Distribution of unselectively bound ligands along DNA

Unselective and reversible adsorption of ligands on DNA for a model of binding proposed by Zasedatelev, Gursky, and Volkenshtein is considered. In this model, the interaction between neighboring ligands located at the distance of i binding centers is characterized by the statistical weight ai. Each ligand covers L binding centers. For this model, expressions for binding averages are represented in a new simple form. This representation is convenient for the calculation of the fraction of inter-ligand distances of i binding centers fd(i) and the fraction of binding centers included in the distances of i binding centers fbc(i) for various types of interaction between bound ligands. It is shown that, for non-cooperative binding, contact cooperativity and long-range cooperativity, the fraction of the zero inter-ligand distance fd(0) is maximal at any relative concentration of bound ligands (r). Calculations demonstrate that, at low r, fd(0) approximately r.ao, and fd(i) approximately r at 11/r-L, then fd(i) rapidly decreases with i at any r for all types of inter-ligand interaction. At high ligand concentration (r is close to rmax=L(-1)), fd(0) is close to unity and fd(i) rapidly decreases with i for any type of inter-ligand interaction. For strong contact cooperativity, fd(0) is close to unity in a much lager r interval ((0.5-1).rmax), and fd(1) approximately ao(-1) at r approximately 0.5.rmax. In the case of long-range interaction between bound ligands, the dependence fd(i) is more complex and has a maximum at i approximately (1/r-L)1/2 for anti-cooperative binding. fbc(i) is maximal at i approximately 1/r-L for all types of binding except the contact cooperativity. A strong asymmetry in the influence of contact cooperativity and anticooperativity on the ligand distribution along DNA is demonstrated.