Protein-Folding Dynamics: Overview of Molecular Simulation Techniques

Computational models of protein kinematics and dynamics: beyond simulation

Physics-based simulation represents a powerful method for investigating the time-varying behavior of dynamic protein systems at high spatial and temporal resolution. Such simulations, however, can be prohibitively difficult or lengthy for large proteins or when probing the lower-resolution, long-timescale behaviors of proteins generally. Importantly, not all questions about a protein system require full space and time resolution to produce an informative answer. For instance, by avoiding the simulation of uncorrelated, high-frequency atomic movements, a larger, domain-level picture of protein dynamics can be revealed. The purpose of this review is to highlight the growing body of complementary work that goes beyond simulation. In particular, this review focuses on methods that address kinematics and dynamics, as well as those that address larger organizational questions and can quickly yield useful information about the long-timescale behavior of a protein.

Structural modelling and dynamics of proteins for insights into drug interactions

Proteins are the workhorses of biomolecules and their function is affected by their structure and their structural rearrangements during ligand entry, ligand binding and protein-protein interactions. Hence, the knowledge of protein structure and, importantly, the dynamic behaviour of the structure are critical for understanding how the protein performs its function. The predictions of the structure and the dynamic behaviour can be performed by combinations of structure modelling and molecular dynamics simulations. The simulations also need to be sensitive to the constraints of the environment in which the protein resides. Standard computational methods now exist in this field to support the experimental effort of solving protein structures. This review presents a comprehensive overview of the basis of the calculations and the well-established computational methods used to generate and understand protein structure and function and the study of their dynamic behaviour with the reference to lung-related targets.

Folding of a helix is critically stabilized by polarization of backbone hydrogen bonds: study in explicit water

Multiple single-trajectory molecular dynamics (MD) simulation at room temperature (300 K) in explicit water was carried out to study the folding dynamics of an α-helix (PDB 2I9M ) using a polarized charge scheme that includes electronic polarization of backbone hydrogen bonds. Starting from an extended conformation, the 17-residue peptide was successfully folded into the native structure (α-helix) between 80 and 130 ns with a root-mean-square deviation of ~1.0 Å. Analysis of the time-dependent trajectories revealed that helix formation of the peptide started at the terminals and progressed toward the center of the peptide. For comparison, MD trajectories generated under various versions of standard AMBER force fields failed to show any significant or stable helix formation in our simulation. Our result shows clear evidence that the electronic polarization of backbone hydrogen bonds energetically stabilizes the helix formation and is critical to the stable folding of the short helix structure.

Conformational modes in biomolecules: dynamics and approximate invariance

Understanding the physical mechanisms behind the folding and conformational dynamics of biomolecules is one of the major unsolved challenges of soft matter theory. In this contribution, a theoretical framework for biomolecular dynamics is introduced, employing selected aspects of statistical mechanics, dimensionality reduction, the perturbation theory, and the theory of matrices. Biomolecular dynamics is represented by time-dependent orthogonal conformational modes, the dynamics of the modes is investigated, and invariant properties that persist are identified. As an example, the dynamics of a human prion protein is considered. The theory provides a rigorous background for assessing the stable dynamical properties of biomolecules, such as their coarse-grained structure, through a multiscale approach using short subnanosecond segments of molecular dynamics trajectories. Furthermore, the paper offers a theoretical platform for models of conformational changes in macromolecules, which may allow complementing molecular dynamics simulations.

Folding simulations of the A and B domains of protein G

We study wild type and mutants of the A and B domain of protein G using all-atom Go-models. Our data substantiate the usefulness of such simulation for probing the folding mechanism of proteins and demonstrate that multifunnel versions of such models also allow probing of more complicated funnel landscapes. In our case, such models reproduce the experimentally observed distributions of the GA98 and GB98 mutants which differ only by one residue but fold into different structures. They also reveal details on the folding mechanism in these two proteins.

Molecular dynamics

Molecular dynamics (MD) simulation holds the promise of revealing the mechanisms of biological processes in their ultimate detail. It is carried out by computing the interaction forces acting on each atom and then propagating the velocities and positions of the atoms by numerical integration of Newton's equations of motion. In this review, we present an overview of how the MD simulation can be conducted to address computational toxicity problems. The study cases will cover a standard MD simulation performed to investigate the overall flexibility of a cytochrome P450 (CYP) enzyme and a set of more advanced MD simulations to examine the barrier to ion conduction in a human α7 nicotinic acetylcholine receptor (nAChR).

