Simulation of folding of a small alpha-helical protein in atomistic detail using worldwide-distributed computing

Ab initio machine learning of phase space averages

Equilibrium structures determine material properties and biochemical functions. We here propose to machine learn phase space averages, conventionally obtained by ab initio or force-field-based molecular dynamics (MD) or Monte Carlo (MC) simulations. In analogy to ab initio MD, our ab initio machine learning (AIML) model does not require bond topologies and, therefore, enables a general machine learning pathway to obtain ensemble properties throughout the chemical compound space. We demonstrate AIML for predicting Boltzmann averaged structures after training on hundreds of MD trajectories. The AIML output is subsequently used to train machine learning models of free energies of solvation using experimental data and to reach competitive prediction errors (mean absolute error ∼ 0.8 kcal/mol) for out-of-sample molecules-within milliseconds. As such, AIML effectively bypasses the need for MD or MC-based phase space sampling, enabling exploration campaigns of Boltzmann averages throughout the chemical compound space at a much accelerated pace. We contextualize our findings by comparison to state-of-the-art methods resulting in a Pareto plot for the free energy of solvation predictions in terms of accuracy and time.

In-Silico Selection of Aptamer Targeting SARS-CoV-2 Spike Protein

Aptamers are single-stranded, short DNA or RNA oligonucleotides that can specifically bind to various target molecules. To diagnose the infected cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in time, numerous conventional methods are applied for viral detection via the amplification and quantification of DNA or antibodies specific to antigens on the virus. Herein, we generated a large number of mutated aptamer sequences, derived from a known sequence of receptor-binding domain (RBD)-1C aptamer, specific to the RBD of SARS-CoV-2 spike protein (S protein). Structural similarity, molecular docking, and molecular dynamics (MD) were utilized to screen aptamers and characterize the detailed interactions between the selected aptamers and the S protein. We identified two mutated aptamers, namely, RBD-1CM1 and RBD-1CM2, which presented better docking results against the S protein compared with the RBD-1C aptamer. Through the MD simulation, we further confirmed that the RBD-1CM1 aptamer can form the most stable complex with the S protein based on the number of hydrogen bonds formed between the two biomolecules. Based on the experimental data of quartz crystal microbalance (QCM), the RBD-1CM1 aptamer could produce larger signals in mass change and exhibit an improved binding affinity to the S protein. Therefore, the RBD-1CM1 aptamer, which was selected from 1431 mutants, was the best potential candidate for the detection of SARS-CoV-2. The RBD-1CM1 aptamer can be an alternative biological element for the development of SARS-CoV-2 diagnostic testing.

Size-and-Shape Space Gaussian Mixture Models for Structural Clustering of Molecular Dynamics Trajectories

Determining the optimal number and identity of structural clusters from an ensemble of molecular configurations continues to be a challenge. Recent structural clustering methods have focused on the use of internal coordinates due to the innate rotational and translational invariance of these features. The vast number of possible internal coordinates necessitates a feature space supervision step to make clustering tractable but yields a protocol that can be system type-specific. Particle positions offer an appealing alternative to internal coordinates but suffer from a lack of rotational and translational invariance, as well as a perceived insensitivity to regions of structural dissimilarity. Here, we present a method, denoted shape-GMM, that overcomes the shortcomings of particle positions using a weighted maximum likelihood alignment procedure. This alignment strategy is then built into an expectation maximization Gaussian mixture model (GMM) procedure to capture metastable states in the free-energy landscape. The resulting algorithm distinguishes between a variety of different structures, including those indistinguishable by root-mean-square displacement and pairwise distances, as demonstrated on several model systems. Shape-GMM results on an extensive simulation of the fast-folding HP35 Nle/Nle mutant protein support a four-state folding/unfolding mechanism, which is consistent with previous experimental results and provides kinetic details comparable to previous state-of-the art clustering approaches, as measured by the VAMP-2 score. Currently, training of shape-GMMs is recommended for systems (or subsystems) that can be represented by ≲200 particles and ≲100k configurations to estimate high-dimensional covariance matrices and balance computational expense. Once a shape-GMM is trained, it can be used to predict the cluster identities of millions of configurations.

Molecular Paradigms for Biological Mechanosensing

Many proteins in living cells are subject to mechanical forces, which can be generated internally by molecular machines, or externally, e.g., by pressure gradients. In general, these forces fall in the piconewton range, which is similar in magnitude to forces experienced by a molecule due to thermal fluctuations. While we would naively expect such moderate forces to produce only minimal changes, a wide variety of "mechanosensing" proteins have evolved with functions that are responsive to forces in this regime. The goal of this article is to provide a physical chemistry perspective on protein-based molecular mechanosensing paradigms used in living systems, and how these paradigms can be explored using novel computational methods.

