Generalized born models of macromolecular solvation effects

Mollack: a web server for the automated creation of conformational ensembles for intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) play central roles in many biological processes. Consequently, an accurate description of the disordered state is an important step towards a comprehensive understanding of a number of important biological functions. In this work we describe a new web server, Mollack, for the automated construction of unfolded ensembles that uses both experimental and molecular simulation data to construct models for the unfolded state. An important aspect of the method is that it calculates a quantitative estimate of the uncertainty in the constructed ensemble, thereby providing an objective measure of the quality of the final model. Overall, Mollack facilitates structure-function studies of disordered proteins.

AVAILABILITY AND IMPLEMENTATION

http://cmstultz-mollack.mit.edu

CONTACT

cmstultz@mit.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Oxidative Deamination of Serum Albumins by (-)-Epigallocatechin-3-O-Gallate: A Potential Mechanism for the Formation of Innate Antigens by Antioxidants

(-)-Epigallocatechin-3-O-gallate (EGCG), the most abundant polyphenol in green tea, mediates the oxidative modification of proteins, generating protein carbonyls. However, the underlying molecular mechanism remains unclear. Here we analyzed the EGCG-derived intermediates generated upon incubation with the human serum albumin (HSA) and established that EGCG selectively oxidized the lysine residues via its oxidative deamination activity. In addition, we characterized the EGCG-oxidized proteins and discovered that the EGCG could be an endogenous source of the electrically-transformed proteins that could be recognized by the natural antibodies. When HSA was incubated with EGCG in the phosphate-buffered saline (pH 7.4) at 37°C, the protein carbonylation was associated with the formation of EGCG-derived products, such as the protein-bound EGCG, oxidized EGCG, and aminated EGCG. The aminated EGCG was also detected in the sera from the mice treated with EGCG in vivo. EGCG selectively oxidized lysine residues at the EGCG-binding domains in HSA to generate an oxidatively deaminated product, aminoadipic semialdehyde. In addition, EGCG treatment results in the increased negative charge of the protein due to the oxidative deamination of the lysine residues. More strikingly, the formation of protein carbonyls by EGCG markedly increased its cross-reactivity with the natural IgM antibodies. These findings suggest that many of the beneficial effects of EGCG may be partly attributed to its oxidative deamination activity, generating the oxidized proteins as a target of natural antibodies.

On the ability of molecular dynamics force fields to recapitulate NMR derived protein side chain order parameters

Molecular dynamics (MD) simulations have become a central tool for investigating various biophysical questions with atomistic detail. While many different proxies are used to qualify MD force fields, most are based on largely structural parameters such as the root mean square deviation from experimental coordinates or nuclear magnetic resonance (NMR) chemical shifts and residual dipolar couplings. NMR derived Lipari-Szabo squared generalized order parameter (O(2) ) values of amide NH bond vectors of the polypeptide chain were also often employed for refinement and validation. However, with a few exceptions, side chain methyl symmetry axis order parameters have not been incorporated into experimental reference sets. Using a test set of five diverse proteins, the performance of several force fields implemented in the NAMDD simulation package was examined. It was found that simulations employing explicit water implemented using the TIP3 model generally performed significantly better than those using implicit water in reproducing experimental methyl symmetry axis O(2) values. Overall the CHARMM27 force field performs nominally better than two implementations of the Amber force field. It appeared that recent quantum mechanics modifications to side chain torsional angles of leucine and isoleucine in the Amber force field have significantly hindered proper motional modeling for these residues. There remained significant room for improvement as even the best correlations of experimental and simulated methyl group Lipari-Szabo generalized order parameters fall below an R(2) of 0.8.

Hydration Properties and Solvent Effects for All-Atom Solutes in Polarizable Coarse-Grained Water

Due to the importance of water in chemical and biological systems, a coarse-grained representation of the solvent can greatly simplify the description of the system while retaining key thermodynamic properties of the medium. A multiscale solvation model that couples all-atom solutes and polarizable Martini coarse-grained water (AAX/CGS) is developed to reproduce free energies of hydration of organic solutes. Using Monte Carlo/free energy perturbation (MC/FEP) calculations, results from multiscale and all-atom simulations are compared. Improved accuracy is obtained with the AAX/CGS approach for hydrophobic and sulfur- or halogen-containing solutes, but larger deviations are found for polar solute molecules where hydrogen bonding is featured. Furthermore, solvent effects on conformational and tautomeric equilibria of AA solutes were investigated using AA, CG, and GB/SA solvent models. It is found that the CG solvent model can reproduce well the medium effects from experiment and AA simulations; however, the GB/SA solvent model fails in some cases. A 7-30-fold reduction in computational cost is found for the present AAX/CGS multiscale simulations compared to the AA alternative.

Albumin (BSA) Adsorption over Graphene in Aqueous Environment: Influence of Orientation, Adsorption Protocol, and Solvent Treatment

We report 150 ns explicit solvent MD simulations of the adsorption on graphene of albumin (BSA) in two orientations and using two different adsorption protocols, i.e., free and forced adsorption. Our results show that free adsorption occurs with little structural rearrangements. Even taking adsorption to an extreme, by forcing it with a 5 nN downward force applied during the initial 20 ns, we show that along a particular orientation BSA is able to preserve the structural properties of the majority of its binding sites. Furthermore, in all the cases considered in this work, the ibuprofen binding site has shown a strong resilience to structural changes. Finally, we compare these results with implicit solvent simulations and find that the latter predicts an extreme protein unfolding upon adsorption. The origin of this discrepancy is attributed to a poor description of the water entropic forces at interfaces in the implicit solvent methods.

