Speed, Sensitivity, and Bistability in Auto-activating Signaling Circuits

Cells employ a myriad of signaling circuits to detect environmental signals and drive specific gene expression responses. A common motif in these circuits is inducible auto-activation: a transcription factor that activates its own transcription upon activation by a ligand or by post-transcriptional modification. Examples range from the two-component signaling systems in bacteria and plants to the genetic circuits of animal viruses such as HIV. We here present a theoretical study of such circuits, based on analytical calculations, numerical computations, and simulation. Our results reveal several surprising characteristics. They show that auto-activation can drastically enhance the sensitivity of the circuit's response to input signals: even without molecular cooperativity, an ultra-sensitive threshold response can be obtained. However, the increased sensitivity comes at a cost: auto-activation tends to severely slow down the speed of induction, a stochastic effect that was strongly underestimated by earlier deterministic models. This slow-induction effect again requires no molecular cooperativity and is intimately related to the bimodality recently observed in non-cooperative auto-activation circuits. These phenomena pose strong constraints on the use of auto-activation in signaling networks. To achieve both a high sensitivity and a rapid induction, an inducible auto-activation circuit is predicted to acquire low cooperativity and low fold-induction. Examples from Escherichia coli's two-component signaling systems support these predictions

Bistability: Requirements on Cell-Volume, Protein Diffusion, and Thermodynamics

Bistability is considered wide-spread among bacteria and eukaryotic cells, useful e.g. for enzyme induction, bet hedging, and epigenetic switching. However, this phenomenon has mostly been described with deterministic dynamic or well-mixed stochastic models. Here, we map known biological bistable systems onto the well-characterized biochemical Schloegl model, using analytical calculations and stochastic spatio-temporal simulations. In addition to network architecture and strong thermodynamic driving away from equilibrium, we show that bistability requires fine-tuning towards small cell volumes (or compartments) and fast protein diffusion (well mixing). Bistability is thus fragile and hence may be restricted to small bacteria and eukaryotic nuclei, with switching triggered by volume changes during the cell cycle. For large volumes, single cells generally loose their ability for bistable switching and instead undergo a first-order phase transition.Comment: 23 pages, 8 figure

Contribution of bistability and noise to cell fate transitions determined by feedback opening

AbstractAlternative 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

PLoS Comput Biol

Cells employ a myriad of signaling circuits to detect environmental signals and drive specific gene expression responses. A common motif in these circuits is inducible auto-activation: a transcription factor that activates its own transcription upon activation by a ligand or by post-transcriptional modification. Examples range from the two-component signaling systems in bacteria and plants to the genetic circuits of animal viruses such as HIV. We here present a theoretical study of such circuits, based on analytical calculations, numerical computations, and simulation. Our results reveal several surprising characteristics. They show that auto-activation can drastically enhance the sensitivity of the circuit's response to input signals: even without molecular cooperativity, an ultra-sensitive threshold response can be obtained. However, the increased sensitivity comes at a cost: auto-activation tends to severely slow down the speed of induction, a stochastic effect that was strongly underestimated by earlier deterministic models. This slow-induction effect again requires no molecular cooperativity and is intimately related to the bimodality recently observed in non-cooperative auto-activation circuits. These phenomena pose strong constraints on the use of auto-activation in signaling networks. To achieve both a high sensitivity and a rapid induction, an inducible auto-activation circuit is predicted to acquire low cooperativity and low fold-induction. Examples from Escherichia coli's two-component signaling systems support these predictions.R01 GM095903/GM/NIGMS NIH HHS/United StatesR01GM-077298/GM/NIGMS NIH HHS/United StatesT32 GM008326/GM/NIGMS NIH HHS/United StatesT32GH08326/GH/CGH CDC HHS/United States22125482PMC321961

Coupling between feedback loops in autoregulatory networks affects bistability range, open-loop gain and switching times

Biochemical regulatory networks governing diverse cellular processes such as stress-response, differentiation and cell cycle often contain coupled feedback loops. We aim at understanding how features of feedback architecture, such as the number of loops, the sign of the loops and the type of their coupling, affect network dynamical performance. Specifically, we investigate how bistability range, maximum open-loop gain and switching times of a network with transcriptional positive feedback are affected by additive or multiplicative coupling with another positive- or negative-feedback loop. We show that a network's bistability range is positively correlated with its maximum open-loop gain and that both quantities depend on the sign of the feedback loops and the type of feedback coupling. Moreover, we find that the addition of positive feedback could decrease the bistability range if we control the basal level in the signal-response curves of the two systems. Furthermore, the addition of negative feedback has the capacity to increase the bistability range if its dissociation constant is much lower than that of the positive feedback. We also find that the addition of a positive feedback to a bistable network increases the robustness of its bistability range, whereas the addition of a negative feedback decreases it. Finally, we show that the switching time for a transition from a high to a low steady state increases with the effective fold change in gene regulation. In summary, we show that the effect of coupled feedback loops on the bistability range and switching times depends on the underlying mechanistic details