Atomistic Force Fields for Proteins

All-atom, classical force fields for protein molecular dynamics (MD) simulations currently occupy a sweet spot in the universe of computational models, sufficiently detailed to be of predictive value in many cases, yet also simple enough that some biologically relevant time scales (microseconds or more) can now be sampled via specialized hardware or enhanced sampling methods. However, due to their long evolutionary history, there is now a myriad of force field branches in current use, which can make it hard for those entering the simulation field to know which would be the best set of parameters for a given application. In this chapter, I try to give an overview of the historical motivation for the different force fields available, suggestions for how to determine the most appropriate model and what to do if the results are in conflict with experimental evidence.

Chemically Accurate Relative Folding Stability of RNA Hairpins from Molecular Simulations

To benchmark RNA force fields, we compared the folding stabilities of three 12-nucleotide hairpin stem loops estimated by simulation to stabilities determined by experiment. We used umbrella sampling and a reaction coordinate of end-to-end (5' to 3' hydroxyl oxygen) distance to estimate the free energy change of the transition from the native conformation to a fully extended conformation with no hydrogen bonds between non-neighboring bases. Each simulation was performed four times using the AMBER FF99+bsc0+χ_OL3 force field, and each window, spaced at 1 Å intervals, was sampled for 1 μs, for a total of 552 μs of simulation. We compared differences in the simulated free energy changes to analogous differences in free energies from optical melting experiments using thermodynamic cycles where the free energy change between stretched and random coil sequences is assumed to be sequence-independent. The differences between experimental and simulated ΔΔ G° are, on average, 0.98 ± 0.66 kcal/mol, which is chemically accurate and suggests that analogous simulations could be used predictively. We also report a novel method to identify where replica free energies diverge along a reaction coordinate, thus indicating where additional sampling would most improve convergence. We conclude by discussing methods to more economically perform these simulations.

Finding the needle in the haystack: towards solving the protein-folding problem computationally

Prediction of protein tertiary structures from amino acid sequence and understanding the mechanisms of how proteins fold, collectively known as "the protein folding problem," has been a grand challenge in molecular biology for over half a century. Theories have been developed that provide us with an unprecedented understanding of protein folding mechanisms. However, computational simulation of protein folding is still difficult, and prediction of protein tertiary structure from amino acid sequence is an unsolved problem. Progress toward a satisfying solution has been slow due to challenges in sampling the vast conformational space and deriving sufficiently accurate energy functions. Nevertheless, several techniques and algorithms have been adopted to overcome these challenges, and the last two decades have seen exciting advances in enhanced sampling algorithms, computational power and tertiary structure prediction methodologies. This review aims at summarizing these computational techniques, specifically conformational sampling algorithms and energy approximations that have been frequently used to study protein-folding mechanisms or to de novo predict protein tertiary structures. We hope that this review can serve as an overview on how the protein-folding problem can be studied computationally and, in cases where experimental approaches are prohibitive, help the researcher choose the most relevant computational approach for the problem at hand. We conclude with a summary of current challenges faced and an outlook on potential future directions.

The BioFragment Database (BFDb): An open-data platform for computational chemistry analysis of noncovalent interactions

Accurate potential energy models are necessary for reliable atomistic simulations of chemical phenomena. In the realm of biomolecular modeling, large systems like proteins comprise very many noncovalent interactions (NCIs) that can contribute to the protein's stability and structure. This work presents two high-quality chemical databases of common fragment interactions in biomolecular systems as extracted from high-resolution Protein DataBank crystal structures: 3380 sidechain-sidechain interactions and 100 backbone-backbone interactions that inaugurate the BioFragment Database (BFDb). Absolute interaction energies are generated with a computationally tractable explicitly correlated coupled cluster with perturbative triples [CCSD(T)-F12] "silver standard" (0.05 kcal/mol average error) for NCI that demands only a fraction of the cost of the conventional "gold standard," CCSD(T) at the complete basis set limit. By sampling extensively from biological environments, BFDb spans the natural diversity of protein NCI motifs and orientations. In addition to supplying a thorough assessment for lower scaling force-field (2), semi-empirical (3), density functional (244), and wavefunction (45) methods (comprising >1M interaction energies), BFDb provides interactive tools for running and manipulating the resulting large datasets and offers a valuable resource for potential energy model development and validation.

Imaging Metastable States and Transitions in Proteins by Trajectory Map

It has been a long-standing and intriguing issue to develop robust methods to identify metastable states and interstate transitions from simulations or experimental data to understand the functional conformational changes of proteins. It is usually hard to define the complicated boundaries of the states in the conformational space using most of the existing methods, and they often lead to parameter-sensitive results. Here, we present a new approach, visualized Trajectory Map (vTM), to identify the metastable states and the rare interstate transitions, by considering both the conformational similarity and the temporal successiveness of conformations. The vTM is able to give a nonambiguous description of slow dynamics. The case study of a β-hairpin peptide shows that the vTM can reveal the states and transitions from all-atom MD trajectory data even when a single observable (i.e, one-dimensional reaction coordinate) is used. We also use the vTM to refine the folding/unfolding mechanism of HP35 in explicit water by analyzing a 125 μs all-atom MD trajectory and obtain folding/unfolding rates of about 1/μs, which are in good agreement with the experimental values.

