Designing a 20-residue protein

Is Gum Arabic a Good Emulsifier Due to CH...π Interactions? How Urea Effectively Destabilizes the Hydrophobic CH...π Interactions in the Proteins of Gum Arabic than Amides and GuHCl?

The photophysical studies of gum arabic (GA) in the presence of urea, 1,3-dimethylurea (DMU), tetramethylurea (TMU), guanidine hydrochloride (GuHCl), formamide (FA), acetamide (AA), and dimethyl formamide (DMF) were carried out by monitoring the emission, three-dimensional emission contour, and time-correlated fluorescence lifetime techniques. On addition of only 1 × 10-3 M urea, 75.0% of the fluorescence of GA is quenched, while the same occurs in GuHCl at 3.0 M. FA quenched 50% of the fluorescence of GA at 5.0 M. However, DMU, TMU, AA, and DMF resulted in a fluorescence enhancement. The unusual fluorescence trends reveal the existence of CH...π interactions in the proteins of GA. The experimental results and the structural aspects of proteins in GA led us to propose that the aggregation of polyproline helices in GA, through several CH...π interactions, would have a major role to play in the emulsification mechanism of GA.

Approximating dynamic proximity with a hybrid geometry energy-based kernel for diffusion maps

The diffusion map is a dimensionality reduction method. The reduction coordinates are associated with the leading eigenfunctions of the backward Fokker-Planck operator, providing a dynamic meaning for these coordinates. One of the key factors that affect the accuracy of diffusion map embedding is the dynamic measure implemented in the Gaussian kernel. A common practice in diffusion map study of molecular systems is to approximate dynamic proximity with RMSD (root-mean-square deviation). In this paper, we present a hybrid geometry-energy based kernel. Since high energy-barriers may exist between geometrically similar conformations, taking both RMSD and energy difference into account in the kernel can better describe conformational transitions between neighboring conformations and lead to accurate embedding. We applied our diffusion map method to the β-hairpin of the B1 domain of streptococcal protein G and to Trp-cage. Our results in β-hairpin show that the diffusion map embedding achieves better results with the hybrid kernel than that with the RMSD-based kernel in terms of free energy landscape characterization and a new correlation measure between the cluster center Euclidean distances in the reduced-dimension space and the reciprocals of the total net flow between these clusters. In addition, our diffusion map analysis of the ultralong molecular dynamics trajectory of Trp-cage has provided a unified view of its folding mechanism. These promising results demonstrate the effectiveness of our diffusion map approach in the analysis of the dynamics and thermodynamics of molecular systems. The hybrid geometry-energy criterion could be also useful as a general dynamic measure for other purposes.

Selection Rules for Outliers in Outlier Flooding Method Regulate Its Conformational Sampling Efficiency

The outlier flooding method (OFLOOD) has been proposed as an enhanced conformational sampling method of proteins. In OFLOOD, rarely occurring states of proteins are detected as sparse conformational distributions (outliers) with a clustering algorithm. The detected outliers are intensively resampled with short-time molecular dynamics (MD) simulations. As a set of cycles, OFLOOD repeats selections of outliers and their conformational resampling. Herein, as an essential issue to be tackled to perform OFLOOD efficiently, a selection rule for outliers should be carefully specified. Generally, many outliers are detected from distributions on conformational subspaces with the clustering. Judging from its computational costs, it is unreasonable to select all the detected outliers upon the conformational resampling. Therefore, it is important to consider which outliers should be selected from the sparse distributions when restarting their short-time MD simulations with limited computational costs. In this sense, we investigated the conformational sampling efficiency of OFLOOD by changing the selection rules for outliers. To address the conformational sampling efficiency of OFLOOD depending on its selection rules, outliers to be resampled were selected by focusing their probability occurrences (populations of outliers). As a comparison, a random selection rule for outliers was also considered. Through the present assessment, the random selection of outliers showed the most efficient conformational sampling efficiency compared to the other OFLOOD trials using the biased selection rules, indicating that a variety of outliers should be selected and resampled during the OFLOOD cycles. In conclusion, the random outlier selection rule is the best strategy to perform OFLOOD efficiently.

Enhancing Biomolecular Sampling with Reinforcement Learning: A Tree Search Molecular Dynamics Simulation Method

This paper proposes a novel molecular simulation method, called tree search molecular dynamics (TS-MD), to accelerate the sampling of conformational transition pathways, which require considerable computation. In TS-MD, a tree search algorithm, called upper confidence bounds for trees, which is a type of reinforcement learning algorithm, is applied to sample the transition pathway. By learning from the results of the previous simulations, TS-MD efficiently searches conformational space and avoids being trapped in local stable structures. TS-MD exhibits better performance than parallel cascade selection molecular dynamics, which is one of the state-of-the-art methods, for the folding of miniproteins, Chignolin and Trp-cage, in explicit water.

