Biophysical Limits of Control Implementations in Synthetic Gene Networks

Synthetic biology has made progress in applying engineering principles to forward-engineer cellular behavior, but there are still knowledge gaps for moving from high-level design to functional systems. One such gap is choosing the correct parts for a given network topology and ensuring optimal performance in a cell that has limited resources. While network motifs have been evaluated for different functions, the precise implementations have not been studied to determine differences in robustness and efficiency.

Here, we analyze the biophysical limits imposed by different molecular mechanisms when engineering bio-molecular control. As an example, we focus on the ability of incoherent feedforward loops (IFFLs) to achieve adaptation and maintain a set-point despite changing inputs. Unlike the simplest models of the IFFL motif, our model includes biophysical parameters that allow comparison of system error and resource usage over a range of input values.

For the same IFFL network topology we model three implementations of the negative interaction: TetR transcriptional repressor, T7 RNA polymerase (RNAP) that transcribes a small RNA (sRNA) that blocks translation, and mf-Lon protease that degrades target protein. Each implementation takes a general input u (e.g. copy number, transcriptional machinery, or translational machinery) that activates transcription or translation of both the target protein and each of the three regulating nodes. All can be shown to exhibit adaptation in the simplest mathematical model, but have tradeoffs in error and resource usage in our mechanistic model.

All three implementations were tuned to the same starting expression and steady-state error for a transcriptional input change of 1 to 10, then input changes were simulated over 3 orders of magnitude. Over this range, the percent error for all three are within one percent of each other but ribosome usage can differ by orders of magnitude. The T7 RNAP-sRNA circuit uses the least ribosomes, but has monotonically increasing error as the input increases beyond the transcriptional input for which the circuit was tuned.  The TetR repressor circuit uses more ribosomes but the error goes to a fixed amount as the input goes to infinity.  Similar adaptation is achieved for input changes to translational capacity but ribosome usage still differs by orders of magnitude. 

Our work can be used to choose biological realizations of gene networks that satisfy design constraints on error and resource usage. Such a theoretical framework can demonstrate quantitative tradeoffs among transcriptional, translational, and post-translational control that are not readily apparent. For instance, T7 RNAP-sRNA feedforward may be better for ribosome limited applications while TetR feedforward may be better for cases in which a small error is needed over a large transcriptional input range. We use these insights to guide our experimental realizations of feedforward or feedback control that can be tested and compared to the mathematical model. This analysis provides guidelines for modeling and designing circuits that are robust in resource limited cells.