Modeling of peptides and proteins in a membrane environment: II. Structural and energetic aspects of glycophorin A in a lipid bilayer

The conformational space of a hydrophobic peptide fragment of glycophorin A in a lipid membrane was studied with the Monte Carlo method using the solvation model described in the first communication of this series. The simulation was performed for various starting orientations of the peptide relative the membrane bilayer: outside, inside, partially immersed, and transbilayer. We showed that the membrane substantially stabilizes the α-helical conformation of the central hydrophobic part of the glycophorin A molecule, which for the most part is immersed in the apolar core of the bilayer. For various conformational states, energy values were calculated and the orientations of the peptide relative to the membrane were characterized. Depending on the thickness of the bilayer, either an entirely α-helical conformation in transbilayer orientation or a conformation with a kink in the central part of the helix with theN- andC-termini exposed on one side of the membrane corresponds to the minimal-energy structure. The transmembrane orientation of glycophorin A is energetically advantageous when the membrane thickness is close to the length of its hydrophobic helical portion, which is consistent with the effect ofhydrophobic match observed experimentally. The prospects for further refinement of the model are discussed. For communication I, see [1].     

Estimation of the hydrophobic effect based on the density functional theory

Using the fundamental measure treatment of the density functional theory, we have developed a method to calculate the solvation of hydrophobic solutes. The method allows one to calculate the density profile and the solvation energy for hydrophobic molecules. An additional benefit of the method is the possibility to calculate interaction forces and the mean force potential between hydrophobic nanoparticles. On the basis of the method, the solvation energies for spherical solutes of different sizes from one angstrom up to several nanometers were calculated.     

A hydrophobic similarity analysis of solvation effects on nucleic acid bases

We investigate the changes in the solvation properties of the natural nucleic acid bases due to the formation of the canonical Watson–Crick hydrogen-bonded complexes. To this end, the changes in the free energy of solvation of the bases induced upon hydrogen-bonded dimerization are analyzed by means of the hydrophobic similarity index, which relies on the atomic contributions to the free energy of solvation determined by the partitioning method implemented in the framework of the MST continuum model. Such an index is also used to examine the hydrophobic similarity between the canonical nucleic acid bases and a series of highly apolar analogues, which have been designed as potential candidates to expand the genetic alphabet. The ability of these analogues to be incorporated into modified DNA duplexes can be related to the large reduction in the hydrophilicity of the natural bases upon formation of the canonical hydrogen-bonded dimers. The results illustrate the suitability of the hydrophobic similarity index to rationalize the role played by solvation in molecular recognition. Proceedings of “Modeling Interactions in Biomolecules II”, Prague, September 5th–9th, 2005.     

Picosecond-resolved solvent reorganization and energy transfer in biological and model cavities

Water molecules in hydrophobic biological cleft/cavities are of contemporary interest for the biomolecular structure and molecular recognition of hydrophobic ligands/drugs. Here, we have explored picosecond-resolved solvation dynamics of water molecules and associated polar amino acids in the hydrophobic cleft around Cys-34 position of Endogenous Serum Albumin (ESA). While site selective acrylodan labeling to Cys-34 allows us to probe solvation in the cleft, Förster resonance energy transfer (FRET) from intrinsic fluorescent amino acid Trp 214 to the extrinsic acrylodan probes structural integrity of the protein in our experimental condition. Temperature dependent solvation in the cleft clearly shows that the dynamics follows Arrhenius type behavior up to 60 °C, after which a major structural perturbation of the protein is evident. We have also monitored polarization gated dynamics of the acrylodan probe and FRET from Trp 214 to acrylodan at various temperatures. The dynamical behavior of the immediate environments around the probe acrylodan in the cleft has been compared with a model biomimetic cavity of a reverse micelle (w₀ = 5). Using same fluorescent probe of acrylodan, we have checked the structural integrity of the model cavity at various temperatures using picosecond-resolved FRET from Trp to acrylodan in the cavity. We have also estimated possible distribution of donor-acceptor distances in the protein and reverse micelles. Our studies reveal that the energetics of the water molecules in the biological cleft is comparable to that in the model cavity indicating a transition from bound state to quasibound state, closely consistent with a recent MD simulation study.     

