In vivo thermodynamic analysis of repression with and without looping in lac constructs. Estimates of free and local lac repressor concentrations and of physical properties of a region of supercoiled plasmid DNA in vivo.

A strong-binding primary (O1) lac operator located 100 to 200 base-pairs (bp) upstream from a lac promoter control region reduces expression from a lac promoter controlled by a weaker-binding (Oc) lac operator between 3 and 20-fold on a multicopy plasmid in E. coli. We attribute this effect to loop formation in which a thermodynamically stable complex is formed between bidentate lac repressor tetramers and the O1 and Oc operators. A thermodynamic model for repression is developed to interpret these data in terms of the composite effects of free lac repressor concentration and of local repressor concentration (from looping) at the Oc site. The local repressor concentration is found to vary periodically with the distance in base-pairs between the O1 and the Oc operators, ranging from 2 to 20-fold larger than the free concentration (i.e. the bulk thermodynamic activity) of repressor in this F'Iq overproducing strain (estimated to be approximately less than 0.5 microM). The amplitude of the periodic variation in expression and in local concentration appears to decrease with increasing interoperator distance in the range examined. Quantitative analysis of the looping data provides estimates of the physical properties of the intervening DNA region in vivo. For distances in the range 127 to 197 bp, the periodicity of modulation is uniformly 11.28(+/- 0.04) bp, which we interpret as the helical repeat of this region of supercoiled plasmid DNA in vivo. Possible origins of this altered helical repeat include the global linking deficit of the supercoiled DNA and any local linking deficit induced by divergent transcription from promoters bracketing the interoperator region. DNA cyclization analysis yields an apparent in vivo persistence length of this interoperator region of 64(+/- 26) A (which is approximately 15% of the in vivo result) and an in vivo torsional rigidity constant of 1.1(+/- 0.1) x 10(-19) erg cm, which is at the lower end of the range of values found in vitro.