Chain−Chain Interactions for Methyl Polygalacturonate: Models for

The ability of pectins to form gels in the presence of calcium is well-known, and it implies the interaction of carboxylate groups and bivalent ions. ...
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Biomacromolecules 2005, 6, 1322-1328

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Chain-Chain Interactions for Methyl Polygalacturonate: Models for High Methyl-Esterified Pectin Junction Zones Isabelle Braccini,† Miguel A. Rodrı´guez-Carvajal,‡ and Serge Pe´ rez*,† Centre de Recherches sur les Macromole´ cules Ve´ ge´ tales,§ CNRS, BP 53, 38041 Grenoble Cedex 9, France, and Departamento de Quı´mica Orga´ nica, Facultad de Quı´mica, Universidad de Sevilla, 41071 Sevilla, Spain Received September 3, 2004; Revised Manuscript Received January 18, 2005

The ability of pectins to form gels in the presence of calcium is well-known, and it implies the interaction of carboxylate groups and bivalent ions. However, even when most of the galacturonic units are methyl esterified, pectins are able to form gels but only under certain experimental conditions. In this case, hydrogen bonding and hydrophobic interactions are believed to be responsible for gel formation, and it is likely, as in the other mechanisms of polysaccharide gel formation, that stable junction zones consist of cooperatively ordered chains linked together throughout nonbonded interactions to provide a three-dimensional network. To investigate the junction zones in HM-pectin gels, we investigated, by molecular modeling, all of the ways to associate two, and then three, fully methyl-esterified galacturonic acid chains. Two models are obtained: the first one is based on a packing of parallel chains; it agrees with the hypothetical model derived from fiber diffraction study (Walkinshaw, M. D.; Arnott, S. J. Mol. Biol. 1981, 153, 1075-1085); the second one displays an antiparallel orientation of the chains; it presents a better arrangement of the chains and, theoretically, a much lower potential energy. In both cases, all of the favorable associations occur within a network of hydrogen bonds and of hydrophobic contacts. Introduction Pectins with a degree of methyl esterification higher than about 40% (HM-pectin) are able to form gels under specific conditions: the pH has to be adjusted to below 3.5 and large quantities of a cosolute (typically sucrose, at a concentration greater than 55 wt %) have to be added.1 This behavior has been rationalized in terms of reduction in water activity by the cosolute and suppression of electrostatic repulsion between chains by protonation of the carboxylate groups.2 The function of sucrose in the gel formation of HM pectins would be to stabilize the junction zones by reducing water activity and promoting hydrophobic interaction between ester methyl groups. The concomitant occurrence of hydrogen bonding and hydrophobic interactions is believed to be responsible for gel formation. This is supported by the fact that urea substantially weakens the gel.2 Furthermore, Morris and co-workers2 have shown that ester groups make a positive contribution to the stability of interchain association in HM-pectin gels. The nature of junction zones in HMpectin gels is apparently very different from that of low methyl-esterified (LM) pectin gels.3-5 If the formation of LM-pectin junction zones is initiated by the formation of dimers, there is experimental evidence that junction zones in HM-pectin gels involve several chains. The presence of * To whom correspondence should be addressed. Telephone: 33-47603-76-30. Fax: 33-476-03-76-29. E-mail: [email protected]. † Centre de Recherches sur les Macromole ´ cules Ve´ge´tales. ‡ Universidad de Sevilla. § Institut de Chimie Mole ´ culaire de Grenoble, FR-CNRS 2607, affiliated with the Universite´ Joseph Fourier, Grenoble, France.

