Stereochemical metrics of lectin–carbohydrate interactions: comparison with protein–protein interfaces

Enrique García-Hernández1, Rafael A. Zubillaga2, Adela Rodríguez-Romero and Andrés Hernández-Arana1,2

Instituto de Química, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México D.F., México 04510 and 2Departamento de Química, Universidad Autónoma Metropolitana Iztapalapa, A.P. 55–534, México D.F., México 09340

Received on February 16, 2000; revised on May 9, 2000; accepted on May 17, 2000.


    Abstract
 Top
 Abstract
 Introduction
 Results and discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
A global census of stereochemical metrics including interface size, hydropathy, amino acid propensities, packing and hydrogen bonding was carried out on 32 x-ray-elucidated structures of lectin–carbohydrate complexes covering eight different lectin families. It is shown that the interactions at primary binding subsites are more efficient than at other subsites. Another salient behavior found for primary subsites was a marked negative correlation between the interface size and the polar surface content. It is noteworthy that this demographic rule is delineated by lectins with unrelated phylogenetic origin, indicating that independent interface architectures have evolved through common optimization paths. The structural properties of lectin–carbohydrate interfaces were compared with those characterizing a set of 32 protein homodimers. Overall, the analysis shows that the stereochemical bases of lectin–carbohydrate and protein–protein interfaces differ drastically from each other. In comparison with protein–protein complexes, lectin–carbohydrate interfaces have superior packing efficiency, better hydrogen bonding stereochemistry, and higher interaction cooperativity. A similar conclusion holds in the comparison with protein–protein heterocomplexes. We propose that the energetic consequence of this better interaction geometry is a larger decrease in free energy per unit of area buried, feature that enables lectins and carbohydrates to form stable complexes with relatively small interface areas. These observations lend support to the emerging notion that systems differing from each other in their stereochemical metrics may rely on different energetic bases.

Key words: hydrogen bonding/hydropathy/packing/protein–protein complex/protein-sugar complex


    Introduction
 Top
 Abstract
 Introduction
 Results and discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
Lectins are a diverse and widely spread group of proteins that bind carbohydrates with high specificity (Rini, 1995Go). Although many biological functions depend on the recognition of lectins and carbohydrates, the binding between these molecules is characterized by low energetic changes, with dissociation constants that rarely exceed the millimolar range. Nevertheless, a comparative analysis of the structural and energetic properties of lectin–carbohydrate (L–C) binding and protein folding recently showed that L–C interactions are, in relative terms, actually much stronger than they appear in absolute terms (García-Hernández and Hernández-Arana, 1999Go). Indeed, it was found that the decrease in free energy per unit of buried area is on the average one order of magnitude larger in the formation of a L–C complex than in the folding of a globular protein. As judged by the extent of the enthalpic contributions and the overall hydrogen bonding stereochemistry, the stronger specific stabilization achieved by lectins and carbohydrates relies on more energetic polar-to-polar interactions.

In an attempt to further understand the molecular origins of the affinity between lectins and carbohydrates, we have carried out a detailed statistical analysis of the interfacial structure of 32 L–C complexes comprising eight different lectin families. In the examination of properties such as interfacial surface area, surface hydropathy, amino acid propensities, hydrogen bonding and packing, novel demographic trends were revealed. In addition, the overall properties of these heterologous interfaces were compared with those characterizing protein dimers, an exercise that helps contextualize L–C complexes within the wide and varied spectrum of complex classes that proteins are able to form. In general, the study shows that L–C interactions have been optimized in such a way that their packing is significantly tighter than the packing of protein–protein (P–P) interfaces or protein interiors. The origin of this behavior seems to be related to a much stronger prevalence of polar–polar interactions and a higher interaction cooperativity. Finally, an energetic comparison of L–C and P–P complexes is presented to further reinforce the emerging notion that systems differing from each other in their stereochemical metrics also rely on different energetic bases (Xu et al., 1997Go; García-Hernández and Hernández-Arana, 1999Go).


