Red fluorescent protein DsRed: Parametrization of its chromophore as an amino acid residue for computer modeling in the OPLS-AA force field

Topology of the neutral form of the DsRed fluorescent protein chromophore as a residue of [(4-cis)-2-[(1-cis)-4-amino-4-oxobutanimidoyl]-4-(4-hydroxybenzylidene)-5-oxo-4,5-dihydro-1H-imidazol-1-yl]acetic acid was calculated with OPLS-AA force field. Use of this topology and molecular dynamics simulation allows calculating the parameters of proteins that contain such residue in their polypeptide chains. The chromophore parameters were obtained by ab initio (RHF/6-31G**) quantum chemical calculations applying density functional theory (B3LYP). Using this chromophore, we have calculated the molecular dynamics trajectory of tetrameric fluorescent protein DsRed in solution at 300 K (4 nsec). Correctness of the chromophore parametrization was revealed by comparison of quantitative characteristics of the chromophore structure obtained from the molecular dynamic simulations of DsRed protein with the quantitative characteristics of the chromophore based on the crystallographic X-ray data of fluorescent protein DsRed (PDB ID: 1ZGO, 1G7K, and 1GGX), and also with the quantitative characteristics of the chromophore obtained by quantum chemical calculations. Inclusion of the neutral form of DsRed protein chromophore topology into the OPLS-AA force field yielded the extended force field OPLS-AA/DsRed. This force field can be used for molecular dynamics calculations of proteins containing the DsRed chromophore. The parameter set presented in this study can be applied for similar extension in any other force fields.     

Calculation of binding affinities of HIV-1 RT and β-secretase inhibitors using the linear interaction energy method with explicit and continuum solvation approaches

The linear interaction energy (LIE) approach has been applied to estimate the binding free energies of representative sets of HIV-1 RT and β-Secretase inhibitors, using both molecular dynamics (MD) and tethered energy minimization sampling protocols with the OPLS-AA potential, using a range of solvation methodologies. Generalized Born (GB), ‘shell’ and periodic boundary condition (PBC) solvation were used, the latter with reaction field (RF) electrostatics. Poisson-Boltzmann (PB) and GB continuum electrostatics schemes were applied to the simulation trajectories for each solvation type to estimate the electrostatic ligand-water interaction energy in both the free and bound states. Reasonable agreement of the LIE predictions was obtained with respect to experimental binding free energy estimates for both systems: for instance, ‘PB’ fits on MD trajectories carried out with PBC solvation and RF electrostatics led to models with standard errors of 1.11 and 1.03 kcal mol⁻¹ and coefficients of determination, r ² of 0.76 and 0.75 for the HIV-1 RT and β-Secretase sets. However, it was also found that results from MD sampling using PBC solvation provided only slightly better fits than from simulations using shell or Born solvation or tethered energy minimization sampling. Figure Evolution of the running averages for compound H11 (binding to HIV-1RT) of the bound state ligand-water and ligand-protein interaction energies. The ligand-water electrostatic terms are twice the corresponding GB and PB electrostatic solvation free energies. The ligand-receptor van der Waals and Coulombic interaction energies are also shown, in addition to the ligand-water van der Waals interaction term. The terms were calculated (without application of a cut-off) from a trajectory sampled under PBC solvation with reaction field electrostatics Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Prokaryotic gene finding based on physicochemical characteristics of codons calculated from molecular dynamics simulations

An ab initio model for gene prediction in prokaryotic genomes is proposed based on physicochemical characteristics of codons calculated from molecular dynamics (MD) simulations. The model requires a specification of three calculated quantities for each codon: the double-helical trinucleotide base pairing energy, the base pair stacking energy, and an index of the propensity of a codon for protein-nucleic acid interactions. The base pairing and stacking energies for each codon are obtained from recently reported MD simulations on all unique tetranucleotide steps, and the third parameter is assigned based on the conjugate rule previously proposed to account for the wobble hypothesis with respect to degeneracies in the genetic code. The third interaction propensity parameter values correlate well with ab initio MD calculated solvation energies and flexibility of codon sequences as well as codon usage in genes and amino acid composition frequencies in ∼175,000 protein sequences in the Swissprot database. Assignment of these three parameters for each codon enables the calculation of the magnitude and orientation of a cumulative three-dimensional vector for a DNA sequence of any length in each of the six genomic reading frames. Analysis of 372 genomes comprising ∼350,000 genes shows that the orientations of the gene and nongene vectors are well differentiated and make a clear distinction feasible between genic and nongenic sequences at a level equivalent to or better than currently available knowledge-based models trained on the basis of empirical data, presenting a strong support for the possibility of a unique and useful physicochemical characterization of DNA sequences from codons to genomes.     