Accelerating physical simulations of proteins by leveraging external knowledge

It is challenging to compute structure-function relationships of proteins using molecular physics. The problem arises from the exponential scaling of the computational searching and sampling of large conformational spaces. This scaling challenge is not met by today's methods, such as Monte Carlo, simulated annealing, genetic algorithms, or molecular dynamics (MD) or its variants such as replica exchange. Such methods of searching for optimal states on complex probabalistic landscapes are referred to more broadly as Explore-and-Exploit (EE), including in contexts such as computational learning, games, industrial planning and modeling military strategies. Here we describe a Bayesian method, called MELD, that 'melds' together explore-and-exploit approaches with externally added information that can be vague, combinatoric, noisy, intuitive, heuristic, or from experimental data. MELD is shown to accelerate physical MD simulations when using experimental data to determine protein structures; for predicting protein structures by using heuristic directives; and when predicting binding affinities of proteins from limited information about the binding site. Such Guided Explore-and-Exploit approaches might also be useful beyond proteins and beyond molecular science.

Optimized parameter selection reveals trends in Markov state models for protein folding

As molecular dynamics simulations access increasingly longer time scales, complementary advances in the analysis of biomolecular time-series data are necessary. Markov state models offer a powerful framework for this analysis by describing a system's states and the transitions between them. A recently established variational theorem for Markov state models now enables modelers to systematically determine the best way to describe a system's dynamics. In the context of the variational theorem, we analyze ultra-long folding simulations for a canonical set of twelve proteins [K. Lindorff-Larsen et al., Science 334, 517 (2011)] by creating and evaluating many types of Markov state models. We present a set of guidelines for constructing Markov state models of protein folding; namely, we recommend the use of cross-validation and a kinetically motivated dimensionality reduction step for improved descriptions of folding dynamics. We also warn that precise kinetics predictions rely on the features chosen to describe the system and pose the description of kinetic uncertainty across ensembles of models as an open issue.

Implicit Solvent Model for Million-Atom Atomistic Simulations: Insights into the Organization of 30-nm Chromatin Fiber

Molecular dynamics (MD) simulations based on the implicit solvent generalized Born (GB) models can provide significant computational advantages over the traditional explicit solvent simulations. However, the standard GB becomes prohibitively expensive for all-atom simulations of large structures; the model scales poorly, ∼n2, with the number of solute atoms. Here we combine our recently developed optimal point charge approximation (OPCA) with the hierarchical charge partitioning (HCP) approximation to present an ∼n log n multiscale, yet fully atomistic, GB model (GB-HCPO). The HCP approximation exploits the natural organization of biomolecules (atoms, groups, chains, and complexes) to partition the structure into multiple hierarchical levels of components. OPCA approximates the charge distribution for each of these components by a small number of point charges so that the low order multipole moments of these components are optimally reproduced. The approximate charges are then used for computing electrostatic interactions with distant components, while the full set of atomic charges are used for nearby components. We show that GB-HCPO can deliver up to 2 orders of magnitude speedup compared to the standard GB, with minimal impact on its accuracy. For large structures, GB-HCPO can approach the same nominal speed, as in nanoseconds per day, as the highly optimized explicit-solvent simulation based on particle mesh Ewald (PME). The increase in the nominal simulation speed, relative to the standard GB, coupled with substantially faster sampling of conformational space, relative to the explicit solvent, makes GB-HCPO a suitable candidate for MD simulation of large atomistic systems in implicit solvent. As a practical demonstration, we use GB-HCPO simulation to refine a ∼1.16 million atom structure of 30 nm chromatin fiber (40 nucleosomes). The refined structure suggests important details about spatial organization of the linker DNA and the histone tails in the fiber: (1) the linker DNA fills the core region, allowing the H3 histone tails to interact with the linker DNA, which is consistent with experiment; (2) H3 and H4 tails are found mostly in the core of the structure, closer to the helical axis of the fiber, while H2A and H2B are mostly solvent exposed. Potential functional consequences of these findings are discussed. GB-HCPO is implemented in the open source MD software NAB in Amber 2016.

