PLP-Dependent Enzyme Methionine γ-Lyase: Insights into the Michaelis Complex from Molecular Dynamics and Free Energy Simulations.

Methionine γ-lyase (MGL) breaks down methionine, with the help of its cofactor pyridoxal-5'-phosphate (PLP), or vitamin B6. Methionine depletion is damaging for cancer cells but not normal cells, so MGL is of interest as a therapeutic protein. To increase our understanding and help engineer improved activity, we focused on the reactive, Michaelis complex M between MGL, covalently bound PLP, and substrate Met. M is not amenable to crystallography, as it proceeds to products. Experimental activity measurements helped exclude a mechanism that would bypass M. We then used molecular dynamics and alchemical free energy simulations to elucidate its structure and dynamics. We showed that the PLP phosphate has a pKa strongly downshifted by the protein, whether Met is present or not. Met binding affects the structure surrounding the reactive atoms. With Met, the Schiff base linkage between PLP and a nearby lysine shifts from a zwitterionic, keto form to a neutral, enol form that makes it easier for Met to approach its labile, target atom. The Met ligand also stabilizes the correct orientation of the Schiff base, more strongly than in simulations without Met, and in agreement with structures in the Protein Data Bank, where the Schiff base orientation correlates with the presence or absence of a co-bound anion or substrate analogue in the active site. Overall, the Met ligand helps organize the active site for the enzyme reaction by reducing fluctuations and shifting protonation states and conformational populations.

Adaptive landscape flattening allows the design of both enzyme: Substrate binding and catalytic power.

Designed enzymes are of fundamental and technological interest. Experimental directed evolution still has significant limitations, and computational approaches are a complementary route. A designed enzyme should satisfy multiple criteria: stability, substrate binding, transition state binding. Such multi-objective design is computationally challenging. Two recent studies used adaptive importance sampling Monte Carlo to redesign proteins for ligand binding. By first flattening the energy landscape of the apo protein, they obtained positive design for the bound state and negative design for the unbound. We have now extended the method to design an enzyme for specific transition state binding, i.e., for its catalytic power. We considered methionyl-tRNA synthetase (MetRS), which attaches methionine (Met) to its cognate tRNA, establishing codon identity. Previously, MetRS and other synthetases have been redesigned by experimental directed evolution to accept noncanonical amino acids as substrates, leading to genetic code expansion. Here, we have redesigned MetRS computationally to bind several ligands: the Met analog azidonorleucine, methionyl-adenylate (MetAMP), and the activated ligands that form the transition state for MetAMP production. Enzyme mutants known to have azidonorleucine activity were recovered by the design calculations, and 17 mutants predicted to bind MetAMP were characterized experimentally and all found to be active. Mutants predicted to have low activation free energies for MetAMP production were found to be active and the predicted reaction rates agreed well with the experimental values. We suggest the present method should become the paradigm for computational enzyme design.

Physics-Based Computational Protein Design: An Update.

We describe methods for physics-based protein design and some recent applications from our work. We present the physical interpretation of a MC simulation in sequence space and show that sequences and conformations form a well-defined statistical ensemble, explored with Monte Carlo and Boltzmann sampling. The folded state energy combines molecular mechanics for solutes with continuum electrostatics for solvent. We usually assume one or a few fixed protein backbone structures and discrete side chain rotamers. Methods based on molecular dynamics, which introduce additional backbone and side chain flexibility, are under development. The redesign of a PDZ domain and an aminoacyl-tRNA synthetase enzyme were successful. We describe a versatile, adaptive, Wang-Landau MC method that can be used to design for substrate affinity, catalytic rate, catalytic efficiency, or the specificity of these properties. The methods are transferable to all biomolecules, can be systematically improved, and give physical insights.

Hybrid MC/MD for protein design.

