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.actin ͉ bundle ͉ liquid crystal ͉ network F ilamentous actin (F-actin) is a highly charged, stiff biopolymer that is abundant in the cell and a key component of the cellular cytoskeleton. A cell controls the assembly of actin filaments into structures ranging from dilute networks, where filaments cross at large angles, to dense bundles, where filaments are closely packed and nearly parallel to one another (1). This structural polymorphism of actin filaments is crucial to cell function because different structures have different roles. Actin bundles have a key role during cell locomotion and cell adhesion (1). However, actin networks near the periphery of an animal cell form the cell cortex, which controls the mechanical properties of the cell surface. To exploit the functional differences between bundles and networks, cells switch between formation of these two structures during cell crawling and cell division (2, 3).Regulation of actin architecture requires control of both the kinetics of assembly and disassembly and of the morphology of actin aggregates. The assembly and disassembly of actin structures are carefully regulated by a number of specific actinbinding proteins, such as branching, capping, and severing proteins (1). However, the morphology, structure, and stability of actin aggregates are controlled by linker proteins, architectural proteins that can bind two filaments together (see refs. 4 and 5 and references therein). These linker proteins are typically classified into bundling proteins, primarily found in bundles, and crosslinking proteins, primarily found in networks. In addition, multivalent cationic species such as Ca 2ϩ , Mg 2ϩ , and spermine can control the morphology of actin aggregation and, therefore, should also be regarded as linkers.In this article, we focus on the equilibrium phase behavior of actin͞linker systems, with a view toward understanding structural polymorphism in the cytosk...

Self-assembled charged hydrogels control the alignment of filamentous actin

“…For example, Janmey and Tang 7,8 studied the effect of polycations on bundle formation of F-actin and found that a critical concentration of ions is required to induce bundling. By modeling actin as a charged rod in the presence of linker proteins, Liu et al 9 predicted the structural arrangements that lead to the formation of isotropic, nematic, cubatic, and bundle phases. These predictions were later confirmed by synchrotron X-ray scattering experiments.…”

Orientational order and glassy states in networks of semiflexible polymers

“…As a consequence, we are free to redefine the fields for later convenience by doing the replacements ℜΩ(k,m) → √ ∆m ℜΩ(k,m) and for the imaginary part accordingly. The advantage of this transformation is that the saddle-point fields Ω SP (k,m) are now directly related to an expectation value of Q(k,m) as presented in the main part, equation (12). This connection between Q and its corresponding field Ω is derived by means of an external field that couples to Q.…”

“…[11]. Theoretical attempts to study the formation of ordered structures in this kind of systems involve a generalized Onsager approach [12][13][14], a Flory-Huggins theory [15], and a semi-microscopic replica field theory [16]. In Refs.…”

“…In Refs. [12][13][14][15] the filaments are modeled as perfectly rigid rods whereas in Ref. [16] they are considered to be semiflexible polymers and the thermal bending fluctuations (finite persistence length) are fully taken into account.…”

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“…These may either be represented as a series of domains capable of unfolding (DiDonna & Levine, 2006), or as inextensible wormlike chains (Broedersz et al, 2008), leading to a softening or stiffening response, respectively. Recently theoretically studied problems also include thermodynamic properties and complex phase diagrams of polymer networks (Borukhov et al, 2005;Benetatos & Zippelius, 2007). An interesting interplay between single polymer and crosslinker dynamics arises in transiently connected networks, where the kinetics of the crosslinker leads to an additional viscous dissipation mechanism Wolff et al, 2010) (see Sec.…”