As Simple As Possible, but Not Simpler: Exploring the Fidelity of Coarse-Grained Protein Models for Simulated Force Spectroscopy

Mechanical unfolding of a single domain of loop-truncated superoxide dismutase protein has been simulated via force spectroscopy techniques with both all-atom (AA) models and several coarse-grained models having different levels of resolution: A Gō model containing all heavy atoms in the protein (HA-Gō), the associative memory, water mediated, structure and energy model (AWSEM) which has 3 interaction sites per amino acid, and a Gō model containing only one interaction site per amino acid at the Cα position (Cα-Gō). To systematically compare results across models, the scales of time, energy, and force had to be suitably renormalized in each model. Surprisingly, the HA-Gō model gives the softest protein, exhibiting much smaller force peaks than all other models after the above renormalization. Clustering to render a structural taxonomy as the protein unfolds showed that the AA, HA-Gō, and Cα-Gō models exhibit a single pathway for early unfolding, which eventually bifurcates repeatedly to multiple branches only after the protein is about half-unfolded. The AWSEM model shows a single dominant unfolding pathway over the whole range of unfolding, in contrast to all other models. TM alignment, clustering analysis, and native contact maps show that the AWSEM pathway has however the most structural similarity to the AA model at high nativeness, but the least structural similarity to the AA model at low nativeness. In comparison to the AA model, the sequence of native contact breakage is best predicted by the HA-Gō model. All models consistently predict a similar unfolding mechanism for early force-induced unfolding events, but diverge in their predictions for late stage unfolding events when the protein is more significantly disordered.

Studying the role of cooperative hydration in stabilizing folded protein states

Understanding and modelling protein folding remains a key scientific and engineering challenge. Two key questions in protein folding are (1) why many proteins adopt a folded state and (2) how these proteins transition from the random coil ensemble to a folded state. In this paper we employ molecular dynamics simulations to address the first of these questions. Computational methods are well-placed to address this issue due to their ability to analyze systems at atomic-level resolution. Traditionally, the stability of folded proteins has been ascribed to the balance of two types of intermolecular interactions: hydrogen-bonding interactions and hydrophobic contacts. In this study, we explore a third type of intermolecular interaction: cooperative hydration of protein surface residues. To achieve this, we consider multiple independent simulations of the villin headpiece domain to quantify the contributions of different interactions to the energy of the native and fully extended states. In addition, we consider whether these findings are robust with respect to the protein forcefield, the water model, and the presence of salt. In all cases, we identify many cooperatively hydrated interactions that are transient but energetically favor the native state. Whilst further work on additional protein structures, forcefields, and water models is necessary, these results suggest a role for cooperative hydration in protein folding that should be explored further. Rational design of cooperative hydration on the protein surface could be a viable strategy for increasing protein stability.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Speed of conformational change: comparing explicit and implicit solvent molecular dynamics simulations

Adequate sampling of conformation space remains challenging in atomistic simulations, especially if the solvent is treated explicitly. Implicit-solvent simulations can speed up conformational sampling significantly. We compare the speed of conformational sampling between two commonly used methods of each class: the explicit-solvent particle mesh Ewald (PME) with TIP3P water model and a popular generalized Born (GB) implicit-solvent model, as implemented in the AMBER package. We systematically investigate small (dihedral angle flips in a protein), large (nucleosome tail collapse and DNA unwrapping), and mixed (folding of a miniprotein) conformational changes, with nominal simulation times ranging from nanoseconds to microseconds depending on system size. The speedups in conformational sampling for GB relative to PME simulations, are highly system- and problem-dependent. Where the simulation temperatures for PME and GB are the same, the corresponding speedups are approximately onefold (small conformational changes), between ∼1- and ∼100-fold (large changes), and approximately sevenfold (mixed case). The effects of temperature on speedup and free-energy landscapes, which may differ substantially between the solvent models, are discussed in detail for the case of miniprotein folding. In addition to speeding up conformational sampling, due to algorithmic differences, the implicit solvent model can be computationally faster for small systems or slower for large systems, depending on the number of solute and solvent atoms. For the conformational changes considered here, the combined speedups are approximately twofold, ∼1- to 60-fold, and ∼50-fold, respectively, in the low solvent viscosity regime afforded by the implicit solvent. For all the systems studied, 1) conformational sampling speedup increases as Langevin collision frequency (effective viscosity) decreases; and 2) conformational sampling speedup is mainly due to reduction in solvent viscosity rather than possible differences in free-energy landscapes between the solvent models.

Characterizing a partially ordered miniprotein through folding molecular dynamics simulations: Comparison with the experimental data

The villin headpiece helical subdomain (HP36) is one of the best known model systems for computational studies of fast-folding all-α miniproteins. HP21 is a peptide fragment-derived from HP36-comprising only the first and second helices of the full domain. Experimental studies showed that although HP21 is mostly unfolded in solution, it does maintain some persistent native-like structure as indicated by the analysis of NMR-derived chemical shifts. Here we compare the experimental data for HP21 with the results obtained from a 15-μs long folding molecular dynamics simulation performed in explicit water and with full electrostatics. We find that the simulation is in good agreement with the experiment and faithfully reproduces the major experimental findings, namely that (a) HP21 is disordered in solution with <10% of the trajectory corresponding to transiently stable structures, (b) the most highly populated conformer is a native-like structure with an RMSD from the corresponding portion of the HP36 crystal structure of <1 Å, (c) the simulation-derived chemical shifts-over the whole length of the trajectory-are in reasonable agreement with the experiment giving reduced χ(2) values of 1.6, 1.4, and 0.8 for the Δδ(13) C(α) , Δδ(13) CO, and Δδ(13) C(β) secondary shifts, respectively (becoming 0.8, 0.7, and 0.3 when only the major peptide conformer is considered), and finally, (d) the secondary structure propensity scores are in very good agreement with the experiment and clearly indicate the higher stability of the first helix. We conclude that folding molecular dynamics simulations can be a useful tool for the structural characterization of even marginally stable peptides.

