In silico evolved lac operons exhibit bistability for artificial inducers, but not for lactose

Bistability in the lac operon of Escherichia coli has been widely studied, both experimentally and theoretically. Experimentally, bistability has been observed when E. coli is induced by an artificial, nonmetabolizable, inducer. However, if the lac operon is induced with lactose, the natural inducer, bistability has not been demonstrated. We derive an analytical expression that can predict the occurrence of bistability both for artificial inducers and lactose. We find very different conditions for bistability in the two cases. Indeed, for artificial inducers bistability is predicted, but for lactose the condition for bistability is much more difficult to satisfy. Moreover, we demonstrate that in silico evolution of the lac operon generates an operon that avoids bistability with respect to lactose, but does exhibit bistability with respect to artificial inducers. The activity of this evolved operon strikingly resembles the experimentally observed activity of the operon. Thus our computational experiments suggest that the wild-type lac operon, which regulates lactose metabolism, is not a bistable switch. Nevertheless, for engineering purposes, this operon can be used as a bistable switch with artificial inducers.