Towards a quantum mechanical force field for carbohydrates: a reparametrized semi-empirical MO approach

Chitosan Polysaccharides from a Polarizable Multiscale Approach

We report simulations of chitosan polysaccharides in the aqueous phase, at infinite dilute conditions and zero ionic strength. Those simulations are performed by means of a polarizable multiscale modeling scheme that relies on a polarizable all atom force field to model solutes and on a polarizable solvent coarse grained approach. Force field parameters are assigned only from quantum chemistry ab initio data. We simulate chitosan monomer units, dimers and 50-long chains. Regarding the 50-long chains we simulate three sets of ten randomly built chain replica at three different pH conditions (corresponding to different chain protonation states, the chain degree of deacetylation is 85%). Our simulations show the persistence length of 50-long chitosan chains at strong acidic conditions (pH <5) to be 24 ± 2 nm (at weak/negligible ionic strength conditions), and to be 1 order of magnitude shorter at usual pH conditions. Our simulation data support the most recent simulation and experimental studies devoted to chitosan polysaccharides in the aqueous phase.

Modeling pyranose ring pucker in carbohydrates using machine learning and semi-empirical quantum chemical methods

Pyranose ring pucker is a key coordinate governing the structure, interactions and reactivity of carbohydrates. We assess the ability of the machine learning potentials, ANI-1ccx and ANI-2x, and the GFN2-xTB semiempirical quantum chemical method, to model ring pucker conformers of five monosaccharides and oxane in the gas phase. Relative to coupled-cluster quantum mechanical calculations, we find that ANI-1ccx most accurately reproduces the ring pucker energy landscape for these molecules, with a correlation coefficient r2 of 0.83. This correlation in relative energies lowers to values of 0.70 for ANI-2x and 0.60 for GFN2-xTB. The ANI-1ccx also provides the most accurate estimate of the energetics of the 4 C1 -to-1 C4 minimum energy pathway for the six molecules. All three models reproduce chair more accurately than non-chair geometries. Analysis of small model molecules suggests that the ANI-1ccx model favors puckers with equatorial hydrogen bonding substituents; that ANI-2x and GFN2-xTB models overstabilize conformers with axially oriented groups; and that the endo-anomeric effect is overestimated by the machine learning models and underestimated via the GFN2-xTB method. While the pucker conformers considered in this study correspond to a gas phase environment, the accuracy and computational efficiency of the ANI-1ccx approach in modeling ring pucker in vacuo provides a promising basis for future evaluation and application to condensed phase environments.

Studies of carbohydrate-carbohydrate-interactions by atomic force microscopy employing functionalized 4-acetylthio-butyl glucopyranosides

By Fischer glycosylation both anomers of 4-chlorobutyl gluco-as well as galactopyranosides were obtained and transformed into the corresponding 4-acetylthio-butyl glycopyranosides. Dependent on the precursors two straightforward routes were followed to obtain the appropriate 3-O-sulfated derivatives. Unsubstituted and sulfated glucopyranosides were attached to gold surfaces a gold tips. Their interactions were studied using atomic force microscopy for simulations of intercellular glycoside-based interactions and discussed in-depth.

Multidimensional Free Energy and Accelerated Quantum Library Methods Provide a Gateway to Glycoenzyme Conformational, Electronic, and Reaction Mechanisms

