ABSTRACT: Actin filaments are semiflexible polymers that display large-scale conformational twisting and bending motions. Modulation of filament bending and twisting dynamics has been linked to regulatory actin-binding protein function, filament assembly and fragmentation, and overall cell motility. The relationship between actin filament bending and twisting dynamics has not been evaluated. The numerical and analytical experiments presented here reveal that actin filaments have a strong intrinsic twist-bend coupling that obligates the reciprocal interconversion of bending energy and twisting stress. We developed a mesoscopic model of actin filaments that captures key documented features, including the subunit dimensions, interaction energies, helicity, and geometrical constraints coming from the double-stranded structure. The filament bending and torsional rigidities predicted by the model are comparable to experimental values, demonstrating the capacity of the model to assess the mechanical properties of actin filaments, including the coupling between twisting and bending motions. The predicted actin filament twist-bend coupling is strong, with a persistence length of 0.15-0.4 ?m depending on the actin-bound nucleotide. Twist-bend coupling is an emergent property that introduces local asymmetry to actin filaments and contributes to their overall elasticity. Up to 60% of the filament subunit elastic free energy originates from twist-bend coupling, with the largest contributions resulting under relatively small deformations. A comparison of filaments with different architectures indicates that twist-bend coupling in actin filaments originates from their double protofilament and helical structure.
Project description:We present a general model of actin filament deformation and fragmentation in response to compressive forces. The elastic free energy density along filaments is determined by their shape and mechanical properties, which were modeled in terms of bending, twisting, and twist-bend coupling elasticities. The elastic energy stored in filament deformation (i.e., strain) tilts the fragmentation-annealing reaction free-energy profile to favor fragmentation. The energy gradient introduces a local shear force that accelerates filament intersubunit bond rupture. The severing protein, cofilin, renders filaments more compliant in bending and twisting. As a result, filaments that are partially decorated with cofilin are mechanically heterogeneous (i.e., nonuniform) and display asymmetric shape deformations and energy profiles distinct from mechanically homogenous (i.e., uniform), bare actin, or saturated cofilactin filaments. The local buckling strain depends on the relative size of the compliant segment as well as the bending and twisting rigidities of flanking regions. Filaments with a single bare/cofilin-decorated boundary localize energy and force adjacent to the boundary, within the compliant cofilactin segment. Filaments with small cofilin clusters were predicted to fragment within the compliant cofilactin rather than at boundaries. Neglecting contributions from twist-bend coupling elasticity underestimates the energy density and gradients along filaments, and thus the net effects of filament strain to fragmentation. Spatial confinement causes compliant cofilactin segments and filaments to adopt higher deformation modes and store more elastic energy, thereby promoting fragmentation. The theory and simulations presented here establish a quantitative relationship between actin filament fragmentation thermodynamics and elasticity, and reveal how local discontinuities in filament mechanical properties introduced by regulatory proteins can modulate both the severing efficiency and location along filaments. The emergent behavior of mechanically heterogeneous filaments, particularly under confinement, emphasizes that severing in cells is likely to be influenced by multiple physical and chemical factors.
Project description:Computational and structural studies have been indispensable in investigating the molecular origins of actin filament mechanical properties and modulation by the regulatory severing protein cofilin. All-atom molecular dynamics simulations of cofilactin filament structures determined by electron cryomicroscopy reveal how cofilin enhances the bending and twisting compliance of actin filaments. Continuum mechanics models suggest that buckled cofilactin filaments localize elastic energy at boundaries between bare and cofilin-decorated segments because of their nonuniform elasticity, thereby accelerating filament severing. Here, we develop mesoscopic length-scale (cofil)actin filament models and evaluate the effects of compressive and twisting loads on strain energy distribution at specific interprotein interfaces. The models reliably capture the filament bending and torsional rigidities and intersubunit torsional flexibility measured experimentally with purified protein components. Buckling is predicted to enhance cofilactin filament severing with minimal effects on cofilin occupancy, whereas filament twisting enhances cofilin dissociation without compromising filament integrity. Preferential severing at actin-cofilactin boundaries of buckled filaments is more prominent than predicted by continuum models because of the enhanced spatial resolution. The models developed here will be valuable for evaluating the effects of filament shape deformations on filament stability and interactions with regulatory proteins, and analysis of single filament manipulation assays.
