The use of gel electrophoresis for quantitative studies of DNA-protein interactions is described. This rapid and simple technique involves separation of free DNA from DNA-protein complexes based on differences in their electrophoretic mobilities in polyacrylamide gels. Under favorable conditions both unbound DNA and DNA associated with protein can be quantified. This gel method is applied to the study of the E. coli lactose operon regulatory system. At ionic strengths in the physiological range, the catabolite activator protein (CAP) is shown to form a long-lived complex with the wild type lac promotor, but not with a CAP-insensitive mutant. Formation of a stable "open" or "melted-in" complex of RNA polymerase with the wild type promoter requires the participation of CAP and cyclic AMP. Further, it is demonstrated that even when pre-formed in the presence of CAP-cAMP, the polymerase-promoter open complex becomes unstable if CAP is then selectively removed.

The regulatory system of the lactose operon has been "modeled" by a set of mass action equations and conservation constraints which describe the system at equilibrium. A "base-set" of values of binding constants and total component concentrations has been assembled from the available experimental data, and the simultaneous equations solved by computer procedures, to yield equilibrium concentrations of all the relevant molecular species. Considering the operator-repressorinducer system alone, it is shown that the in vivo basal and induced (derepressed) levels of lac enzyme synthesis in both wild-type and certain mutant Escherichia coli can be accounted for only if binding of repressor and repressor-inducer complexes to non-specific DNA sites is included in the calculations as an integral component of the overall control system. A similar approach was applied to the RNA polymerase-promoter system to show that sigma factor may modulate the general level of transcription in the cell by "inducing" polymerase off non-specific DNA binding sites, thus making it available to promoters. Competitive and non-competitive models for the interaction of repressor and polymerase at the lac operon can, in principle, be distinguished by these computational procedures, though data sufficient to permit unambiguous differentiation between the models are not available at this time. However, for any competitive binding model the resultsshow that repression in the entire (operator-repressor-RNA polymerase-lac promoter) system can occur only because non-specific binding of the regulatory proteins reduces the concentration of free polymerase, relative to that of repressor, to appropriate levels.The interaction of genome-regulating proteins (repressors, polymerases, etc.) with their specific target sequences on DNA can be perturbed by the relatively weak binding of such proteins to the non-specific DNA sites which are present in overwhelming preponderance within the cell. The equilibrium distribution of these proteins will depend on their relative affinities for the available sites, and on the relative concentrations of site types. Under physiological conditions the regulatory proteins (which are often present in fairly few copies per cell) are likely to be almost entirely complexed with non-functional sites, i.e., the concentration (activity) of free regulatory proteins in the cell will be very low. As a consequence the kinetics of the association (and dissociation) of such proteins with functional sites on the Escherichia coli chromosome will also depend on the relative numbers and spatial distribution of specific and non-specific binding sites on the DNA (1).In this paper we consider equilibrium aspects of these effects, as illustrated by a computer modeling study of the lac repressor-operator-inducer-non-specific DNA binding system, and the coupling of these interactions with the RNA polymerase-promoter-non-specific DNA ensemble. Experimental results required for the calculations are taken largely from the literature, though so...

ABSTBACr Binding of genome regulatory proteins to nonspecific DNA sites may play an important role in controlling the thermodynamics and kinetics of the interactions of these proteins with their specific target DNA sequences. An estimate of the fraction of Escherchia colilac repressor molecules bound in vivo to the operator region and to nonoperator sites on the E coli chromosome is derived by measurement of the distribution of repressor between a minicell-producing E. coli strain (P678-54) and the DNA-free minicells derived therefrom. Assuming the minicell cytoplasm to be representative of that of the parent E. coli cells, we find that less than 10% of the repressor tetramers of the average cell are free in solution; the remainder are presumed to be bound to the bacterial chromosome. The minimum in vivo value of the association constant for repressor to bulk nonoperator DNA (Kim) (1-4).The lactose operon of Escherichia coli is currently the best molecularly characterized genome regulatory system. The lac repressor controls the level of expression of the lac genes by binding tightly to the operator region and preventing transcription of the operon by DNA-dependent RNA polymerase (5-7). The affinity of repressor for operator in vitro, and the level of repression of the operon in vivo, are allosterically modulated by the binding to repressor of small molecule inducers structurally related to allolactose, the "natural" inducer which occurs as an early intermediate in the metabolic degradation of lactose (5, 8). Nonoperator DNA also binds lac repressor, albeit much more weakly than does operator (9-12), and this nonspecific affinity is not changed by the binding of inducer to the repressor (9, 11, 12). Furthermore, RNA polymerase also binds to DNA sites other than promoters, and its affinity for nonpromoter sequences may be modified by interaction with a factor (1, 4, 13). Based on these observations and direct in vitro measurement of most of the relevant binding constants, a model has been developed to account quantitatively for the observed levels of repression and derepression of the lactose operon; this model includes, as a central feature, nonspecific binding of regulatory proteins to the E. coli chromosome (1, 11).The validity of such models is not crucially dependent on knowledge of the absolute binding constants of (e.g.) the lac repressor (R) and repressor-inducer complex (RI) to operator (0) and nonoperator DNA (D)

Binding parameters for the interaction of lac repressor with non-operator DNA have been determined using a sedimentation velocity technique. Analytical ultracentrifugation is used to separate DNA-protein complexes from unbound protein, thereby permitting direct optical determination of the concentration of free protein as a function of input DNA and repressor concentrations. The method yields absolute values for the association constant ( K ) for proteins binding nonspecifically to nucleic acid lattices; the binding site size ( n ) , and the binding cooperativity parameter ( w ) can also be estimated by this approach. Values of K for the binding of repressor to non-operator DNA have been determined under a variety of solvent conditions. At 0.15 M Na+, 20 OC, pH 7.5, the average value of K for repressor binding to native phage X DNA is 2.4 X IO5 M-' (DNA concentration in base pairs, protein in repressor tetramers). Binding is very ionic strength dependent; we find that 6 log K/6 log [Na+] N -10. Analysis of the ionic strength dependence by the method of Record, M. T., Jr., Lohman, T. M., and de Haseth, P. ((1976), J . Mol.

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