Validation of density functional modeling protocols on experimental bis(μ-oxo)/μ-η<Superscript>2</Superscript>:η<Superscript>2</Superscript>-peroxo dicopper equilibria

The bis(μ-oxo)/μ-η²:η²-peroxo equilibria for seven supported Cu₂O₂ cores were studied with different hybrid and nonhybrid density functional theory models, namely, BLYP, mPWPW, TPSS, TPSSh, B3LYP, mPW1PW, and MPW1K. Supporting ligands 3,3′-iminobis(N,N-dimethylpropylamine), N,N,N′,N′,N″-pentamethyldipropylenetriamine, N-[2-(pyridin-2-yl)ethyl]-N,N,N′-trimethylpropane-1,3-diamine, bis[2-(2-pyridin-2-yl)ethyl]methylamine, bis[2-(4-methoxy-2-pyridin-2-yl)ethyl]methylamine, bis[2-(4-N,N-dimethylamino-2-pyridin-2-yl)ethyl]methylamine, and 1,4,7-triisopropyl-1,4,7-triazacyclononane were chosen on the basis of the availability of experimental data for comparison. Density functionals were examined with respect to their ability accurately to reproduce experimental properties, including, in particular, geometries and relative energies for the bis(μ-oxo) and side-on peroxo forms. While geometries from both hybrid and nonhybrid functionals were in good agreement with experiment, the incorporation of Hartree–Fock (HF) exchange in hybrid density functionals was found to have a large, degrading effect on predicted relative isomer energies. Specifically, hybrid functionals predicted the μ-η²:η²-peroxo isomer to be too stable by roughly 5–10 kcal mol⁻¹ for each 10% of HF exchange incorporated into the model. Continuum solvation calculations predict electrostatic effects to favor bis(μ-oxo) isomers by 1–4 kcal mol⁻¹ depending on ligand size, with larger ligands having smaller differential solvation effects. Analysis of computed molecular partition functions suggests that nonzero measured entropies of isomerization are likely to be primarily associated with interactions between molecular solutes and their first solvation shell. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Estimation of hydrophobic effects using the fundamental measure theory

A method is developed on the basis of the fundamental measure model of the density functional theory for calculating solvation of hydrophobic particles. This method allows one to calculate density and solvation energy profiles for hydrophobic molecules. An additional merit of the method is the possibility to calculate the interaction forces and mean force potential for hydrophobic nanoparticles. Solvation parameters for spherical solutes with sizes from one angstrom to several nanometers have been calculated using this method.     

Density functional study of closed-shell attraction on X(ML)<Subscript>3</Subscript><Superscript>+</Superscript>(<Emphasis Type="Italic">X</Emphasis> = O,S, Se; <Emphasis Type="Italic">M</Emphasis> = Au,Ag, Cu) systems

With the help of quantum mechanical calculations, we have examined the series of central system X(ML)₃ ⁺(X = O, S, Se; M = Au, Ag, Cu). Using a scalar–relativistic density functional approach, we studied the geometry structures, Mulliken populations and charges of the systems. Structure parameters of the experimental systems are reproduced well with Xα method. The metallophilic interaction energy is analyzed and decomposed. For the systems with different central atoms and different metal atoms, the nature of the metallophilic attraction interaction is analyzed.     

Accurate Aqueous Proton Dissociation Constants Calculations for Selected Angiotensin-Converting Enzyme Inhibitors

Abstract

Studies that allow computing values of aqueous proton dissociation constants (pK_a), gas phase proton affinities, and the free energy of solvation have been performed for six members of angiotensin-I-converting enzyme (ACE) inhibitor family (captopril, enalaprilat, imidaprilat, ramiprilat, perindoprilat, and spiraprilat). Density functional theory (DFT) calculations using PBE1PBE functional on optimized molecular geometries have been carried out to investigate the thermodynamics of gas-phase protonation. The conductor-like polarizable continuum model (CPCM) solvation method at various levels of theory was applied to calculate the free energy of solvation for the ACE inhibitors and their respective anions. The CPCM solvation calculations were performed on both gas-phase and solvent-phase optimized structures. The combination of gas-phase and solvation energies according to the thermodynamic cycle enabled us to compute accurate pK_a values for the all studied molecules.     

Structure and electronic absorption spectra of nematogenic alkoxycinnamic acids - a comparative study based on semiempirical and DFT methods

Structure of nematogenic p-n-Alkoxy cinnamic acids (nOCAC) with various alkyl chain carbon atoms (n = 2, 4, 6, 8) has been optimized using density functional B3LYP with 6-31+G (d) basis set using crystallographic geometry as input. Using the optimized geometry, electronic structure of the molecules has been evaluated using the semiempirical methods and DFT calculations. Molecular charge distribution and phase stability of these systems have been analyzed based on Mulliken and L?wdin population analysis. The electronic absorption spectra of nOCAC molecules have been simulated by employing DFT method, semiempirical CNDO/S and INDO/S parameterizations. Two types of calculations have been performed for model systems containing single and double molecules of nOCAC. UV-Visible spectra have been calculated for all single molecules. The UV stability of the molecules has been discussed in light of the electronic transition oscillator strength (f). The dimer complexes of higher homologues (n = 6, 8) have also been reported to enable the comparison between single and double molecules.     

