2.1 Types of multivalency

Multivalence can range from one molecule to clusters, self-assembled monolayers and 3D platforms. Biological systems use various types of multivalency depending on the local environment and/or a particular function. In particular, lectins exhibit diverse architectures and modes of multivalence relating to their function. Some typical examples can be found in Fig. 2. Con A [24] (in pH neutral environments) and PA-IL [25], for example, are both tetrameric proteins with tetrahedral and planar structures respectively, with all carbohydrate binding sites facing different directions. PA-IL and BclA [26] are soluble lectins implied in bacterial invasion and adhesion [27], whose roles may be to explore local environments (in solution or on surfaces), therefore their structures may reflect this purpose (Fig. 2). The cholera toxin has what is known as an AB₅ architecture with the lectin domains forming a pentameric structure, with the receptor binding sites located on the same face of the macromolecule, and all oriented in the same direction [28]. This is indicative of its function – finding a suitable invasion site at the host epithelial surface [29].

These lectins exhibit “architectural multivalence”, consisting of one macromolecular structure which presents several, equivalent carbohydrate recognition domains. Other lectins, such as the adhesins, are membrane bound and consist of a lectin structure which presents only one carbohydrate recognition domain, attached to fimbriae or flagella tethered to the cell surface [30,31]. Several fimbrial structures clustered together at the cell surface would also give a multivalent presentation of the lectins in the extracellular environment. The galectins, which are membrane bound and specific for β-galactosides, as well as other C-type lectins, exhibit many different macrostructural formations giving rise to several different forms of multivalent presentation. Galectins-1 and 2 form homodimers in solution (like BclA), whereas Galectin-3 exhibits a carbohydrate recognition (lectin) domain tethered to a non-lectin domain which forms oligomeric structures in solution and on surfaces. Other galectins (galectin-4, galectin-8) form tandem repeat units, where the two carbohydrate recognition sub-units are attached via a (relatively) flexible linking molecule [30,32]. The collectins are a group of mannose binding lectins (C-type III lectins) that associate together forming oligomers. Three sub-units combine to form a trimer; the trimers are bound together via a collagen-like α-helix which is tethered to the cell membrane. Trimer structures associate to form larger oligomers such as bouquets of trimers (where all binding domains are presented adjacent to one another) or cruciform (cross-like) structures where four bouquet trimer sets present their recognition domains in four different directions [30,32,33]. Biological systems take advantage of several modes of multivalence in many normal and pathological processes depending on their position, function and status (Fig. 3). Often, these systems will present a wide variety of different “tools” in order to increase the likelihood of successful interactions or invasion pathways.

3.1 Monovalent reaction kinetics

First, interactions of a ligand to its receptor at the monovalent level shall be considered (Fig. 2A). We will assume that the reaction follows the typical reaction kinetics and thermodynamics where:

A is one binding partner, B is the second binding partner, AB is the bound complex and k represents the rate constant for the forward (association rate constant, k_a, M⁻¹ s⁻¹) and reverse (dissociation rate constant, k_d, s⁻¹) reactions. Equilibrium association constants (K_a, M⁻¹) and equilibrium dissociation rate constants (K_d, M) can be calculated from k_a and k_d from the equation:

From the van’t Hoff equation, one can link the effects of rate constants (kinetic parameters) to the Gibbs free energy (G, a thermodynamic parameter).

The Gibbs free energy is in turn associated with the enthalpy (H) and entropy (S) of the interaction. From this, the dependence of kinetics and thermodynamics have over each other can be seen, as well as their dependence on temperature.

3.2 Monovalent thermodynamics

3.2.1 Enthalpy

The change in enthalpy, ΔH, is the difference between the final and initial enthalpic states of all components in the reaction, and can be separated into several components:

ΔHmono=ΔHAB+ΔHconf+ΔHsol

ΔH_AB represents the enthalpy change upon bond formation between the two reactants. In the case of lectin–carbohydrate interactions, these non-covalent bonds may be hydrogen bonds between the hydroxyl groups of the carbohydrate and the amino acids of the binding pocket, as well as coordination bonds to metal ions or indeed aromatic stacking and stabilization of hydrophobic surfaces on either binding partner. Van der Waals and dipole–dipole interactions may also be included in this term.

ΔH_conf represents the enthalpy change required to induce a particular conformational change of either binding partner. For example, the rotation of hydroxyl groups in order to maximize hydrogen bond formation, the rotation of glycosidic bonds or the twisting or displacement of any large amino acid groups to better accommodate the ligand such as the histidine residue around the binding pocket of BclA [26], or the “tyrosine gate” in FimH [35].

ΔH_sol is the solvent contribution to the enthalpy of the interaction. More specifically, this would represent the making and breaking of hydrogen bonds between the solvent molecules and the binding pocket, the carbohydrate ligands and bulk solvent upon the displacement of ordered water molecules during lectin–carbohydrate binding (Fig. 5).

3.3 Monovalent to multivalent

Described above are the various contributions to the enthalpy and entropy of a monovalent lectin–carbohydrate interaction. These in turn influence the Gibbs free energy of this monovalent event which itself influences the kinetics of the interaction. The association constant represents the affinity of the lectin for its monovalent ligand. However, on a multivalent scale, one must also consider additional contributions to the enthalpy and entropy and their influence on the kinetics of the interaction.

3.3.3 Enthalpies of multivalent interactions

The multimeric free energy, ΔG^mul,n, consists of its enthalpic and entropic components where:

ΔGmul,n=ΔHmul,n−TΔSmul,n

ΔH^mul representing the total enthalpy change for the multimeric interaction which will be related to the enthalpy change of the monomeric interaction.

ΔHmul,n=αnΔHmono

α, being as before, the cooperativity coefficient and n the number of individual binding events. If α is greater than one, the overall enthalpy observed will be greater than the sum of the individual enthalpies. The multivalent interaction is enthalpically enhanced. If α is less than one, the overall enthalpy observed will be less than the sum of the individual enthalpies, resulting in an enthalpically diminished multivalent interaction.

