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

This paper reports dissociation constants and “effective molarities” (Meff) for the intramolecular binding of a ligand covalently attached to the surface of a protein by oligo(ethylene glycol) (EGn) 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 Meff 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 ∼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 p...