1

Abstract

Conformational analysis was performed on the branched repeating unitof the O-antigenic polysaccharides of two pathogenic bacteria: Shigelladysenteriae type 4 and Escherichia coli 159. These two antigens show notonly some similarity in the primary structure but also immunological cross-reactivity.

Our studies have been performed with molecular mechanics using theMM3 force field and systematic search on the Φ/Ψ-torsions of the glycosidiclinkages. We performed a multidimensional filtered search for the glycosidiclinkages in the branch region. The results show that the O-antigen of E. coli159 has only one highly restricted conformation in the branch region. TheO-antigen of S. dysenteriae type 4 has a higher flexibility with three almostequal energy minima. The interbranch region shows high flexibility in bothO-antigens.

One of the minimum energy conformations of the branch region of theO-antigen of Shigella dysenteriae type 4 shows high similarity in the elec-trostatic and lipophilic properties of the solvent accessible surface to thehomologous region in the O-antigen of E. coli 159. Based on this we suggestthat the exposed branching units constitute the binding epitope. Certainlythe conformational freedom in the case of Shigella dysenteriae type 4 can re-duce the occurrence of the common epitope. NMR studies on the branchingunit of Shigella dysenteriae type 4 have to be done to answer this question.

Contents

1 Introduction 4

2 Basic carbohydrate bio-chemistry 52.1 Structural aspects . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Functional aspects . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Bacterial Polysaccharides 83.1 O-antigens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.1.1 Structure of O-antigens . . . . . . . . . . . . . . . . . 83.1.2 Immunological importance, Vaccine development . . . 9

3.2 O-Antigens of E. coli 159 and S. dysenteriae type 4 . . . . . 10

4 Methods for theoretical conformational analyses of saccha-rides 134.1 Methods for calculation of molecular energy . . . . . . . . . . 13

4.1.1 Ab initio . . . . . . . . . . . . . . . . . . . . . . . . . 134.1.2 Force field methods . . . . . . . . . . . . . . . . . . . . 144.1.3 Complete force fields . . . . . . . . . . . . . . . . . . . 154.1.4 Truncated force fields - e.g. HSEA . . . . . . . . . . . 16

4.2 Methods for the generation of molecular conformations . . . . 164.2.1 Systematic search . . . . . . . . . . . . . . . . . . . . 164.2.2 Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . 194.2.3 Molecular Dynamics . . . . . . . . . . . . . . . . . . . 19

4.3 Methods used in the present study . . . . . . . . . . . . . . . 204.3.1 Glycan - a modified HSEA program . . . . . . . . . . 204.3.2 MM3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3.3 Nomenclature of the torsion angles . . . . . . . . . . . 244.3.4 Sweet . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3.5 Calculation of surface properties . . . . . . . . . . . . 25

5 Results 265.1 Results from molecular mechanics calculations . . . . . . . . 26

5.1.1 Potential Energy surfaces of glycosidic linkages . . . . 265.1.2 Modelling of favored conformations . . . . . . . . . . . 26

CONTENTS 3

5.2 Comparative results from Glycan and Sweet . . . . . . . . . . 26

6 Discussion 336.1 Favored Energy conformation . . . . . . . . . . . . . . . . . . 336.2 Surface properties . . . . . . . . . . . . . . . . . . . . . . . . 336.3 Relationship between structural properties & immunological

reactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

7 Resources and tools 357.1 Molecular Modeling . . . . . . . . . . . . . . . . . . . . . . . 357.2 Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357.3 Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

8 Acknowledgements 36

Chapter 1

Introduction

The 3D structure of saccharides is of great importance for their functionin biological systems. However, the experimental determination of theirstructure through X-ray crystallography and NMR is often impossible orvery time consuming.

Fortunately, there are computational methods available today which al-low a reliable prediction of the 3D-structure for many oligosaccharides. How-ever, it is still not an easy task to predict the structure of many complexsaccharides.

O-antigens are constituents of the lipopolysaccharides of Gram-negativebacteria. They give rise to very specific antibody responses and their 3Dstructure is of great interest for vaccine development. This study is partof a research project concerning the O-antigens of the Shigella family. Thecomputational methods used were molecular mechanics and HSEA calcula-tions.

The work was performed as a paired master project together with JimmyRosen. My part of the project dealt with the 3D structures of the O-antigensof Shigella dysenteriae type 4 and Escherichia coli 159 as described in thisthesis. The results have also been reported in a manuscript [1]. To someextend I have also contributed to a study on the O-antigen of Shigella dysen-teriae type 2 which has resulted in a publication [2].

Chapter 2

Basic carbohydratebio-chemistry

2.1 Structural aspects

Carbohydrate are just like lipids, nucleic acids, and proteins a major class ofconstituents of living cells [3, 4]. They are important as building blocks e.g.in DNA and RNA which contain pentose sugars in their back-bone. Furthermore lipids and proteins are often conjugated with sugars (glycoproteins,glycolipids).

Carbohydrates are a very heterogeneous group of compounds. The com-pounds first studied had formulas of the kind CxH2yOy and tasted sweet.That is where they got their names from: carbohydrates and saccharides.Today the terms carbohydrate and saccharide are not connected to a specificformula or taste, but through structural properties. Also the term glycansis used for this class of compounds.

Monosaccharides are aldehydes or ketones with many hydroxyl groups,they are the simplest group of carbohydrate, since they can not be hydrolyzedinto simpler substructures. Depending on the carbonyl group one can distin-guish between aldoses and ketoses. The number of monosaccharides knownin biological systems is high, but most of them are very exotic and appearonly in few structures or species. There are about 20 monosaccharides whichbuild up most of the carbohydrates in the biosphere. Glucose is the by farmost common monosaccharide in the living world and therefore also themost common organic substructure on earth. Cellulose, starch, and glyco-gen are built entirely by glucose, but it can also be found as a buildingblock in many oligosaccharides. Some properties of monosaccharides aredemonstrated here using glucose as an example.

Monosaccharides can exist in an acyclic form and they can also formcyclic half acetals (or half ketals). In fact most monosaccharides with fivecarbon atoms or more prefer to form rings, both in aqueous solution and

2.1 Structural aspects 6

in crystalline state. In the acyclic form the aldehyde group is available tooxidation which gives the saccharide reducing power.