varying levels of polygalacturonate blocks having different degrees of esterification in the preparation of low water activity pectin gels has no inhibition effect on gel formation.6 This suggests that the cross-linking is predominantly through large aggregates involving a variable number of chains. The added segments in the competitive inhibition studies are presumably incorporated into aggregate structures without displacement of intact molecules. It is likely, as in the other mechanisms of polysaccharide gel formation, that stable junction zones consist of cooperatively ordered chains linked together by a nonbonded interaction to provide a three-dimensional network. As water is hardly present and the junction zones apparently involve several chains, the arrangement of ordered methyl pectate chains packed together in the junction zones must be similar to the packing arrangement found in the solid state. This is the reason all of the structural features of the junction zones in methyl pectate gels described in the literature refer to the model derived from a diffraction study performed on highly oriented fibers of dried pectinic acid solutions.5 As explained in the following section, this model is speculative. The unique accurate data extracted from this study concern the conformation of the methyl polygalacturonate ester chains: there is no doubt that the helical form is a 3-fold helix with a rise per residue of 4.3 Å. To investigate the structural basis underlying the formation of the junction zones in HM-pectin gels, we studied, by molecular modeling, all of the ways to associate two, and then three, fully methyl-esterified galacturonic acid chains. We also made calculations with the associations restricted to those corresponding to space group

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Interactions for Methyl Polygalacturonate

Figure 1. Schematic representation of the methyl polygalacturonate with the labeling of the atoms and the torsion angles of interest.

P21, and to parallel arrangement in order to evaluate the model proposed by Walkinshaw and Arnott.5 This molecular modeling procedure has been successfully applied to the study of the associations of polygalacturonate and polyguluronate chains.4 In these calculations, we used the optimized 31 helical conformation previously determined for polygalacturonic acid4,7 as it has been shown8 that the methoxyl group does not have a significant influence on the conformational behavior of the polysaccharide. Moreover, the preliminary study performed on fully esterified galacturonic acid oligomer8 (model for pectinic acid) to identify the stable ordered conformations of this structure has indicated that the 31 conformation is more favorable that the 32 one. Consequently, we limited the present study to the associations of 31 helical chains. Methodology and Computational Methods Nomenclature. A schematic drawing of the methyl polygalacturonate, along with the labeling of the atoms and the torsional angles of interest, is given in Figure 1. The conformation about the glycosidic linkage is described by two torsional angles Φ ) O5-C1-O1-C4 Ψ ) C1-O1-C4-C5

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was excellent. Thus, the potential energy surface obtained is representative of the conformational behavior of the disaccharide unit and could be used to model the most stable helical conformations. The values obtained for a helix made from the most stable conformer gave a 31 helix with h ) 4.4 Å, which was used in this study. The regular helices were then generated from the monosaccharides using the program POLYS14 (see ref 7 for the detailed description of the procedure). The generated 9-unit chains correspond to 31 helical conformations, with Φ ) 74° and Ψ ) 94°. As a prerequisite for the chain-chain interaction procedure, the helix axes of all of the individual chains are coincident with the Z axis. Interchain Energy Calculations. The interaction energy of the two chains is considered on an atom-atom potential basis and is calculated as the sum over all contributions of pairwise interactions. The expression used in the evaluation of the interchain interaction energy is NA N B

EAB )

∑ ∑Elj + Ehb + Eel i)1 j)1

where NA and NB are the number of atoms in chains A and B respectively, Elj, Ehb, and Eel are the three enthalpic components Lennard-Jones, hydrogen bonds, and electrostatics of the interaction, respectively. The van der Waals contribution is represented by the 6-12 Lennard-Jones potential Elj(i,j) ) A/rij12 - B/rij6 where rij is the interatomic distance (in Å), and A and B are coefficients related to the atomic van der Waals radii, polarizabilities, and effective numbers of electrons. The hydrogen bonds are defined on the oxygen-oxygen distance criteria, and the energy contribution is calculated using

The orientation of the methyl ester groups is described by the dihedral angles

Ehb(i,j) ) 33.14(rij - 2.55)(rij - 3.05)

ω ) O5-C5-C6-O7

The distance between the two oxygen atoms should lie between 2.55 and 3.05 Å. The electrostatic term is defined following the expression used in the GRID program16

