[Precise relationships for calculating the binding of regulatory proteins and other lattice ligands in double-stranded polynucleotides]

The binding of long multisite ligands to double-stranded nucleic acids is considered. The ligand is taken as a lattice of AT- and GC-specific reaction centres the sequence of which is complementary to the base pair sequence in the specific ligand interaction site on DNA. Exact equations are derived for the two cases: that when a ligand binds in a fixed orientation relative to the DNA and that when it can be attached to DNA in the two alternative orientations related by two-fold rotation. Included in the formulation are two alternative orientations related by two-fold rotation. Included in the formulation are the ligand size effects as well as cooperative effects for which the interactions between the nearest neighbour adsorbed molecules are responsible. In particular, if cooperative interactions are allowed only between the adjacent ligand molecules related by two-fold rotation symmetry, the ligands would tend to associate into symmetrical "dimers" upon binding to DNA. This model enables one to explain the recognition of specific base sequences which are related by two-fold rotation symmetry and are complementary to the sequence of ligand reaction centres. Numerical calculations are carried out for several specific cases and for various values of parameters involved in the theoretical model.