Mechanical properties of chiral actin filaments

TL;DR

Actin filaments are intrinsically chiral, and their helicity influences mechanical properties and motor-driven dynamics. The authors introduce a highly coarse-grained, yet chiral, double-protofilament actin model implemented in Cytosim, linking five microscopic inputs to five macroscopic observables ($R$, $P$, $L_P$, $K_\tau$, $K_S$) and demonstrating that geometry and mechanics emerge from energy minimization. The study shows that actin chirality biases motor-driven dynamics in gliding, spiral, and bundle configurations, producing clockwise bundle rotation and other chiral behaviors that resemble filopodial dynamics. This framework provides a general, extensible tool for mesoscale simulations of helical filaments and can be extended to other helices beyond actin, enabling rapid exploration of chiral cytoskeletal dynamics.

Abstract

The mechanical properties of actin filaments are essential to their biological functions. Here, we introduce a highly coarse-grained model of actin filaments that preserves helicity and chirality while enabling mesoscale simulations. The framework is implemented in Cytosim, an open-source cytoskeleton simulation platform. We can predict and finely control the shape and mechanical properties of this helical filament, that can be matched to experimental values. Using this model, we investigated the role of filament chirality in motor-driven dynamics. We first show that in two different experimental configurations, motor movement along a helical filament results in a chiral motion of the filament. In a bundle of helical filaments, dimeric motors exert torques on each filament, inducing collective behaviors in the bundle such as rotation, coiling, and helical buckling, reminiscent of those observed in filopodia. Together, these results demonstrate the central role of helicity and chirality in actin mechanics and motor-driven dynamics, and establish our framework as a powerful tool for mesoscale simulations. This framework can also be used for other helical filaments beyond actin.

Figures (10)

• Figure 1: (a) Schematic representation of a helical actin filament. The filament consists of two linear, flexible protofilaments, each discretized to a series of segments. The two protofilaments are interconnected by a series of springs. A torque, $\Gamma$, applied to each pair of facing segments induces a twist that transforms the whole structure into a double-helical filament. This torque is implemented as four equal forces acting at the ends of each segment in opposite directions. The mechanical behavior of the helical filament is characterized by three main mechanical properties: torsional rigidity ($K_\tau$), bending persistence length ($L_P$), and inter-protofilament separation rigidity ($K_S$). (b) Snapshot of the helical filament obtained from Cytosim simulations.
• Figure 2: Variation of normalized radius $R/R_0$ as a function of (a) spring stiffness $K$, (b) torque stiffness $\Gamma$, and (c) bending rigidity of the protofilaments $\kappa$. Symbols represent simulation results, while solid lines correspond to theoretical predictions from the total energy minimization (Eq. \ref{['eq1']}). Panels (d--f) show the corresponding variation of normalized pitch $P/P_0$ as a function of $K$, $\Gamma$, and $\kappa$, respectively.
• Figure 3: Effect of (a) spring stiffness $K$, (b) torque stiffness $\Gamma$, and (c) protofilament bending rigidity $\kappa$ on the bending persistence length $L_P$ of the helical filament. Panels (d--f) show the corresponding effect of these parameters on the torsional rigidity $K_{\tau}$. (g) inter-protofilament separation rigidity $K_S$ as a function of spring stiffness $K$, (h) torque stiffness $\Gamma$, and (i) protofilament bending rigidity $\kappa$. The order of magnitude of $K_S$ is $10^6$, corresponding to a Young’s modulus of roughly $1~\text{GPa}$ for the helical filament.
• Figure 4: Minimal models of helix mechanical properties. (a) torsional rigidity behaves as two coupled (in parrallel) springs of two independent modes (in series). (b) persistence length behaves as two modes coupled by torsional rigidity ; each mode is made of two independent modes, both controlled by bending rigidity $\kappa$ and spring stiffness $K$. (c) separation stiffness behaves as three coupled units, one of them being pure spring stiffness $K$, and the two others being spring stiffness or bending/torsional rigidity.
• Figure 5: (a) Schematic illustration of a gliding assay, with anchored motor proteins shown in green. The surface normal is denoted by $\bm{n}$, and $\bm{u}$ represents the radial unit vector of the helix directed from one protofilament to the other. (b) Sinusoidal variation of the rotational angle, $\bm{n} \cdot \bm{u}$, of the gliding filament as a function of time. (c) Dependence of the angular velocity, $\dot{\theta}$, of the gliding filament on motor density. The filament consistently rotates counterclockwise relative to its translational axis, from the barbed (+) end to the pointed (-) end. (d) Time trajectory of a long helical filament ($2 \mu m$) in the gliding assay, showing a counter-clockwise pattern.