Adapting Poisson-Boltzmann to the self-consistent mean field theory: application to protein side-chain modeling

We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ(1) for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains.     

Conformational relaxation and water penetration coupled to ionization of internal groups in proteins

Molecular dynamics simulations were used to examine the effects of ionization of internal groups on the structures of eighteen variants of staphylococcal nuclease (SNase) with internal Lys, Asp, or Glu. In most cases the RMSD values of internal ionizable side chains were larger when the ionizable moieties were charged than when they were neutral. Calculations of solvent-accessible surface area showed that the internal ionizable side chains were buried in the protein interior when they were neutral and moved toward crevices and toward the protein-water interface when they were charged. The only exceptions are Lys-36, Lys-62, and Lys-103, which remained buried even after charging. With the exception of Lys-38, the number of internal water molecules surrounding the ionizable group increased upon charging: the average number of water oxygen atoms within the first hydration shell increased by 1.7 for Lys residues, by 5.2 for Asp residues, and by 3.2 for Glu residues. The polarity of the microenvironment of the ionizable group also increased when the groups were charged: the average number of polar atoms of any kind within the first hydration shell increased by 2.7 for Lys residues, by 4.8 for Asp residues, and by 4.0 for Glu residues. An unexpected correlation was observed between the absolute value of the shifts in pK(a) values measured experimentally, and several parameters of structural relaxation: the net difference in the polarity of the microenvironment of the charged and neutral forms of the ionizable groups, the net difference in hydration of the charged and neutral forms of the ionizable groups, and the difference in RMSD values of the charged and neutral forms of the ionizable groups. The effects of ionization of internal groups on the conformation of the backbone were noticeable but mostly small and localized to the area immediately next to the internal ionizable moiety. Some variants did exhibit local unfolding.     

基于原子表面的蛋白质水合自由能预测模型

提出了一种计算蛋白质水合自由能的简化模型（SAWSA 2）.模型把蛋白质分子中的原子分为20种不同的原子类型,通过每类原子的溶剂可及化表面以及相应的溶剂化参数,就可以得到分子的水合自由能.不同原子类型的溶剂化参数通过110个蛋白质分子水合自由能拟合得到,水合自由能的标准值采用了基于求解Possion-Boltzmann方程（PB）以及分子表面计算（SA） 相结合的方法.采用得到的模型,预测了20个蛋白质分子的水合自由能,预测值的相对值和绝对值都能和PB/SA的计算值很好地吻合,大大优于两种已报导的水合自由能模型.     

Intramolecular quenching of tryptophan phosphorescence in short peptides and proteins

The phosphorescence lifetime (tau) of tryptophan (Trp) residues in proteins in aqueous solutions at ambient temperature can vary several orders of magnitude depending on the flexibility of the local structure and the rate of intramolecular quenching reactions. For a more quantitative interpretation of tau in terms of the local protein structure, knowledge of all potential quenching moieties in proteins and of their reaction rates is required. The quenching effectiveness of each amino acid (X) side chain and of the peptide backbone was investigated by monitoring their intramolecular quenching rate (k(obs)) in tripeptides of the form acetyl-Trp-Gly-X-CONH2 (WGX), where Trp is joined to X by a flexible Gly link. The results indicate that among the various groups present in proteins only the side chains of Cys, His, Tyr and Phe are able to quench Trp phosphorescence at a detectable rate (k(obs) > 40 s(-1)), with the quenching effectiveness for rotationally unrestricted side chains ranking in the order Cys > His+ > Tyr > Phe approximately His. For the aromatic side chains the corresponding contact rate at 20 degrees C is estimated to be between 3-4 x 10(9) s(-1) for Cys (as determined by Lapidus et al.), 0.8-8 x 10(6) s(-1) for His+, 0.37-3.7 x 10(6) s(-1) for Tyr and 0.2-2 x 10(5) s(-1) for Phe and His. In the cases of His and Tyr, k(obs) drops sharply with increasing pH, with midpoint transitions about 1 pH unit above the pKa, indicating that quenching is almost exclusive to the protonated form. From the temperature dependence of the rate, obtained in 50/50 propylene glycol/water between -20 degrees C and 20 degrees C, the reaction is characterized by activation energies of about 5 kcal.M(-1) for His+ and Tyr and 8 kcal.M(-1) for Phe. An analysis of the groups in contact with Trp residues in proteins that exhibit long phosphorescence lifetimes at ambient temperature leads to the conclusion that the contact rate of the peptide group and of the remaining side chains is lower than 0.1 s(-1), showing that these moieties are practically inert with respect to the triplet-state lifetime. It shows further that the immobilization of the aromatic side chains within the globular fold cuts their quenching effectiveness drastically to contact rates < 2 s(-1), a phenomenon attributed to the low probability of forming a stacked exciplex with the indole ring. All evidence suggests that, except in the case of nearby Cys or Trp residues, whose interaction with the triplet state reaches beyond van der Waals contact, the emission of buried Trp residues is unlikely to be quenched by surrounding protein groups.     