The case of a dimeric lectin interacting with two monovalent ligands is shown in Fig. 6A. The two monovalent ligands interact with the two binding sites in the same fashion. Therefore, the enthalpy involved in the dimeric interaction is double the amount of the monovalent interaction. In the case of a divalent ligand interacting with the divalent receptor, several situations can occur depending on the nature of the linkage between the ligands. Firstly, the linking molecule can be of ideal length to present the two ligands in a fashion complementary to the receptor binding sites (case B). This means that no effort is required by the linker to modify the presentation of its ligands, its enthalpic contribution is negligible and the second intramolecular interaction occurs as in case A. In case C, the linking molecule is shorter than the ideal length. The first interaction occurs as before, as this first interaction is independent of the linker molecule. However, for the second intramolecular interaction to occur, the receptor has to alter the position and orientation or conformation of the binding sites. This invokes an energy penalty, reducing the observed enthalpy for this second interaction. Likewise for situation D where the linker is too long. The second interaction has to pay a conformational enthalpy penalty in order for the linker molecules to present the ligands in the correct fashion. In this case, the flexibility of the linker will play an important role. A rigid linker would have to pay a large conformational enthalpy penalty, whereas a flexible linker would pay only a small penalty. Generally, the more conformationally rigid a multivalent entity is, the more likely small, spatial mismatches between ligands and receptors will result in enthalpically diminished interactions [2].

In case C, where the linker molecule is too short, it is unlikely that the receptor will alter its conformation in order to accept the second ligand in an intramolecular interaction. Probably, the receptor will accept only one ligand presented, the second binding site being free to interact with a second bivalent ligand intermolecularly, thus removing the enthalpic penalty (Fig. 7A). In case D, where a long, rigid linker is used, it may be more beneficial for the bivalent linker to bind to two separate receptor molecules (Fig. 7B). The above situations where intermolecular association is more favorable than intramolecular association may lead to the formation of aggregates via ligand-receptor cross-linking. These aggregates would develop in length and become insoluble in the media resulting in irreversible precipitation.

One can summarize the multivalent enthalpy change as contributions from the monovalent enthalpy change and the conformational enthalpy dictated by the linker molecule used in the multivalent ligand architecture as follows:

ΔHmul=nΔHmono+(n−1)ΔHlink,confmono+ΔHlink,sol

the ΔHlink,confmono term representing the conformation enthalpy penalty induced by the size and rigidity of the linker molecule. The (n – 1) comes from the fact that the first binding event would not have to pay this conformational enthalpy penalty, only the subsequent binding events. This, of course, assumes that the following binding events would experience identical conformational constraints. ΔH_link,sol refers to the influence of the linker molecule on the surrounding solvent molecules. Depending on the proximity of the linker molecule to the binding domains of the receptors, it could contribute non-specific interactions with the binding pocket or any associated (ordered) water molecules. Also, the linker molecule may induce hydrogen bond contacts with bulk solvent molecules which may be displaced upon ligand-receptor interactions. Also, ligands which are presented multivalently may interact with each other, independent of the linker molecules, via hydrogen bond networks. The breaking of this network would also contribute to the overall enthalpy of the interaction.

3.3.4 Entropies of multivalent interactions

When moving from a monovalent to a multivalent system, the entropies involved change dramatically, particularly when considering intramolecular associations. As with the case for enthalpy, the multivalent entropy change (ΔS^mul) will be related to the entropy change experienced by each ligand with respect to translational and rotational degrees of freedom of the ligand as it is immobilized in the binding pocket, as well as the release of ordered water molecules (ΔS^mono). This can also be expressed in terms of cooperativity:

ΔSmul,n=αnΔSmono

This would imply that a value of α greater than one would equate to an entropically enhanced multivalent interaction, whereas α less than one would imply an entropically diminished multivalent interactions.

However, in the multivalent system, one must also include the effect of linker molecule conformation (ΔS_link,conf) and solvent effects (ΔS_link,sol). Thus, the multivalent entropy contribution can be broken down further and described as:

ΔSmul=nΔSmono′+ΔSlink,conf+ΔSlink,sol

In the monovalent system, the entropy change was related to the rotational and translational degrees of freedom of the ligand and receptors before and after intermolecular association as well as the entropy related to conformation and solvent effects. By considering case A presented in Fig. 8, the interaction of a bivalent receptor with two monovalent ligands, the change in entropy (ΔS^mono) will be the same for both interactions as, again, the two ligands will be interacting independently of each other and without memory. In terms of molecularity, this would be disfavored entropically as it would involve the conversion of three entities into one, causing the loss of a total of 12 degrees of translational and rotational freedom (three translational and three rotational for each ligand). This loss of independent translational and rotational freedom has also been referred to as the Gibbs connections energy [36]. In case B (Fig. 8B), where the bivalent ligand is ideally presented, the interaction of a bivalent ligand would again be entropically disfavored (however less so than the monovalent situation) as this would involve the conversion of only two entities to one, causing the loss of only six degrees of rotational and translational freedom i.e. the entropic cost of the perfect bivalent ligand will be half of that of two monovalent ligands. It is for this reason that ΔS^mono has to be corrected to ΔSmono′ for multivalent ligands:

ΔSmono′=ln(ΔSrot+ΔStrans)+ΔSconf+ΔSsol

where l is the total number of multivalent ligands associated to the multivalent receptor and n remains as before, the total number of individual receptor-ligand interactions. This means the first ligand-receptor interaction would pay the entropic penalty, whereas the second intramolecular interaction would not, meaning that this interaction occurs with a greater free energy change and hence greater affinity. Therefore this second, intramolecular interaction would be entropically enhanced.

