Dynamic Responses of Laci/Galr Chimera-Based Transcriptional Logic Gates

Within the synthetic biology field, various logic gates have been constructed with broad applications in mind such as biological computing and sensors in a dynamic environment. Additionally, these logic gates may be integrated into larger networks, mediating response or coupling dynamics of modular genetic circuits based on environmental conditions. However, less work has been done to understand the limitations of transcriptional logic gates in these varied applications.  It is clear that reliable logic gates necessitate responses on a faster time-scale than time-varying environmental conditions. Therefore, we aim to understand the fundamental limitations on the dynamic range of transcriptional logic gates. Transcriptional logic gates function as low-pass filters, responding faithfully to low frequency (long period) signals and unfaithfully to high frequency (short period) signals.  

The focus of this study is chimera-based transcriptional logic gates. Recently, Shis et al. (2014) showed that chimeric proteins derived from the LacI/GalR family of transcriptional repressors can be used to create transcriptional AND gates in vivo. These chimeric proteins have the same operator (DNA) binding domain but different ligand binding domains; hence, they will bind to the same operator site but are induced by different sugars. Only if all repressors are induced will repression of the reporter be relieved, creating a multi-input AND gate.

We consider chimera-based transcriptional logic gates in this study for two reasons: 1) we predict their dynamic range will be larger than repressors with transcriptionally mediated inputs and 2) they provide us with a multitude of orthogonal inputs. By utilizing different inducible or constitutive promoters, and different combinations of inducer ligands, we have created two different transcriptional logic gates– IMPLY and AND. Using microfluidic devices capable of delivering either one or two input signals, we have measured the response of these two gates to different periodic inducer input frequencies and created frequency response plots.

We use a mathematical model to predict the critical frequency at which the response of the logic gates begins to degrade. Using control theory tools, we find that the critical frequency is dependent on the degradation rate of the fluorescent reporter. Furthermore, we find that modeling enzymatic degradation can play a critical role in predicting dynamic range depending on the range of protein expression. This nonlinearity can further complicate the frequency drop-off rate of the logic gate response.  Experimentally, at the higher frequencies we see a large delay in initial response of the logic gates despite a minimal phase shift at steady state response. These delays are much larger than transcriptional delays and require further investigation.

Additionally, we are currently constructing and testing NOT and NOR logic gates. These are similar to the IMPLY and AND gates with an added inverter, increasing the number of genes that need to be transcribed for “computation”. We predict that the ‘direct induction’ gates (IMPLY, AND) will have a much lower delay and act on timescales more relevant to synthetic circuits, while the ‘indirect induction’ gates (NOT, NOR) have higher delay and respond on slower time scales than IMPLY and AND.