Structural polymorphism of the cytoskeleton: a model of linker-assisted filament aggregation

Abstract

The phase behavior of charged rods in the presence of interrod linkers is studied theoretically as a model for the equilibrium behavior underlying the organization of actin filaments by linker proteins in the cytoskeleton. The presence of linkers in the solution modifies the effective interrod interaction and can lead to interfilament attraction. Depending on the composition and physical properties of the system, such as linker-binding energies, filaments will orient either perpendicular or parallel to each other, leading to network-like or bundled structures. We show that such a system can have one of three generic phase diagrams, one dominated by bundles, another by networks, and the third containing both bundle and network-like phases. The first two diagrams can be found over a wide range of interaction energies, whereas the third diagram occurs only for a narrow range. These results provide theoretical understanding of the classification of linker proteins as bundling proteins or crosslinking proteins. In addition, they suggest possible mechanisms by which the cell may control cytoskeletal morphology.

Fig. 1.

The different phases included in our calculation and their corresponding rod-orientational distributions. In the isotropic phase, rods can be oriented in any direction. In the nematic phase, rods tend to align in a preferential direction. In the cubatic phase, rods tend to align in three mutually perpendicular directions, and in the bundle phase, rods are aligned and hexagonally close-packed.

Fig. 2.

The effective rod–rod potential described by Eqs. 1, 2, 3. This potential is characterized by a short-ranged repulsion, an intermediate-ranged attraction, and a longer-ranged repulsion. It is characterized by four energies; u_∥ < 0 and represent the linker-mediated attractions, and Γ_∥ > 0 and are the electrostatic repulsions when the rods are parallel and perpendicular, respectively. The minima at 0° and 90° can rise or fall depending on these four energies.

Fig. 3.

The three possible phase diagrams for solutions of charged rods and linkers. In all three cases, we use ε₁ = ε_∥ =-7_. (a) Bundle-dominated phase diagram. Here, . Note that this phase diagram does not contain the cubatic phase anywhere. (b) Intermediate-phase diagram. Here, . This diagram contains the cubatic phase at low linker concentration and the bundle phase at higher linker concentrations. (c) Network-dominated phase diagram. Here, . Note that this diagram does not contain bundles anywhere.