Calculating Free Energy Changes in Continuum Solvation Models

We recently showed for a large data set of pKas and reduction potentials that free energies calculated directly within the SMD continuum model compares very well with corresponding thermodynamic cycle calculations in both aqueous and organic solvents [ Phys. Chem. Chem. Phys. 2015 , 17 , 2859 ]. In this paper, we significantly expand the scope of our study to examine the suitability of this approach for calculating general solution phase kinetics and thermodynamics, in conjunction with several commonly used solvation models (SMD-M062X, SMD-HF, CPCM-UAKS, and CPCM-UAHF) for a broad range of systems. This includes cluster-continuum schemes for pKa calculations as well as various neutral, radical, and ionic reactions such as enolization, cycloaddition, hydrogen and chlorine atom transfer, and SN2 and E2 reactions. On the basis of this benchmarking study, we conclude that the accuracies of both approaches are generally very similar-the mean errors for Gibbs free energy changes of neutral and ionic reactions are approximately 5 and 25 kJ mol(-1), respectively. In systems where there are significant structural changes due to solvation, as is the case for certain ionic transition states and amino acids, the direct approach generally afford free energy changes that are in better agreement with experiment.

Parallelization and improvements of the generalized born model with a simple sWitching function for modern graphics processors

Two fundamental challenges of simulating biologically relevant systems are the rapid calculation of the energy of solvation and the trajectory length of a given simulation. The Generalized Born model with a Simple sWitching function (GBSW) addresses these issues by using an efficient approximation of Poisson-Boltzmann (PB) theory to calculate each solute atom's free energy of solvation, the gradient of this potential, and the subsequent forces of solvation without the need for explicit solvent molecules. This study presents a parallel refactoring of the original GBSW algorithm and its implementation on newly available, low cost graphics chips with thousands of processing cores. Depending on the system size and nonbonded force cutoffs, the new GBSW algorithm offers speed increases of between one and two orders of magnitude over previous implementations while maintaining similar levels of accuracy. We find that much of the algorithm scales linearly with an increase of system size, which makes this water model cost effective for solvating large systems. Additionally, we utilize our GPU-accelerated GBSW model to fold the model system chignolin, and in doing so we demonstrate that these speed enhancements now make accessible folding studies of peptides and potentially small proteins.

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.

Production of a soluble single-chain variable fragment antibody against okadaic acid and exploration of its specific binding

Okadaic acid is a lipophilic marine algal toxin commonly responsible for diarrhetic shellfish poisoning (DSP). Outbreaks of DSP have been increasing and are of worldwide public health concern; therefore, there is a growing demand for more rapid, reliable, and economical analytical methods for the detection of this toxin. In this study, anti-okadaic acid single-chain variable fragment (scFv) genes were prepared by cloning heavy and light chain genes from hybridoma cells, followed by fusion of the chains via a linker peptide. An scFv-pLIP6/GN recombinant plasmid was constructed and transformed into Escherichia coli for expression, and the target scFv was identified with IC-CLEIA (chemiluminescent enzyme immunoassay). The IC15 was 0.012 ± 0.02 μg/L, and the IC50 was 0.25 ± 0.03 μg/L. The three-dimensional structure of the scFv was simulated with computer modeling, and okadaic acid was docked to the scFv model to obtain a putative structure of the binding complex. Two predicted critical amino acids, Ser32 and Thr187, were then mutated to verify this theoretical model. Both mutants exhibited significant loss of binding activity. These results help us to understand this specific scFv-antigen binding mechanism and provide guidance for affinity maturation of the antibody in vitro. The high-affinity scFv developed here also has potential for okadaic acid toxin detection.

Molecular dynamics simulations of biological membranes and membrane proteins using enhanced conformational sampling algorithms

This paper reviews various enhanced conformational sampling methods and explicit/implicit solvent/membrane models, as well as their recent applications to the exploration of the structure and dynamics of membranes and membrane proteins. Molecular dynamics simulations have become an essential tool to investigate biological problems, and their success relies on proper molecular models together with efficient conformational sampling methods. The implicit representation of solvent/membrane environments is reasonable approximation to the explicit all-atom models, considering the balance between computational cost and simulation accuracy. Implicit models can be easily combined with replica-exchange molecular dynamics methods to explore a wider conformational space of a protein. Other molecular models and enhanced conformational sampling methods are also briefly discussed. As application examples, we introduce recent simulation studies of glycophorin A, phospholamban, amyloid precursor protein, and mixed lipid bilayers and discuss the accuracy and efficiency of each simulation model and method. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Molecular determinants for selective C25-hydroxylation of vitamins D2and D3by fungal peroxygenases

Regioselective hydroxylation of vitamin D byAgrocybe aegeritaandCoprinopsis cinereaperoxygenases was investigated in an experimental and computational study.

Selective targeting of MAPK family kinases JNK over p38 by rationally designed peptides as potential therapeutics for neurological disorders and epilepsy

A systematic strategy is described to optimize peptide selectivity between the MAPK family kinases JNK and p38 for epilepsy therapy.

Re-designing the substrate binding pocket of laccase for enhanced oxidation of sinapic acid

Iterative saturation mutagenesis was performed over six residues delimiting the substrate binding pocket of a high redox potential chimeric laccase with the aim of enhancing its activity over sinapic acid, a lignin-related phenol of industrial interest.