OPLS3: A Force Field Providing Broad Coverage of Drug-like Small Molecules and Proteins

The parametrization and validation of the OPLS3 force field for small molecules and proteins are reported. Enhancements with respect to the previous version (OPLS2.1) include the addition of off-atom charge sites to represent halogen bonding and aryl nitrogen lone pairs as well as a complete refit of peptide dihedral parameters to better model the native structure of proteins. To adequately cover medicinal chemical space, OPLS3 employs over an order of magnitude more reference data and associated parameter types relative to other commonly used small molecule force fields (e.g., MMFF and OPLS_2005). As a consequence, OPLS3 achieves a high level of accuracy across performance benchmarks that assess small molecule conformational propensities and solvation. The newly fitted peptide dihedrals lead to significant improvements in the representation of secondary structure elements in simulated peptides and native structure stability over a number of proteins. Together, the improvements made to both the small molecule and protein force field lead to a high level of accuracy in predicting protein-ligand binding measured over a wide range of targets and ligands (less than 1 kcal/mol RMS error) representing a 30% improvement over earlier variants of the OPLS force field.

X-ray refinement significantly underestimates the level of microscopic heterogeneity in biomolecular crystals

Biomolecular X-ray structures typically provide a static, time- and ensemble-averaged view of molecular ensembles in crystals. In the absence of rigid-body motions and lattice defects, B-factors are thought to accurately reflect the structural heterogeneity of such ensembles. In order to study the effects of averaging on B-factors, we employ molecular dynamics simulations to controllably manipulate microscopic heterogeneity of a crystal containing 216 copies of villin headpiece. Using average structure factors derived from simulation, we analyse how well this heterogeneity is captured by high-resolution molecular-replacement-based model refinement. We find that both isotropic and anisotropic refined B-factors often significantly deviate from their actual values known from simulation: even at high 1.0 Å resolution and Rfree of 5.9%, B-factors of some well-resolved atoms underestimate their actual values even sixfold. Our results suggest that conformational averaging and inadequate treatment of correlated motion considerably influence estimation of microscopic heterogeneity via B-factors, and invite caution in their interpretation.

Assessment of the utility of contact-based restraints in accelerating the prediction of protein structure using molecular dynamics simulations

Molecular dynamics (MD) simulation is a well-established tool for the computational study of protein structure and dynamics, but its application to the important problem of protein structure prediction remains challenging, in part because extremely long timescales can be required to reach the native structure. Here, we examine the extent to which the use of low-resolution information in the form of residue-residue contacts, which can often be inferred from bioinformatics or experimental studies, can accelerate the determination of protein structure in simulation. We incorporated sets of 62, 31, or 15 contact-based restraints in MD simulations of ubiquitin, a benchmark system known to fold to the native state on the millisecond timescale in unrestrained simulations. One-third of the restrained simulations folded to the native state within a few tens of microseconds-a speedup of over an order of magnitude compared with unrestrained simulations and a demonstration of the potential for limited amounts of structural information to accelerate structure determination. Almost all of the remaining ubiquitin simulations reached near-native conformations within a few tens of microseconds, but remained trapped there, apparently due to the restraints. We discuss potential methodological improvements that would facilitate escape from these near-native traps and allow more simulations to quickly reach the native state. Finally, using a target from the Critical Assessment of protein Structure Prediction (CASP) experiment, we show that distance restraints can improve simulation accuracy: In our simulations, restraints stabilized the native state of the protein, enabling a reasonable structural model to be inferred.

Evaluation of conformational changes in diabetes-associated mutation in insulin a chain: a molecular dynamics study

Insulin plays a central role in the regulation of metabolism in humans. Mutations in the insulin gene can impair the folding of its precursor protein, proinsulin, and cause permanent neonatal-onset diabetes mellitus known as Mutant INS-gene induced Diabetes of Youth (MIDY) with insulin deficiency. To gain insights into the molecular basis of this diabetes-associated mutation, we perform molecular dynamics simulations in wild-type and mutant (Cys(A7) to Tyr or C(A7)Y) insulin A chain in aqueous solutions. The C(A7)Y mutation is one of the identified mutations that impairs the protein folding by substituting the cysteine residue which is required for the disulfide bond formation. A comparative analysis reveals structural differences between the wild-type and the mutant conformations. The analyzed mutant insulin A chain forms a metastable state with major effects on its N-terminal region. This suggests that MIDY mutant involves formation of a partially folded intermediate with conformational change in N-terminal region in A chain that generates flexible N-terminal domain. This may lead to the abnormal interactions with other proinsulins in the aggregation process.