Molecular dynamics applied in drug discovery: the case of HIV-1 protease

Molecular dynamics (MD) is a way to computationally simulate the movement of particles and it is widely used to provide a dynamic perspective on biomolecules. Nowadays, the ever-growing computer power and the improvement in methodology further strengthen the role of MD in drug discovery. In this chapter, an overview of MD's application in drug discovery will be given first, using HIV-1 protease as an example. Then, the underlying theories of MD will be briefly outlined. The second half of this chapter will provide a practical protocol on how to simulate a soluble protein in solvent. All-atom simulation with either implicit solvent or explicit solvent will be covered. The former samples global conformational change more efficiently, and post-processing including angle/distance measurement, structural deviation measurement, Ramachandran plot, and secondary structure analysis will be introduced. The latter is more realistic/expensive and is generally used to finely examine local conformational rearrangement and water-mediated interactions. Post-processing including water density analysis will be described.

Modelling zwitterions in solution: 3-fluoro-γ-aminobutyric acid (3F-GABA)

The conformations and relative stabilities of folded and extended 3-fluoro-γ-aminobutyric acid (3F-GABA) conformers were studied using explicit solvation models. Geometry optimisations in the gas phase with one or two explicit water molecules favour folded and neutral structures containing intramolecular NH···O-C hydrogen bonds. With three or five explicit water molecules zwitterionic minima are obtained, with folded structures being preferred over extended conformers. The stability of folded versus extended zwitterionic conformers increases on going from a PCM continuum solvation model to the microsolvated complexes, though extended structures become less disfavoured with the inclusion of more water molecules. Full explicit solvation was studied with a hybrid quantum-mechanical/molecular-mechanical (QM/MM) scheme and molecular dynamics simulations, including more than 6000 TIP3P water molecules. According to free energies obtained from thermodynamic integration at the PM3/MM level and corrected for B3LYP/MM total energies, the fully extended conformer is more stable than folded ones by about -4.5 kJ mol(-1). B3LYP-computed (3)J(F,H) NMR spin-spin coupling constants, averaged over PM3/MM-MD trajectories, agree best with experiment for this fully extended form, in accordance with the original NMR analysis. The seeming discrepancy between static PCM calculations and experiment noted previously is now resolved. That the inexpensive semiempirical PM3 method performs so well for this archetypical zwitterion is encouraging for further QM/MM studies of biomolecular systems.

PROTEIN FOLDING AS A PHYSICAL STOCHASTIC PROCESS

We model protein folding as a physical stochastic process as follows. The unfolded protein chain is treated as a random coil described by SAW (self-avoiding walk). Folding is induced by hydrophobic forces and other interactions, such as hydrogen bonding, which can be taken into account by imposing conditions on SAW. The resulting model is termed CSAW (conditioned self-avoiding walk). Conceptually, the mathematical basis is a generalized Langevin equation. In practice, the model is implemented on a computer by combining SAW and Monte Carlo. To illustrate the flexibility and capabilities of the model, we consider a number of examples, including folding pathways, elastic properties, helix formation, and collective modes.

Condensed phase molecular dynamics using interpolated potential energy surfaces with application to the resolvation process of coumarin 153

Interpolated potential energy surfaces (PESs) have been used for performing reliable molecular dynamics (MD) simulations of small molecular reactions. In this article, we extend this method to MD simulations in condensed phase and show that the same scheme can also be feasibly used when it is supplemented with additional terms for describing intermolecular interactions. We then apply the approach for studying the resolvation process of coumarin 153 in a number of polar solvents. We find that the interpolated surface actually reproduces experimentally found features much better than the conventional force field based potential especially in terms of both dynamics Stokes shift in the short time limit and solute vibrational decoherence. This shows that the solute vibrational effect is important to some degree along the resolvation and should be modeled properly for accurate description of the related dynamics. The stability issue of trajectories on the interpolated PESs is also discussed, in regard to the goal of reliably performing long time simulations. Operational limitations of the present scheme are also discussed.

Respice, adspice, and prospice

The title, "Look to the past, Look to the present, and Look to the future," the motto of City College of New York, expresses how my family life and education led me to an academic career in physical chemistry and ultimately to a study of proteins. The economic depression of the 1930s left a lasting impression on my outlook and career aspirations. With fortunate experiences at several stages in my life, I was able to participate in the great adventure of the last half of the twentieth century: the revolution in biology that advanced the field of protein chemistry to so great an extent. The future is bright and limitless, with greater understanding of biology yet to come.