Preparation and characterization of a highly soluble Aβ1-42 peptide variant

Alzheimer's disease (AD) is a progressive neurological disease marked by the accumulation and deposition of misfolded amyloid beta or Abeta (Aβ) peptide. Two species of Aβ peptides are found in amyloid plaques, Aβ_1-40 and Aβ_1-42, with the latter being the more amyloidogenic of the two. Understanding how and why Aβ peptides misfold, oligomerize and form amyloid plaques requires a detailed understanding of their structure and dynamics. The poor solubility and strong aggregation tendencies of Aβ_1-42 has made the isolation and characterization of its different structural isoforms (monomer, dimer, oligomer, amyloid) exceedingly difficult. Furthermore, while synthetic Aβ_1-42 peptides (Aβ₄₂syn) are readily available, the cost of isotopically labeled peptide is substantial, making their characterization by NMR spectroscopy cost prohibitive. Here we describe the design, cloning, high-level production, isotopic labeling and biophysical characterization of a modified (solubility-tagged) Aβ_1-42 variant that exhibits excellent water solubility and shares similar aggregation properties as wildtype Aβ_1-42. Specifically, we attached six lysines (6K) to the C-terminus of native Aβ_1-42 to create a more soluble, monomeric form of Aβ_1-42 called Aβ₄₂C6K. A gene for the Aβ₄₂C6K was designed, synthesized and cloned into Escherichia coli (E. coli) and the peptide was expressed at milligram levels. The Aβ₄₂C6K peptide was characterized using circular dichroism (CD), NMR, electron microscopy and thioflavin T fluorescence. Its ability to form stable monomers, oligomers and fibrils under different conditions was assessed. Our results indicate that Aβ₄₂C6K stays monomeric at high concentrations (unlike Aβ_1-42) and can be induced to oligomerize and form fibrils like Aβ_1-42. Our novel construct could be used to explore the structure and dynamics of Aβ_1-42 as well as the interaction of ligands with Aβ_1-42 via NMR.

Computational investigation of retro-isomer equilibrium structures: Intrinsically disordered, foldable, and cyclic peptides

We use all-atom modeling and advanced-sampling molecular dynamics simulations to investigate quantitatively the effect of peptide bond directionality on the equilibrium structures of four linear (two foldable, two disordered) and two cyclic peptides. We find that the retro forms of cyclic and foldable linear peptides adopt distinctively different conformations compared to their parents. While the retro form of a linear intrinsically disordered peptide with transient secondary structure fails to reproduce a secondary structure content similar to that of its parent, the retro form of a shorter disordered linear peptide shows only minor differences compared to its parent.

Directed C(sp3)-H arylation of tryptophan: transformation of the directing group into an activated amide

The aminoquinoline-directed C–H activation was used to synthezise unnatural tryptophans for solid phase peptide synthesis for the first time.

The 8-aminoquinoline (8AQ) directed C(sp³)–H functionalization was applied in the synthesis of β-arylated tryptophan derivatives. The laborious protecting group reorganization towards α-amino acids compatible for solid phase peptide synthesis (SPPS) was cut short by the transformation of the directing group into an activated amide, which was either used directly in peptide coupling or in the gram scale synthesis of storable Fmoc-protected amino acids for SPPS. In this work, directed C–H activation and nonplanar amide chemistry complement each other for the synthesis of hybrids between phenylalanine and tryptophan with restricted side chain mobility.

A hybrid, bottom-up, structurally accurate, Go¯-like coarse-grained protein model

Coarse-grained (CG) protein models in the structural biology literature have improved over the years from being simple tools to understand general folding and aggregation driving forces to capturing detailed structures achieved by actual folding sequences. Here, we ask whether such models can be developed systematically from recent advances in bottom-up coarse-graining methods without relying on bioinformatic data (e.g., protein data bank statistics). We use relative entropy coarse-graining to develop a hybrid CG but Go¯-like CG peptide model, hypothesizing that the landscape of proteinlike folds is encoded by the backbone interactions, while the sidechain interactions define which of these structures globally minimizes the free energy in a unique native fold. To construct a model capable of capturing varied secondary structures, we use a new extended ensemble relative entropy method to coarse-grain based on multiple reference atomistic simulations of short polypeptides with varied α and β character. Subsequently, we assess the CG model as a putative protein backbone forcefield by combining it with sidechain interactions based on native contacts but not incorporating native distances explicitly, unlike standard Go¯ models. We test the model's ability to fold a range of proteins and find that it achieves high accuracy (∼2 Å root mean square deviation resolution for both short sequences and large globular proteins), suggesting the strong role that backbone conformational preferences play in defining the fold landscape. This model can be systematically extended to non-natural amino acids and nonprotein polymers and sets the stage for extensions to non-Go¯ models with sequence-specific sidechain interactions.

Stabilizing and Understanding a Miniprotein by Rational Redesign

Miniproteins reduce the complexity of the protein-folding problem allowing systematic studies of contributions to protein folding and stabilization. Here, we describe the rational redesign of a miniprotein, PPα, comprising a polyproline II helix, a loop, and an α helix. The redesign provides a de novo framework for interrogating noncovalent interactions. Optimized PPα has significantly improved thermal stability with a midpoint unfolding temperature (T_M) of 51 °C. Its nuclear magnetic resonance structure indicates a density of stabilizing noncovalent interactions that is higher than that of the parent peptide, specifically an increased number of CH-π interactions. In part, we attribute this to improved long-range electrostatic interactions between the two helical elements. We probe further sequence-stability relationships in the miniprotein through a series of rational mutations.

