Ab initio folding of helix bundle proteins using molecular dynamics simulations

We have demonstrated that ab initio fast folding simulations at 400 K using a GB implicit solvent model with an all-atom based force field can describe the spontaneous formation of nativelike structures for the 36-residue villin headpiece and the 46-residue fragment B of Staphylococcal protein A. An implicit solvent model combined with high-temperature MD makes it possible to perform direct folding simulations of small- to medium-sized proteins by reducing the computational requirements tremendously. In the early stage of folding of the villin headpiece and protein A, initial hydrophobic collapse and rapid formation of helices were found to play important roles. For protein A, the third helix forms first in the early stage of folding and exhibits higher stability. The free energy profiles calculated from the folding simulations suggested that both of the helix-bundle proteins show a two-state thermodynamic behavior and protein A exhibits rather broad native basins.     

Theoretical study of the enol imine <--> enaminone tautomeric equilibrium in organic solvents

The tautomeric enol imine <--> enaminone (phenol <--> quinone) equilibrium of the 1-hydroxy-2-naphthaldehyde Schiff base (2-phenyliminomethyl-naphthalen-1-ol) was investigated by density functional theory (B3LYP) and ab initio (MP2) methods in the IEF-PCM polarizable continuum dielectric solvent approximation and by a combined ab initio + FEP/MC study by considering an explicit solvent model. Special emphasis was put on the effect of solvation on this equilibrium by using an apolar (CCl4), polar aprotic (CH3CN), and polar protic (CH3OH) solvent. Compared with experimental tautomerization Gibbs free energies, the IEF-PCM/B3LYP calculations apparently overestimate the stability of the quinone form both when the 6-31G(d,p) and the 6-311++G(d,p) basis sets are applied. IEF-PCM/MP2 studies with the above basis sets predict the preference of the aromatic phenol tautomer, in contrast to the experiment in methanol and acetonitrile solvent. Calculation of the total relative free energy as DeltaG(tot) = DeltaE(int)(IEF-PCM/QCISD(T)/6-31G(d)) + DeltaG(solv, FEP/MC) + DeltaG(thermal) provided agreement with the experimental values up to 0.6 kcal/mol in the three solvents, and the predominant tautomer was always correctly predicted. In-solution relevant atomic charges, derived by a fit to the molecular electrostatic potential generated by the IEF-PCM/B3LYP/6-31G(d,p) wave function, show strong dependence on the fitting procedure (CHELPG or RESP) and are fairly insensitive to the chemical nature of the actual solvent. Use of the CHELPG charges in FEP/MC simulations revealed to be superior in comparison with the use of the RESP charge set.     

Probing the planar tetra-, penta-, and hexacoordinate carbon in carbon-boron mixed clusters

The concept of planar hypercoordinate (e.g., penta- and hexacoordinate) carbons is intriguing [Exner, K.; Schleyer, P. v. R. Science 2000, 290, 1937] as it is neither compatible with the standard rule of three-dimensional chemical bonding nor with the maximum tetracoordination. Herein we undertake a comprehensive study of the planar tetra- (ptC), penta- (ppC), and hexacoordinate carbon (phC) by covering the whole family of carbon-boron mixed clusters C(m=1-4)B(n=4-8) and their anions. The potential energy surface of every carbon-boron cluster is sampled by using the basin-hopping global search algorithm coupled with ab initio geometry optimization. A large number of planar tetra-, penta-, and hexacoordinate carbon (local-minimum) structures are obtained. Several structures such as the phC consisting of C2B5, C2B5(-), etc. are reported for the first time. In particular, a ptC corresponding to the global minimum of CB4 is revealed, which appears to be highly stable for future synthesis. The boron-centered isomers are generally the more stable structures for planar multicoordinate carbons (ptC, ppC, and phC). The planar tetra-, penta-, and hexacoordinate boron are the prevalent structural motifs in low-lying isomers of the carbon-boron clusters. However, stability of the ptC and ppC units can be reinforced over the boron-centered isomers by attaching proper hydrocarbon unit -(CH)n- to form the so-called "hyparenes" [Wang, Z. X.; Schleyer, P. v. R. Science 2001, 292, 2465]). A new hyparene molecule is suggested for future synthesis of novel planar hypercoordinate carbon compounds.     