Correlating disease-related mutations to their effect on protein stability: a large-scale analysis of the human proteome

Single residue mutations in proteins are known to affect protein stability and function. As a consequence, they can be disease associated. Available computational methods starting from protein sequence/structure can predict whether a mutated residue is or not disease associated and whether it is promoting instability of the protein-folded structure. However, the relationship among stability changes in proteins and their involvement in human diseases still needs to be fully exploited. Here, we try to rationalize in a nutshell the complexity of the question by generalizing over information already stored in public databases. For each single aminoacid polymorphysm (SAP) type, we derive the probability of being disease-related (Pd) and compute from thermodynamic data three indexes indicating the probability of decreasing (P-), increasing (P+), and perturbing the protein structure stability (Pp). Statistically validated analysis of the different P/Pd correlations indicate that Pd best correlates with Pp. Pp/Pd correlation values are as high as 0.49, and increase up to 0.67 when data variability is taken into consideration. This is indicative of a medium/good correlation among Pd and Pp and corroborates the assumption that protein stability changes can also be disease associated at the proteome level.

Comparative analysis of essential collective dynamics and NMR-derived flexibility profiles in evolutionarily diverse prion proteins

Collective motions on ns-μs time scales are known to have a major impact on protein folding, stability, binding and enzymatic efficiency. It is also believed that these motions may have an important role in the early stages of prion protein misfolding and prion disease. In an effort to accurately characterize these motions and their potential influence on the misfolding and prion disease transmissibility we have conducted a combined analysis of molecular dynamic simulations and NMR-derived flexibility measurements over a diverse range of prion proteins. Using a recently developed numerical formalism, we have analyzed the essential collective dynamics (ECD) for prion proteins from 8 different species including human, cow, elk, cat, hamster, chicken, turtle and frog. We also compared the numerical results with flexibility profiles generated by the random coil index (RCI) from NMR chemical shifts. Prion protein backbone flexibility derived from experimental NMR data and from theoretical computations show strong agreement with each other, demonstrating that it is possible to predict the observed RCI profiles employing the numerical ECD formalism. Interestingly, flexibility differences in the loop between second beta strand (S2) and the second alpha helix (HB) appear to distinguish prion proteins from species that are susceptible to prion disease and those that are resistant. Our results show that the different levels of flexibility in the S2-HB loop in various species are predictable via the ECD method, indicating that ECD may be used to identify disease resistant variants of prion proteins, as well as the influence of prion proteins mutations on disease susceptibility or misfolding propensity.

Using the Wimley-White Hydrophobicity Scale as a Direct Quantitative Test of Force Fields: The MARTINI Coarse-Grained Model

The partitioning of proteins and peptides at the membrane/water interface is a key step in many processes, including the action of antimicrobial peptides, cell-penetrating peptides, and toxins, as well as signaling. To develop a computational model that can be used to accurately represent such systems, the underlying model must be able to quantitatively represent the partitioning preferences of amino acids in the lipid membrane. The MARTINI model provides a consistent set of parameters for building coarse-grained models of systems involving lipids and proteins. Even though MARTINI is parametrized to reproduce the partitioning behavior of small molecules, its ability to reproduce partitioning preferences of amino acids at lipid/water interfaces has never been tested. In this study, we measured the partitioning free energies of side chains of amino acids using alchemical simulations and umbrella sampling. The pentapeptides of sequence Ac-WLXLL were simulated at the POPC/water and cyclohexane/water interfaces using MARTINI, and the computed free energies were compared with the Wimley-White hydrophobicity scale. The free energy values obtained using the free energy perturbation, thermodynamic integration, and umbrella sampling methods were compared to gain insight into the most efficient method and the degree of sampling required to obtain statistically accurate free energies for use with atomistic force fields in future work. With the standard MARTINI water model, the amino acids D, E, K, and R were found to be significantly too favorable in hydrophobic environments, whereas with the polarizable water model, the amino acids D, E, K, and R were found to give correct free energies of partitioning. The amino acids P and F showed significant deviations from the experimental values. This model system will be used in future improvements to the MARTINI model.

Simulation of chaperonin effect on protein folding: a shift from nucleation-condensation to framework mechanism

The iterative annealing mechanism (IAM) of chaperonin-assisted protein folding is explored in a framework of a well-established coarse-grained protein modeling tool, which enables the study of protein dynamics in a time-scale well beyond classical all-atom molecular mechanics. The chaperonin mechanism of action is simulated for two paradigm systems of protein folding, B domain of protein A (BdpA) and B1 domain of protein G (GB1), and compared to chaperonin-free simulations presented here for BdpA and recently published for GB1. The prediction of the BdpA transition state ensemble (TSE) is in perfect agreement with experimental findings. It is shown that periodic distortion of the polypeptide chains by hydrophobic chaperonin interactions can promote rapid folding and leads to a decrease in folding temperature. It is also demonstrated how chaperonin action prevents kinetically trapped conformations and modulates the observed folding mechanisms from nucleation-condensation to a more framework-like.

