Intermediate scattering function for polymer molecules: An approach based on relaxation mode analysis.

The theory of polymer dynamics describes the intermediate scattering function for a polymer molecule in terms of relaxation modes defined by normal coordinates for the corresponding coarse-grained model. However, due to the difficulty of defining the normal coordinates for arbitrary polymer molecules, it is generally challenging to express the intermediate scattering function for a polymer molecule in terms of relaxation modes. To overcome this challenge, we propose a general method to calculate the intermediate scattering function for a polymer molecule on the basis of a relaxation mode analysis approach [Takano and Miyashita, J.

Structural and Computational Insights into Dynamics and Intermediate States of Orexin 2 Receptor Signaling.

Orexin 2 receptor (OXR) is a G protein-coupled receptor (GPCR) whose activation is crucial to regulation of the sleep-wake cycle. Recently, inactive and active state structures were determined from X-ray crystallography and cryo-electron microscopy single particle analysis, and the activation mechanisms have been discussed based on these static data. GPCRs have multiscale intermediate states during activation, and insights into these dynamics and intermediate states may aid the precise control of intracellular signaling by ligands in drug discovery.

Effect of Main and Side Chains on the Folding Mechanism of the Trp-Cage Miniprotein.

Proteins that do not fold into their functional native state have been linked to diseases. In this study, the influence of the main and side chains of individual amino acids on the folding of the tryptophan cage (Trp-cage), a designed 20-residue miniprotein, was analyzed. For this purpose, we calculated the solvation free energy (SFE) contributions of individual atoms by using the 3D-reference interaction site model with the atomic decomposition method.

Analysis of Protein Folding Simulation with Moving Root Mean Square Deviation.

We apply moving root-mean-square deviation (mRMSD), which does not require a reference structure, as a method for analyzing protein dynamics. This method can be used to calculate the root-mean-square deviation (RMSD) of structure between two specified time points and to analyze protein dynamics behavior through time series analysis. We applied this method to the Trp-cage trajectory calculated by the Anton supercomputer and found that it shows regions of stable states as well as the conventional RMSD.

Non-Markov-Type Analysis and Diffusion Map Analysis for Molecular Dynamics Trajectory of Chignolin at a High Temperature.

We apply the non-Markov-type analysis of state-to-state transitions to nearly microsecond molecular dynamics (MD) simulation data at a folding temperature of a small artificial protein, chignolin, and we found that the time scales obtained are consistent with our previous result using the weighted ensemble simulations, which is a general path-sampling method to extract the kinetic properties of molecules. Previously, we also applied diffusion map (DM) analysis, which is one of a manifold of learning techniques, to the same trajectory of chignolin in order to cluster the conformational states and found that DM and relaxation mode analysis give similar results for the eigenvectors. In this paper, we divide the same trajectory into shorter pieces and further apply DM to such short-length trajectories to investigate how the obtained eigenvectors are useful to characterize the conformational change of chignolin.

Computational Analysis of the SARS-CoV-2 RBD-ACE2-Binding Process Based on MD and the 3D-RISM Theory.

The binding process of angiotensin-converting enzyme 2 (ACE2) to the receptor-binding domain (RBD) of the severe acute respiratory syndrome-like coronavirus 2 spike protein was investigated using molecular dynamics simulation and the three-dimensional reference interaction-site model theory. The results suggested that the protein-binding process consists of a protein-protein approaching step, followed by a local structural rearrangement step. In the approaching step, the interprotein interaction energy decreased as the proteins approached each other, whereas the solvation free energy increased.

Characteristic structural difference between inactive and active states of orexin 2 receptor determined using molecular dynamics simulations.

To investigate the dynamics of the orexin 2 receptor, which is a class A G protein-coupled receptor, we recently performed several microsecond-scale molecular dynamics simulations of the wild-type protein, of a mutant that stabilizes the inactive state, and of constitutively active mutants of the class A G protein-coupled receptors. Herein, we review the results of these molecular dynamics simulations of the orexin 2 receptor. In these simulations, characteristic conformational changes were observed in the V309Y mutant.

Molecular Dynamics Simulations for the Determination of the Characteristic Structural Differences between Inactive and Active States of Wild Type and Mutants of the Orexin2 Receptor.

The orexin2 receptor (OX2R), which is classified as a class A G protein-coupled receptor (GPCR), is the target of our study. We performed over 20 several-microsecond-scale molecular dynamics simulations of the wild type and mutants of OX2R to extract the characteristics of the structural changes taking place in the active state. We introduced mutations that exhibited the stable inactive state and the constitutively active state in class A GPCRs.

Universal Relation between Instantaneous Diffusivity and Radius of Gyration of Proteins in Aqueous Solution.

Protein conformational fluctuations are highly complex and exhibit long-term correlations. Here, molecular dynamics simulations of small proteins demonstrate that these conformational fluctuations directly affect the protein's instantaneous diffusivity D_{I}. We find that the radius of gyration R_{g} of the proteins exhibits 1/f fluctuations that are synchronous with the fluctuations of D_{I}.

Mutation-induced change in chignolin stability from π-turn to α-turn.

Chignolin, which consists of 10 amino acids, adopts two stable states in simulations at room temperature at 1 atm: the native and misfolded states. The sequence of chignolin is optimized to form a stable π-turn and thus the native state has a π-turn from Asp3 to Thr8. On the other hand, the misfolded state adopts an α-turn from Asp3 to Gly7.

Analysis of molecular dynamics simulations of 10-residue peptide, chignolin, using statistical mechanics: Relaxation mode analysis and three-dimensional reference interaction site model theory.