Project description:The assembly of actin filaments and filament networks generate forces that drive cell and vesicle movement. These structures and the comprising actin filaments must be mechanically stable to sustain these forces and maintain their structural integrity. Filaments in these dynamic structures must also be disassembled to recycle and replenish the pool of actin monomers available for polymerization. Actin-severing proteins such as cofilin and contractile myosin motor proteins fragment these nominally stable structures. We developed a mesoscopic-length-scale actin filament model to investigate force-induced filament fragmentation. We show that fragmentation in our model occurs at curvatures similar to previous measurements of fragmentation within (cofil)actin and actin-cofilactin boundaries. Boundaries between bare and cofilin-decorated segments are brittle and fragment at small bending and twisting deformations. Extending filaments disperses strain uniformly over subunit interfaces, and filaments fragment with no detectable partial rupture or plastic deformation. In contrast, bending or twisting filaments imposes nonuniform interface strain and leads to partial interface rupture, accelerating filament fragmentation. As a result, the rupture force under compressive loads is an order of magnitude lower than under tensile loads. Partial interface rupture may be a primary mechanism of accelerating actin filament fragmentation by other actin-destabilizing proteins.
Project description:Coiled-coil tropomyosin, localized on actin filaments in virtually all eukaryotic cells, serves as a gatekeeper regulating access of the motor protein myosin and other actin-binding proteins onto the thin filament surface. Tropomyosin's modular pseudo-repeating pattern of approximately 39 amino acid residues is designed to allow binding of the coiled-coil to successive actin subunits along thin filaments. Even though different tropomyosin isoforms contain varying numbers of repeat modules, the pseudo-repeat length, in all cases, matches that of a single actin subunit. Thus, the seven pseudo-repeats of 42nm long muscle tropomyosin bind to seven successive actin subunits along thin filaments, while simultaneously bending into a super-helical conformation that is preshaped to the actin filament helix. In order to form a continuous cable on thin filaments that is free of gaps, adjacent tropomyosin molecules polymerize head-to-tail by means of a short (?9 residue) overlap. Several laboratories have engineered peptides to mimic the N- and C-terminal tropomyosin association and to characterize the overlap structure. All overlapping domains examined show a compact N-terminal coiled-coil inserting into a partially opened C-terminal partner, where the opposing coiled-coils at the overlap junction face each other at up to ?90° twist angles. Here, Molecular Dynamics (MD) simulations were carried out to determine constraints on the formation of the tropomyosin overlap complex and to assess the amount of twisting exhibited by full-length tropomyosin when bound to actin. With the exception of the last 20-40 C- and N-terminal residues, we find that the average tropomyosin structure closely resembles a "canonical" model proposed in the classic work of McLachlan and Stewart, displaying perfectly symmetrical supercoil geometry matching the F-actin helix with an integral number of coiled-coil turns, a coiled-coil helical pitch of 137Å, a superhelical pitch of 770Å, and no localized pseudo-rotation. Over the middle 70% of tropomyosin, the average twisting of the coiled-coil deviates only by 10° from the canonical model and the torsional freedom is very small (std. dev. of 7°). This small degree of twisting cannot yield the orthogonal N- and C-termini configuration observed experimentally. In marked contrast, considerable coiled-coil unfolding, splaying and twisting at N- and C-terminal ends is observed, providing the conformational plasticity needed for head-to-tail nexus formation.
