Achieving Rigorous Accelerated Conformational Sampling in Explicit Solvent

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. In addition, we extracted a characteristic structure in which the side chains of Asp1 and Arg16 form hydrogen bonds near the most stable structure of the Trp-cage. We also determined that ≥20 ns is an appropriate time interval to investigate protein dynamics using mRMSD. Applying this method to NuG2 protein, we found that mRMSD can be used to detect regions of metastable states in addition to the stable state. This method can be applied to molecular dynamics simulations of proteins whose stable structures are unknown.

Simu-D: A Simulator-Descriptor Suite for Polymer-Based Systems under Extreme Conditions

We present Simu-D, a software suite for the simulation and successive identification of local structures of atomistic systems, based on polymers, under extreme conditions, in the bulk, on surfaces, and at interfaces. The protocol is built around various types of Monte Carlo algorithms, which include localized, chain-connectivity-altering, identity-exchange, and cluster-based moves. The approach focuses on alleviating one of the main disadvantages of Monte Carlo algorithms, which is the general applicability under a wide range of conditions. Present applications include polymer-based nanocomposites with nanofillers in the form of cylinders and spheres of varied concentration and size, extremely confined and maximally packed assemblies in two and three dimensions, and terminally grafted macromolecules. The main simulator is accompanied by a descriptor that identifies the similarity of computer-generated configurations with respect to reference crystals in two or three dimensions. The Simu-D simulator-descriptor can be an especially useful tool in the modeling studies of the entropy- and energy-driven phase transition, adsorption, and self-organization of polymer-based systems under a variety of conditions.

Simulating Multiple Substrate-Binding Events by γ-Glutamyltransferase Using Accelerated Molecular Dynamics

γ-Glutamyltransferase (GGT) is an enzyme that uses γ-glutamyl compounds as substrates and catalyzes their transfer to a water molecule or an acceptor substrate with varied physiological function in bacteria, plants, and animals. Crystal structures of GGT are known for different species and in different states of the chemical reaction; however, the structural dynamics of the substrate binding to the catalytic site of GGT are unknown. Here, we modeled Escherichia coli GGT's glutamine binding by using a swarm of accelerated molecular dynamics (aMD) simulations. Characterization of multiple binding events identified three structural binding motifs composed of polar residues in the binding pocket that govern glutamine binding into the active site. Simulated open and closed conformations of a lid-loop protecting the binding cavity suggest its role as a gating element by allowing or blocking substrates entry into the binding pocket. Partially open states of the lid-loop are accessible within thermal fluctuations, while the estimated free energy cost of a complete open state is 2.4 kcal/mol. Our results suggest that both specific electrostatic interactions and GGT conformational dynamics dictate the molecular recognition of substrate-GGT complexes.

Systematic Dissociation Pathway Searches Guided by Principal Component Modes

We introduce a novel method, Pathway Search guided by Internal Motions (PSIM), that efficiently finds molecular dissociation pathways of a ligand-receptor system with guidance from principal component (PC) modes obtained from molecular dynamics (MD) simulations. Modeling ligand-receptor dissociation pathways can provide insights into molecular recognition and has practical applications, including understanding kinetic mechanisms and barriers to binding/unbinding as well as design of drugs with desired kinetic properties. PSIM uses PC modes in multilayer internal coordinates to identify natural molecular motions that guide the search for conformational switches and unbinding pathways. The new multilayer internal coordinates overcome problems with Cartesian and classical internal coordinates that fail to smoothly present dihedral rotation or generate nonphysical distortions. We used HIV-1 protease, which has large-scale flap motions, as an example protein to demonstrate use of the multilayer internal coordinates. We provide examples of algorithms and implementation of PSIM with alanine dipeptide and chemical host-guest systems, 2-naphthyl ethanol-β-cyclodextrin and tetramethylammonium-cryptophane complexes. Tetramethylammonium-cryptophane has slow binding/unbinding kinetics. Its residence time, the length to dissociate tetramethylammonium from the host, is ∼14 s from experiments, and PSIM revealed 4 dissociation pathways in approximately 150 CPU h. We also searched the releasing pathways for the product glyceraldehyde-3-phosphate from tryptophan synthase, and one complete dissociation pathway was constructed after running multiple search iterations in approximately 300 CPU h. With guidance by internal PC modes from MD simulations, the PSIM method has advantages over simulation-based methods to search for dissociation pathways of molecular systems with slow noncovalent kinetic behavior.