When the ring is formed the C1 atom (= the anomeric atom) becomeschiral as well, therefore two different rings can be built by the same sugar.Depending on the configuration of the anomeric oxygen, these are referredto as α and β forms. These two forms can interconvert in solution via theacyclic form as shown in Fig. 2.1.

Figure 2.1: D-Glucose exists mainly as two cyclic forms α and β-D-Glucose.These six membered rings with an oxygen atom in the ring are derivativesof pyrane and are therefore called pyranose rings. The hydroxyl group atC1, corresponding to the aldehyde group of the acyclic form, can have axial(α) or equatorial (β) configuration. Sugars are rich of chiral centers. Thefour asymmetric carbons in the acyclic form of D-Glucose are indicated byasterisks. This gives rise to stereoisomers. An aldohexose can build 24 = 16different stereoisomers (8 pairs of enantiomers).

Almost all pyranoses form a ring in chair conformation, with the oxygenin the plane. Those rings can ‘flip’ or invert. Such inversions are of greatsignificance since all groups in an equatorial position become axial and viceversa, changing the 3D-structure completely (see Fig. 2.2).

Monosaccharides can be linked though glycosidic links forming morecomplex structures where the anomeric carbon of one sugar binds throughan oxygen to a carbon atom of the another sugar. Whether the anomericcenter is α or β is of great importance for the 3-dimensional structure.

With several monosaccharides linked together, the residue at one of theends of the chain will still have its anomeric carbon atom available for ox-idation. This end of the chain is called the reducing end due to the powerof the free anomeric carbon to reduce oxidizing agents. The other end(s) is(are) called non-reducing end(s). The monosaccharide units are numberedstarting at the reducing end, due to its uniqueness.

The hydroxyl groups of the sugar units are often substituted by N-acetyl-, O-acetyl-, sulfate-, or phosphate- groups. In some cases one of the carbon

2.2 Functional aspects 7

Figure 2.2: β-D-Glucopyranose can theoretically exist in a 4C1- or a 1C4-conformation. However the 4C1-conformation is greatly favored since it hasall large groups in equatorial position.

atoms is oxidized and part of a carboxyl group (uronic acids and sialic acids).The primary structure of a branched saccharide cannot be represented as

a 1-dimensional string as with peptides but is rather given as a tree structurewith the reducing sugar as the ‘root’.

2.2 Functional aspects

The function of carbohydrates in biological systems is in many cases un-known. However, carbohydrates are considered to have 3 major functions:

• Storage of energy e.g. in glycogen and starch

• Mechanical stabilization e.g. as structural element in the cell walls andmembranes of bacteria and plants and the connective tissue of animals.Possibly also involving stabilization of the fold of glycoproteins.

• Recognition. Of importance for cell-cell recognition and for the im-mune system.

This thesis will focus on bacterial carbohydrates, which are known to berecognized by antibodies of the host.

Chapter 3

Bacterial Polysaccharides

Bacterial Polysaccharides are a very diverse class of biomolecules. One maydivide them into the following groups [5].

• Peptidoglycan or murein is a major component of the cell wall in Gram-negative bacteria. It is important for cell wall integrity protecting thebacteria from death due to osmotic swelling. Its biosynthesis can beinhibited by beta-lactam antibiotics like penicillin.

• Capsular polysaccharides are found in capsules. Because of their im-munological importance they are also called K-antigens.

• In eukaryotes the glycosylation of proteins is done in the ER. Procary-otes don’t have this organelle but some of them are known to be ableto synthesize glyco-proteins.

• O-antigens are repetitive polysaccharide moieties of the lipopolysac-charides located in the outer membrane of Gram-negative bacteria.

3.1 O-antigens

3.1.1 Structure of O-antigens

Lipopolysaccharides consist of a hydrophobic part, Lipid A anchored in theouter membrane and a large carbohydrate moiety (Fig. 3.1). The carbohy-drate part contains an inner core region, typically containing exotic sugars(heptoses and phosphorylated residues) and an outer portion, called theO-antigen which has a repetitive sequence.

O-antigens consist of a repeating unit with two to eight sugars, which isrepeated 50 times or even more. There is a great diversity in the structureof O-antigens, e.g. for E. coli more than 100 different O-antigens are known.

3.1 O-antigens 9

Figure 3.1: Schematic drawing showing the structure of the cell membranesof a Gram-negative bacterium.

3.1.2 Immunological importance, Vaccine development

The biological function of lipopolysaccharides of bacteria is poorly under-stood [6]. In the host LPS acts as a strong heat stable toxin inducing feverand shock reactions [5]. This effect is considered to be due to the lipid por-tion. In many cases the immune system of the host detects the O-antigensas foreign material resulting in the production of specific antibodies, usuallyof the IgM-type.

Most O-Antigens give rise to very specific antibody responses and it ispossible to use these immunological properties to type different strains ofbacteria using various methods. Humans suffering a bacterial disease canbecome immune to the disease caused by that particular serotype but notnecessarily to other serotypes of that species. This has been shown forShigella flexneri [7]. Generally the O-antigen is believed to be a major anti-gen on Gram-negative bacteria which makes these polysaccharide structuresimportant targets for vaccine development.

In some cases antibodies raised against one O-antigen react also withan O-antigen of another serotype. Such cross-reactivity has been observedbetween Escherichia coli 159 and Shigella dysenteriae type 4 [8], which

3.2 O-Antigens of E. coli 159 and S. dysenteriae type 4 10

were studied in the present thesis. Escherichia coli 159 is a common type ofETEC (Enterotoxigenic Escherichia coli). ETECs cause infectious diarrheain infants and children in developing countries [9]. The type 159 was themost common ETEC among British troops in Saudi Arabia [10]. ETECs arethe most common cause of travelers diarrhea. They adhere to the mucosalcells in the small intestine, and produce toxins which are very similar to thecholera toxin and act on mucosal cells to cause diarrhea.

Shigella dysenteriae type 4 belongs to the big Shigella family. It isestimated that the Shigella family causes 5-10% of diarrhea illnesses and75% of diarrhea death, which makes it a major health problem in developingcountries. More that 150 million people suffer shigellosis every year andmore than 1 million die of this disease every year. The Shigella family isdivided into 4 main serogroups: Shigella sonnei (only 1 serotype), Shigellaflexneri (6 serotypes including 15 subtypes), Shigella boydii (18 serotypes)and Shigella dysenteriae (13 serotypes) [11]. Most cases of shigellosis (60%)are caused by Shigella flexneri, followed by sonnei (15%), dysenteriae, andboydii (6% each). Shigella dysenteriae is more common in Sub-SaharanAfrica and South Asia where it contributes to 30% of the cases.

