Cooperative effects on binding of proteins to DNA.

Equations are derived for description of cooperative binding of large ligands to a homogeneous polynucleotide lattice for a wide variety of binding models. Both short- and long-range interactions between nearest-neighbour bound ligands are taken into account. It is shown that cooperative binding of ligand at high levels of occupancy can be described with good accuracy by the equation derived for the noncooperative binding of the same ligand with an apparent binding constant Keff. A new method is proposed for the analysis of cooperative binding isotherms. It is based on a comparison of the asymptotic behavior of cooperative and noncooperative binding isotherms in the limit when the occupancy of lattice by ligand approaches the saturation level of binding. It is demonstrated that cooperative effects mediated by direct contact between bound ligands can be divided into two classes depending on whether dimeric species or aggregates of unrestricted size are formed by bound ligands on the lattice at high levels of occupancy. These two classes can be easily distinguished on strictly empirical grounds. In particular, if interligand interactions favor the formation of dimeric species on DNA, Keff approximately a 1/2 where a is the interligand interaction constant. If interligand interactions generate aggregates of unrestricted size, Keff approximately aL + 1 where L is the size of binding site for the ligand on DNA. We also demonstrate that cooperative systems in which interligand interaction extends over two or more free polymer residues can be distinguished from systems in which only short-range interactions mediated by direct contacts between bound ligands are allowed.