Poisson-Boltzmann analysis of the lambda repressor-operator interaction

A theoretical study of the ion atmosphere contribution to the binding free energy of the lambda repressor-operator complex is presented. The finite-difference form of the Poisson-Boltzmann equation was solved to calculate the electrostatic interaction energy of the amino-terminal domain of the lambda repressor with a 9 or 45 base pair oligonucleotide. Calculations were performed at various distances between repressor and operator as well as at different salt concentrations to determine ion atmosphere contributions to the total electrostatic interaction. Details in the distribution of charges on DNA and protein atoms had a strong influence on the calculated total interaction energies. In contrast, the calculated salt contributions are relatively insensitive to changes in the details of the charge distribution. The results indicate that the ion atmosphere contribution favors association at all protein-DNA distances studied. The theoretical number of ions released upon repressor-operator binding appears to be in reasonable agreement with experimental data.