Robust and Accurate Computational Estimation of the Polarizability Tensors of Macromolecules

Alignment of molecules through electric fields minimizes the averaging over orientations, e.g., in single-particle-imaging experiments. The response of molecules to external ac electric fields is governed by their polarizability tensor, which is usually calculated using quantum chemistry methods. These methods are not feasible for large molecules. Here, we calculate the polarizability tensor of proteins using a regression model that correlates the polarizabilities of the 20 amino acids with perfect conductors of the same shape. The dielectric constant of the molecules could be estimated from the slope of the regression line based on the Clausius-Mossotti equation. We benchmark our predictions against the quantum chemistry results for the Trp cagemini protein and the measured dielectric constants of larger proteins. Our method has applications in computing laser alignment of macromolecules, for instance, benefiting single-particle imaging, as well as for estimation of the optical and electrostatic characteristics of proteins and other macromolecules.

The Fragment Molecular Orbital Method Based on Long-Range Corrected Density-Functional Tight-Binding

The presently available linear scaling approaches to density-functional tight-binding (DFTB) based on the fragment molecular orbital (FMO) method are severely impacted by the problem of artificial charge transfer due to the self-interaction error (SIE), which hampers the simulation of zwitterionic systems such as biopolymers or ionic liquids. Here we report an extension of FMO-DFTB where we included a long-range corrected (LC) functional designed to mitigate the DFTB SIE, called the FMO-LC-DFTB method, resulting in a robust method which succeeds in simulating zwitterionic systems. Both energy and analytic gradient are developed for the gas phase and the polarizable continuum model of solvation. The scaling of FMO-LC-DFTB with system size N is shown to be almost linear, O( N^1.13-1.28), and its numerical accuracy is established for a variety of representative systems including neutral and charged polypeptides. It is shown that pair interaction energies between fragments for two mini-proteins are in excellent agreement with results from long-range corrected density functional theory. The new method was employed in long time scale (1 ns) molecular dynamics simulations of the tryptophan cage protein (PDB: 1L2Y ) in the gas phase for four different protonation states and in stochastic global minimum structure searches for 1-ethyl-3-methylimidazolium nitrate ionic liquid clusters containing up to 2300 atoms.

Computational Investigation of the Effect of Pressure on Protein Stability

Previous studies show parabolic or elliptical regions of protein stability in the pressure-temperature ( P, T) plane. The construction of stability diagrams requires accessing a sufficiently broad ( P, T) range, which is often frustrated by ice formation in experiments and sampling challenges in simulations. We perform a fully atomistic computational study of the miniprotein Trp-cage over the range of temperatures 210 ≤ T ≤ 420 K and pressures P ≤ 5 kbar and construct the corresponding stability diagram. At ambient temperature, pressure shifts the conformational states toward unfolding. Below 250 K, the native fold's stability depends nonmonotonically on pressure. While cold unfolding and thermal denaturation differ significantly at ambient pressure, they exhibit progressive similarity at elevated pressures. At ambient pressure, cold denaturation is an enthalpically driven process that preserves significant elements of Trp-cage's secondary structure. In contrast, cold unfolding at elevated pressures involves a more substantial loss of secondary and tertiary structure, similar to thermal denaturation.

Examination of Trifluoroethanol Interactions with Trp-Cage in Trifluoroethanol-Water at 298 K through Molecular Dynamics Simulations and Intermolecular Nuclear Overhauser Effects

Molecular dynamics simulations of the protein model Trp-cage in 42% trifluoroethanol (TFE)-water at 298 K have been carried out with the goal of exploring peptide hydrogen-solvent fluorine nuclear spin cross-relaxation. The TFE5 model of TFE developed in a previous work was used with the TIP5P-Ew model of water. System densities and component translational diffusion coefficients predicted by the simulations were within 20% of the experimental values. Consideration of the calculated relative amounts of TFE and water surrounding the hydrogens of Trp-cage indicated that the composition of the solvent mixture beyond ∼1.5 nm from the van der Waals surface of the peptide is close to the composition of the bulk solvent, but as observed by others, TFE accumulates preferentially near the peptide surface. In the simulations, both TFE and water molecules make contacts with the peptide surface; water molecules predominate in contacts with the peptide backbone atoms and TFE molecules generally preferentially interact with side chains. Translational diffusion of solvent molecules appears to be slowed near the surface of the peptide. Depending on the location in the structure, TFE molecules form complexes with the peptide that may persist for up to ∼7 ns. Many of the peptide spin-solvent fluorine cross-relaxation parameters (Σ_HF) for which experimental values are available are reasonably well-predicted from the simulations. However, the calculated Σ_HF values were too small for some hydrogens of the 6Trp indole ring and the amino acid hydrogens near this residue in the native structure, whereas Σ_HF values for hydrogens on the side chains of 1Asn, 4Ile, and 7Leu are too large. In 42% TFE-water, persistent conformations of Trp-cage are found, which differ from the conformation found in water by the orientation of the 3Tyr ring.