The ΔS_link,conf term in the above statement comes from the inclusion of the linker molecule and its associated degrees of freedom. Assuming that the linker molecule is again perfectly shaped, rigid and conformationally locked (allows for no free rotation about its bonds), the entropy change for intramolecular association (ΔS_link,conf) will effectively be zero. This, however, is very unlikely, as all linker molecules would assume some form of flexibility (meaning ΔS_link,conf < 0, unfavorable), Fig. 8C. A linker molecule which is suitable and rigid would require only small entropic constraints (ΔS_link,conf < ΔS^mono) and it would therefore be in the interests of both molecules to form the second intramolecular interaction, still being entropically enhanced. If, however, the linker molecule is unsuitably shaped or too flexible, this conformational entropy penalty would be very large. If this conformational entropy penalty is larger than the entropic penalty of the monomeric interaction ΔS_link,conf > ΔS^mono, it would become more economical to form a second intermolecular interaction than to continue with intramolecular association, as the intramolecular interaction would no longer be entropically enhanced. In the case where the entropic penalty of linker conformation equals that of the monomeric interaction, an equilibrium between intra- and intermolecular interactions would occur.

ΔS_link,sol comes from the effect of the linker molecule on the local solvated environment. Assuming that the linker molecule does not affect the ligand-receptor interactions, ΔS_link,sol will be zero. However, this may not always be the case. The linker molecule may disrupt the organization of water molecules around the ligand before or during interaction. Therefore, the organized water around the ligand which would be displaced by the receptor binding site upon multivalent interaction may be different to the monovalent interaction due to the influence of the linker molecule. Likewise, organized water molecules around the linker molecule, which would not be present in the monovalent ligand, may find themselves displaced by the receptor binding site. Also, if the linker molecule interacts in some way (hydrophobic interactions or aromatic stacking for example), the linker may displace ordered water molecules associated with the protein surface which may not have otherwise been disturbed. Finally, the ligand in the monovalent form may organize water around itself in a particular fashion. Upon multivalent presentation, independent of the linker molecule, ligand molecules may associate together by forming close-knit networks of hydrogen bonds and ordered water molecules. Carbohydrate molecules are particularly effective at organizing intermolecular hydrogen bond networks (Fig. 9) [37].

3.4 Effective concentration

The above description of the multivalent effect is based solely on the thermodynamics of the system, which in turn define the Gibbs free energy and its resultant effect on the equilibrium constants. Essentially, the multivalence effect (and thus the cluster glycoside effect) was analyzed in terms of entropy and is a concept brought by Mammen et al. [2]. An alternative binding model can be used to describe multivalence, in terms of effective concentrations (C_eff) which was proposed by Kramer and Karpen and applied to carbohydrate–protein interactions by Gargano et al. [38,39]. The example by Mulder et al. describes the interaction of a β-cyclodextrin receptor dimer with a bis-adamantyl ligand [40]. The bivalent interaction should again be treated as a two-stage system with an initial intermolecular interaction, followed by a second intramolecular interaction. This first interaction obliges the second ligand of the dimer to be in close proximity to the second available binding site. Therefore, this second binding site experiences a localized high concentration of neighboring free ligands. If this local concentration density is greater than the ligand concentration in the bulk solution, intramolecular (multivalent) binding will be favored [41]. Thus, the term C_eff represents this local concentration density experienced by both the ligand and receptor. The theory of effective concentration thus gives a concentration-dependent association constant for the second binding event. At low concentrations of ligand, the effective concentration experienced by a multivalent receptor due to a multivalent ligand would be much greater than the concentration of free ligands in the bulk solution (C_eff ≫ C_bulk) and thus a multimeric intramolecular interaction is more likely to occur. However, at higher ligand concentrations, (C_eff < C_bulk), the concentration of ligand experienced by the receptor will not be influenced by the ligand molecule already bound and therefore a second, intermolecular interaction is more likely to occur (Fig. 10). Naturally, when C_eff = C_bulk, the system will be in equilibrium between the intra- and intermolecular interactions.

C_eff is dependent on the ligand-receptor distance, which is also dependent on the length of the linker molecule. C_eff will also be influenced by linker molecule flexibility. The length, of course, determines the radius of the sphere occupied by both potential interacting partners. Longer molecular lengths lead to smaller C_eff values, decreasing cubically with the increase in length. Therefore it is important that the linker molecule is long enough and flexible enough to allow the intramolecular interaction, but not too long so that C_eff approaches C_bulk. The flexibility of the linker molecule would also influence the nature of the theoretical sphere occupied by the second ligand after the first binding event has occurred. A flexible ligand would theoretically be allowed to occupy any position within this sphere (excluding regions occupied by the receptor or the other parts of the ligand). A less flexible linker molecule would reduce the sphere in size or dimensionality depending on the nature of its rigid properties. In this reduced system, the C_eff would be increased, increasing the probability of the intramolecular interaction occurring. Too rigid, however, and the intramolecular interaction may be inhibited thermodynamically (enthalpy or entropy penalties) or logistically (the second ligand is simply blocked from entering the second binding site).

3.4.1 Reaction kinetics and the effective concentration

For a divalent receptor interacting with a divalent ligand in the example given by Mulder et al., the first binding event would occur more readily by a factor of four in comparison to its monomeric counterpart [40], due solely to statistical considerations. These statistic considerations are the ratio of possible permutations of the forward reaction, leading to the monomerically bound complex, and the permutations of the reverse reaction, dissociation back to the reactants (Fig. 11) [39].

The overall binding constant for the divalent interaction being dependent on C_eff then becomes:

Kamul=2Ceff(Kamono)2

where the general formula for multivalent interactions becomes [42]:

Kamul=b(Ceff)n−1(Kamono)n

where b is a statistical factor, representing the ratio of permutations leading to products divided by permutations in the reverse reaction.