χ ) C5-C6-O7-C7 The signs of the torsion angles are in agreement with the IUPAC-IUB commission of Biochemical Nomenclature.9 Single Chain Conformation. The two most favorable orientations of the methyl ester group in methyl R-Dgalacturonate (ω ) 180°, and χ ) 140° or 0°) were taken from a previous work.8 Methyl R-D-galacturonate monosaccharides were minimized using the general molecular mechanics program MM3(92)10,11 (with specific terms for the acidic moieties included in the force field12) and then implemented in the MONOBANK13 database (bundled to POLYS14). Molecular modeling and NMR study of methylated pectic disaccharide and digalacturonic acid have been reported.7,8,15 In the case of methyl galacturonate disacharide, several conformers could be identified having (Φ, Ψ) of (80°, 100°) (the most stable conformer), (80°, 140°), and (120°, 160°). The agreement of NMR data and the expected NOESY values calculated from the relaxed map of this disaccharide

(

Eel(i,j) ) Kqiqj

)

1 2 M + W rij

where K is a constant, qi and qj are the partial atomic charges of the i and j interacting atoms, and M and W are the dielectric constants of the target system and the surrounding medium, respectively. In the present study, we used M ) 4 and W ) 80 (water). A cutoff distance of 12.5 Å was used in computing the electrostatic contribution. All of the parameters used in these calculations were extracted from, or computed (partial charges, qi) by, the GRID program and are listed in Table 1. Chain-Chain Interaction Procedure. To evaluate the favorable chain pairing configurations for methyl polygalacturonate, a computer program capable of evaluating chain-chain interactions was utilized.17 In this procedure, the inter-helical distance, ∆X, along with the interaction energy between two chains is computed for all of the relative

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Table 1. Atom Types and Associated Parameters Used in the Calculations atom number

1

atom type polarizability effective number of electrons vdW radius partial charge

(sp3)

C 0.98 5 1.8 0.048

2

3

4

5

6

O (hydroxyl) 1.00 6 1.6 -0.269

H (aliphatic) 0.10 1 1.15 0.100

O (ether) 0.64 6 1.6 -0.269

O (CdO, ester) 0.84 6 1.6 -0.319

C (ester) 1.65 5 1.8 0.253

positions of one chain (A) with respect to the other (B). Initially, the two chains are superimposed in either a parallel or in an antiparallel arrangement, with their helical axes coinciding with the Z axis. Then, the calculation is performed by rotating A (µA) and B (µB) by 10° increments over the angular range 360°/n (using the symmetry of the system, in this case, n ) 3) and by translating B (∆Z) over the length of a whole fiber repeat, by about 0.25 Å increments. For each combination of the µA, µB, and ∆Z parameters, the chain B is moved away from A chain along the X axis, until the van der Waals surfaces of the A and B chains are in contact, with no interpenetrating atoms. As this criterion is not valid for two atoms involved in a hydrogen bond, the hydroxyl protons cannot be considered in the interaction procedure, to not violate the above-mentioned van der Waals radii conditions. Three-Chain Interaction Procedure. Two procedures have been developed for the computation of the position and energy of three-chain associations. The first one is based on the P21 symmetry proposed in the model of Walkinshaw and Arnott,5 which implies that two chains have coupled rotation (the two chains that describe two consecutive rows) and the orientation of the third chain is obtained by a pure translation of one of them. Thus, the association of two chains (named A and B) is studied according to the procedure described above. For each AB couple, characterized by µA, µB, and ∆Z, a rotation along the Z axis (centered in A) is carried out (µAB angle); finally, a copy of the first chain is added (C chain) and translated along the X axis. The energy of the whole system is then calculated. This procedure is schematically represented in Figure 2. The second developed procedure allows the study of all of the associations of the three interacting chains, without any symmetry constraint. For that purpose, one needs to introduce the necessary parameters describing the relative position of the third C chain with respect to the A and B chains. The procedure is similar to that described above, except that the chain C is not only a translated copy of A, but it is, in addition, rotated (µC) and translated along Z axis (∆Z2). A scheme of this procedure is shown in Figure 3. The procedure has now six variables: µA, µB, ∆Z, µAB, µC, and ∆Z2. The angles µA, µB, and µC vary over the whole angular range; ∆Z and ∆Z2 vary over the crystallographic h parameter (rise per residue); and µAB is computed over 180° (to place B chain between both A and C chains). An energy cut off is applied to save the results, as a considerable number of possible associations is generated. Results Model for HM-Pectin Derived from Fiber Diffraction Study. Walkinshaw and Arnott studied by X-ray diffraction

Figure 2. Scheme of the procedure used in the calculation of the three-chain interactions considering a strong symmetry. (1) Starting from A chain, a coupled pair of chains (2) is generated by rotation (µA, µB) and translation along the Z axis (∆Z); (3) this pair is rotated (µAB) and (4) a new chain (labeled C) is added by translation of A chain through the X axis.

