Complex intramolecular mechanics of G-actin--an elastic network study

Abstract

Systematic numerical investigations of conformational motions in single actin molecules were performed by employing a simple elastic-network (EN) model of this protein. Similar to previous investigations for myosin, we found that G-actin essentially behaves as a strain sensor, responding by well-defined domain motions to mechanical perturbations. Several sensitive residues within the nucleotide-binding pocket (NBP) could be identified, such that the perturbation of any of them can induce characteristic flattening of actin molecules and closing of the cleft between their two mobile domains. Extending the EN model by introduction of a set of breakable links which become effective only when two domains approach one another, it was observed that G-actin can possess a metastable state corresponding to a closed conformation and that a transition to this state can be induced by appropriate perturbations in the NBP region. The ligands were roughly modeled as a single particle (ADP) or a dimer (ATP), which were placed inside the NBP and connected by elastic links to the neighbors. Our approximate analysis suggests that, when ATP is present, it stabilizes the closed conformation of actin. This may play an important role in the explanation why, in the presence of ATP, the polymerization process is highly accelerated.

Figure 1. Actin and its elastic network: (A) G-actin in the ribbon representation, colored according to its subdomains S1 (orange), S2 (yellow), S3 (blue) and S4 (green).

The bound ADP molecule (red) is shown. (B) The elastic network of G-actin, colored in the same way. Magenta dotted lines indicate breakable links (Lennard-Jones type bonds) between some residues (also marked magenta) in the subdomains S2 and S4. The nucleotide-binding pocket (NBP) is schematically displayed.

Figure 2. Responses to global perturbations. 100 relaxation trajectories (red curves) start from different initial conditions, generated by application of random, globally distributed static forces.

Each trajectory begins from a stationary state obtained after application of a different random set of static forces. Such forces are removed when the subsequent relaxation trajectories are considered. The final states for each of these trajectories are marked by green points. Panel B shows the projection of relaxation trajectories on the plane defined by the dihedral angle and the distance between the mass centers of the two mobile subdomains.

Figure 3. Responses to global perturbations (A) and to local pertubations of sensitive residues in the NBP region (B) are shown in the presence of breakable bonds.

100 relaxation trajectories (red curves) start from random initial conditions. The final states for each initial deformation are marked by green points. In addition to the equilibrium, metastable closed states are observed.

Figure 4. Residues in the neighborhood of the phosphate (red cross) which belong to the three sensory loops G, H and S inside the NBP.

Red beads indicate the sensitive residues as identified in Table 1.

Figure 5. Simple modeling of ligands.

(A) The ADP is modeled as an additional node (purple bead) added to the elastic network. It is connected to all its neighbors (grey beads) by elastic links. (B) The ATP is modeled as a dimer consisting of ADP (purple bead) and (grey bead), connected by an elastic link. The ADP is elastically connected to its neighbors and the phosphate is elastically linked to the three sensitive nodes (red beads).

Figure 6. Ligand-dependent conformational states of G-actin.

(A) Equilibrium state with the ADP ligand bound. (B) Equilibrium state with the ATP ligand bound. (C) Metastable state with the ADP ligand bound. ADP is shown as a bigger red bead, and is visualized as a small red bead; ATP is modeled as a dimer consisting of ADP and Pi. Magenta-colored beads indicate residues between which additional breakable links can become established. Such breakable links are shown by solid magenta lines, if they are actually present, and by dashed lines if they are broken.

Figure 7. The pattern of relaxation trajectories for the ligand-network complex.

The blue trajectory shows relaxation starting from the open equilibrium conformation of G-actin without the ligand. The others start from the perturbed conformations which were obtained by applying random static forces to the three sensitive residues in the NBP region. The open conformation does not correspond to a stationary state of the complex and all trajectories converge to the new equilibrium closed state indicated by the green dot.

Figure 8. Statistical distributions of interdomain distances in G-actin under thermal noise in the presence of ADP (black) or ATP (red) ligands.