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

A Mode Evolution Metric to Extract Reaction Coordinates for Biomolecular Conformational Transitions

The complex, multidimensional energy landscape of biomolecules makes the extraction of suitable, nonintuitive collective variables (CVs) that describe their conformational transitions challenging. At present, dimensionality reduction approaches and machine learning (ML) schemes are employed to obtain CVs from molecular dynamics (MD)/Monte Carlo (MC) trajectories or structural databanks for biomolecules. However, minimum sampling conditions to generate reliable CVs that accurately describe the underlying energy landscape remain unclear. Here, we address this issue by developing a Mode evolution Metric (MeM) to extract CVs that can pinpoint new states and describe local transitions in the vicinity of a reference minimum from nonequilibrated MD/MC trajectories. We present a general mathematical formulation of MeM for both statistical dimensionality reduction and machine learning approaches. Application of MeM to MC trajectories of model potential energy landscapes and MD trajectories of solvated alanine dipeptide reveals that the principal components which locate new states in the vicinity of a reference minimum emerge well before the trajectories locally equilibrate between the associated states. Finally, we demonstrate a possible application of MeM in designing efficient biased sampling schemes to construct accurate energy landscape slices that link transitions between states. MeM can help speed up the search for new minima around a biomolecular conformational state and enable the accurate estimation of thermodynamics for states lying on the energy landscape and the description of associated transitions.

Modeling the Homologous Recombination Process: Methods, Successes and Challenges

Homologous recombination (HR) is a fundamental process common to all species. HR aims to faithfully repair DNA double strand breaks. HR involves the formation of nucleoprotein filaments on DNA single strands (ssDNA) resected from the break. The nucleoprotein filaments search for homologous regions in the genome and promote strand exchange with the ssDNA homologous region in an unbroken copy of the genome. HR has been the object of intensive studies for decades. Because multi-scale dynamics is a fundamental aspect of this process, studying HR is highly challenging, both experimentally and using computational approaches. Nevertheless, knowledge has built up over the years and has recently progressed at an accelerated pace, borne by increasingly focused investigations using new techniques such as single molecule approaches. Linking this knowledge to the atomic structure of the nucleoprotein filament systems and the succession of unstable, transient intermediate steps that takes place during the HR process remains a challenge; modeling retains a very strong role in bridging the gap between structures that are stable enough to be observed and in exploring transition paths between these structures. However, working on ever-changing long filament systems submitted to kinetic processes is full of pitfalls. This review presents the modeling tools that are used in such studies, their possibilities and limitations, and reviews the advances in the knowledge of the HR process that have been obtained through modeling. Notably, we will emphasize how cooperative behavior in the HR nucleoprotein filament enables modeling to produce reliable information.

Beta-rich intermediates in denaturation of lysozyme: accelerated molecular dynamics simulations

Amyloid fibrillar aggregates play a critical role in many neurodegenerative disorders. Conversion of globular proteins into fibrils is associated with global conformational rearrangement and involves the transformation of α-helices to β-sheets. In the present work, the accelerated molecular dynamics technique was applied to study the unfolding of hen egg-white lysozyme at elevated temperatures, and the transformation of the native structure to a disordered one was analyzed. The influence of the disulfide bonds on the conformational dynamics and the energy landscape of denaturation process was considered. Our results show that formation of the metastable β-enriched conformers of individual protein molecules may precede the aggregation process. These β-rich intermediates can play a role of bricks making up fibrils.Communicated by Ramaswamy H. Sarma.

Modeling structural interconversion in Alzheimers' amyloid beta peptide with classical and intrinsically disordered protein force fields

A comprehensive understanding of the aggregation mechanism in amyloid beta 42 (Aβ42) peptide is imperative for developing therapeutic drugs to prevent or treat Alzheimer's disease. Because of the high flexibility and lack of native tertiary structures of Aβ42, molecular dynamics (MD) simulations may help elucidate the peptide's dynamics with atomic details and collectively improve ensembles not seen in experiments. We applied microsecond-timescale MD simulations to investigate the dynamics and conformational changes of Aβ42 by using a newly developed Amber force field (ff14IDPSFF). We compared the ff14IDPSFF and the regular ff14SB force field by examining the conformational changes of two distinct Aβ42 monomers in explicit solvent. Conformational ensembles obtained by simulations depend on the force field and initial structure, Aβ42^α-helix or Aβ42^β-strand. The ff14IDPSFF sampled a high ratio of disordered structures and diverse β-strand secondary structures; in contrast, ff14SB favored helicity during the Aβ42^α-helix simulations. The conformations obtained from Aβ42^β-strand simulations maintained a balanced content in the disordered and helical structures when simulated by ff14SB, but the conformers clearly favored disordered and β-sheet structures simulated by ff14IDPSFF. The results obtained with ff14IDPSFF qualitatively reproduced the NMR chemical shifts well. In-depth peptide and cluster analysis revealed some characteristic features that may be linked to early onset of the fibril-like structure. The C-terminal region (mainly M35-V40) featured in-registered anti-parallel β-strand (β-hairpin) conformations with tested systems. Our work should expand the knowledge of force field and structure dependency in MD simulations and reveals the underlying structural mechanism-function relationship in Aβ42 peptides. Communicated by Ramaswamy H. Sarma.