A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson-Boltzmann electrostatics

Dielectric boundary based implicit-solvent models provide efficient descriptions of coarse-grained effects, particularly the electrostatic effect, of aqueous solvent. Recent years have seen the initial success of a new such model, variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett. 96, 087802 (2006) and J. Chem. Phys. 124, 084905 (2006)], in capturing multiple dry and wet hydration states, describing the subtle electrostatic effect in hydrophobic interactions, and providing qualitatively good estimates of solvation free energies. Here, we develop a phase-field VISM to the solvation of charged molecules in aqueous solvent to include more flexibility. In this approach, a stable equilibrium molecular system is described by a phase field that takes one constant value in the solute region and a different constant value in the solvent region, and smoothly changes its value on a thin transition layer representing a smeared solute-solvent interface or dielectric boundary. Such a phase field minimizes an effective solvation free-energy functional that consists of the solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic free energy described by the Poisson-Boltzmann theory. We apply our model and methods to the solvation of single ions, two parallel plates, and protein complexes BphC and p53/MDM2 to demonstrate the capability and efficiency of our approach at different levels. With a diffuse dielectric boundary, our new approach can describe the dielectric asymmetry in the solute-solvent interfacial region. Our theory is developed based on rigorous mathematical studies and is also connected to the Lum-Chandler-Weeks theory (1999). We discuss these connections and possible extensions of our theory and methods.

Optimized Radii for Poisson-Boltzmann Calculations with the AMBER Force Field

Implicit solvent models are a standard tool for assessing the electrostatics of biomolecular systems. The accuracy of quantitative predictions, such as pKa values, transfer free energies, binding energies, and solvation forces, is strongly dependent on one's choice of continuum parameters:  the solute charges, dielectric coefficient, and radii, which define the dielectric boundary. To ensure quantitative accuracy, these parameters can be benchmarked against explicit solvent simulations. Here we present two sets of optimized radii to define either abrupt or cubic-spline smoothed dielectric boundaries in Poisson-Boltzmann calculations of protein systems with AMBER (parm99) charges. Spline smoothing stabilizes the electrostatic potential at the molecular surface, allowing for continuum force calculations. Most implementations, however, require significantly different radii than the abrupt boundary surfaces. The optimal continuum radii are initially approximated from the solvent radial charge distribution surrounding each atom type. A genetic algorithm is then used to fine-tune the starting values to reproduce charging free energies measured from explicit solvent simulations. The optimized radii are tested on four protein-like polypeptides. The results show increased accuracy of molecular solvation energies and atomic forces relative to commonly used continuum parameter sets. These radii are suitable for Poisson-Boltzmann calculations with the AMBER force field and offer energetic congruence to any model that combines molecular mechanics and Poisson-Boltzmann solvation energies.

Polarization Effects in Aqueous and Nonaqueous Solutions

Polarization effects in aqueous and nonaqueous solutions were analyzed for nine neutral and three charged organic solutes by the SM8 universal implicit solvation model and class IV partial atomic charges based on Charge Model 4M (CM4M) with the M06-2X density functional. The CM4M partial atomic charges in neutral and ionic solutes and in the corresponding clustered solutes (supersolutes), which included one solute molecule and one or two solvent molecules, were modeled in three solvents (benzene, methylene chloride, and water) and compared to those in the gas phase. The use of the supersolute approach (microsolvation) allows one to account for charge transfer from the solute to the solvent, and we find charge transfers as large as 0.06 atomic units for neutral solutes (pyridine in water) and 0.32 atomic units for ions (methoxide anion in water). Relaxation of the electronic structure of the solute in the presence of solvent increases the polarization free energy of the neutral solutes studied here, on average, by 16% in benzene, 30% in methylene chloride, and 43% in water. The increase for the ions in water averaged 43%.

Base-Displaced Intercalated Structure of the N-(2'-Deoxyguanosin-8-yl)-3-aminobenzanthrone DNA Adduct

3-Nitrobenzanthrone (3-NBA), an environmental mutagen found in diesel exhaust and a suspected carcinogen, undergoes metabolic reduction followed by reaction with DNA to form aminobenzanthrone (ABA) adducts, with the major alkylation product being N-(2'-deoxyguanosin-8-yl)-3-aminobenzanthrone (C8-dG-ABA). Site-specific synthesis of the C8-dG-ABA adduct in the oligodeoxynucleotide 5'-d(GTGCXTGTTTGT)-3':5'-d(ACAAACACGCAC)-3'; X = C8-dG-ABA adduct, including codons 272-275 of the p53 gene, has allowed for investigation into the structural and thermodynamic properties of this adduct. The conformation of the C8-dG-ABA adduct was determined using NMR spectroscopy and was refined using molecular dynamics (MD) calculations restrained by experimentally determined interproton distance restraints obtained from NOE experiments. The refined structure revealed that the C8-dG-ABA adduct formed a base-displaced intercalated conformation. The adducted guanine was shifted into the syn conformation about the glycosidic bond. The 5'- and 3'-neighboring base pairs remained intact. While this facilitated π-stacking interactions between the ABA moiety and neighboring bases, the thermal melting temperature (Tm) of the adduct-containing duplex showed a decrease of 11 °C as compared to the corresponding unmodified oligodeoxynucleotide duplex. Overall, in this sequence, the base-displaced intercalated conformation of the C8-dG-ABA lesion bears similarity to structures of other arylamine C8-dG adducts. However, in this sequence, the base-displaced intercalated conformation for the C8-dG-ABA adduct differs from the conformation of the N(2)-dG-ABA adduct reported by de los Santos and co-workers, in which it is oriented in the minor groove toward the 5' end of the duplex, with the modified guanine remaining in the anti conformation about the glyosidic torsion angle, and the complementary base remaining within the duplex. The results are discussed in relationship to differences between the C8-dG-ABA and N(2)-dG-ABA adducts with respect to susceptibility to nucleotide excision repair (NER).