Enzyme reactions are complex to simulate accurately, and none more so than glycoenzymes (glycosyltransferase and glycosidases). A rigorous sampling of the protein frame and the conformationally plural carbohydrate substrate coupled with an unbiased treatment of the electron dynamics is needed to discover the true reaction landscapes. Here, we demonstrate the effectiveness of two computational methods ported in libraries that we have developed. The first is a flat histogram free energy method called FEARCF capable of multidimensional sampling and rapidly converging to a complete coverage of phase space. The second, the Quantum Supercharger Library (QSL), is a method that accelerates the computation of the ab initio electronic wave function as well as the integral derivatives on graphical processing units (GPUs). These QSL accelerated computations form the core components needed for direct quantum dynamics and QM/MM dynamics when coupled with legacy codes such as GAMESS and NWCHEM, making state of the art hyper-parallel electronic computations in chemistry and chemical biology possible. The combination of QSL (acceleration of ab initio QM computation) and FEARCF (multidimensional hyper-parallel reaction dynamics) makes the simulation of ab initio QM/MM reaction dynamics of enzyme catalysis feasible. Enzymes that process carbohydrates pose an added challenge as their pyranose ring substrates span multidimensional conformational space whose sampling is an intimate function of the catalytic mechanism. Here, we use the pairing of FEARCF and QSL to simulate the catalytic effect of the glycoenzyme β-N-acetylglucosamine transferase (OGT). The reaction mechanism is discovered from a variable three bond reaction surface using SCCDFTB. The role of the OGT in distorting the pyranose ring of β-N-acetylglucosamine (GlcNAc) away from the equilibrium 4C1 chair conformation toward the E3 envelope needed for the transition state is discovered from its pucker free energy hypersurfaces (or free energy volume, FEV). A complete GlcNAc ring pucker HF 6-31g FEV is constructed from ab initio QM dynamics in vacuum and ab initio QM/MM dynamics in the OGT catalytic domain. The OGT is shown to clearly lower the pathway toward the transition state E3 ring conformer as well as stabilize it by 1.63 kcal/mol. Illustrated here is the use of QSL accelerated ab initio QM/MM dynamics that thoroughly explores carbohydrate catalyzed reactions through a FEARCF multidimensional sampling of the interdependence between reaction and conformational space. This demonstrates how experimentally inaccessible molecular and electronic mechanisms that underpin enzyme catalysis can be discovered by directly modeling the dynamics of these complex reactions.

Assessing the Performance of MM/PBSA, MM/GBSA, and QM-MM/GBSA Approaches on Protein/Carbohydrate Complexes: Effect of Implicit Solvent Models, QM Methods, and Entropic Contributions

Rapid and accurate binding affinity prediction of protein-carbohydrate complexes is a major challenge in glycomimetics design. Among the existing computational techniques, end-point methods have received considerable interest because of their low computational cost. However, significant obstacles remain when such methods are applied to protein-glycan complexes. This article reports the performance of end-point free-energy calculation methods: molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA), MM/generalized Born surface area (MM/GBSA), and quantum mechanics-MM/GBSA (QM-MM/GBSA) on monosaccharides bound to RSL lectin from Ralstonia solanacearum. A careful investigation of the molecular dynamics simulation length, van der Waals radii sets, GB models, QM Hamiltonians, and entropic compensation has been made, and the results are compared with the experimental binding free energies from isothermal titration calorimetry/surface plasmon resonance measurements. The binding free energies using implicit solvent methods are found to be sensitive to the simulation length, radii set, GB model, and QM Hamiltonian. A simulation length of 10 ns using the radii set mbondi provides the best agreement with the experimental values ( r² = 0.96) by MM/PBSA. The GB^HCT model is in accord with the experimental values in MM/GBSA ( r² = 0.91) or in combination with parameterized model number 6 (PM6) ( r² = 0.98) in QM-MM/GBSA. Out of 12 QM Hamiltonians tested, PM6, density functional theory-based tight binding (DFTB), and their variants proved to be more efficient than other semiempirical methods. These methods perform equally well in predicting both absolute and relative binding free energies.

Multiscale modeling of glycosaminoglycan structure and dynamics: current methods and challenges

Glycosaminoglycans are long unbranched and complex polysaccharides that are an essential component of mammalian extracellular matrices. Characterization of their molecular structure, dynamics and interactions are essential to understand important biological phenomena in health and disease, and will lead to novel therapeutics and medical devices. However, this has proven to be a challenge experimentally and theoretical techniques are needed to develop new hypotheses, and interpret experiments. This review aims to examine the current theoretical (rather than experimental) methods used by researchers to investigate glycosaminoglycan structure, dynamics and interactions, from the monosaccharide to the macromolecular scale. It will consider techniques such as quantum mechanics, molecular mechanics, molecular dynamics, coarse graining and docking.