Effect of charge redistribution on the binding of DNA nucleotide to carbon nanotube in molecular dynamics

All-atom molecular dynamics (MD) simulations are performed to study the binding of DNA nucleotides with two carbon nanotubes (CNTs) with similar diameters but different chiralities. Two schemes for assigning partial atomic charges (PACs) are adopted: (I) using PACs obtained from isolated DNA nucleotide and CNT optimised in vacuum, and (II) using PACs obtained from optimising nucleotide-CNT hybrid in solution. The former approach is what most MD simulations have used in the study of DNA-CNT hybrids, while in the latter approach, a redistribution of the PACs has occurred upon the hybridisation. Our results show that the charge redistribution has a profound effect on the dynamics of binding. In particular, PACs obtained from (II) lead to more stable binding structures in the MD simulations. The findings suggest that care should be taken in simulating DNA-CNT interactions using the classical force field approach.     

An energetic correlation of ab initio and NMR studies of the 3'-gauche effect in 3'-substituted thymidines

A straightforward correlation of our experimental NMR findings on 3'-substituted thymidine derivatives with that of the ab initio calculations shows that (i) the delta Go298kNRM of N reversible S equilibrium in nucleoside can be predicted from the ab initio calculated delta ES-N obtained from 6-311++G** level of theory; (ii) the substituent-dependent steric and stereoelectronic effects on the bias of the two-state N reversible S equilibrium in nucleosides can also be predicted from the ab initio calculations with sufficiently large basis functions, and (iii) the necessity of mimicking the solvation behaviour of the experimental NMR measurement condition in the ab initio calculations of biomolecules is also emphasized.     

Structural prediction of peptides bound to MHC class I

An ab initio structure prediction approach adapted to the peptide-major histocompatibility complex (MHC) class I system is presented. Based on structure comparisons of a large set of peptide-MHC class I complexes, a molecular dynamics protocol is proposed using simulated annealing (SA) cycles to sample the conformational space of the peptide in its fixed MHC environment. A set of 14 peptide-human leukocyte antigen (HLA) A0201 and 27 peptide-non-HLA A0201 complexes for which X-ray structures are available is used to test the accuracy of the prediction method. For each complex, 1000 peptide conformers are obtained from the SA sampling. A graph theory clustering algorithm based on heavy atom root-mean-square deviation (RMSD) values is applied to the sampled conformers. The clusters are ranked using cluster size, mean effective or conformational free energies, with solvation free energies computed using Generalized Born MV 2 (GB-MV2) and Poisson-Boltzmann (PB) continuum models. The final conformation is chosen as the center of the best-ranked cluster. With conformational free energies, the overall prediction success is 83% using a 1.00 Angstroms crystal RMSD criterion for main-chain atoms, and 76% using a 1.50 Angstroms RMSD criterion for heavy atoms. The prediction success is even higher for the set of 14 peptide-HLA A0201 complexes: 100% of the peptides have main-chain RMSD values < or =1.00 Angstroms and 93% of the peptides have heavy atom RMSD values < or =1.50 Angstroms. This structure prediction method can be applied to complexes of natural or modified antigenic peptides in their MHC environment with the aim to perform rational structure-based optimizations of tumor vaccines.     

Computational studies on carbohydrates: solvation studies on maltose and cyclomaltooligosaccharides (cyclodextrins) using a DFT/ab initio-derived empirical force field, AMB99C

An empirical force field, denoted AMB99C, has been used to study molecular properties of alpha-(1-->4)-linked carbohydrates in solution. AMB99C was parameterized using structural and energetic parameters from density functional ab initio methodology. In this work we examine the solution behavior of the beta anomer of maltose and cyclohexa-, cyclohepta-, and cyclooctaamyloses (alpha-, beta-, and gamma-cyclodextrins or alpha-, beta-, and gamma-CDs, respectively), as well as of two larger (DP 10, epsilon-CD; DP 21) cyclomaltooligosaccharides, CA10 and CA21. Experimental data used for comparison purposes include X-ray structures, small-angle scattering radius of gyration values, NMR nuclear Overhauser enhancements (NOEs), and proton coupling constants. Molecular dynamics simulations were carried out using explicit water molecules (TIP3P) to establish equilibrium populations of conformations in solution, and these results are compared with other calculated values and a variety of experimental parameters, such as average H-1-H-4' distances between the rings in beta-maltose, and the primary hydroxyl groups' conformational populations. Medium-to-large cyclomaltooligosaccharide molecules were studied to test for glucose ring puckering and stability of kinked and 'flipped' conformations. The results of the solvation studies are in excellent agreement with experimental structural parameters.     