    Results and discussion
 Top
 Abstract
 Introduction
 Results and discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
Data bases of lectin–carbohydrate and protein–protein complex structures
A recent release of the protein data bank (PDB; Bernstein et al., 1977Go) was surveyed for L–C structures, and the process of selection (see Materials and methods) led to a final group of 32 complexes, as detailed in Table I. To perform a comparative analysis of the geometric properties of L–C interfaces with those characterizing P–P interfaces, the data set of 32 non-homologous protein homodimers studied by Jones and Thornton (1996)Go was analyzed here with the tools and criteria described in Materials and methods. In two cases (3sdh and 3ssi), structures solved recently with an improved resolution were included instead of the entries (1sdh and 2ssi) used by Jones and Thornton (1996)Go. All other PDB entries were identical: 1cdt, 1fc1, 1il8, 1msb, 1phh, 1pp2, 1pyp, 1utg, 1vsg, 1ypi, 2ccy, 2cts, 2gn5, 2or1, 2rhe, 2rus, 2rve, 2sod, 2ts1, 2tsc, 2wrp, 3aat, 3enl, 3gap, 3grs, 3icd, 3sdp, 4mdh, 5adh, 5hvp. Additionally, the exterior and interior of 42 globular monomeric proteins (Stickle et al., 1992Go) were analyzed for surface polarity and residue composition.


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Table I. Data set of lectin–carbohydrate complexes
 
Interface size
Table II shows the size of the 32 L–C contact zones as measured through the total accessible surface area buried upon binding ({Delta}ASAt). As shown in Table III, the binding of lectins to monosaccharides buries on average lesser amounts of surface area than those buried in the binding to di- or trisaccharides. Yet, by normalizing the interface size with the number of carbohydrate units that meet the lectin, it becomes evident that the largest burying of area takes place at the primary subsite. This property coincides with the observation that the enthalpy change accompanying the binding of a lectin to its disaccharide (trisaccharide) is substantially lower than the double (triple) of the value observed in the binding to the monosaccharide.


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Table II. .Size (Å2) and hydropathy of L–C interfacesa
 

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Table III. Absolute and relative average interface sizes (Å2) for lectin–carbohydrates complexes
 
The data set of L–C complexes yields a mean {Delta}ASAt of 435 ± 129 Å2. This size is almost one order of magnitude smaller than the mean value of 3317 ± 2057 Å2 that we obtained for the 32 protein homodimeric interfaces. As pointed out by Stites (1997)Go, both theoretical and experimental considerations strongly suggest that a minimum interface area of ~800 Å2 is required for the formation of a P–P complex. Strikingly, this lower limit is close to the size of the largest L–C interface in our database.

Interface hydropathy
Interface hydropathy indexes (¶p) were calculated from the ratio of the change in accessibility of polar surfaces ({Delta}ASAp) to {Delta}ASAt. It can be seen in Table II that ¶p values of L–C interfaces vary across a broad interval, ranging from 0.342 to 0.662. Notably, marked differences in polar content can be observed also between complexes of the same lectin, as in the case of the concanavalin A complexes 5cna and 1cvn. Thus, even when common binding patterns can be distinguished within a given lectin family (Sharma and Surolia, 1997Go), complexes of homologous lectins are not necessarily redundant under the interfacial hydropathy metrics.

A plot of ¶p versus {Delta}ASAt (Figure 1A) reveals that these parameters are strongly correlated (p = -0.91) in the case of lectin–monosaccharide complexes. Although this correlation dissipates considerably in oligosaccharide complexes (p = -0.38), when only their primary binding subsites (see Materials and methods) are considered, the data gather into the same trend as monosaccharide complexes (Figure 1B). Saliently, this demographic behavior is delineated by lectins with unrelated phylogenetic origin, indicating that independent interface architectures have evolved through common optimization paths. In contrast, since protein interiors and P–P interfaces do not present a covariance between size and hydropathy (p = 0.24 and -0.32, respectively), it seems that P–P recognition events are based on different principles to those observed in L–C interactions.



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Fig. 1. Hydropathy versus size ({Delta}ASAt) for lectin–carbohydrate interfaces. (A) Lectin-monosaccharide complexes. (B) Lectin–monosaccharide complexes plus primary subsite interfaces of lectin–oligosaccharide complexes. The solid lines come from least squares linear fittings to the data.

 
Table IV presents the average hydropathy index of the 32 L–C interfaces, and compares it with those obtained from other protein environments. A virtually identical mean ¶p (0.490 ± 0.083) results from the average of the mean values of lectin families. According to these data, L–C interfaces have on the average a notably larger polarity than other protein zones, including protein surfaces, although some of them can be as hydrophobic as a protein interior.