Peptide Dynamics and Metadynamics: Leveraging Enhanced Sampling Molecular Dynamics to Robustly Model Long-Timescale Transitions

Molecular dynamics simulations can in theory reveal the thermodynamics and kinetics of peptide conformational transitions at atomic-level resolution. However, even with modern computing power, they are limited in the timescales they can sample, which is especially problematic for peptides that are fully or partially disordered. Here, we discuss how the enhanced sampling methods accelerated molecular dynamics (aMD) and metadynamics can be leveraged in a complementary fashion to quickly explore conformational space and then robustly quantify the underlying free energy landscape. We apply these methods to two peptides that have an intrinsically disordered nature, the histone H3 and H4 N-terminal tails, and use metadynamics to compute the free energy landscape along collective variables discerned from aMD simulations. Results show that these peptides are largely disordered, with a slight preference for α-helical structures.

Metadynamics-Based Approaches for Modeling the Hypoxia-Inducible Factor 2α Ligand Binding Process

Several methods based on enhanced-sampling molecular dynamics have been proposed for studying ligand binding processes. Here, we developed a protocol that combines the advantages of steered molecular dynamics (SMD) and metadynamics. While SMD is proposed for investigating possible unbinding pathways of the ligand and identifying the preferred one, metadynamics, with the path collective variable (PCV) formalism, is suggested to explore the binding processes along the pathway defined on the basis of SMD, by using only two CVs. We applied our approach to the study of binding of two known ligands to the hypoxia-inducible factor 2α, where the buried binding cavity makes simulation of the process a challenging task. Our approach allowed identification of the preferred entrance pathway for each ligand, highlighted the features of the bound and intermediate states in the free-energy surface, and provided a binding affinity scale in agreement with experimental data. Therefore, it seems to be a suitable tool for elucidating ligand binding processes of similar complex systems.

Fibril fragments from the amyloid core of lysozyme: An accelerated molecular dynamics study

Protein aggregation and formation of amyloid fibrils are associated with many diseases and present a ubiquitous problem in protein science. Hen egg white lysozyme (HEWL) can form fibrils both from the full length protein and from its fragments. In the present study, we simulated unfolding of the amyloidogenic fragment of HEWL encompassing residues 49-101 to study the conformational aspects of amyloidogenesis. The accelerated molecular dynamics approach was used to speed up the sampling of the fragment conformers under enhanced temperature. Analysis of conformational transformation and intermediate structures was performed. During the unfolding, the novel short-living and long-living β-structures are formed along with the unstructured random coils. Such β-structure enriched monomers can interact with each other and propagate into fibril-like forms. The stability of oligomers assembled from these monomers was evaluated in the course of MD simulations with explicit water. The residues playing a key role in fibril stabilization were determined. The work provides new insights into the processes occurring at the early stages of amyloid fibril assembly.

Adaptively Iterative Multiscale Switching Simulation Strategy and Applications to Protein Folding and Structure Prediction

Structure prediction is an important means to quickly understand new protein functions. However, the prediction of effects of proteins that have no detectable templates is still to be improved. Molecular dynamics simulation is supposed to be the primary research tool for structure predictions, but it still has limitations of huge computational cost in all-atom (AA) models and rough accuracy in coarse-grained (CG) models. We propose a universal multiscale simulation strategy named AIMS in which simulations can iteratively switch among multiple resolutions in order to adaptively trade off AA accuracy and CG high-efficiency. AIMS follows the idea of CG-guided enhanced sampling so that final results always keep AA accuracy. We successfully achieve four ab initio and four data-assisted protein structure predictions using AIMS. The prediction result is an ensemble rather than a structure and provides special insights on folding metastable states. AIMS is estimated to achieve a computational speed about 40 times faster than that of conventional AA simulations.