Figure 3. Scheme of the procedure used in the calculation of the full three-chain interactions. (1) Starting from A chain, a coupled pair of chains (2) is generated by rotation (µA, µB) and translation along the Z axis (∆Z); (3) this pair is rotated (µAB) and finally, (4) a copy of A chain through the X axis (C chain) is rotated (µC) and translated along the Z axis (∆Z2).

HM-pectin gels condensed into uniaxially oriented fibers.5 They observed that periodic ordering was quite local and that the independent definition of a unique structure was impossible. A strong meridional intensity at a spacing of 4.3 Å showed that, as for solid sodium pectate and pectic acid, the chain conformation was a 3-fold screw axis helix, presumably right-handed as in the two cited cases. A Bragg reflection with 7.3 Å spacing was (hypothetically) assigned to the separation of rows of helices isometrically arranged

Interactions for Methyl Polygalacturonate

Figure 4. Model for methyl polygalacturonate structure. Parallel chains are packed in a hexagonal lattice. Taken from ref 5.

on a hexagonal net with a ) b ) 8.4 Å, as in sodium pectate. The parallel arrangement of the chains was reported to provide the most efficient packing for the postulated net on the basis of theoretical calculations. All of these hypothetical structural features led to the following model for methyl polygalacturonate packing (Figure 4) and, consequently, for the junction zones in HM-pectin gels. This structure presents a network of O6- - -O3 interchain hydrogen bonds and a hydrophobic columnar stacking of methyl ester groups. These hydrogen bonds and hydrophobic interactions are thought to be the driving forces for chain association and concomitant junction zone formation. Computation of Chain-Chain Associations of Methyl Polygalacturonate Chains. As a first step in our study, all of the ways to connect two chains of methyl polygalacturonate (model for HM-pectin) under the stable ordered 31 form were explored, for the two different favorable orientations of the methyl ester group8 (ω ) 180°, χ ) 160° and -4.5°) (see Methodology section). The atom types and associated parameters for the structure used in the calculations are given in Table 1. The calculations performed on 31 methyl polygalacturonate chains indicated that, irrespective of the parallel or antiparallel arrangement, the best associations were obtained for the second stable orientation of the methyl group, χ ) -4.5°. This orientation corresponds to that found in the crystal structure of methyl (methyl R-D-galactopyranosiduronate).18 The geometric and energetic parameters of the best associations obtained for the parallel (|) and antiparallel (anti-|) arrangements of the regular methyl polygalacturonate chains under this methyl ester group orientation are reported in Table 2. The data reported in Table 2 indicate that the antiparallel arrangement of methyl polygalacturonate chains is much more favorable than the parallel one. There is nearly a 2-fold ratio between the interaction energies of the best associations. The electrostatic term presents a positive value which arises from the contribution of the methyl-ester group interactions. This type of interaction, which correlates with the hydrophobic interactions, should have a specific treatment. As the phenomenon is very complex (involving, for example, an entropic component) and there is no available parametrization of these interactions in the literature, we did not modify the electrostatic term to take into account this