Approximate quantum chemical methods for modelling carbohydrate conformation and aromatic interactions: β-cyclodextrin and its adsorption on a single-layer graphene sheet

Adsorption of carbohydrates on graphene has the potential to improve graphene dispersibility in water. Here we assess the ability of DFTB-based and NDDO-based quantum chemical methods to model β-cyclodextrin conformations and interactions with graphene.

Different QM/MM Approaches To Elucidate Enzymatic Reactions: Case Study on ppGalNAcT2

Hybrid QM/MM computational studies can provide invaluable insight into the mechanisms of enzymatic reactions that can be exploited for rational drug design. Various approaches are available for such studies. However, their strengths and weaknesses may not be immediately apparent. Using the retaining glycosyltransferase ppGalNAcT2 as a case study, we compare different methodologies used to obtain reaction paths and transition state information. Ab Initio MD using CPMD coupled with the String Method is used to derive the minimum free energy reaction path. The geometrical features of the free energy path, especially around the transition state, agree with the minimum potential energy path obtained by the much less computationally expensive Nudged Elastic Band method. The barrier energy, however, differs by 8 kcal/mol. The free energy surface generated by metadynamics provides a rough overview of the reaction and can confirm the physical relevance of optimized paths or provide an initial guess for path optimization methods. Calculations of enzymatic reactions are usually performed at best at the DFT level of theory. A comparison of widely used functionals with high-level DLPNO-CCSD(T)/CBS data on the potential energy profile serves as a validation of the usability of DFT for this type of enzymatic reaction. The M06-2X meta-hybrid functional in particular matches the DLPNO-CCSD(T)/CBS reference extremely well with errors within 1 kcal/mol. However, even pure-GGA functional OPBE provides sufficient accuracy for this type of study.

Improved Sugar Puckering Profiles for Nicotinamide Ribonucleoside for Hybrid QM/MM Simulations

The coenzyme nicotinamide adenine dinucleotide (NAD⁺) and its reduced form (NADH) play ubiquitous roles as oxidizing and reducing agents in nature. The binding, and possibly the chemical redox step, of NAD⁺/NADH may be influenced by the cofactor conformational distribution and, in particular, by the ribose puckering of its nicotinamide-ribonucleoside (NR) moiety. In many hybrid quantum mechanics-molecular mechanics (QM/MM) studies of NAD⁺/NADH dependent enzymes, the QM region is treated by semiempirical (SE) methods. Recent work suggests that SE methods do not adequately describe the ring puckering in sugar molecules. In the present work we adopt an efficient and practical strategy to correct for this deficiency for NAD⁺/NADH. We have implemented a cost-effective correction to a SE Hamiltonian by adding a correction potential, which is defined as the difference between an accurate benchmark density functional theory (DFT) potential energy surface (PES) and the SE PES. In practice, this is implemented via a B-spline interpolation scheme for the grid-based potential energy difference surface. We find that the puckering population distributions obtained from free energy QM(SE)/MM simulations are in good agreement with DFT and in fair accord with experimental results. The corrected PES should facilitate a more accurate description of the ribose puckering in the NAD⁺/NADH cofactor in simulations of biological systems.

