Coarse-grained modeling of the actin filament derived from atomistic-scale simulations

Abstract

A coarse-grained (CG) procedure that incorporates the information obtained from all-atom molecular dynamics (MD) simulations is presented and applied to actin filaments (F-actin). This procedure matches the averaged values and fluctuations of the effective internal coordinates that are used to define a CG model to the values extracted from atomistic MD simulations. The fluctuations of effective internal coordinates in a CG model are computed via normal-mode analysis (NMA), and the computed fluctuations are matched with the atomistic MD results in a self-consistent manner. Each actin monomer (G-actin) is coarse-grained into four sites, and each site corresponds to one of the subdomains of G-actin. The potential energy of a CG G-actin contains three bonds, two angles, and one dihedral angle; effective harmonic bonds are used to describe the intermonomer interactions in a CG F-actin. The persistence length of a CG F-actin was found to be sensitive to the cut-off distance of assigning intermonomer bonds. Effective harmonic bonds for a monomer with its third nearest neighboring monomers are found to be necessary to reproduce the values of persistence length obtained from all-atom MD simulations. Compared to the elastic network model, incorporating the information of internal coordinate fluctuations enhances the accuracy and robustness for a CG model to describe the shapes of low-frequency vibrational modes. Combining the fluctuation-matching CG procedure and NMA, the achievable time- and length scales of modeling actin filaments can be greatly enhanced. In particular, a method is described to compute the force-extension curve using the CG model developed in this work and NMA. It was found that F-actin is easily buckled under compressive deformation, and a writhing mode is developed as a result. In addition to the bending and twisting modes, this novel writhing mode of F-actin could also play important roles in the interactions of F-actin with actin-binding proteins and in the force-generation process via polymerization.

FIGURE 1

Atomic model of F-actin (left) of Holmes et al. (40) and the CG representation (right). Each actin monomer has four sites denoted as Dn, where n = 1–4. Actin monomers are denoted by italic numbers.

FIGURE 2

Log of the cosine function of binding angles of an F-actin as a function of its contour length. θ(s) is the bending angle at contour length s, and θ₀(s) is the equilibrium angle at s. In the x axis, the contour length, s, is normalized by the average length corresponding to each monomer, δs₀; that is, the contour length is represented as the number of G-actin monomers along an actin filament.

FIGURE 3

Persistence lengths of the A models (left) and the B models (right; see text for definitions of the models) of the CG F-ATP (solid) and F-ADP (shaded). The values computed from all-atom simulations are also labeled.

FIGURE 4

Force constant, k, of the effective bonds in the B₆ model of F-ATP (left) and F-ADP (right) as a function of their equilibrium length, b₀. The effective bond between a monomer and its nearest neighbor monomers is shown as solid circles. The longer-range effective bonds, including the interactions with the second and third nearest monomers are shown in open circles. The fitted scaling orders of k and a function of b₀ for the solid circles and the open circles are also shown.

FIGURE 5

Dot products of the vibrational eigenvectors computed from the NMA of the A₆ CG model to that from the quasiharmonic analysis of the all-atom MD trajectories. The values of Mode 1 (the mode with the smallest vibrational frequency; solid) and the averaged values of modes 1–5 (shaded) are shown for both F-ATP (left) and F-ADP (right).

FIGURE 6

Force-extension curves of F-actin with three repeat units (3 × 13 = 39 monomers) of F-ATP (left) and F-ADP (right). The corresponding stretching stiffness per μm of the filament are also labeled. Under compression, the filament buckles and a writhing mode is developed.