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Table IV. Hydropathy of L–C interfaces and other protein environmentsa
 
Amino acid composition and residue propensities
Table V shows the percentage frequency of hydrophobic, polar and charged residues of lectin binding sites. The composition of protein-binding sites, and of protein exteriors and interiors are presented for comparison. It is evident that lectin binding sites exhibit the lowest incidence of hydrophobic groups, while they are the most enriched in polar groups.


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Table V. Percentage composition of residue classes at L–C interfaces and other protein environments
 
Figure 2 shows residue propensities of carbohydrate- and protein-binding sites. Overall, the figure is in agreement with the more qualitative descriptions made previously for lectin binding sites (Rini, 1995Go; Weis and Drickamer, 1996Go). According to these results, the evolution of lectins to bind carbohydrates has been accomplished by overexpressing a subset of polar amino acids at the combining site in relation to the rest of the protein surface, with a strong preference for Asn, Arg, Asp, and His. Consistent with the trend to form polar environments, the preference for aromatic amino acids is strongly biased towards Trp and Tyr, while Phe, the most hydrophobic one, is rarely expressed. In contrast, it is clear that hydrophobic groups are in general more likely to be incorporated into protein- than into carbohydrate-binding sites.



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Fig. 2. Residue interface propensities for carbohydrate- (open bars) and protein-binding (solid bars) sites. A propensity value > 1 (< 1) indicates that the residue is more (less) preferred to be incorporated at the binding site than elsewhere in the protein surface.

 
Peptide bond groups have been found to play a crucial role in the formation of a number of L–C complexes (Weis and Drickamer, 1996Go). In a second step, we recalculated the composition of lectin combining sites by differentiating peptide groups from side chains, finding an average peptide composition of 13.6%. In relation to the rest of lectin surfaces, this composition corresponds to a propensity of 0.3, with a variation interval from 0.0 (C-type binding sites) to 0.6 (legume binding sites), a result that indicates that actually peptide bonds belong to the subset of polar groups which tend to be segregated from lectin combining sites.

Being polyhydroxy compounds, carbohydrates are highly hydrophilic molecules. Not surprisingly, binding sites in lectins were found to have a higher hydrophilicity than other protein regions, including protein exteriors. Hence, lectin binding sites could be described as hydrophilic patches on protein surfaces. This picture contrasts with that for binding sites of protein homodimers, which have been realized to be more hydrophobic than the remainder of the protein exterior (Stites, 1997Go).

Surface complementarity
As detailed in Materials and methods, the interface compactness was measured using two different approaches: the gap index (GI), which is a measure of the total cavity volume at an interface, normalized by {Delta}ASAt, and the average distance (D) between closest interface atom pairs.

GI values for L–C interfaces were found to be distributed in the range of 0.20–1.98 Å, with a mean of 1.00 ± 0.48 Å. This value is significantly smaller (risk level <1%) than the mean GI of 2.20 ± 0.83 found for protein homodimer interfaces (Jones and Thornton, 1996Go).

As a second measure of intermolecular packing, average distances for closest polar-polar (Dp), polar-apolar (Dp-ap), apolar-apolar (Dap), and any (Dt) atom pairs at L–C interfaces were obtained. Furthermore, Di values were normalized by the sum of the van der Waals radii to obtain a relative measure (Ri) of the interatomic distance to the size of the two neighboring atoms. As shown in Table VI, distances of closest polar–polar neighbors at L–C interfaces were found to be significantly shorter than distances of other atom pair classes. As indicated by an average Rp value less than one, they are the only pair class whose van der Waals spheres tend to overlap. Moreover, differences in interatomic distances were also realized between subsites, with much shorter Dt values (~0.4 Å) at primary subsites than at other loci. Table VI also shows average distances for closest atom pairs at P–P interfaces. According to these data, intermolecular distances are significantly larger for P–P than for L–C adducts. It is interesting to note that while Dap and Rap are similar in the two systems, Dp and Rp are significantly shorter in L–C complexes.


