HF/6-31G* energy surfaces for disaccharide analogs

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<ul><li><p>HF/6-31G Energy Surfaces forDisaccharide Analogs</p><p>ALFRED D. FRENCH,1 ANNE-MARIE KELTERER,2 GLENN P. JOHNSON,1</p><p>MICHAEL K. DOWD,1 CHRISTOPHER J. CRAMER31Southern Regional Research Center, Agricultural Research Service, U.S. Department of Agriculture,1100 Robt. E. Lee Blvd., P.O. Box 19687, New Orleans, Louisiana 70179-06872Institut fr Physikalische und Theoretische Chemie, Technische Universitt Graz, Technikerstrasse 4,A-8010 Graz, Austria3Department of Chemistry and Supercomputer Institute, 207 Pleasant St. SE, Minneapolis,Minnesota 55455-0431</p><p>Received 10 February 2000; accepted 20 June 2000</p><p>ABSTRACT: The HF/6-31G level of theory was used to calculate relaxedpotential energy surfaces for 12 analogs of disaccharides. The analogs were madeby replacing glucose with tetrahydropyran and fructose with2-methyltetrahydrofuran. Molecules had zero, one or two anomeric carbonatoms, and di-axial, axial-equatorial, and di-equatorial linkages. Despite theabsence of hydroxyl groups, the surfaces account well for conformations that areobserved in crystals of the parent disaccharides. Thus, torsional energy and thesimple bulk of ring structures are major factors in determining disaccharideconformation. The contour shapes around the global minima depend on thenumber of anomeric carbons involved in the linkage, while the presence ofalternative minima that have relative energies less than 4 kcal/mol mostlyrequires equatorial bonds. However, molecules with two adjacent anomericcenters gave exceptions to these rules. Flexibility values related to a partitionfunction show that the di-axial trehalose analog is the most rigid. Thedi-equatorial pseudodisaccharide analog with no anomeric centers is mostflexible. Reproduction of these surfaces is proposed as a simple test of force fieldsfor modeling carbohydrates. Also, these surfaces can be used in a simple hybridmethod for calculating disaccharide energy surfaces. c 2000 John Wiley &amp;Sons, Inc. J Comput Chem 22: 6578, 2001</p><p>Dedicated to the memory of Professor Georgy A. Jeffrey, de-ceased February 13, 2000</p><p>Correspondence to: A. D. French; e-mail: afrench@nola.srrc.usda.gov or to: A.-M. Kelterer; e-mail: kelterer@ptc.tu-graz.ac.at</p><p>This article includes Supplementary Material available fromthe author upon request or via the Internet at ftp.wiley.com/public/journals/jcc/suppmat/22/65 or http://journals.wiley.com/jcc</p><p>Journal of Computational Chemistry, Vol. 22, No. 1, 6578 (2001)c 2000 John Wiley &amp; Sons, Inc. This article is a US Government work and, as such, is in the public domain in the United Statesof America.</p></li><li><p>FRENCH ET AL.</p><p>Keywords: ab initio; anomeric effect; carbohydrate; conformational analysis;cellobiose; laminarabiose; galabiose; maltose; nigerose; quantum mechanics;sucrose; tetrahydrofuran; trehalose</p><p>Introduction</p><p>T he main descriptors of disaccharide shape arethe torsion angles (designated and ) for thebonds that link the two monosaccharide residuestogether. Calculated relative energies for such mole-cules can be plotted on grids of and , yieldingenergy surfaces that are often called Ramachandranplots.1 These maps predict the relative likelihood ofdifferent molecular conformations and characterizethe barriers among the various shapes. They alsopermit the assessment of the distortion of experi-mentally determined structures. The energies canbe calculated by methods of varying sophisticationand computational cost. Initial efforts used simpleallowed/disallowed energy functions, but weresoon improved to include van der Waals forces.2, 3</p><p>Those methods only allowed variation of the torsionangles for the linkage bonds.</p><p>The HSEA (Hard Sphere Exo-Anomeric Effect)program of Lemieux and coworkers4 6 used vander Waals energies and also incorporated tor-sional potentials to reproduce exo-anomeric effects.The exo-anomeric effect7 preferentially orients sub-stituents that are attached to the glycosidic oxy-gen atom to locations that are gauche to the ringoxygen. Thus, the magnitude and exact orienta-tion resulting from the exo-anomeric effect are ofdirect importance to the study of disaccharide con-formation. The torsional potentials for HSEA, onefor -linkages and one for -linkages, were pa-rameterized with single-point HF/4-31G ab initiocalculations on dimethoxymethane. Results fromHSEA sufficed to interpret some NMR spectra, butlimitations gradually became apparent.8 In partic-ular, the rigid linkage bond angle and geometriesof the monomeric residues led to strain energiesthat were much too high for some observed con-formations. Therefore, in the late 1980s, so-calledrelaxed-residue calculations9 12 were undertaken,in which energy minimization is employed at eachincrement of and . These more complex, relaxed-residue calculations can now be carried out withavailable molecular mechanics (MM) force fields.