Semiempirical Quantum Mechanical Methods for Noncovalent Interactions for Chemical and Biochemical Applications

Semiempirical (SE) methods can be derived from either Hartree-Fock or density functional theory by applying systematic approximations, leading to efficient computational schemes that are several orders of magnitude faster than ab initio calculations. Such numerical efficiency, in combination with modern computational facilities and linear scaling algorithms, allows application of SE methods to very large molecular systems with extensive conformational sampling. To reliably model the structure, dynamics, and reactivity of biological and other soft matter systems, however, good accuracy for the description of noncovalent interactions is required. In this review, we analyze popular SE approaches in terms of their ability to model noncovalent interactions, especially in the context of describing biomolecules, water solution, and organic materials. We discuss the most significant errors and proposed correction schemes, and we review their performance using standard test sets of molecular systems for quantum chemical methods and several recent applications. The general goal is to highlight both the value and limitations of SE methods and stimulate further developments that allow them to effectively complement ab initio methods in the analysis of complex molecular systems.

Improved Hydrogen Bonding at the NDDO-Type Semiempirical Quantum Mechanical/Molecular Mechanical Interface

A semiempirical quantum mechanical (QM)/molecular mechanical (MM) potential with reformulated QM core-MM charge interactions is introduced, specifically to more accurately model hydrogen bonding at the QM/MM interface. Application of this potential using the PM3 Hamiltonian shows improved prediction of geometry and interaction energy for hydrogen bonded small molecule complexes typical of biomolecular interactions, without significantly impacting the modeling of other interaction types. Using this potential, more quantitative prediction of interaction energies is also found at a protein-ligand interface.

Carbohydrate-protein interactions: molecular modeling insights

The article reviews the significant contributions to, and the present status of, applications of computational methods for the characterization and prediction of protein-carbohydrate interactions. After a presentation of the specific features of carbohydrate modeling, along with a brief description of the experimental data and general features of carbohydrate-protein interactions, the survey provides a thorough coverage of the available computational methods and tools. At the quantum-mechanical level, the use of both molecular orbitals and density-functional theory is critically assessed. These are followed by a presentation and critical evaluation of the applications of semiempirical and empirical methods: QM/MM, molecular dynamics, free-energy calculations, metadynamics, molecular robotics, and others. The usefulness of molecular docking in structural glycobiology is evaluated by considering recent docking- validation studies on a range of protein targets. The range of applications of these theoretical methods provides insights into the structural, energetic, and mechanistic facets that occur in the course of the recognition processes. Selected examples are provided to exemplify the usefulness and the present limitations of these computational methods in their ability to assist in elucidation of the structural basis underlying the diverse function and biological roles of carbohydrates in their dialogue with proteins. These test cases cover the field of both carbohydrate biosynthesis and glycosyltransferases, as well as glycoside hydrolases. The phenomenon of (macro)molecular recognition is illustrated for the interactions of carbohydrates with such proteins as lectins, monoclonal antibodies, GAG-binding proteins, porins, and viruses.

Water interactions with hydrophobic groups: assessment and recalibration of semiempirical molecular orbital methods

In this work, we present a study of the ability of different semiempirical methods to describe intermolecular interactions in water solution. In particular, we focus on methods based on the Neglect of Diatomic Differential Overlap approximation. Significant improvements of these methods have been reported in the literature in the past years regarding the description of non-covalent interactions. In particular, a broad range of methodologies has been developed to deal with the properties of hydrogen-bonded systems, with varying degrees of success. In contrast, the interactions between water and a molecule containing hydrophobic groups have been little analyzed. Indeed, by considering the potential energy surfaces obtained using different semiempirical Hamiltonians for the intermolecular interactions of model systems, we found that none of the available methods provides an entirely satisfactory description of both hydrophobic and hydrophilic interactions in water. In addition, a vibrational analysis carried out in a model system for these interactions, a methane clathrate cluster, showed that some recent methods cannot be used to carry out studies of vibrational properties. Following a procedure established in our group [M. I. Bernal-Uruchurtu, M. T. C. Martins-Costa, C. Millot, and M. F. Ruiz-López, J. Comput. Chem. 21, 572 (2000); W. Harb, M. I. Bernal-Uruchurtu, and M. F. Ruiz-López, Theor. Chem. Acc. 112, 204 (2004)], we developed new parameters for the core-core interaction terms based on fitting potential energy curves obtained at the MP2 level for our model system. We investigated the transferability of the new parameters to describe a system, having both hydrophilic and hydrophobic groups, interacting with water. We found that only by introducing two different sets of parameters for hydrophilic and hydrophobic hydrogen atom types we are able to match the features of the ab initio calculated properties. Once this assumption is made, a good agreement with the MP2 reference is achieved. The results reported in this work provide therefore a direction for future developments of semiempirical approaches that are still required to investigate chemical processes in biomolecules and in large disordered systems.