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Table VI. Packing at lectin–carbohydrate and protein–protein interfaces as measured from average distances (Å) between closest atom neighborsa
 
The above measurements clearly support the picture that the interacting surfaces in L–C complexes are tighter packed than P–P interfaces. In particular, the larger intermolecular distances in P–P complexes seem to be due to the combination of more distant polar-to-polar interactions and lower densities of polar groups. Since packing densities of P–P interfaces and protein interiors have been found to be very similar (Levitt et al., 1997Go; Conte et al., 1999Go), it also follows that atoms at L–C interfaces achieve a tighter compactness than in the core of a protein. This is an observation with no precedent for non-covalent interactions of macromolecules.

Hydrogen bonding
With the aim of comparing the metrics of interfacial hydrogen bonds, the structures of L–C and P–P complexes were analyzed by means of the program HBPLUS (McDonald and Thornton, 1994Go). As shown in Table VII, the average hydrogen bond density per unit of total area buried ({delta}hb/At) was found to be almost three times larger in the case of L–C complexes. This dramatic discrepancy is partially due to differences in the abundance of polar surfaces, since the ¶p magnitude of L–C interfaces is only 55% higher than the mean value of P–P interfaces. In this respect, it is interesting to note that the density of hydrogen bonds per unit of polar area ({delta}hb/Ap) is significantly larger (~87%) for L–C complexes. Indeed, by considering the relative magnitudes of ¶p and {delta}hb/Ap, the global hydrogen densities of the two systems become interconvertible. Finally, an analysis of the fraction of cooperative hydrogen bonds (¶C-hb, in Table VII) reveals that hydrogen bonding is more cooperative at L–C interfaces in an excess that allows to account for the difference in {delta}hb/Ap values.


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Table VII. . Hydrogen bonding at L–C and P–P interfaces
 
A comparison of hydrogen bond geometry between L–C and P–P complexes was accomplished on high resolution structures (< 2.3 Å). As shown in Table VII, distances between donor (D) and acceptor (A) atoms forming hydrogen bonds at L–C interfaces were found to be significantly shorter and distributed in narrower ranges than those at P–P interfaces, regardless of the kind of atom pair considered. At the same time, values of the acceptor antecedent-acceptor-donor (AA-A-D) angle for both sp2 and sp3 atoms were found to be farther from ideal values (120.0° and 109.5° for sp2 and sp3 acceptors, respectively), and distributed in wider ranges in the case of P–P complexes (Table VII). Since co-operativity can contribute to additional hydrogen-bonding strength (Legon and Millen, 1987Go; Jeffrey and Saenger, 1991Go), which in turn is related to bond distance, it is likely that the smaller bond distances in L–C adducts are a reflection of their higher degree of cooperativity. In fact, within L–C interfaces non-cooperative hydrogen bonds are on the average 0.18 Å larger than cooperative bonds. Overall, the results of hydrogen bonding metrics provide the basis of the results obtained in the analysis of interface packing, which revealed that intermolecular distances are considerably shorter in L–C than in P–P complexes due to closer polar-to-polar contacts. Moreover, since the largest densities of cooperative bonds occur at primary subsites, the higher packing efficiency realized at those loci in relation to other subsites seems to be also originated from a larger hydrogen bonding cooperativity.

Comparison of L–C and P–P heterocomplexes
L–C complexes are transient complexes (i.e., both parts of the complex can exist as separate entities), whereas most of the homodimers studied here are permanent (i.e., the subunits unfold upon dissociation). In general, P–P heterointerfaces have been found to be smaller in size than protein homodimeric interfaces. For instance, both protease-inhibitor and antibody-antigen interfaces amount on average to 1600 Å2 per interface (Janin and Chothia, 1990Go; Jones and Thornton, 1996Go). However, this value is still considerably larger than the average size of L–C interfaces. The mean size of a set of protein–nucleic acid complexes was found to be 3100 Å2 (Nadassy et al., 1999Go), which indicates that L–C interfaces are also small in comparison with other heteromolecular interfaces. Furthermore, packing at protein heterodimeric interfaces seems to be, at best, as good as those in homodimeric complexes or protein interiors (Jones and Thornton, 1996Go; Conte et al., 1999Go; Nadassy et al., 1999Go). Thus, L–C compounds stand out as the protein complexes with the highest packing density at the contact interface.