Equilibrium kinetic network of the villin headpiece in implicit solvent

We applied the single-replica multiple-state transition-interface sampling method to elucidate the equilibrium kinetic network of the 35-residue-fragment (HP-35) villin headpiece in implicit water at room temperature. Starting from the native Protein Data Bank structure, nine (meta)stable states of the system were identified, from which the kinetic network was built by sampling pathways between these states. Application of transition path theory allowed analysis of the (un)folding mechanism. The resulting (un)folding rates agree well with experiments. This work demonstrates that high (un)folding barriers can now be studied.

De novo peptide structure prediction: an overview

Peptide structure identification is an important contribution to the further characterization of the residues involved in functional interactions. De novo structure peptide prediction has, in the past few years, made significant progresses that make reasonable, for peptides up to 50 amino acids, its use for the fast identification of their structural topologies. Here, we introduce some of the concepts underlying approaches of the field, together with their limits.

REMD and umbrella sampling simulations to probe the energy barrier of the folding pathways of engrailed homeodomain

Proteins fold by diverse pathways which depend on the energy barriers involved in reaching different intermediates. There has been a lot of development in the theoretical aspects of protein folding, from force-field to simulation techniques. One such simulation approach is replica exchange molecular dynamics simulation (REMD), which provides an efficient conformational sampling method to understand the events involved in protein folding. In this study, an attempt is made to explore the folding funnel of engrailed homeodomain protein (EnHD) using REMD simulations. EnHD is a 54 residue long helix bundle protein which has a folding time of about 15 μs. The protein was represented using the Amber United atom model in order to reduce the system size which helped to speed up the simulation. Individual replicas were simulated for 1.4-2 μs making cumulative time of more than 100 μs of REMD simulations. Free energy analysis was carried out to understand the folding behavior of EnHD protein. Effects of temperature range and exchange frequency in REMD simulations have been explored. In addition to this, multiple umbrella sampling (US) simulations of a total of 320 ns were also carried out, followed by weighted histogram analysis method (WHAM) to investigate the energy barriers involved during the folding of various intermediates. US studies were also carried on mutational variants of EnHD protein to see effect of the mutations on the folding pathway of the protein. The use of US technique may be helpful for predicting fast folding mutants or protein engineering. The combination of REMD with US may help in understanding the energetics between multiple pathways of fast folding proteins and their mutant counterparts.

Exploring the free energy landscape of a model β-hairpin peptide and its isoform

Secondary structural transitions from α-helix to β-sheet conformations are observed in several misfolding diseases including Alzheimer's and Parkinson's. Determining factors contributing favorably to the formation of each of these secondary structures is therefore essential to better understand these disease states. β-hairpin peptides form basic components of anti-parallel β-sheets and are suitable model systems for characterizing the fundamental forces stabilizing β-sheets in fibrillar structures. In this study, we explore the free energy landscape of the model β-hairpin peptide GB1 and its E2 isoform that preferentially adopts α-helical conformations at ambient conditions. Umbrella sampling simulations using all-atom models and explicit solvent are performed over a large range of end-to-end distances. Our results show the strong preference of GB1 and the E2 isoform for β-hairpin and α-helical conformations, respectively, consistent with previous studies. We show that the unfolded states of GB1 are largely populated by misfolded β-hairpin structures which differ from each other in the position of the β-turn. We discuss the energetic factors contributing favorably to the formation of α-helix and β-hairpin conformations in these peptides and highlight the energetic role of hydrogen bonds and non-bonded interactions.

Electronic polarization stabilizes tertiary structure prediction of HP-36

Molecular dynamic (MD) simulations with both implicit and explicit solvent models have been carried out to study the folding dynamics of HP-36 protein. Starting from the extended conformation, the secondary structure of all three helices in HP-36 was formed in about 50 ns and remained stable in the remaining simulation. However, the formation of the tertiary structure was difficult. Although some intermediates were close to the native structure, the overall conformation was not stable. Further analysis revealed that the large structure fluctuation of loop and hydrophobic core regions was devoted mostly to the instability of the structure during MD simulation. The backbone root-mean-square deviation (RMSD) of the loop and hydrophobic core regions showed strong correlation with the backbone RMSD of the whole protein. The free energy landscape indicated that the distribution of main chain torsions in loop and turn regions was far away from the native state. Starting from an intermediate structure extracted from the initial AMBER simulation, HP-36 was found to generally fold to the native state under the dynamically adjusted polarized protein-specific charge (DPPC) simulation, while the peptide did not fold into the native structure when AMBER force filed was used. The two best folded structures were extracted and taken into further simulations in water employing AMBER03 charge and DPPC for 25 ns. Result showed that introducing polarization effect into interacting potential could stabilize the near-native protein structure.