A theoretical estimate of C_eff (mM) is cited as:

Ceff=1NAV32πr¯023/2

where N_AV is Avogadro's number and r¯0 is the root mean squared distance between the free ligand and the free receptor of the mono-linked entity (Å). r¯0 was calculated by Mulder et al. statistically for this particular example [40]. The above equations are given for the example of multivalent binding in solution, however, this model can equally be applied to multivalent binding to SAMs as well as other systems, with some modification (the effective concentration will only vary linearly with r¯0 in 2D as opposed to r¯03 in solution).

If we consider the case presented in Fig. 11 again, the monomerically bound complex is an intermediate between the reactants in free solution and the multivalently bound complex. This intermediate could be regarded as being in a ‘steady state’. The lifetime of this intermediate would then depend on kdmul,1 (the dissociation rate constant from the intermediate back to free reactants) and kamul,2 (the association rate constant from the intermediate to the multivalently bound complex). If the association/dissociation rate constants (i.e. kdmul,1 and kamul,2) are low in magnitude, the lifetime of this intermediate species may be sufficient for the effective concentration to have an effect on the conversion to the multivalent species. If however kdmul,1 is large and monovalent dissociation a very fast process, the lifetime of the intermediate would be very short, meaning that there would be a higher probability the ligand would escape the proximity of the binding sites. Similarly, if kamul,2 was large in magnitude, the intermediate species would be too short-lived as to experience any beneficial effects offered by the effective concentration, being swiftly and independently converted to the multivalently-bound complex.

4.1 Small molecule glycoclusters

A great number and variety of ligands have been reported with the specific purpose of investigating multivalent interactions. A large proportion of these include small clusters (dimers, trimers, tetramers, etc.) fixed on to small multivalent scaffolds of varying size and flexibilities. Often, these small synthetic molecules can incorporate multiple functionalities (Fig. 12A).

Brewer's group tested several small divalent glycoclusters when investigating interactions with Con A and DGL [43,45]. Several of these clusters were developed around aromatic (alkyne or benzylic) scaffolds, giving very short, rigid structures. Also presented are dimers connected by alkyl chains of varying length or aromatic rings bound via thiourea bridges, again of varying length. The same group investigated di-, tri- and tetravalent trimannoside structures with a longer, more flexible thiourea bridge to an aromatic core [45]. All multivalent structures showed some improvement in K_a with enhancements ranging from ∼2- to 10-fold for the monosaccharide structures and up to 1000-fold for the tri-mannosides in the case of Con A. More impressive improvements were observed for DGL. Summaries can be found in Table 1 for the most efficient of each cluster type. Isothermal titration microcalorimetry (ITC) was used to determine the K_a of each cluster. Toone's group also investigated the cluster glycoside effect observed in Con A [46]. Several multivalent clusters were developed around an aromatic core allowing the synthesis of di-, tri-, tetra- and hexamannosides, the most potent of which being the dimer structure, shown in Table 1. It must be noted that the results from Toone's group are presented with respect to mannose equivalents [46], whereas results from Brewer's group [43,45] are presented with respect to the whole cluster.

Other small glycoclusters used for lectin–carbohydrate interactions were developed by Roy's group for the PA-IIL lectin [47]. These scaffolds include aromatic centers or ethylene glycol chains coupled to Le^a moieties via triazole rings via the commonly used “click” chemistry. Several dimers and trimers were synthesized, the most potent of which are listed in Table 1.

Other glycoclusters include mannose functionalized pentaerythritol and bis-pentaerythritol scaffolds developed by Roy's group for the inhibition of Con A activity on Mesenchymal stromal cells and the inhibition of the FimH lectin [48,49]. As well as aromatic molecules, other scaffolds can be found in the literature. Lindhorst's group used carbohydrates as the scaffold base, with mannose functionalized linkers coupled to the pendant hydroxyl groups (Fig. 12A) [50–52]. These “octopus” clusters were used to study multivalence and inhibiting Con A and FimH. They also added further functionalities to several of these clusters [53].

In relation to the application of the cluster glycoside effect, small molecules have proven to be very efficient. The di-, tri-, tetra- and hexavalent scaffolds designed by the groups of Brewer [43,45] and Toone [46] all show increased affinities towards their target ligand. However, in considering the thermodynamic and kinetic applications of the cluster glycoside effect with respect to the interactions studied, the inter-binding site distance of the lectin is significantly larger than the inter-ligand distance. This would lead to the situation described in Fig. 6C, where it is more likely that the lectin will choose to pay the entropic penalty and interact with two separate ligands (intermolecular association) than pay the enthalpy penalty of internal structural change for intramolecular association. This, of course, means that the ligands designed exhibit an effective valency of one (when considering one multivalent ligand interacting with one lectin). However, Dam et al. [43,45] observed that n values calculated from calorimetry data were inversely proportional to the functional valency of the multivalent ligand. This demonstrates that all carbohydrate epitopes were still available and interacting with a lectin binding site. This leads to the conclusion, which they also show with microscopy data, that cross-linking occurs, where a network of lectin–ligand complexes are formed, driven by intermolecular association. They also show that multivalent scaffolds with flexible linker molecules exhibit greater changes in enthalpy but larger entropy penalties as predicted earlier – flexible linkers allow optimum ligand-receptor interactions, yet a larger entropy penalty has to be paid resulting from constricted movement of flexible groups. This still leads, however, to an enthalpically enhanced affinity. This was also observed by Dimick et al. with the aggregation of tetrameric Con A [46]. Enthalpically enhanced affinities which are partly compensated by unfavorable entropic penalties. However, in both cases, enthalpic enhancement may not be the only cause of increased affinity. Due to their small sizes, these multivalent molecules exhibit a high local concentration of ligands. Therefore, upon lectin–ligand association, there may be a greater chance of a successful binding event with one of several ligands presented on the scaffold. This, of course, is related to the effective ligand concentration and its statistical contribution, the multivalent scaffold providing a “high density” binding partner with more possible binding permutations. However, as experiments were not carried out with monomeric analogues, it is not possible to compare observed affinity enhancements with those calculated from differences in free energy changes.

