Inside a prokaryote, such as e. coli, an operon controls for the production of the amino acid tryptophan. what occurs in the cell in order to turn off the production of tryptophan?
tryptophan binds with the promoter to block the dna polymerase.
the operon binds to the rna polymerase and releases the repressor.
tryptophan binds with the repressor, allowing it to attach to the operator site, blocking rna polymerase.
the rna polymerase binds to the tryptophan, activating the repressor, blocking the promoter.

cells use diffusion to get substances in and out of themselves. that diffusion will occur across the cell membrane or the outer covering of the cell. because we are talking about the surface of the cell, surface area and volume are  important factors here. as a cell increases in size, its surface area and volume increase as well.  we call that the surface area to volume ratio (sa: vol).  but the catch is that  volume increases at a greater rate than surface  area. in other words, as a cell gets bigger, the sa: vol gets smaller. so a really small cell like bacteria is mostly cell membrane (surface) with very little contents (volume). a really big cell like an egg, is mostly insides with a super thin membrane. so what ends up happening is that the cell cannot efficiently diffuse all of the stuff it needs in/out to survive. therefore cell size is limited to about 100mm. so how do we make organisms bigger than 100mm? cells divide! by dividing and becoming multicellular, organisms are able to grow!   check out the diagrams i attached to see the effect of sa: vol. i hope this ! good luck!