Protein-Ligand Complexes: Computation of the Relative Free Energy of Different Scaffolds and Binding Modes

A methodology for the calculation of the free energy difference between a pair of molecules of arbitrary topology is proposed. The protocol relies on a dual-topology paradigm, a softening of the intermolecular interactions, and a constraint that prevents the perturbed molecules from drifting away from each other at the end states. The equivalence and the performance of the methodology against a single-topology approach are demonstrated on a pair of harmonic oscillators, the calculation of the relative solvation free energy of ethane and methanol, and the relative binding free energy of two congeneric inhibitors of cyclooxygenase 2. The stability of two alternative binding modes of an inhibitor of cyclin-dependent kinase 2 is then investigated. Finally, the relative binding free energy of two structurally different inhibitors of cyclin-dependent kinase 2 is calculated. The proposed methodology allows the study of a range of problems that are beyond the reach of traditional relative free energy calculation protocols and should prove useful in drug design studies.

Benchmarking pKa Prediction Methods for Residues in Proteins

Methods for estimation of pKa values of residues in proteins were tested on a set of benchmark proteins with experimentally known pKa values. The benchmark set includes 80 different residues (20 each for Asp, Glu, Lys, and His), half of which consists of significantly variant cases (ΔpKa ≥ 1 pKa unit from the amino acid in solution). The method introduced by Case and co-workers [J. Am. Chem. Soc. 2004, 126, 4167-4180], referred to as the molecular dynamics/generalized-Born/thermodynamic integration (MD/GB/TI) technique, gives a root-mean-square deviation (rmsd) of 1.4 pKa units on the benchmark set. The use of explicit waters in the immediate region surrounding the residue was shown to generally reduce high errors for this method. Longer simulation time was also shown to increase the accuracy of this method. The empirical approach developed by Jensen and co-workers [Proteins 2005, 61, 704-721], PROPKA, also gives an overall rmsd of 1.4 pKa units and is more or less accurate based on residue type-the method does very well for Lys and Glu, but less so for Asp and His. Likewise, the absolute deviation is quite similar for the two methods-5.2 for PROPKA and 5.1 for MD/GB/TI. A comparison of these results with several prediction methods from the literature is presented. The error in pKa prediction is analyzed as a function of variation of the pKa from that in water and the solvent accessible surface area (SASA) of the residue. A case study of the catalytic lysine residue in 2-deoxyribose-5-phosphate aldolase (DERA) is also presented.

Effective Approximation of Molecular Volume Using Atom-Centered Dielectric Functions in Generalized Born Models

The generalized Born (GB) theory is a prime choice for implicit treatment of solvent that provides a favorable balance between efficiency and accuracy for reliable simulation of protein conformational equilibria. In GB, the dielectric boundary is a key physical property that needs to be properly described. While it is widely accepted that the molecular surface (MS) should provide the most physical description, most existing GB models are based on van der Waals (vdW)-like surfaces for computational simplicity and efficiency. A simple and effective approximation to molecular volume is explored here using atom-centered dielectric functions within the context of a generalized Born model with simple switching (GBSW). The new model, termed GBSW/MS2, is as efficient as the original vdW-like-surface-based GBSW model, but is able to reproduce the Born radii calculated from the "exact" Poisson-Boltzmann theory with a correlation of 0.95. More importantly, examination of the potentials of mean force of hydrogen-bonding and charge-charge interactions demonstrates that GBSW/MS2 correctly captures the first desolvation peaks, a key signature of true MS. Physical parameters including atomic input radii and peptide backbone torsion were subsequently optimized on the basis of solvation free energies of model compounds, potentials of mean force of their interactions, and conformational equilibria of a set of helical and β-hairpin model peptides. The resulting GBSW/MS2 protein force field reasonably recapitulates the structures and stabilities of these model peptides. Several remaining limitations and possible future developments are also discussed.

Evaluations of the Absolute and Relative Free Energies for Antidepressant Binding to the Amino Acid Membrane Transporter LeuT with Free Energy Simulations

The binding of ligands to protein receptors with high affinity and specificity is central to many cellular processes. The quest for the development of computational models capable of accurately evaluating binding affinity remains one of the main goals of modern computational biophysics. In this work, free energy perturbation/molecular dynamics simulations were used to evaluate absolute and relative binding affinity for three different antidepressants to a sodium-dependent membrane transporter, LeuT, a bacterial homologue of human serotonin and dopamine transporters. Dysfunction of these membrane transporters in mammals has been implicated in multiple diseases of the nervous system, including bipolar disorder and depression. Furthermore, these proteins are key targets for antidepressants including fluoxetine (aka Prozac) and tricyclic antidepressants known to block transport activity. In addition to being clinically relevant, this system, where multiple crystal structures are readily available, represents an ideal testing ground for methods used to study the molecular mechanisms of ligand binding to membrane proteins. We discuss possible pitfalls and different levels of approximation required to evaluate binding affinity, such as the dependence of the computed affinities on the strength of constraints and the sensitivity of the computed affinities to the particular partial charges derived from restrained electrostatic potential fitting of quantum mechanics electrostatic potential. Finally, we compare the effects of different constraint schemes on the absolute and relative binding affinities obtained from free energy simulations.