Hydration shell differentiates folded and disordered states of a Trp-cage miniprotein, allowing characterization of structural heterogeneity by wide-line NMR measurements

Hydration properties of folded and unfolded/disordered miniproteins were monitored in frozen solutions by wide-line 1H-NMR. The amount of mobile water as function of T (-80 °C < T < 0 °C) was found characteristically different for folded (TC5b), semi-folded (pH < 3, TCb5(H+)) and disordered (TC5b_N1R) variants. Comparing results of wide-line 1H-NMR and molecular dynamics simulations we found that both the amount of mobile water surrounding proteins in ice, as well as their thaw profiles differs significantly as function of the compactness and conformational heterogeneity of their structure. We found that (i) at around -50 °C ~50 H2Os/protein melt (ii) if the protein is well-folded then this amount of mobile water remains quasi-constant up to -20 °C, (iii) if disordered then the quantity of the lubricating mobile water increases with T in a constant manner up to ~200 H2Os/protein by reaching -20 °C. Especially in the -55 °C ↔ -15 °C temperature range, wide-line 1H-NMR detects the heterogeneity of protein fold, providing the size of the hydration shell surrounding the accessible conformers at a given temperature. Results indicate that freezing of protein solutions proceeds by the gradual selection of the enthalpically most favored states that also minimize the number of bridging waters.

Reversing the typical pH stability profile of the Trp-cage

The Trp-cage, an 18-20 residue miniprotein, has emerged as a primary test system for evaluating computational fold prediction and folding rate determination efforts. As it turns out, a number of stabilizing interactions in the Trp-cage folded state have a strong pH dependence; all prior Trp-cage mutants have been destabilized under carboxylate-protonating conditions. Notable among the pH dependent stabilizing interactions within the Trp-cage are: (1) an Asp as the helix N-cap, (2) an H-bonded Asp9/Arg16 salt bridge, (3) an interaction between the chain termini which are in close spatial proximity, and (4) additional side chain interactions with Asp9. In the present study, we have prepared Trp-cage species that are significantly more stable at pH 2.5 (rather than 7) and quantitated the contribution of each interaction listed above. The Trp-cage structure remains constant with the pH change. The study has also provided measures of the stabilizing contribution of indole ring shielding from surface exposure and the destabilizing effects of an ionized Asp at the C-terminus of an α-helix.

Cryo-Cooling Effect on DHFR Crystal Studied by Replica-Exchange Molecular Dynamics Simulations

Cryo-cooling is routinely performed before x-ray diffraction image collection to reduce the damage to crystals due to ionizing radiation. It has been suggested that although backbone structures are usually very similar between room temperature and cryo-temperature, cryo-cooling may hamper biologically relevant dynamics. In this study, the crystal of Escherichia coli dihydrofolate reductase is studied with replica-exchange molecular dynamics simulation, and the results are compared with the crystal structure determined at cryo-temperature and room temperature with the time-averaged ensemble method. Although temperature dependence of unit cell compaction and root mean-square fluctuation of Cα is found in accord with experiment, it is found that the protein structure at low temperature can be more heterogeneous than the ensemble of structures reported by using the time-averaged ensemble method, encouraging further development of the time-averaged ensemble method and indicating that data should be examined carefully to avoid overinterpretation of one average structure.

A Hybrid Hamiltonian for the Accelerated Sampling along Experimental Restraints

In this article, we present an enhanced sampling method based on a hybrid Hamiltonian which combines experimental distance restraints with a bias dependent from multiple path-dependent variables. This simulation method determines the bias-coordinates on the fly and does not require a priori knowledge about reaction coordinates. The hybrid Hamiltonian accelerates the sampling of proteins, and, combined with experimental distance information, the technique considers the restraints adaptively and in dependency of the system's intrinsic dynamics. We validate the methodology on the dipole relaxation of two water models and the conformational landscape of dialanine. Using experimental NMR-restraint data, we explore the folding landscape of the TrpCage mini-protein and in a second example apply distance restraints from chemical crosslinking/mass spectrometry experiments for the sampling of the conformation space of the Killer Cell Lectin-like Receptor Subfamily B Member 1A (NKR-P1A). The new methodology has the potential to adaptively introduce experimental restraints without affecting the conformational space of the system along an ergodic trajectory. Since only a limited number of input- and no-order parameters are required for the setup of the simulation, the method is broadly applicable and has the potential to be combined with coarse-graining methods.

