  The induction of the lac operon follows cooperative kinetics.The first
mechanistic model of these kinetics is the de facto standard in the modeling
literature (Yagil & Yagil, Biophys J, 11, 11-27, 1971). Yet, subsequent studies
have shown that the model is based on incorrect assumptions. Specifically, the
repressor is a tetramerwith four (not two) inducer-binding sites, and the
operon contains two auxiliary operators (in addition to the main operator).
Furthermore, these structural features are crucial for the formation of DNA
loops, the key determinants of lac repression and induction. Indeed, the
repression is determined almost entirely (>95%) by the looped complexes (Oehler
et al, EMBO J, 13, 3348, 1990), and the pronounced cooperativity of the
induction curve hinges upon the existence of the looped complexes (Oehler et
al, Nucleic Acids Res, 34, 606, 2006). Here, we formulate a model of lac
induction taking due account of the tetrameric structure of the repressor and
the existence of looped complexes. We show that: (1) The kinetics are
significantly more cooperative than those predicted by the Yagil & Yagil model.
(2) The model provides good fits to the repression data for cells containing
tetrameric (or mutant dimeric) repressor, as well as the induction curves for 6
different strains of E. coli. It also implies that the ratios of certain looped
and non-looped complexes are independent of inducer and repressor levels, a
conclusion that can be rigorously tested by gel electrophoresis. (3) Repressor
overexpression dramatically increases the cooperativity of the induction curve.
This suggests that repressor overexpression can induce bistability in systems,
such as growth of E. coli on lactose, that are otherwise monostable.