Solution Structure of the HIV-1 Intron Splicing Silencer and Its Interactions with the UP1 Domain of Heterogeneous Nuclear Ribonucleoprotein (hnRNP) A1

Splicing patterns in human immunodeficiency virus type 1 (HIV-1) are maintained through cis regulatory elements that recruit antagonistic host RNA-binding proteins. The activity of the 3' acceptor site A7 is tightly regulated through a complex network of an intronic splicing silencer (ISS), a bipartite exonic splicing silencer (ESS3a/b), and an exonic splicing enhancer (ESE3). Because HIV-1 splicing depends on protein-RNA interactions, it is important to know the tertiary structures surrounding the splice sites. Herein, we present the NMR solution structure of the phylogenetically conserved ISS stem loop. ISS adopts a stable structure consisting of conserved UG wobble pairs, a folded 2X2 (GU/UA) internal loop, a UU bulge, and a flexible AGUGA apical loop. Calorimetric and biochemical titrations indicate that the UP1 domain of heterogeneous nuclear ribonucleoprotein A1 binds the ISS apical loop site-specifically and with nanomolar affinity. Collectively, this work provides additional insights into how HIV-1 uses a conserved RNA structure to commandeer a host RNA-binding protein.

Molecular dynamics simulations: advances and applications

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

Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved-up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

Insights into the effects of mutations on Cren7-DNA binding using molecular dynamics simulations and free energy calculations

A novel, highly conserved chromatin protein, Cren7 is involved in regulating essential cellular processes such as transcription, replication and repair. Although mutations in the DNA-binding loop of Cren7 destabilize the structure and reduce DNA-binding activity, the details are not very clear. Focusing on the specific Cren7-dsDNA complex (PDB code ), we applied molecular dynamics (MD) simulations and the molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) free energy calculations to explore the structural and dynamic effects of W26A, L28A, and K53A mutations in comparison to the wild-type protein. The energetic analysis indicated that the intermolecular van der Waals interaction and nonpolar solvation energy play an important role in the binding process of Cren7 and dsDNA. Compared with the wild type Cren7, all the studied mutants W26A, L28A, and K53A have obviously reduced binding free energies with dsDNA in the reduction of the polar and/or nonpolar interactions. These results further elucidated the previous experiments to understand the Cren7-DNA interaction comprehensively. Our work also would provide support for an understanding of the interactions of proteins with nucleic acids.

Parameter optimization in differential geometry based solvation models

Differential geometry (DG) based solvation models are a new class of variational implicit solvent approaches that are able to avoid unphysical solvent-solute boundary definitions and associated geometric singularities, and dynamically couple polar and non-polar interactions in a self-consistent framework. Our earlier study indicates that DG based non-polar solvation model outperforms other methods in non-polar solvation energy predictions. However, the DG based full solvation model has not shown its superiority in solvation analysis, due to its difficulty in parametrization, which must ensure the stability of the solution of strongly coupled nonlinear Laplace-Beltrami and Poisson-Boltzmann equations. In this work, we introduce new parameter learning algorithms based on perturbation and convex optimization theories to stabilize the numerical solution and thus achieve an optimal parametrization of the DG based solvation models. An interesting feature of the present DG based solvation model is that it provides accurate solvation free energy predictions for both polar and non-polar molecules in a unified formulation. Extensive numerical experiment demonstrates that the present DG based solvation model delivers some of the most accurate predictions of the solvation free energies for a large number of molecules.

Applications of MMPBSA to Membrane Proteins I: Efficient Numerical Solutions of Periodic Poisson-Boltzmann Equation

Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membranes into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multigrid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations.

Coarse-grained modeling of DNA oligomer hybridization: length, sequence, and salt effects

A recently published coarse-grained DNA model [D. M. Hinckley, G. S. Freeman, J. K. Whitmer, and J. J. de Pablo, J. Chem. Phys. 139, 144903 (2013)] is used to study the hybridization mechanism of DNA oligomers. Forward flux sampling is used to construct ensembles of reactive trajectories from which the effects of sequence, length, and ionic strength are revealed. Heterogeneous sequences are observed to hybridize via the canonical zippering mechanism. In contrast, homogeneous sequences hybridize through a slithering mechanism, while more complex base pair displacement processes are observed for repetitive sequences. In all cases, the formation of non-native base pairs leads to an increase in the observed hybridization rate constants beyond those observed in sequences where only native base pairs are permitted. The scaling of rate constants with length is captured by extending existing hybridization theories to account for the formation of non-native base pairs. Furthermore, that scaling is found to be similar for oligomeric and polymeric systems, suggesting that similar physics is involved.

Polar Desolvation and Position 226 of Pancreatic and Neutrophil Elastases Are Crucial to their Affinity for the Kunitz-Type Inhibitors ShPI-1 and ShPI-1/K13L

The Kunitz-type protease inhibitor ShPI-1 inhibits human neutrophil elastase (HNE, K_i = 2.35·10⁻⁸ M) but does not interact with the porcine pancreatic elastase (PPE); whereas its P1 site variant, ShPI-1/K13L, inhibits both HNE and PPE (K_i = 1.3·10⁻⁹ M, and K_i = 1.2·10⁻⁸ M, respectively). By employing a combination of molecular modeling tools, e.g., structural alignment, molecular dynamics simulations and Molecular Mechanics Generalized-Born/Poisson-Boltzmann Surface Area free energy calculations, we showed that D226 of HNE plays a critical role in the interaction of this enzyme with ShPI-1 through the formation of a strong salt bridge and hydrogen bonds with K13 at the inhibitor’s P1 site, which compensate the unfavorable polar-desolvation penalty of the latter residue. Conversely, T226 of PPE is unable to establish strong interactions with K13, thereby precluding the insertion of K13 side-chain into the S1 subsite of this enzyme. An alternative conformation of K13 site-chain placed at the entrance of the S1 subsite of PPE, similar to that observed in the crystal structure of ShPI-1 in complex with chymotrypsin (PDB: 3T62), is also unfavorable due to the lack of stabilizing pair-wise interactions. In addition, our results suggest that the higher affinity of ShPI-1/K13L for both elastases mainly arises from the lower polar-desolvation penalty of L13 compared to that of K13, and not from stronger pair-wise interactions of the former residue with those of each enzyme. These results provide insights into the PPE and HNE inhibition and may contribute to the design of more potent and/or specific inhibitors toward one of these proteases.