Structure Elucidation of Helical Aromatic Foldamer–Protein Complexes with Large Contact Surface Areas

The development of large synthetic ligands could be useful to target the sizeable surface areas involved in protein–protein interactions. Herein, we present long helical aromatic oligoamide foldamers bearing proteinogenic side chains that cover up to 450 Ų of the human carbonic anhydrase II (HCA) surface. The foldamers are composed of aminoquinolinecarboxylic acids bearing proteinogenic side chains and of more flexible aminomethyl-pyridinecarboxylic acids that enhance helix handedness dynamics. Crystal structures of HCA-foldamer complexes were obtained with a 9- and a 14-mer both showing extensive protein–foldamer hydrophobic contacts. In addition, foldamer–foldamer interactions seem to be prevalent in the crystal packing, leading to the peculiar formation of an HCA superhelix wound around a rod of stacked foldamers. Solution studies confirm the positioning of the foldamer at the protein surface as well as a dimerization of the complexes.     

Molecular dynamics study of the solvation of an alpha-helical transmembrane peptide by DMSO

A 10-ns molecular dynamics study of the solvation of a hydrophobic transmembrane helical peptide in dimethyl sulfoxide (DMSO) is presented. The objective is to analyze how this aprotic polar solvent is able to solvate three groups of amino acid residues (i.e., polar, apolar, and charged) that are located in a stable helical region of a transmembrane peptide. The 25-residue peptide (sMTM7) used mimics the cytoplasmic proton hemichannel domain of the seventh transmembrane segment (TM7) from subunit a of H(+)-V-ATPase from Saccharomyces cerevisiae. The three-dimensional structure of peptide sMTM7 in DMSO has been previously solved by NMR spectroscopy. The radial and spatial distributions of the DMSO molecules surrounding the peptide as well as the number of hydrogen bonds between DMSO and the side chains of the amino acid residues involved are extracted from the molecular dynamics simulations. Analysis of the molecular dynamics trajectories shows that the amino acid side chains are fully embedded in DMSO. Polar and positively charged amino acid side chains have dipole-dipole interactions with the oxygen atom of DMSO and form hydrogen bonds. Apolar residues become solvated by DMSO through the formation of a hydrophobic pocket in which the methyl groups of DMSO are pointing toward the hydrophobic side chains of the residues involved. The dual solvation properties of DMSO cause it to be a good membrane-mimicking solvent for transmembrane peptides that do not unfold due to the presence of DMSO.     