</p><p>For any given values of and , however, rel-ative energies from various force fields often differby a few kcal (all energies herein are molar).13 This</p><p>degree of uncertainty for values near importantminima is large enough that important questionscannot be answered with confidence. In the questto obtain greater accuracy, the use of ab initio quan-tum mechanics (QM) is increasing. QM can be usedin studies of disaccharides in several ways besidessimply parameterizing the potential function forthe glycosidic torsion angle. Some MM force fieldsare now based exclusively on QM studies of smallmolecules.14 16 Alternatively, one might use QMto study disaccharides directly. However, such cal-culations are too time-consuming due to the largenumber of alternative orientations of the exo-cyclicgroups that must be considered to avoid biasing theanalysis.</p><p>Another approach is to combine QM withMM. We have recently developed a simple hy-brid method for making Ramachandran plots.17 Itinvolves the separate calculation of the MM en-ergy surface for the complete disaccharide, with therequisite extensive variation of the exo-cyclic ori-entations. Also required are separate MM and QMenergy surfaces for the critical part of the disac-charide. The hybrid energy for the disaccharide atany , point is the MM energy for the disaccha-ride, minus the MM energy for the critical part,plus the QM energy for the critical part. In thesestudies, the critical part is the disaccharide withall of the exo-cyclic hydroxyl and hydroxymethylgroups replaced by hydrogen. The resulting mole-cules (Fig. 1), except for the sucrose analog, aredimers of tetrahydropyran (THP). The analog of su-crose in the present work retains a methyl groupattached to its tetrahydrofuran (THF) ring at C2.</p><p>These molecules include all the atoms used inconventional MM to define the torsion angles, andthus the torsional energies, of the glycosidic linkage.As discussed by Woods,8 calculation by the differentforce fields of glycosidic bond torsional energy is asource of variable modeling results, so a direct QMcalculation of all linkage torsional energies shouldbe advantageous. It also avoids the undesirable sit-uation implemented in the HSEA software whereinthe torsional parameters are different for axial andequatorial bonds.</p><p>While the hybrid energy surfaces for the variousdisaccharides are the finished product of this effort,we found the QM energy surfaces for the analogs</p><p>66 VOL. 22, NO. 1</p></li><li><p>HF/6-31G ENERGY SURFACES FOR DISACCHARIDE ANALOGS</p><p>FIGURE 1. The molecules used in this study. Only the hydrogen atoms that define H and H are shown. Thenumbers of the atoms are based on standard carbohydrate nomenclature for the disaccharides. These molecules arealso analogs of many other disaccharides. As far as we know, these analogs do not exist, nor do the parent 3,3-linkedpseudodisaccharides.</p><p>to be interesting in their own right. The purpose ofthis article is to present and discuss these QM ana-log maps and their implications for prediction ofthe structures of disaccharides and larger carbohy-drates.</p><p>Analogs of sucrose, the three trehaloses, nigerose,laminarabiose, maltose, cellobiose, and galabiose(di-axial, -1,4-linked galactosyl-galactose) are in-</p><p>cluded. The three other included molecules lack gly-cosidic linkages, so we consider them to be analogsof pseudodisaccharides. Their simple ether link-ages connect what would be the C3 positions oftwo glucose rings. These isomers include di-axial,axial-equatorial, and di-equatorial linkages. The su-crose and trehalose analogs have two connectedanomeric centers. The cellobiose, galabiose, lami-</p><p>JOURNAL OF COMPUTATIONAL CHEMISTRY 67</p></li><li><p>FRENCH ET AL.</p><p>narabiose, maltose, and nigerose analogs have onlyone anomeric center, and the analogs of pseudo dis-accharides have no anomeric centers. The moleculesin Figure 1 are also analogs for many other mole-cules. For example, the analog of cellobiose is alsoan analog of lactose and of the -1,4linked dimersof mannose and xylose. It may also be suited forstudies of -1,2linked dimers.</p><p>This is not the first instance of studying confor-mations of disaccharide linkages by QM. In particu-lar, axial and equatorial 2-methoxytetrahydropyranhave been widely studied. Tvaroka and Carver18</p><p>have made especially thorough studies of variousmethoxytetrahydropyrans as models of disaccha-ride linkages. A few limited studies of disaccha-ride analogs based on cyclohexane, tetrahydropy-ran (THP), and tetrahydrofuran (THF) have beencarried out with ab initio QM theory.19 21 Full mapsfor trehalose analogs based on semiempirical QMtheory and partially minimized energies were con-structed more than a decade ago.22</p><p>Methods</p><p>Calculations on carbohydrates, which haveboth extensive hydrogen bonding possibilities andanomeric effects, are sensitive to the level of QMtheory.23 The HF/6-31G level was chosen for sev-eral reasons. It has been used previously to studyanomeric effects in many molecules that are smallerthan our analogs.16, 24, 25 Because of fortuitous can-cellation of errors, HF/6-31G relative energies forglucopyranose are similar to those