Toru Ekimoto

Finite-Size Effect on the Charging Free Energy of Protein in Explicit Solvent

The finite-size effect in periodic system is examined for the charging free energy of protein in explicit solvent over a variety of charged states. The key to the finite-size correction is the self-energy, which is defined as the interaction energy of the solute with its own periodic images and the neutralizing background. By employing the thermodynamic-integration method with systematically varied sizes of the unit cell of molecular dynamics (MD) simulations, we show for ubiquitin that the self-energy corrects the finite-size effect on the charging free energy within 1 kcal/mol at total charges of -5e, -1e, neutral, and +1e and within 5 kcal/mol even for a highly charged state with +8e. We then sought the additional correction from the solvation effect using the numerical solution to the Poisson equation of the protein with implicit solvent. This correction reduces the cell-size dependence of the charging free energy at +8e to 3 kcal/mol and is well expressed as the self-energy divided by the dielectric constant of solvent water.

An accurate and efficient computation method of the hydration free energy of a large, complex molecule

The hydration free energy (HFE) is a crucially important physical quantity to discuss various chemical processes in aqueous solutions. Although an explicit-solvent computation with molecular dynamics (MD) simulations is a preferable treatment of the HFE, huge computational load has been inevitable for large, complex solutes like proteins. In the present paper, we propose an efficient computation method for the HFE. In our method, the HFE is computed as a sum of 〈UUV〉/2 (〈UUV〉 is the ensemble average of the sum of pair interaction energy between solute and water molecule) and the water reorganization term mainly reflecting the excluded volume effect. Since 〈UUV〉 can readily be computed through a MD of the system composed of solute and water, an efficient computation of the latter term leads to a reduction of computational load. We demonstrate that the water reorganization term can quantitatively be calculated using the morphometric approach (MA) which expresses the term as the linear combinations of the four geometric measures of a solute and the corresponding coefficients determined with the energy representation (ER) method. Since the MA enables us to finish the computation of the solvent reorganization term in less than 0.1 s once the coefficients are determined, the use of the MA enables us to provide an efficient computation of the HFE even for large, complex solutes. Through the applications, we find that our method has almost the same quantitative performance as the ER method with substantial reduction of the computational load.

Rotation Mechanism of Molecular Motor V1-ATPase Studied by Multiscale Molecular Dynamics Simulation

Enterococcus hirae V1-ATPase is a molecular motor composed of the A3B3 hexamer ring and the central stalk. In association with ATP hydrolysis, three catalytic AB pairs in the A3B3 ring undergo conformational changes, which lead to a 120° rotation of the central stalk. To understand how the conformational changes of three catalytic pairs induce the 120° rotation of the central stalk, we performed multiscale molecular dynamics (MD) simulations in which coarse-grained and all-atom MD simulations were combined using a fluctuation matching methodology. During the rotation, a catalytic AB pair spontaneously adopted an intermediate conformation, which was not included in the initial inputs of the simulations and was essentially close to the “bindable-like” structure observed in a recently solved crystal structure. Furthermore, the creation of a space between the bindable-like and tight pairs was required for the central stalk to rotate without steric hindrance. These cooperative rearrangements of the three catalytic pairs are crucial for the rotation of the central stalk.

Separation of Dynamics in the Free Energy Landscape

The dynamics of a representative point in a model free energy landscape (FEL) is analyzed by the Langevin equation with the FEL as the driving potential. From the detailed analysis of the generalized susceptibility, fast, slow and Johari‐Goldstein (JG) processes are shown to be well described by the FEL. Namely, the fast process is determined by the stochastic motion confined in a basin of the FEL and the relaxation time is related to the curvature of the FEL at the bottom of the basin. The jump motion among basins gives rise to the slow relaxation whose relaxation time is determined by the distribution of the barriers in the FEL and the JG process is produced by weak modulation of the FEL.

Multiscale molecular dynamics simulations of rotary motor proteins

Protein functions require specific structures frequently coupled with conformational changes. The scale of the structural dynamics of proteins spans from the atomic to the molecular level. Theoretically, all-atom molecular dynamics (MD) simulation is a powerful tool to investigate protein dynamics because the MD simulation is capable of capturing conformational changes obeying the intrinsically structural features. However, to study long-timescale dynamics, efficient sampling techniques and coarse-grained (CG) approaches coupled with all-atom MD simulations, termed multiscale MD simulations, are required to overcome the timescale limitation in all-atom MD simulations. Here, we review two examples of rotary motor proteins examined using free energy landscape (FEL) analysis and CG-MD simulations. In the FEL analysis, FEL is calculated as a function of reaction coordinates, and the long-timescale dynamics corresponding to conformational changes is described as transitions on the FEL surface. Another approach is the utilization of the CG model, in which the CG parameters are tuned using the fluctuation matching methodology with all-atom MD simulations. The long-timespan dynamics is then elucidated straightforwardly by using CG-MD simulations.