Emergence of switch-like behavior in a large family of simple biochemical networks

Bistability plays a central role in the gene regulatory networks (GRNs) controlling many essential biological functions, including cellular differentiation and cell cycle control. However, establishing the network topologies that can exhibit bistability remains a challenge, in part due to the exceedingly large variety of GRNs that exist for even a small number of components. We begin to address this problem by employing chemical reaction network theory in a comprehensive in silico survey to determine the capacity for bistability of more than 40,000 simple networks that can be formed by two transcription factor-coding genes and their associated proteins (assuming only the most elementary biochemical processes). We find that there exist reaction rate constants leading to bistability in ~90% of these GRN models, including several circuits that do not contain any of the TF cooperativity commonly associated with bistable systems, and the majority of which could only be identified as bistable through an original subnetwork-based analysis. A topological sorting of the two-gene family of networks based on the presence or absence of biochemical reactions reveals eleven minimal bistable networks (i.e., bistable networks that do not contain within them a smaller bistable subnetwork). The large number of previously unknown bistable network topologies suggests that the capacity for switch-like behavior in GRNs arises with relative ease and is not easily lost through network evolution. To highlight the relevance of the systematic application of CRNT to bistable network identification in real biological systems, we integrated publicly available protein-protein interaction, protein-DNA interaction, and gene expression data from Saccharomyces cerevisiae, and identified several GRNs predicted to behave in a bistable fashion.Comment: accepted to PLoS Computational Biolog

Interplay of Extrinsic and Intrinsic Cues in Cell-Fate Decisions

A cell’s decision making process is coordinated by dynamic interplay between its extracellular environment and its intracellular milieu. For example, during stem cell differentiation, fate decisions are believed to be ultimately controlled by differential expression of lineage-specific transcription factors, but cytokine receptor signals also play a crucial instructive role in addition to providing permissive proliferation and survival cues. Here, we present a minimal computational framework that integrates the intrinsic and extrinsic regulatory elements implicated in the commitment of hematopoietic progenitor cells to mature red blood cells (Chapter 2). Our model highlights the importance of bidirectional interactions between cytokine receptors and transcription factors in conferring properties such as ultrasensitivity and bistability to differentiating cells. These system-level properties can induce a switch-like characteristic during differentiation and provide robustness to the mature state. We then experimentally test predictions from this lineage commitment model in a model system for studying erythropoiesis (Chapter 3). Our experiments show that hemoglobin synthesis is highly switch-like in response to cytokine and cells undergoing lineage commitment possess memory of earlier cytokine signals. We show that erythrocyte-specific receptor and transcription factor are indeed synchronously co-upregulated and the heterogeneity in their expression is positively correlated during differentiation, confirming the presence of autofeedback and receptor-mediated positive feedback loops. To evaluate the possibility of employing this minimal topology as a synthetic “memory module” for cell engineering applications, we constructed this topology synthetically in Saccharomyces cerevisiae by integrating Arabidopsis thaliana signaling components with an endogenous yeast pathway (Chapter 4). Our experiments show that any graded and unimodal signaling pathway can be rationally rewired to achieve our desired topology and the resulting network immediately attains high ultrasensitivity and bimodality without tweaking. We further show that this topology can be tuned to regulate system dynamics such as activation/deactivation kinetics, signal amplitude, switching threshold and sensitivity. We conclude with a computational study to explore the generality of this interplay between extrinsic and intrinsic cues in hematopoiesis. We extend our minimal model analysis in Chapter 2 to examine the more complex fate decisions in bipotent and multipotent progenitors, particularly how these cells can make robust decisions in the presence of multiple extrinsic cues and intrinsic noise (Chapter 5). Our model provides support to both the instructive and stochastic theories of commitment: cell fates are ultimately driven by lineage-specific transcription factors, but cytokine signaling can strongly bias lineage commitment by regulating these inherently noisy cell-fate decisions with complex, pertinent behaviors such as ligand-mediated ultrasensitivity and robust multistability. The simulations further suggest that the kinetics of differentiation to a mature cell state can depend on the starting progenitor state as well as on the route of commitment that is chosen. Lastly, our model shows good agreement with lineage-specific receptor expression kinetics from microarray experiments and provides a computational framework that can integrate both classical and alternative commitment paths in hematopoiesis that have been observed experimentally

