K

s flexible tether flexible tether tether too long (or too short)

Because ASmono Is usually less than zero, In such a system AGbi Is even more favorable than 2AGmono and, therefore, Kbi > (Kmono)2. For systems with greater flexibility calculation of the binding enhancement is more complex. A suitable theoretical model has been published recently [11].

The discussion of a bivalent interaction in the general sense is applicable to N-valent interactions and illustrates that the design of the tethers connecting individual binding sites within a multivalent ligand is critical to obtaining high-affinity ligands. Usually, however, the optimization of multivalent ligands is performed by trial and error. In these cases the mechanisms by which binding occurs are less critical. To describe the binding enhancement in such uncharacterized multivalent systems compared with the corresponding monovalent system, Whitesides et al. proposed the empirical parameter b, which is the ratio of the association constants Kmulti and Kmono as defined by Eqs (4) and (5) [8].

Systems with high values of b are useful, irrespective of their mechanism of action. In fact, many multivalent systems with large values of b do not reach the binding enhancement which would be possible in the case of maximum entropic enhancement and enthalpic additivity.

Many examples of multivalent ligands employing numerous scaffolds have been described; these differ in size, carbohydrate content, and flexibility [3, 6-8]. Glyco-polymers, for example, are able to cover large areas of cell surfaces and bridge several membrane-located lectins ("statistical" multivalency). Low-valent glyco-clusters (miniclusters), on the other hand, bind preferentially to several binding sites of a single (oligomeric) lectin proximate in space and may be tailored to lec-tins with known 3D structure ("directed" multivalency).

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