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particular interaction. As a consequence, the electrostatic energy term is meaningless and was not computed in the rest of the calculations (with three chains, see the next section). The most efficient way to connect the chains was roughly the same, as illustrated in Figure 5 by the best structures of each possible parallel or antiparallel arrangement. These structures interact side by side offering the maximum possible number of van der Waals contacts, which are nevertheless rather low due to the steric hindrance caused by the methyl ester groups. In both arrangements, the associations build an intermolecular network of hydrogen bonds and hydrophobic contacts between the methyl groups. The C-C distance between these groups is similar: 4.41 Å (|) and 4.51 Å (anti-|), which correspond to an efficient interaction. The parallel arrangement provides two interchain hydrogen bonds (HB): a strong HB O2(A)- - -HO3(B) (oxygen-hydrogen distance) of 1.79 Å, being O2(A)- - O3(B) of 2.73 Å, and a weak HB HO3(A)- - -O3(B) of 2.53 Å (Figure 5), being O3(A)- - -O3(B) of 3.34 Å. The antiparallel arrangement generates a more efficient hydrogen bond network with two efficient HBs: HO3(A)- - -O2(B) (1.98 Å, being O3(A)- - -O2(B) of 2,78 Å) and O3(A)- - HO3(B) (1.81 Å, being O3(A)- - -O3(B) of 2,75 Å), and a weaker one O2(A)- - -HO3(B) of 2.36 Å (being O2(A)- - O3(B) of 2,78 Å). The ensemble of these interactions involves one-third of the methyl galacturonate residues, as a consequence of the 3-fold helical conformation. These results indicate that, irrespective of the orientation of the arrangement, the hydrogen bonds, but also the hydrophobic contacts between methyl groups, are the important parameters for an efficient association of the chains. This is in agreement with the experimental data, which all suggest that hydrogen bonding and hydrophobic interactions are the driving forces for the formation of the junction zones in HM-pectins.5 Furthermore, these models clearly indicate that hydrogen bonds involve hydroxyl groups at C2 and/or C3. As the hydrogen bonding contribution is essential for the association of the chains, any substitution at these positions would prevent, at the same time, both the formation of the hydrogen bonds and the connection of the chains, as already put forward for calcium pectate system.4,19 Computation of the Associations of Three Methyl Polygalacturonate Chains. Considering the fact that the junction zones in HM-pectin involve several chains packed together and that the conformation is a 3-fold helical conformation, we envisaged the calculations of three interacting chains. This situation is in better agreement with the structural features described.5 (1) EValuation of the Model DeriVed from the Fiber Diffraction Data. Based on poor X-ray data and on the structure of solid sodium pectate, a model was proposed for solid methyl polygalacturonate. As in all the other structures of pectate (sodium of calcium) and pectic acid, this model considers that there is a strong symmetry between the chains: two chains have coupled rotation (the two chains that describe two consecutive rows) and the orientation of the third chain is obtained by a pure translation of the first

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Table 2. Calculated Interchaina and Energyb Parameters for the Best Chain-Pairing Situations of Methyl Galacturonate Oligomer in Both Parallel (|) and Antiparallel (anti-|) Arrangements parameters | arrangement

anti-| arrangement

minimum

µA

µB

∆Z

∆X

ET

Elj

Ehb

Eel

1 2 3 1 2 3

80 100 80 80 100 0

20 40 40 100 70 60

9.74 2.21 0.00 8.42 7.53 0.44

7.11 8.21 7.86 6.77 7.35 8.33

-13.5 -12.4 -12.5 -25.6 -16.8 -16.0

-9.2 -6.4 -6.1 -13.5 -10.5 -7.0

-11.6 -11.9 -11.7 -18.3 -11.8 -12.2

7.3 6.0 5.4 6.2 5.5 3.2

a µ and µ in degrees, ∆Z and ∆X in Å. b Energies are expressed in kcal/mol (E , total energy; E , Lennard-Jones energy contribution; E , hydrogen A B T lj hb bond energy contribution; Eel, electrostatic energy contribution).

Figure 5. Best chain situations for (a) parallel and (b) antiparallel arrangement of methyl polygalacturonate chains. Distances are given in Å.

one. The model proposed presented a parallel arrangement of the chains (see above). This procedure has been applied on the parallel arrangement of methyl polygalacturonate chains. The best association obtained is very close to the structure proposed by Walkinshaw and Arnott.5 The rotational position is identical, and there is only a slight discrepancy with respect to the interhelical distances, which probably arises from a small difference in the position of the methyl ester groups. The structure calculated is represented in Figure 6. The agreement between the “experimental-derived” model (Figure 4) and the best calculated one indicates that, if the arrangement is effectively parallel and the space group is the postulated one (P21), then the structure of solid methyl polygalacturonate corresponds to that presented in Figure 6, and it may also represent the structure of the junction zones in low water activity HM-pectin gels. For information, we point out that the structure presented by Oakenfull and Scott20 as the front view of the model