Gaussian Accelerated Molecular Dynamics in NAMD

Gaussian accelerated molecular dynamics (GaMD) is a recently developed enhanced sampling technique that provides efficient free energy calculations of biomolecules. Like the previous accelerated molecular dynamics (aMD), GaMD allows for “unconstrained” enhanced sampling without the need to set predefined collective variables and so is useful for studying complex biomolecular conformational changes such as protein folding and ligand binding. Furthermore, because the boost potential is constructed using a harmonic function that follows Gaussian distribution in GaMD, cumulant expansion to the second order can be applied to recover the original free energy profiles of proteins and other large biomolecules, which solves a long-standing energetic reweighting problem of the previous aMD method. Taken together, GaMD offers major advantages for both unconstrained enhanced sampling and free energy calculations of large biomolecules. Here, we have implemented GaMD in the NAMD package on top of the existing aMD feature and validated it on three model systems: alanine dipeptide, the chignolin fast-folding protein, and the M₃ muscarinic G protein-coupled receptor (GPCR). For alanine dipeptide, while conventional molecular dynamics (cMD) simulations performed for 30 ns are poorly converged, GaMD simulations of the same length yield free energy profiles that agree quantitatively with those of 1000 ns cMD simulation. Further GaMD simulations have captured folding of the chignolin and binding of the acetylcholine (ACh) endogenous agonist to the M₃ muscarinic receptor. The reweighted free energy profiles are used to characterize the protein folding and ligand binding pathways quantitatively. GaMD implemented in the scalable NAMD is widely applicable to enhanced sampling and free energy calculations of large biomolecules.

Unconstrained Enhanced Sampling for Free Energy Calculations of Biomolecules: A Review

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations.

Targeting electrostatic interactions in accelerated molecular dynamics with application to protein partial unfolding

Accelerated molecular dynamics (aMD) is a promising sampling method to generate an ensemble of conformations and to explore the free energy landscape of proteins in explicit solvent. Its success resides in its ability to reduce barriers in the dihedral and the total potential energy space. However, aMD simulations of large proteins can generate large fluctuations of the dihedral and total potential energy with little conformational changes in the protein structure. To facilitate wider conformational sampling of large proteins in explicit solvent, we developed a direct intrasolute electrostatic interactions accelerated MD (DISEI-aMD) approach. This method aims to reduce energy barriers within rapidly changing electrostatic interactions between solute atoms at short-range distances. It also results in improved reconstruction quality of the original statistical ensemble of the system. Recently, we characterized a pH-dependent partial unfolding of diphtheria toxin translocation domain (T-domain) using microsecond long MD simulations. In this work, we focus on the study of conformational changes of a low-pH T-domain model in explicit solvent using DISEI-aMD. On the basis of the simulations of the low-pH T-domain model, we show that the proposed sampling method accelerates conformational rearrangement significantly faster than multiple standard aMD simulations and microsecond long conventional MD simulations.

Investigation of Structural Dynamics of Enzymes and Protonation States of Substrates Using Computational Tools

This review discusses the use of molecular modeling tools, together with existing experimental findings, to provide a complete atomic-level description of enzyme dynamics and function. We focus on functionally relevant conformational dynamics of enzymes and the protonation states of substrates. The conformational fluctuations of enzymes usually play a crucial role in substrate recognition and catalysis. Protein dynamics can be altered by a tiny change in a molecular system such as different protonation states of various intermediates or by a significant perturbation such as a ligand association. Here we review recent advances in applying atomistic molecular dynamics (MD) simulations to investigate allosteric and network regulation of tryptophan synthase (TRPS) and protonation states of its intermediates and catalysis. In addition, we review studies using quantum mechanics/molecular mechanics (QM/MM) methods to investigate the protonation states of catalytic residues of β-Ketoacyl ACP synthase I (KasA). We also discuss modeling of large-scale protein motions for HIV-1 protease with coarse-grained Brownian dynamics (BD) simulations.