Introducing Charge Hydration Asymmetry into the Generalized Born Model

The effect of charge hydration asymmetry (CHA)-non-invariance of solvation free energy upon solute charge inversion-is missing from the standard linear response continuum electrostatics. The proposed charge hydration asymmetric-generalized Born (CHA-GB) approximation introduces this effect into the popular generalized Born (GB) model. The CHA is added to the GB equation via an analytical correction that quantifies the specific propensity of CHA of a given water model; the latter is determined by the charge distribution within the water model. Significant variations in CHA seen in explicit water (TIP3P, TIP4P-Ew, and TIP5P-E) free energy calculations on charge-inverted "molecular bracelets" are closely reproduced by CHA-GB, with the accuracy similar to models such as SEA and 3D-RISM that go beyond the linear response. Compared against reference explicit (TIP3P) electrostatic solvation free energies, CHA-GB shows about a 40% improvement in accuracy over the canonical GB, tested on a diverse set of 248 rigid small neutral molecules (root mean square error, rmse = 0.88 kcal/mol for CHA-GB vs 1.24 kcal/mol for GB) and 48 conformations of amino acid analogs (rmse = 0.81 kcal/mol vs 1.26 kcal/mol). CHA-GB employs a novel definition of the dielectric boundary that does not subsume the CHA effects into the intrinsic atomic radii. The strategy leads to finding a new set of intrinsic atomic radii optimized for CHA-GB; these radii show physically meaningful variation with the atom type, in contrast to the radii set optimized for GB. Compared to several popular radii sets used with the original GB model, the new radii set shows better transferability between different classes of molecules.

Fast protein folding kinetics

Fast-folding proteins have been a major focus of computational and experimental study because they are accessible to both techniques: they are small and fast enough to be reasonably simulated with current computational power, but have dynamics slow enough to be observed with specially developed experimental techniques. This coupled study of fast-folding proteins has provided insight into the mechanisms, which allow some proteins to find their native conformation well <1 ms and has uncovered examples of theoretically predicted phenomena such as downhill folding. The study of fast folders also informs our understanding of even 'slow' folding processes: fast folders are small; relatively simple protein domains and the principles that govern their folding also govern the folding of more complex systems. This review summarizes the major theoretical and experimental techniques used to study fast-folding proteins and provides an overview of the major findings of fast-folding research. Finally, we examine the themes that have emerged from studying fast folders and briefly summarize their application to protein folding in general, as well as some work that is left to do.

Reconstructing protein structures by neural network pairwise interaction fields and iterative decoy set construction

Predicting the fold of a protein from its amino acid sequence is one of the grand problems in computational biology. While there has been progress towards a solution, especially when a protein can be modelled based on one or more known structures (templates), in the absence of templates, even the best predictions are generally much less reliable. In this paper, we present an approach for predicting the three-dimensional structure of a protein from the sequence alone, when templates of known structure are not available. This approach relies on a simple reconstruction procedure guided by a novel knowledge-based evaluation function implemented as a class of artificial neural networks that we have designed: Neural Network Pairwise Interaction Fields (NNPIF). This evaluation function takes into account the contextual information for each residue and is trained to identify native-like conformations from non-native-like ones by using large sets of decoys as a training set. The training set is generated and then iteratively expanded during successive folding simulations. As NNPIF are fast at evaluating conformations, thousands of models can be processed in a short amount of time, and clustering techniques can be adopted for model selection. Although the results we present here are very preliminary, we consider them to be promising, with predictions being generated at state-of-the-art levels in some of the cases.

Dependence of protein crystal stability on residue charge states and ion content of crystal solvent

Protein crystallization is frequently induced by the addition of various precipitants, which directly affect protein solubility. In addition to organic cosolvents and long-chain polymers, salts belong to the most widely used precipitants in protein crystallography. However, despite such widespread usage, their mode of action at the atomistic level is still largely unknown. Here, we perform extensive molecular dynamics simulations of the villin headpiece crystal unit cell to examine its stability at different concentrations of sodium sulfate. We show that the inclusion of ions in crystal solvent at high concentration can prevent large rearrangements of the asymmetric units and a loss of symmetry of the unit cell without significantly affecting protein dynamics. Of importance, a similar result can be achieved by neutralizing several specific charged residues suggesting that they may play an active role in crystal destabilization due to unfavorable electrostatic interactions. Our results provide a microscopic picture behind salt-induced stabilization of a protein crystal and further suggest that adequate modeling of realistic crystallization conditions may be necessary for successful molecular dynamics simulations of protein crystals.

Protein structure modeling in the proteomics era

Structural proteomics aims to understand the structural basis of protein interactions and functions. A prerequisite for this is the availability of 3D protein structures that mediate the biochemical interactions. The explosion in the number of available gene sequences set the stage for the next step in genome-scale projects -- to obtain 3D structures for each protein. To achieve this ambitious goal, the slow and costly structure determination experiments are supplemented with theoretical approaches. The current state and recent advances in structure modeling approaches are reviewed here, with special emphasis on comparative protein structure modeling techniques.