Free-energy landscapes and thermodynamic parameters of complex molecules from nonequilibrium simulation trajectories

Thermodynamic parameters such as free energies and heat capacities are important quantities for understanding processes involving structural transitions in complex molecules such as proteins. Computational investigations provide simulated data that can be used for calculating thermodynamic parameters. However, calculations give accurate results only if the simulations sample all of configuration space with the appropriate temperature-dependent Boltzmann equilibrium probabilities. For many systems, truly comprehensive sampling of configuration space is not computationally feasible. We present an approximation technique for the calculations that will give accurate values for thermodynamic parameters when the data is incomplete. Our work is applicable to systems in which there are two distinct, important regions of configuration space that must be sampled. Importantly, the results are also valid when the system is more complex than two-state systems. Transition pathways that involve intermediate configurations between two stable regions are allowed in this treatment, and therefore the results are valid for multistate systems.

Internal and environmental effects on folding and dimerization of the Alzheimer's β amyloid peptide

Amyloid deposits are a hallmark of many diseases. In the case of Alzheimer's disease a turn between 21Ala and 30Ala, stabilized by a salt bridge between 22Glu/23Asp and 28Lys, may nucleate folding and aggregation of the Aβ peptide. In the present paper we test this hypothesis by studying how salt bridge and turn formation vary with intrinsic and environmental changes, and how these changes effect folding and aggregation of the Aβ peptide.

Statistical measures on residue-level protein structural properties

The atomic-level structural properties of proteins, such as bond lengths, bond angles, and torsion angles, have been well studied and understood based on either chemistry knowledge or statistical analysis. Similar properties on the residue-level, such as the distances between two residues and the angles formed by short sequences of residues, can be equally important for structural analysis and modeling, but these have not been examined and documented on a similar scale. While these properties are difficult to measure experimentally, they can be statistically estimated in meaningful ways based on their distributions in known proteins structures. Residue-level structural properties including various types of residue distances and angles are estimated statistically. A software package is built to provide direct access to the statistical data for the properties including some important correlations not previously investigated. The distributions of residue distances and angles may vary with varying sequences, but in most cases, are concentrated in some high probability ranges, corresponding to their frequent occurrences in either α-helices or β-sheets. Strong correlations among neighboring residue angles, similar to those between neighboring torsion angles at the atomic-level, are revealed based on their statistical measures. Residue-level statistical potentials can be defined using the statistical distributions and correlations of the residue distances and angles. Ramachandran-like plots for strongly correlated residue angles are plotted and analyzed. Their applications to structural evaluation and refinement are demonstrated. With the increase in both number and quality of known protein structures, many structural properties can be derived from sets of protein structures by statistical analysis and data mining, and these can even be used as a supplement to the experimental data for structure determinations. Indeed, the statistical measures on various types of residue distances and angles provide more systematic and quantitative assessments on these properties, which can otherwise be estimated only individually and qualitatively. Their distributions and correlations in known protein structures show their importance for providing insights into how proteins may fold naturally to various residue-level structures.

Analysis of the bacterial luciferase mobile loop by replica-exchange molecular dynamics

Bacterial luciferase contains an extended 29-residue mobile loop. Movements of this loop are governed by binding of either flavin mononucleotide (FMNH2) or polyvalent anions. To understand this process, loop dynamics were investigated using replica-exchange molecular dynamics that yielded conformational ensembles in either the presence or absence of FMNH2. The resulting data were analyzed using clustering and network analysis. We observed the closed conformations that are visited only in the simulations with the ligand. Yet the mobile loop is intrinsically flexible, and FMNH2 binding modifies the relative populations of conformations. This model provides unique information regarding the function of a crystallographically disordered segment of the loop near the binding site. Structures at or near the fringe of this network were compatible with flavin binding or release. Finally, we demonstrate that the crystallographically observed conformation of the mobile loop bound to oxidized flavin was influenced by crystal packing. Thus, our study has revealed what we believe are novel conformations of the mobile loop and additional context for experimentally determined structures.

Optimizing Protein-Solvent Force Fields to Reproduce Intrinsic Conformational Preferences of Model Peptides

While most force field efforts in biomolecular simulation have focused on the parametrization of the protein, relatively little attention has been paid to the quality of the accompanying solvent model. These considerations are especially relevant for simulations of intrinsically disordered peptides and proteins, for which energy differences between conformations are small and interactions with water are enhanced. In this work, we investigate the accuracy of the AMBER ff99SB force field when combined with the standard TIP3P model or the more recent TIP4P-Ew water model, to generate conformational ensembles for disordered trialanine (Ala3), triglycine (Gly3), and trivaline (Val3) peptides. We find that the TIP4P-Ew water model yields significantly better agreement with experimentally measured scalar couplings-and therefore more accurate conformational ensembles-for both Ala3 and Gly3. For Val3, however, we find that the TIP3P and TIP4P-Ew ensembles are equivalent in their performance. To further improve the protein-water force field combination and obtain more accurate intrinsic conformational preferences, we derive a straightforward perturbation to the ϕ' backbone dihedral potential that shifts the β-PPII equilibrium. We find that the revised ϕ' backbone dihedral potential yields improved conformational ensembles for a variety of small peptides and maintains the stability of the globular ubiquitin protein in TIP4P-Ew water.