Neutral gold clusters studied by the isothermal Brownian-type molecular dynamics and metadynamics molecular dynamics simulations

The DFTB theory was combined with the isothermal Brownian-type molecular dynamics (MD) and metadynamics molecular dynamics (MMD) algorithms to perform simulation studies for Au clusters. Two representative DFTB parametrizations were investigated. In one parametrization, the DFTB-A, the Slater-Koster parameters in the DFTB energy function were determined focusing on the ionic repulsive energy part, E_rep and the other, the DFTB-B, due attention was paid to the electronic band-structure energy part, E_band . Minimized structures of these two parametrizations were separately applied in MD and MMD simulations to generate unbiased and biased trajectories in collective variable (CV) space, respectively. Here, we found the MD simulations monitored at 300 K manifest fluxional characteristics in planar cluster Au₉ /DFTB-A, but give no discernible tracts of fluxionality for planar Au₈ /DFTB-A and Au₈ /DFTB-B, for nonplanar Au₁₀ /DFTB-A and, to some extent, for nonplanar Au₉ /DFTB-B; they are plausibly being hindered by higher-than k_B T energy barriers. Very recent FIR-MPD spectroscopy measurements, however, were reported to have detected at 300 K both the planar and nonplanar neutral Au_n clusters in the size range 5 ≤ n ≤ 13. The failure of MD simulations has prompted us to apply the MMD simulation and construct the free energy landscape (FEL) in CV space. Through scrutinizing the FELs of these clusters and their associated structures, we examine the relative importance of E_rep /DFTB-A and E_band /DFTB-B in unraveling the covalent-like behavior of valence electrons in Au_n . Most important of all, we shall evaluate the DFTB parametrization in MMD strategy through comparing extensively the simulation data recorded with the gas-phase experimental data.

Deciphering collaborative sidechain motions in proteins during molecular dynamics simulations

The dynamic structure of proteins is essential for their functions and may include large conformational transitions which can be studied by molecular dynamics (MD) simulations. However, details of these transitions are difficult to automatically track. To facilitate their analysis, we developed two scores of correlation between sidechain dihedral angles. The CIRCULAR and OMES scores are computed from, respectively, dihedral angle values and rotamer distributions. As a case study, we applied our methods to an activation-like transition of the chemokine receptor CXCR4, observed during accelerated MD simulations. The principal component analysis of the correlation matrices was consistent with the networking structure of the top ranking pairs. Both scores identify a set of residues whose “collaborative” sidechain rotamerization immediately preceded or accompanied the conformational transition of CXCR4. Detailed analysis of the sequential order of these rotamerizations suggests that an allosteric mechanism, involving the outward motion of an asparagine residue in transmembrane helix 3, might be a prerequisite to the large scale conformational transition of CXCR4. This case study provides the proof-of-concept that the correlation methods developed here are valuable exploratory techniques to help decipher complex reactional pathways.

Scalable molecular dynamics on CPU and GPU architectures with NAMD

NAMDis a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures. NAMD is a versatile, multipurpose code that gathers state-of-the-art algorithms to carry out simulations in apt thermodynamic ensembles, using the widely popular CHARMM, AMBER, OPLS, and GROMOS biomolecular force fields. Here, we review the main features of NAMD that allow both equilibrium and enhanced-sampling molecular dynamics simulations with numerical efficiency. We describe the underlying concepts utilized by NAMD and their implementation, most notably for handling long-range electrostatics; controlling the temperature, pressure, and pH; applying external potentials on tailored grids; leveraging massively parallel resources in multiple-copy simulations; and hybrid quantum-mechanical/molecular-mechanical descriptions. We detail the variety of options offered by NAMD for enhanced-sampling simulations aimed at determining free-energy differences of either alchemical or geometrical transformations and outline their applicability to specific problems. Last, we discuss the roadmap for the development of NAMD and our current efforts toward achieving optimal performance on GPU-based architectures, for pushing back the limitations that have prevented biologically realistic billion-atom objects to be fruitfully simulated, and for making large-scale simulations less expensive and easier to set up, run, and analyze. NAMD is distributed free of charge with its source code at www.ks.uiuc.edu.

Cholestenoic acid analogues as inverse agonists of the liver X receptors

Liver X Receptors (LXRs) are ligand dependent transcription factors activated by oxidized cholesterol metabolites (oxysterols) that play fundamental roles in the transcriptional control of lipid metabolism, cholesterol transport and modulation of inflammatory responses. In the last decade, LXRs have become attractive pharmacological targets for intervention in human metabolic diseases and thus, several efforts have concentrated on the development of synthetic analogues able to modulate LXR transcriptional response. In this sense, we have previously found that cholestenoic acid analogues with a modified side chain behave as LXR inverse agonists. To further investigate the structure-activity relationships and to explore how cholestenoic acid derivatives interact with the LXRs, we evaluated the LXR biological activity of new analogues containing a C24-C25 double bond. Furthermore, a microarray assay was performed to evaluate the recruitment of coregulators to recombinant LXR LBD upon ligand binding. Also, conventional and accelerated molecular dynamics simulations were applied to gain insight on the molecular determinants involved in the inverse agonism. As LXR inverse agonists emerge as very promising candidates to control LXR activity, the cholestenoic acid analogues here depicted constitute a new relevant steroidal scaffold to inhibit LXR action.

