Identification of optimal parameter combinations for the emergence of bistability

Measurement of In Vivo Protein Binding Affinities in a Signaling Network with Mass Spectrometry

Protein interaction networks play a key role in signal processing. Despite the progress in identifying the interactions, the quantification of their strengths lags behind. Here we present an approach to quantify the in vivo binding of proteins to their binding partners in signaling-transcriptional networks, by the pairwise genetic isolation of each interaction and by varying the concentration of the interacting components over time. The absolute quantification of the protein concentrations was performed with targeted mass spectrometry. The strengths of the interactions, as defined by the apparent dissociation constants, ranged from subnanomolar to micromolar values in the yeast galactose signaling network. The weak homodimerization of the Gal4 activator amplifies the signal elicited by glucose. Furthermore, combining the binding constants in a feedback loop correctly predicted cellular memory, a characteristic network behavior. Thus, this genetic-proteomic binding assay can be used to faithfully quantify how strongly proteins interact with proteins, DNA and metabolites.

An open-loop approach to calculate noise-induced transitions

Bistability permits the co-existence of two distinct cell fates in a population of genetically identical cells. Noise induced transitions between two fates of a bistable system are difficult to calculate due to the intricate interplay between nonlinear dynamics and noise in bistable positive feedback loops. Here we opened multivariable feedback loops at the slowest variable to obtain the open-loop function and the fluctuations in the open-loop output. By the subsequent reclosing of the loop, we calculated the mean first passage time (MFPT) using the Fokker-Planck equation in good agreement with the exact stochastic simulation. When an external component interacts with a feedback component, it amplifies the extrinsic noise in the loop. Consequently, the open-loop function is shifted and the transition rates between the two states in the closed loop are increased. Despite this shift, the open-loop output reflects the system faithfully to predict the MFPT in the feedback loop. Therefore, the open-loop approach can help theoretical analysis. Furthermore, the measurement of the mean value, variance, and the reaction time-scale of the open-loop output permits the prediction of MFPT simply from experimental data, which underscores the practical value of the stochastic open-loop approach.

Measurement of bistability in a multidimensional parameter space

Bistability plays an important role to generate two stable states for alternative cell fates, or to promote cellular diversity and cell cycle oscillations. Positive feedback loops are necessary for the existence of bistability and ultrasensitive reactions in the loops broaden the parameter range of bistability. The broader parameter range a system's bistability covers, the more robust the two states are. It is challenging to determine the bistable range of a parameter because noise and transient processes induce transitions between the two states. We found that a threshold of transition rates coincides with the bistability boundaries determined by the open-loop approach. With this threshold, we estimated the boundaries for various synthetic single-gene positive feedback loops in yeast in a two dimensional parameter space: the inducer concentration and promoter dynamic range. While the bistable range of inducer concentration was influenced by many factors, the promoter dynamic range was more informative. The narrowest promoter dynamic range at which bistability can emerge revealed whether the full potential of an ultrasensitive reaction, such as dimerization, is exploited in the feedback loop. The convenient control of basal expression to adjust the promoter dynamic range permits a practical and reliable comparison of robustness of related positive feedback loops.

Contribution of Bistability and Noise to Cell Fate Transitions Determined by Feedback Opening

Alternative cell fates represent a form of non-genetic diversity, which can promote adaptation and functional specialization. It is difficult to predict the rate of the transition between two cell fates due to the strong effect of noise on feedback loops and missing parameters. We opened synthetic positive feedback loops experimentally to obtain open-loop functions. These functions allowed us to identify a deterministic model of bistability by bypassing noise and the requirement to resolve individual processes in the loop. Combining the open-loop function with kinetic measurements and reintroducing the measured noise, we were able to predict the transition rates for the feedback systems without parameter tuning. Noise in gene expression was the key determinant of the transition rates inside the bistable range. Transitions between two cell fates were also observed outside of the bistable range, evidenced by bimodality and hysteresis. In this case, a slow transient process was the rate-limiting step in the transitions. Thus, feedback opening is an effective approach to identify the determinants of cell fate transitions and to predict their rates.