Strategies for articulated multibody-based adaptive coarse grain simulation of RNA

Efficient modeling approaches are necessary to accurately predict large-scale structural behavior of biomolecular systems like RNA (ribonucleic acid). Coarse-grained approximations of such complex systems can significantly reduce the computational costs of the simulation while maintaining sufficient fidelity to capture the biologically significant motions. However, given the coupling and nonlinearity of RNA systems (and effectively all biopolymers), it is expected that different parameters such as geometric and dynamic boundary conditions, and applied forces will affect the system's dynamic behavior. Consequently, static coarse-grained models (i.e., models for which the coarse graining is time invariant) are not always able to adequately sample the conformational space of the molecule. We introduce here the concept of adaptive coarse-grained molecular dynamics of RNA, which automatically adjusts the coarseness of the model, in an effort to more optimally increase simulation speed, while maintaining accuracy. Adaptivity requires two basic algorithmic developments: first, a set of integrators that seamlessly allow transitions between higher and lower fidelity models while preserving the laws of motion. Second, we propose and validate metrics for determining when and where more or less fidelity needs to be integrated into the model to allow sufficiently accurate dynamics simulation. Given the central role that multibody dynamics plays in the proposed framework, and the nominally large number of dynamic degrees of freedom being considered in these applications, a computationally efficient multibody method which lends itself well to adaptivity is essential to the success of this effort. A suite of divide-and-conquer algorithm (DCA)-based approaches is employed to this end. These algorithms have been selected and refined for this purpose because they offer a good combination of computational efficiency and modular structure.

Quantitative Assessment of Force Fields on Both Low-Energy Conformational Basins and Transition-State Regions of the (ϕ-ψ) Space

The free energy surfaces (FESs) of alanine dipeptide are studied to illustrate a new strategy to assess the performance of classical molecular mechanics force field on the full range of the (ϕ-ψ) conformational space. The FES is obtained from metadynamics simulations with five commonly used force fields and from ab initio density functional theory calculations in both gas phase and aqueous solution. The FESs obtained at the B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d,p) level of theory are validated by comparison with previously reported MP2 and LMP2 results as well as with experimentally obtained probability distribution between the C5-β (or β-PPII) and αR states. A quantitative assessment is made for each force field in three conformational basins, LeRI (C5-β-C7eq), LeRII (β2-αR), and LeRIII(αL-C7ax-αD) as well as three transition-state regions linking the above conformational basins. The performance of each force field is evaluated in terms of the average free energy of each region in comparison with that of the ab initio results. We quantify how well a force field FES matches the ab initio FES through the calculation of the standard deviation of a free energy difference map between the two FESs. The results indicate that the performance varies largely from region to region or from force field to force field. Although not one force field is able to outperform all others in all conformational areas, the OPLSAA/L force field gives the best performance overall, followed by OPLSAA and AMBER03. For the three top performers, the average free energies differ from the corresponding ab initio values from within the error range (<0.4 kcal/mol) to ∼1.5 kcal/mol for the low-energy regions and up to ∼2.0 kcal/mol for the transition-state regions. The strategy presented and the results obtained here should be useful for improving the parametrization of force fields targeting both accuracy in the energies of conformers and the transition-state barriers.

Intrinsically disordered proteins in a physics-based world

Intrinsically disordered proteins (IDPs) are a newly recognized class of functional proteins that rely on a lack of stable structure for function. They are highly prevalent in biology, play fundamental roles, and are extensively involved in human diseases. For signaling and regulation, IDPs often fold into stable structures upon binding to specific targets. The mechanisms of these coupled binding and folding processes are of significant importance because they underlie the organization of regulatory networks that dictate various aspects of cellular decision-making. This review first discusses the challenge in detailed experimental characterization of these heterogeneous and dynamics proteins and the unique and exciting opportunity for physics-based modeling to make crucial contributions, and then summarizes key lessons from recent de novo simulations of the structure and interactions of several regulatory IDPs.