proposed by Walkinshaw and Arnott (these authors reported only a top view of their model) and reused in many other articles is totally wrong: the structure presented corresponds to an antiparallel arrangement of the chains, which is in complete disagreement with the parallel arrangement proposed by the authors of the model. (2) Computation of all of the Associations of Three Interacting Chains. As the model discussed above is highly speculative, we considered the interaction of three chains together with no assumption concerning their relative positions: all of the possible associations were screened for both parallel and antiparallel arrangements (see Methodology section). As mentioned above, the electrostatic term is meaningless and was not computed in these calculations. Generally, the resulting favorable associations share a common feature: two chains, at least, present a packing corresponding to one of the best associations identified in the computation of chain-chain interactions. The geometrical and energetic parameters of the best parallel and antiparallel

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Interactions for Methyl Polygalacturonate

Figure 6. Botton (a) and front (b) views of the resulting calculated model for methyl polygalacturonate based on a P21 symmetry. Distances are given in Å.

Figure 7. Best associations of three interacting methyl polygalacturonate chains for (a) parallel and (b) antiparallel arrangements. For the sake of simplicity, the hydroxylic hydrogen atoms are not represented. Distances are given in Å.

arrangements of methyl polygalacturonate are reported in Table 3. The results reported in Table 3 indicate that, as for the chain pairing situations, the antiparallel arrangement is largely better than the parallel one. The best association found in the antiparallel arrangement corresponds to the best chainpairing (see above) with the C chain symmetrical to the A chain. This is a very compact association which presents a network of hydrogen bonds and hydrophobic contacts. Moreover, the best association of three parallel chains corresponds twice to one of the best chain-chain associa-

Table 3. Calculated Interchaina and Energyb Parameters for the Best Associations of Three Methyl Polygalacturonate Chains in Both Parallel (|) and Antiparallel (anti-|) Arrangements µA

µB

∆Z

∆X µAB µC

∆Z2 ∆X2

ET

Elj

Ehb

| 80 40 0.00 7.86 20 20 0.00 14.78 -35.8 -12.4 -23.4 anti-| 80 100 8.42 6.77 30 110 0.00 11.74 -63.7 -27.1 -36.6 a µ , µ , µ , and µ in degrees. ∆Z, ∆X, ∆Z2, and ∆X2, in Å. b Energies A B AB C are expressed in kcal/mol (ET, total energy; Elj, Lennard-Jones energy contribution; Ehb, hydrogen bond energy contribution).

tions, named “minimum 3” in Table 2. The structure is symmetrical: the A-B interaction being identical to the

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B-C interaction. Such an arrangement is interesting as it presents two different networks of hydrophobic contacts: one being horizontal through A-B-C and the other one being vertical through A-B and B-C. These two structures are given in Figure 7. Conclusions The present study provides some structural information on the association of methyl polygalacturonate chains, which might be applied to the structure of the junction zones in low water activity HM-pectin gels. The model derived from a fiber diffraction study, which presents a packing of parallel chains related by a strong symmetry relationship, corresponds to the best association when these conditions, i.e., the parallel arrangement and the symmetry between the chains, are imposed. If these features are valid, this model may be representative of the solid methyl polygalacturonate structure and of the association of the chains inducing gel formation. This paper describes a systematic approach to the study of the methyl polygalacturonate chain associations based on energy considerations. We have found a model very close to that described by Walkinshaw and Arnott,5 which indicates that this latter is suitable for describing low-energy chain associations. Nevertheless, this model is not unique: we have found another possible packing considering antiparallel chains. Moreover, all of the calculations performed on two and three interacting chains indicate this antiparallel arrangement is much better than the parallel one, at least in relation to the arrangement of the chains. In both arrangements, all of the favorable associations present a network of hydrogen bonds and of hydrophobic contacts. These interactions are essential for the connection of the chains and, as suggested by numerous experimental results, are probably the driving forces for the formation of the junction zones of methyl polygalacturonate under low water activity conditions. The calculated structures are models and cannot be considered as fully representative of the junction zones in methyl polygalacturonate gels. We seriously miss some accurate crystallographic data that, at least, allow the parallel or antiparallel packing of chains to be identified, as well as profitable comparisons to be made with theoretical structures and to guide the study with experimental constraints applied on the modeling work. Furthermore, a specific energy term for the hydrophobic interaction should improve the validity of the calculations, and allow for the computation of the electrostatic energy term. The model here proposed is very simple. It describes the interactions between large blocks of

