Comparison of charge models for fixed-charge force fields: small-molecule hydration free energies in explicit solvent

In molecular simulations with fixed-charge force fields, the choice of partial atomic charges influences numerous computed physical properties, including binding free energies. Many molecular mechanics force fields specify how nonbonded parameters should be determined, but various choices are often available for how these charges are to be determined for arbitrary small molecules. Here, we compute hydration free energies for a set of 44 small, neutral molecules in two different explicit water models (TIP3P and TIP4P-Ew) to examine the influence of charge model on agreement with experiment. Using the AMBER GAFF force field for nonbonded parameters, we test several different methods for obtaining partial atomic charges, including two fast methods exploiting semiempirical quantum calculations and methods deriving charges from the electrostatic potentials computed with several different levels of ab initio quantum calculations with and without a continuum reaction field treatment of solvent. We find that the best charge sets give a root-mean-square error from experiment of roughly 1 kcal/mol. Surprisingly, agreement with experimental hydration free energies does not increase substantially with increasing level of quantum theory, even when the quantum calculations are performed with a reaction field treatment to better model the aqueous phase. We also find that the semiempirical AM1-BCC method for computing charges works almost as well as any of the more computationally expensive ab initio methods and that the root-mean-square error reported here is similar to that for implicit solvent models reported in the literature. Further, we find that the discrepancy with experimental hydration free energies grows substantially with the polarity of the compound, as does its variation across theory levels.     

A protein molecule in an aqueous mixed solvent: fluctuation theory outlook

In the present paper a procedure to calculate the properties of proteins in aqueous mixed solvents, particularly the excesses of the constituents of the mixed solvent near the protein molecule and the preferential binding parameters, is suggested. Expressions for the Kirkwood-Buff integrals in ternary mixtures and for the preferential binding parameter were derived and used to calculate various properties of infinitely dilute proteins in aqueous mixed solvents. The derived expressions and experimental information regarding the partial molar volumes and the preferential binding parameters were used to calculate the excesses (deficits) of water and cosolvent (in comparison with the bulk concentrations of protein-free mixed solvent) in the vicinity of ribonuclease A, ribonuclease T1, and lysozyme molecules. The calculations showed that water was in excess in the vicinity of ribonuclease A for water/glycerol and water/trehalose mixtures, and the cosolvent urea was in excess in the vicinity of ribonuclease T1 and lysozyme. The derivative of the activity coefficient of the protein with respect to the mole fraction of water was also calculated. This derivative was negative for the water/glycerol and water/trehalose mixed solvents and positive for the water/urea mixture. The mixture of lysozyme in the water/urea solvent is of particular interest, because the lysozyme at pH 7.0 is in its native state up to 9.3M urea, while at pH 2.0 it is denaturated between 2.5 and 5M and higher concentrations of urea. Our results demonstrated a striking similarity in the hydration of lysozyme at both pHs. It is worthwhile to note that the excesses of urea were only weakly composition dependent on both cases.     

Free-energy analysis of the electron-density fluctuation in the quantum-mechanical/molecular-mechanical simulation combined with the theory of energy representation

The relationship is investigated for QM/MM (quantum-mechanical/molecular-mechanical) systems between the fluctuations of the electronic state of the QM subsystem and of the solvation effect due to the QM-MM interaction. The free-energy change due to the electron-density fluctuation around its average is highlighted, and is evaluated through an approximate functional formulated in terms of distribution functions of the many-body coupling (pairwise non-additive) part of the QM-MM interaction energy. A set of QM/MM simulations are conducted in MM water solvent for QM water solute in ambient and supercritical conditions and for QM glycine solute in the neutral and zwitterionic forms. The variation of the electronic distortion energy of the QM solute in the course of QM/MM simulation is then shown to be compensated by the corresponding variation of the free energy of solvation. The solvation free energy conditioned by the electronic distortion energy is further analyzed with its components. It is found that the many-body contribution is essentially equal between the free energy and the average sum of solute-solvent interaction energy.     