Exhaustive mutagenesis in silico: multicoordinate free energy calculations on proteins and peptides

We have extended and applied a multicoordinate free energy method, chemical Monte Carlo/Molecular Dynamics (CMC/MD), to calculate the relative free energies of different amino acid side-chains. CMC/MD allows the calculation of the relative free energies for many chemical species from a single free energy calculation. We have previously shown its utility in host:guest chemistry (Pitera and Kollman, J Am Chem Soc 1998;120:7557-7567)1 and ligand design (Eriksson et al., J Med Chem 1999;42:868-881)2, and here demonstrate its utility in calculations of amino acid properties and protein stability. We first study the relative solvation free energies of N-methylated and acetylated alanine, valine, and serine amino acids. With careful inclusion of rotameric states, internal energies, and both the solution and vacuum states of the calculation, we calculate relative solvation free energies in good agreement with thermodynamic integration (TI) calculations. Interestingly, we find that a significant amount of the unfavorable solvation of valine seen in prior work (Sun et al., J Am Chem Soc 1992;114:6798-6801)3 is caused by restraining the backbone in an extended conformation. In contrast, the solvation free energy of serine is calculated to be less favorable than expected from experiment, due to the formation of a favorable intramolecular hydrogen bond in the vacuum state. These monomer calculations emphasize the need to accurately consider all significant conformations of flexible molecules in free energy calculations. This development of the CMC/MD method paves the way for computations of protein stability analogous to the biochemical technique of "exhaustive mutagenesis." We have carried out just such a calculation at position 133 of T4 lysozyme, where we use CMC/MD to calculate the relative stability of eight different side-chain mutants in a single free energy calculation. Our T4 calculations show good agreement with the prior free energy calculations of Veenstra et al. (Prot Eng 1997;10:789-807)4 and excellent agreement with the experiments of Mendel et al. (Science 1992;256:1798-1802).     

Modeling of peptides and proteins in a membrane environment: I. A solvation model mimicking a lipid bilayer

A theoretical solvation model of peptides and proteins that mimics the heterogeneous membrane-water system was proposed. Our approach is based on the combined use of atomic parameters of solvation for water and hydrocarbons, which approximates the hydrated polar groups and acyl chains of lipids, respectively. This model was tested in simulations of several peptides: a nonpolar 20-mer polyleucine, a hydrophobic peptide with terminal polar groups, and a strongly amphiphilic peptide. The conformational space of the peptides in the presence of the membrane was studied by the Monte Carlo method. Unlike a polar solvent and vacuum, the membrane-like environment was shown to stabilize the α-helical conformation: low-energy structures have a helicity index of 100% in all cases. At the same time, the energetically most favorable orientations of the peptides relative to the membrane depend on their hydrophobic properties: nonpolar polyleucine is entirely immersed in the bilayer and the hydrophobic peptide with polar groups at the termini adopts a transbilayer orientation, whereas the amphiphilic peptide lies at the interface parallel to the membrane plane. The results of the simulations agree well with the available experimental data for these systems. In the following communications of this series, we plan to describe applications of the solvation model to membrane-bound proteins and peptides with biologically important functional activities.     

Accurate aqueous proton dissociation constants calculations for selected angiotensin-converting enzyme inhibitors

Studies that allow computing values of aqueous proton dissociation constants (pKa), gas phase proton affinities, and the free energy of solvation have been performed for six members of angiotensin-I-converting enzyme (ACE) inhibitor family (captopril, enalaprilat, imidaprilat, ramiprilat, perindoprilat, and spiraprilat). Density functional theory (DFT) calculations using PBE1PBE functional on optimized molecular geometries have been carried out to investigate the thermodynamics of gas-phase protonation. The conductor-like polarizable continuum model (CPCM) solvation method at various levels of theory was applied to calculate the free energy of solvation for the ACE inhibitors and their respective anions. The CPCM solvation calculations were performed on both gas-phase and solvent-phase optimized structures. The combination of gas-phase and solvation energies according to the thermodynamic cycle enabled us to compute accurate pKa values for the all studied molecules.     