Project description:From a geometrical point of view, a non-sessile leaf is composed of two parts: a large flat plate called the lamina, and a long beam called the petiole which connects the lamina to the branch/stem. While wind is exerting force (e.g. drag) on the lamina, the petiole undergoes twisting and bending motions. To survive in harsh abiotic conditions, leaves may have evolved to form in different shapes, resulting from a coupling between the lamina geometry and the petiole mechanical properties. In this study, we measure the shape of laminae from 120 simple leaf species (no leaflets). Leaves of the same species are found to be geometrically similar regardless of their size. From tensile/torsional tests, we characterize the bending rigidity (EI) and the twisting rigidity (GJ) of 15 petioles of 4 species in the Spring/Summer: Red Oak (Quercus Rubra), American Sycamore (Platanus occidentalis), Yellow Poplar (Liriodendron tulipifera), and Sugar Maple (Acer saccharum). A twist-to-bend ratio EI/GJ is found to be around 4.3, within the range in previous studies conducted on similar species (EI/GJ?=?2.7~8.0 reported in S. Vogel, 1992). In addition, we develop a simple energetic model to find a relation between geometrical shapes and mechanical properties (EI/GJ?=?2LL/WC where LL is the laminar length and WC is the laminar width), verified with experimental data. Lastly, we discuss leaf's ability to reduce stress at the stem-petiole junction by choosing certain geometry, and also present exploratory results on the effect that seasons have on the Young's and twisting moduli.
Project description:Motivated to understand the behavior of biological filaments interacting with membranes of various types, we employ a theoretical model for the shape and thermodynamics of intrinsically helical filaments bound to curved membranes. We show that filament-surface interactions lead to a host of nonuniform shape equilibria, in which filaments progressively unwind from their native twist with increasing surface interaction and surface curvature, ultimately adopting uniform-contact curved shapes. The latter effect is due to nonlinear coupling between elastic twist and bending of filaments on anisotropically curved surfaces such as the cylindrical surfaces considered here. Via a combination of numerical solutions and asymptotic analysis of shape equilibria, we show that filament conformations are critically sensitive to the surface curvature in both the strong- and weak-binding limits. These results suggest that local structure of membrane-bound chiral filaments is generically sensitive to the curvature radius of the surface to which it is bound, even when that radius is much larger than the filament's intrinsic pitch. Typical values of elastic parameters and interaction energies for several prokaryotic and eukaryotic filaments indicate that biopolymers are inherently very sensitive to the coupling between twist, interactions, and geometry and that this could be exploited for regulation of a variety of processes such as the targeted exertion of forces, signaling, and self-assembly in response to geometric cues including the local mean and Gaussian curvatures.
Project description:Often considered an archetypal dimeric coiled coil, tropomyosin nonetheless exhibits distinctive "noncanonical" core residues located at the hydrophobic interface between its component ?-helices. Notably, a charged aspartate, D137, takes the place of nonpolar residues otherwise present. Much speculation has been offered to rationalize potential local coiled-coil instability stemming from D137 and its effect on regulatory transitions of tropomyosin over actin filaments. Although experimental approaches such as electron cryomicroscopy reconstruction are optimal for defining average tropomyosin positions on actin filaments, to date, these methods have not captured the dynamics of tropomyosin residues clustered around position 137 or elsewhere. In contrast, computational biochemistry, involving molecular dynamics simulation, is a compelling choice to extend the understanding of local and global tropomyosin behavior on actin filaments at high resolution. Here, we report on molecular dynamics simulation of actin-free and actin-associated tropomyosin, showing noncanonical residue D137 as a locus for tropomyosin twist variation, with marked effects on actin-tropomyosin interactions. We conclude that D137-sponsored coiled-coil twisting is likely to optimize electrostatic side-chain contacts between tropomyosin and actin on the assembled thin filament, while offsetting disparities between tropomyosin pseudorepeat and actin subunit periodicities. We find that D137 has only minor local effects on tropomyosin coiled-coil flexibility, (i.e., on its flexural mobility). Indeed, D137-associated overtwisting may actually augment tropomyosin stiffness on actin filaments. Accordingly, such twisting-induced stiffness of tropomyosin is expected to enhance cooperative regulatory translocation of the tropomyosin cable over actin.