Solvent effects on the optical rotation of (S)-(-)-alpha-methylbenzylamine

The optical rotation of (S)-(-)-alpha-methylbenzylamine at 589 nm has been measured in 39 different solvents at five different concentrations: 0.25, 0.50, 1.00, 2.00, and 3.00 M. A correlation of the intrinsic rotations (i.e., extrapolation of specific rotations to zero concentration) with Kamlet's and Taft's solvent parameters (alpha, beta, and pi) is established. The polarity/polarizability, pi, and solvent acidity, alpha, terms are found to have a greater effect upon the optical rotation than the basicity of the solvent, beta. The specific rotation for (S)-(-)-alpha-methylbenzylamine has been calculated with Gaussian03 using a PCM model (B3LYP aug-cc-pVDZ) for all 39 solvated systems. Comparisons between the experimental and calculated values show the importance of hydrogen bonding on specific rotation.     

Excluded volume effect for large and small solutes in water

The cavitation effect, i.e., the process of the creation of a void of excluded volume in bulk solvent (a cavity), is considered. The cavitation free energy is treated in terms of the information theory (IT) approach [Hummer, G.; Garde, S.; Garcia, A. E.; Paulaitis, M. E.; Pratt, L. R. J. Phys. Chem. B 1998, 102, 10469]. The binomial cell model suggested earlier is applied as the IT default distribution p(m) for the number m of solute (water) particles occupying a cavity of given size and shape. In the present work, this model is extended to cover the entire range of cavity size between small ordinary molecular solutes and bulky biomolecular structures. The resulting distribution consists of two binomial peaks responsible for producing the free energy contributions, which are proportional respectively to the volume and to the surface area of a cavity. The surface peak dominates in the large cavity limit, when the two peaks are well separated. The volume effects become decisive in the opposite limit of small cavities, when the two peaks reduce to a single-peak distribution as considered in our earlier work. With a proper interpolation procedure connecting these two regimes, the MC simulation results for model spherical solutes with radii increasing up to R = 10 A [Huang, D. H.; Geissler, P. L.; Chandler, D. J. Phys. Chem. B 2001, 105, 6704] are well reproduced. The large cavity limit conforms to macroscopic properties of bulk water solvent, such as surface tension, isothermal compressibility and Tolman length. The computations are extended to include nonspherical solutes (hydrocarbons C1-C6).     

The docking of chiral epoxides on the Whelk-O1 stationary phase: a molecular dynamics study

The docking of analytes on the Whelk-O1 chiral stationary phase is explored for two chiral epoxides in a hexane solvent. Density functional theory calculations are employed to develop flexible models for R/S-styrene oxide (phenyl oxirane) and (R,R/S,S)-stilbene oxide (2,3-diphenyl oxirane). Molecular dynamics simulations of the racemates in the presence of the Whelk-O1 chiral stationary phase reveal the distribution of the enantiomers at the interface. The importance of hydrogen bonding and ring-ring interactions is explored along with an examination of the major docking arrangements. The interactions between the Whelk-O1 molecules and the chiral epoxide enantiomers are quite distinct and consistent with the experimental elution orders [S.E. Schaus, B.D. Brandes, J.F. Larrow, M. Tokunage, K.B. Hansen, A.E. Gould, M.E. Furrow, E.N. Jacobsen, J. Am. Chem. Soc. 124 (2001) 1307] and separation factors [W.H. Pirkle, C.J. Welch, Tetrahedron: Asymm. 5 (1994) 777]. The impact of a polar solvent modifier is examined for R/S-styrene oxide where selectivity in 80:20 n-hexane:2-propanol is assessed.     

DFT and AIM study of the protonation of nitrous acid and the pKa of nitrous acidium ion

The gas phase and aqueous thermochemistry, NMR chemical shifts, and the topology of chemical bonding of nitrous acid (HONO) and nitrous acidium ion (H(2)ONO(+)) have been investigated by ab initio methods using density functional theory. By the same methods, the dissociation of H(2)ONO(+) to give the nitrosonium ion (NO(+)) and water has also been investigated. We have used Becke's hybrid functional (B3LYP), and geometry optimizations were performed with the 6-311++G(d,p) basis set. In addition, highly accurate ab initio composite methods (G3 and CBS-Q) were used. Solvation energies were calculated using the conductor-like polarizable continuum model, CPCM, at the B3LYP/6-311++G(d,p) level of theory, with the UAKS cavity model. The pK(a) value of H(2)ONO(+) was calculated using two different schemes: the direct method and the proton exchange method. The calculated pK(a) values at different levels of theory range from -9.4 to -15.6, showing that H(2)ONO(+) is a strong acid (i.e., HONO is only a weak base). The equilibrium constant, K(R), for protonation of nitrous acid followed by dissociation to give NO(+) and H(2)O has also been calculated using the same methodologies. The pK(R) value calculated by the G3 and CBS-QB3 methods is in best (and satisfactory) agreement with experimental results, which allows us to narrow down the likely value of the pK(a) of H(2)ONO(+) to about -10, a value appreciably more acidic than literature values.     

