The diagram shown here is a model of the gene regulatory circuit for light production by V. fischeri cells. The lux operon contains genes for luminescence (luxCDABE) and a gene, luxI, that encodes an enzyme that catalyzes the production of an inducer. This inducer easily moves back and forth across the plasma membrane and acts as a signaling molecule. The lux operon is never completely turned off. The luxR gene codes for the activator LuxR. The inducer can bind to LuxR, and when it does, the LuxR–inducer complex can bind to a regulatory site to activate transcription of the lux operon and inhibit transcription of luxR. Explain how this gene regulatory circuit accounts for bacteria emitting light only when they reach a high cell density.