Direct and high resolution characterization of cytochrome c equilibrium folding

Protein folding has emerged as a central problem in biophysics, and the equilibrium folding mechanism of cytochrome c (cyt c) has served as a model system. Unfortunately, the detailed characterization of both the folding process and of any intermediate that might be populated has been limited by the low structural and/or temporal resolution of the available techniques. Here, we report the use of a recently developed technique to study folding that is based on the site-selective incorporation of carbon-deuterium (C-D) bonds and their characterization by IR spectroscopy. Specifically, we synthesize and characterize the protein with deuterated residues spread throughout four structural motifs: (d3)Leu68 in the 60's helix, (d8)Lys72 and (d8)Lys73 in the 70's helix, (d8)Lys79, (d3)Met80, and (d3)Ala83 in the D-loop, and (d3)Leu94, (d3)Leu98, and (d3)Ala101 in the C-terminal helix. The data reveal correlated behavior of the residues within each structural motif, as well as between the residues of the 60's and C-terminal helices and between residues of the 70's helix and D-loop. Residues of the 70's helix and the D-loop are more stable than those within the 60's and C-terminal helices, although the former are more sensitive to added denaturant. The data also suggest that the hydrophobicity of the heme cofactor plays a central role in folding. These results contrast with those from previous H/D exchange studies and suggest that the low denaturant fluctuations observed in the H/D exchange experiments are not similar to those through which the protein actually unfolds. The inherently fast time scale of IR also allows us to characterize the folding intermediate, long thought to be present, but which has proven difficult to characterize by other techniques.     

Implicit solvent simulations of DNA and DNA-protein complexes: agreement with explicit solvent vs experiment

Molecular dynamics simulations of biomolecules with implicit solvent reduce the computational cost and complexity of such simulations so that longer time scales and larger system sizes can be reached. While implicit solvent simulations of proteins have become well established, the success of implicit solvent in the simulation of nucleic acids has not been fully established to date. Results obtained in this study demonstrate that stable and efficient simulations of DNA and a protein-DNA complex can be achieved with an implicit solvent model based on continuum dielectric electrostatics. Differences in conformational sampling of DNA with two sets of atomic radii that are used to define the dielectric interface between the solute and the continuum dielectric model of the solvent are investigated. Results suggest that depending on the choice of atomic radii agreement is either closer to experimental data or to explicit solvent simulations. Furthermore, partial conformational transitions toward A-DNA conformations when salt is added within the implicit solvent framework are observed.     

Hydrophobic aided replica exchange: an efficient algorithm for protein folding in explicit solvent

A hydrophobic aided replica exchange method (HAREM) is introduced to accelerate the simulation of all-atom protein folding in explicit solvent. This method is based on exaggerating the hydrophobic effect of various protein amino acids in water by attenuating the protein-water attractive interactions (mimicking the Chaperon effect) while leaving other interactions among protein atoms and water molecules unchanged. The method is applied to a small representative protein, the alpha-helix 3K(I), and it is found that the HAREM method successfully folds the protein within 4 ns, while the regular replica exchange method does not fold the same protein within 5 ns, even with many more replicas.     

Probing the hydration of lipid bilayers using a solvent isotope effect on phospholipid mixing

Nearest-neighbor recognition experiments, which have been carried out using exchangeable dimers derived from 1,2-dimyristoyl-sn-glycero-3-phosphoethanolamine, 1,2-distearoyl-sn-glycero-3-phosphoethanolamine,and 1-palmitoyl-2-oleoyl-sn-glycerophosphoethanolamine, indicate that replacement of H2O by D2O can significantly influence phospholipid mixing, but only in bilayers that are saturated and devoid of cholesterol. These findings, together with those of previous electron spin resonance spin-labeling studies,indicate that mammalian membranes, which are rich in cholesterol and unsaturated phospholipids, are ideal hydrophobic barriers.     

A fluctuation theory analysis of the salting-out effect

An analysis of the salting-out, or Sechenow, effect is given in terms of Kirkwood-Buff, or fluctuation, integrals. The analysis is formally exact but cannot easily be applied in its original form. When the solute that is being salted out is sparingly soluble, simplifications arise and the theory can be used to compute one of the Kirkwood-Buff integrals which is otherwise difficult to obtain.     

Steric stabilization of spherical colloidal particles: Implicit and explicit solvent

We present the results of Monte Carlo simulations and density functional theory treatment of interactions between spherical colloidal brushes both in implicit (good) solvent and in an explicit polymeric solution. Overall, theory is seen to be in good agreement with simulations. We find that interactions between hard-sphere particles grafted with hard-sphere chains are always repulsive in implicit solvent. The range and steepness of the repulsive interaction is sensitive to the grafting density and the length of the grafted chains. When the brushes are immersed in an explicit solvent of hard-sphere chains, a weak mid-range attraction arises, provided the length of the free chains exceeds that of the grafted chains.     