AM1/d-CB1: A Semiempirical Model for QM/MM Simulations of Chemical Glycobiology Systems

A semiempirical method based on the AM1/d Hamiltonian is introduced to model chemical glycobiological systems. We included in the parameter training set glycans and the chemical environment often found about them in glycoenzymes. Starting with RM1 and AM1/d-PhoT models we optimized H, C, N, O, and P atomic parameters targeting the best performing molecular properties that contribute to enzyme catalyzed glycan reaction mechanisms. The training set comprising glycans, amino acids, phosphates and small organic model systems was used to derive parameters that reproduce experimental data or high-level density functional results for carbohydrate, phosphate and amino acid heats of formation, amino acid proton affinities, amino acid and monosaccharide dipole moments, amino acid ionization potentials, water-phosphate interaction energies, and carbohydrate ring pucker relaxation times. The result is the AM1/d-Chemical Biology 1 or AM1/d-CB1 model that is considerably more accurate than existing NDDO methods modeling carbohydrates and the amino acids often present in the catalytic domains of glycoenzymes as well as the binding sites of lectins. Moreover, AM1/d-CB1 computed proton affinities, dipole moments, ionization potentials and heats of formation for transition state puckered carbohydrate ring conformations, observed along glycoenzyme catalyzed reaction paths, are close to values computed using DFT M06-2X. AM1/d-CB1 provides a platform from which to accurately model reactions important in chemical glycobiology.

QM/MM investigations of organic chemistry oriented questions

About 35 years after its first suggestion, QM/MM became the standard theoretical approach to investigate enzymatic structures and processes. The success is due to the ability of QM/MM to provide an accurate atomistic picture of enzymes and related processes. This picture can even be turned into a movie if nuclei-dynamics is taken into account to describe enzymatic processes. In the field of organic chemistry, QM/MM methods are used to a much lesser extent although almost all relevant processes happen in condensed matter or are influenced by complicated interactions between substrate and catalyst. There is less importance for theoretical organic chemistry since the influence of nonpolar solvents is rather weak and the effect of polar solvents can often be accurately described by continuum approaches. Catalytic processes (homogeneous and heterogeneous) can often be reduced to truncated model systems, which are so small that pure quantum-mechanical approaches can be employed. However, since QM/MM becomes more and more efficient due to the success in software and hardware developments, it is more and more used in theoretical organic chemistry to study effects which result from the molecular nature of the environment. It is shown by many examples discussed in this review that the influence can be tremendous, even for nonpolar reactions. The importance of environmental effects in theoretical spectroscopy was already known. Due to its benefits, QM/MM can be expected to experience ongoing growth for the next decade.In the present chapter we give an overview of QM/MM developments and their importance in theoretical organic chemistry, and review applications which give impressions of the possibilities and the importance of the relevant effects. Since there is already a bunch of excellent reviews dealing with QM/MM, we will discuss fundamental ingredients and developments of QM/MM very briefly with a focus on very recent progress. For the applications we follow a similar strategy.