Determining the Energetics of Small β-Sheet Peptides using Adaptive Steered Molecular Dynamics

Mechanically driven unfolding is a useful computational tool for extracting the energetics and stretching pathway of peptides. In this work, two representative β-hairpin peptides, chignolin (PDB: 1UAO ) and trpzip1 (PDB: 1LE0 ), were investigated using an adaptive variant of the original steered molecular dynamics method called adaptive steered molecular dynamics (ASMD). The ASMD method makes it possible to perform energetic calculations on increasingly complex biological systems. Although the two peptides are similar in length and have similar secondary structures, their unfolding energetics are quite different. The hydrogen bonding profile and specific residue pair interaction energies provide insight into the differing stabilities of these peptides and reveal which of the pairs provides the most significant stabilization.

General trends of dihedral conformational transitions in a globular protein

Dihedral conformational transitions are analyzed systematically in a model globular protein, cytochrome P450cam, to examine their structural and chemical dependences through combined conventional molecular dynamics (cMD), accelerated molecular dynamics (aMD) and adaptive biasing force (ABF) simulations. The aMD simulations are performed at two acceleration levels, using dihedral and dual boost, respectively. In comparison with cMD, aMD samples protein dihedral transitions approximately two times faster on average using dihedral boost, and ∼ 3.5 times faster using dual boost. In the protein backbone, significantly higher dihedral transition rates are observed in the bend, coil, and turn flexible regions, followed by the β bridge and β sheet, and then the helices. Moreover, protein side chains of greater length exhibit higher transition rates on average in the aMD-enhanced sampling. Side chains of the same length (particularly Nχ = 2) exhibit decreasing transition rates with residues when going from hydrophobic to polar, then charged and aromatic chemical types. The reduction of dihedral transition rates is found to be correlated with increasing energy barriers as identified through ABF free energy calculations. These general trends of dihedral conformational transitions provide important insights into the hierarchical dynamics and complex free energy landscapes of functional proteins.

Accelerating the Conformational Sampling of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are a class of proteins lacking a well-defined secondary structure. Instead, they are able to attain multiple conformations, bind to multiple targets, and respond to changes in their surroundings. Functionally, IDPs have been associated with molecular recognition, cell regulation, and signal transduction. The dynamic conformational ensemble of IDPs is highly environmental and binding partner dependent, rendering the characterization of IDPs extremely challenging. Here, we compare the sampling efficiencies of conventional molecular dynamics (MD), well-tempered metadynamics (WT-META), and bias-exchange metadynamics (BE-META). The total simulation time was over 10 μs, and a 20-mer peptide derived from the Neh2 domain of the Nuclear factor erythroid 2-related factor 2 (Nrf2) protein was simulated. BE-META, with a neutral replica and seven biased replicas employing a set of seven relevant collective variables (CVs), provided the most reliable and efficient sampling. Finally, we propose a free-energy reconstruction method based on the probability distribution of the secondary structure contents. This postprocessing analysis confirms the presence of not only the β-hairpin conformation of the free Neh2 peptide but also its rare bound-state-like conformation, both of that have been experimentally observed. In addition, our simulations also predict other possible conformations to be verified with future experiments.

Conformational Ensemble of the Poliovirus 3CD Precursor Observed by MD Simulations and Confirmed by SAXS: A Strategy to Expand the Viral Proteome?

The genomes of RNA viruses are relatively small. To overcome the small-size limitation, RNA viruses assign distinct functions to the processed viral proteins and their precursors. This is exemplified by poliovirus 3CD protein. 3C protein is a protease and RNA-binding protein. 3D protein is an RNA-dependent RNA polymerase (RdRp). 3CD exhibits unique protease and RNA-binding activities relative to 3C and is devoid of RdRp activity. The origin of these differences is unclear, since crystal structure of 3CD revealed "beads-on-a-string" structure with no significant structural differences compared to the fully processed proteins. We performed molecular dynamics (MD) simulations on 3CD to investigate its conformational dynamics. A compact conformation of 3CD was observed that was substantially different from that shown crystallographically. This new conformation explained the unique properties of 3CD relative to the individual proteins. Interestingly, simulations of mutant 3CD showed altered interface. Additionally, accelerated MD simulations uncovered a conformational ensemble of 3CD. When we elucidated the 3CD conformations in solution using small-angle X-ray scattering (SAXS) experiments a range of conformations from extended to compact was revealed, validating the MD simulations. The existence of conformational ensemble of 3CD could be viewed as a way to expand the poliovirus proteome, an observation that may extend to other viruses.