Similarly, the polar character of L–C interfaces is prominent among protein complexes; their average hydropathy (~0.5) is only paralleled by those of antibody–antigen (0.49 ± 0.04) and protein–nucleic acid (0.48 ± 0.08) complexes (Conte et al., 1999Go; Nadassy et al., 1999Go). However, even these latter types of complexes display average hydrogen bonding densities (smaller than one bond per 100 Å2) which are much smaller than the bond density for L–C complexes.

Comparison of L–C and P–P interaction energetics
For a data set of P–P complexes including 3 homo- and 18 heterodimers, Xu et al. (1997)Go found that the average standard free energy, {Delta}G, of binding is –13.1 ± 4.3 cal · mol–1 at 25 °C. From the analysis of these authors it is seen that the average change in accessible molecular area ({Delta}AMA) is 505 Å2. Normalization of the binding free energy by {Delta}AMA gives a value of {Delta}G/{Delta}AMA equal to 26 ± 5 cal · mol–1 · Å–2. In the case of L–C complexes, the average {Delta}G of binding at 25 °C is only –5.4 ± 1.2 calmol–1 (García-Hernández and Hernández-Arana, 1999Go); however, the molecular area buried is so small (–90 to –190 Å2) that when the normalization by {Delta}AMA is performed the resulting {Delta}G/{Delta}AMA amounts to 41 ± 7 cal · mol–1 · Å–2. As expected, these magnitudes indicate that as the contact area in a recognition process decreases, the diminution in free energy per unit area is larger.

What is the origin of the larger stabilization (free energy change) per unit of area buried in L–C interactions? In a previous report, which analyzed the energetics of L–C interactions versus protein folding (García-Hernández and Hernández-Arana, 1999Go), it has been shown that the larger stabilization per unit of contact area in L–C complexes has an enthalpic origin. All evidence there analyzed seems to indicate that polar-polar contacts at L–C interfaces are stronger than those in the protein interior. According to the results obtained in the present work, the same conclusion may hold true for a comparison between L–C and P–P associations. Better packing of polar–polar contacts, especially manifested in shorter hydrogen bond distances, would likely be a source of more favorable binding enthalpy for L–C complexes. Unfortunately, calorimetric data for P–P associations are scarce, so that no direct comparison of binding enthalpies is possible at the present.

Concluding remarks
Undoubtedly, good surface complementarity is a requisite to achieve tight packing at the interface of two interacting molecules. In this regard, binding sites in lectins, and in particular primary subsites, seem to be well adapted for the recognition of sugar molecules. They constitute, in a broad sense, regions with the appropriate hydropathy to interact with the highly polar carbohydrate surface. At a finer level of detail, there is a precise stereochemical matching between the carbohydrate and its binding site that enhances hydrogen bonding cooperativity, in particular, and polar interatomic interactions, in general. At the same time, apolar–apolar interactions do not appear to be seriously compromised, since their packing is as good as at P–P interfaces. This evidence is at variance with the notion that hydrophobic stacking could be the predominant force in L–C binding. Overall, the energetic consequences of such a high surface complementarity between a lectin and its ligand seem to be that stable complexes can be formed despite the reduced number of contacts across the interface.


    Materials and methods
 Top
 Abstract
 Introduction
 Results and discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
Construction of the data set of L–C complex structures
A global survey in the February-1999 Protein Data Bank for "lectin" or "agglutinin" structures yielded a data set of 130 entries. Of these, 75 were found to be L–C complexes. Only x-ray solved structures with resolution better than 3.0 Å were retained. Complexes formed of either lectin mutants or glycopeptide ligands were discarded. Complexes sharing the same lectin but differing in the carbohydrate moiety were considered redundant when the interfacial hydrogen-bonding patterns were found to be identical, selecting that with the better resolution.

Changes in accessible surface area upon binding
Structure-based determinations of water-accessible surface areas (ASA) were performed with the NACCESS program (Hubbard and Thornton, 1993Go), using a probe radius of 1.4 Å, and a slice width of 0.1 Å. Total changes in ASA upon binding ({Delta}ASAt) were estimated from the difference between the complex and the sum of free molecules. Polar area changes ({Delta}ASAp) were calculated from the changes in accessibility of nitrogen plus oxygen atoms.