The small molecules designed by Marotte et al. also exhibited interesting binding kinetics to PA-IIL [47]. As expected, the monomer equivalents exhibited normal monomeric kinetics to multimeric receptors. The dimers, based on both aromatic and polyethylene glycol scaffolds, showed that each carbohydrate epitope binds to one binding site. The observed enthalpy was shown to be double that of the monomer as both carbohydrate epitopes are available for binding. However, the entropy contribution to the system's thermodynamics is not proportional to the valency of the scaffold. In fact, a large entropy penalty is incurred which significantly reduces their binding affinities. Even though the aromatic and linear dimer structures are long enough to theoretically induce multiple binding events on the same lectin molecule, this was shown not to occur. One explanation for this is related to the orientation of the ligands, which in linear form point in opposite directions. Therefore, a large conformational change may be required to present the ligands in the correct manner to induce multivalent binding. The trimer exhibited a stoicheometry of 1, indicating that one trimer binds to only one binding site. Thermodynamically, trimer binding is more or less equivalent to monomer binding with reduced enthalpic enhancement and favorable entropic contributions due to its rigid nature.

Dubber et al., although not dealing with a multimeric lectin, showed the increased inhibitory power of their ligands via ELISA tests [51]. Even though no quantitative thermodynamic or kinetic data can be extracted, it is clear from the data that ligand presentations varied with the carbohydrate scaffold base. This, in turn, altered the binding/inhibiting properties of the ligands towards the bacterial lectins.

4.2 Cyclodextrins and calixarenes

Cyclodextrins are cyclic oligosaccharide molecules of units of α-(1-4)-linked glucose. They exist in three conformations: α-, β- and γ-cyclodextrin which contain six, seven and eight glucose units respectively (Fig. 12B). The structures present a hydrophobic cavity and a hydrophilic exterior and it is for this reason they are very popular in supramolecular chemistry and host–guest interactions; the cavity acts as a host for a wide range of guest molecules, as well as biocompatibility [54]. Reinhoudt's group used cyclodextrins and guest molecules as a model system for multivalence interactions [41,55]. The hydroxyl groups on the two faces of the cyclodextrin can be modified in order to present molecules multivalently. Several cyclodextrins have been functionalized with carbohydrates giving rise to various glycoclusters for use as drug delivery vehicles [56,57], as well as high affinity ligands for lectins. Furuike et al. modified β-cyclodextrins with galactose and lactose to study their enhanced binding with the WGA and ECorL lectins [58], showing an enhancement factor of 40 (per epitope) for GalNAc functionalized CDs with WGA and factors of 2 and 4 for Galactose/GalNAc and LacNAc – CDs respectively with ECorL. Lactose functionalized α-cyclodextrins have also been used for the inhibition of peanut agglutinin (PNA) [59].

Calix[n]arenes are similar to cyclodextrins in that they are cyclic ring structures with a hydrophobic cavity capable of hosting a small hydrophobic guest molecule. They are composed of cyclic phenol-formaldehyde oligomers (Fig. 12C), the number of rings in the structure denoted by the [n]. As with the cyclodextrins, n can be varied in order to tune the size of the hydrophobic cavity. The phenol functionality and aromatic nuclei can be converted to most functional groups to attach ligating units. Their conformation can also be altered (conical or tetrahedral), allowing tunability in the presentation mode of functional groups added to the scaffold [42,60] (and references therein). There are several examples of the addition of carbohydrate molecules to form glycoclusters [60,61]. Fujimoto et al. functionalized calix[4]arenes with galactose and glucosides to study their specificities with PNA and Con A respectively, with a view to using the calixarenes as site-specific drug delivery vectors [62]. Ungaro's group have synthesized several calixarenes ranging from n = 4 to n = 8 [63]. These calixarenes were functionalized with two to eight galactose or lactose moieties via thiourea bridges. A range of conformers was possible due to the flexibility of the large aromatic scaffold. Inhibition tests were carried out using Viscum album agglutinin (VAA), a galactose binding AB type plant toxin from Viscul album, and galectins -1, -3 and -4. Inhibitory enhancements of factors of 8, 1.5, 1 (no affinity enhancement) and 0.7 (diminished affinity) were observed. Affinity investigations with cholera toxin were also carried out by fluorescence spectroscopy and SPR, showing an affinity enhancement factor of 5 and 18, respectively, per sugar epitope emphasizing that different analysis methods may give different results [64]. Recent studies using galactose functionalized calixarenes tethered to a microarray for studying the binding of RCA 120 and PA-IL lectins showed an affinity enhancement of 23 per sugar epitope for RCA 120 (no affinities recorded for PA-IL), as measured by fluorescence spectroscopy [65]. The results support the idea that different glycoclusters are required for different multivalent receptors.

For the interactions of ligands attached multivalently to cyclodextrin and calixarenes, there are few studies published providing fully quantitative information with regards to the thermodynamics of binding to multivalent lectins. This makes the thermodynamic interpretation of their multivalent properties difficult. Several studies have used ELISA and ELLA type assays to study their inhibition powers. Chwalek et al. showed that polymers functionalized with oligosaccharide functionalized cyclodextrins exhibited stronger inhibition powers per oligosaccharide compared to the monomer unit [59]. However, no significant synergic effects were noted, suggesting that there is no, or only very little, thermodynamic enhancement towards affinity augmentation. Again, this augmentation may be due to an increase in effective ligand densities. The studies of Ungaro's group were also conducted using inhibition effects [63]. They showed that the inhibition power of calixarenes varied between several lectins. This demonstrates that the calixarenes exhibit a relatively rigid platform which can be used for structure selective lectin targeting. This rigid nature would contribute to the increase in entropic enhancement to interaction affinity. A more recent study by Cecioni et al. uses calix[4]arenes functionalized with galactosides for inhibition/interaction studies of PA-IL binding [66]. Several topologies were developed in order to study the influence of calixarene structure and ligand presentation on lectin recognition. ITC studies revealed that a 2:2-trans conformation proved to be the most efficient binding partner, with an 850-fold increase in K_a. Results showed Gibbs free energies that were enthalpically enhanced in this conformation, yet with greater entropic penalties as multivalency increases, but nevertheless resulting in a net improvement of ΔG. Molecular modeling (docking) studies showed the potential for this particular topology to induce chelate binding to two of the binding sites on a PA-IL tetramer, which may lead to further aggregate structures. It is this chelation-aggregation which has been attributed to the multivalence effect observed with this particular scaffold.