A molecular mechanics/continuum reaction field investigation of the interactions between polar amino acid side chains in water and organic solvents

An integrated procedure that computes in a consistent way both the intermolecular interaction energies and the solvation energies is reported. It interfaces the Sum of Interactions Between Fragments Ab initio computed molecular mechanics and the Langlei–Claverie continuum reaction field procedures. These two methodologies formulate the interaction energy as a sum of separate electrostatic, polarization, dispersion, and repulsion terms; the first two are computed with the help of distributed charges, dipoles, and quadrupoles derived from the ab initio SCF or MP2 molecular wave fundctions of individual solutes. This computational procedure will be used to estimate the solvent contribution to the interaction energy between polar amino acids side chains. We will consider, on the one hand, the terminal fragments of the side chains of aspartate and glutamate—namely the acetate anion and its protonated counterpart, acetic acid—and on the other hand, the terminal fragments of the cationic residues lysine, histidinium, and arginine, as represented by methylammonium, imidazolium, and methylguanidinium cations, respectively. The deprotonated counterpart of imidazolium, imidazole, is also investigated. With water as a solvent, and for each of the three anion-cation complexes investigated, the total energy value DE (intermolecular + solvation) of the associated ion pair is only slightly larger (≈ 5 kcal/mol out of ≈ 170) than that of the fully dissociated arrangement and has a virtually flat dependence as a function of intermolecular separation. The associated complex has an enhanced stability in DMSO , a trend accented in chloroform and carbon tetrachloride. In water, the acetic acid–imidazole complex is less than 1 kcal/mol more stable than the dissociated pair. Energy balances, taking into account the experimental values of protonation energies of acetate and imidazole, indicate that the acetate-imidazolium complex is more stable than its nonzwitterionic counterpart, acetic acid-imidazole in water. In carbon tetrachloride, by contrast, the two complexes are of similar stabilities in terms of internal energies. When we consider free instead of internal energies of solvation, the three organic solvents stabilize the complex between the neutral molecules. The investigation of the interaction of two methylguanidiniums in the polar solvents suggests that the solvation energy of a complex, larger than that of the two isolated entities, could be able to overcome their electrostatic repulsion. This results in a small preference in favor of the complex. Implications of the findings of this study, and future prospects of applications to molecular recognition and conformational studies of oligopeptides and possibly proteins, are discussed. © 1995 John Wiley & Sons, Inc.     

Alpha-ketoamides and alpha-ketocarbonyls: conformational analysis and development of all-atom OPLS force field

The molecular structures and barriers for the internal rotation around the OC-CO single bond in four alpha-ketoamides and eight alpha-ketocarbonyls have been determined from the MP3/aug-cc-pVDZ and MP2/aug-cc-pVDZ calculations. Alpha-ketocarbonyls with non-bulky substituents adopt planar conformations with two carbonyl oxygens in s-trans arrangement. The s-cis conformation is significantly less stable due to the electrostatic repulsion between the two carbonyl groups. Primary and secondary alpha-ketoamides are planar when the substituent at the carbonyl carbon is hydrogen or methyl group but tertiary alpha-ketoamides adopt a conformation where the OC-CO unit is significantly bent. Based on current ab initio structural data, a set of OPLS-AA force field parameters has been derived. These parameters can be used for the modeling of a variety of alpha-ketoamide or alpha-ketocarbonyl containing drugs such as novel protease inhibitors or neuroregenerative polyketides.     

Refinement of homology-based protein structures by molecular dynamics simulation techniques

The use of classical molecular dynamics simulations, performed in explicit water, for the refinement of structural models of proteins generated ab initio or based on homology has been investigated. The study involved a test set of 15 proteins that were previously used by Baker and coworkers to assess the efficiency of the ROSETTA method for ab initio protein structure prediction. For each protein, four models generated using the ROSETTA procedure were simulated for periods of between 5 and 400 nsec in explicit solvent, under identical conditions. In addition, the experimentally determined structure and the experimentally derived structure in which the side chains of all residues had been deleted and then regenerated using the WHATIF program were simulated and used as controls. A significant improvement in the deviation of the model structures from the experimentally determined structures was observed in several cases. In addition, it was found that in certain cases in which the experimental structure deviated rapidly from the initial structure in the simulations, indicating internal strain, the structures were more stable after regenerating the side-chain positions. Overall, the results indicate that molecular dynamics simulations on a tens to hundreds of nanoseconds time scale are useful for the refinement of homology or ab initio models of small to medium-size proteins.     

