Characterization of bistability and transition rates in transcriptional positive feedback loops

Abstract

Positive feedback commonly displays bistability, the ability to maintain overtime in the same conditions two alternative states of activity. The presence and the range of bistability depend on ultrasensitive reactions within the loop. To investigate bistability in genetic network, we constructed synthetic feedback loops in yeast where a transcription factor activates its own expression. By measuring the presence of hysteresis behavior, which is a sign of bistability, in those loops we identified the ultrasensitive reactions supporting bistability: homodimerization and cooperative binding of transcription factor. In the absence of those reactions the feedback loop was strictly monostable and when combined an even wider range of bistability arises than when there was only a single reaction. The detection of those reactions was made possible because we introduced RNA stem-loop upstream of the coding sequence of the transcription factor to reduce its translation rate. Indeed, the initial constructs had strong growth defect due to the overexpression of the transcription factor. Next, we aimed to predict transition rates between the two states of activity. Indeed, Even though the activity converges to either of the two states in the bistable range, due to the noise arising from the low number of some chemical species, transitions between the two states occur. The prediction of those transitions is difficult as the noise is amplified by feedback loop. First, we obtained a deterministic description of the loops by the open-loop approach. By breaking the loops at the mRNA of the transcription factor, we were able to fit the main parameter values of the system and map the steady states and the bistable range. Then, we determined the transient kinetics which is the activation delay which is not inherent to feedback loop, in our case it was the slow diffusion or binding of a ligand of the transcription factor. We determined also the noise of the system by measuring the distribution of mRNA at the steady states of the feedback loops. By building a stochastic model with the information from open-loop approach and expending it and fitting its parameter values to match the transient kinetics and noise observed, we were able to predict the transition rates observed in the feedback loops. With this better understanding, we discovered that the transitions are led by either noise or slow transient kinetics depending whether the system is inside or outside in the vicinity of the bistable range, respectively. Finally, we showed that the transition rates were abruptly changing around the boundaries of the bistable region. Therefore, the bistable region can be estimated in similar feedback loops by simply measuring transition rates.