-strain behavior in the interface. Simple cubic lattices of nodes are fit to the ECM substrate and membrane/cortex plate and all nearest and next nearest nodes in each lattice are connected by springs to represent the solid mechanics of these materials. Additional springs between the nodes in the top of the substrate and bottom of the plate are added to describe the mechanics of the glycocalyx as a simple harmonic potential. Some nodes on the top surface of the substrate LSM are designated as ligand binding sites. Integrin-ligand bonds are represented by additional spring connections between these ligand sites and the bottom of the membrane/cortex LSM.
Table 1.
Model parameters.
Figure 2.
Flow-diagram of the simulation algorithm.
Figure 3.
Membrane deformations in response to integrin-ligand bonds.
The membrane surface is depicted in the presence of one, two, or three bonds with a rigid substrate (xy- and z- coordinates are not to scale); σs = 1000 pN/nm, lg = 45 nm, σg = 0.01 pN/nm. The inlays are the corresponding xy- contour maps of the z- membrane displacements. Note that larger areas of the membrane are brought in closer proximity to the ECM substrate when more bonds are placed in close proximity to each other.
Figure 4.
The glycocalyx mediates integrin binding cooperativity and clustering on rigid matrixes.
(A) Hill plots of the steady-state integrin bond fraction versus ligand density for various effective glycocalyx thicknesses (lg−lb). The best-fit lines to the Hill equation are also shown. Bond fractions were determined by simulating integrin dynamics on rigid ECM substrates; s−1. (B) The Hill coefficients derived from non-linear least squares curve fitting of the Hill plots. (C) The extent of integrin clustering, as indicated by the Ripley K-statistic (maximum R(s)), as a function of effective glycocalyx thickness. (D) Correlation between integrin binding cooperativity (nHill) and the extent of integrin clustering. (E) Maps of the steady-state xy- integrin positions in the membrane for different effective glycocalyx thicknesses.
Figure 5.
Chemical and mechanical evolution of the integrin system.
The plots in (A) are temporal snapshots of the xy- positions of inactive integrins (red circles), active unbound integrins (light blue squares), and bound integrins (dark blue dots) obtained during simulation of integrin dynamics on a rigid ECM substrate with best-estimate parameters (Table 1). The corresponding equilibrium z-direction membrane deformations are depicted in (B). Simulated area: 3 µm×3 µm.
Figure 6.
Kinetic profiles of bond formation and clustering.
Plots showing the kinetic profiles of integrin bond formation (A) and the extent of integrin clustering (B) generated by simulating integrin dynamics on a rigid matrix with best-estimate parameters (Table 1).
Figure 7.
Integrin-ligand affinity, glycocalyx thickness, and bond length control integrin bond formation and clustering.
The maximal Ripley clustering statistic (A) and equilibrium integrin bond fraction (B) resulting from simulations on rigid substrates with various combinations of effective glycocalyx thickness (lg−lb) and integrin-ligand affinity (See Table 1 for parameters not depicted).
Figure 8.
Bond length and stiffness control integrin clustering.
Quantification of steady-state integrin clustering in simulations run with various values of bond stiffness (σb) and bond length (effective glycocalyx thickness; lg−lb). All additional simulation parameters are best-estimate and listed in Table 1.
Figure 9.
Cell and glycocalyx stiffness modulate integrin clustering and response to ligand spacing.
For various values of glycocalyx stiffness, (A) depicts xy-maps of the magnitude of z- direction membrane deformations that occur in response to a single integrin bond between the membrane/cortex and a rigid ECM substrate; lg = 39 nm. (B) depicts the steady-state integrin positions for various σg/σm ratios acquired by simulating integrin dynamics on a rigid ECM substrate; simulated area = 2 µm×2 µm. For various effective glycocalyx thicknesses, (C) plots the steady-state maximal Ripley clustering statistic against ligand density for integrin simulations on rigid substrates; s−1. (D) plots the steady-state Ripley clustering statistic against ligand density for various values of glycocalyx stiffness;
s−1.
Figure 10.
Integrin binding cooperativity and clustering are diminished on compliant ECM substrates.
(A) Hill plots and the corresponding best-fit lines to the Hill equation for integrin simulations on ECM substrates of varying stiffness as indicated by the Young's modulus, Y; s−1. The corresponding best-fit Hill coefficients (B) and maximum Ripley clustering statistic (C) as a function of substrate stiffness, demonstrating that integrin binding cooperativity and clustering are sensitive to the rigidity of the ECM substrate.