produced by ad-vanced electronic structure theory.23, 26 Our workon calculated heats of formation27 showed that therelative electronic energies for the minimum en-ergy conformations of these analog molecules at theHF/6-31G level of theory were similar to B3LYP/6-31G calculations. That similarity is perhaps sur-prising because B3LYP/6-31G and (MP2/6-31G)calculations for monosaccharides23, 26, 28 give rela-tive energies for different configurations and con-formations of carbohydrates that are quite differ-ent from energies from either HF/6-31G or largecalculations. This was confirmed recently by Lii,Ma, and Allinger,29 who attributed the differencesto large Basis Set Superposition Errors (BSSE) inB3LYP/6-31G calculations on hydrogen bonds. Be-cause there are no hydroxyl groups in our analogs,the relative energies should depend less on the levelof theory than would the relative energies of com-plete carbohydrates. Therefore, HF/6-31G can bea representative, yet relatively economical, level oftheory for these models.</p><p>Energies for the analogs of sucrose, the tre-haloses, and the pseudodisaccharides were calcu-lated with GAMESS,30 and the other maps werecalculated with Gaussian 94.31 Starting modelsof sucrose and the trehalose analogs were basedon crystal structures of the actual disaccharideswith the exo-cyclic groups replaced with hydrogenatoms. These structures were then minimized withQM. Those molecules were then used to generate,by rigid rotations about the linkage bonds, the vari-ous initial structures. In the cases when the startingstructures were badly congested, with interpenetra-tion of the two monomeric residues, structures withthe required and values were generated froma successfully optimized neighbor. A similar strat-egy was used for the pseudo disaccharide analogs.Analogs of galabiose, nigerose, maltose, laminara-biose, and cellobiose were sketched with CHEM-X32</p><p>and energy-minimized with MM3.33 The glycosidicangle was increased to 150 and MM3 was then usedto optimize individual starting structures at each, point for the QM calculations. The increase to150 avoided interpenetration of the atoms of thetwo rings in high-energy regions when starting eachMM3 minimization after rigid rotations about thelinkage bonds from the otherwise identical startingmolecule. All searches of conformation space werecarried out with 20 increments of and . Thosetorsion angles were held fixed at each , point,but all other internal coordinates were optimized.Structures at the lowest energy grid point on eachmap were subsequently minimized without ,constraints by computation of the Hessian matrixto precisely locate and confirm the minima. Furtherdetails of these methods are described elsewhere.34</p><p>We define the flexibility over the Ramachan-dran surface as the probability volume in degreessquared, with the probability calculated by a Boltz-mann relationship, pi = e1E/RT. Therein, 1E is theelectronic energy relative to the global minimum de-termined by QM, R is the universal gas constant,and T is 298 K. This probability volume is relatedto the partition function, a summation of the proba-bility values over the surface. A completely flexiblemolecule would have a relative energy of 0 kcal (andpi = 1) everywhere on the surface. On a grid witha 1 spacing there are 360 360 = 129,600 ,points. A completely rigid molecule would havea pi of 1 at only one point and a value of zeroat all others. Thus, the maximum possible valueof the partition function would be 129,600, andthe minimum on that basis would be 1. Similarly,the maximum and minimum probability volumeswould be 129,600 deg deg, and 1 deg deg, re-</p><p>68 VOL. 22, NO. 1</p></li><li><p>HF/6-31G ENERGY SURFACES FOR DISACCHARIDE ANALOGS</p><p>FIGURE 2. Three-dimensional representation of theprobability volume from the QM surface for the maltoseanalog. The maximum, with a pi of 1, is at the globalminimum of = 57C, = 33C. The outermostcontour line shown on this surface has a relativeprobability value of 0.00001. It correspondsapproximately to what would be the 7 kcal contour forthe maltose map shown in Figure 4b.</p><p>spectively. Numerical values of the dimensionlesspartition function were essentially the same as theprobability volume for the analog surfaces whenusing a 1 grid spacing and the Trapezoidal Rule,Simpsons Rule, or Simpsons 3/8 Rule. At largergrid increments, the probability volume representsa reasonably fine quadrature approach to the par-tition function calculated for a 1 grid, but valuesof the partition function for other grid incrementswere, of course, quite dependent on the numberof grid points in the summation. Figure 2 showsthe probability volume (2425 deg deg), calculatedfor the maltose analog surface. The electronic en-ergy was interpolated to 1 intervals with the Gridfunction of Surfer 7.0,35 the program used to calcu-late the probability volume and produce the contourplots.</p><p>All maps herein are presented based on linkagetorsion angles defined by the exo-cyclic atoms (hy-drogen atoms except for C1 on the sucrose analog)attached to the carbon atoms of the...</p></li></ul>