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

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

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

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

Paradoxical signaling regulates structural plasticity in dendritic spines

Transient spine enlargement (3-5 min timescale) is an important event associated with the structural plasticity of dendritic spines. Many of the molecular mechanisms associated with transient spine enlargement have been identified experimentally. Here, we use a systems biology approach to construct a mathematical model of biochemical signaling and actin-mediated transient spine expansion in response to calcium-influx due to NMDA receptor activation. We have identified that a key feature of this signaling network is the paradoxical signaling loop. Paradoxical components act bifunctionally in signaling networks and their role is to control both the activation and inhibition of a desired response function (protein activity or spine volume). Using ordinary differential equation (ODE)-based modeling, we show that the dynamics of different regulators of transient spine expansion including CaMKII, RhoA, and Cdc42 and the spine volume can be described using paradoxical signaling loops. Our model is able to capture the experimentally observed dynamics of transient spine volume. Furthermore, we show that actin remodeling events provide a robustness to spine volume dynamics. We also generate experimentally testable predictions about the role of different components and parameters of the network on spine dynamics

The case for absolute ligand discrimination : modeling information processing and decision by immune T cells

Some cells have to take decision based on the quality of surroundings ligands, almost irrespective of their quantity, a problem we name "absolute discrimination". An example of absolute discrimination is recognition of not-self by immune T Cells. We show how the problem of absolute discrimination can be solved by a process called "adaptive sorting". We review several implementations of adaptive sorting, as well as its generic properties such as antagonism. We show how kinetic proofreading with negative feedback implements an approximate version of adaptive sorting in the immune context. Finally, we revisit the decision problem at the cell population level, showing how phenotypic variability and feedbacks between population and single cells are crucial for proper decision

Stochastic Effects in Quorum Sensing

[cat] En aquesta tesi, estudiem els efectes de la estocàsticitat en la aparició del comportament col·lectiu en poblacions de bacteris que comuniquen per quorum sensing (QS). Ens centrem en el interruptor genètic com a paradigma dels processos de decisió cel·lulars tant en sistemes de bacteris naturals com sintètics. El nostre mètode es basa en la modelització matemàtica i en les simulacions estocàstiques, tant a nivell d'una cèl·lula individual com a nivell d'una població de cèl·lules. A nivell d'una cèl·lula individual, mostrem que el soroll afavoreix l'estabilitat del fenotip de l'estat ``baix'' de l'interruptor genètic autoactivador i que la regió de biestabilitat s'estén quan creix la intensitat de les fluctuacions, un efecte que hem anomenat estabilització estocàstica. A nivell d'una població de cèl·lules, mostrem que el procés de difusió del mecanisme de QS modifica les fluctuacions i la dinàmica de la molècula autoinductora dins de la cèl·lula i interactua amb el soroll en la expressió genètica. En el sistema canònic de QS LuxR/LuxI, mostrem que el soroll en la expressió genètica de LuxR és el principal factor que controla la variabilitat transitòria de l'activació del QS. El soroll intrínsec disminueix la precisió de la coordinació de la població i modifica la dinàmica de la transició de QS. A més, presentem un model d'una població d'interruptors genètics de toggle switch que comuniquen per l'intercanvi de dos senyals difusius de QS. Mostrem que l'increment de la velocitat de difusió, que augmenta la força de l'acoblament entre les cèl·lules, porta a una transició de fase: va des d'una fase desordenada on les cèl·lules salten de manera aleatòria entre els dos estats de l'interruptor, fins a una fase ordenada amb totes les cèl·lules bloquejades en el mateix estat estable. La mateixa transició s'ha trobat en una població de cèl·lules que creixen exponencialment en un volum tancat, amb totes les cèl·lules entrant en l'estat ordenat quan arriben a una mida crítica del sistema. Els nostres resultats suggereixen un nou mecanisme per la decisió cel·lular col·lectiva basat en el fenomen de la transició de fase.[eng] Stochastic fluctuations, or noise, are ubiquitous in biological systems and play an important role in many cellular processes. Experimental evidences have shown that noise affects the reliability of cell coordination in populations of communicating cells. In this thesis, we study the effects of stochasticity in the emergence of collective behavior in populations of bacteria communicating by QS. We focus on the genetic switch as a paradigm of cellular decision making in both natural and synthetic bacterial systems. Our approach is based on mathematical modeling and stochastic simulations, both at the level of the single cell and at the level of the cell population. We focus on four main topics. In the first topic, we analyze the interplay between intracellular noise and the diffusion process of the QS signaling mechanism. We build a model describing the expression of the signaling molecule and its diffusion in a population of cells, focusing on the situation of very low constitutive expression rate. We show that varying the diffusion rate produces a repertoire of dynamics for the signaling molecule. Our results reveal the contribution of intrinsic noise and transcriptional noise (mRNA copy number fluctuations) in the fluctuations of the signaling molecule. We observe that the total noise exhibits a maximum as a function of the diffusion rate, in contrast to previous studies. Thus, the QS communication mechanism modifies the fluctuations of the signaling molecule inside the cell and interacts with the gene expression noise. In the second topic, we study the effects of gene expression noise on the precision of the population coordination in the QS activation of the LuxR/LuxI system. We analyze the response and dynamics of a population of cells to different levels of autoinducer. Our results show that gene expression noise in LuxR is the main factor that controls the transient variability of the QS activation. This study sheds light on the relation between the single cell stochastic dynamics and the collective behavior in a population of communicating cells. In the third topic, we analyze the effects of intrinsic noise in an autoactivating switch in an isolated single cell. We show that noise promotes the stability of the low-state phenotype of the switch and that the bistable region is extended when increasing the intensity of the fluctuations, an effect that we call stochastic stabilization. Our results show that intrinsic noise modifies the epigenetic landscape as well as the switching rate, which results in complex behavior of the stochastic switching dynamics when varying the intensity of noise. Thus, at the level of a single cell, intrinsic noise contributes to the cell-to-cell variability of the genetic switch and can modify its stable states and its dynamics. In the fourth topic, we build a model of a population of toggle switches communicating by the exchange of two diffusible QS signals. We show that increasing the diffusion rate, which increases the coupling strength between the cells, leads to a phase transition from an unordered phase where the cells randomly flip between the two states of the switch, to an ordered phase with all the cells locked into the same stable state. The same transition is found in a population of cells growing exponentially in a closed volume. Moreover, the response of the cells to a varying external signal exhibits a hysteresis loop. We show that the cell-cell coupling enhances the sensitivity of the population response to the external signal and suggest that this new mechanism could be used to increase the robustness and sensitivity of biosensors. Our results suggest a new mechanism for collective cell decision making based on the phenomenon of phase transition