Accurate Calculation of Free Energy Changes upon Amino Acid Mutation

Molecular dynamics based free energy calculations allow for a robust and accurate evaluation of free energy changes upon amino acid mutation in proteins. In this chapter we cover the basic theoretical concepts important for the use of calculations utilizing the non-equilibrium alchemical switching methodology. We further provide a detailed step-by-step protocol for estimating the effect of a single amino acid mutation on protein thermostability. In addition, the potential caveats and solutions to some frequently encountered issues concerning the non-equilibrium alchemical free energy calculations are discussed. The protocol comprises details for the hybrid structure/topology generation required for alchemical transitions, equilibrium simulation setup, and description of the fast non-equilibrium switching. Subsequently, the analysis of the obtained results is described. The steps in the protocol are complemented with an illustrative practical application: a destabilizing mutation in the Trp cage mini protein. The concepts that are described are generally applicable. The shown example makes use of the pmx software package for the free energy calculations using Gromacs as a molecular dynamics engine. Finally, we discuss how the current protocol can readily be adapted to carry out charge-changing or multiple mutations at once, as well as large-scale mutational scans.

Selective enhanced sampling in dihedral energy facilitates overcoming the dihedral energy increase in protein folding and accelerates the searching for protein native structure

A dihedral-energy-based selective enhanced sampling method (D-SITSMD) is presented with improved capabilities for searching a protein's natively folded structure and for providing the underlying folding pathway.

Peptide and Protein Structure Prediction with a Simplified Continuum Solvent Model

A continuum solvent model based on screened Coulomb potentials has been simplified and parametrized to sample native-like structures in replica-exchange simulations of each of six different peptides and miniproteins. Low-energy, native, and non-native structures were used to iteratively refine 11 parameter values. The centroid of the largest cluster of structures sampled in simulations initiated from an extended conformation represents the predicted structure. The main-chain rms deviation of this prediction from the experimental structure was 0.47 Å for the 12-residue Trp-zip2, 0.86 Å for the 14-residue MBH12, 2.53 Å for the 17-residue U(1-17)T9D, 2.03 Å for the 20-residue BS1, 1.08 Å for the 20-residue Trp-cage, and 3.64 Å for the 35-residue villin headpiece subdomain HP35. The centroid of the sixth largest cluster sampled for HP35 deviated by 0.91 Å. The CHARMM22/CMAP force field was used, with an additional ψ torsion term for residues other than glycine and proline. Six parameters govern the dielectric response of the continuum solvent, and four values of surface tension approximate nonpolar effects. An atom's self-energy and interaction energies are screened independently, each depending on whether the atom is part of a charged group, a neutral hydrogen-bonding main-chain group, or any other neutral group. The parameters inferred result in strong main-chain hydrogen bonds, consistent with the view that protein folding is dominated by the formation of these bonds. (1,2) Conformations of MBH12 and BS1 were excluded from the energy-function refinement, suggesting the parameters, referred to as SCP18, are transferable. An efficient estimate of solvent-accessible surface area is also described.

Hybrid Cascade-Type Molecular Dynamics with a Markov State Model for Efficient Free Energy Calculations

A protocol for calculating free energy landscapes (FELs) is proposed based on a combination of two cascade-type molecular dynamics (MD) methods, parallel cascade selection MD (PaCS-MD) and outlier flooding method (OFLOOD), with the help of a Markov state model (MSM). The former rapidly generates approximated transition paths directly connecting reactants with products, and the latter complementary resamples marginal conformational subspaces. Trajectories obtained by them give reliable microstates in MSM providing accurate FEL with low computational costs. As a demonstration, the present method was applied to a miniprotein (Chignolin and Trp-cage) in explicit water and successfully elucidated multiple folding paths on their free energy landscapes. Our method could be applicable to a wide variety of biological systems to estimate their free energy profiles.

Recovery of Protein Folding Funnels from Single-Molecule Time Series by Delay Embeddings and Manifold Learning

The stability and folding of proteins is governed by the underlying single-molecule free energy surface (smFES) mapping the free energy of the molecule as a function of configurational state. Ascertaining the smFES is of great value in understanding and engineering protein structure and function. By integrating tools from dynamical systems theory and nonlinear manifold learning, we describe an approach to reconstruct the multidimensional smFES for a protein from a time series in a single experimentally measurable observable. We employ Takens' delay embeddings to project the time series into a high-dimensional space in which the projected dynamics are C¹-equivalent to the true system dynamics and employ diffusion maps to recover a low-dimensional reconstruction of the smFES that is equivalent to the true smFES up to a smooth and invertible transformation. We validate the approach in molecular dynamics simulations of Trp-cage, Villin, and BBA to demonstrate that landscapes recovered from univariate time series in the head-to-tail distance are topologically identical-they precisely preserve the metastable states and folding pathways-and topographically approximate-the free energy barrier heights and well depths are approximately preserved-to the true landscapes determined from complete knowledge of all atomic coordinates. We go on to show that the reconstructed landscapes reliably predict temperature denaturation and identify point mutations and groups of mutations critical to folding. These results demonstrate that protein folding funnels can be reconstructed from experimentally measurable time series and used to understand and engineer folding.