Study of the betulin molecule in a water environment; ab initio and molecular simulation calculations

Ab initio and molecular simulation methods were used in calculations of the neutral individual betulin molecule, and molecular simulations were used to optimize the betulin molecule immersed in various amounts of water. Individual betulin was optimized in different force fields to find the one exhibiting best agreement with ab initio calculations obtained in the Gaussian03 program. Dihedral torsions of active groups of betulin were determined for both procedures, and related calculated structures were compared successfully. The selected force field was used for subsequent optimization of betulin in a water environment, and a conformational search was performed using quench molecular dynamics. The total energies of betulin and its interactions in water bulk were calculated, and the influence of water on betulin structure was investigated.     

Calculation of atom-centered partial charges for heme

Atom-centered partial charges are calculated for the Fe-heme in cytochrome P450cam for use in molecular dynamics simulations of polar substrates bound in the active site of the enzyme. Charges are fit to the electrostatic potential produced by ab initio UHF wavefunctions for an Fe-porphine model. Basis set dependence of these charges is observed using the LANL1DZ, LANL2DZ and augmented 6–31G levels of theory. Upon geometry optimization of the enzyme, these charge sets cause varying degrees of distortion of the porphyrin from its crystallographically observed conformation. Scaling the charges calculated from the augmented 6–31G basis by 75% reduces the heme distortion while preserving reasonable interactions with a polar substrate. A comparison of the calculated charges with other published values is presented.     

QM/MM free energy simulations: recent progress and challenges

Due to the higher computational cost relative to pure molecular mechanical (MM) simulations, hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here, we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chemical reactions, we highlight the value of invoking enhanced sampling technique (e.g. replica-exchange) in umbrella sampling calculations and the value of including collective environmental variables (e.g. hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calculations, especially free energy along the path, to various parameters in the computation. Alchemical free energy simulations with a specific thermodynamic cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyse two different approaches: the QM/MM–MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analysed here, both approaches seem productive although care needs to be exercised when analysing the perturbative corrections.     

Effective energy function for proteins in solution

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.     

Ab initio prediction of the solution structures and populations of a cyclic pentapeptide in DMSO based on an implicit solvation model

Using a recently developed statistical mechanics methodology, the solution structures and populations of the cyclic pentapeptide cyclo(D-Pro(1)-Ala(2)-Ala(3)-Ala(4)-Ala(5)) in DMSO are obtained ab initio, i.e., without using experimental restraints. An important ingredient of this methodology is a novel optimization of implicit solvation parameters, which in our previous publication [Baysal, C.; Meirovitch, H. J Am Chem Soc 1998, 120, 800-812] has been applied to a cyclic hexapeptide in DMSO. The molecule has been described by the simplified energy function E(tot) = E(GRO) + summation operator(k) sigma(k)A(k), where E(GRO) is the GROMOS force-field energy, sigma(k) and A(k) are the atomic solvation parameter (ASP) and the solvent accessible surface area of atom k. This methodology, which relies on an extensive conformational search, Monte Carlo simulations, and free energy calculations, is applied here with E(tot) based on the ASPs derived in our previous work, and for comparison also with E(GRO) alone. For both models, entropy effects are found to be significant. For E(tot), the theoretical values of proton-proton distances and (3)J coupling constants agree very well with the NMR results [Mierke, D. F.; Kurz, M.; Kessler, H. J Am Chem Soc 1994, 116, 1042-1049], while the results for E(GRO) are significantly worse. This suggests that our ASPs might be transferrable to other cyclic peptides in DMSO as well, making our methodology a reliable tool for an ab initio structure prediction; obviously, if necessary, parts of this methodology can also be incorporated in a best-fit analysis where experimental restraints are used.     

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.     

Ab initio conformational maps for disaccharides in gas phase and aqueous solution

Ab initio conformational maps for beta-lactose in both the gas phase and in aqueous solution have been constructed at the HF/6-31G(d,p) level of calculation. The results of the gas-phase ab initio calculations allow us to conclude that a rigid conformational map is able to predict the regions of the minima in the potential energy surface of beta-lactose, in full agreement with those found in the relaxed conformational map. The solvation effects do not give rise to any new local minimum in the potential energy surface of beta-lactose, but just change the relative Boltzmann populations of the conformers found in the gas-phase calculations. The values obtained for heteronuclear spin coupling constant (3J(H,C)), using the seven most stable conformers in solution are in good agreement with the available experimental values. This is a good indication that ab initio rigid conformational maps can be reliably used to sort the most stable conformers of beta-lactose.