Kinetics of large-ligand binding to one-dimensional lattices: theory of irreversible binding

Exact solutions are obtained for the time dependence of the extent of irreversible binding of ligands that cover more than one lattice site to a homogeneous one-dimensional lattice. The binding may be cooperative or noncooperative and the lattice either finite or infinite. Although the form of the solution is most convenient when the ligand concentration is buffered, exact numerical or approximate analytical solutions, including upper and lower bounds, can be derived for the case of variable ligand concentration as well. The physical reason behind the relative simplicity of the kinetics of irreversible as opposed to reversible binding in such systems is discussed.