A study for the static properties of symmetric linear multiblock copolymers under poor solvent conditions

We use a standard bead-spring model and molecular dynamics simulations to study the static properties of symmetric linear multiblock copolymer chains and their blocks under poor solvent conditions in a dilute solution from the regime close to theta conditions, where the chains adopt a coil-like formation, to the poorer solvent regime where the chains collapse obtaining a globular formation and phase separation between the blocks occurs. We choose interaction parameters as is done for a standard model, i.e., the Lennard-Jones fluid and we consider symmetric chains, i.e., the multiblock copolymer consists of an even number n of alternating chemically different A and B blocks of the same length N(A) = N(B) = N. We show how usual static properties of the individual blocks and the whole multiblock chain can reflect the phase behavior of such macromolecules. Also, how parameters, such as the number of blocks n can affect properties of the individual blocks, when chains are in a poor solvent for a certain range of n. A detailed discussion of the static properties of these symmetric multiblock copolymers is also given. Our results in combination with recent simulation results on the behavior of multiblock copolymer chains provide a complete picture for the behavior of these macromolecules under poor solvent conditions, at least for this most symmetrical case. Due to the standard choice of our parameters, our system can be used as a benchmark for related models, which aim at capturing the basic aspects of the behavior of various biological systems.     

Understanding the role of stereoelectronic effects in determining collagen stability. 1. A quantum mechanical study of proline, hydroxyproline, and fluoroproline dipeptide analogues in aqueous solution.

The importance of local (intraresidue) effects in determining the stability of the collagen triple helix has been investigated with special reference to the role played by hydroxyproline. To this end the dipeptide analogues of L-proline (ProDA), 4(R)-hydroxy-L-proline (HypDA), and 4(R)-fluoro-L-proline (FlpDA) have been studied by means of quantum mechanical ab initio calculations, taking into account solvent effects by the polarizable continuum model (PCM). Our results confirm that the relative stability of up puckerings of the pyrrolidine ring increases with the electronegativity of the 4(R) substituent (X), whereas down puckerings are favored by 4(S) electronegative substituents. Calculations on model compounds show that this effect is due to the interaction between vicinal C-H bonding and C-X antibonding orbitals. Electronegative substituents on the pyrrolidine ring affect cis-trans isomerism around the peptidic bond, with trans isomers stabilized by 4(R) substituents and cis isomers by 4(S) substituents. Also the hydrogen bonding power of the carbonyl moiety following the pyrrolidine ring is affected by 4(R) substituents, but this effect is tuned by the polarity of the embedding medium. Finally, up puckering favors smaller values of the backbone dihedrals phi and psi. All these results strongly support the proposal that the stability of triple helices containing fluorinated or hydroxylated prolines in Y positions is related to the necessity of having up puckerings in those positions.     

On use of the Amber potential with the Langevin dipole method

Inclusion of solvent effects in biomolecular simulations is most ideally done using explicit methods, as they are able to capture the heterogeneous environment typical of biomolecules and systems involving them (e.g., proteins at solid interfaces). Common explicit methods based on molecular solvent models (e.g., TIP and SPC models) and molecular dynamic or Monte Carlo simulation are computationally expensive and are, therefore, not well-suited to situations where many simulations are required (e.g., in the ab initio structure prediction or design contexts). In such cases, more coarse-grained explicit approaches such as the Langevin dipole (LD) method of Warshel and co-workers are more appropriate. The recent incarnations of the LD method appear to produce good solvation free energy estimates. These incarnations use charges and solute structures obtained from high-level quantum mechanics simulations. As such an approach is clearly not possible for larger solutes or when many structures are to be considered, an alternative must be sought. One possibility is to use structures and charges derived from an existing analytical potential model-we report on such a coupling here with the Amber potential model. The accuracy and computational performance of this hybrid approach, which we term LD-Amber to distinguish it from previous incarnations of the LD method, was assessed by comparing results obtained from the approach with those from experiment and other theoretical methods for the solvation of 18 amino acid analogues and the alanine dipeptide. This comparison shows that the LD-Amber approach can yield results in line with experiment both qualitatively and quantitatively and is as accurate as other explicit methods while being computationally much cheaper.     