Considering the statistics it seems that Shigella sonnei is an relativelyeasy target since it occurs only in one serotype and efforts are currentlymade to develop vaccines against it. Targeting S. flexneri is much moredifficult due to the high number of serotypes. An innovative strategy has tobe found to develop a broad vaccine in this case.

A considerable amount of work has been done on S. dysenteriae type 1[7, 12]. It causes very severe shigellosis, and its O-antigen has been studiedin great detail [7, 13].

An effective Shigella vaccine cocktail should protect against Shigella son-nei, Shigella flexneri (covering as many serotypes as possible) and Shigelladysenteriae type 1. The other serogroups and serotypes have secondary pri-ority.

3.2 O-Antigens of E. coli 159 and S. dysenteriaetype 4

Figure 3.2: The repeating unit of the E. coli 159 O-antigen

3.2 O-Antigens of E. coli 159 and S. dysenteriae type 4 11

Figure 3.3: The repeating unit of the S. dysenteriae type 4 O-antigen

As one can see in figure 3.2 and 3.3 the sequences are quite similar.However, there are several major differences. There are only α-linkages inthe S. dysenteriae type 4 O-antigen whereas in the E. coli 159 O-antigen thetwo linkages in the branch region are β. The GlcA in S. dysenteriae type 4is replaced by a GalA in E. coli 159. This is also of high importance sincethe C4 to which the glycosidic link is made has different configurations inthem (axial in GalA, equatorial in GlcA). The O-antigen of S. dysenteriaetype 4 has an O-acetyl group. However the position of this group on thefucose has not be determined yet.

Figure 3.4: The repeating unit of the O-antigen of Escherichia coli 159. Thethree red sugar units form the constrained branch region. The glycosidiclinkages are labeled with letters.

Figures 3.4 and 3.5 show the repeating units of the two studied O-antigens in stereo projections. The sugar units in the branch region of eachO-antigen are indicated in red. One of the GlcNAc is substituted with sugarresidues in 3 and in 4 position. Their interactions reduce the conformationalfreedom at the branching point significantly.

3.2 O-Antigens of E. coli 159 and S. dysenteriae type 4 12

Figure 3.5: The repeating unit of the O-antigen of Shigella dysenteriae type4. The three red sugar units form the constrained branch region. Theglycosidic linkages are labeled with letters. The O-acetyl group on the fucoseis not shown, since its exact position has not yet been determined.

Chapter 4

Methods for theoreticalconformational analyses ofsaccharides

4.1 Methods for calculation of molecular energy

4.1.1 Ab initio

Here the attempt is made to calculate the minimum energy directly throughquantum mechanics, that is the Schrodinger equation. This approach worksdirectly on interacting electrons and atomic nuclei and therefore needs noemperical data regarding favored conformations. It has to be rememberedthat the Schrodinger equation in its exact form can only be solved for thehydrogen atom (one proton, one electron). For any more complex systemapproximations have to be used [14].

Two basic approximations are used in ab initio calculations:

1. The Born-Oppenheimer (BO) approximation, that the nuclei are fixedand only the electrons are in motion. This approximation is generallysafe since the mass of the nucleus is more than 1000 times larger thanthe electron’s mass.

2. When atoms form molecules their atomic orbitals interact and formmolecular orbitals (molecular orbital theory or MO-theory). This for-mation can be formulated as a linear combination of atomic orbitals(LCAO).

For example the atomic orbitals of two hydrogen atoms can be combinedto two molecular orbitals, a binding and an anti-binding orbital. N linearcombined atomic orbitals always give rise to N molecular orbitals [15, 14].

The energy of formation calculated through LCAO is only about 60%of the real (experimental) value. A big deviation for a simple system, but

4.1 Methods for calculation of molecular energy 14

still a good result if one considers that absolutely no empirical informationis used. In complex molecules there are more atoms, more electrons, moreatomic orbitals and therefore many more LCAOs to calculate. The compu-tational time rises exponentially with the number of atoms. A large numberof integrals has to be evaluated, which takes a lot of CPU-time. Detailed abinitio calculations on disaccharides are very time consuming. For oligosac-charides huge amounts of computational power is needed. Thus detailed abinitio calculations on oligosaccharides are not yet possible with the presentmethods.

However, ab initio calculations are useful for studies on small model sys-tems, consisting of a few atoms in cases where no empirical data is available.

Also chemical reactions can be predicted with ab initio methods. Usuallythe transition state is predicted.

There are attempts to use some empirical data in quantum mechanicalcalculations to improve the reliability and speed up the calculations. Thesemethods are referred as semi-empirical methods.

4.1.2 Force field methods

A force field defines the energy of the molecule as a sum of terms, each ofwhich is a function of a distortion from an ideal geometry. The terms whichare considered are usually bond lengths, bond angles, dihedral angles, vander Waals and Coulomb interactions.

The definition of bond length is trivial. It is the distance of the twonuclei of two linked atoms. It can be given in pico-meter (pm) or Angstrom(1 A=100 pm). Bond lengths are very constrained, that is they have a verysteep energy well.

Bond angle is defined by three consecutively linked atoms. It is the anglebetween the connection lines of the two atoms linked to the middle atom.Usually it is given in degrees. Bond angles are very constrained as well.

Dihedral angle or torsion angle is defined by four consecutively linkedatoms. First the atoms are turned until one looks exactly along the linkagesof the two atoms in the middle (B, C), Then one has to rotate the the B-C-linkage until the substituents (A, D) eclipse. The rotation is done by holding,the substituent in the background fixed and turning the substituent in theforeground only. The degree of turning is the torsion - or dihedral angle.One can allow only clockwise rotation and therefore get only positive valuesranging from 0 to 360 degree, or one may allow anti-clockwise rotation andget values between -180 to +180 degrees.