Area buried in globular protein interiors
{Delta}ASAp and {Delta}ASAt values for the folding of 42 globular monomeric proteins, estimated as the difference between the native and unfolded states, were taken from García-Hernández and Hernández-Arana (1999).

Amino acid compositions and propensities
A residue was considered to form part of the binding site when its {Delta}ASA was >1 Å2. A residue was counted as exterior when having at least 5% of its total surface area accessible to the solvent. From these counts, percentage frequencies for each amino acid in the protein surface (Fls) and at the binding site (Fbs) were calculated. The propensity (P) of the residue i to form a binding site was evaluated by means of the ratio Fbs/Fls (Jones and Thornton, 1996Go). P values > 1 (< 1) indicate that the residue is more (less) preferred to be incorporated at binding sites than elsewhere in the protein surface.

Surface complementary
For each carbohydrate atom whose accessibility changed upon binding by more than 0.1 Å2, the distance (D) to the nearest lectin-atom was determined. Closest atom pairs were classified into polar-polar (O··O, O··N), polar-apolar (O··C, N··C), apolar-apolar (C··C), and any (X··X) contacts, and the corresponding average distances (Dp, Dp-ap, Dap, and Dt, respectively) were obtained. D values were normalized with the sum of the van der Waals radii (Rvdw) to obtain a relative measure (R) of the inter-atomic distance to the size of the two neighboring atoms: R = D/(Rvdw1 + Rvdw2).

Surface complementary was also evaluated by determining the volume of the gaps existing between lectin and carbohydrate atoms beyond their van der Waals spheres by means of the SURFNET software (Laskowski, 1995Go). A gap index (GI) was then obtained by dividing the total interfacial gap volume by the {Delta}ASAt value.

Hydrogen bonding analysis
L–C interfaces were analyzed by means of the software HBPLUS (McDonald and Thornton, 1994Go) to identify hydrogen bonds. Since hydrogen atoms are rarely observed in x-ray solved structures of proteins, the identification of potential hydrogen bonds was based only on the geometric arrangement of atoms forming suitable acceptor-donor pairs, imposing the constraints derived by Stickle et al. (1992)Go from small-molecule crystal structures. To reduce the uncertainties due to the experimental determination of atomic positions, only structures with a resolution of 2.3 Å or better (i.e., 25 L–C and 18 P–P complexes) were considered in the statistics of hydrogen bond lengths and scalar angles. The mean resolutions for the reduced data sets of L–C and homodimer structures are 2.03 and 1.95 Å, respectively, while the mean temperature factors of the interfacial atoms are 22 and 18 Å2, respectively. Thus, the structural qualities of both data sets are comparable.

Identification of the primary binding subsite
For the majority of the L–C complexes here analyzed, the primary binding subsite was operationally identified as that zone of the protein surface occupied by the monosaccharide that defines the primary selectivity of the lectin. Experimentally, the primary selectivity is established by determining the monosaccharide that inhibits the activity of the lectin. Nevertheless, the cholerae toxin (1chb) and the GS4 lectin (1led) are not able to bind monosaccharides, reason for which they were not considered in the analysis of primary binding subsites. Five complexes in Table I have oligosaccharide ligands composed of only one type of monosaccharide. For two of these cases (1cvn and 1jpc), the corresponding monosaccharide complexes are included in the data set (5cna and 1msa). The primary binding subsites of the complexes 1a78 and 1npl were identified by comparison with the homologous complexes 1gan and 1jpc, respectively. Finally, the primary subsite for 2msb was established according with the structural analysis performed by Weis et al. (1992)Go over different kinds of monosaccharides.


    Acknowledgments
 Top
 Abstract
 Introduction
 Results and discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
This work was supported in part by CONACYT (Grants 32417-E and 29124-E) and DGAPA (Grant IN-201997).


    Abbreviations
 Top
 Abstract
 Introduction
 Results and discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
L–C, lectin–carbohydrate; P–P, protein–protein; PDB, protein data bank; {Delta}ASAt, total change of accessible surface area; ¶p, hydropathy index; {Delta}ASAp, change in accessibility of polar surfaces; D, interatomic distance; GI, gap index.


    Footnotes
 
1 To whom correspondence should be addressed Back


    References
 Top
 Abstract
 Introduction
 Results and discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
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