Detecting Functional Dynamics in Proteins with Comparative Perturbed-Ensembles Analysis

Recent advances have made all-atom molecular dynamics (MD) a powerful tool to sample the conformational energy landscape. There are still however three major challenges in the application of MD to biological systems: accuracy of force field, time scale, and the analysis of simulation trajectories. Significant progress in addressing the first two challenges has been made and extensively reviewed previously. This Account focuses on strategies of analyzing simulation data of biomolecules that also covers ways to properly design simulations and validate simulation results. In particular, we examine an approach named comparative perturbed-ensembles analysis, which we developed to efficiently detect dynamics in protein MD simulations that can be linked to biological functions. In our recent studies, we implemented this approach to understand allosteric regulations in several disease-associated human proteins. The central task of a comparative perturbed-ensembles analysis is to compare two or more conformational ensembles of a system generated by MD simulations under distinct perturbation conditions. Perturbations can be different sequence variations, ligand-binding conditions, and other physical/chemical modifications of the system. Each simulation is long enough (e.g., microsecond-long) to ensure sufficient sampling of the local substate. Then, sophisticated bioinformatic and statistical tools are applied to extract function-related information from the simulation data, including principal component analysis, residue-residue contact analysis, difference contact network analysis (dCNA) based on the graph theory, and statistical analysis of side-chain conformations. Computational findings are further validated with experimental data. By comparing distinct conformational ensembles, functional micro- to millisecond dynamics can be inferred. In contrast, such a time scale is difficult to reach in a single simulation; even when reached for a single condition of a system, it is elusive as to what dynamical motions are related to functions without, for example, comparing free and substrate-bound proteins at the minimum. We illustrate our approach with three examples. First, we discuss using the approach to identify allosteric pathways in cyclophilin A (CypA), a member of a ubiquitous class of peptidyl-prolyl cis-trans isomerase enzymes. By comparing side-chain torsion-angle distributions of CypA in wild-type and mutant forms, we identified three pathways: two are consistent with recent nuclear magnetic resonance experiments, whereas the third is a novel pathway. Second, we show how the approach enables a dynamical-evolution analysis of the human cyclophilin family. In the analysis, both conserved and divergent conformational dynamics across three cyclophilin isoforms (CypA, CypD, and CypE) were summarized. The conserved dynamics led to the discovery of allosteric networks resembling those found in CypA. A residue wise determinant underlying the unique dynamics in CypD was also detected and validated with additional mutational MD simulations. In the third example, we applied the approach to elucidate a peptide sequence-dependent allosteric mechanism in human Pin 1, a phosphorylation-dependent peptidyl-prolyl isomerase. We finally present our outlook of future directions. Especially, we envisage how the approach could help open a new avenue in drug discovery.

A Variable Neighbourhood Descent Heuristic for Conformational Search Using a Quantum Annealer

Discovering the low-energy conformations of a molecule is of great interest to computational chemists, with applications in in silico materials design and drug discovery. In this paper, we propose a variable neighbourhood search heuristic for the conformational search problem. Using the structure of a molecule, neighbourhoods are chosen to allow for the efficient use of a binary quadratic optimizer for conformational search. The method is flexible with respect to the choice of molecular force field and the number of discretization levels in the search space, and can be further generalized to take advantage of higher-order binary polynomial optimizers. It is well-suited for the use of devices such as quantum annealers. After carefully defining neighbourhoods, the method easily adapts to the size and topology of these devices, allowing for seamless scaling alongside their future improvements.

Human p38α mitogen-activated protein kinase in the Asp168-Phe169-Gly170-in (DFG-in) state can bind allosteric inhibitor Doramapimod

Doramapimod (BIRB-796) is widely recognized as one of the most potent and selective type II inhibitors of human p38α mitogen-activated protein kinase (MAPK); however, the understanding of its binding mechanism remains incomplete. Previous studies indicated high affinity of the ligand to a so-called allosteric pocket revealed only in the 'out' state of the DFG motif (i.e. Asp168-Phe169-Gly170) when Phe169 becomes fully exposed to the solvent. The possibility of alternative binding in the DFG-in state was hypothesized, but the molecular mechanism was not known. Methods of bioinformatics, docking and long-time scale classical and accelerated molecular dynamics have been applied to study the interaction of Doramapimod with the human p38α MAPK. It was shown that Doramapimod can bind to the protein even when the Phe169 is fully buried inside the allosteric pocket and the kinase activation loop is in the DFG-in state. Orientation of the inhibitor in such a complex is significantly different from that in the known crystallographic complex formed by the kinase in the DFG-out state; however, the Doramapimod's binding is followed by the ligand-induced conformational changes, which finally improve accommodation of the inhibitor. Molecular modelling has confirmed that Doramapimod combines the features of type I and II inhibitors of p38α MAPK, i.e. can directly and indirectly compete with the ATP binding. It can be concluded that optimization of the initial binding in the DFG-in state and the final accommodation in the DFG-out state should be both considered at designing novel efficient type II inhibitors of MAPK and homologous proteins. Communicated by Ramaswamy H. Sarma.

