Modeling of DNA condensation and decondensation caused by ligand binding

A theoretical method for computer modeling of DNA condensation caused by ligand binding is developed. In the method, starting (s) and condensed (c) states are characterized by different free energies for ligand free DNA (F(s) and F(c) respectively), ligand binding constants (K(s) and K(c)) and stoichiometry dependent parameters (c(sm) and c(cm) - maximum relative concentration of bound ligands (per base pair) for starting and condensed state respectively). The method allows computation of the dependence of the degree of condensation (the fraction of condensed DNA molecules) on ligand concentration. Calculations demonstrate that condensation transition occurs under an increase in ligand concentration if F(s) < F(c) (i.e. S(sc) = exp [- (F(c) - F(s)) / (RT)], the equilibrium constant of the s-c transition, is low (S(sc) << 1)) and K(s) < K(c). It was also found that condensation is followed by decondensation at high ligand concentration if the condensed DNA state provides the number of sites for ligand binding less than the starting state (c(sm) > c(cm)). A similar condensation-decondensation effect was found in recent experimental studies. We propose its simple explanation.