Measurement of solvation responses at multiple sites in a globular protein

Proteins respond to electrostatic perturbations through complex reorganizations of their charged and polar groups, as well as those of the surrounding media. These solvation responses occur both in the protein interior and on its surface, though the exact mechanisms of solvation are not well understood, in part because of limited data on the solvation responses for any given protein. Here, we characterize the solvation kinetics at sites throughout the sequence of a small globular protein, the B1 domain of streptococcal protein G (GB1), using the synthetic fluorescent amino acid Aladan. Aladan was incorporated into seven different GB1 sites, and the time-dependent Stokes shift was measured over the femtosecond to nanosecond time scales by fluorescence upconversion and time-correlated single photon counting. The seven sites range from buried within the protein core to fully solvent-exposed on the protein surface, and are located on different protein secondary structures including beta-sheets, helices, and loops. The dynamics in the protein sites were compared against the free fluorophore in buffer. All protein sites exhibited an initial, ultrafast Stokes shift on the subpicosecond time scale similar to that observed for the free fluorophore, but smaller in magnitude. As the probe is moved from the surface to more buried sites, the dynamics of the solvation response become slower, while no clear correlation between dynamics and secondary structure is observed. We suggest that restricted movements of the surrounding protein residues give rise to the observed long time dynamics and that such movements comprise a large portion of the protein's solvation response. The proper treatment of dynamic Stokes shift data when the time scale for solvation is comparable to the fluorescence lifetime is discussed.     

A new method for side-chain conformation prediction using a Hopfield network and reproduced rotamers

We present a new side-chain prediction method based on energy minimization using a Hopfield network, focusing on the buried residues of proteins. In this method, the network is composed of automata assigned to each rotamer to restrict side-chain conformational space. We reproduced a rotamer library that enabled us to more widely cover the space for side-chain conformations than those previously produced. The accuracy of the side-chain modeling was estimated by three standards: root mean square deviations (rmsds) between the modeled and the crystal structures, the percentages of correctly predicted side-chain torsion angles, and the percentages of correctly predicted hydrogen bonds. The average rmsd for buried side chains of 21 proteins was 1.10 Å. The value was almost always improved relative to the previous works. The percentage of side-chain X₁ angles for buried residues was 87.3%. By considering the hydrogen bond energy, the average percentage of correctly predicted hydrogen bonds rose from 33% without hydrogen bond energy to 52% with the bond energy. We applied this method to homology modeling, where the protein backbone used to predict side-chain conformations deviates from the correct conformation, and could predict side-chain conformations as correctly as those using the correct backbones. © 1996 by John Wiley & Sons, Inc.     

How sensitive are nanosecond molecular dynamics simulations of proteins to changes in the force field?

The sensitivity of molecular dynamics simulations to variations in the force field has been examined in relation to a set of 36 structures corresponding to 31 proteins simulated by using different versions of the GROMOS force field. The three parameter sets used (43a1, 53a5, and 53a6) differ significantly in regard to the nonbonded parameters for polar functional groups and their ability to reproduce the correct solvation and partitioning behavior of small molecular analogues of the amino acid side chains. Despite the differences in the force field parameters no major differences could be detected in a wide range of structural properties such as the root-mean-square deviation from the experimental structure, radii of gyration, solvent accessible surface, secondary structure, or hydrogen bond propensities on a 5 to 10 ns time scale. The small differences that were observed correlated primarily with the presence of charged residues as opposed to residues that differed most between the parameter sets. The work highlights the variation that can be observed in nanosecond simulations of protein systems and implications of this for force field validation, as well as for the analysis of protein simulations in general.     

New energy terms for reduced protein models implemented in an off‐lattice force field

Parameterization and test calculations of a reduced protein model with new energy terms are presented. The new energy terms retain the steric properties and the most significant degrees of freedom of protein side chains in an efficient way using only one to three virtual atoms per amino acid residue. The energy terms are implemented in a force field containing predefined secondary structure elements as constraints, electrostatic interaction terms, and a solvent‐accessible surface area term to include the effect of solvation. In the force field the main‐chain peptide units are modeled as electric dipoles, which have constant directions in α‐helices and β‐sheets and variable conformation‐dependent directions in loops. Protein secondary structures can be readily modeled using these dipole terms. Parameters of the force field were derived using a large set of experimental protein structures and refined by minimizing RMS errors between the experimental structures and structures generated using molecular dynamics simulations. The final average RMS error was 3.7 Å for the main‐chain virtual atoms (C_α atoms) and 4.2 Å for all virtual atoms for a test set of 10 proteins with 58–294 amino acid residues. The force field was further tested with a substantially larger test set of 608 proteins yielding somewhat lower accuracy. The fold recognition capabilities of the force field were also evaluated using a set of 27,814 misfolded decoy structures. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1229–1242, 2001     