Computational protein design relies on simulations of a protein structure, where selected amino acids can mutate randomly, and mutations are selected to enhance a target property, such as stability. Often, the protein backbone is held fixed and its degrees of freedom are modeled implicitly to reduce the complexity of the conformational space. We present a hybrid method where short molecular dynamics (MD) segments are used to explore conformations and alternate with Monte Carlo (MC) moves that apply mutations to side chains. The backbone is fully flexible during MD. As a test, we computed side chain acid/base constants or pKa's in five proteins. This problem can be considered a special case of protein design, with protonation/deprotonation playing the role of mutations. The solvent was modeled as a dielectric continuum. Due to cost, in each protein we allowed just one side chain position to change its protonation state and the other position to change its type or mutate. The pKa's were computed with a standard method that scans a range of pH values and with a new method that uses adaptive landscape flattening (ALF) to sample all protonation states in a single simulation. The hybrid method gave notably better accuracy than standard, fixed-backbone MC. ALF decreased the computational cost a factor of 13.

Application of Various Molecular Modelling Methods in the Study of Estrogens and Xenoestrogens.

In this review, applications of various molecular modelling methods in the study of estrogens and xenoestrogens are summarized. Selected biomolecules that are the most commonly chosen as molecular modelling objects in this field are presented. In most of the reviewed works, ligand docking using solely force field methods was performed, employing various molecular targets involved in metabolism and action of estrogens. Other molecular modelling methods such as molecular dynamics and combined quantum mechanics with molecular mechanics have also been successfully used to predict the properties of estrogens and xenoestrogens. Among published works, a great number also focused on the application of different types of quantitative structure-activity relationship (QSAR) analyses to examine estrogen's structures and activities. Although the interactions between estrogens and xenoestrogens with various proteins are the most commonly studied, other aspects such as penetration of estrogens through lipid bilayers or their ability to adsorb on different materials are also explored using theoretical calculations. Apart from molecular mechanics and statistical methods, quantum mechanics calculations are also employed in the studies of estrogens and xenoestrogens. Their applications include computation of spectroscopic properties, both vibrational and Nuclear Magnetic Resonance (NMR), and also in quantum molecular dynamics simulations and crystal structure prediction. The main aim of this review is to present the great potential and versatility of various molecular modelling methods in the studies on estrogens and xenoestrogens.

Differences in Outcomes Reported by Patients With Inflammatory Bowel Diseases vs Their Health Care Professionals.

BACKGROUND & AIMS: Inflammatory bowel disease (IBD) scoring systems combine patient-reported data with physicians' observations to determine patient outcomes, but these systems are believed to have limitations. We used real-world data from a large IBD cohort in Switzerland to compare results between patients and healthcare professionals from scoring systems for Crohn's disease (CD) and ulcerative colitis (UC). METHODS: We collected data from the Swiss IBD cohort, beginning in 2006, using 2453 reports for 1385 patients (52% female, 58% with CD). During office visits, physicians asked patients about signs and symptoms and recorded their answers (health care professional-reported outcomes). On a later date, patients received a questionnaire at home (independently of the medical visit), complete it, and sent it back to the data center. Patients also completed the short form 36 and IBD quality of life (QoL) questionnaires. We calculated Cohen's kappa (κ) statistics to assess the level of agreement in scores between patients and health care professionals (Δt between reports collected less than 2 months apart). We used Spearman correlation coefficients (ρ) to compare general well-being (GWB) and QoL scores determined by patients vs health care professionals. Our primary aim was to investigate the overall and individual level of agreement on signs and symptoms reported by health care professionals vs patients. RESULTS: The best level of agreement (although moderate) was observed for number of stools last week in patients with CD (κ = 0.47), and nocturnal diarrhea in patients with UC (κ = 0.52). Agreement was low on level of abdominal pain (κ = 0.31 for patients with CD and κ = 0.37 for patients with UC) and GWB (κ = 0.23 for patients with CD and κ = 0.26 for patients with UC). Patients reported less severe abdominal pain and worse GWB (CD) or better GWB (UC) than that determined by health care professionals. Patient self-rated GWB correlated with IBD quality of life (ρ = 0.68 for patients with CD and ρ = 0.70 for patients with UC) and SF-36 physical scores (ρ = 0.55 for patients with CD and ρ = 0.60 for patients with UC); there was no correlation between health care professional-rated GWB and QoL. CONCLUSIONS: In a comparison of patient vs health care provider-reported outcomes in a Swiss IBD cohort, we found that health care professionals seem to misinterpret patients' complaints. Patients self-rated GWB correlated with QoL scores, indicating that reporting GWB in a single question is possible and relevant, but can vary based on how the data are collected.

Variable Neighborhood Search with Cost Function Networks To Solve Large Computational Protein Design Problems.