Effect of cooperative hydrogen bonding in azo-hydrazone tautomerism of azo dyes

Azo-hydrazone tautomerism in azo dyes has been modeled by using density functional theory (DFT) at the B3LYP/6-31+G(d,p) level of theory. The most stable tautomer was determined both for model compounds and for azo dyes Acid Orange 7 and Solvent Yellow 14. The effects of the sulfonate group substitution and the replacement of the phenyl group with naphthyl on the tautomer stability and on the behavior in solvent have been discussed. Intramolecular hydrogen bond energies have been estimated for the azo and hydrazone tautomers to derive a relationship between the tautomer stability and the hydrogen bond strength. The transition structures for proton transfer displayed resonance assisted strong hydrogen bonding properties within the framework of the electrostatic-covalent hydrogen bond model (ECHBM). Evolution of the intramolecular hydrogen bond with changing structural and environmental factors during the tautomeric conversion process has been studied extensively by means of the atoms-in-molecules (AIM) analysis of the electron density. The bulk solvent effect was examined using the self-consistent reaction field model. Special solute-solvent interactions were further investigated by means of quantum mechanical calculations after defining the first-solvation shell by molecular dynamics simulations. The effect of cooperative hydrogen bonding with solvent molecules on the tautomer stability has been discussed.     

Ion adsorption at the rutile-water interface: linking molecular and macroscopic properties

A comprehensive picture of the interface between aqueous solutions and the (110) surface of rutile (alpha-TiO2) is being developed by combining molecular-scale and macroscopic approaches, including experimental measurements, quantum calculations, molecular simulations, and Gouy-Chapman-Stern models. In situ X-ray reflectivity and X-ray standing-wave measurements are used to define the atomic arrangement of adsorbed ions, the coordination of interfacial water molecules, and substrate surface termination and structure. Ab initio calculations and molecular dynamics simulations, validated through direct comparison with the X-ray results, are used to predict ion distributions not measured experimentally. Potentiometric titration and ion adsorption results for rutile powders having predominant (110) surface expression provide macroscopic constraints of electrical double layer (EDL) properties (e.g., proton release) which are evaluated by comparison with a three-layer EDL model including surface oxygen proton affinities calculated using ab initio bond lengths and partial charges. These results allow a direct correlation of the three-dimensional, crystallographically controlled arrangements of various species (H2O, Na+, Rb+, Ca2+, Sr2+, Zn2+, Y3+, Nd3+) with macroscopic observables (H+ release, metal uptake, zeta potential) and thermodynamic/electrostatic constraints. All cations are found to be adsorbed as "inner sphere" species bonded directly to surface oxygen atoms, while the specific binding geometries and reaction stoichiometries are dependent on ionic radius. Ternary surface complexes of sorbed cations with electrolyte anions are not observed. Finally, surface oxygen proton affinities computed using the MUSIC model are improved by incorporation of ab initio bond lengths and hydrogen bonding information derived from MD simulations. This multitechnique and multiscale approach demonstrates the compatibility of bond-valence models of surface oxygen proton affinities and Stern-based models of the EDL structure, with the actual molecular interfacial distributions observed experimentally, revealing new insight into EDL properties including specific binding sites and hydration states of sorbed ions, interfacial solvent properties (structure, diffusivity, dielectric constant), surface protonation and hydrolysis, and the effect of solution ionic strength.     

Simulations of solvation free energies and solubilities in supercritical solvents

Computer simulations are used to study solvation free energies and solubilities in supercritical solvents. Solvation free energies are calculated using the particle insertion method. The equilibrium solvent configurations required for these calculations are based on molecular dynamics simulations employing model solvent potentials previously tuned to reproduce liquid-vapor coexistence properties of the fluids Xe, C(2)H(6), CO(2), and CHF(3). Solutes are represented by all-atom potentials based on ab initio calculations and the OPLS-AA parameter set. Without any tuning of the intermolecular potentials, such calculations are found to reproduce the solvation free energies of a variety of typical solid solutes with an average accuracy of +/-2 kJmol. Further calculations on simple model solutes are also used to explore general aspects of solvation free energies in supercritical solvents. Comparisons of solutes in Lennard-Jones and hard-sphere representations of Xe show that solvation free energies and thus solubilities are not significantly influenced by solvent density fluctuations near the critical point. The solvation enthalpy and entropy do couple to these fluctuations and diverge similarly to solute partial molar volumes. Solvation free energies are also found to be little affected by the local density augmentation characteristic of the compressible regime. In contrast to solute-solvent interaction energies, which often provide a direct measure of local solvent densities, solvation free energies are remarkably insensitive to the presence of local density augmentation.     