Project description:In the presence of condensing agents such as nonadsorbing polymer, multivalent counter ions, and specific bundling proteins, chiral biopolymers typically form bundles with a finite thickness, rather than phase-separating into a polymer-rich phase. Although short-range repulsive interactions or geometrical frustrations are thought to force the equilibrium bundle size to be limited, the precise mechanism is yet to be resolved. The importance of the tight control of biopolymer bundle size is illustrated by the ubiquitous cytoskeletal actin filament bundles that are crucial for the proper functioning of cells. Using an in vitro model system, we show that size control relies on a mismatch between the helical structure of individual actin filaments and the geometric packing constraints within bundles. Small rigid actin-binding proteins change the twist of filamentous actin (F-actin) in a concentration-dependent manner, resulting in small, well defined bundle thickness up to approximately 20 filaments, comparable to those found in filopodia. Other F-actin cross-linking proteins can subsequently link these small, well organized bundles into larger structures of several hundred filaments, comparable to those found in, for example, Drosophila bristles. The energetic tradeoff between filament twisting and cross-linker binding within a bundle is suggested as a fundamental mechanism by which cells can precisely adjust bundle size and strength.
Project description:Force generation by actin assembly shapes cellular membranes. An experimentally constrained multiscale model shows that a minimal branched actin network is sufficient to internalize endocytic pits against membrane tension. Around 200 activated Arp2/3 complexes are required for robust internalization. A newly developed molecule-counting method determined that ~200 Arp2/3 complexes assemble at sites of clathrin-mediated endocytosis in human cells. Simulations predict that actin self-organizes into a radial branched array with growing ends oriented toward the base of the pit. Long actin filaments bend between attachment sites in the coat and the base of the pit. Elastic energy stored in bent filaments, whose presence was confirmed by cryo-electron tomography, contributes to endocytic internalization. Elevated membrane tension directs more growing filaments toward the base of the pit, increasing actin nucleation and bending for increased force production. Thus, spatially constrained actin filament assembly utilizes an adaptive mechanism enabling endocytosis under varying physical constraints.
Project description:Many biological processes, including cell division, growth, and motility, rely on rapid remodeling of the actin cytoskeleton and on actin filament severing by the regulatory protein cofilin. Phosphorylation of vertebrate cofilin at Ser-3 regulates both actin binding and severing. Substitution of serine with aspartate at position 3 (S3D) is widely used to mimic cofilin phosphorylation in cells and in vitro The S3D substitution weakens cofilin binding to filaments, and it is presumed that subsequent reduction in cofilin occupancy inhibits filament severing, but this hypothesis has remained untested. Here, using time-resolved phosphorescence anisotropy, electron cryomicroscopy, and all-atom molecular dynamics simulations, we show that S3D cofilin indeed binds filaments with lower affinity, but also with a higher cooperativity than wild-type cofilin, and severs actin weakly across a broad range of occupancies. We found that three factors contribute to the severing deficiency of S3D cofilin. First, the high cooperativity of S3D cofilin generates fewer boundaries between bare and decorated actin segments where severing occurs preferentially. Second, S3D cofilin only weakly alters filament bending and twisting dynamics and therefore does not introduce the mechanical discontinuities required for efficient filament severing at boundaries. Third, Ser-3 modification (i.e. substitution with Asp or phosphorylation) "undocks" and repositions the cofilin N terminus away from the filament axis, which compromises S3D cofilin's ability to weaken longitudinal filament subunit interactions. Collectively, our results demonstrate that, in addition to inhibiting actin binding, Ser-3 modification favors formation of a cofilin-binding mode that is unable to sufficiently alter filament mechanical properties and promote severing.