Enriched Conformational Sampling of DNA and Proteins with a Hybrid Hamiltonian Derived from the Protein Data Bank

In this article, we present a method for the enhanced molecular dynamics simulation of protein and DNA systems called potential of mean force (PMF)-enriched sampling. The method uses partitions derived from the potentials of mean force, which we determined from DNA and protein structures in the Protein Data Bank (PDB). We define a partition function from a set of PDB-derived PMFs, which efficiently compensates for the error introduced by the assumption of a homogeneous partition function from the PDB datasets. The bias based on the PDB-derived partitions is added in the form of a hybrid Hamiltonian using a renormalization method, which adds the PMF-enriched gradient to the system depending on a linear weighting factor and the underlying force field. We validated the method using simulations of dialanine, the folding of TrpCage, and the conformational sampling of the Dickerson⁻Drew DNA dodecamer. Our results show the potential for the PMF-enriched simulation technique to enrich the conformational space of biomolecules along their order parameters, while we also observe a considerable speed increase in the sampling by factors ranging from 13.1 to 82. The novel method can effectively be combined with enhanced sampling or coarse-graining methods to enrich conformational sampling with a partition derived from the PDB.

Fast Pairwise Approximation of Solvent Accessible Surface Area for Implicit Solvent Simulations of Proteins on CPUs and GPUs

We propose a pairwise and readily parallelizable SASA-based nonpolar solvation approach for protein simulations, inspired by our previous pairwise GB polar solvation model development. In this work, we developed a novel function to estimate the atomic and molecular SASAs of proteins, which results in comparable accuracy as the LCPO algorithm in reproducing numerical icosahedral-based SASA values. Implemented in Amber software and tested on consumer GPUs, our pwSASA method reasonably reproduces LCPO simulation results, but accelerates MD simulations up to 30 times compared to the LCPO implementation, which is greatly desirable for protein simulations facing sampling challenges. The value of incorporating the nonpolar term in implicit solvent simulations is explored on a peptide fragment containing the hydrophobic core of HP36 and evaluating thermal stability profiles of four small proteins.

Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration

Macromolecular and biomolecular folding landscapes typically contain high free energy barriers that impede efficient sampling of configurational space by standard molecular dynamics simulation. Biased sampling can artificially drive the simulation along prespecified collective variables (CVs), but success depends critically on the availability of good CVs associated with the important collective dynamical motions. Nonlinear machine learning techniques can identify such CVs but typically do not furnish an explicit relationship with the atomic coordinates necessary to perform biased sampling. In this work, we employ auto-associative artificial neural networks ("autoencoders") to learn nonlinear CVs that are explicit and differentiable functions of the atomic coordinates. Our approach offers substantial speedups in exploration of configurational space, and is distinguished from existing approaches by its capacity to simultaneously discover and directly accelerate along data-driven CVs. We demonstrate the approach in simulations of alanine dipeptide and Trp-cage, and have developed an open-source and freely available implementation within OpenMM. © 2018 Wiley Periodicals, Inc.

Structural Capacitance in Protein Evolution and Human Diseases

Canonical mechanisms of protein evolution include the duplication and diversification of pre-existing folds through genetic alterations that include point mutations, insertions, deletions, and copy number amplifications, as well as post-translational modifications that modify processes such as folding efficiency and cellular localization. Following a survey of the human mutation database, we have identified an additional mechanism that we term "structural capacitance," which results in the de novo generation of microstructure in previously disordered regions. We suggest that the potential for structural capacitance confers select proteins with the capacity to evolve over rapid timescales, facilitating saltatory evolution as opposed to gradualistic canonical Darwinian mechanisms. Our results implicate the elements of protein microstructure generated by this distinct mechanism in the pathogenesis of a wide variety of human diseases. The benefits of rapidly furnishing the potential for evolutionary change conferred by structural capacitance are consequently counterbalanced by this accompanying risk. The phenomenon of structural capacitance has implications ranging from the ancestral diversification of protein folds to the engineering of synthetic proteins with enhanced evolvability.

Atomistic Peptide Folding Simulations Reveal Interplay of Entropy and Long-Range Interactions in Folding Cooperativity

Understanding how proteins fold has remained a problem of great interest in biophysical research. Atomistic computer simulations using physics-based force fields can provide important insights on the interplay of different interactions and energetics and their roles in governing the folding thermodynamics and mechanism. In particular, generalized Born (GB)-based implicit solvent force fields can be optimized to provide an appropriate balance between solvation and intramolecular interactions and successfully recapitulate experimental conformational equilibria for a set of helical and β-hairpin peptides. Here, we further demonstrate that key thermodynamic properties and their temperature dependence obtained from replica exchange molecular dynamics simulations of these peptides are in quantitative agreement with experimental results. Useful lessons can be learned on how the interplay of entropy and sequentially long-range interactions governs the mechanism and cooperativity of folding. These results highlight the great potential of high-quality implicit solvent force fields for studying protein folding and large-scale conformational transitions.