Ring puckering: a metric for evaluating the accuracy of AM1, PM3, PM3CARB-1, and SCC-DFTB carbohydrate QM/MM simulations

The puckered conformations of furanose and pyranose carbohydrate rings are central to analyzing the action of enzymes on carbohydrates. Enzyme reaction mechanisms are generally inaccessible to experiments and so have become the focus of QM(semiempirical)/MM simulations. We show that the complete free energy of puckering is required to evaluate the accuracy of semiempirical methods used to study reactions involving carbohydrates. Interestingly, we find that reducing the free energy space to lower dimensions results in near meaningless minimum energy pathways. We analyze the furanose and pyranose free energy pucker surfaces and volumes using AM1, PM3, PM3CARB-1, and SCC-DFTB. A comparison with DFT optimized structures and a HF free energy surface reveals that SCC-DFTB provides the best semiempirical description of five- and six-membered carbohydrate ring deformation.

Path integral evaluation of equilibrium isotope effects

A general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic approximation for vibrations or rigid rotor approximation for the rotations. In particular, zero point energy and anharmonicity effects are described correctly quantum mechanically. The approach is based on the thermodynamic integration with respect to the mass of isotopes and on the Feynman path integral representation of the partition function. An efficient estimator for the derivative of free energy is used whose statistical error is independent of the number of imaginary time slices in the path integral, speeding up calculations by a factor of approximately 60 at 500 K and more at room temperature. We describe the implementation of the methodology in the molecular dynamics package AMBER 10. The method is tested on three [1,5] sigmatropic hydrogen shift reactions. Because of the computational expense, we use ab initio potentials to evaluate the equilibrium isotope effects within the harmonic approximation and then the path integral method together with semiempirical potentials to evaluate the anharmonicity corrections. Our calculations show that the anharmonicity effects amount up to 30% of the symmetry reduced reaction free energy. The numerical results are compared with recent experiments of Doering et al., [J. Am. Chem. Soc. 128, 9080 (2006); J. Am. Chem. Soc.129, 2488 (2007)] confirming the accuracy of the most recent measurement on 2,4,6,7,9-pentamethyl-5-(5,5-(2)H(2))methylene-11,11a-dihydro-12H-naphthacene as well as concerns about compromised accuracy, due to side reactions, of another measurement on 2-methyl-10-(10,10-(2)H(2))methylenebicyclo[4.4.0]dec-1-ene.

Comparison of different force fields for the study of disaccharides

Eighteen empirical force fields and the semi-empirical quantum method PM3CARB-1 were compared for studying beta-cellobiose, alpha-maltose, and alpha-galabiose [alpha-D-Galp-(1-->4)-alpha-D-Galp]. For each disaccharide, the energies of 54 conformers with differing hydroxymethyl, hydroxyl, and glycosidic linkage orientations were minimized by the different methods, some at two dielectric constants. By comparing these results and the available crystal structure data and/or higher level density functional theory results, it was concluded that the newer parameterizations for force fields (GROMOS, GLYCAM06, OPLS-2005 and CSFF) give results that are reasonably similar to each other, whereas the older parameterizations for Amber, CHARMM or OPLS were more divergent. However, MM3, an older force field, gave energy and geometry values comparable to those of the newer parameterizations, but with less sensitivity to dielectric constant values. These systems worked better than MM2 variants, which were still acceptable. PM3CARB-1 also gave adequate results in terms of linkage and exocyclic torsion angles. GROMOS, GLYCAM06, and MM3 appear to be the best choices, closely followed by MM4, CSFF, and OPLS-2005. With GLYCAM06 and to a lesser extent, CSFF, and OPLS-2005, a number of the conformers that were stable with MM3 changed to other forms.

Biomolecular simulation and modelling: status, progress and prospects

Molecular simulation is increasingly demonstrating its practical value in the investigation of biological systems. Computational modelling of biomolecular systems is an exciting and rapidly developing area, which is expanding significantly in scope. A range of simulation methods has been developed that can be applied to study a wide variety of problems in structural biology and at the interfaces between physics, chemistry and biology. Here, we give an overview of methods and some recent developments in atomistic biomolecular simulation. Some recent applications and theoretical developments are highlighted.