Torsions are much more flexible than bond lengths and bond angles.Specially single bonds can rotate almost freely. Linkages between two sp3-hybridized atoms can have staggered or eclipsed conformation. When turn-ing the linkage one can obtain three staggered and three eclipsed conforma-

4.1 Methods for calculation of molecular energy 15

tions. Staggered conformations are favored.The single bond between C1 and the O1 in glycosidic linkages shows quite

a different behavior from normal C-O-bonds [16]. This is due to the exo-anomeric effect. The exo-anomeric effect can be considered as an interactionbetween the lone pairs of O1 with those of the ring oxygen O5.

Van der Waals- and Coulomb interactions are through space interactionsi.e. interactions which occur between atoms separated by more than 3 linksand even if they are in different molecules (for example one atom could bein a solvent molecule and the other in the solute).

Electrostatic interactions occur between charged atoms. Alternativelythey can be described as bond dipole interactions. Electrostatic interactionscan be attractive or repulsive. They do not only depend on charge anddistance but also on the medium. Electrostatic interactions are weak underaqueous conditions.

Van der Waals interaction are extremely weak at high distance. Theattraction grows slowly until the two atoms reach a distance which is aboutthe sum of their atom radii. When the atoms move even closer the attrac-tion turns into repulsion and rises drastically. VdW interactions are crucialfor energy calculations, in fact some simple force fields only consider VdWinteractions an ignore all the other terms.

Each type of interaction can be described with a separate energy expres-sion. The parameters used in these expressions depend on the atom types.These parameters can be obtained from X-ray and spectroscopic data fromsimple organic molecules. For example the O-H bond angle in ethanol is109.48 degrees. This can be seen as the ideal angle for all primary hydroxylgroups and can therefore be transferred. A very important assumption offorce fields is this transferability of parameters.

The other assumption is that the total potential energy of the moleculeis a sum of the potential energy contributions of the different bonds, angles,torsions, etc. in the molecule.

4.1.3 Complete force fields

Here one tries to include all terms that can be parameterized. The potentialenergy function of the force field may look like this:

E = Ebl + Eba + Etor + Eoop + EV dW + Eel + [Ehb] + (Esol)

Explanation:Ebl describes the deviation from the ideal bond length, Eba considers bondangles, Etor torsion angles, Eoop out of plane deformations of planar systems,EV dW represents Van der Waals interactions, and Eel the electrostatic in-teractions. Some force fields may have a term for hydrogen bonding Ehb.However, this is not essential since hydrogen bonds can be considered in Eel.

4.2 Methods for the generation of molecular conformations 16

What about the impact of the solvent? All biochemistry happens in anaqueous environment. Water may have a strong influence on the folding ofthe molecules. Unfortunately it is very hard to include water in calculationsbut some force fields have a term for the solvation energy, Esol. This termis usually based on area and the properties of the molecular surface exposedto the solvent.

Minimization

A force fields allows the calculation of the potential energy of a rigid molecule.However, usually one is interested in finding the energy minima and theirgeometries by allowing the molecule to relax. Several minimization methodshave been developed. They all require the first derivative of the potentialenergy function with respect of each variable (x,y,z). Some of these meth-ods also require the second derivatives. All partial derivatives are usuallyobtained analytically [17].

4.1.4 Truncated force fields - e.g. HSEA

For some applications it is possible to ignore certain energy term in theforce field. One such truncated force field commonly used for carbohydratesis called the HSEA-method. In this method only Van der Waals interactionsand one particular torsion interaction, the exo-anomeric effect [18], are con-sidered. The Glycan program [13], used in the present study is based on theHSEA-method.

SWEET [19] also uses hard sphere calculations, but the exo-anomericeffect is not considered.

Truncated force fields only give a rough estimate of the molecular energy.However, these methods can be very valuable for preliminary studies offavored conformations, in particular for very complex systems.

4.2 Methods for the generation of molecular con-formations

The methods discussed above allow energy calculations for a given 3D struc-ture. In order to find the energetically favored conformations it is necessaryto generate different 3D structures for energy evaluation and for energyminimization.

4.2.1 Systematic search

Systematic search, also called grid-search is the traditional approach to findlocal minima. The torsion angles are systematically changed in small steps(max. 30 ◦). In the case of calculations on saccharides the systematic search

4.2 Methods for the generation of molecular conformations 17

Figure 4.1: Schematic picture showing the different energy terms of a typicalforce field.

4.2 Methods for the generation of molecular conformations 18

is usually performed only with respect to the Φ/Ψ-torsions of the glycosidiclinkages. These torsion angles have a dominating influence on the overallconformation and the effect of the other torsions on the conformationalenergy can often be neglected.

It is possible to identify the global energy minimum and the secondaryenergy minima on an 2-dimensional energy surface as a function of Φ/Ψ.The energy levels of the surface are often indicated by colors on the surface.In this study the low energy regions are drawn in blue, the high ones in red.

If the molecule is treated as rigid (like in HSEA) during the search onegets rigid potential energy maps. If the whole structure is minimized in eachstep one gets a relaxed energy surface.

Rigid maps are fast to calculate since the time consuming minimizationstep is skipped. If filtering is used ‘rigid searches’ can be used for six or evenmore degrees of freedom (dimensions). Rigid maps give a rough estimateof the energy surface and should be interpreted carefully for more complexsystems. On disaccharides rigid maps and relaxed maps look rather different.Fig. 4.2 compares a rigid map obtained from the Glycan program with arelaxed map using MM3. Relaxed maps have wider allowed energy areas.The energy surface appears smoother in the relaxed map.

Figure 4.2: The rigid (left), and relaxed (right) energy maps of α-D-GlcpNAc(1→3)α-D-GlcpNAc a disaccharide unit found in the O-antigenof Shigella dysenteriae type 4. The rigid map was obtained from the Glycanprogram using a modified HSEA, the relaxed map was obtained from theMM3 program using its own force field.

A relaxed Φ/Ψ search can be performed with several sensibly chosenstarting conformations for torsions which are not involved in the glycosidiclinkages. The relaxed maps are united to one single map by choosing foreach data point the lowest value from all relaxed maps. The resulting mapis an adiabatic map.

Also it is possible to perform a multidimensional Φ/Ψ search and obtainan adiabatic map of the Φ/Ψ torsions of a specific glycosidic linkage.

