Dependence of Effective Molarity on Linker Length for an Intramolecular Protein−Ligand System

This paper reports dissociation constants and "effective molarities" (M(eff)) for the intramolecular binding of a ligand covalently attached to the surface of a protein by oligo(ethylene glycol) (EG(n)) linkers of different lengths (n = 0, 2, 5, 10, and 20) and compares these experimental values with theoretical estimates from polymer theory. As expected, the value of M(eff) is lowest when the linker is too short (n = 0) to allow the ligand to bind noncovalently at the active site of the protein without strain, is highest when the linker is the optimal length (n = 2) to allow such binding to occur, and decreases monotonically as the length increases past this optimal value (but only by a factor of approximately 8 from n = 2 to n = 20). These experimental results are not compatible with a model in which the single bonds of the linker are completely restricted when the ligand has bound noncovalently to the active site of the protein, but they are quantitatively compatible with a model that treats the linker as a random-coil polymer. Calorimetry revealed that enthalpic interactions between the linker and the protein are not important in determining the thermodynamics of the system. Taken together, these results suggest that the manifestation of the linker in the thermodynamics of binding is exclusively entropic. The values of M(eff) are, theoretically, intrinsic properties of the EG(n) linkers and can be used to predict the avidities of multivalent ligands with these linkers for multivalent proteins. The weak dependence of M(eff) on linker length suggests that multivalent ligands containing flexible linkers that are longer than the spacing between the binding sites of a multivalent protein will be effective in binding, and that the use of flexible linkers with lengths somewhat greater than the optimal distance between binding sites is a justifiable strategy for the design of multivalent ligands.