There are of course many other cyclic structures that have been used for presenting carbohydrates for lectin recognition. Wilczewski et al. investigated multivalence and clustering using mannose regioselectively addressable functionalized templates (RAFT) polymers – cyclodecapeptide templates with up to four possible ligand attachment sites [67]. A second, regioselectively distinct site, can be used for adding other functionalities (biomarkers, functional groups for surface attachment, etc.).

4.3 Dendrons and dendrimers

Often, the small glycoclusters, such as those mentioned above, can be functionalized in such a way that they allow multimerization of the cluster groups themselves. This leads to higher order structures known as dendrons and dendrimers. Dendrimers have a regular branching pattern with predictable physical properties and display multiple copies of functional groups in a spherical arrangement [6]. Dendrons are branched structures with typically non-spherical arrangements; segments of whole dendrimers. Both dendrimers and dendrons have the capability of producing nanometer scale formations of very high valency (up to 400). The number and nature of the tethered functional groups can be controlled by the number of “generations” allowed, as can various physical properties such as solubility and reactivity [68]. The use of different sub-units would also allow for multiple functionalities. Several commercially available dendrimer frameworks include poly(amidoamine) (PAMAM), poly(propylene imine) (PPI, Fig. 12D) and poly(ethylene imine) (PEI) [6,69]. Several dendrimers with the PAMAM framework were developed by Cloninger's group and tested for their ability to bind with Con A, pea lectins and cyanovirin, stating an affinity enhancement of 350 and 0.38 (reduced activity) for Con A and pea lectins respectively [68,70,71]. Bifunctional dendrimers were also developed to alter mannose presentation and valency [72].

Roy's group built several dendron and dendrimer structures in order to inhibit Pseudomonas aeruginosa lectins to great effect [73,74]. The dendrimers developed included spherical and linear structures with a poly(lysine) and phosphodiester frameworks. Dual functionality (galactose and fucose) was incorporated in order to bind both PA-IL and PA-IIL. Other dendrimers were developed to inhibit the FimH lectin and as mimics of T-antigen markers from breast cancer, bearing a β-d-Gal-(1-3)-α-d-GalNAc moiety [7,75,76].

Trehalose-centred PAMAM dendrimers were developed by Lindhorst's group, following on from the octopus glycosides [50]. The pendant hydroxyl groups of the trehalose dimer were functionalized with the PAMAM framework, to which mannosides were attached via thiourea bridges. Several carbohydrate-based dendrons were developed for FimH inhibition [9,77]. There are many other examples of the use of carbohydrate functionalized dendrimers and dendrons in the literature using different core structures for studying different interactions [69,78].

One significant example is that of Bundle's group and the development of their STARFISH ligand [79]. This ligand is comprised of a glucose centre with each of the hydroxyl groups functionalized with divalent dendrons presenting P^k trisaccharides, giving rise to (up to and including) decavalent structures. The STARFISH was designed to inhibit shiga-like toxin (SLT) lectin systems which present carbohydrate recognition domains in a pentameric architecture such as that described earlier for cholera toxin. The presentation of the ligands on the starfish scaffold allowed complementarity towards the arrangement of the receptors, with each ligand occupying a binding site. Furthermore, ligand presentation not only allowed pentavalent binding to one SLT unit, but in fact two SLT binding units, with each arm of every dendron binding intermolecularly to two different SLT units. This resulted in an impressive 10⁶–10⁷-fold increase in ligand activity as seen by ELISA, with further improvements anticipated upon increasing the rigidity of the dendron arms.

There is little data available for quantitative measurements of thermodynamic contributions to the multivalence effect offered by dendrimers. ITC experiments by Mangold and Cloninger [70] showed that interactions with monomeric Con A demonstrated that all epitopes were available for binding. Increasing dendrimer valency lead to increased enthalpy contributions per epitope, but also increased entropy penalties, thus only marginally increasing the free energy of the interactions and lectin affinities. Interactions with dimeric Con A showed similar traits with respect to enthalpy and entropy, yet the affinity increases were much more exaggerated, suggesting that effective concentrations of both ligands and binding sites are important. However, in some cases, more than half of the carbohydrate epitopes were unavailable for binding. Typically, the larger generation dendrimers have larger binding constants, which could be a reflection on the larger inter-ligand distance and flexibility allowing for optimized interactions.