Ligand Access Channels in Cytochrome P450 Enzymes: A Review

Quantitative structure-activity relationships may bring invaluable information on structural elements of both enzymes and substrates that, together, govern substrate specificity. Buried active sites in cytochrome P450 enzymes are connected to the solvent by a network of channels exiting at the distal surface of the protein. This review presents different in silico tools that were developed to uncover such channels in P450 crystal structures. It also lists some of the experimental evidence that actually suggest that these predicted channels might indeed play a critical role in modulating P450 functions. Amino acid residues at the entrance of the channels may participate to a first global ligand recognition of ligands by P450 enzymes before they reach the buried active site. Moreover, different P450 enzymes show different networks of predicted channels. The plasticity of P450 structures is also important to take into account when looking at how channels might play their role.

Neuraminidase A from Streptococcus pneumoniae has a modular organization of catalytic and lectin domains separated by a flexible linker

Neuraminidase A (NanA) of the pathogen Streptococcus pneumoniae cleaves receptors of the human respiratory epithelial surface during bacterial colonization. The full-size structure of NanA that contains one lectin and one catalytic domain within a single polypeptide chain remains unresolved. Both domains are crucial for the microorganism's virulence and considered as promising antimicrobial targets. Methods of bioinformatics and molecular dynamics have been implemented to model NanA's structure and study interaction between the lectin and catalytic domains in three neuraminidases NanA, NanB, and NanC from Streptococcus pneumoniae. A significant difference in spatial organization of these homologous enzymes has been revealed. The lectin and catalytic domains of NanB and NanC form rigid globules stabilized by multiple interdomain interactions, whereas in NanA, the two domains are separated by a 16 amino acids long flexible linker - a characteristic of proteins that require conformational flexibility for their functioning. The biological role of this structural adaptation of NanA as a key virulence enzyme is discussed.

Atomistic molecular dynamics simulations of bioactive engrailed 1 interference peptides (EN1-iPeps)

The neural-specific transcription factor Engrailed 1 - is overexpressed in basal-like breast tumours. Synthetic interference peptides - comprising a cell-penetrating peptide/nuclear localisation sequence and the Engrailed 1-specific sequence from the N-terminus have been engineered to produce a strong apoptotic response in tumour cells overexpressing EN1, with no toxicity to normal or non Engrailed 1-expressing cells. Here scaled molecular dynamics simulations were used to study the conformational dynamics of these interference peptides in aqueous solution to characterise their structure and dynamics. Transitions from disordered to α-helical conformation, stabilised by hydrogen bonds and proline-aromatic interactions, were observed throughout the simulations. The backbone of the wild-type peptide folds to a similar conformation as that found in ternary complexes of anterior Hox proteins with conserved hexapeptide motifs important for recognition of pre-B-cell leukemia Homeobox 1, indicating that the motif may possess an intrinsic preference for helical structure. The predicted NMR chemical shifts of these peptides are consistent with the Hox hexapeptides in solution and Engrailed 2 NMR data. These findings highlight the importance of aromatic residues in determining the structure of Engrailed 1 interference peptides, shedding light on the rational design strategy of molecules that could be adopted to inhibit other transcription factors overexpressed in other cancer types, potentially including other transcription factor families that require highly conserved and cooperative protein-protein partnerships for biological activity.

Pathways to Structure-Property Relationships of Peptide-Materials Interfaces: Challenges in Predicting Molecular Structures

