In vivo Affinity of Repressor for Operator
The equilibrium dissociation constant for repressor binding to operator can be determined either from equilibrium measurements or from the ratio of the association and dissociation rates. The dissociation constant obtained by either of these methods can also be compared to in vivo data. A correspondence in the numbers suggests, but does not prove, that the in vitro reactions and conditions closely mimic the in vivo environment.
An estimation of the in vivo equilibrium dissociation constant of repressor for the operator uses the thousand-fold inducibility of the lac operon. Assume that the operator is completely free of repressor when the operon is fully induced and that the operator is free of repressor 1/1000 of the time when the operon is not induced. By definition,
Earlier we discussed the fact that the concentration of repressor, R, is approximately 10-8 M. The thousand-fold inducibility means that O/RO is approximately 1/1000. Thus,
This result closely agrees with the values found in vitro in buffers with salt concentrations equal to the in vivo value of about 0.15 M.