Biochimica et Biophysica Acta (BBA) - General Subjects
ReviewTheoretical approaches for dynamical ordering of biomolecular systems
Graphical Abstract
Introduction
This review explains the theoretical approaches for understanding the dynamical ordering of biomolecules. The desirable approach depends on the size of the target systems, as shown in Fig. 1. Chemical reactions require a quantum mechanical (QM) calculation based on the Shrödinger equation. In chemically inert systems, an all-atom (AA) model or a coarse-grained (CG) model can be used. The AA model is appropriate for small molecules such as ligands, peptides, protein subdomains, and sometimes, whole proteins. Glycans, lipids, and amphiphilic polymers are also usually treated by the AA model. Larger molecules such as relatively big proteins or networks of multiple proteins are handled by CG modeling. Because CG modeling reduces the number of degrees of freedom of biomolecules, it generally incurs much lower computational cost than the AA model.
These hierarchal methods can be combined with molecular dynamics (MD) simulations and/or integral equation theory for liquids. MD simulations follow the atomic and molecular motions by numerically solving the Hamilton's equations of motion. To investigate a dynamically ordering biomolecular system with chemical reactions, such as photoisomerization or proton transfer, we must follow the dynamics of the biomolecules, which requires both QM calculations and MD simulations. QM and molecular mechanical (MM) calculations can be combined into (QM/MM) MD simulations, in which the important part of the system is calculated quantum-mechanically and the other part is treated by the AA model. MD simulations can also be performed in the AA and CG models, depending on the system size.
Solvents around biomolecules, such as water and aqueous solution, can be treated not only by AA MD and CG MD simulations but also by integral equation theories for liquids, which provide information on the structure and thermodynamic properties of the liquid. These results provide the biomolecule–solvent interactions in the CG model. The theories are also compatible with QM calculations or AA models, and can be combined with MD simulations. For example, integral equation theory can be applied to an AA MD simulation of a protein in a solvent.
Our basic policy is to select the most suitable method for a target problem. The choice of the method depends on the size hierarchy of the problem. However, it is sometimes desirable to combine these methods; for example, QM/MM MD simulations and combined MD and integral equation theory are suitable for some problems, as mentioned above.
This review outlines four common approaches—QM/MM calculation, AA MD simulation, CG modeling, and integral equation theory for liquids—and applies them to the dynamical ordering of biomolecules. As shown below, these four approaches are useful for understanding ordering phenomena. Although there exist other common methods such as full QM, first-principle MD, Monte Carlo (MC), united-atom CGMD, and various continuum models, the above four methods were chosen because they are typically across the size hierarchy in biomolecular and artificial molecular systems.
Section snippets
Recent advances in QM/MM methods
As it is indicated that Karplus, Levitt, and Warshel won the Nobel Prize in 2013, the combined QM/MM method [1], [2] have been widely used for studying the chemical reactions and physical properties of molecules in condensed phases such as solutions and proteins. This section briefly describes the QM/MM method and its recent implementation techniques. Combined with MD simulations, the QM/MM method enables us to investigate various phenomena that are largely governed by thermal fluctuations,
AA MD simulations for dynamical ordering of biomolecules
The AA MD method is a strong theoretical tool for analyzing the dynamical ordering of biomolecules at the atomic level. This section briefly describes the framework of AA MD simulations and reviews recent progress in AA MD techniques. It also introduces the applications of AA MD to dynamical ordering of biomolecules, such as protein folding, amyloid-fibril formation, oligosaccharides, and surfactant molecules.
CG modeling of self-assembly
Self-assembly is the spontaneous combination of relatively simple building blocks into highly ordered complexes [104]. As described in the previous section, molecular simulation is a powerful tool for understanding self-assembly phenomena, and has been extensively applied to various systems.
CG modeling has successfully simulated biological systems, condensed phases, and other complicated systems [105], [106]. The model is employed by two reasons that are closely related to each other. The first
Integral equation theories for liquids and the dynamical ordering of biomolecules
Integral equation theories for liquids [145] provide information on liquid structures such as radial distribution functions g(r) (see Fig. 13). The thermodynamic quantities calculated from these correlation functions are important for discussing the dynamical ordering of macromolecular systems because the stability of the associations between macromolecules in a solution. Especially, the location and orientation dependencies of the solvation free energy are important in this subject. This
Conclusions
In this review, we outlined QM/MM calculations, AA MD simulations, CG modeling, and integral equation theories for liquids. QM/MM calculations are needed for simulating chemical reactions in dynamically ordering systems of biomolecules. The QM/MM calculation treats the important part of the system by a QM approach, and the other part by an MM force field. Although the QM/MM method incurs lower computational cost than the full QM calculation, the QM part is time consuming even for small QM
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Acknowledgments
This work was supported by JSPS KAKENHI Grant Numbers JP15K05249, JP15K21708, JP16H00774, JP16H00778, JP16H00790, JP25102001, and JP25102002. H. O. thanks Prof. Y. Okamoto, Prof. N. Yoshii, and Prof. S. Okazaki for providing their figures. R. A. is grateful to Prof. N. Yoshida, Dr. A. Suematsu, Mr. A. Oshima, Dr. T. Imai, and Dr. T. Yamazaki for valuable discussions.
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