Computational protein design (CPD) aims to predict amino acid sequences that fold to specific structures and perform desired functions. CPD depends on a rotamer library, an energy function, and an algorithm to search the sequence/conformation space. Variable neighborhood search (VNS) with cost function networks is a powerful framework that can provide tight upper bounds on the global minimum energy. We propose a new CPD heuristic based on VNS in which a subset of the solution space (a "neighborhood") is explored, whose size is gradually increased with a dedicated probabilistic heuristic. The algorithm was tested on 99 protein designs with fixed backbones involving nine proteins from the SH2, SH3, and PDZ families. The number of mutating positions was 20, 30, or all of the amino acids, while the rest of the protein explored side-chain rotamers. VNS was more successful than Monte Carlo (MC), replica-exchange MC, and a heuristic steepest-descent energy minimization, providing solutions with equal or lower best energies in most cases. For complete protein redesign, it gave solutions that were 2.5 to 11.2 kcal/mol lower in energy than those obtained with the other approaches. VNS is implemented in the toulbar2 software. It could be very helpful for large and/or complex design problems.

Accurate PDZ/Peptide Binding Specificity with Additive and Polarizable Free Energy Simulations.

PDZ domains contain 80-100 amino acids and bind short C-terminal sequences of target proteins. Their specificity is essential for cellular signaling pathways. We studied the binding of the Tiam1 PDZ domain to peptides derived from the C-termini of its Syndecan-1 and Caspr4 targets. We used free energy perturbation (FEP) to characterize the binding energetics of one wild-type and 17 mutant complexes by simulating 21 alchemical transformations between pairs of complexes. Thirteen complexes had known experimental affinities. FEP is a powerful tool to understand protein/ligand binding. It depends, however, on the accuracy of molecular dynamics force fields and conformational sampling. Both aspects require continued testing, especially for ionic mutations. For six mutations that did not modify the net charge, we obtained excellent agreement with experiment using the additive, AMBER ff99SB force field, with a root mean square deviation (RMSD) of 0.37 kcal/mol. For six ionic mutations that modified the net charge, agreement was also good, with one large error (3 kcal/mol) and an RMSD of 0.9 kcal/mol for the other five. The large error arose from the overstabilization of a protein/peptide salt bridge by the additive force field. Four of the ionic mutations were also simulated with the polarizable Drude force field, which represents the first test of this force field for protein/ligand binding free energy changes. The large error was eliminated and the RMS error for the four mutations was reduced from 1.8 to 1.2 kcal/mol. The overall accuracy of FEP indicates it can be used to understand PDZ/peptide binding. Importantly, our results show that for ionic mutations in buried regions, electronic polarization plays a significant role.

Classical Drude Polarizable Force Field Model for Methyl Phosphate and Its Interactions with Mg2.

Phosphate groups are essential components of nucleic acids and proteins, whose interactions with solvent, metal ions, and ionic side chains help control folding and binding. Methyl phosphate (MP) represents a simple analog of phosphate moieties that are post-translation modifications in proteins and present at the termini of nucleic acids, among other environments. In the present study, we optimized parameters for use in polarizable molecular dynamics simulations of MP in its mono- and dianionic forms, MP- ≡ CH3HPO4- and MP2- ≡ CH3PO42-, along with P i2- ≡ HPO42-, in the context of the classical Drude oscillator model. Parameter optimization was done in a manner consistent with the remainder of the Drude molecular mechanics force field, choosing atomic charges and polarizabilities to reproduce molecular properties from quantum mechanics as well as experimental hydration free energies. Optimized parameters were similar to existing dimethyl phosphate parameters, with a few significant differences. The developed parameters were then used to compute magnesium binding affinities in aqueous solution, using alchemical molecular dynamics free energy simulations. Good agreement with experiment was obtained, and outer sphere binding was shown to be predominant for MP- and MP2-.

Adaptive landscape flattening in amino acid sequence space for the computational design of protein:peptide binding.