Computational and theoretical methods for protein folding

A computational approach is essential whenever the complexity of the process under study is such that direct theoretical or experimental approaches are not viable. This is the case for protein folding, for which a significant amount of data are being collected. This paper reports on the essential role of in silico methods and the unprecedented interplay of computational and theoretical approaches, which is a defining point of the interdisciplinary investigations of the protein folding process. Besides giving an overview of the available computational methods and tools, we argue that computation plays not merely an ancillary role but has a more constructive function in that computational work may precede theory and experiments. More precisely, computation can provide the primary conceptual clues to inspire subsequent theoretical and experimental work even in a case where no preexisting evidence or theoretical frameworks are available. This is cogently manifested in the application of machine learning methods to come to grips with the folding dynamics. These close relationships suggested complementing the review of computational methods within the appropriate theoretical context to provide a self-contained outlook of the basic concepts that have converged into a unified description of folding and have grown in a synergic relationship with their computational counterpart. Finally, the advantages and limitations of current computational methodologies are discussed to show how the smart analysis of large amounts of data and the development of more effective algorithms can improve our understanding of protein folding.

Formulation of probabilistic models of protein structure in atomic detail using the reference ratio method

We propose a method to formulate probabilistic models of protein structure in atomic detail, for a given amino acid sequence, based on Bayesian principles, while retaining a close link to physics. We start from two previously developed probabilistic models of protein structure on a local length scale, which concern the dihedral angles in main chain and side chains, respectively. Conceptually, this constitutes a probabilistic and continuous alternative to the use of discrete fragment and rotamer libraries. The local model is combined with a nonlocal model that involves a small number of energy terms according to a physical force field, and some information on the overall secondary structure content. In this initial study we focus on the formulation of the joint model and the evaluation of the use of an energy vector as a descriptor of a protein's nonlocal structure; hence, we derive the parameters of the nonlocal model from the native structure without loss of generality. The local and nonlocal models are combined using the reference ratio method, which is a well-justified probabilistic construction. For evaluation, we use the resulting joint models to predict the structure of four proteins. The results indicate that the proposed method and the probabilistic models show considerable promise for probabilistic protein structure prediction and related applications.

Rational modification of protein stability by targeting surface sites leads to complicated results

The rational modification of protein stability is an important goal of protein design. Protein surface electrostatic interactions are not evolutionarily optimized for stability and are an attractive target for the rational redesign of proteins. We show that surface charge mutants can exert stabilizing effects in distinct and unanticipated ways, including ones that are not predicted by existing methods, even when only solvent-exposed sites are targeted. Individual mutation of three solvent-exposed lysines in the villin headpiece subdomain significantly stabilizes the protein, but the mechanism of stabilization is very different in each case. One mutation destabilizes native-state electrostatic interactions but has a larger destabilizing effect on the denatured state, a second removes the desolvation penalty paid by the charged residue, whereas the third introduces unanticipated native-state interactions but does not alter electrostatics. Our results show that even seemingly intuitive mutations can exert their effects through unforeseen and complex interactions.

How kinetics within the unfolded state affects protein folding: an analysis based on markov state models and an ultra-long MD trajectory

Understanding how kinetics in the unfolded state affects protein folding is a fundamentally important yet less well-understood issue. Here we employ three different models to analyze the unfolded landscape and folding kinetics of the miniprotein Trp-cage. The first is a 208 μs explicit solvent molecular dynamics (MD) simulation from D. E. Shaw Research containing tens of folding events. The second is a Markov state model (MSM-MD) constructed from the same ultralong MD simulation; MSM-MD can be used to generate thousands of folding events. The third is a Markov state model built from temperature replica exchange MD simulations in implicit solvent (MSM-REMD). All the models exhibit multiple folding pathways, and there is a good correspondence between the folding pathways from direct MD and those computed from the MSMs. The unfolded populations interconvert rapidly between extended and collapsed conformations on time scales ≤40 ns, compared with the folding time of ∼5 μs. The folding rates are independent of where the folding is initiated from within the unfolded ensemble. About 90% of the unfolded states are sampled within the first 40 μs of the ultralong MD trajectory, which on average explores ∼27% of the unfolded state ensemble between consecutive folding events. We clustered the folding pathways according to structural similarity into "tubes", and kinetically partitioned the unfolded state into populations that fold along different tubes. From our analysis of the simulations and a simple kinetic model, we find that, when the mixing within the unfolded state is comparable to or faster than folding, the folding waiting times for all the folding tubes are similar and the folding kinetics is essentially single exponential despite the presence of heterogeneous folding paths with nonuniform barriers. When the mixing is much slower than folding, different unfolded populations fold independently, leading to nonexponential kinetics. A kinetic partition of the Trp-cage unfolded state is constructed which reveals that different unfolded populations have almost the same probability to fold along any of the multiple folding paths. We are investigating whether the results for the kinetics in the unfolded state of the 20-residue Trp-cage is representative of larger single domain proteins.