Reliable Prediction of Complex Phenotypes from a Modular Design in Free Energy Space: An Extensive Exploration of the lac Operon

The basic methodology for designing, altering, and constructing biological systems is increasingly relying on well-established engineering principles to move forward from trial and error approaches to reliably predicting the system behavior from the properties of the components and their interactions. The inherent complexity of even the simplest biological systems, however, often precludes achieving such predictive power. A prototypical example is the lac operon, one of the best-characterized genetic systems, which still poses serious challenges for understanding the results of combining its parts into novel setups. The reason is the pervasive complex hierarchy of events involved in gene regulation that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. Here, we integrate such complexity into a few-parameter model to accurately predict gene expression from a few simple rules to connect the parts. The model accurately reproduces the observed transcriptional activity of the lac operon over a 10,000-fold range for 21 different operator setups, different repressor concentrations, and tetrameric and dimeric forms of the repressor. Incorporation of the calibrated model into more complex scenarios accurately captures the induction curves for key operator configurations and the temporal evolution of the beta-galactosidase activity of cell populations.