For the high throughput design of protein:peptide binding, one must explore a vast space of amino acid sequences in search of low binding free energies. This complex problem is usually addressed with either simple heuristic scoring or expensive sequence enumeration schemes. Far more efficient than enumeration is a recent Monte Carlo approach that adaptively flattens the energy landscape in sequence space of the unbound peptide and provides formally exact binding free energy differences. The method allows the binding free energy to be used directly as the design criterion. We propose several improvements that allow still more efficient sampling and can address larger design problems. They include the use of Replica Exchange Monte Carlo and landscape flattening for both the unbound and bound peptides. We used the method to design peptides that bind to the PDZ domain of the Tiam1 signaling protein and could serve as inhibitors of its activity. Four peptide positions were allowed to mutate freely. Almost 75 000 peptide variants were processed in two simulations of 109 steps each that used 1 CPU hour on a desktop machine. 96% of the theoretical sequence space was sampled. The relative binding free energies agreed qualitatively with values from experiment. The sampled sequences agreed qualitatively with an experimental library of Tiam1-binding peptides. The main assumption limiting accuracy is the fixed backbone approximation, which could be alleviated in future work by using increased computational resources and multi-backbone designs.

Comparing pairwise-additive and many-body generalized Born models for acid/base calculations and protein design.

Generalized Born (GB) solvent models are common in acid/base calculations and protein design. With GB, the interaction between a pair of solute atoms depends on the shape of the protein/solvent boundary and, therefore, the positions of all solute atoms, so that GB is a many-body potential. For compute-intensive applications, the model is often simplified further, by introducing a mean, native-like protein/solvent boundary, which removes the many-body property. We investigate a method for both acid/base calculations and protein design that uses Monte Carlo simulations in which side chains can explore rotamers, bind/release protons, or mutate. The fluctuating protein/solvent dielectric boundary is treated in a way that is numerically exact (within the GB framework), in contrast to a mean boundary. Its originality is that it captures the many-body character while retaining the residue-pairwise complexity given by a fixed boundary. The method is implemented in the Proteus protein design software. It yields a slight but systematic improvement for acid/base constants in nine proteins and a significant improvement for the computational design of three PDZ domains. It eliminates a source of model uncertainty, which will facilitate the analysis of other model limitations. © 2017 Wiley Periodicals, Inc.

Simple models for nonpolar solvation: Parameterization and testing.

Implicit solvent models are important for many biomolecular simulations. The polarity of aqueous solvent is essential and qualitatively captured by continuum electrostatics methods like Generalized Born (GB). However, GB does not account for the solvent-induced interactions between exposed hydrophobic sidechains or solute-solvent dispersion interactions. These "nonpolar" effects are often modeled through surface area (SA) energy terms, which lack realism, create mathematical singularities, and have a many-body character. We have explored an alternate, Lazaridis-Karplus (LK) gaussian energy density for nonpolar effects and a dispersion (DI) energy term proposed earlier, associated with GB electrostatics. We parameterized several combinations of GB, SA, LK, and DI energy terms, to reproduce 62 small molecule solvation free energies, 387 protein stability changes due to point mutations, and the structures of 8 protein loops. With optimized parameters, the models all gave similar results, with GBLK and GBDILK giving no performance loss compared to GBSA, and mean errors of 1.7 kcal/mol for the stability changes and 2 Å deviations for the loop conformations. The optimized GBLK model gave poor results in MD of the Trpcage mini-protein, but parameters optimized specifically for MD performed well for Trpcage and three other small proteins. Overall, the LK and DI nonpolar terms are valid alternatives to SA treatments for a range of applications. © 2017 Wiley Periodicals, Inc.

Equivalence of M- and P-Summation in Calculations of Ionic Solvation Free Energies.

Condensed-phase simulations commonly use periodic boundary conditions (PBCs) to represent the thermodynamic limit. For the vapor to liquid transfer of an ion, the gas/liquid boundary and its associated potential change are then missing. Furthermore, the electric potential and field at a given point are given by conditionally convergent infinite series, for which different summation schemes give different results. Nevertheless, standard simulation protocols can be used to compute experimental quantities unambiguously. In particular, using an auxiliary test particle and a multistep solvation path, we show that particle-based, Ewald, and common molecule-based summation schemes for the potential and field are all essentially equivalent. However, all methods require prior knowledge of the gas/liquid boundary potential to compute ionic solvation free energies using PBC protocols for both force-field and quantum-mechanical models.

Electrostatic free energies in translational GTPases: Classic allostery and the rest.