Conformational profile of bombesin assessed using different computational protocols

The present work involves the study of the conformational profile of bombesin using different computational procedures used to explore the configurational space based on molecular dynamics simulations. Specifically, the present study describes the effect of using Berendsen's versus Langevin's thermostat and on the other hand, the use of the multicanonical replica exchange molecular dynamics as compared to standard molecular dynamics. In these simulations the solvent was modeled using the Onufriev, Bashford and Case implementation of Generalized Born procedure. The detailed computational analysis agrees well with the aggregated information previously reported in the NMR study of the peptide in a mixture of trifluoroethanol/water. Present results show a clear preference for the peptide to attain a helical structure on the segment 6-14, with a tendency to adopt a α-helix at the C-terminus aligning the aromatic residues Trp8 and His12 together with Gln7, known to be important for peptide mediated activation. Finally, the three methodologies used in the present work yield similar structural results, although a detailed analysis reveals biases that need to be considered when performing this kind of studies.

Folding of a helix at room temperature is critically aided by electrostatic polarization of intraprotein hydrogen bonds

We report direct folding of a 17-residue helix protein (pdb:2I9M) by standard molecular dynamics simulation (single trajectory) at room temperature with implicit solvent. Starting from a fully extended structure, 2I9M successfully folds into the native conformation within 16 ns using adaptive hydrogen bond-specific charges to take into account the electrostatic polarization effect. Cluster analysis shows that conformations in the native state cluster have the highest population (78.4%) among all sampled conformations. Folding snapshots and the secondary structure analysis demonstrate that the folding of 2I9M begins at terminals and progresses toward the center. A plot of the free energy landscape indicates that there is no significant free energy barrier during folding, which explains the observed fast folding speed. For comparison, exactly the same molecular dynamics simulation but carried out under existing AMBER charges failed to fold 2I9M into native-like structures. The current study demonstrates that electrostatic polarization of intraprotein hydrogen bonding, which stabilizes the helix, is critical to the successful folding of 2I9m.

Coarse-grained model for simulation of RNA three-dimensional structures

The accurate prediction of an RNA's three-dimensional structure from its "primary structure" will have a tremendous influence on the experimental design and its interpretation and ultimately our understanding of the many functions of RNA. This paper presents a general coarse-grained (CG) potential for modeling RNA 3-D structures. Each nucleotide is represented by five pseudo atoms, two for the backbone (one for the phosphate and another for the sugar) and three for the base to represent base-stacking interactions. The CG potential has been parametrized from statistical analysis of 688 RNA experimental structures. Molecular dynamic simulations of 15 RNA molecules with the length of 12-27 nucleotides have been performed using the CG potential, with performance comparable to that from all-atom simulations. For ~75% of systems tested, simulated annealing led to native-like structures at least once out of multiple repeated runs. Furthermore, with weak distance restraints based on the knowledge of three to five canonical Watson-Crick pairs, all 15 RNAs tested are successfully folded to within 6.5 Å of native structures using the CG potential and simulated annealing. The results reveal that with a limited secondary structure model the current CG potential can reliably predict the 3-D structures for small RNA molecules. We also explored an all-atom force field to construct atomic structures from the CG simulations.

Modelling proteins: conformational sampling and reconstruction of folding kinetics

In the last decades biomolecular simulation has made tremendous inroads to help elucidate biomolecular processes in-silico. Despite enormous advances in molecular dynamics techniques and the available computational power, many problems involve long time scales and large-scale molecular rearrangements that are still difficult to sample adequately. In this review we therefore summarise recent efforts to fundamentally improve this situation by decoupling the sampling of the energy landscape from the description of the kinetics of the process. Recent years have seen the emergence of many advanced sampling techniques, which permit efficient characterisation of the relevant family of molecular conformations by dispensing with the details of the short-term kinetics of the process. Because these methods generate thermodynamic information at best, they must be complemented by techniques to reconstruct the kinetics of the process using the ensemble of relevant conformations. Here we review recent advances for both types of methods and discuss their perspectives to permit efficient and accurate modelling of large-scale conformational changes in biomolecules. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

Water-benzene interactions: an effective fragment potential and correlated quantum chemistry study

Structures and binding in small water-benzene complexes (1-8 water molecules and 1-2 benzene molecules) are studied using the general effective fragment potential (EFP) method. The lowest energy conformers of the clusters were found using a Monte Carlo technique. The binding energies in the smallest clusters (dimers, trimers, and tetramers) were also evaluated with second order perturbation theory (MP2) and coupled cluster theory (CCSD(T)). The EFP method accurately predicts structures and binding energies in the water-benzene complexes. Benzene is polarizable and consequently participates in hydrogen bond networking of water. Since the water-benzene interactions are only slightly weaker than water-water interactions, structures with different numbers of water-water, benzene-water, and benzene-benzene bonds often have very similar binding energies. This is a challenge for computational methods.