Accelerated molecular dynamics simulations of protein folding

Folding of four fast-folding proteins, including chignolin, Trp-cage, villin headpiece and WW domain, was simulated via accelerated molecular dynamics (aMD). In comparison with hundred-of-microsecond timescale conventional molecular dynamics (cMD) simulations performed on the Anton supercomputer, aMD captured complete folding of the four proteins in significantly shorter simulation time. The folded protein conformations were found within 0.2-2.1 Å of the native NMR or X-ray crystal structures. Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second-order are in good agreement with those obtained from cMD simulations. This allows us to identify distinct conformational states (e.g., unfolded and intermediate) other than the native structure and the protein folding energy barriers. Detailed analysis of protein secondary structures and local key residue interactions provided important insights into the protein folding pathways. Furthermore, the selections of force fields and aMD simulation parameters are discussed in detail. Our work shows usefulness and accuracy of aMD in studying protein folding, providing basic references in using aMD in future protein-folding studies.

Tuning the Attempt Frequency of Protein Folding Dynamics via Transition-State Rigidification: Application to Trp-Cage

The attempt frequency or prefactor (k0) of the transition-state rate equation of protein folding kinetics has been estimated to be on the order of 10(6) s(-1), which is many orders of magnitude smaller than that of chemical reactions. Herein we use the mini-protein Trp-cage to show that it is possible to significantly increase the value of k0 for a protein folding reaction by rigidifying the transition state. This is achieved by reducing the conformational flexibility of a key structural element (i.e., an α-helix) formed in the transition state via photoisomerization of an azobenzene cross-linker. We find that this strategy not only decreases the folding time of the Trp-cage peptide by more than an order of magnitude (to ∼100 ns at 25°C) but also exposes parallel folding pathways, allowing us to provide, to the best of our knowledge, the first quantitative assessment of the curvature of the transition-state free-energy surface of a protein.

Folding dynamics and pathways of the trp-cage miniproteins

Using alternate measures of fold stability for a wide variety of Trp-cage mutants has raised the possibility that prior dynamics T-jump measures may not be reporting on complete cage formation for some species. NMR relaxation studies using probes that only achieve large chemical shift difference from unfolded values on complete cage formation indicate slower folding in some but not all cases. Fourteen species have been examined, with cage formation time constants (1/kF) ranging from 0.9-7.5 μs at 300 K. The present study does not change the status of the Trp-cage as a fast folding, essentially two-state system, although it does alter the stage at which this description applies. A diversity of prestructuring events, depending on the specific analogue examined, may appear in the folding scenario, but in all cases, formation of the N-terminal helix is complete either at or before the cage-formation transition state. In contrast, the fold-stabilizing H-bonding interactions of the buried Ser14 side chain and the Arg/Asp salt bridge are post-transition state features on the folding pathway. The study has also found instances in which a [P12W] mutation is fold destabilizing but still serves to accelerate the folding process.

Towards fast, rigorous and efficient conformational sampling of biomolecules: Advances in accelerated molecular dynamics

BACKGROUND

Accelerated molecular dynamics (aMD) has been proven to be a powerful biasing method for enhanced sampling of biomolecular conformations on general-purpose computational platforms. Biologically important long timescale events that are beyond the reach of standard molecular dynamics can be accessed without losing the detailed atomistic description of the system in aMD. Over other biasing methods, aMD offers the advantages of tuning the level of acceleration to access the desired timescale without any advance knowledge of the reaction coordinate.

SCOPE OF REVIEW

Recent advances in the implementation of aMD and its applications to small peptides and biological macromolecules are reviewed here along with a brief account of all the aMD variants introduced in the last decade.

MAJOR CONCLUSIONS

In comparison to the original implementation of aMD, the recent variant in which all the rotatable dihedral angles are accelerated (RaMD) exhibits faster convergence rates and significant improvement in statistical accuracy of retrieved thermodynamic properties. RaMD in conjunction with accelerating diffusive degrees of freedom, i.e. dual boosting, has been rigorously tested for the most difficult conformational sampling problem, protein folding. It has been shown that RaMD with dual boosting is capable of efficiently sampling multiple folding and unfolding events in small fast folding proteins.

GENERAL SIGNIFICANCE

RaMD with the dual boost approach opens exciting possibilities for sampling multiple timescales in biomolecules. While equilibrium properties can be recovered satisfactorily from aMD-based methods, directly obtaining dynamics and kinetic rates for larger systems presents a future challenge. This article is part of a Special Issue entitled Recent developments of molecular dynamics.