Collective variable discovery and enhanced sampling using autoencoders: Innovations in network architecture and error function design

Auto-associative neural networks ("autoencoders") present a powerful nonlinear dimensionality reduction technique to mine data-driven collective variables from molecular simulation trajectories. This technique furnishes explicit and differentiable expressions for the nonlinear collective variables, making it ideally suited for integration with enhanced sampling techniques for accelerated exploration of configurational space. In this work, we describe a number of sophistications of the neural network architectures to improve and generalize the process of interleaved collective variable discovery and enhanced sampling. We employ circular network nodes to accommodate periodicities in the collective variables, hierarchical network architectures to rank-order the collective variables, and generalized encoder-decoder architectures to support bespoke error functions for network training to incorporate prior knowledge. We demonstrate our approach in blind collective variable discovery and enhanced sampling of the configurational free energy landscapes of alanine dipeptide and Trp-cage using an open-source plugin developed for the OpenMM molecular simulation package.

Flexible selection of the solute region in replica exchange with solute tempering: Application to protein-folding simulations

Replica-exchange molecular dynamics (REMD) and their variants have been widely used in simulations of the biomolecular structure and dynamics. Replica exchange with solute tempering (REST) is one of the methods where temperature of a pre-defined solute molecule is exchanged between replicas, while solvent temperatures in all the replicas are kept constant. REST greatly reduces the number of replicas compared to the temperature REMD, while replicas at low temperatures are often trapped under their conditions, interfering with the conformational sampling. Here, we introduce a new scheme of REST, referred to as generalized REST (gREST), where the solute region is defined as a part of a molecule or a part of the potential energy terms, such as the dihedral-angle energy term or Lennard-Jones energy term. We applied this new method to folding simulations of a β-hairpin (16 residues) and a Trp-cage (20 residues) in explicit water. The protein dihedral-angle energy term is chosen as the solute region in the simulations. gREST reduces the number of replicas necessary for good random walks in the solute-temperature space and covers a wider conformational space compared to the conventional REST2. Considering the general applicability, gREST should become a promising tool for the simulations of protein folding, conformational dynamics, and an in silico drug design.

Transferable Dynamic Molecular Charge Assignment Using Deep Neural Networks

The ability to accurately and efficiently compute quantum-mechanical partial atomistic charges has many practical applications, such as calculations of IR spectra, analysis of chemical bonding, and classical force field parametrization. Machine learning (ML) techniques provide a possible avenue for the efficient prediction of atomic partial charges. Modern ML advances in the prediction of molecular energies [i.e., the hierarchical interacting particle neural network (HIP-NN)] has provided the necessary model framework and architecture to predict transferable, extensible, and conformationally dynamic atomic partial charges based on reference density functional theory (DFT) simulations. Utilizing HIP-NN, we show that ML charge prediction can be highly accurate over a wide range of molecules (both small and large) across a variety of charge partitioning schemes such as the Hirshfeld, CM5, MSK, and NBO methods. To demonstrate transferability and size extensibility, we compare ML results with reference DFT calculations on the COMP6 benchmark, achieving errors of 0.004e^- (elementary charge). This is remarkable since this benchmark contains two proteins that are multiple times larger than the largest molecules in the training set. An application of our atomic charge predictions on nonequilibrium geometries is the generation of IR spectra for organic molecules from dynamical trajectories on a variety of organic molecules, which show good agreement with calculated IR spectra with reference method. Critically, HIP-NN charge predictions are many orders of magnitude faster than direct DFT calculations. These combined results provide further evidence that ML (specifically HIP-NN) provides a pathway to greatly increase the range of feasible simulations while retaining quantum-level accuracy.

Hydrophobicity-driven unfolding of Trp-cage encapsulated between graphene sheets

Understanding the interaction between proteins and graphene not only helps elucidate the behaviors of proteins in confined geometries, but is also imperative to the development of a plethora of graphene-based biotechnologies, such as the graphene liquid cell transmission electron microscopy. To discuss the overall geometrical-thermal effects on proteins, we performed molecular dynamics simulations of hydrated Trp-cage miniprotein sandwiched between two graphene sheets and in the bulk environment at the temperatures below and above its unfolding temperature. The structural fluctuations of Trp-cage were characterized using the backbone root mean square displacement and the radius of gyration, from which the free energy landscape of Trp-cage was further constructed. We observed that at both temperatures the confined protein became adsorbed to the graphene surfaces and exhibited unfolded structures. Residue-specific analyses clearly showed the preference for the graphene to interact with the hydrophobic regions of Trp-cage. These results suggested that the conformation space accessible to the protein results from the competition between the thermodynamic driving forces and the geometrical restraints. While confinement usually tends to restrict the conformation of proteins by volume exclusion, it may also induce the unfolding of proteins by hydrophobic interactions.

Adaptive enhanced sampling with a path-variable for the simulation of protein folding and aggregation

In this article, we present a novel adaptive enhanced sampling molecular dynamics (MD) method for the accelerated simulation of protein folding and aggregation. We introduce a path-variable L based on the un-biased momenta p and displacements dq for the definition of the bias s applied to the system and derive 3 algorithms: general adaptive bias MD, adaptive path-sampling, and a hybrid method which combines the first 2 methodologies. Through the analysis of the correlations between the bias and the un-biased gradient in the system, we find that the hybrid methodology leads to an improved force correlation and acceleration in the sampling of the phase space. We apply our method on SPC/E water, where we find a conservation of the average water structure. We then use our method to sample dialanine and the folding of TrpCage, where we find a good agreement with simulation data reported in the literature. Finally, we apply our methodologies on the initial stages of aggregation of a hexamer of Alzheimer's amyloid β fragment 25-35 (Aβ 25-35) and find that transitions within the hexameric aggregate are dominated by entropic barriers, while we speculate that especially the conformation entropy plays a major role in the formation of the fibril as a rate limiting factor.