Protein functional landscapes, dynamics, allostery: a tortuous path towards a universal theoretical framework

Energy landscape theories have provided a common ground for understanding the protein folding problem, which once seemed to be overwhelmingly complicated. At the same time, the native state was found to be an ensemble of interconverting states with frustration playing a more important role compared to the folding problem. The landscape of the folded protein – the native landscape – is glassier than the folding landscape; hence, a general description analogous to the folding theories is difficult to achieve. On the other hand, the native basin phase volume is much smaller, allowing a protein to fully sample its native energy landscape on the biological timescales. Current computational resources may also be used to perform this sampling for smaller proteins, to build a ‘topographical map’ of the native landscape that can be used for subsequent analysis. Several major approaches to representing this topographical map are highlighted in this review, including the construction of kinetic networks, hierarchical trees and free energy surfaces with subsequent structural and kinetic analyses. In this review, we extensively discuss the important question of choosing proper collective coordinates characterizing functional motions. In many cases, the substates on the native energy landscape, which represent different functional states, can be used to obtain variables that are well suited for building free energy surfaces and analyzing the protein's functional dynamics. Normal mode analysis can provide such variables in cases where functional motions are dictated by the molecule's architecture. Principal component analysis is a more expensive way of inferring the essential variables from the protein's motions, one that requires a long molecular dynamics simulation. Finally, the two popular models for the allosteric switching mechanism, ‘preexisting equilibrium’ and ‘induced fit’, are interpreted within the energy landscape paradigm as extreme points of a continuum of transition mechanisms. Some experimental evidence illustrating each of these two models, as well as intermediate mechanisms, is presented and discussed.

A comprehensive multidimensional-embedded, one-dimensional reaction coordinate for protein unfolding/folding

The goal of the Dynameomics project is to perform, store, and analyze molecular dynamics simulations of representative proteins, of all known globular folds, in their native state and along their unfolding pathways. To analyze unfolding simulations, the location of the protein along the unfolding reaction coordinate (RXN) must be determined. Properties such as the fraction of native contacts and radius of gyration are often used; however, there is an issue regarding degeneracy with these properties, as native and nonnative species can overlap. Here, we used 15 physical properties of the protein to construct a multidimensional-embedded, one-dimensional RXN coordinate that faithfully captures the complex nature of unfolding. The unfolding RXN coordinates for 188 proteins (1534 simulations and 22.9 mus in explicit water) were calculated. Native, transition, intermediate, and denatured states were readily identified with the use of this RXN coordinate. A global native ensemble based on the native-state properties of the 188 proteins was created. This ensemble was shown to be effective for calculating RXN coordinates for folds outside the initial 188 targets. These RXN coordinates enable, high-throughput assignment of conformational states, which represents an important step in comparing protein properties across fold space as well as characterizing the unfolding of individual proteins.

The Binding Energy Distribution Analysis Method (BEDAM) for the Estimation of Protein-Ligand Binding Affinities

The Binding Energy Distribution Analysis Method (BEDAM) for the computation of receptor-ligand standard binding free energies with implicit solvation is presented. The method is based on a well established statistical mechanics theory of molecular association. It is shown that, in the context of implicit solvation, the theory is homologous to the test particle method of solvation thermodynamics with the solute-solvent potential represented by the effective binding energy of the protein-ligand complex. Accordingly, in BEDAM the binding constant is computed by means of a weighted integral of the probability distribution of the binding energy obtained in the canonical ensemble in which the ligand is positioned in the binding site but the receptor and the ligand interact only with the solvent continuum. It is shown that the binding energy distribution encodes all of the physical effects of binding. The balance between binding enthalpy and entropy is seen in our formalism as a balance between favorable and unfavorable binding modes which are coupled through the normalization of the binding energy distribution function. An efficient computational protocol for the binding energy distribution based on the AGBNP2 implicit solvent model, parallel Hamiltonian replica exchange sampling and histogram reweighting is developed. Applications of the method to a set of known binders and non-binders of the L99A and L99A/M102Q mutants of T4 lysozyme receptor are illustrated. The method is able to discriminate without error binders from non-binders, and the computed standard binding free energies of the binders are found to be in good agreement with experimental measurements. Analysis of the results reveals that the binding affinities of these systems reflect the contributions from multiple conformations spanning a wide range of binding energies.