Packing density and structure effects on energy-transfer dynamics in argon collisions with organic monolayers

A combined experimental and molecular-dynamics simulation study has been used to investigate energy-transfer dynamics of argon atoms when they collide with n-alkanethiols adsorbed to gold and silver substrates. These surfaces provide the opportunity to explore how surface structure and packing density of alkane chains affect energy transfer in gas-surface collisions while maintaining the chemical nature of the surface. The chains pack standing up with 12 degrees and 30 degrees tilt angles relative to the surface normal and number densities of 18.9 and 21.5 A(2)molecule on the silver and gold substrates, respectively. For 7-kJmol argon scattering, the two surfaces behave equivalently, fully thermalizing all impinging argon atoms. In contrast, these self-assembled monolayers (SAMs) are not equally efficient at absorbing the excess translational energy from high-energy, 35 and 80 kJmol, argon collisions. When high-energy argon atoms are scattered from a SAM on silver, the fraction of atoms that reach thermal equilibrium with the surface and the average energy transferred to the surface are lower than for analogous SAMs on gold. In the case of argon atoms with 80 kJmol of translational energy scattering from long-chain SAMs, 60% and 45% of the atoms detected have reached thermal equilibrium with the monolayers on gold and silver surfaces, respectively. The differences in the scattering characteristics are attributed to excitation efficiencies of different types of surface modes. The high packing density of alkyl chains on silver restricts certain low-energy degrees of freedom from absorbing energy as efficiently as the lower-density monolayers. In addition, molecular-dynamics simulations reveal that the extent to which argon penetrates into the monolayer is related to packing density. For argon atoms with 80-kJmol incident energy, we find 16% and 7% of the atoms penetrate below the terminal methyl groups of C(10) SAMs on gold and silver, respectively.     

Importance of chirality and reduced flexibility of protein side chains: a study with square and tetrahedral lattice models

Side chains of amino acid residues are the determining factor that distinguishes proteins from other unstable chain polymers. In simple models they are often represented implicitly (e.g., by spin states) or simplified as one atom. Here we study side chain effects using two-dimensional square lattice and three-dimensional tetrahedral lattice models, with explicitly constructed side chains formed by two atoms of different chirality and flexibility. We distinguish effects due to chirality and effects due to side chain flexibilities, since residues in proteins are L residues, and their side chains adopt different rotameric states. For short chains, we enumerate exhaustively all possible conformations. For long chains, we sample effectively rare events such as compact conformations and obtain complete pictures of ensemble properties of conformations of these models at all compactness region. This is made possible by using sequential Monte Carlo techniques based on chain growth method. Our results show that both chirality and reduced side chain flexibility lower the folding entropy significantly for globally compact conformations, suggesting that they are important properties of residues to ensure fast folding and stable native structure. This corresponds well with our finding that natural amino acid residues have reduced effective flexibility, as evidenced by statistical analysis of rotamer libraries and side chain rotatable bonds. We further develop a method calculating the exact side chain entropy for a given backbone structure. We show that simple rotamer counting underestimates side chain entropy significantly for both extended and near maximally compact conformations. We find that side chain entropy does not always correlate well with main chain packing. With explicit side chains, extended backbones do not have the largest side chain entropy. Among compact backbones with maximum side chain entropy, helical structures emerge as the dominating configurations. Our results suggest that side chain entropy may be an important factor contributing to the formation of alpha helices for compact conformations.     