4.4 Functionalized polymers

Polymers are linear structures which present functional groups as branches from the main chain. Polymers, like dendrimers, are constructed by the polymerization of building units of natural or synthetic origin, and can be of controlled size and valency. Due to their potential large size, they can exhibit very high valency. Their nature and physical properties can be controlled by the use of different building blocks and side-chain functionalities resulting in highly tunable platforms. A wide range of building block molecules can be used to synthesize the polymer. Poly(phenylacetylene) was used by Otsuka et al. for the construction of glucose and galactose polymers for interaction studies with Con A and peanut agglutinin (PNG) lectins [80]. The polymers also gave chiral helical structures, the chirality imparted by the carbohydrate, which showed enhanced affinity towards the lectins. Block copolymers had also been developed by Lin et al. for the glucose sensitive aggregation of Con A [81]. Gestwicki et al. synthesized galactose functionalized polymers based on ROMP in order to investigate bacterial signaling in Escherichia coli [14]. Ogata et al. developed N-linked glycopolypeptides to inhibit influenza infections [82]. More recently, Zinger-Yosovich and Gilboa-Garber have used naturally occurring branched polysaccharides, normally used as food additives, for their anti-infection properties towards P. aeruginosa, Chromobacterium violaceum and Ralstonia solanacearum [83]. A further contribution from Bundle's research group includes the methodology of covalently pre-organized ligands presented on a polymer scaffold, designated as polyBAIT, which allowed for ligand activity enhancement of several orders of magnitude as seen by ELISA [84]. Natural polymers such as polypeptides can also be used as multivalent scaffolds [85].

As for several cases above, there is little quantitative data available for interpreting the thermodynamic and kinetic contributions of the cluster glycoside effect with polymer scaffolds. Dam et al. have conducted a thorough analysis of lectin binding to carbohydrate functionalized polymers [86]. They show that a “bind and slide”, or “bind and hop” model explains the large augmentations in lectin affinity. This model was designed to describe how enzymes bind to DNA, initially binding to a low affinity site then sliding along the DNA chain until a high affinity site is reached. In lectin–carbohydrate systems, the first lectin molecule binds with high affinity to the first available epitope. Dissociation–re-association occurs rapidly so that the overall kinetics show highly favorable binding. Upon saturation of the carbohydrate epitopes, subsequent binding (and re-binding) events occur with increasingly negative cooperativity. This resembles the effective concentration model for multivalent binding, with statistical effects strongly influencing the first and subsequent binding events – a reduction in further binding permutations upon saturation of the ligands presented on the polymer chain. The effective concentration model may not be able to fully explain this large augmentation in activity as steric effects may arise under high saturation conditions, reducing the affinity further.

4.5 Micelles and capsules

Molecules which consist of hydrophobic and hydrophilic building blocks allow for the construction of amphiphilic structures. When placed in polar solvents, the hydrophobic components collapse on themselves in order to be shielded from the aqueous environment. Simultaneously, the hydrophilic components expose themselves to the external environment, forming stable particles (Fig. 12E). This is one of the bases of the formation of capsules and micelles. Capsules are typically made of diblock polymers, whereas micelles consist of molecules which exhibit hydrophilic and hydrophobic components. If the hydrophilic components are functionalized with carbohydrates, these molecules can be presented on the micelle surface, in a multivalent arrangement. Micelles and capsules typically have a size range of nm – μm. Rieger et al. have produced several capsules as models for smart drug carriers, functionalized with mannosides, and tested with the BclA lectin [87,88]. Amphiphilic capsules based on polysaccharides (hyaluronic acid) and other biopolymers were also developed [89]. These hyaluronic acid capsules were developed by the layer by layer (LbL) adsorption of oppositely charged polymers around a sacrificial nanoparticle core. Iwasaki et al. also developed capsules to specifically target and tag non-natural carbohydrate molecules presented on carcinoma cells [90]. Micelles of mannose functionalized glycolipids have also been synthesized as multivalent ligands for Con A [91,92]. These nano- and microstructures present interesting candidates for intelligent drug delivery vectors as various biologically important molecules (drugs, fluorophores, etc.) can be trapped inside this hollow core to be released when and where necessary.

ITC studies conducted by Rieger et al. on polyethylene oxide – polycaprolactone micelles revealed that most of the carbohydrate epitopes were available for binding with the BclA lectin [88]. However, the enthalpy change of the interaction is slightly smaller, as is the entropy contribution, leading to a K_a one order of magnitude lower than that of Me-α-d-Mannose. This demonstrates a negative cluster glycoside effect, with no cooperativity or affinity enhancement.

4.6 Neoglycoproteins

Proteins and peptides are often glycosylated in nature, with glycosylation representing up to 70% of post-translational modifications [93]. Amino acids presenting O (serine or threonine) and N (asparagine) atoms on the peptide side chain provide potential glycosylation sites. Up to 90% of these naturally occurring glycosylation sites are occupied [23]. To produce this synthetically, however, solid state peptide methodologies have to be employed, requiring protection/deprotection of both carbohydrate and amino acids, and is limited to only 50 amino acids [93]. However, a variety of methods are available for introducing non-natural glycosylation sites. Typically, chemically modified carbohydrate molecules are coupled to modified amino acids in the peptide chain. Such examples include the use of thiohexoses which give thioether-linked (S-linked) glycoproteins upon coupling to sulfamidate-modified serine residues and Michael addition to unsaturated amino acids. Several site-specific methods have also been used such as disulfide bridge formation between thiohexoses (or functionalized thiohexoses: selenyl sulfides, methanethiosulfonates) and cystein residues [94].

Apart from only a few examples of their use as multivalent platforms for carbohydrate presentation, “glycodendriproteins” have so far not been widely used, despite their advantages as biocompatible, site-specific and targeting capabilities. Inhibition studies with galactose specific FimA and mannose specific Con A were reported; however, only a small (1.5-fold) increase in affinity enhancement was noted for Con A [95]. Yet a 20 nM inhibition of FimA was recorded, 10⁶-enhancement compared to that of lactose [96]. One more prominent example in the use of proteins as multivalent scaffolds was developed by Bundle's group, following on from their STARFISH scaffold [97]. This elegant methodology employed an anti-nitrophenol antigen (anit-NP IgM) as a (up to and including) decavalent protein scaffold for presenting NeuAcα2-6Gal ligands to CD22 receptors. The organized assembly of antibody-CD22 complexes allowed for the assembly of antibody scaffolds of optimal inter-ligand distances for cell surface glycan binding.

