The Operator Competes with Low-Affinity Sites to Bind Repressor

KEY CONCEPTS
- Proteins that have a high affinity for a specific DNA sequence also have a low affinity for other DNA sequences.
- Every base pair in the bacterial genome is the start of a low-affinity binding site for repressor.
- The large number of low-affinity sites ensures that all repressor protein is bound to DNA.
- Repressor binds to the operator by moving from a low affinity site rather than by equilibrating from solution.
- In the absence of inducer, the operator has an affinity for repressor that is 10⁷ times that of a low-affinity site.
- The level of 10⁴ repressor tetramers per cell ensures that the operator is bound by repressor 96% of the time.
- Induction reduces the affinity for the operator to 10 times that of low-affinity sites, so that the operator is bound only 3% of the time.
Probably all proteins that have a high affinity for a specific sequence also possess a low affinity for any random DNA sequence. A large number of low-affinity sites will compete just as well for a repressor as a small number of high-affinity sites. The E. coli genome contains only one lac operon, which contains the only high-affinity sites. The remainder of the DNA provides low-affinity binding sites. Every base pair in the genome starts a new lowaffinity binding site. Simply moving one base pair from the operator creates a low-affinity site! That means that there are 4.2 × 10⁶ low-affinity sites in the E. coli genome.
The large number of low-affinity sites means that even in the absence of a specific binding site almost all of the repressor is bound to DNA, and very little remains free in solution. LacI binding to nonspecific genomic sites has been visualized in vivo by singlemolecule experiments. Using the binding affinities, it can be deduced that all but 0.01% of repressors are bound to random DNA. There are only about 10 molecules of repressor tetramer per wild-type cell; this indicates that there is no free repressor protein. Thus, the critical factor of the repressor–operator interaction is the partitioning of the repressor on DNA; the single high-affinity site of the operator must compete with a large number of low-affinity sites.  

The efficiency of repression therefore depends on the relative affinity of the repressor for its operator compared with other random DNA sequences. The affinity must be great enough to overcome the large number of random sites. How this works can be determined by comparing the equilibrium constants for lac repressor–operator binding with repressor–general DNA binding.
TABLE.1 shows that the ratio is 10 for an active repressor, enough to ensure that the operator is bound by repressor 96% of the time so that transcription is effectively—but not completely— repressed. (Remember that because allolactose, not lactose, is the inducer, a little β-galactosidase is always needed in the cell.) When inducer is added, the ratio is reduced to 10⁴ . At this level, only 3% of the operators are bound, and the operon is effectively induced.
TABLE .1 lac repressor binds strongly and specifically to its operator, but is released by inducer. All equilibrium constants are in M^-1 .

The consequence of these affinities is that in an uninduced cell one tetramer of repressor usually is bound to the operator. All, or almost all, of the remaining tetramers are bound at random to other regions of DNA, . It is likely that there are very few or no free repressor tetramers within the cell. The addition of inducer abolishes the ability of repressor to bind specifically at the operator. Those repressors bound at the operator are released and bind to random (low-affinity) sites. Thus, in an induced cell, the repressor tetramers are “stored” on random DNA sites. In a noninduced cell a tetramer is bound at the operator, whereas the remaining repressor molecules are bound to nonspecific sites. The effect of induction is therefore to change the distribution of repressor on DNA, rather than to generate free repressor. In the same way that RNA polymerase probably moves between promoters and other DNA by swapping one sequence for another, the repressor also may directly displace one bound DNA sequence with another in order to move between sites. The parameters that influence the ability of a regulator protein to saturate its target site can be defined by comparing the equilibrium equations for specific and nonspecific binding. As might be expected, the important parameters are as follows:
- The size of the genome dilutes the ability of a protein to bind specific target sites (recall how large eukaryote genomes are).
- The specificity of a protein counters the effect of the mass of the DNA.
-The amount of the protein that is required increases with the total amount of DNA in the genome and decreases the specificity of DNA binding.
- The amount of the protein also must be in reasonable excess of the total number of specific target sites, thus regulators with many targets would be expected to be found in greater quantities than regulators with fewer targets.