The implementation of a fast and accurate QM/MM potential method in Amber

Version 9 of the Amber simulation programs includes a new semi-empirical hybrid QM/MM functionality. This includes support for implicit solvent (generalized Born) and for periodic explicit solvent simulations using a newly developed QM/MM implementation of the particle mesh Ewald (PME) method. The code provides sufficiently accurate gradients to run constant energy QM/MM MD simulations for many nanoseconds. The link atom approach used for treating the QM/MM boundary shows improved performance, and the user interface has been rewritten to bring the format into line with classical MD simulations. Support is provided for the PM3, PDDG/PM3, PM3CARB1, AM1, MNDO, and PDDG/MNDO semi-empirical Hamiltonians as well as the self-consistent charge density functional tight binding (SCC-DFTB) method. Performance has been improved to the point where using QM/MM, for a QM system of 71 atoms within an explicitly solvated protein using periodic boundaries and PME requires less than twice the cpu time of the corresponding classical simulation.

Correlated ab initio quantum chemical calculations of di- and trisaccharide conformations

High level correlated quantum chemical calculations, using MP2 and local MP2 theory, have been performed for conformations of the disaccharide, beta-maltose, and the trisaccharide, 3,6-di-O-(alpha-D-mannopyranosyl)-alpha-D-mannopyranose. For beta-maltose, MP2 and local MP2 calculations using the 6-311++G** basis set are in good agreement, predicting a global minimum gas-phase conformation with a counterclockwise hydrogen bond network and the experimentally-observed intersaccharide hydrogen bonding arrangement. For conformations of 3,6-di-O-(alpha-D-mannopyranosyl)-alpha-D-mannopyranose, MP2/6-311++G**, and local MP2/6-311++G** calculations do not provide a consensus prediction of relative energetics, with the MP2 method finding large differences in stability between extended and folded trisaccharide conformations. Local MP2 calculations, less susceptible to intramolecular basis set superposition errors, predict a narrower range of trisaccharide energetics, in line with estimates from Hartree-Fock theory and B3LYP and BP86 density functionals. All levels of theory predict compact, highly hydrogen-bonded conformations as lowest in energy on the in vacuo potential energy surface of the trisaccharide. These high level, correlated local MP2/6-311++G** calculations of di- and trisaccharide energetics constitute potential reference data in the development and testing of improved empirical and semiempirical potentials for modeling of carbohydrates in the condensed phase.

Semi-empirical molecular orbital methods including dispersion corrections for the accurate prediction of the full range of intermolecular interactions in biomolecules

Semi-empirical calculations including an empirical dispersive correction are used to calculate intermolecular interaction energies and structures for a large database containing 156 biologically relevant molecules (hydrogen-bonded DNA base pairs, interstrand base pairs, stacked base pairs and amino acid base pairs) for which MP2 and CCSD(T) complete basis set (CBS) limit estimates of the interaction energies are available. The dispersion corrected semi-empirical methods are parameterised against a small training set of 22 complexes having a range of biologically important non-covalent interactions. For the full molecule set (156 complexes), compared to the high-level ab initio database, the mean unsigned errors of the interaction energies at the corrected semi-empirical level are 1.1 (AM1-D) and 1.2 (PM3-D) kcal mol(-1), being a significant improvement over existing AM1 and PM3 methods (8.6 and 8.2 kcal mol(-1)). Importantly, the new semi-empirical methods are capable of describing the diverse range of biological interactions, most notably stacking interactions, which are poorly described by both current AM1 and PM3 methods and by many DFT functionals. The new methods require no more computer time than existing semi-empirical methods and therefore represent an important advance in the study of important biological interactions.

