Thermodynamic Approaches to the Study of Affinity of Clustered Carbohydrate Epitopes in Galectin-Glycoconjugate Interactions

Many biological ligands possess clustered epitopes that bind to speci c receptor molecules. However, the effects of clustered epitopes on ligand-receptor interactions are not well understood. For example, Equation 3.1 illustrates binding of monovalent ligand L to a receptor R. Their interactions can be described by af nity constant Ka in Equation 3.2: [L] [R] [LR]+ (3.1) a [LR]/[L][R]K = (3.2) Binding of tetravalent ligand L4 to receptor R is more complicated. In this case, L is covalently clustered into four epitopes (L4), with each epitope of L4 binding an individual R molecule (no steric effects). Historically, the binding of L4 to R is often described by a single inhibition or binding constant. However, binding of L4 to R cannot be described by Equation 3.1 since four molecules of R bind to one molecule of L4. Therefore, a single binding constant such as that in Equation 3.2 is not correct. Instead, binding of L4 to R must be minimally written as the four microequilibria below: [L4] [R] [L4R]+ (3.3) [L4R] [R] [L4R2]+ (3.4) [L4R2] [R] [L4R3]+ (3.5) [L4R3] [R] [L4R4]+ (3.6) It follows that there are four microequilibrium binding constants, Ka1, Ka2, Ka3, and Ka4, associated with microequilibria Equations 3.3, 3.4, 3.5, and 3.6, respectively. Until recently, the presence of these microequilibria for multivalent ligand-receptor interactions have not been widely described (cf. [1]), nor has the range of values for the microaf nity constants, Ka1, Ka2, Ka3, and Ka4, in the present example, been estimated or determined.