Stoichiometry of irreversible ligand binding to a one-dimensional lattice

In this paper we investigate the problem of irreversible binding of a ligand that covers several identical binding sites on a macromolecule with a one-dimensional lattice. Due to steric constraints, irreversible binding or binding with slow kinetics results in partial saturation of the binding sites thus impacting the stoichiometry of the interaction. Here we present a recursive formula to calculate the exact fraction of the occupied binding sites for a ligand and macromolecule of arbitrary lengths. We also provide an analytical result for the exact fraction of the occupied sites in case of an infinitely long lattice. We conclude with a simplified empirical formula for the exact fraction of the occupied sites in case of an infinitely long lattice.