Examining the assumptions underlying continuum-solvent models

Continuum-solvent models (CSMs) have successfully predicted many quantities, including the solvation-free energies (ΔG) of small molecules, but they have not consistently succeeded at reproducing experimental binding free energies (ΔΔG), especially for protein-protein complexes. Several CSMs break ΔG into the free energy (ΔGvdw) of inserting an uncharged molecule into solution and the free energy (ΔGel) gained from charging. Some further divide ΔGvdw into the free energy (ΔGrep) of inserting a nearly hard cavity into solution and the free energy (ΔGatt) gained from turning on dispersive interactions between the solute and solvent. We show that for 9 protein-protein complexes neither ΔGrep nor ΔGvdw was linear in the solvent-accessible area A, as assumed in many CSMs, and the corresponding components of ΔΔG were not linear in changes in A. We show that linear response theory (LRT) yielded good estimates of ΔGatt and ΔΔGatt, but estimates of ΔΔGatt obtained from either the initial or final configurations of the solvent were not consistent with those from LRT. The LRT estimates of ΔGel differed by more than 100 kcal/mol from the explicit solvent model's (ESM's) predictions, and its estimates of the corresponding component (ΔΔGel) of ΔΔG differed by more than 10 kcal/mol. Finally, the Poisson-Boltzmann equation produced estimates of ΔGel that were correlated with those from the ESM, but its estimates of ΔΔGel were much less so. These findings may help explain why many CSMs have not been consistently successful at predicting ΔΔG for many complexes, including protein-protein complexes.

Protein-Ligand Electrostatic Binding Free Energies from Explicit and Implicit Solvation

Accurate yet efficient computational models of solvent environment are central for most calculations that rely on atomistic modeling, such as prediction of protein-ligand binding affinities. In this study, we evaluate the accuracy of a recently developed generalized Born implicit solvent model, GBNSR6 (Aguilar et al. J. Chem. Theory Comput. 2010, 6, 3613-3639), in estimating the electrostatic solvation free energies (ΔG(pol)) and binding free energies (ΔΔG(pol)) for small protein-ligand complexes. We also compare estimates based on three different explicit solvent models (TIP3P, TIP4PEw, and OPC). The two main findings are as follows. First, the deviation (RMSD = 7.04 kcal/mol) of GBNSR6 binding affinities from commonly used TIP3P reference values is comparable to the deviations between explicit models themselves, e.g. TIP4PEw vs TIP3P (RMSD = 5.30 kcal/mol). A simple uniform adjustment of the atomic radii by a single scaling factor reduces the RMS deviation of GBNSR6 from TIP3P to within the above "error margin" - differences between ΔΔG(pol) estimated by different common explicit solvent models. The simple radii scaling virtually eliminates the systematic deviation (ΔΔG(pol)) between GBNSR6 and two out of the three explicit water models and significantly reduces the deviation from the third explicit model. Second, the differences between electrostatic binding energy estimates from different explicit models is disturbingly large; for example, the deviation between TIP4PEw and TIP3P estimates of ΔΔG(pol) values can be up to ∼50% or ∼9 kcal/mol, which is significantly larger than the "chemical accuracy" goal of ∼1 kcal/mol. The absolute ΔG(pol) calculated with different explicit models could differ by tens of kcal/mol. These discrepancies point to unacceptably high sensitivity of binding affinity estimates to the choice of common explicit water models. The absence of a clear "gold standard" among these models strengthens the case for the use of accurate implicit solvation models for binding energetics, which may be orders of magnitude faster.

Accelerated Molecular Mechanical and Solvation Energetics on Multicore CPUs and Manycore GPUs

MOTIVATION

Despite several reported acceleration successes of programmable GPUs (Graphics Processing Units) for molecular modeling and simulation tools, the general focus has been on fast computation with small molecules. This was primarily due to the limited memory size on the GPU. Moreover simultaneous use of CPU and GPU cores for a single kernel execution - a necessity for achieving high parallelism - has also not been fully considered.

RESULTS

We present fast computation methods for molecular mechanical (Lennard-Jones and Coulombic) and generalized Born solvation energetics which run on commodity multicore CPUs and manycore GPUs. The key idea is to trade off accuracy of pairwise, long-range atomistic energetics for higher speed of execution. A simple yet efficient CUDA kernel for GPU acceleration is presented which ensures high arithmetic intensity and memory efficiency. Our CUDA kernel uses a cache-friendly, recursive and linear-space octree data structure to handle very large molecular structures with up to several million atoms. Based on this CUDA kernel, we present a hybrid method which simultaneously exploits both CPU and GPU cores to provide the best performance based on selected parameters of the approximation scheme. Our CUDA kernels achieve more than two orders of magnitude speedup over serial computation for many of the molecular energetics terms. The hybrid method is shown to be able to achieve the best performance for all values of the approximation parameter.

AVAILABILITY

The source code and binaries are freely available as PMEOPA (Parallel Molecular Energetic using Octree Pairwise Approximation) and downloadable from http://cvcweb.ices.utexas.edu/software.

