Nucleation and decay initiation are the stiffness-sensitive phases of focal adhesion maturation

Abstract

A cell plated on a two-dimensional substrate forms adhesions with that surface. These adhesions, which consist of aggregates of various proteins, are thought to be important in mechanosensation, the process by which the cell senses and responds to the mechanical properties of the substrate (e.g., stiffness). On the basis of experimental measurements, we model these proteins as idealized molecules that can bind to the substrate in a strain-dependent manner and can undergo a force-dependent state transition. The model forms molecular aggregates that are similar to adhesions. Substrate stiffness affects whether a simulated adhesion is initially formed and how long it grows, but not how that adhesion grows or shrinks. Our own experimental tests support these predictions, suggesting that the mechanosensitivity of adhesions is an emergent property of a simple molecular-mechanical system.

Figure 1

Molecular-mechanical adhesion model. (A) A schematic diagram of a small focal adhesion (adapted in part from Kanchanawong et al. (13)). (B) A schematic diagram of a modeled adhesion. Each molecule may form four lateral bonds to its neighbors, may bind to the surface through a flexible domain, and may exist in two states. (C) The globular domain undergoes a load-dependent extension of length ΔH from a circle state to an ellipse state, mimicking the load-dependent extension of proteins in the adhesion. (D) The flexible domain may reversibly bind to the surface, mimicking the surface-binding properties of proteins in the adhesion.

Figure 2

Thought experiment demonstrating how ECM stiffness affects bond formation. Under applied force, the ECM deforms more on a soft surface (left) than on a stiff surface (right). Bond formation is then slower on softer ECMs as described by Eq. 2.

Figure 3

Comparison between simulations and experimental measurements of cultured cells. In plots B–F, simulations are shown on the left and experimental measurements are shown on the right. Time is measured in arbitrary units, and stiffness is measured in units of 3κ / 2πR in the simulations. (A) Still shots of a simulation, showing adhesion growth and subsequent decay. (B) Adhesion size as a function of time, showing growth and decay. Fits are the best-fit quadratic. (C) Adhesion growth as a function of time for two different ECM stiffnesses. The best-fit quadratic is shown as a black line. (D) Adhesion decay as a function of time for two different ECM stiffnesses. The best-fit quadratic is shown as a black line. (E) Steady-state adhesion number per cell, as a function of ECM stiffness (note log scale). The solid curve is a guide for the eye. In simulations, an adhesion is defined as an aggregate > 20 molecules. (F) Steady-state average adhesion size per cell, as a function of ECM stiffness (note log scale). The solid curve is a guide for the eye.

Figure 4

Comparison between simulations and simplified theory. Simulation details and theoretical expressions are presented in the Supporting Material. (A) The simple model, based on a three-step adhesion growth process. (B) Nucleation, the formation of a small molecular aggregate (10 molecules, in these simulations) from a single molecule as a function of force (left) and substrate stiffness (right). The gray point represents the same conditions in both plots. (C) Phase plot of stability as a function of adhesion size and surface stiffness. Here, stability is defined as an adhesion with a nonzero steady-state size.