Review
Theoretical approaches for dynamical ordering of biomolecular systems

https://doi.org/10.1016/j.bbagen.2017.10.001Get rights and content

Highlights

  • Four theoretical approaches to understand ordering phenomena are reviewed.

  • QM/MM calculation enables to study chemical reactions in large systems.

  • All-atom molecular dynamics simulations can follow longer time-scale phenomena.

  • Besides computational efficiency, CG model offers abstraction of the target system.

  • Integral equation theories elucidate the stability of biomolecular association.

Abstract

Background

Living systems are characterized by the dynamic assembly and disassembly of biomolecules. The dynamical ordering mechanism of these biomolecules has been investigated both experimentally and theoretically. The main theoretical approaches include quantum mechanical (QM) calculation, all-atom (AA) modeling, and coarse-grained (CG) modeling. The selected approach depends on the size of the target system (which differs among electrons, atoms, molecules, and molecular assemblies). These hierarchal approaches can be combined with molecular dynamics (MD) simulation and/or integral equation theories for liquids, which cover all size hierarchies.

Scope of review

We review the framework of quantum mechanical/molecular mechanical (QM/MM) calculations, AA MD simulations, CG modeling, and integral equation theories. Applications of these methods to the dynamical ordering of biomolecular systems are also exemplified.

Major conclusions

The QM/MM calculation enables the study of chemical reactions. The AA MD simulation, which omits the QM calculation, can follow longer time-scale phenomena. By reducing the number of degrees of freedom and the computational cost, CG modeling can follow much longer time-scale phenomena than AA modeling. Integral equation theories for liquids elucidate the liquid structure, for example, whether the liquid follows a radial distribution function.

General significance

These theoretical approaches can analyze the dynamic behaviors of biomolecular systems. They also provide useful tools for exploring the dynamic ordering systems of biomolecules, such as self-assembly. This article is part of a Special Issue entitled “Biophysical Exploration of Dynamical Ordering of Biomolecular Systems” edited by Dr. Koichi Kato.

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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