The active form of lactose repressor binds to the operator with a dissociation constant of 10-13 M for the reaction R + O ⇆ RO. About 10 molecules per E. coli cell suffice to keep the operon turned off in the absence of inducer.
(a) If the average E. coli cell has an intracellular volume of 0.3 × 10-12 mL, calculate the approximate intracellular concentration of repressor.
(b) If the average cell contains two copies of the lac operon, calculate the approximate intracellular concentration of operators.
(c) Calculate the average intracellular concentration of free operators under these conditions.
(d) Explain how a cell with a haploid chromosome could contain an average of two copies of the lac operon.