I am trying to grow E coli to high cell densities in order to enhance the yield of my recombinant protein. I understand that auto-induction media with appropriate aeration give good results here. My question concerns how to determine the exact concentration of lactose and glucose in the medium, so that the glucose is depleted at the right time and the lactose then kicks in (between them, a "buffer" of glycerol as interim carbon source, of course).
How are these concentrations determined? Are they connected to the doubling time or growth rate in any way? Is there a rule of thumb or anything does it have to be determined empirically?