Promoter search by Escherichia coli RNA polymerase on a circular DNA template

Using the rapid-mixing/photocross-linking technique developed in our laboratory, we have investigated the kinetics of interaction between Escherichia coli RNA polymerase and pAR1319, a recombinant plasmid DNA containing the bacteriophage T7 A2 early promoter. By monitoring the time-dependent density of bound RNA polymerase along the relaxed circular DNA molecule using this technique, we have been able to demonstrate kinetic evidence for linear diffusion of RNA polymerase along DNA in a different system from that previously described (Park, C. S., Hillel, Z., and Wu, C.-W. (1982) J. Biol. Chem. 251, 6950-6956). The nonspecific association rate constant kon was measured to be 7.7 x 10(4) M-1 s-1 at a DNA chain concentration of 22.4 nM. By taking advantage of the fact that rapid mixing displaces bound protein molecules from DNA, but leaves them within the domain of the DNA, the rate of intradomain binding of RNA polymerase to pAR1319 DNA was determined to be 8.2 s-1. Since the plasmid is described by a radius of gyration of 0.22 microns, the intradomain concentration of base pairs could be calculated. Using this concentration (180 microM), the rate constant for intradomain nonspecific association of RNA polymerase to pAR1319 DNA was estimated to be 4.6 x 10(4) M-1 s-1. In addition, a mathematical model has been used to fit the other two important rate constants to the experimental data: koff, which describes the dissociation of RNA polymerase from nonspecific binding sites, and D1, the one-dimensional diffusion coefficient of the enzyme along the DNA molecule. In this model, the circular DNA molecule is described as a ring of interconnected binding sites which together comprise a DNA "domain." RNA polymerase, which enters the domain via three-dimensional diffusion and binds to each site, is allowed to diffuse linearly between adjacent sites and three-dimensionally on and off the DNA molecule. The rate equations for the time-dependent occupancy of each site by RNA polymerase could be written, based on general principles. By solving the resulting family of differential equations, koff and D1 were determined to be 0.3 s-1 and 1.5 x 10(-9) cm2 s-1, respectively.