Computational Study of the Conformational Space of Methyl 2,4-Diacetyl-β-d-xylopyranoside: 4C1 and 1C4 Chairs, Skew-Boats (2SO, 1S3), and B3,O Boat Forms

Ring and substituent rotamer conformations of methyl 2,4-diacetyl-beta-D-xylopyranoside, for which experimental results are controversial, were studied in the gas phase and in solvents of different polarity (CCl4, CHCl3, DMSO, and H2O) by B3LYP density functional theory. The 1C4 chair is the most stable ring form in the gas phase, followed by 4C1 and 2S0. Solvents of increasing polarity shift the equilibrium toward the 4C1 chair. Homodesmotic reaction energies show that the 1C4 and 2SO forms are stabilized by hydrogen bonding and anomeric effects and that steric repulsion is smallest in the 4C1 chair and largest in skew-boats.

Development of parameter sets for semi-empirical MO calculations of transition metal systems: Iron parameters for iron–sulfur proteins

A semi-empirical parameter set for iron has been developed which is appropriate for the study of iron-sulfur proteins having a single iron atom, by fitting to density-functional theory (DFT) calculations obtained for a series of small models of iron-containing proteins. These parameters are obtained using a modified BFGS optimisation procedure previously used to obtain semi-empirical parameters for the main group elements. The modifications to this procedure for obtaining parameters for transition metal atoms are outlined. In addition to modifications to the semi-empirical core repulsion function, which yield significant improvements in the calculation of molecular structures, compared to the standard core repulsion function, are outlined. The reported parameters are then tested on a set of model complexes containing a variety of ligands and show good agreement with both DFT and experimental data for these species.

Conformational Pathways of Saturated Six-Membered Rings. A Static and Dynamical Density Functional Study

The conformation of the six-membered ring of pyranosyl sugars has pronounced effects on the physical and chemical properties of carbohydrates. We present a method to determine key features of the potential energy surfaces, such as transition states associated with the inversion pathways of the model compounds cyclohexane, tetrahydropyran, p-dioxane, m-dioxane, s-trioxane, and 2-oxanol. Finally, we make the first determination of the pathways for inversion of penta-O-methyl-alpha-D-glucopyranose and penta-O-methyl-beta-D-glucopyranose. For both anomers, a transition state with five coplanar atoms with appreciable (O)E character was found. The method is based on constrained Car-Parrinello ab initio molecular dynamics, as implemented in the projector augmented-wave (PAW) method. The constraints are derived from the normal modes of six-membered rings and are described in terms of the canonical conformations (1)C(4) chair, (1,4)B boat, and (O)S(2) skew-boat. The PAW derived trajectories are in agreement with previous suggestions in the literature that pseudorotation is an important feature of such conformational interconversions. The dynamic nature as well as the internal coordinate-based constraints provide a method which can reliably accommodate pseudorotation. To determine semiquantitative energies, we recalculate key conformations using standard quantum mechanical calculations while keeping the ring dihedral angles frozen at their values found in the dynamics. In all cases where experimental barriers are known, our results are in excellent agreement.

Hydrogen Bonding and Cooperativity in Isolated and Hydrated Sugars: Mannose, Galactose, Glucose, and Lactose

The conformation of phenyl-substituted monosaccharides (mannose, galactose, and glucose) and their singly hydrated complexes has been investigated in the gas phase by means of a combination of mass selected, conformer specific ultraviolet and infrared double resonance hole burning spectroscopy experiments, and ab initio quantum chemistry calculations. In each case, the water molecule inserts into the carbohydrate at a position where it can replace a weak intramolecular interaction by two stronger intermolecular hydrogen bonds. The insertion can produce significant changes in the conformational preferences of the carbohydrates, and there is a clear preference for structures where cooperative effects enhance the stability of the monosaccharide conformers to which the water molecule chooses to bind. The conclusions drawn from the study of monosaccharide-water complexes are extended to the disaccharide lactose and discussed in the light of the underlying mechanisms that may be involved in the binding of carbohydrate assemblies to proteins and the involvement, or not, of key structural water molecules.