An in-depth appreciation of how to manipulate the molecular-level recognition between peptides and aqueous materials interfaces, including nanoparticles, will advance technologies based on self-organized metamaterials for photonics and plasmonics, biosensing, catalysis, energy generation and harvesting, and nanomedicine. Exploitation of the materials-selective binding of biomolecules is pivotal to success in these areas and may be particularly key to producing new hierarchically structured biobased materials. These applications could be accomplished by realizing preferential adsorption of a given biomolecule onto one materials composition over another, one surface facet over another, or one crystalline polymorph over another. Deeper knowledge of the aqueous abiotic-biotic interface, to establish clear structure-property relationships in these systems, is needed to meet this goal. In particular, a thorough structural characterization of the surface-adsorbed peptides is essential for establishing these relationships but can often be challenging to accomplish via experimental approaches alone. In addition to myriad existing challenges associated with determining the detailed molecular structure of any molecule adsorbed at an aqueous interface, experimental characterization of materials-binding peptides brings new, complex challenges because many materials-binding peptides are thought to be intrinsically disordered. This means that these peptides are not amenable to experimental techniques that rely on the presence of well-defined secondary structure in the peptide when in the adsorbed state. To address this challenge, and in partnership with experiment, molecular simulations at the atomistic level can bring complementary and critical insights into the origins of this abiotic/biotic recognition and suggest routes for manipulating this phenomenon to realize new types of hybrid materials. For the reasons outlined above, molecular simulation approaches also face challenges in their successful application to model the biotic-abiotic interface, related to several factors. For instance, simulations require a plausible description of the chemistry and the physics of the interface, which comprises two very different states of matter, in the presence of liquid water. Also, it is essential that the conformational ensemble be comprehensively characterized under these conditions; this is especially challenging because intrinsically disordered peptides do not typically admit one single structure or set of structures. Moreover, a plausible structural model of the substrate is required, which may require a high level of detail, even for single-element materials such as Au surfaces or graphene. Developing and applying strategies to make credible predictions of the conformational ensemble of adsorbed peptides and using these to construct structure-property relationships of these interfaces have been the goals of our efforts. We have made substantial progress in developing interatomic potentials for these interfaces and adapting advanced conformational sampling approaches for these purposes. This Account summarizes our progress in the development and deployment of interfacial force fields and molecular simulation techniques for the purpose of elucidating these insights at biomolecule-materials interfaces, using examples from our laboratories ranging from noble-metal interfaces to graphitic substrates (including carbon nanotubes and graphene) and oxide materials (such as titania). In addition to the well-established application areas of plasmonic materials, biosensing, and the production of medical implant materials, we outline new directions for this field that have the potential to bring new advances in areas such as energy materials and regenerative medicine.

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.

Balancing Accuracy and Cost of Confinement Simulations by Interpolation and Extrapolation of Confinement Energies

Improvements to the confinement method for the calculation of conformational free energy differences are presented. By taking advantage of phase space overlap between simulations at different frequencies, significant gains in accuracy and speed are reached. The optimal frequency spacing for the simulations is obtained from extrapolations of the confinement energy, and relaxation time analysis is used to determine time steps, simulation lengths, and friction coefficients. At postprocessing, interpolation of confinement energies is used to significantly reduce discretization errors in the calculation of conformational free energies. The efficiency of this protocol is illustrated by applications to alanine n-peptides and lactoferricin. For the alanine-n-peptide, errors were reduced between 2- and 10-fold and sampling times between 8- and 67-fold, while for lactoferricin the long sampling times at low frequencies were reduced 10-100-fold.

Variability of the Cyclin-Dependent Kinase 2 Flexibility Without Significant Change in the Initial Conformation of the Protein or Its Environment; a Computational Study

BACKGROUND

Protein flexibility, which has been referred as a dynamic behavior has various roles in proteins' functions. Furthermore, for some developed tools in bioinformatics, such as protein-protein docking software, considering the protein flexibility, causes a higher degree of accuracy. Through undertaking the present work, we have accomplished the quantification plus analysis of the variations in the human Cyclin Dependent Kinase 2 (hCDK2) protein flexibility without affecting a significant change in its initial environment or the protein per se.

OBJECTIVES

The main goal of the present research was to calculate variations in the flexibility for each residue of the hCDK2, analysis of their flexibility variations through clustering, and to investigate the functional aspects of the residues with high flexibility variations.

MATERIALS AND METHODS

Using Gromacs package (version 4.5.4), three independent molecular dynamics (MD) simulations of the hCDK2 protein (PDB ID: 1HCL) was accomplished with no significant changes in their initial environments, structures, or conformations, followed by Root Mean Square Fluctuations (RMSF) calculation of these MD trajectories. The amount of variations in these three curves of RMSF was calculated using two formulas.

RESULTS

More than 50% of the variation in the flexibility (the distance between the maximum and the minimum amount of the RMSF) was found at the region of Val-154. As well, there are other major flexibility fluctuations in other residues. These residues were mostly positioned in the vicinity of the functional residues. The subsequent works were done, as followed by clustering all hCDK2 residues into four groups considering the amount of their variability with respect to flexibility and their position in the RMSF curves.

CONCLUSIONS

This work has introduced a new class of flexibility aspect of the proteins' residues. It could also help designing and engineering proteins, with introducing a new dynamic aspect of hCDK2, and accordingly, for the other similar globular proteins. In addition, it could provide a better computational calculation of the protein flexibility, which is, especially important in the comparative studies of the proteins' flexibility.