4.2 Methods for the generation of molecular conformations 19

Adiabatic maps are of great importance since they can show the energybarriers in complex systems. However, to produce a good adiabatic maprequires many relaxed surface runs which takes a lot of time. At presentthis cannot be done for more than 4-5 degrees of freedom.

4.2.2 Monte Carlo

Systematic search even with the very fast HSEA is limited to relativelysmall systems. With the Monte Carlo method much bigger systems can bestudied.

The glycosidic linkages are changed randomly (eg. in 15 ◦ steps). Foreach newly generated structure the energy is calculated. If the energy ofthe new structure is lower or equal to the old structure the new structureis accepted. If it is higher the difference in energy (∆E = Enew − Eold) isused to calculate the Boltzmann factor (e−

∆ERT ) which is then compared to a

random number between 0 and 1. If the Boltzmann factor is higher or equalto that random number the new structure is accepted, despite of its higherenergy. This can prevent getting stuck in local minima. After repeating thisseveral hundred thousand times, one obtains the Boltzmann distribution forthe conformational space at the temperature T.

So far Monte Carlo simulations on saccharides have only been used usingtruncated force fields which makes the results rather unreliable [20].

4.2.3 Molecular Dynamics

Another method to generate different conformations are molecular dynamics(MD) methods. They also allow the analyses of time dependent molecularproperties. Another advantage with MD is that explicit solvent moleculesmay be included in the simulation. This is not possible with SystematicSearch and Monte Carlo simulations. The big conformational changes donewith these methods at every step disrupt the solvent structure to such anextent that it becomes impossible to relax the solvent shell by minimization.

A disadvantage of MD simulations is that they are computationally ex-tremely expensive. To make realistic simulations, the timestep can not bebe longer than about 1 fs. Even for a simulation time of only 1 ns 1,000,000structures have to be generated and their energy calculated. When twominima are separated by 3–4 kcal/mol (like for the hydroxymethyl group),then a transition will happen on average once in 1 ns at room temperaturewhich is too infrequent to obtain reliable Boltzmann distribution from asimulation.

One may solve that problem either by using an artificial negative energypotential to lower the energy barriers or by rising the simulation tempera-ture. However, high temperature simulations with temperatures of 1000 Khave some disadvantages. For instance the rings have to be stabilized by

4.3 Methods used in the present study 20

an additional energy potential. Otherwise they may flip into conformations(eg. twist, boat, inverted chair) which are disfavored under physiologicalconditions. Another drawback is the fact that water molecules cannot beincluded in high temperature simulations.

4.3 Methods used in the present study

4.3.1 Glycan - a modified HSEA program

Initial conformations

All monosaccharides in this study are aldo-hexoses forming pyranose rings.The linkages in the ring are unlike aromatic rings still twistable but theycan’t twist independently from each other but rather in an all at once way.Through twisting, six membered rings can form chair, boat, twist, and en-velope forms [16]. Since we have one hetero atom in the ring (an O), thetotal number of theoretically possible conformations is huge. Fortunatelythere are only few energetically sensible forms for most mono saccharides.

The mono saccharides building up the O-antigens studied in the presentthesis work are known to have one clearly preferred conformation and we canassume them to retain this form in the oligosaccharide [16]. For the Glycanruns we used the repeating unit with D-sugars in 4C1-conformation and theL-sugars in 1C4-conformation [16]. The geometries in the sugar units wereobtained from X-ray diffraction studies.

Glycan uses a modified HSEA method to find the preferred conforma-tion. It’s force field takes only van der Waals interaction and a specialtorsion term, the exo-anomeric effect, into account. Since Glycan does notconsider electrostatic interactions, no dielectric constant has to be defined.In aqueous conditions electrostatic interactions are weak anyway. The hy-droxy methylene groups were replaced by methyl groups during the energycalculations and all hydrogens from the hydroxyl groups are removed.

The neglect of the hydroxyl hydrogens is a safe approximation since thespace needed by hydrogens bound to oxygen is very small (smaller than forthe lone pairs) and hydrogen bonds are very weak in aqueous solutions.

Search

Glycan turns each torsion angle in each glycosidic linkage systematically in15 degree steps. For a tetrasaccharide saccharide with 3 glycosidic linkagesthat means a search in 6 Φ/Ψ dimensions. Therefore 246 > 190 million (!)conformations must be generated and calculated. How can such a confor-mational space be searched in a finite time scale?

1. Glycan treats each sugar unit with its substituents as a rigid unit. Nominimization is used to relax the structure for each Φ/Ψ point.

4.3 Methods used in the present study 21

2. Glycan uses filtering i.e. it makes two dimensional runs on disac-charide moieties first and takes only the Φ/Ψ angles below a certaincut-off level for the actual multidimensional search. In practice onlyabout 10% of the Φ/Ψ conformations in each disaccharide are allowedwith this filtering (see Fig. 4.2). Therefore this filtering has a greateffect on the number of conformations to be calculated. In a typicaltetrasaccharide the number of generated and evaluated conformationsis therefore reduced to about 400,000, which is about 0.2 % of the totalnumber of permutations of linkage conformations.

3. Glycan uses a very simple force field which considers only van derWaals interactions and the exo-anomeric effect (HSEA). The algorithmis highly optimized and written in FORTRAN [13].

4. The hydroxyl hydrogens are left away and the hydroxy methylenegroup is replaced by a simple methyl group. This reduction of thetotal number of atoms makes a small but significant speed-up.

Reliability of HSEA

The simplifications used in HSEA calculations especially the treatment ofthe rings as rigid units, is quite drastic. The filter criterium is very harsh aswell. One may ask how such an extremely simplified model can give usefulresults.

Glycan maps fits well to the maps from more accurate (but much slower)calculations using molecular mechanics. However, the allowed area of Φ/Ψangles in rigid maps is smaller than in relaxed energy maps. This bearsthe risk that Φ/Ψ values which might be interesting in the oligosaccharideare filtered out already during the disaccharide stage. That can easily hap-pen with branched constrained saccharides with vicinal substitutions on thesame sugar unit (see figures 3.2 and 3.3). For this reason Glycan is not gen-erally reliable on branched saccharides, even though it might give correctresults in special cases. All such calculations should therefore be checkedusing molecular mechanics. However Glycan does deal well with unbranchedoligosaccharides especially those with (1→3) or (1→4) linkages.