Infrared and vibrational CD spectra of partially solvated alpha-helices: DFT-based simulations with explicit solvent

Theoretical simulations are used to investigate the effects of aqueous solvent on the vibrational spectra of model alpha-helices, which are only partly exposed to solvent to mimic alpha-helices in proteins. Infrared absorption (IR) and vibrational circular dichroism (VCD) amide I' spectra for 15-amide alanine alpha-helices are simulated using density functional theory (DFT) calculations combined with the property transfer method. The solvent is modeled by explicit water molecules hydrogen bonded to the solvated amide groups. Simulated spectra for two partially solvated model alpha-helices, one corresponding to a more exposed and the other to a more buried structure, are compared to the fully solvated and unsolvated (gas phase) simulations. The dependence of the amide I spectra on the orientation of the partially solvated helix with respect to the solvent and effects of solvation on the amide I' of 13C isotopically substituted alpha-helices are also investigated. The partial exposure to solvent causes significant broadening of the amide I' bands due to differences in the vibrational frequencies of the explicitly solvated and unsolvated amide groups. The different degree of partial solvation is reflected primarily in the frequency shifts of the unsolvated (buried) amide group vibrations. Depending on which side of the alpha-helix is exposed to solvent, the simulated IR band-shapes exhibit significant changes, from broad and relatively featureless to distinctly split into two maxima. The simulated amide I' VCD band-shapes for the partially solvated alpha-helices parallel the broadening of the IR and exhibit more sign variation, but generally preserve the sign pattern characteristic of the alpha-helical structures and are much less dependent on the alpha-helix orientation with respect to the solvent. The simulated amide I' IR spectra for the model peptides with explicitly hydrogen-bonded water are consistent with the experimental data for small alpha-helical proteins at very low temperatures, but overestimate the effects of solvent on the protein spectra at ambient temperatures, where the peptide-water hydrogen bonds are weakened by thermal motion.     

Communication: Second-order multireference perturbation theory with explicit correlation: CASPT2-F12

An explicitly correlated complete active space second-order perturbation (CASPT2-F12) method is presented which strongly accelerates the convergence of CASPT2 energies and properties with respect to the basis set size. A Slater-type geminal function is employed as a correlation factor to represent the electron-electron cusp of the wave function. The explicitly correlated terms in the wave function are internally contracted. The required density matrix elements and coupling coefficients are the same as in conventional CASPT2, and the additional computational effort for the F12 correction is small. The CASPT2-F12 method is applied to the singlet-triplet splitting of methylene, the dissociation energy of ozone, and low-lying excited states of pyrrole.     

Theoretical analysis on changes in thermodynamic quantities upon protein folding: essential role of hydration

The free energy change associated with the coil-to-native structural transition of protein G in aqueous solution is calculated by using the molecular theory of solvation, also known as the three-dimensional reference interaction site model theory, to uncover the molecular mechanism of protein folding. The free energy is decomposed into the protein intramolecular energy, the hydration energy, and the hydration entropy. The folding is accompanied with a large gain in the protein intramolecular energy. However, it is almost canceled by the correspondingly large loss in the hydration energy due to the dehydration, resulting in the total energy gain about an order of magnitude smaller than might occur in vacuum. The hydration entropy gain is found to be a substantial driving force in protein folding. It is comparable with or even larger than the total energy gain. The total energy gain coupled with the hydration entropy gain is capable of suppressing the conformational entropy loss in the folding. Based on careful analysis of the theoretical results, the authors present a challenging physical picture of protein folding where the overall folding process is driven by the water entropy effect.     

Electrochemistry of cytochrome C in aqueous and mixed solvent solutions: thermodynamics, kinetics, and the effect of solvent dielectric constant

The solvent dielectric constant is considered an important factor in determining the redox potential of the heme-containing protein cytochrome c in solution. In this study, we investigate the electrochemical response of cytochrome c in aqueous/organic solvent mixtures (100% aqueous buffer, 30% acetonitrile, 40% dimethyl sulfoxide, and 50% methanol), reporting the redox potential (E degrees'), enthalpy, and entropy of reduction. The temperature dependence of the solvent dielectric constant (epsilon) was also measured. The results show that epsilon alone cannot regulate the E degrees' of cytochrome c in mixed solvent systems. The implications of the temperature dependence of epsilon on the validity of the thermodynamic data are also discussed. The effect of solvent and temperature on the electron-transfer rate constant, k(s), was determined in each solvent mixture. A substantial increase in the activation energy for electron transfer was observed in 40% DMSO.     

Phase transitions of a single polyelectrolyte in a poor solvent with explicit counterions

Conformational properties of a single flexible polyelectrolyte chain in a poor solvent are studied using constant temperature molecular dynamics simulation. The effects of counterions are explicitly taken in to account. Structural properties of various phases and the transition between these phases are studied by tracking the values of asphericity, radius of gyration, fraction of condensed counterions, number of non-bonded neighbours, and Coulomb interaction energies. From our simulations, we find strong evidence for a first-order phase transition from extended to collapsed phase consistent with earlier theoretical predictions. We also identify a continuous phase transition associated with the condensation of counterions and estimate the critical exponents associated with the transition. Finally, we argue that previous suggestions of existence of an independent intermediate phase between extended and collapsed phases is only a finite size effect.     