On positive solutions and the Omega limit set for a class of delay differential equations

This paper studies the positive solutions of a class of delay differential equations with two delays. These equations originate from the modeling of hematopoietic cell populations. We give a sufficient condition on the initial function for $t\leq 0$ such that the solution is positive for all time $t>0$. The condition is "optimal". We also discuss the long time behavior of these positive solutions through a dynamical system on the space of continuous functions. We give a characteristic description of the $\omega$ limit set of this dynamical system, which can provide informations about the long time behavior of positive solutions of the delay differential equation.Comment: 15 pages, 2 figure

Multistable Decision Switches for Flexible Control of Epigenetic Differentiation

It is now recognized that molecular circuits with positive feedback can induce two different gene expression states (bistability) under the very same cellular conditions. Whether, and how, cells make use of the coexistence of a larger number of stable states (multistability) is however largely unknown. Here, we first examine how autoregulation, a common attribute of genetic master regulators, facilitates multistability in two-component circuits. A systematic exploration of these modules' parameter space reveals two classes of molecular switches, involving transitions in bistable (progression switches) or multistable (decision switches) regimes. We demonstrate the potential of decision switches for multifaceted stimulus processing, including strength, duration, and flexible discrimination. These tasks enhance response specificity, help to store short-term memories of recent signaling events, stabilize transient gene expression, and enable stochastic fate commitment. The relevance of these circuits is further supported by biological data, because we find them in numerous developmental scenarios. Indeed, many of the presented information-processing features of decision switches could ultimately demonstrate a more flexible control of epigenetic differentiation

Modeling Reveals Bistability and Low-Pass Filtering in the Network Module Determining Blood Stem Cell Fate

Combinatorial regulation of gene expression is ubiquitous in eukaryotes with multiple inputs converging on regulatory control elements. The dynamic properties of these elements determine the functionality of genetic networks regulating differentiation and development. Here we propose a method to quantitatively characterize the regulatory output of distant enhancers with a biophysical approach that recursively determines free energies of protein-protein and protein-DNA interactions from experimental analysis of transcriptional reporter libraries. We apply this method to model the Scl-Gata2-Fli1 triad—a network module important for cell fate specification of hematopoietic stem cells. We show that this triad module is inherently bistable with irreversible transitions in response to physiologically relevant signals such as Notch, Bmp4 and Gata1 and we use the model to predict the sensitivity of the network to mutations. We also show that the triad acts as a low-pass filter by switching between steady states only in response to signals that persist for longer than a minimum duration threshold. We have found that the auto-regulation loops connecting the slow-degrading Scl to Gata2 and Fli1 are crucial for this low-pass filtering property. Taken together our analysis not only reveals new insights into hematopoietic stem cell regulatory network functionality but also provides a novel and widely applicable strategy to incorporate experimental measurements into dynamical network models

A robust method for designing multistable systems by embedding bistable subsystems

Although multistability is an important dynamic property of a wide range of complex systems, it is still a challenge to develop mathematical models for realising high order multistability using realistic regulatory mechanisms. To address this issue, we propose a robust method to develop multistable mathematical models by embedding bistable models together. Using the GATA1-GATA2-PU.1 module in hematopoiesis as the test system, we first develop a tristable model based on two bistable models without any high cooperative coefficients, and then modify the tristable model based on experimentally determined mechanisms. The modified model successfully realises four stable steady states and accurately reflects a recent experimental observation showing four transcriptional states. In addition, we develop a stochastic model, and stochastic simulations successfully realise the experimental observations in single cells. These results suggest that the proposed method is a general approach to develop mathematical models for realising multistability and heterogeneity in complex systems