Chapter 10
QM/MM Simulations of Carbohydrates 1
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Abdul-Mueed Muslim , Jonathan P. McNamara , Hoda Abdel-Aal , Ian H. Hillier , and Richard A. Bryce Downloaded by CORNELL UNIV on September 23, 2016 | http://pubs.acs.org Publication Date: March 9, 2006 | doi: 10.1021/bk-2006-0930.ch010
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S c h o o l of Pharmacy and Pharmaceutical Sciences, University of Manchester, Manchester M 1 3 9 P L , United Kingdom Department of Chemistry, University of Manchester, Manchester M 1 3 9 P L , United Kingdom 2
Hybrid quantum mechanical (QM)/molecular mechanical ( M M ) molecular dynamics simulations were used to investigate disaccharide conformation in aqueous solution. In vacuo and aqueous solution conformational free energy surfaces were constructed from potential of mean force calculations, using weighted histogram analysis of combined Q M / M M molecular dynamics simulations of 8.5 ns and 13.5 ns respectively. Calculations indicated the presence of direct and water-bridged intersaccharide hydrogen bonds, the latter consistent with a broad range of φψ space. To improve the accuracy o f the description of carbohydrates by semi-empirical Q M methods, we also detail our work on reparameterization o f the P M 3 Hamiltonian. This is based on fitting to 1,2-ethanediol structures and energies. Application of the resulting model, P M 3 C A R B - 1 , to modeling of glucose is discussed. Improvement in energetic ranking of C and C conformations was found. Q M / M M dynamics simulations of a disaccharide using PM3CARB-1 did not exhibit transitions from C to C structures. 4
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© 2006 American Chemical Society
Vliegenthar and Woods; NMR Spectroscopy and Computer Modeling of Carbohydrates ACS Symposium Series; American Chemical Society: Washington, DC, 2006.
187 With advances in glycobiology, the complex and significant role of carbohydrates is being elucidated at the physiological and molecular levels. Carbohydrates are found as oligosaccharides, polysaccharides, proteoglycans, glycoproteins and glycolipids, and are implicated in a wide range of processes, many involving cell-cell interactions. For example, regulation of intercellular signaling pathways for embryonic cell fate decisions involves fucose-specific GlcNAc-transferases, known as "Fringe" proteins. The complexity of carbohydrates is reflected by the number of constitutional isomers. A trisaccharide, for example, can form 119,736 isomers from a pool of nine possible monosaccharides; a tripeptide, with 20 possible amino acid constituents, can form only 8000 isomers. In actuality, there are greater than 100 known monosaccharides. Beyond constitutional isomerism, carbohydrates are also conformationally flexible. For a linear polysaccharide of η monomers and assuming three staggered orientations for rotatable single bonds, the number of potential rotamers increases as 3 . Thus, for maltose, there are over half a million possible conformations; for a trisaccharide, the number of conformers potentially contributing to the equilibrium population increases to greater than a third of a billion. It is perhaps unsurprising that given this constitutional and conformational flexibility, carbohydrates have been proposed as informational bridges, spanning at a molecular level the acknowledged gap in complexity of the genome relative to the human brain. Carbohydrate flexibility presents a considerable challenge to experimental and theoretical approaches to structural characterization. This may in part be responsible for the arguable lag in computational modelling approaches applied to carbohydrates relative to nucleic acids and proteins. To permit evaluation of the many accessible conformers, conformational analysis demands a computationally efficient potential energy function. In this regard, classical force fields employing fixed charges have been the mainstay of biomolecular modelling. In the case of carbohydrates, however, describing the correct physical behaviour of these polar molecules, which incorporate stereoelectronic subtleties (anomeric, exo-anomeric and gauche effects), has been somewhat problematic at the molecular mechanical level; for example, this is evidenced by several reparametrizations of the widelyused force fields, A M B E R " , C H A R M M and O P L S . ' 1
Downloaded by CORNELL UNIV on September 23, 2016 | http://pubs.acs.org Publication Date: March 9, 2006 | doi: 10.1021/bk-2006-0930.ch010
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Hybrid Q M / M M calculations on carbohydrates Ideally, carbohydrates should be modelled in electronic detail, incorporating both intrinsic and external influences on electronic structure, and thus, their effect on molecular conformation and condensed phase behaviour. For example, calculations have estimated that electric polarization due to aqueous solvent contributes 10-20% of the solute-solvent interaction energy. With many hydrogen bond donor and acceptor groups, 15
Vliegenthar and Woods; NMR Spectroscopy and Computer Modeling of Carbohydrates ACS Symposium Series; American Chemical Society: Washington, DC, 2006.