Molecular dynamics simulation is a fruitful tool for investigating the structural stability, dynamics, and functions of biopolymers at an atomic level. In recent years, simulations can be performed on time scales of the order of milliseconds using special purpose systems. Since the most stable structure, as well as meta-stable structures and intermediate structures, is included in trajectories in long simulations, it is necessary to develop analysis methods for extracting them from trajectories of simulations.

Folding pathways of NuG2-a designed mutant of protein G-using relaxation mode analysis.

Dynamic analysis methods are important for analyzing long simulations such as folding simulations. Relaxation mode analysis, which approximately extracts slow modes and rates, has been applied in molecular dynamics (MD) simulations of protein systems. Previously, we showed that slow modes are suitable for analyzing simulations in which large conformational changes occur.

Identification of slow relaxation modes in a protein trimer via positive definite relaxation mode analysis.

Recently, dynamic analysis methods in signal processing have been applied to the analysis of molecular dynamics (MD) trajectories of biopolymers. In the context of a relaxation mode analysis (RMA) method, based on statistical physics, it is explained why the signal-processing methods work well for the simulation trajectories of biopolymers. A distinctive difference between the RMA method and the signal-processing methods is the introduction of an additional parameter, called an evolution time parameter.

Conformational change of a biomolecule studied by the weighted ensemble method: Use of the diffusion map method to extract reaction coordinates.

We simulate the nonequilibrium ensemble dynamics of a biomolecule using the weighted ensemble method, which was introduced in molecular dynamics simulations by Huber and Kim and further developed by Zuckerman and co-workers. As the order parameters to characterize its conformational change, we here use the coordinates derived from the diffusion map (DM) method, one of the manifold learning techniques. As a concrete example, we study the kinetic properties of a small peptide, chignolin in explicit water, and calculate the conformational change between the folded and misfolded states in a nonequilibrium way.

Relaxation mode analysis for molecular dynamics simulations of proteins.

Molecular dynamics simulation is a powerful method for investigating the structural stability, dynamics, and function of biopolymers at the atomic level. In recent years, it has become possible to perform simulations on time scales of the order of milliseconds using special hardware. However, it is necessary to derive the important factors contributing to structural change or function from the complicated movements of biopolymers obtained from long simulations.

Analysis of Structural Stability of Chignolin.

We discuss the stability of an entire protein and the influence of main chains and side chains of individual amino acids to investigate the protein-folding mechanism. For this purpose, we calculated the solvation free-energy contribution of individual atoms using the three-dimensional reference interaction site model with the atomic decomposition method. We generated structures of chignolin miniprotein by a molecular dynamics simulation and classified them into six types: native 1, native 2, misfolded 1, misfolded 2, intermediate, and unfolded states.

Application of reference-modified density functional theory: Temperature and pressure dependences of solvation free energy.

Recently, we proposed a reference-modified density functional theory (RMDFT) to calculate solvation free energy (SFE), in which a hard-sphere fluid was introduced as the reference system instead of an ideal molecular gas. Through the RMDFT, using an optimal diameter for the hard-sphere reference system, the values of the SFE calculated at room temperature and normal pressure were in good agreement with those for more than 500 small organic molecules in water as determined by experiments. In this study, we present an application of the RMDFT for calculating the temperature and pressure dependences of the SFE for solute molecules in water.

Stability of Unfolded and Folded Protein Structures Using a 3D-RISM with the RMDFT.

Protein stability is determined by the characteristics of the protein itself as well as the surrounding solvent. Herein, we discuss the stability of the folded and unfolded structures of proteins obtained from Anton's long simulations (Lindorff-Larsen, K.; Piana, S.

A reference-modified density functional theory: An application to solvation free-energy calculations for a Lennard-Jones solution.

In the conventional classical density functional theory (DFT) for simple fluids, an ideal gas is usually chosen as the reference system because there is a one-to-one correspondence between the external field and the density distribution function, and the exact intrinsic free-energy functional is available for the ideal gas. In this case, the second-order density functional Taylor series expansion of the excess intrinsic free-energy functional provides the hypernetted-chain (HNC) approximation. Recently, it has been shown that the HNC approximation significantly overestimates the solvation free energy (SFE) for an infinitely dilute Lennard-Jones (LJ) solution, especially when the solute particles are several times larger than the solvent particles [T.

Relaxation mode analysis and Markov state relaxation mode analysis for chignolin in aqueous solution near a transition temperature.

It is important to extract reaction coordinates or order parameters from protein simulations in order to investigate the local minimum-energy states and the transitions between them. The most popular method to obtain such data is principal component analysis, which extracts modes of large conformational fluctuations around an average structure. We recently applied relaxation mode analysis for protein systems, which approximately estimates the slow relaxation modes and times from a simulation and enables investigations of the dynamic properties underlying the structural fluctuations of proteins.

A solvation-free-energy functional: a reference-modified density functional formulation.

The three-dimensional reference interaction site model (3D-RISM) theory, which is one of the most applicable integral equation theories for molecular liquids, overestimates the absolute values of solvation-free-energy (SFE) for large solute molecules in water. To improve the free-energy density functional for the SFE of solute molecules, we propose a reference-modified density functional theory (RMDFT) that is a general theoretical approach to construct the free-energy density functional systematically. In the RMDFT formulation, hard-sphere (HS) fluids are introduced as the reference system instead of an ideal polyatomic molecular gas, which has been regarded as the appropriate reference system of the interaction-site-model density functional theory for polyatomic molecular fluids.

Enhanced sampling algorithms.

In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. Enhanced conformational sampling techniques are thus in great demand.