Computational study on the difference between the Co–C bond dissociation energy in methylcobalamin and adenosylcobalamin

The bond dissociation energies of the Co–C bonds in the cobalamin cofactors methylcobalamin and adenosylcobalamin were calculated using the hybrid quantum mechanics/molecular mechanics method IMOMM (integrated molecular orbital and molecular mechanics). Calculations were performed on models of differing complexities as well as on the full systems. We investigated the origin of the different experimental values for the Co–C bond dissociation energies in methylcobalamin and adenosylcobalamin, and have provided an explanation for the difficulties encountered when we attempt to reproduce this difference in quantum chemistry. Additional calculations have been performed using the Miertus–Scrocco–Tomasi method in order to estimate the influence of solvent effects on the homolytic Co–C bond cleavage. Introduction of these solvation effects is shown to be necessary for the correct reproduction of experimental trends in bond dissociation energies in solution, which consequently have no direct correlation with dissociation processes in the enzyme.     

Electroweak Parity-Violating Energy Shifts of Amino Acids: The “Conformation Problem”

The preceding paper described our coupled-perturbed Hartree-Fock (CPHF) and density functional theory (DFT) methods of computing the parity-violating energy shift (PVES). This paper addresses the “conformation problem”—the difficulty determining which hand of amino acids in solution is favoured by the weak force due to the difficulty determining the solution conformation. We attempt to resolve this by using the methods of the preceding paper to compute the PVES of solution and gas-phase amino acid structures determined by other groups from high level optimizations that include solvation. We conclude that the conformational hypersensitivity of the PVES still precludes a definite conclusion as to the sign of the PVES of L-alanine in solution, but that there is no problem in the gas phase: the PVES of gas-phase L-alanine is decisively negative. We show that the PVES is very sensitive to certain torsion angles, but is not hypersensitive to bondlengths or bond angles. In determining structures for PVES computations, there is therefore no need for expensive full optimizations: one can just optimize the crucial torsion angles. We present new computations of gas-phase amino acids PVESs, using partial optimizations with small basis sets, and the results agree well with those from higher level techniques. In the following paper we apply these less costly techniques to larger amino acids. The “conformation problem” has led some to dismiss the PVES as the source of life’s handedness, but we believe this is premature: we show here that amino acids are a special case because their favoured conformations are almost achiral.     

Quantum chemical studies of the catalytic mechanism of N-terminal nucleophile hydrolase

Modeling of the catalytic mechanism of penicillin acylase, a member of the N-terminal nucleophile hydrolase superfamily, is for the first time conducted at ab initio quantum chemistry level. The uniqueness of this family of enzymes is that their active site lacks His and Asp (Glu) residues, comprising together with a serine residue the classical catalytic triad. The current investigation confirms that the amino group of the N-terminal serine residue in N-terminal hydrolases is capable of activating its own hydroxyl group. Using the MP2/RHF method with the 6−31+G** basis set, stationary points on the potential energy surface of the considered molecular system were located, corresponding to local minima (complexes of reagents, products, intermediate) and to saddle points (transition states). It turned out that the stage of acyl-serine formation proceeds via two transition states; the first one, which separates reagents from the so-called tetrahedral intermediate, has the highest relative energy (30 kcal/mol). In contrast to recently proposed empiric suggestions, we have found that participation of a bridging water molecule in proton shuttling is not necessary for the catalysis. The quantum chemical calculations showed a crucial role of a specific solvation in decreasing the activation barrier of the reaction by approximately 10 kcal/mol. Published in Russion in Biokhimiya, 2007, Vol. 72, No. 5, pp. 615–621.     

Ion channel gates: comparative analysis of energy barriers

The energetic profile of an ion translated along the axis of an ion channel should reveal whether the structure corresponds to a functionally open or closed state of the channel. In this study, we explore the combined use of Poisson–Boltzmann electrostatic calculations and evaluation of van der Waals interactions between ion and pore to provide an initial appraisal of the gating state of a channel. This approach is exemplified by its application to the bacterial inward rectifier potassium channel KirBac3.1, where it reveals the closed gate to be formed by a ring of leucine (L124) side chains. We have extended this analysis to a comparative survey of gating profiles, including model hydrophobic nanopores, the nicotinic acetylcholine receptor, and a number of potassium channel structures and models. This enables us to identify three gating regimes, and to show the limitation of this computationally inexpensive method. For a (closed) gate radius of 0.4 nm < R < 0.8 nm, a hydrophobic gate may be present. For a gate radius of 0.2 nm < R < 0.4 nm, both electrostatic and van der Waals interactions will contribute to the barrier height. Below R = 0.2 nm, repulsive van der Waals interactions are likely to dominate, resulting in a sterically occluded gate. In general, the method is more useful when the channel is wider; for narrower channels, the flexibility of the protein may allow otherwise-unsurmountable energetic barriers to be overcome.     