A DFT/CDM Study of metal-carboxylate interactions in metalloproteins: factors governing the maximum number of metal-bound carboxylates

The number of negatively charged metal-bound Asp/Glu residues determines the net charge of the carboxylate-rich metal-binding site, which has been found to play a role in enhancing the affinity and/or selectivity of a protein cavity for a given metal cofactor. Therefore, it is of interest to know the maximum number of carboxylates that could bind to a given metal (M(q)()(+)) of charge q and the key factors determining this upper limit in protein cavities, which are usually relatively buried. Using density functional theory combined with the continuum dielectric method to compute the H(2)O --> CH(3)COO(-) exchange free energies, the maximum number of carboxylates bound to M(q)()(+) in a relatively buried metal-binding site is found to depend on (i) the metal charge, q, (ii) the carboxylate-binding mode, and (iii) the first-shell carboxylate-second-shell ligand interactions. The maximum number of carboxylates bound to M(q)()(+) in a fully/partially solvent inaccessible protein cavity would not likely exceed q + 2 if (a) the metal-bound Asp/Glu side chains are hydrogen bonded to a Lys/Arg side chain or several peptide backbone amides/Asn/Gln side chains in the metal's second coordination shell or (b) at least one acidic residue binds bidentately, as opposed to monodentately, to the metal cofactor. This number is reduced to q + 1 in the absence of stabilizing interactions from outer-shell ligand(s) and if all the carboxylates are bound monodentately to the metal cofactor in a buried cavity. The computational results are consistent with findings from a PDB survey of uni-, di-, and trivalent metal-binding sites containing Asp/Glu residues.     

On the origin of the thermostabilization of proteins induced by sodium phosphate

The B1 domain of protein L shows a linear rise in thermostability with increasing concentrations of sodium phosphate. Equal behavior is observed for a set of mutant proteins where surface lysines are mutated to noncharged residues, but the mutant's thermostabilities show different sensitivities to phosphate, encoded in the varying slopes observed (mi). The melting temperature in the absence of the cosolute also correlates linearly with mi. The stabilizing effect of the phosphate ion reaches a saturation point, which has been experimentally determined for protein L (1610 mM phosphate). These results indicate that the phosphate-induced stabilization is an inherent property of the protein, encoded in the amino acid sequence. Changes in stability upon mutation are attributed to a redistribution of the overall network of solvated surface charges. Stabilization by phosphate is understood in terms of interactions with the protein surface, reducing the unfavorable contacts between like charges, maximizing the number of accessible conformations of the surface-charged side chains, and optimizing solvation.     

A fast pairwise evaluation of molecular surface area

A fast and general analytical approach was developed for the calculation of the approximate van der Waals and solvent-accessible surface areas. The method is based on three basic ideas: the use of the Lorentz transformation formula, a rigid-geometry approximation, and a single fitting parameter that can be refitted on the fly during a simulation. The Lorentz transformation equation is used for the summation of the areas of an atom buried by its neighboring contacting atoms, and implies that a sum of the buried pairwise areas cannot be larger than the surface area of the isolated spherical atom itself. In a rigid-geometry approximation we numerically calculate and keep constant the surface of each atom buried by the atoms involved in 1-2 and 1-3 interactions. Only the contributions from the nonbonded atoms (1-4 and higher interactions) are considered in terms of the pairwise approximation. The accuracy and speed of the method is competitive with other pairwise algorithms. A major strength of the method is the ease of parametrization.     

Parametric models to compute tryptophan fluorescence wavelengths from classical protein simulations

Fluorescence spectroscopy is an important method to study protein conformational dynamics and solvation structures. Tryptophan (Trp) residues are the most important and practical intrinsic probes for protein fluorescence due to the variability of their fluorescence wavelengths: Trp residues emit in wavelengths ranging from 308 to 360 nm depending on the local molecular environment. Fluorescence involves electronic transitions, thus its computational modeling is a challenging task. We show that it is possible to predict the wavelength of emission of a Trp residue from classical molecular dynamics simulations by computing the solvent‐accessible surface area or the electrostatic interaction between the indole group and the rest of the system. Linear parametric models are obtained to predict the maximum emission wavelengths with standard errors of the order 5 nm. In a set of 19 proteins with emission wavelengths ranging from 308 to 352 nm, the best model predicts the maximum wavelength of emission with a standard error of 4.89 nm and a quadratic Pearson correlation coefficient of 0.81. These models can be used for the interpretation of fluorescence spectra of proteins with multiple Trp residues, or for which local Trp environmental variability exists and can be probed by classical molecular dynamics simulations. © 2018 Wiley Periodicals, Inc.     