4.3.2 MM3

MM3 is seen as one of the best force field for saccharids [21, 22, 23, 24, 25]and small molecules in general. In addition to the standard force field termslisted in 4.1.3, MM3 includes three cross-terms, which should improve theaccuracy. Energy minima found with MM3 fit well to experimental datafrom X-ray crystallography experiments on simple disaccharides. Therefore,we chose MM3 as the main method for our studies. All calculations weredone with a dielectric constant of 80 to simulate aqueous conditions. The

4.3 Methods used in the present study 22

energy minimization of each conformation was carried out using the so called“block diagonal minimization” [17].

Initial structures

As starting conformations we used the minimum energy conformations ob-tained in a run with Glycan. The hydroxyl hydrogens were added in Sybyl.Most pyranoses have 6 free torsion angles, each with three stable conforma-tions (local minima close to −60 ◦, +60 ◦, and 180 ◦). Therefore 36 = 729stable conformations exist already for a monosaccharide! For a trisaccharidethere would be 318 = 4∗108 stable conformations. In practice the real num-ber would be much higher since the inter-glycosidic bonds must be searchedwith higher resolution, e.g. with a step length of 15 ◦ or 20 ◦.

To reduce the number of starting conformations we used the followingassumptions first described by French et al. [24]. The hydroxyl groups inone monosaccharide unit have all either clockwise (c) or anti-clockwise (r)orientation. There is also a stable conformation where the hydroxyl groupspoint into the ring, but that is highly unfavored and can be neglected.

Of the three stable torsions of the C5 − C6 − linkage two are alwaysmore stable depending on the C4-carbon. For monosaccharides with equa-torial hydroxyl group in C4 (glyco-form) we used gg and gt conformationfor the C6. For monosaccharides with axial hydroxyl group on C4 (galacto-form) we used gt and tg conformation. The preference is due to the stericalhindrance of the two oxygens. In Fuc, GlcA and GalA the C6 has no hy-droxyl group and shows symmetry which makes it possible to consider onlya single staggered conformation.

With these assumptions the total number of stable conformations for amonosaccharide is reduced to 4 for GlcNAc (ggr, gtr, ggc, ggr) and 2 forGlcA, GalA, and Fuc (c, r). For the disaccharides in the present study wetherefore considered 4, 8, or 16 starting conformations, depending on whichmonosaccharides they contained.1

The amide unit of the N -acetyl groups are set to be in trans form, sinceit is far more stable than the cis form. The H2 − C2 − N − Cam dihedralangle is set to 0. That is known to be a preferred conformation since itallows favorable dipole interaction between the C2 − H2 and the carbonylgroup.

The carboxyl groups of GlcA and GalA could not be typed automati-cally, due to an MM3 interface problem. They were typed manually. MM3lacked a parameter in its library for the carboxyl groups so the calculationswere done with estimated parameters. This estimation was done by MM3automatically.

1Note that this complication is avoided in the Glycan runs where the hydroxyl groupsin the ring are replaced by (hypothetical) single oxygen atoms, and the hydroxymethylgroups are replaced by methyl groups.

4.3 Methods used in the present study 23

Figure 4.3: 4C1-α-D-glucose minimized with MM3. 4 stable conformationsare assumed (ggc, ggr, gtc, and gtr) of which the gtr (left) and ggc (right) areshown above. The hydroxymethyl group can be in gt or gg conformation,while the tg conformation is unfavored due to the collision with the C4-hydroxyl group. The secondary hydroxyl groups can point in clockwise (c)or anti-clockwise (r) direction, but never directly up or down. (Note thatthe anomeric hydroxyl group has clockwise orientation in both minimizedstructures. This can be explained by the exo-anomeric effect.)

Search

First MM3 was used for systematic Φ/Ψ search on all the constituent dis-accharide moieties. Φ/Ψ were systematically searched in 15 degree steps.The disaccharides were calculated with driver option 4, which ensures thatthe starting conformation at each Φ/Ψ point was generated from the initialstructure. In each run 242 = 576 structures were generated and drawn ona relaxed energy map. The starting conformations were generated manu-ally with Sybyl. The runs were repeated using different starting conforma-tions with respect of the hydroxymethyl groups and the secondary hydroxylgroups (see section above).

The relaxed energy maps were united to an adiabatic map for every dis-accharide. An adiabatic map is produced by taking all relaxed energy mapsof the same molecule and picking the lowest energy value for each Φ/Ψ datapoint. Thus we obtained five adiabatic maps for each O-antigen. For thelinkages A and B this is however not enough, they are vicinal linkages andthe sugar units interact strongly with each other. The correct Φ/Ψ anglesmay be very different from the conformations obtained from the adiabaticmaps of the disaccharides.

For proper analysis of the branch region we had to set up a four dimen-

4.3 Methods used in the present study 24

sional search. In order to do so, some problems had to be solved. In MM3drivers cannot have more than two dimensions. Another problem is thehigh number of conformations (244 = 331776) which had to be generatedand minimized.

To solve that problem we used filtering i.e. Φ/Ψ conformations whichhad an energy above 10 kcal/mol from the global minimum for each disac-charide were ignored in the permutation of the starting conformations forthe trisaccharide. In analogy to Glycan this method explores the fact thatΦ/Ψ torsion angles which are energetically very unfavored already in the dis-accharide are unlikely to be favored in the trisaccharide. The filtering wasapplied using a utility program [13] which writes the starting conformationsas single entries with constrained Φ/Ψ angles. The starting conformationswere generated with Sybyl using gt conformation for the C5 − C6 links andr conformation for the secondary hydroxyl groups [24].

The primary output was a file with energy values as a function of 4torsion angles. This 4D-surface contained several gaps due to the filtering.Usually each Φ/Ψ value for any given linkage had several energy valuesdepending on the Φ/Ψ values of the other glycosidic linkage. Another utilityprogram (mm3extract) was used to pick out the lowest energy we could findfor every Φ/Ψ point of each linkage, and two adiabatic maps were generatedfrom the data. To the Φ/Ψ values where no values had been calculated(because of the filtering) a high energy value was assigned. Thereby thesevalues can be distinguished in the contour diagrams, which were generatedwith Gsharp.