The interplay between metabolic stochasticity and regulation in single E. coli cells

Metabolism is inherently stochastic at the cellular level. Whether cells actively regulate processes in response to these random internal variations is a fundamental problem that remains unaddressed, yet critical to understanding biological homeostasis. Here, we show that in E. coli cells, expression of the main catabolic enzymes is continuously adjusted in response to metabolic fluctuations under constant external conditions. This noise feedback is performed by the cAMP-CRP system, which controls transcription of the catabolic enzymes by modulating concentrations of the second messenger cAMP upon changes in metabolite abundance. Using time-lapse microscopy, genetic constructs that selectively disable cAMP-CRP noise feedback, and mathematical modelling, we show how fluctuations circulate through this hybrid metabolic-genetic network at sub cell-cycle timescales. This circulation of stochastic fluctuations is explained by four distinct noise propagation modes, one of which describes the continuous cAMP-CRP regulation. The model successfully predicts how noise circulation is impacted by C-sector under and over-expression. The results raise the question whether the cAMP-CRP system, as well as other metabolic regulation mechanisms, have evolved to manage internal metabolic fluctuations in addition to external growth conditions. We conjecture that second messengers may broadly function to control metabolic stochasticity and achieve cellular homeostasis

An open-loop approach to study the stochastic properties

Randomness is an inevitable aspect of biological networks. It has been long accepted that variability of components in a network can propagate throughout the network. In this thesis, we introduce a method that allows us to decompose the total variability of a single component into individual contributions from the other components in a network. Our method of noise decomposition helps us investigate key parameters and their relative impact on the total normalized noise and also allows us to illustrate the importance of different system modifications by adding or omitting biological processes. With our generally applicable noise decomposition method, we are able to determine the strength of individual correlations induced by different co-regulation processes that connect different components of a network. In bistable systems, variability can occur through stochastic transitions from one steady state to another. Noise induced transitions between two steady states are difficult to calculate due to the intricate interplay between nonlinear dynamics and noise in bistable positive feedback loops. We open multicomponent feedback loops at the slowest variables in order to calculate the transition rates from one steady state to another. By reclosing the feedback loop, we calculate the mean first passage time (MFPT) using the Fokker-Planck equation. It is important to emphasize that the accurate approximation of the open-loop results is not a sufficient condition for a good prediction of the MFPT. We show that only the opening at the slowest variable warrants an accurate prediction of MFPT. Multiplicative interactions among different components can introduce correlations among noises. We show that the introduced correlations affect the mean and variance of the open loop function and consequently increase the transition rate between two steady states in the closed-loop system. Our results indicate that the open-loop approach can contribute to the theoretical prediction of the MFPT. The theoretical results are shown to be in good agreement with the results of stochastic simulation

Principles for Designing Robust and Stable Synthetic Microbial Consortia

Engineering stable microbial consortia with robust functions are useful in many areas, including bioproduction and human health. Robust and stable properties depend on proper control of dynamics ranging from single cell-level to population-environment interactions. In this thesis, I discuss principles of building microbial consortia with synthetic circuits in two design scenarios. First, for one microbial population, strong disturbances in environments often severely perturb cell states and lead to heterogeneous responses. Single cell-level design of control circuits may fail to induce a uniform response as needed. I demonstrate that cell-cell signaling systems can facilitate coordination among cells and achieve robust population-level behaviors. Moreover, I show that heterogeneity can be harnessed for robust adaptation at population-level via a bistable state switch. Second, multi-pecies consortia are intrinsically unstable due to competitive exclusion. Previous theoretical investigations based on models of pairwise interactions mainly explored what interaction network topology ensures stable coexistence. Yet neglecting detailed interaction mechanisms and spatial context results in contradictory predictions. Focusing on chemical-mediated interaction, I show that detailed mechanisms of chemical consumption/accumulation and chemical-induced growth/death, interaction network topology and spatial structures of environments all are critical factors to maintain stable coexistence. With a two population-system, I demonstrate that the same interaction network topology can exhibit qualitatively different or even opposite behaviors due to interaction mechanisms and spatial conditions.</p