Braccini et al.

esterified galacturonate residues, such as those found in pectins with a degree of methylation of about 70%. Its application to mixed zones with both methyl galacturonate and galacturonic acid units has not been tested, although it is reasonable to think that the arrangement of chains will not change while the degree of methylation remains high: since the required pH for gelation is bellow 3.5, there is a predominance of nondissociated acid groups; according to the X-ray study by Walkinshaw and Arnott,5 the pectic acid forms a 3-fold helix with torsion angles (Φ, Ψ) close to (80°, 90°); that is, there is no significant influence on the conformation of the helices. The nature of the interactions, however, could be modified, as the number of hydrogen bonds that could be formed is higher. Nevertheless, the proposed models can describe the interactions between chains in methyl polygalacturonate junction zones, where both parallel and antiparallel associations are possible. Acknowledgment. Financial support from Hercules Incorporated is acknowledged. The authors thank Dr. Robert P. Grasso (Hercules Research Center, Wilmington, DE) for his help and comments. References and Notes (1) Thakur, B. R.; Singh, R. K.; Handa, A. K. Crit. ReV. Food Sci. Nutr. 1997, 37, 47-73. (2) Morris, E. R.; Gidley, M. J.; Murray, E. J.; Powell, D. A.; Rees, D. A. Int. J. Biol. Macromol. 1980, 2, 327-330. (3) Ravanat, G.; Rinaudo, M. Biopolymers 1980, 19, 2209-2222. (4) Braccini, I.; Pe´rez, S. Biomacromolecules 2001, 2, 1089-1096. (5) Walkinshaw, M. D.; Arnott, S. J. Mol. Biol. 1981, 153, 1075-1085. (6) Powell, D. A.; Morris, E. R.; Gidley, M. J.; Rees, D. A. J. Mol. Biol. 1982, 155, 517-531. (7) Braccini, I.; Grasso, R. P.; Pe´rez, S. Carbohydr. Res. 1999, 317, 119130. (8) Cros, S.; du Penhoat, C. H.; Bouchemal, N.; Ohassan, H.; Imberty, A.; Pe´rez, S. Int. J. Biol. Macromol. 1992, 14, 313-320. (9) IUPAC-IUB. Arch. Biochem. Biophys. 1971, 145, 405-621. (10) Allinger, N. L.; Yuh, Y. H.; Lii, J.-H. J. Am. Chem. Soc. 1989, 111, 8551-8566. (11) Allinger, N. L.; Rahman, M.; Lii, J.-H. J. Am. Chem. Soc. 1990, 112, 8293-8307. (12) Allinger, N. L.; Zhu, Z.-Q.; Chen, K. J. Am. Chem. Soc. 1992, 114, 6120-6133. (13) Pe´rez, S.; Delage, M. M. Carbohydr. Res. 1991, 212, 253-259. (14) Engelsen, S. B.; Cros, S.; Mackie, W.; Pe´rez, S. Biopolymers 1996, 39, 417-433. (15) Gouvion, C.; Mazeau, K.; Heyraud, A.; Taravel, F. R.; Tvaroska, I. Carbohydr. Res. 1994, 261. (16) Goodford, P. J. J. Med. Chem. 1985, 28, 849-857. (17) Scaringe, R. P.; Pe´rez, S. J. Phys. Chem. 1987, 91, 2394-2403. (18) Hjortas, J.; Larsen, B.; Mo, F.; Thanomkul, S. Acta Chem. Scand. B 1974, 28, 133. (19) Rombouts, F. M.; Thibault, J. F. Carbohydr. Res. 1986, 154, 177187. (20) Oakenfull, D.; Scott, A. J. Food. Sci. 1984, 49, 1093-1098.

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