4.3.3 Nomenclature of the torsion angles

Throughout this study we defined Φ as the torsion between H1−C1−O1−Cx

and Ψ as the torsion of C1−O1−Cx−Ox where x is 3 or 4 depending on thelinkage. The minimizations were performed with constrains applied for thesetorsions. The use of hydrogens to define the glycosidic torsions complies withNMR methods which are usually based on distances between hydrogens.

An alternative way to define the glycosidic torsions is the use of thesequences O5−C1−O1−Cx and C1−O1−Cx−Cx+1. This “heavy atom”definition is commonly used by crystallographers.

4.3.4 Sweet

The Sweet server [19] initially performs a hard-sphere search. Eventuallythe whole structure is minimized with MM3-Tinker which is an open sourceimplementation of the MM3 force field.

4.3 Methods used in the present study 25

4.3.5 Calculation of surface properties

Solvent accessible surfaces of the major minimum energy conformations werecalculated using the Connolly method implemented in the MOLCAD mod-ule of Sybyl. This surface was analyzed with respect to its electrostaticproperties and with respect to its lipophilicity using methods implementedin the MOLCAD module of Sybyl [26].

For calculations of electrostatic properties we used the Poisson-Boltz-mann method in which the protein is defined as a low dielectric cavity (ε =2) in a high dielectric medium (ε = 80) representing water. The chargedistributions were calculated using the Gasteiger method which is knownthe be the best method for small molecules. The ionic strength was set tozero in our calculations. There was therefore no need to to define an ionexclusion layer.

Lipophilicity plays an important role in molecular interactions. There isno simple physical model to calculate this effect. However the lipophilicityof a molecule can be measured in studying its partion in a polar/apolarheterogeneous system like water/octanol. This can lead to a determinationof the hydrophobic contributions of single atoms in their specific structuralenvironment which can then be generalized for all molecules. This methodis applicable only for small molecules.

Chapter 5

Results

5.1 Results from molecular mechanics calculations

5.1.1 Potential Energy surfaces of glycosidic linkages

From our calculations with Glycan and MM3, we obtained potential energysurfaces. Only adiabatic maps from MM3 are shown here (see Fig. 5.1–5.4).

They show that the rigid β glycosidic linkages are very restricted com-pared to the α linkages. Ψ angles around ±120 ◦ are highly unfavored inthe β-linkages. The rigidity of linkage A in the O-antigen of E. coli 159gives rise to one clearly defined conformation (Fig. 5.1). In the case of S.dysenteriae type 4 three (or six) almost equal energy minima can be foundin the branch unit. It can also be observed that the the minimum in linkageB is shifted in the trisaccharide as compered to the disaccharide (Fig. 5.2).

5.1.2 Modelling of favored conformations

Fig. 5.5 shows the minimum conformations of the branched tetrasaccharideunit of E. coli 159 and S. dysenteriae type 4. The torsion angles were setto the absolute energy minima we found using MM3 calculations.

Favored conformations of a sequence of 4 repeating units were built (seeFig. 5.6) using the results obtained from the systematic search with MM3on the branched tetrasaccharide. However, it has to be mentioned that thereare two highly flexible torsions in each repeating unit.

5.2 Comparative results from Glycan and Sweet

The Sweet server can produce preliminary energy maps. However, thesemaps are not evaluated here, only the torsion angles with the lowest energyare given in the Figures 5.7 and 5.8.

All three programs give different results for the Ψ values in linkages Dand E but they all lie within broad low energy areas according to MM3 (see.

5.2 Comparative results from Glycan and Sweet 27

Figure 5.1: Linkage A and B in E. coli 159 (see Fig. 3.4 on page 11 Theadiabatic energy maps of the disaccharides are on the left. The adiabaticenergy maps from the 4-dimensional filtered search of the whole trisaccharideare on the right. As one can see linkage A is highly restricted with a globalminimum Φ/Ψ = 60 ◦/10 ◦ both in the disaccharide and in the branchedtrisaccharide. Linkage B in the trisaccharide is restricted as well with anenergy minimum at Φ/Ψ = 30 ◦/−30 ◦. However in the trisaccharide linkageB shows a global minimum at Φ/Ψ = 50 ◦/50 ◦ and a secondary one atΦ/Ψ = 20 ◦/ − 30 ◦. It is apparent that the steric interference from theupstream β-D-GlcNAc residue causes a significant displacement of the globalminimum for the α-L-Fuc(1→4)-α-D-GlcNAc disaccharide moiety.

5.2 Comparative results from Glycan and Sweet 28

Figure 5.2: Linkage A and B in S. dysenteriae type 4 (see Fig. 3.5 onpage 12). The adiabatic energy maps of the disaccharides are on the left.The adiabatic energy maps of the 4-dimensional filtered search of the wholetrisaccharide are on the right. Linkage A shows two energy minima, theglobal minimum at Φ/Ψ = −30 ◦/ − 30 ◦ and a local minimum at Φ/Ψ =0 ◦/45 ◦. These minima are separated by an energy barrier which is dueto a collision of the hydroxymethyl group of the upstream residues withthe N -acetyl group of the downstream residue. Our results are supportedexperimentally by NMR and X-Ray experiments from α-D-GalNAc(1→3)β-D-GalNAc, which occurs in the Forssman antigen and has a structure similarto Linkage A. Linkage B has an energy map similar to that of Linkage B inE. coli 159 (see Fig. 5.1 on page 27)

5.2 Comparative results from Glycan and Sweet 29

Figure 5.3: Adiabatic maps of 2-dimensional runs of the linkages C, D, andE in E. coli 159 (see Fig. 3.4 on page 11). Linkage C shows a major energyminimum at Φ/Ψ = 30 ◦/30 ◦. Linkage D and E are highly flexible. TheΨ-torsion can rotate form −60 ◦ to +60 ◦ without any significant restriction.

Figure 5.4: Adiabatic maps of 2-dimensional runs of the linkage C, D, andE in S. dysenteriae type 4 (see Fig. 3.5 on page 12). Linkage C shows amajor energy minimum at Φ/Ψ = −30 ◦/−45 ◦. The adiabatic energy mapsof linkage D and E look, not surprisingly, almost exactly like the adiabaticenergy maps from the corresponding linkages in E. coli 159 (see above).