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

Intrinsic noise profoundly alters the dynamics and steady state of morphogen-controlled bistable genetic switches

During tissue development, patterns of gene expression determine the spatial arrangement of cell types. In many cases, gradients of secreted signaling molecules - morphogens - guide this process. The continuous positional information provided by the gradient is converted into discrete cell types by the downstream transcriptional network that responds to the morphogen. A mechanism commonly used to implement a sharp transition between two adjacent cell fates is the genetic toggle switch, composed of cross-repressing transcriptional determinants. Previous analyses emphasize the steady state output of these mechanisms. Here, we explore the dynamics of the toggle switch and use exact numerical simulations of the kinetic reactions, the Chemical Langevin Equation, and Minimum Action Path theory to establish a framework for studying the effect of gene expression noise on patterning time and boundary position. This provides insight into the time scale, gene expression trajectories and directionality of stochastic switching events between cell states. Taking gene expression noise into account predicts that the final boundary position of a morphogen-induced toggle switch, although robust to changes in the details of the noise, is distinct from that of the deterministic system. Moreover, stochastic switching introduces differences in patterning time along the morphogen gradient that result in a patterning wave propagating away from the morphogen source. The velocity of this wave is influenced by noise; the wave sharpens and slows as it advances and may never reach steady state in a biologically relevant time. This could explain experimentally observed dynamics of pattern formation. Together the analysis reveals the importance of dynamical transients for understanding morphogen-driven transcriptional networks and indicates that gene expression noise can qualitatively alter developmental patterning

A coarse-grained bacterial cell model for resource-aware analysis and design of synthetic gene circuits

Within a cell, synthetic and native genes compete for expression machinery, influencing cellular process dynamics through resource couplings. Models that simplify competitive resource binding kinetics can guide the design of strategies for countering these couplings. However, in bacteria resource availability and cell growth rate are interlinked, which complicates resource-aware biocircuit design. Capturing this interdependence requires coarse-grained bacterial cell models that balance accurate representation of metabolic regulation against simplicity and interpretability. We propose a coarse-grained E. coli cell model that combines the ease of simplified resource coupling analysis with appreciation of bacterial growth regulation mechanisms and the processes relevant for biocircuit design. Reliably capturing known growth phenomena, it provides a unifying explanation to disparate empirical relations between growth and synthetic gene expression. Considering a biomolecular controller that makes cell-wide ribosome availability robust to perturbations, we showcase our model's usefulness in numerically prototyping biocircuits and deriving analytical relations for design guidance