Exploring biomolecular dynamics and interactions using advanced sampling methods

Molecular dynamics (MD) and Monte Carlo (MC) simulations have emerged as a valuable tool to investigate statistical mechanics and kinetics of biomolecules and synthetic soft matter materials. However, major limitations for routine applications are due to the accuracy of the molecular mechanics force field and due to the maximum simulation time that can be achieved in current simulations studies. For improving the sampling a number of advanced sampling approaches have been designed in recent years. In particular, variants of the parallel tempering replica-exchange methodology are widely used in many simulation studies. Recent methodological advancements and a discussion of specific aims and advantages are given. This includes improved free energy simulation approaches and conformational search applications.

Electrostatics, structure prediction, and the energy landscapes for protein folding and binding

While being long in range and therefore weakly specific, electrostatic interactions are able to modulate the stability and folding landscapes of some proteins. The relevance of electrostatic forces for steering the docking of proteins to each other is widely acknowledged, however, the role of electrostatics in establishing specifically funneled landscapes and their relevance for protein structure prediction are still not clear. By introducing Debye-Hückel potentials that mimic long-range electrostatic forces into the Associative memory, Water mediated, Structure, and Energy Model (AWSEM), a transferable protein model capable of predicting tertiary structures, we assess the effects of electrostatics on the landscapes of thirteen monomeric proteins and four dimers. For the monomers, we find that adding electrostatic interactions does not improve structure prediction. Simulations of ribosomal protein S6 show, however, that folding stability depends monotonically on electrostatic strength. The trend in predicted melting temperatures of the S6 variants agrees with experimental observations. Electrostatic effects can play a range of roles in binding. The binding of the protein complex KIX-pKID is largely assisted by electrostatic interactions, which provide direct charge-charge stabilization of the native state and contribute to the funneling of the binding landscape. In contrast, for several other proteins, including the DNA-binding protein FIS, electrostatics causes frustration in the DNA-binding region, which favors its binding with DNA but not with its protein partner. This study highlights the importance of long-range electrostatics in functional responses to problems where proteins interact with their charged partners, such as DNA, RNA, as well as membranes.

Multibody correlations in the hydrophobic solvation of glycine peptides

Protein collapse during folding is often assumed to be driven by a hydrophobic solvation energy (ΔGvdw) that scales linearly with solvent-accessible surface area (A). In a previous study, we argued that ΔGvdw, as well as its attractive (ΔGatt) and repulsive (ΔGrep) components, was not simply a linear function of A. We found that the surface tensions, γrep, γatt, and γvdw, gotten from ΔGrep, ΔGatt, and ΔGvdw against A for four configurations of deca-alanine differed from those obtained for a set of alkanes. In the present study, we extend our analysis to fifty decaglycine structures and atomic decompositions. We find that different configurations of decaglycine generate different estimates of γrep. Additionally, we considered the reconstruction of the solvation free energy from scaling the free energy of solvation of each atom type, free in solution. The free energy of the isolated atoms, scaled by the inverse surface area the atom would expose in the molecule does not reproduce the γrep for the intact decaglycines. Finally, γatt for the decaglycine conformations is much larger in magnitude than those for deca-alanine or the alkanes, leading to large negative values of γvdw (-74 and -56 cal/mol/Å(2) for CHARMM27 and AMBER ff12sb force fields, respectively). These findings imply that ΔGvdw favors extended rather than compact structures for decaglycine. We find that ΔGrep and ΔGvdw have complicated dependencies on multibody correlations between solute atoms, on the geometry of the molecular surface, and on the chemical identities of the atoms.

A Practical Implicit Membrane Potential for NMR Structure Calculations of Membrane Proteins

The highly anisotropic environment of the lipid bilayer membrane imposes significant constraints on the structures and functions of membrane proteins. However, NMR structure calculations typically use a simple repulsive potential that neglects the effects of solvation and electrostatics, because explicit atomic representation of the solvent and lipid molecules is computationally expensive and impractical for routine NMR-restrained calculations that start from completely extended polypeptide templates. Here, we describe the extension of a previously described implicit solvation potential, eefxPot, to include a membrane model for NMR-restrained calculations of membrane protein structures in XPLOR-NIH. The key components of eefxPot are an energy term for solvation free energy that works together with other nonbonded energy functions, a dedicated force field for conformational and nonbonded protein interaction parameters, and a membrane function that modulates the solvation free energy and dielectric screening as a function of the atomic distance from the membrane center, relative to the membrane thickness. Initial results obtained for membrane proteins with structures determined experimentally in lipid bilayer membranes show that eefxPot affords significant improvements in structural quality, accuracy, and precision. Calculations with eefxPot are straightforward to implement and can be used to both fold and refine structures, as well as to run unrestrained molecular-dynamics simulations. The potential is entirely compatible with the full range of experimental restraints measured by various techniques. Overall, it provides a useful and practical way to calculate membrane protein structures in a physically realistic environment.