GTPases typically switch between an inactive, OFF conformation and an active, ON conformation when a GDP ligand is replaced by GTP. Their ON/OFF populations and activity thus depend on the stabilities of four protein complexes, two apo-protein forms, and GTP/GDP in solution. A complete characterization is usually not possible experimentally and poses major challenges for simulations. We review the most important methodological challenges and we review thermodynamic data for two GTPases involved in translation of the genetic code: archaeal Initiation Factors 2 and 5B (aIF2, aIF5B). One main challenge is the multiplicity of states and conformations, including those of GTP/GDP in solution. Another is force field accuracy, especially for interactions of GTP/GDP with co-bound divalent Mg(2+) ions. The calculation of electrostatic free energies also poses specific challenges, and requires careful protocols. For aIF2, experiments and earlier simulations showed that it is a "classic" GTPase, with distinct ON/OFF conformations that prefer to bind GTP and GDP, respectively. For aIF5B, we recently proposed a non-classic mechanism, where the ON/OFF states differ only in the protonation state of Glu81 in the nucleotide binding pocket. This model is characterized here using free energy simulations. The methodological analysis should help future studies, while the aIF2, aIF5B examples illustrate the diversity of ATPase/GTPase mechanisms. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Protein side chain conformation predictions with an MMGBSA energy function.

The prediction of protein side chain conformations from backbone coordinates is an important task in structural biology, with applications in structure prediction and protein design. It is a difficult problem due to its combinatorial nature. We study the performance of an "MMGBSA" energy function, implemented in our protein design program Proteus, which combines molecular mechanics terms, a Generalized Born and Surface Area (GBSA) solvent model, with approximations that make the model pairwise additive. Proteus is not a competitor to specialized side chain prediction programs due to its cost, but it allows protein design applications, where side chain prediction is an important step and MMGBSA an effective energy model. We predict the side chain conformations for 18 proteins. The side chains are first predicted individually, with the rest of the protein in its crystallographic conformation. Next, all side chains are predicted together. The contributions of individual energy terms are evaluated and various parameterizations are compared. We find that the GB and SA terms, with an appropriate choice of the dielectric constant and surface energy coefficients, are beneficial for single side chain predictions. For the prediction of all side chains, however, errors due to the pairwise additive approximation overcome the improvement brought by these terms. We also show the crucial contribution of side chain minimization to alleviate the rigid rotamer approximation. Even without GB and SA terms, we obtain accuracies comparable to SCWRL4, a specialized side chain prediction program. In particular, we obtain a better RMSD than SCWRL4 for core residues (at a higher cost), despite our simpler rotamer library. Proteins 2016; 84:803-819. © 2016 Wiley Periodicals, Inc.

Redesigning the stereospecificity of tyrosyl-tRNA synthetase.

D-Amino acids are largely excluded from protein synthesis, yet they are of great interest in biotechnology. Unnatural amino acids have been introduced into proteins using engineered aminoacyl-tRNA synthetases (aaRSs), and this strategy might be applicable to D-amino acids. Several aaRSs can aminoacylate their tRNA with a D-amino acid; of these, tyrosyl-tRNA synthetase (TyrRS) has the weakest stereospecificity. We use computational protein design to suggest active site mutations in Escherichia coli TyrRS that could increase its D-Tyr binding further, relative to L-Tyr. The mutations selected all modify one or more sidechain charges in the Tyr binding pocket. We test their effect by probing the aminoacyl-adenylation reaction through pyrophosphate exchange experiments. We also perform extensive alchemical free energy simulations to obtain L-Tyr/D-Tyr binding free energy differences. Agreement with experiment is good, validating the structural models and detailed thermodynamic predictions the simulations provide. The TyrRS stereospecificity proves hard to engineer through charge-altering mutations in the first and second coordination shells of the Tyr ammonium group. Of six mutants tested, two are active towards D-Tyr; one of these has an inverted stereospecificity, with a large preference for D-Tyr. However, its activity is low. Evidently, the TyrRS stereospecificity is robust towards charge rearrangements near the ligand. Future design may have to consider more distant and/or electrically neutral target mutations, and possibly design for binding of the transition state, whose structure however can only be modeled.

Comparing three stochastic search algorithms for computational protein design: Monte Carlo, replica exchange Monte Carlo, and a multistart, steepest-descent heuristic.

