[Paper Review] On Stretching, Bending, Shearing and Twisting of Actin Filaments II: Multi-Resolution Modelling

Ravinda S. Gunaratne, Carlos Floyd+3 more|arXiv (Cornell University)|Mar 2, 2022

Cellular Mechanics and Interactions4 citations

TL;DR

This paper introduces a multi-resolution model for actin filaments that combines a detailed monomer-based ellipsoid representation with a coarse-grained Cosserat rod model to simulate stretching, bending, shearing, and twisting efficiently. By incorporating curvature-dependent rigidity and twist-stretch coupling derived from all-atom-like simulations, the method accurately captures torsional behavior, especially under over-twisting, where filaments contract significantly—improving upon standard Cosserat models that fail to reproduce this asymmetry.

ABSTRACT

We present a multi-resolution methodology for modelling F-actin filaments. It provides detailed microscopic information at the level of individual monomers at a lower computational cost by replacing the monomer-based model in parts of the simulated filament by a rod-based macroscopic model. In the monomer-based description, G-actin is represented by ellipsoids bound at the surface in a double helical configuration to form F-actin. The rod-based model is coarser, in which F-actin is described using a Cosserat model, as seen in the preceding paper [arXiv:2112.01480]. The multi-resolution methodology is illustrated using three case studies, designed to test the properties of F-actin under stretching, bending, shearing and twisting. The methodology is especially suited for situations where filaments are subject to bending deformations. We investigate the limitations of using the standard Cosserat model to capture the complete torsional behaviour of F-actin, presenting its extensions which account for curvature dependent rigidities and a twist-stretch coupling to improve accuracy of the overall multi-resolution scheme.

Motivation & Objective

• To develop a computationally efficient multi-resolution model for F-actin that combines microscopic monomer detail with macroscopic rod mechanics.
• To address the limitations of standard Cosserat models in capturing the asymmetric torsional response of actin filaments under over- and under-twisting.
• To derive and implement a twist-stretch coupling mechanism based on data from ellipsoid-based simulations to improve mechanical fidelity.
• To enable large-scale simulations of actin filaments under complex mechanical loads while retaining key mechanical details in critical regions.
• To validate the model through case studies on stretching, bending, shearing, and twisting, focusing on torsional behavior and curvature-dependent rigidity.

Proposed method

• The model uses a monomer-based description of F-actin as ellipsoids arranged in a double helix, representing individual G-actin subunits with explicit interactions.
• In regions of interest, the filament is modeled using a Cosserat rod model with parameters derived from the ellipsoid model to reduce computational cost.
• A curvature-dependent twist rigidity function ξ(κ̂L,3) is introduced, where the rest length of segments is adjusted based on local curvature to simulate twist-induced extension or contraction.
• The trapezoidal quadrature operator Âih is used to estimate segment curvature from discrete Voronoi region curvatures, enabling accurate local adaptation of mechanical properties.
• The twist-stretch coupling is parameterized using data from ellipsoid simulations under varying torsion, with a polynomial fit p6 to p0 used to define ξ(κ̂L,3).
• The model integrates these corrections into the normal acceleration calculations of the Cosserat rod, allowing dynamic response to torsional deformation.

Experimental results

Research questions

• RQ1 How can a multi-resolution model be designed to simulate F-actin under stretching, bending, shearing, and twisting with high computational efficiency?
• RQ2 Why does the standard Cosserat model fail to accurately capture the torsional behavior of F-actin, particularly under over-twisting?
• RQ3 What is the nature of the twist-stretch coupling in F-actin, and how can it be quantitatively modeled to improve mechanical fidelity?
• RQ4 Can curvature-dependent rigidity improve the accuracy of Cosserat rod models in simulating actin filament mechanics?
• RQ5 How does the filament length change under different torsional states, and can this asymmetry be captured in a coarse-grained model?

Key findings

• The standard Cosserat model underperforms under torsional loads, failing to reproduce the asymmetric length change observed in the ellipsoid model.
• Under over-twisting (e.g., 240°), the filament contracts by 4.34% of its original length, while under-twisting leads to a smaller contraction of 1.26% at 240°, indicating non-symmetric mechanical response.
• The twist-stretch coupling function ξ(κ̂L,3) was successfully parameterized using a sixth-order polynomial with coefficients p6 = -2.6662×10⁶ to p0 = -5.0666×10⁻⁴, enabling accurate length adaptation under torsion.
• The inclusion of curvature-dependent rigidity and twist-stretch coupling significantly improves the mechanical fidelity of the Cosserat model, especially in torsional regimes.
• The multi-resolution model enables accurate simulation of complex mechanical behaviors at a fraction of the computational cost of all-atom or monomer-based models.
• Case studies confirm the model’s capability to reproduce key mechanical responses, including bending dynamics and asymmetric torsional deformation, validating its use in large-scale biological simulations.