The origin of specificity and insight into recognition between an aminoacyl carrier protein and its partner ligase

Acyl carrier proteins (ACPs) are among the most promiscuous proteins in terms of protein-protein interactions and it is quite puzzling how ACPs select the correct partner between many possible upstream and downstream binding proteins. To address this question, we performed molecular dynamics simulations on dimeric Bradyrhizobium japonicum Gly:CP ligase 1 to inspect the origin of its selectivity towards the three types of carrier proteins, namely holoCP, apoCP, and holoCP-Gly, which only differ in the attached prosthetic group. In line with experiments, MM-GBSA analysis revealed that the ligase preferentially binds the holoCP form to both subunits with the binding free energies of -20.7 and -19.1 kcal mol(-1), while the apoCP form, without the prosthetic group, is also recognized, but the binding values of -9.2 and -3.6 kcal mol(-1) suggest that there is no competition for the ligase binding as long as the holoCP is present. After the prosthetic group becomes glycylated, the holoCP-Gly dissociates from the ligase, as supported by its endergonic binding free energies of 2.9 and 20.9 kcal mol(-1). Our results indicate that these affinity differences are influenced by three aspects: the form of the prosthetic group and the specific non-polar hydrophobic interactions, as well as charge complementarity dominantly manifested through Arg220-Glu53 ion pair within the binding region among proteins. A careful examination of the bonding patterns within the ligase active site elucidated the interactions with Arg258, Asp215 and Tyr132 as being predominant in stabilizing the prosthetic group, which are significantly diminished upon glycation, thus promoting complex dissociation.

The systematic approach to describing conformational rearrangements in G-quadruplexes

Conformational changes in DNA G-quadruplex (GQ)-forming regions affect genome function and, thus, compose an interesting research topic. Computer modelling may yield insight into quadruplex folding and rearrangement, particularly molecular dynamics simulations. Here, we show that specific parameters, which are distinct from those commonly used in DNA conformational analyses, must be introduced for adequate interpretation and, most importantly, convenient visual representation of the quadruplex modelling results. We report a set of parameters that comprehensively and systematically describe GQ geometry in dynamics. The parameters include those related to quartet planarity, quadruplex twist, and quartet stacking; they are used to quantitatively characterise various types of quadruplexes and rearrangements, such as quartet distortion/disruption or deviation/bulging of a single nucleotide from the quartet plane. Our approach to describing conformational changes in quadruplexes using the new parameters is exemplified by telomeric quadruplex rearrangement, and the benefits of applying this approach to analyse other structures are discussed.

Base-Displaced Intercalated Conformation of the 2-Amino-3-methylimidazo[4,5-f]quinoline N(2)-dG DNA Adduct Positioned at the Nonreiterated G(1) in the NarI Restriction Site

The conformation of an N²-dG adduct arising from the heterocyclic amine 2-amino-3-methylimidazo[4,5-f]quinoline (IQ), a potent food mutagen, was determined in 5′-d(C¹T²C³X⁴G⁵C⁶G⁷C⁸C⁹A¹⁰T¹¹C¹²)-3′:5′-d(G¹³A¹⁴T¹⁵G¹⁶G¹⁷C¹⁸G¹⁹C²⁰C²¹G²²A²³G²⁴)-3′; X = N²-dG-IQ, in which the modified nucleotide X⁴ corresponds to G¹ in the 5′-d(G¹G²CG³CC)-3′ NarI restriction endonuclease site. Circular dichroism (CD) revealed blue shifts relative to the unmodified duplex, consistent with adduct-induced twisting, and a hypochromic effect for the IQ absorbance in the near UV region. NMR revealed that the N²-dG-IQ adduct adopted a base-displaced intercalated conformation in which the modified guanine remained in the anti conformation about the glycosidic bond, the IQ moiety intercalated into the duplex, and the complementary base C²¹ was displaced into the major groove. The processing of the N²-dG-IQ lesion by hpol η is sequence-dependent; when placed at the reiterated G³ position, but not at the G¹ position, this lesion exhibits a propensity for frameshift replication [Choi, J. Y., et al. (2006) J. Biol. Chem., 281, 25297–25306]. The structure of the N²-dG-IQ adduct at the nonreiterated G¹ position was compared to that of the same adduct placed at the G³ position [Stavros, K. M., et al. (2014) Nucleic Acids Res., 42, 3450–3463]. CD indicted minimal spectral differences between the G¹ vs G³N²-dG-IQ adducts. NMR indicated that the N²-dG-IQ adduct exhibited similar base-displaced intercalated conformations at both the G¹ and G³ positions. This result differed as compared to the corresponding C8-dG-IQ adducts placed at the same positions. The C8-dG-IQ adduct adopted a minor groove conformation when placed at position G¹ but a base-displaced intercalated conformation when placed at position G³ in the NarI sequence. The present studies suggest that differences in lesion bypass by hpol η may be mediated by differences in the 3′-flanking sequences, perhaps modulating the ability to accommodate transient strand slippage intermediates.

On the Possibility of Facilitated Diffusion of Dendrimers Along DNA

We investigate the electrostatics, energetics, and dynamics of dendrimer-DNA interactions that mimic protein-DNA complexes as a means to design facilitated mechanisms by which dendrimers can slide and search DNA for targets. By using all-atom molecular dynamics simulations, we calculated the free energy profiles of dendrimer-binding around the DNA via umbrella sampling. We also calculated electrostatic interaction maps in comparison to proteins, as well as the dynamical changes induced by DNA-dendrimer interactions via NMR-measurable order parameters. Our results show that for dendrimers to go around DNA, there is a free-energy barrier of 8.5 kcal/mol from the DNA major groove to DNA minor groove, with a minimum in the major groove. This barrier height makes it unlikely for an all-amine dendrimer to slide along DNA longitudinally, but following a helical path may be possible along the major groove. Comparison of the nonbonded interaction energy and the interaction free-energy profiles reveal a considerable entropic cost as the dendrimer binds to DNA. This is also supported by the mobility patterns obtained from NMR-measurable order parameter values, which show a decreased mobility of the dendrimer N-H bond vectors in the DNA-binding mode.