This proposed device consists of operator sites taken from the tetracycline operon (tetO) and the lactose operon (lacO) placed in the two flanking positions around the -35 and -10 sequences of the prokaryotic promoter and in the space between these critical sequences. Given two operator sequences and three possible sites within the promoter, all 6 potential configurations are constructed and evaluated. Since the cell line used (DH5αPro) has been configured to constitutively express both the LacI and TetR repressor proteins, these putative AND gate promoters are responsive to the commonly-used inducers IPTG and aTc. Only when the IPTG clears the LacI from its operator sites, and the aTc clears the TetR from its operator sites can expression of the attached gene commence. In this work, the promoter is coupled to a gene that produces GFP as an output signal. Its behavior is observed in vivo through fluorescence-activated cell sorting. The quantitative behavior of the AND gate phenotype is then studied both in silico and in vivo as a function of promoter topology.
The in silico model is constructed from kinetic data obtained from the literature and yields clearly-defined ON/OFF logical behavior at realistic inducer concentrations, matching the in vivo data. A non-reductionist modeling approach is pursued. That is, instead of developing the simplest possible model that can capture the behavior of the biological system, we include all the biomolecular interactions involved in transcription, translation, regulation and induction in order quantify the influence of each individual interaction on the overall behavior of the system. The models thus acquire a predictive character that renders them well suited for engineering purposes.
These models are then simulated by applying a hybrid stochastic-discrete/stochastic-continuous algorithm developed by Salis and Kaznessis. This approach correctly accounts for the behavior of scarce species (such as promoter and operator sites) which may be present in very small quantities – as small as one copy per cell – but whose behavior is critical to the performance of the overall system.
Because these models are stochastic, they generate probability distributions of phenotypes that are directly comparable to experimentally observed variation. Because they are detailed, the models provide the opportunity to gain molecular level insight and quantify previously undetermined biomolecular interactions.
It is observed in vivo that engineered promoters containing two tetO sites and one lacO site form AND gates of varying levels of fidelity and promoter activity, while those containing two lacO sites and one tetO site cannot be induced over the range of aTc and IPTG concentrations tested. This effect is examined and investigated in the in silico system as well, and a potential explanation for the effect is offered.
The incomplete repression by the weaker LacI repressor is also investigated and quantified. These studies generate a new parameter – a rate constant that describes the displacement of the LacI repressor by RNA polymerase – that was not obtained from the literature, but may prove helpful in future in silico design work, as it provides a critical link between the in vivo and in silico results.
The in silico results, coupled with in vivo data, not only identify important design degrees of freedom, but provide previously uncharacterized parameters that can be used to guide future synthetic designs with these commonly-used regulatory elements from the Lac and Tet operons. The design rules and insights elucidated in this work can easily be applied to the construction of future hybrid promoters. Additionally, the detailed stochastic-kinetic modeling methodology described in this work is more broadly applicable to the design of complex transcriptional systems – both single promoters and gene networks, provided the component parts are well characterized.