Multisite proteins and randomly coiled polymeric ligands. Chain length dependence of binding constants

A model mechanism was developed for the binding of a rigid multisite protein with a randomly coiled multivalent ligand. Probabilities of the formation of chain loops between sites located at given distances at the protein were calculated by an extension of the concept of ring closure in coiled chain molecules. Expressions were derived for the dependence of overall equilibrium quantities, such as the binding constant between the protein and the ligand, on intrinsic parameters such as intrinsic binding constants, number of sites at the protein and their distances and on the chain length of the polymeric ligand. A pronounced chain length dependence of the overall binding constant was predicted even at chain lengths much longer than the size of the protein. Such a dependence was previously observed for the enzyme prolyl hydroxylase which acts on polymeric substrates like (ProProGly)n. This so far unexplained feature is quantitatively described by the model mechanism which is believed to be applicable to many other interactions of biological importance.