Reducing the number of mean-square deviation calculations with floating close structure in metadynamics

Metadynamics is an important collective-coordinate-based enhanced sampling simulation method. Its performance depends significantly on the capability of collective coordinates to describe the studied molecular processes. Collective coordinates based on comparison with reference landmark structures can be used to enhance sampling in highly complex systems; however, they may slow down simulations due to high number of structure-structure distance (e.g., mean-square deviation) calculations. Here we introduce an approximation of root-mean-square or mean-square deviation that significantly reduces numbers of computationally expensive operations. We evaluate its accuracy and theoretical performance gain with metadynamics simulations on two molecular systems.

Effect of osmolytes on the thermal stability of proteins: replica exchange simulations of Trp-cage in urea and betaine solutions

Although osmolytes are known to modulate the folding equilibrium, the molecular mechanism of their effect on thermal denaturation of proteins is still poorly understood. Here, we simulated the thermal denaturation of a small model protein (Trp-cage) in the presence of denaturing (urea) and stabilizing (betaine) osmolytes, using the all-atom replica exchange molecular dynamics simulations. We found that urea destabilizes Trp-cage by enthalpically-driven association with the protein, acting synergistically with temperature to induce unfolding. In contrast, betaine is sterically excluded from the protein surface thereby exerting entropic depletion forces that contribute to the stabilization of the native state. In fact, we find that while at low temperatures betaine slightly increases the folding free energy of Trp-cage by promoting another near-native conformation, it protects the protein against temperature-induced denaturation. This, in turn, can be attributed to enhanced exclusion of betaine at higher temperatures that arises from less attractive interactions with the protein surface.

Reproducibility of single protein explosions induced by X-ray lasers

Single particle imaging (SPI) using X-ray pulses has become increasingly attainable with the advent of high-intensity free electron lasers. Eliminating the need for crystallized samples enables structural studies of molecules previously inaccessible by conventional crystallography. While this emerging technique already demonstrates substantial promise, some obstacles need to be overcome before SPI can reach its full potential. One such problem is determining the spatial orientation of the sample at the time of X-ray interaction. Existing solutions rely on diffraction data and are computationally demanding and sensitive to noise. In this in silico study, we explore the possibility of aiding these methods by mapping the ion distribution as the sample undergoes a Coulomb explosion following the intense ionization. By detecting the ions ejected from the fragmented sample, the orientation of the original sample should be possible to determine. Knowledge of the orientation has been shown earlier to be of substantial advantage in the reconstruction of the original structure. 150 explosions of each of twelve separate systems - four polypeptides with different amounts of surface bound water - were simulated with molecular dynamics (MD) and the average angular distribution of carbon and sulfur ions was investigated independently. The results show that the explosion maps are reproducible in both cases, supporting the idea that orientation information is preserved. Additional water seems to restrict the carbon ion trajectories further through a shielding mechanism, making the maps more distinct. For sulfurs, water has no significant impact on the trajectories, likely due to their higher mass and greater ionization cross section, indicating that they could be of particular interest. Based on these findings, we conclude that explosion data can aid spatial orientation in SPI experiments and could substantially improve the capabilities of the novel technique.

Installation, validation, and application examples of two instrumental setups for gas-phase HDX-MS analysis of peptides and proteins

Gas-phase hydrogen/deuterium exchange measured by mass spectrometry in a millisecond timeframe after ESI (gas-phase HDX-MS) is a fast and sensitive, yet unharnessed method to analyze the primary- and higher-order structure, intramolecular and intermolecular interactions, surface properties, and charge location of peptides and proteins. During a gas-phase HDX-MS experiment, heteroatom-bound non-amide hydrogens are made to exchange with deuterium during a millisecond timespan after electrospray ionization (ESI) by reaction with the highly basic reagent ND₃, enabling conformational analysis of protein states that are pertinent to the native solution-phase. Here, we describe two different instrumental approaches to enable gas-phase HDX-MS for analysis of peptides and proteins on high-resolution Q-TOF mass spectrometers. We include a description of the procedure and equipment required for successful installation as well as suggested procedures for testing, validation, and troubleshooting of a gas-phase HDX-MS setup. In the two described approaches, gas-phase HDX-MS are performed either immediately after ESI in the cone exit region by leading N₂-gas over a deuterated ND₃/D₂O solution, or by leading purified ND₃-gas into different traveling wave ion guides (TWIG) of the mass spectrometer. We envision that a detailed description of the two gas-phase HDX-MS setups and their practical implementation and validation can pave the way for gas-phase HDX-MS to become a more routinely used MS technique for structural analysis of peptides and proteins.