Role of Conformational Motions in Enzyme Function: Selected Methodologies and Case Studies

It is now common knowledge that enzymes are mobile entities relying on complex atomic-scale dynamics and coordinated conformational events for proper ligand recognition and catalysis. However, the exact role of protein dynamics in enzyme function remains either poorly understood or difficult to interpret. This mini-review intends to reconcile biophysical observations and biological significance by first describing a number of common experimental and computational methodologies employed to characterize atomic-scale residue motions on various timescales in enzymes, and second by illustrating how the knowledge of these motions can be used to describe the functional behavior of enzymes and even act upon it. Two biologically relevant examples will be highlighted, namely the HIV-1 protease and DNA polymerase β enzyme systems.

Enhanced sampling simulations to construct free-energy landscape of protein-partner substrate interaction

Molecular dynamics (MD) simulations using all-atom and explicit solvent models provide valuable information on the detailed behavior of protein-partner substrate binding at the atomic level. As the power of computational resources increase, MD simulations are being used more widely and easily. However, it is still difficult to investigate the thermodynamic properties of protein-partner substrate binding and protein folding with conventional MD simulations. Enhanced sampling methods have been developed to sample conformations that reflect equilibrium conditions in a more efficient manner than conventional MD simulations, thereby allowing the construction of accurate free-energy landscapes. In this review, we discuss these enhanced sampling methods using a series of case-by-case examples. In particular, we review enhanced sampling methods conforming to trivial trajectory parallelization, virtual-system coupled multicanonical MD, and adaptive lambda square dynamics. These methods have been recently developed based on the existing method of multicanonical MD simulation. Their applications are reviewed with an emphasis on describing their practical implementation. In our concluding remarks we explore extensions of the enhanced sampling methods that may allow for even more efficient sampling.

Molecular dynamics simulations: advances and applications

Molecular dynamics simulations have evolved into a mature technique that can be used effectively to understand macromolecular structure-to-function relationships. Present simulation times are close to biologically relevant ones. Information gathered about the dynamic properties of macromolecules is rich enough to shift the usual paradigm of structural bioinformatics from studying single structures to analyze conformational ensembles. Here, we describe the foundations of molecular dynamics and the improvements made in the direction of getting such ensemble. Specific application of the technique to three main issues (allosteric regulation, docking, and structure refinement) is discussed.

Flexible receptor docking for drug discovery

INTRODUCTION

Molecular docking has become a popular method for virtual screening. Docking small molecules to a rigid biological receptor is fast but could produce many false negatives and identify less diverse compounds. Flexible receptor docking has alleviated this problem.

AREAS COVERED

This article focuses on reviewing ensemble docking as an approximate but inexpensive method to incorporate receptor flexibility in molecular docking. It outlines key features and recent advances of this method and points out problem areas that need to be addressed to make it even more useful in drug discovery.

EXPERT OPINION

Among the different methods introduced for flexible receptor docking, ensemble docking represents one of the most popular approaches, especially for high-throughput virtual screening. One can generate structural ensembles by using experimental structures, by structural modeling and by various types of molecular simulations. In building a structural ensemble, a judicious choice of the structures to be included can improve performance. Furthermore, reducing the size of the structural ensemble can cut computational costs, and removing the structures that can bind few ligands well could enrich the number of true actives identified by ensemble docking. The ability of ensemble docking to identify more true positives at the top of a rank-ordered list also depends on the choice of the methods to score and rank compounds, an area that needs further research.

Atomic-resolution dissection of the energetics and mechanism of isomerization of hydrated ATP-Mg(2+) through the SOMA string method

The atomic mechanisms of isomerization of ATP-Mg(2+) in solution are characterized using the recently developed String Method with Optimal Molecular Alignment (SOMA) and molecular-dynamics simulations. Bias-Exchange Metadynamics simulations are first performed to identify the primary conformers of the ATP-Mg(2+) complex and their connectivity. SOMA is then used to elucidate the minimum free-energy path (MFEP) for each transition, in a 48-dimensional space. Analysis of the per-atom contributions to the global free-energy profiles reveals that the mechanism of these transitions is controlled by the Mg(2+) ion and its coordinating oxygen atoms in the triphosphate moiety, as well as by the ion-hydration shell. Metadynamics simulations in path collective variables based on the MFEP demonstrate these isomerizations proceed across a narrow channel of configurational space, thus validating the premise underlying SOMA. This study provides a roadmap for the examination of conformational changes in biomolecules, based on complementary enhanced-sampling techniques with different strengths. © 2015 Wiley Periodicals, Inc.