The disadvantage of the use of neoglycoproteins is that they are often produced in heterogeneous mixtures, although the protein is coded for by DNA, the addition of carbohydrates is not controlled genetically. The carbohydrate functionalities are thus subject to various conditions such as enzymatic degradation, etc. which leads to the production of several different glycan structures, termed “glycoforms” [23,93].

As for, the functionalized polymers above, there is no information available describing the thermodynamic parameters of the cluster glycoside effect observed in neoglycoproteins. However, one can imagine that, even with modification of the amino acid sequence at particular positions, it would be very difficult to control the display and presentation of the carbohydrate ligands. It may also be difficult to control the valency and presentation density of these ligands, as increased conjugation of carbohydrate molecules may denature the protein, effectively giving an (oligo)saccharide functionalized polypeptide.

4.7 Self-assembled monolayers (SAMs)

Carbohydrate functionalized (glyco-)SAMs provide a 2D model of the glycocalyx. They allow control over ligand density and orientation in addition to being supported by analytical techniques such as microarrays, surface plasmon resonance (SPR), quartz crystal microbalances and atomic force microscopy (AFM). Several surfaces can be used to which saccharide molecules are mobilized. Typically, target molecules consist of a thio- or thioacetate functionalized linker molecule to allow the formation of a stable S-Au bond upon SAM formation, for which there are many examples [98–100]. The linker molecule will terminate in the carbohydrate epitope. Dilution of these carbohydrate functionalized alkane thiols with non-functionalized alkane thiols allows density control on the 2D matrix. The ligands form highly organized, densely packed, oriented monolayers. Although density control is possible, distribution is not, meaning that the inter-carbohydrate distance may not be regular throughout the SAM. With SPR applications, gold surfaces and SAMs were popularized, as were various surface immobilization methods. Dextran can typically be found coated onto the gold sensor chips to which a wide variety of functional groups can be coupled (amines, thiols, carbonyls and streptavidin-biotin coupling as well as hydrophobic and bilayer attachment). There are numerous examples of the use of monolayers for the multivalent presentation of carbohydrate ligands and their interactions with lectins. In microarray technology, several hundreds of amine functionalized glycans have been immobilized to functionalized glass slides. Plastics and modified cellulose have also been used to immobilize carbohydrate molecules [101]. Glycan arrays are often, if not always, used to determine the preferences of lectins for particular mono- or oligosaccharide structures and motifs.

Due to the limited dimensionality of SAMs, there are currently no experimental methods for evaluating the thermodynamic contribution to the multivalence effect – only affinity measurements by SPR or similar experiments. Also, the current technology for immobilizing molecules to 2D surfaces does not yet allow for a great deal of control. For example, one can control well the quantity of material immobilized to form the SAM, however, the distribution of ligands on the surface would be at random, assuming experimental design has no effect on ligand deposition (flow direction, flow speed, surface size, etc.).

4.8 Gold nanoparticles

There are many examples in the literature of carbohydrate functionalized gold nanoparticles – (glyconanoparticles, GNPs) for investigating carbohydrate interactions. GNPs are similar in size to many common biomacromolecules and provide an ideal scaffold for presenting carbohydrate molecules in a globular polyvalent configuration, much like the glycocalyx (Fig. 13). Also, the physical properties of the AuNPs described above may be applied to the detection and evaluation of their interactions [18,102]. Penades’ group have developed several GNP systems as a 3D model of the glycocalyx for studying carbohydrate–protein interactions [16,103,104]. Lin et al. synthesized mannose functionalized GNPs for the labeling of FimH on type I pili [105], as well as demonstrating an increase in lectin affinity for the GNP scaffolded mannosides. The same group studied the interaction of their mannose GNPs with Con A by SPR showing a 100-fold increase in inhibitory potential with regards to Me-α-d-Mannose. Kamerling's group also developed glucose and mannose functionalized GNPs for studying the interaction of Con A by SPR [15], UV/vis aggregation and TEM, showing an increased affinity of Con A for the GNP scaffolded mannosides. Chien et al. also used SPR competition studies to investigate the interaction between shiga-like toxin and globotriose functionalized GNPs [17]. Relative inhibitory potencies up to 200,000-times higher were observed for these GNPs with reference to the monomer ligand.

The augmentation of lectin affinity for nanoparticle based carbohydrate ligands has been observed both qualitatively by haemagglutination inhibition assays with Con A and PA-IL as well as quantitatively using surface plasmon resonance, and the first use of isothermal titration microcalorimetry (ITC) for nanoparticle systems, for the BclA and PA-IL lectins [106]. As observed for BclA, hybrid GNPs with low density coverages (10, 25% presentation density in mannoside ligands) exhibited no improvement in lectin affinity in comparison with the ligand in free solution. This is thought to be because the inter-mannoside distance on the GNP surface is too great for the dimeric lectin to experience enthalpic complementarity, entropic enhancement or an increased local effective concentration to induce multivalent interactions. At 50% presentation density however, the K_a increases almost 40-fold, with enthalpic enhancement being strongly observed. Augmentation in PA-IL affinity was also observed for galactose functionalized GNPs by ITC. Ten-fold increases in interaction affinity were recorded from 17 to 33 and again to 100% galactose presentation densities. Although this augmentation was shown to be enthalpically enhanced, entropic enhancement also made a significant contribution. This confirms what was observed earlier by Barrientos et al. with the investigation of GNP presentation density on interactions with Viscum albumin agglutinin (lectin) and the enzyme E. coli β-galactosidase in competition and hydrolysis experiments respectively [16]. Investigations into the binding of mannose oligosaccharide functionalized GNPs with the DC-SIGN lectin also showed similar trends in HIV – DC-SIGN transfection and SPR inhibition studies [107,108].

In general, augmentation of K_a was observed when the inter-ligand distances approached half of those of the target lectin, suggesting that a combination of thermodynamic enhancement as well as effective concentrations and statistical considerations may be important for inducing multivalent interactions.