Self-assembly of patterned monolayers with nanometer features: molecular selection based on dipole interactions and chain length

Patterned cocrystal monolayers self-assemble on HOPG in contact with solutions containing complementary pairs of 1,5-chain-substituted anthracene derivatives. Monolayer unit cells containing three or four molecules and spanning 9-11 nm are generated. The monolayers consist of alternating aromatic and aliphatic columns. The designs and dimensions of the cocrystal patterns (unit cells) are determined by (i) the preferred packing alignment of identical length side chains, (ii) the selectivity of each side chain for neighboring chains, (iii) the identities of the two side chains on each anthracene, and (iv) the 2D-chirality of 1,5-substituted anthracenes. The aliphatic columns form by interdigitation of identical length side chains arrayed in an antiparallel alignment, with the nth heavy atom of one side chain in registration with the (omega+2-n)th heavy atom of two adjacent chains ((omega <--> 2) packing). Adjacent side chains are attached, alternately, to anthracenes in one of the two flanking aromatic columns. The preference for (omega <--> 2) packing optimizes side-chain van der Waals interactions. The composition and fidelity of patterning in the cocrystal monolayers requires an additional source of "molecular recognition" in addition to side-chain length. Dipolar interactions, both attractive and repulsive, between ether groups in neighboring, (omega <--> 2) packed side chains, constitute a second recognition element needed for cocrystal self-assembly.     

Solvation parameters for amino acids

Atomic radii have been derived for the common amino acid side chains using a solvent interaction potential (SIP) based on quantum mechanically derived charges. Solvation energies calculated using these parameters are compared with those obtained using other sets of radii and charges, and from alternative methods. The differences from the experimental solvation energies for the nonionizable residues are all less than 10 kJ mol⁻¹. The largest error in the solvation energy occurs for acetic acid (−16.0 kJ mol⁻¹). For the charged side chain systems the difference from experiment are all less than 10 kJ mol⁻¹. SIP parameters for the aminoacetaldehyde derivatives of the common amino acids are presented. These are used in the calculation of the relative binding energies of six benzamidine inhibitors with trypsin. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 428–442, 1999     

Complexation of silver(I) with different substituted diaza-18-crown-6 ethers in methanol

A large number of derivatives of the diaza-18-crown-6 ligand have been synthesized and characterized. These derivatives have different alkyl or aryl side arms at the nitrogen donor atoms of the macrocyclic diazacrown ether. In some side chains additional donor atoms are available. These diazacrown ethers are used as ligands for the complexation of Ag^I in MeOH. The complexation reactions have been studied using potentiometric and calorimetric methods. The thermodynamic data show the absence of a lariat effect. The increase of the values of the reaction enthalpies are due only to changes in solvation of the different ligands.     

A comparative theoretical study of dipeptide solvation in water

Molecular dynamics studies have been performed on the zwitterionic form of the dipeptide glycine-alanine in water, with focus on the solvation and electrostatic properties using a range of theoretical methods, from purely classical force fields, through mixed quantum mechanical/molecular mechanical simulations, to fully quantum mechanical Car-Parrinello calculations. The results of these studies show that the solvation pattern is similar for all methods used for most atoms in the dipeptide, but can differ substantially for some groups; namely the carboxy and aminoterminii, and the backbone amid NH group. This might have implications in other theoretical studies of peptides and proteins with charged -NH(3) (+) and -CO(2) (-) side chains solvated in water. Hybrid quantum mechanical/molecular mechanical simulations successfully reproduce the solvation patterns from the fully quantum mechanical simulations (PACS numbers: 87.14.Ee, 87.15.Aa, 87.15.He, 71.15.Pd).