188 carbohydrates experience directional polar interactions with environments such as aqueous solvent or protein clefts. To enable appropriate coupling to this environment, it is possible to employ hybrid potential energy functions, combining an inner region described at a quantum mechanical (QM) level of theory (for example, the carbohydrate) with an outer region (for example, solvent) modelled at a molecular mechanical ( M M ) force field. One type of hybrid Q M / M M approach is afforded by the O N I O M framework of Morokuma. Here, the total energy of the system, E ° f \ is obtained from three separate computations, two of which are performed at the less intensive M M level of theory: Downloaded by CORNELL UNIV on September 23, 2016 | http://pubs.acs.org Publication Date: March 9, 2006 | doi: 10.1021/bk-2006-0930.ch010
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O M { Q M m 4
ONIOM (QM.MM) £ tot
where E ^
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UJ
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is the energy of the inner region, treated at a Q M level of
theory. The second and third terms refer to the total M M energy of the entire system and the inner region respectively. In this scheme, generally called 'mechanical embedding', there is no polarization of the inner Q M region by the outer M M one, the interaction between the two regions being evaluated at the M M level. Although the O N I O M scheme has not been directly applied to carbohydrates in a Q M / M M context, it has been applied to calculation of N M R chemical shifts in β-D-glucose, using a combination of Q M levels of theory. A n interesting variant of O N I O M has been applied by French et al to calculation of carbohydrate φψ maps in aqueous solution and to computation of protein-bound distortion energies of carbohydrates. Here, the inner region is based on the sugar backbone. For example, for sucrose, an analogue based on linked tetrahydropyran and tetrahydrofuran moieties is used. For each φψ calculated for the analogue at the Q M level, many M M evaluations are performed to explore the hydroxyl and primary hydroxymethyl conformations of the sugar. The total energy of the sugar as a function of φψ is then obtained post factofromE q . l . Thus, the approach allows Q M treatment of the sugar backbone, accounting for the overlapping anomeric effect found in sucrose. Although the myriad permutations of the O H and C H O H groups are considered, the interaction of these groups with the Q M ring is considered only at the M M level. Thus, explicit polarization of the ring due to its polar pendant groups is omitted. A n alternative hybrid Q M / M M approach is to couple directly the Q M inner region with the M M outer environment. Here, the total energy, E, can be written as as the sum of the energy of the inner Q M region, the outer M M region and the interaction between the two: 17
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Vliegenthar and Woods; NMR Spectroscopy and Computer Modeling of Carbohydrates ACS Symposium Series; American Chemical Society: Washington, DC, 2006.
189 Γ
— pinner . inter Γ
^tot-^QM
, outer Γ
^ZQMIMM+ZMM
W
For non-covalent interactions between Q M and M M regions, the
EQA^/MM
coupling energy is given by: 1
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Β r
n
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'ms J
The first two terms involve the interaction of the M M point charges, q with the Q M charge density and Q M nuclei, Z respectively, the final term being the van der Waals interaction between the Q M and M M atoms. If we write
Downloaded by CORNELL UNIV on September 23, 2016 | http://pubs.acs.org Publication Date: March 9, 2006 | doi: 10.1021/bk-2006-0930.ch010
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m
EQM/MM
A
=(E "
-Ε™"
E
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UTER
~°
)MM
outer regions at a purely M M level, then the O N I O M scheme (Eq.l) is recovered. A number o f groups have applied the direct coupling approach to characterization o f enzyme reaction mechanisms involving carbohydrates: examples include xylose isomerase, " neuraminidase, human aldose reductase, uracil-DNA glycosylase, triose phosphate isomerase, and glucose oxidase. Here, we describe aspects o f our current work on the conformational behaviour of carbohydrates employing a folly electronic description of the sugar via a directly coupled Q M / M M approach. 21
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Q M / M M free energy surface for a disaccharide in aqueous solution To investigate the conformation of a carbohydrate solute using quantum mechanics in an aqueous environment which is described via an appropriate molecular mechanical force field, we employed a disaccharide model, 4-0α-D-xylopyranosyl-a-D-xylopyranose (Figure 1). This a-(l-»4)-linked analogue of maltose, lacking primary hydroxymethyl groups, is subsequently denoted "dixylose" after Naidoo and Brady. A semi-empirical PM3 Hamiltonian was selected to describe the disaccharide. P M 3 exhibits an improved ability to model hydrogen bonding in organic systems relative to A M I , and has had some success in predicting energy differences o f hydroxyl rotamers o f glucose and methanediol. However, the P M 3 potential underestimates stability of the glucose ring C i conformation, relative to C . Consequently, the dixylose rings were constrained to the C conformation during dynamics calculations. Using this computationally tractable Q M / M M potential, the conformational free energy surface of the disaccharide as a function of the glycosidic angles φ and ψ 31
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Vliegenthar and Woods; NMR Spectroscopy and Computer Modeling of Carbohydrates ACS Symposium Series; American Chemical Society: Washington, DC, 2006.
190 was determined. Here, we define φ and ψ as the dihedrals H1-C1-01-C4* and C l - 0 1 - C 4 ' - H 4 ' respectively (Figure 1). A free energy surface for dixylose in vacuo and in aqueous solution was obtained using the potential of mean force approach. Here, the Helmholtz free energy difference of the system along the coordinates φ and ψ, ΑΑ(φ,ψ), is given by, ΔΑ(