Using one-step perturbation to predict the effect of changing force-field parameters on the simulated folding equilibrium of a beta-peptide in solution

Computer simulation using molecular dynamics is increasingly used to simulate the folding equilibria of peptides and small proteins. Yet, the quality of the obtained results depends largely on the quality of the force field used. This comprises the solute as well as the solvent model and their energetic and entropic compatibility. It is, however, computational very expensive to perform test simulations for each combination of force-field parameters. Here, we use the one-step perturbation technique to predict the change of the free enthalpy of folding of a beta-peptide in methanol solution due to changing a variety of force-field parameters. The results show that changing the solute backbone partial charges affects the folding equilibrium, whereas this is relatively insensitive to changes in the force constants of the torsional energy terms of the force field. Extending the cut-off distance for nonbonded interactions beyond 1.4 nm does not affect the folding equilibrium. The same result is found for a change of the reaction-field permittivity for methanol from 17.7 to 30. The results are not sensitive to the criterion, e.g., atom-positional RMSD or number of hydrogen bonds, that is used to distinguish folded and unfolded conformations. Control simulations with perturbed Hamiltonians followed by backward one-step perturbation indicated that quite large perturbations still yield reliable results. Yet, perturbing all solvent molecules showed where the limitations of the one-step perturbation technique are met. The evaluated methodology constitutes an efficient tool in force-field development for molecular simulation by reducing the number of required separate simulations by orders of magnitude.

Metadynamics as a tool for mapping the conformational and free-energy space of peptides--the alanine dipeptide case study

There is a need for a fast, accurate, and reliable method of sampling the conformational space of peptides and proteins in order to obtain a balanced free-energy profile which can lead to our understanding of protein structure. We have utilized metadynamics for the conformational study of the solvated alanine dipeptide molecule, and our results show that the method has proven to be competent as a fast, robust, and reliable method for the conformation free-energy calculations of peptides in an explicit solvent, surpassing traditional methods such as umbrella sampling. We have also addressed the issue of the influence of different water models on the resulting free-energy profile in order to consistently decompose the setting of our simulation. All of the explicit water models for the simulation of biomolecules TIP3P, TIP4P, TIP4P/Ew, TIP5P, and SPCE have exhibited similar effects on the conformational preferences of alanine dipeptide with no significant differences. On the other hand, by comparing the potential energy surface in the gas phase and the free-energy surface in a water environment, we have shown that the interaction with water molecules is one of the most important structure-driving elements, with a great influence on the free-energy surface (FES) of the solvated peptide and the conformational preferences of the peptide backbone. All of the tested force fields (ff03, ff99SB, opls-aa, and charmm27) appreciably differ in the population of the individual conformers and the barriers between them. Significant divergence was found on both the potential energy surface (PES) as well as free-energy surface (FES) calculated by charmm27. We have therefore concluded that the differences originate dominantly from the parametrization of the peptide backbone in the given force field rather than from a noncovalent interaction with water molecules.

Investigation of protein folding by coarse-grained molecular dynamics with the UNRES force field

Coarse-grained molecular dynamics simulations offer a dramatic extension of the time-scale of simulations compared to all-atom approaches. In this article, we describe the use of the physics-based united-residue (UNRES) force field, developed in our laboratory, in protein-structure simulations. We demonstrate that this force field offers about a 4000-times extension of the simulation time scale; this feature arises both from averaging out the fast-moving degrees of freedom and reduction of the cost of energy and force calculations compared to all-atom approaches with explicit solvent. With massively parallel computers, microsecond folding simulation times of proteins containing about 1000 residues can be obtained in days. A straightforward application of canonical UNRES/MD simulations, demonstrated with the example of the N-terminal part of the B-domain of staphylococcal protein A (PDB code: 1BDD, a three-alpha-helix bundle), discerns the folding mechanism and determines kinetic parameters by parallel simulations of several hundred or more trajectories. Use of generalized-ensemble techniques, of which the multiplexed replica exchange method proved to be the most effective, enables us to compute thermodynamics of folding and carry out fully physics-based prediction of protein structure, in which the predicted structure is determined as a mean over the most populated ensemble below the folding-transition temperature. By using principal component analysis of the UNRES folding trajectories of the formin-binding protein WW domain (PDB code: 1E0L; a three-stranded antiparallel beta-sheet) and 1BDD, we identified representative structures along the folding pathways and demonstrated that only a few (low-indexed) principal components can capture the main structural features of a protein-folding trajectory; the potentials of mean force calculated along these essential modes exhibit multiple minima, as opposed to those along the remaining modes that are unimodal. In addition, a comparison between the structures that are representative of the minima in the free-energy profile along the essential collective coordinates of protein folding (computed by principal component analysis) and the free-energy profile projected along the virtual-bond dihedral angles gamma of the backbone revealed the key residues involved in the transitions between the different basins of the folding free-energy profile, in agreement with existing experimental data for 1E0L .