Supramolecular complex of cytochrome c with lariat ether: solubilization, redox behavior and catalytic activity of cytochrome c in methanol

A variety of lariat ethers were employed to solubilize water-soluble cytochrome c in methanol, in which alcohol, ether, ester, amine, and amide functionalities were attached as cation-ligating side arms to 18-crown-6, 15-crown-5, and 12-crown-4 rings. Among these lariat ethers, the alcohol-armed 18-crown-6 derivative offered the highest solubilization efficiency for cytochrome c via supramolecular complexation. The resulting cytochrome c-lariat ether complexes were electrochemically and spectroscopically characterized and confirmed to have redox-active heme structures of 6-coordinate low-spin population in methanol. Some of them catalyzed the oxidation of pinacyanol chloride with hydrogen peroxide in methanol and exhibited higher activities than unmodified cytochrome c and its poly(ethylene glycolated) derivative. Since the supramolecular complexation between lariat ether and cytochrome c includes extremely simple procedures, it provides a facile preparation method of effective biocatalysts working in organic solvents from metalloproteins.     

Chemical glycosylation of cytochrome c improves physical and chemical protein stability

Background

Cytochrome c (Cyt c) is an apoptosis-initiating protein when released into the cytoplasm of eukaryotic cells and therefore a possible cancer drug candidate. Although proteins have been increasingly important as pharmaceutical agents, their chemical and physical instability during production, storage, and delivery remains a problem. Chemical glycosylation has been devised as a method to increase protein stability and thus enhance their long-lasting bioavailability.

Results

Three different molecular weight glycans (lactose and two dextrans with 1 kD and 10 kD) were chemically coupled to surface exposed Cyt c lysine (Lys) residues using succinimidyl chemistry via amide bonds. Five neo-glycoconjugates were synthesized, Lac₄-Cyt-c, Lac₉-Cyt-c, Dex₅(10kD)-Cyt-c, Dex₈(10kD)-Cyt-c, and Dex₃(1kD)-Cyt-c. Subsequently, we investigated glycoconjugate structure, activity, and stability. Circular dichroism (CD) spectra demonstrated that Cyt c glycosylation did not cause significant changes to the secondary structure, while high glycosylation levels caused some minor tertiary structure perturbations. Functionality of the Cyt c glycoconjugates was determined by performing cell-free caspase 3 and caspase 9 induction assays and by measuring the peroxidase-like pseudo enzyme activity. The glycoconjugates showed ≥94% residual enzyme activity and 86?±?3 to 95?±?1% relative caspase 3 activation compared to non-modified Cyt c. Caspase 9 activation by the glycoconjugates was with 92?±?7% to 96?±?4% within the error the same as the caspase 3 activation. There were no major changes in Cyt c activity upon glycosylation. Incubation of Dex₃(1 kD)-Cyt c with mercaptoethanol caused significant loss in the tertiary structure and a drop in caspase 3 and 9 activation to only 24?±?8% and 26?±?6%, respectively. This demonstrates that tertiary structure intactness of Cyt c was essential for apoptosis induction. Furthermore, glycosylation protected Cyt c from detrimental effects by some stresses (i.e., elevated temperature and humidity) and from proteolytic degradation. In addition, non-modified Cyt c was more susceptible to denaturation by a water-organic solvent interface than its glycoconjugates, important for the formulation in polymers.

Conclusion

The results demonstrate that chemical glycosylation is a potentially valuable method to increase Cyt c stability during formulation and storage and potentially during its application after administration.

     

Kinetics of ligand binding to membrane receptors from equilibrium fluctuation analysis of single binding events

Equilibrium fluctuation analysis of single binding events has been used to extract binding kinetics of ligand interactions with cell-membrane bound receptors. Time-dependent total internal reflection fluorescence (TIRF) imaging was used to extract residence-time statistics of fluorescently stained liposomes derived directly from cell membranes upon their binding to surface-immobilized antibody fragments. The dissociation rate constants for two pharmaceutical relevant antibodies directed against different B-cell expressed membrane proteins was clearly discriminated, and the affinity of the interaction could be determined by inhibiting the interaction with increasing concentrations of soluble antibodies. The single-molecule sensitivity made the analysis possible without overexpressed membrane proteins, which makes the assay attractive in early drug-screening applications.     

Influence of solvent on conformational equilibrium in phenyl glycidyl ether

The conformational equilibrium in phenyl glycidyl ether in aprotic solvents was studied by the PMR method over a broad range of changes in the values of the dielectric constant. It was shown that the parameters of the multiplet of noncyclic methylene protons in the PMR spectrum of phenyl glycidyl ether are a sensitive indicator of the position of the conformational equilibrium in the glycidyl fragment. The specific interaction of the molecules of aromatic solvents with the epoxide ring has been discovered.Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 21, No. 2, pp. 245–247, March–April, 1985.