Distribution Function Describing the Binding of Long Ligands to DNA Molecules: Possible Application to DNA Condensation

摘要

The noncooperative binding of ligands to DNA molecules leads to equilibrium in solution between DNA molecules on which different numbers of ligands are adsorbed. At a given concentration of the free ligand in solution, such equilibrium is characterized by the distribution function, which describes the probability of detection of a DNA molecule to which a certain number of ligands are bound in solution. In the case where such ligands are polycations, there can be a phase transition in DNA to which so many ligands are bound that their number is sufficient to neutralize charges on phosphates. An example of such a transition is the formation of liquid-crystal dispersions in the chitosan binding to DNA. The chitosan binding to DNA is analyzed under the assumption that this binding occurs by equilibrium adsorption. At a certain chitosan concentration in solution, DNA molecules are in equilibrium with different numbers of adsorbed chitosan molecules. If the number of adsorbed ligands exceeds a certain critical value, then the DNA molecule to which chitosan molecules are bound becomes capable of interacting with other DNA molecules. Because of such an interaction (attraction), the formation of liquid-crystal dispersions becomes possible.Equations are derived for the concentration of DNA molecules as a function of the ligand concentration in solution. It is shown that the model at certain parameters fits well the experimental data on the formation of cholesteric liquid-crystal dispersions. Data analysis yields both the size of a chitosan-binding site on DNA and the energy of chitosan interaction with DNA.