Modeling the polymerization behavior of vegetable‐oil‐derived macromonomers in solution by computer simulation

A computer simulation model was used to study the polymerization behavior of multifunctional, vegetable‐oil‐derived macromonomers. Mixtures of olefins (A) and acrylates (B) were initially randomly dispersed on a cubic lattice of size L³. Interactions between A, B, and the solvent sites were considered with respect to their relative proximity, mobility and some kinetics. The Metropolis algorithm was used to move each functional group (A and B). Stirred and equilibrated samples were prepared before reaction initiation. Reactions between the functional groups were implemented with a bonding probability k_αβ, which was subject to the availability of unsaturated bonds. The conversion factor, that is, the growth of A–B bonds, was analyzed for a range of polymer concentrations (p = 0.2–0.8) with different reaction probabilities (i.e., k_αβ). A stirred (nonequilibrium) sample did not allow sufficient time for the functional groups to arrange according to the interaction parameters. Therefore, the simulations were rerun with equilibrated samples and were found to be consistent with experimental observations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1164–1172, 2004     

Bonding and (hyper)polarizability in the sodium dimer

We report a conventional ab initio and density functional theory study of the polarizability (alpha(alphabeta)/e(2)a(0) (2)E(h) (-1)) and hyperpolarizability (gamma(alphabetagammadelta)/e(4)a(0) (4)E(h) (-3)) of the sodium dimer. A large [18s14p9d2f1g] basis set is thought to yield near-Hartree-Fock values for both properties: alpha=272.28, Deltaalpha=127.22 and gamma=2157.6 x 10(3) at R(e)=3.078 87 A. Electron correlation has a remarkable effect on the Cartesian components of gamma(alphabetagammadelta). Our best value for the mean is gamma=1460.1 x 10(3). The (hyper)polarizability shows very strong bond-length dependence. The effect is drastically different for the longitudinal and transverse components of the hyperpolarizability. The following first derivatives were extracted from high-level coupled cluster calculations: (dalpha/dR)(e)=54.1, (dDeltaalpha/dR)(e)=88.1e(2)a(0)E(h) (-1), and (dgamma/dR)(e)=210 x 10(3)e(4)a(0) (3)E(h) (-3). We associate the (hyper)polarizability to bonding effects between the two sodium atoms by introducing the differential property per atom Q(diff)/2 identical with (Q[Na(2)(X (1)Sigma(g) (+))]/2-Q[Na((2)S)]). The differential (hyper)polarizability per atom is predicted to be strongly negative for the dimer at R(e), as [alpha(Na(2))/2-alpha(Na)]=-33.8 and [gamma(Na(2))/2-gamma(Na)]=-226.3 x 10(3). The properties calculated with the widely used B3LYP and B3PW91 density functional methods differ significantly. The B3PW91 results are in reasonable agreement with the conventional ab initio values. Last, we observe that low-level ab initio and density functional theory methods underestimate the dipole polarizability anisotropy. Experimental data on this important property are highly desirable.     

Solvation of the Whelk-O1 chiral stationary phase: a molecular dynamics study

Density functional theory calculations and molecular dynamics simulations are employed to explore the solvation of the Whelk-O1 chiral stationary phase. First, a semi-flexible representation of the Whelk-O1 selective molecule is extracted from an extensive series of B3LYP/6-311+ G(2d,p) calculations. The resulting model is used to build a chiral surface, including end-caps, for molecular dynamics study of the interface between solvent and Whelk-O1. Three solvent environments in common use for Whelk-O1 HPLC have been examined: a normal-phase solvent of n-hexane/2-propanol; a reversed-phase solvent of water/methanol; and a supercritical solvent of CO(2) and methanol. In each case, we analyze the interface with an emphasis on solvent composition and solvent hydrogen bonding to the Whelk-O1 selector.     

Computational studies on thermodynamic properties, effective diameters, and free volume of argon using an ab initio potential

A quantum mechanical derived ab initio interaction potential for the argon dimer was tested in molecular simulations to reproduce the thermophysical properties of the vapor-liquid phase equilibria using the Gibbs ensemble Monte Carlo simulations as well as the liquid and supercritical equation of state using the NVT Monte Carlo simulations. The ab initio interaction potential was taken from the literature. A recently developed theory [R. Laghaei et al., J. Chem. Phys. 124, 154502 (2006)] was used to compute the effective diameters of argon in fluid phases and the results were subsequently applied in the generic van der Waals theory to compute the free volume of argon. The calculated densities of the coexisting phases, the vapor pressure, and the equation of state show excellent agreement with experimental values. The effective diameters and free volumes of argon are given over a wide range of densities and temperatures. An empirical formula was used to fit the effective diameters as a function of density and temperature. The computed free volume will be used in future investigations to calculate the transport properties of argon.