Fig. 5.3 on page 29).The minimal energy torsions obtained from Glycan fit almost perfectly

to the results obtained from MM3 for the branch region of E. coli 159. InS. dysenteriae type 4 however, the predictions deviate a lot from the resultsobtained from MM3. The Φ/Ψ values for linkage B are in a high energyarea according to our adiabatic maps obtained from MM3 (Fig. 5.2 on page28).

Sweet gives different results for the same oligosaccharide depending onthe order in which the sugar units are typed into the web interface. This isvery apparent in the branch regions. In one run the Φ/Ψ values of linkage

5.2 Comparative results from Glycan and Sweet 30

Figure 5.5: The rigid tetrasaccharide unit of E. coli 159 (left) comparedwith the homologous unit of S. dysenteriae type 4 (right). Note that theglycosidic linkage for the fucose branch in S. dysenteriae type 4 has twoother conformations with almost equal energy to the one shown here.

Figure 5.6: Modelled conformation of 4 repeating units of the O-antigens ofE. coli 159 (top) and S. dysenteriae type 4 (bottom). The glycosidic linkageswere set to the global energy minima we found in the systematic search. Thegreen sugar unit indicates the flexible region between the branches.

5.2 Comparative results from Glycan and Sweet 31

A fit well to the MM3 results but the Φ/Ψ values of linkage B show a highdeviation. If the ordering of the linkages in the branch is changed in the inputof Sweet, the strong deviation appears for linkage A instead. It seems thatSweet is not performing a full multi-dimensional search but rather a seriesof two dimensional searches, which works fine for the interbranch region butnot in the branch region.

Also the Sweet result for linkage C in S. dysenteriae type 4 (α-D-GlcpNAc-(1→4)-α-D-GlcA) is apparently wrong.

Figure 5.7: Results obtained for E.coli 159 from MM3 (bold, red), Glycan(plain, green), and Sweet (italic, blue).

Figure 5.8: Results obtained for S. dysenteriae type 4 from MM3 (bold,red), Glycan (plain, green), and Sweet (italic, blue).

5.2 Comparative results from Glycan and Sweet 32

Figure 5.9: Same as Fig. 5.5 with solvent accessible surface coded accordingto lipophilicity (high lipophilicity is shown in brown color).

Figure 5.10: The same solvent accessible surface as in Fig. 5.9 but col-ored according to electrostatic potential (blue indicates a strong negativepotential, orange/red is positive).

Chapter 6

Discussion

6.1 Favored Energy conformation

The results obtained from the systematic search with MM3 for the E. coli159 tetrasaccharide can be considered as very reliable. However, the exis-tence of two highly flexible torsions in each repeating unit makes it difficultto predict the overall conformation of this O-antigen. Very little can be saidabout the conformation of the flexible region with certainty.

In the case of the S. dysenteriae type 4 antigen the branch tetrasac-charide is flexible according to the MM3 calculations. Three (or possibly 6conformations) may be predicted for the branch region.

6.2 Surface properties

Fig. 5.10 shows the electrostatic maps of the two rigid tetrasaccharide units.The molecules have an overall negative potential, due to the carboxyl groupwhich is negatively charged under physiological pH but also due to the par-tial charges of the NAc-groups. The carboxyl group can be seen as a deepblue (hydrophilic) spot on the lipophilic surface (Fig. 5.9). The fucosebranch is the only part of the molecules which has a positive electrostaticpotential. This part of the antigens is also characterized by a high lipophilic-ity.

6.3 Relationship between structural properties &immunological reactivity

The anti-serum, which was used to prove the saccharide’s cross-reactivitywith antibodies contained polyclonal antibodies, i.e. a mixture of differentantibodies with different binding strengths and binding sites on the anti-gen. In fact the rabbit-anti serum, was obtained from rabbits which were

6.3 Relationship between structural properties & immunologicalreactivity 34

immunized against S. dysenteriae type 4. It may be that the anti-serumcontains antibodies against different conformers of which some can bind tothe antigen of E. coli 159.

Despite this we tried to predict the binding epitope. Due to the followingreasons, our main candidate was the branch region:

• The branch is always more exposed than the main chain and is there-fore a better target for antibodies.

• This region is rigid, which favors the binding of antibodies for ther-modynamic reasons [27].

The electrostatic potential in Fig. 5.10 suggest that there is a commonepitope comprising the fucose branch, the downstream GlcNAc and the car-boxyl group of the uronic acid. There are, however, some arguments againstthe branch region as the common epitope:

• The molecules have a very similar primary structure in the inter-branch region.

• This part could potentially be significant as an epitope since flexibleglycosidic linkages may loose some of their flexibility in long polysac-charides.

• The flexibility of the fucose branch in S. dysenteriae could limit theoccurrence of a common epitope.

• We did not include the O-acetyl group in S. dysenteriae type 4.

Thus we cannot predict the common epitope with certainty.

Chapter 7

Resources and tools

7.1 Molecular Modeling

Sweet 2 is a website which can be used to calculate minimum energy con-formations of saccharides.

MM3 is a program for molecular mechanics from Prof. Allinger’s group,Univ. of Georgia.

Glycan is an in house developed program to calculate the minimum en-ergy conformation of saccharides (nyholm@medkem.gu.se)

Sybyl is a powerful molecular modeling package from Tripos, Inc. Itincludes MM3 and MOLCAD. It was used for drawing all 3-dimensionalstructures and the molecular surfaces in this thesis.

7.2 Graphics

ChemDraw is a drawing program for chemical stuctures. It is developed byCambridgeSoft Corporation

GSharp from Advanced Visual Systems was used to generate the graph-ical energy maps.

CorelDRAW and Corel PHOTO-PAINT from Corel Corporation aregraphical software packages. They were used to edit and convert our graph-ics.

7.3 Others

This Thesis is written with the MiKTEX2.1 distribution of LATEX. TheTEXnicCenter was the LATEX editor used. We used PDFLATEX to compile theLATEX code into PDF format. 4spell was used to spell check this document.

Chapter 8

Acknowledgements

I would like to thank the people involved in the master program in bioinfor-matics in Goteborg University/Chalmers for creating a stimulating scientificatmosphere with many pleasurable social contacts.

Regarding this thesis I would like to thank Dr. Per-Georg Nyholm andmy master student collegue Jimmy Rosen for contributing and valuable crit-icism.

Armin RobobiAugust 2002

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