Nonspecific binding of the OR repressors CI and Cro of bacteriophage lambda

We estimate the Gibbs free energy for nonspecific binding (DeltaGNSB) to the Escherichia coli DNA for two regulatory proteins of the lambda phage, CI and Cro. By means of a statistical-mechanical approach, we calculate the cI and cro activities associated with the operator OR of an introduced lambda phage genome (prophage). In this statistical model we apply in vitro-measured binding free energies to fit in vivo experimental data for cI and cro activities, respectively, where DeltaGNSB is introduced as a free (fitting) parameter. Without nonspecific binding included in the model, the quality of the description is fairly poor, whereas data are nicely correlating with our model with nonspecific binding included over the entire data range. The obtained values of DeltaGNSB are -4.1+/-0.9 kcal/mol, for CI, and -4.2+/-0.8 kcal/mol, for Cro. In particular, in a lysogen (approximately 250 CI monomers per cell) we conclude that 86% of the total CI in the cell is nonspecifically bound, leaving on average around 10 CI dimers freely available in the E. coli cytoplasma. These findings corroborate the view that due to low free cellular particle numbers a dynamical analysis of genetic regulation at OR and comparable systems should include a stochastic component. In addition, we perform a stability analysis of the OR system in the presence of nonspecific binding.