Surfactant-induced conformational transition of amyloid β-peptide

Accumulating evidence suggests that Aβ_1–42–membrane interactions may play an important role in the pathogenesis of Alzheimer’s disease. However, the mechanism of this structural transition remains unknown. In this work, we have shown that submicellar concentrations of sodium dodecyl sulfate (SDS) can provide a minimal platform for Aβ_1–42 self-assembly. To further investigate the relation between Aβ_1–42 structure and function, we analyzed peptide conformation and aggregation at various SDS concentrations using circular dichroism (CD), Fourier transform infrared spectroscopy, and gel electrophoresis. These aggregates, as observed via atomic force microscopy, appeared as globular particles in submicellar SDS with diameters of 35–60 nm. Upon sonication, these particles increased in disc diameter to 100 nm. Pyrene I ₃/I ₁ ratios and 1-anilinonaphthalene-8-sulfonic acid binding studies indicated that the peptide interior is more hydrophobic than the SDS micelle interior. We have also used Forster resonance energy transfer between N-terminal labeled pyrene and tyrosine (10) of Aβ_1–42 in various SDS concentrations for conformational analysis. The results demonstrate that SDS at submicellar concentrations accelerates the formation of spherical aggregates, which act as niduses to form large spherical aggregates upon sonication. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Investigating the dielectric effects of channel pore water on the electrostatic barriers of the permeation ion by the finite difference Poisson-Boltzmann method

In this paper, the finite difference Poisson-Boltzmann (FDPB) method with four dielectric constants is developed to study the effect of dielectric saturation on the electrostatic barriers of the permeation ion. In this method, the inner shape of the channel pore is explicitly represented, and the fact that the dielectric constant inside the channel pore is different from that of bulk water is taken into account. A model channel system which is a right-handed twist bundle with four α-helical segments is provided for this study. From the FDPB calculations, it is found that the difference of the ionic electrostatic solvation energy for wider domains depends strongly on the pore radius in the vicinity of the ion when the pore dielectric constant is changed from 78 to 5. However, the electrostatic solvation energy of the permeation ion can not be significantly affected by the dielectric constant in regions with small pore radii. Our results indicate that the local electrostatic interactions inside the ion channel are of major importance for ion electrostatic solvation energies, and the effect of dielectric saturation on the electrostatic barriers is coupled to the interior channel dimensions. Received: 28 January 1997 / Accepted: 24 September 1997     

Quantitative structure activity relationships of some pyridine derivatives as corrosion inhibitors of steel in acidic medium

Quantum chemical calculations using the density functional theory (B3LYP/6-31G* DFT) and semi-empirical AM1 methods were performed on ten pyridine derivatives used as corrosion inhibitors for mild steel in acidic medium to determine the relationship between molecular structure and their inhibition efficiencies. Quantum chemical parameters such as total negative charge (TNC) on the molecule, energy of highest occupied molecular orbital (E _HOMO), energy of lowest unoccupied molecular orbital (E _LUMO) and dipole moment (μ) as well as linear solvation energy terms, molecular volume (Vi) and dipolar-polarization (π*) were correlated to corrosion inhibition efficiency of ten pyridine derivatives. A possible correlation between corrosion inhibition efficiencies and structural properties was searched to reduce the number of compounds to be selected for testing from a library of compounds. It was found that theoretical data support the experimental results. The results were used to predict the corrosion inhibition of 24 related pyridine derivatives.     

Molecular recognition of watson–crick base-pair reversals in triple-helix formation: Use of nonnatural oligonucleotide bases

We report the calculated characteristics of nonnatural triplex-forming oligonucleotide (TFO) bases recognizing base-pair reversals (TA → AT) in a double-helical DNA sequence. Ab initio and molecular mechanics calculations have been carried out to characterize the geometric and energetic consequences at the base-pair reversal sites. We have estimated the free energies of solvation of the natural and proposed bases by solving the linearized Poisson–Boltzmann equation. The calculations indicate that the proposed TFO bases should bind with some specificity to the duplex. Implications of the strategy used in the context of molecular biology is discussed. © 1993 John Wiley & Sons, Inc.