Elucidation of Ligand-Dependent Modulation of Disorder-Order Transitions in the Oncoprotein MDM2

Numerous biomolecular interactions involve unstructured protein regions, but how to exploit such interactions to enhance the affinity of a lead molecule in the context of rational drug design remains uncertain. Here clarification was sought for cases where interactions of different ligands with the same disordered protein region yield qualitatively different results. Specifically, conformational ensembles for the disordered lid region of the N-terminal domain of the oncoprotein MDM2 in the presence of different ligands were computed by means of a novel combination of accelerated molecular dynamics, umbrella sampling, and variational free energy profile methodologies. The resulting conformational ensembles for MDM2, free and bound to p53 TAD (17-29) peptide identify lid states compatible with previous NMR measurements. Remarkably, the MDM2 lid region is shown to adopt distinct conformational states in the presence of different small-molecule ligands. Detailed analyses of small-molecule bound ensembles reveal that the ca. 25-fold affinity improvement of the piperidinone family of inhibitors for MDM2 constructs that include the full lid correlates with interactions between ligand hydrophobic groups and the C-terminal lid region that is already partially ordered in apo MDM2. By contrast, Nutlin or benzodiazepinedione inhibitors, that bind with similar affinity to full lid and lid-truncated MDM2 constructs, interact additionally through their solubilizing groups with N-terminal lid residues that are more disordered in apo MDM2.

Life as we know it depends on interactions between proteins. There is substantial evidence that many interactions between proteins involve very flexible protein regions. These disordered regions may undergo disorder/order transitions upon forming an interaction with another protein. Many successful approaches to medicinal chemistry are based on mimicking the interactions of biological molecules with man-made small molecules. However how drug-like small-molecules may modulate protein disorder is currently poorly understood, largely because it is difficult to measure in details this type of interaction with experimental methods. Here we have used computer simulations to resolve with great details the process by which different small-molecules modulate the flexibility of a disordered region of the protein MDM2. This protein is overexpressed in many cancers and small-molecules that recognize MDM2 have been developed over the last decade as possible novel anti-cancer agents. We show that the flexible MDM2 “lid” region adopts different conformational states in the presence of different small-molecules. Our results suggest why some classes of small-molecules form favorable interactions with the lid region, whereas others do not. These findings may prove crucial to develop new and more effective MDM2 inhibitors, and more generally to help drug designers target disordered proteins regions with small-molecules.

Review of the fundamental theories behind small angle X-ray scattering, molecular dynamics simulations, and relevant integrated application

In this paper, the fundamental concepts and equations necessary for performing small angle X-ray scattering (SAXS) experiments, molecular dynamics (MD) simulations, and MD-SAXS analyses were reviewed. Furthermore, several key biological and non-biological applications for SAXS, MD, and MD-SAXS are presented in this review; however, this article does not cover all possible applications. SAXS is an experimental technique used for the analysis of a wide variety of biological and non-biological structures. SAXS utilizes spherical averaging to produce one- or two-dimensional intensity profiles, from which structural data may be extracted. MD simulation is a computer simulation technique that is used to model complex biological and non-biological systems at the atomic level. MD simulations apply classical Newtonian mechanics' equations of motion to perform force calculations and to predict the theoretical physical properties of the system. This review presents several applications that highlight the ability of both SAXS and MD to study protein folding and function in addition to non-biological applications, such as the study of mechanical, electrical, and structural properties of non-biological nanoparticles. Lastly, the potential benefits of combining SAXS and MD simulations for the study of both biological and non-biological systems are demonstrated through the presentation of several examples that combine the two techniques.

Computational perspective and evaluation of plausible catalytic mechanisms of peptidyl-prolyl cis-trans isomerases

BACKGROUND

Peptidyl prolyl cis-trans isomerization of the protein backbone is involved in the regulation of many biological processes. Cis-trans isomerization is notoriously slow and is catalyzed by a family of cis-trans peptidyl prolyl isomerases (PPIases) that have been implicated in many diseases. A general consensus on how these enzymes speed up prolyl isomerization has not been reached after decades of both experimental and computational studies.

SCOPE OF REVIEW

Computational studies carried out to understand the catalytic mechanism of the prototypical FK506 binding protein 12, Cyclophilin A and peptidyl-prolyl cis-trans isomerase NIMA-interacting 1 (Pin1) are reviewed. A summary and an evaluation of the implications of the proposed mechanisms from computational studies are presented.

MAJOR CONCLUSIONS

The analysis of computational studies and evaluation of the proposed mechanisms provide a general consensus and a better understanding of PPIase catalysis. The speedup of the rate of peptidyl-prolyl isomerization by PPIases can be best described by a catalytic mechanism in which the substrate in transition state configuration is stabilized. The enzymes preferentially bind the transition state configuration of the substrate relative to the cis conformation, which in most cases is bound better than the trans conformation of the substrate. Stabilization of the transition state configuration of the substrate leads to a lower free energy barrier and a faster rate of isomerization when compared to the uncatalyzed isomerization reaction.

GENERAL SIGNIFICANCE

Fully understanding the catalytic mechanism of PPIases has broad implications for drug design, elucidation of the molecular basis of many diseases, protein engineering, and enzyme catalysis in general. This article is part of a Special Issue entitled Proline-directed Foldases: Cell Signaling Catalysts and Drug Targets.