Computational protein design depends on an energy function and an algorithm to search the sequence/conformation space. We compare three stochastic search algorithms: a heuristic, Monte Carlo (MC), and a Replica Exchange Monte Carlo method (REMC). The heuristic performs a steepest-descent minimization starting from thousands of random starting points. The methods are applied to nine test proteins from three structural families, with a fixed backbone structure, a molecular mechanics energy function, and with 1, 5, 10, 20, 30, or all amino acids allowed to mutate. Results are compared to an exact, "Cost Function Network" method that identifies the global minimum energy conformation (GMEC) in favorable cases. The designed sequences accurately reproduce experimental sequences in the hydrophobic core. The heuristic and REMC agree closely and reproduce the GMEC when it is known, with a few exceptions. Plain MC performs well for most cases, occasionally departing from the GMEC by 3-4 kcal/mol. With REMC, the diversity of the sequences sampled agrees with exact enumeration where the latter is possible: up to 2 kcal/mol above the GMEC. Beyond, room temperature replicas sample sequences up to 10 kcal/mol above the GMEC, providing thermal averages and a solution to the inverse protein folding problem. © 2016 Wiley Periodicals, Inc.

Protein:Ligand binding free energies: A stringent test for computational protein design.

A computational protein design method is extended to allow Monte Carlo simulations where two ligands are titrated into a protein binding pocket, yielding binding free energy differences. These provide a stringent test of the physical model, including the energy surface and sidechain rotamer definition. As a test, we consider tyrosyl-tRNA synthetase (TyrRS), which has been extensively redesigned experimentally. We consider its specificity for its substrate l-tyrosine (l-Tyr), compared to the analogs d-Tyr, p-acetyl-, and p-azido-phenylalanine (ac-Phe, az-Phe). We simulate l- and d-Tyr binding to TyrRS and six mutants, and compare the structures and binding free energies to a more rigorous "MD/GBSA" procedure: molecular dynamics with explicit solvent for structures and a Generalized Born + Surface Area model for binding free energies. Next, we consider l-Tyr, ac- and az-Phe binding to six other TyrRS variants. The titration results are sensitive to the precise rotamer definition, which involves a short energy minimization for each sidechain pair to help relax bad contacts induced by the discrete rotamer set. However, when designed mutant structures are rescored with a standard GBSA energy model, results agree well with the more rigorous MD/GBSA. As a third test, we redesign three amino acid positions in the substrate coordination sphere, with either l-Tyr or d-Tyr as the ligand. For two, we obtain good agreement with experiment, recovering the wildtype residue when l-Tyr is the ligand and a d-Tyr specific mutant when d-Tyr is the ligand. For the third, we recover His with either ligand, instead of wildtype Gln.

Structure and thermodynamics of Mg:phosphate interactions in water: a simulation study.

The association of Mg(2+) and H2 PO4 (-) in water can give insights into Mg:phosphate interactions in general, which are very widespread, but for which experimental data is surprisingly sparse. It is studied through molecular dynamics simulations (>100 ns) by using the polarizable AMOEBA force field, and the association free energy is computed for the first time. Explicit consideration of outer-sphere and two types of inner-sphere association provides considerable insight into the dynamics and thermodynamics of ion pairing. After careful assessment of the computational approximations, the agreement with experimental values indicates that the methodology can be extended to other inorganic and biological Mg:phosphate interactions in solution.

Pairwise decomposition of an MMGBSA energy function for computational protein design.

Computational protein design (CPD) aims at predicting new proteins or modifying existing ones. The computational challenge is huge as it requires exploring an enormous sequence and conformation space. The difficulty can be reduced by considering a fixed backbone and a discrete set of sidechain conformations. Another common strategy consists in precalculating a pairwise energy matrix, from which the energy of any sequence/conformation can be quickly obtained. In this work, we examine the pairwise decomposition of protein MMGBSA energy functions from a general theoretical perspective, and an implementation proposed earlier for CPD. It includes a Generalized Born term, whose many-body character is overcome using an effective dielectric environment, and a Surface Area term, for which we present an improved pairwise decomposition. A detailed evaluation of the error introduced by the decomposition on the different energy components is performed. We show that the error remains reasonable, compared to other uncertainties.