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.     

Memory switches in chemical reaction space

Just as complex electronic circuits are built from simple Boolean gates, diverse biological functions, including signal transduction, differentiation, and stress response, frequently use biochemical switches as a functional module. A relatively small number of such switches have been described in the literature, and these exhibit considerable diversity in chemical topology. We asked if biochemical switches are indeed rare and if there are common chemical motifs and family relationships among such switches. We performed a systematic exploration of chemical reaction space by generating all possible stoichiometrically valid chemical configurations up to 3 molecules and 6 reactions and up to 4 molecules and 3 reactions. We used Monte Carlo sampling of parameter space for each such configuration to generate specific models and checked each model for switching properties. We found nearly 4,500 reaction topologies, or about 10% of our tested configurations, that demonstrate switching behavior. Commonly accepted topological features such as feedback were poor predictors of bistability, and we identified new reaction motifs that were likely to be found in switches. Furthermore, the discovered switches were related in that most of the larger configurations were derived from smaller ones by addition of one or more reactions. To explore even larger configurations, we developed two tools: the “bistabilizer,” which converts almost-bistable systems into bistable ones, and frequent motif mining, which helps rank untested configurations. Both of these tools increased the coverage of our library of bistable systems. Thus, our systematic exploration of chemical reaction space has produced a valuable resource for investigating the key signaling motif of bistability.     

Characterizing multistationarity regimes in biochemical reaction networks

Switch like responses appear as common strategies in the regulation of cellular systems. Here we present a method to characterize bistable regimes in biochemical reaction networks that can be of use to both direct and reverse engineering of biological switches. In the design of a synthetic biological switch, it is important to study the capability for bistability of the underlying biochemical network structure. Chemical Reaction Network Theory (CRNT) may help at this level to decide whether a given network has the capacity for multiple positive equilibria, based on their structural properties. However, in order to build a working switch, we also need to ensure that the bistability property is robust, by studying the conditions leading to the existence of two different steady states. In the reverse engineering of biological switches, knowledge collected about the bistable regimes of the underlying potential model structures can contribute at the model identification stage to a drastic reduction of the feasible region in the parameter space of search. In this work, we make use and extend previous results of the CRNT, aiming not only to discriminate whether a biochemical reaction network can exhibit multiple steady states, but also to determine the regions within the whole space of parameters capable of producing multistationarity. To that purpose we present and justify a condition on the parameters of biochemical networks for the appearance of multistationarity, and propose an efficient and reliable computational method to check its satisfaction through the parameter space.     

Topology and robustness in the Drosophila segment polarity network

A complex hierarchy of genetic interactions converts a single-celled Drosophila melanogaster egg into a multicellular embryo with 14 segments. Previously, von Dassow et al. reported that a mathematical model of the genetic interactions that defined the polarity of segments (the segment polarity network) was robust (von Dassow et al. 2000). As quantitative information about the system was unavailable, parameters were sampled randomly. A surprisingly large fraction of these parameter sets allowed the model to maintain and elaborate on the segment polarity pattern. This robustness is due to the positive feedback of gene products on their own expression, which induces individual cells in a model segment to adopt different stable expression states (bistability) corresponding to different cell types in the segment polarity pattern. A positive feedback loop will only yield multiple stable states when the parameters that describe it satisfy a particular inequality. By testing which random parameter sets satisfy these inequalities, I show that bistability is necessary to form the segment polarity pattern and serves as a strong predictor of which parameter sets will succeed in forming the pattern. Although the original model was robust to parameter variation, it could not reproduce the observed effects of cell division on the pattern of gene expression. I present a modified version that incorporates recent experimental evidence and does successfully mimic the consequences of cell division. The behavior of this modified model can also be understood in terms of bistability in positive feedback of gene expression. I discuss how this topological property of networks provides robust pattern formation and how large changes in parameters can change the specific pattern produced by a network.     

A model for the dynamics of bipolar disorders

Bipolar disorders are characterized by recurrent, alternating episodes of mania and depression. To examine the dynamical bases of this cyclical illness we consider a minimal model for bipolar disorders based on the observation that the two poles of the disease are mutually exclusive. We assume that the propensities to mania and depression, which are correlated with the activity of two putative neural circuits that promote, respectively, the manic or the depressive state, inhibit each other. When mutual inhibition is sufficiently strong, the model predicts bistability: the bipolar system is then either in a depressive or in a manic state and can display abrupt switches between these stable states. We consider two simple mechanisms which, when added to mutual inhibition, allow the model to pass from bistability to oscillations. Self-sustained oscillations provide a mechanism for the spontaneous, recurrent switching between mania and depression. The model can generate oscillations with a variety of waveforms, including simple periodic oscillations with comparable or unequal durations of the manic and depressive episodes, or small-amplitude oscillations around one of the two states preceding large-amplitude periodic changes in the propensities to mania or depression. The model provides a theoretical framework that covers the bipolar spectrum, i.e., cycling between the two poles of the disease, or evolution to either mania or depression or to an intermediate state without alternating between the two poles of the disease. The model accounts for the clinical observation that antidepressants can trigger the transition to mania or increase the frequency of bipolar cycling.     

Critical slowing down and noise-induced intermittency in bistable perception: bifurcation analysis

Stochastic dynamics and critical slowing down were studied experimentally and numerically near the onset of dynamical bistability in visual perception under the influence of noise. Exploring the Necker cube as the essential example of an ambiguous figure, and using its wire contrast as a control parameter, we measured dynamical hysteresis in two coexisting percepts as a function of both the velocity of the parameter change and the background luminance. The bifurcation analysis allowed us to estimate the level of cognitive noise inherent to brain neural cells activity, which induced intermittent switches between different perception states. The results of numerical simulations with a simple energy model are in good qualitative agreement with psychological experiments.     

An efficient platform for genetic selection and screening of gene switches in Escherichia coli

Engineered gene switches and circuits that can sense various biochemical and physical signals, perform computation, and produce predictable outputs are expected to greatly advance our ability to program complex cellular behaviors. However, rational design of gene switches and circuits that function in living cells is challenging due to the complex intracellular milieu. Consequently, most successful designs of gene switches and circuits have relied, to some extent, on high-throughput screening and/or selection from combinatorial libraries of gene switch and circuit variants. In this study, we describe a generic and efficient platform for selection and screening of gene switches and circuits in Escherichia coli from large libraries. The single-gene dual selection marker tetA was translationally fused to green fluorescent protein (gfpuv) via a flexible peptide linker and used as a dual selection and screening marker for laboratory evolution of gene switches. Single-cycle (sequential positive and negative selections) enrichment efficiencies of >7000 were observed in mock selections of model libraries containing functional riboswitches in liquid culture. The technique was applied to optimize various parameters affecting the selection outcome, and to isolate novel thiamine pyrophosphate riboswitches from a complex library. Artificial riboswitches with excellent characteristics were isolated that exhibit up to 58-fold activation as measured by fluorescent reporter gene assay.     

A simple histone code opens many paths to epigenetics

Nucleosomes can be covalently modified by addition of various chemical groups on several of their exposed histone amino acids. These modifications are added and removed by enzymes (writers) and can be recognized by nucleosome-binding proteins (readers). Linking a reader domain and a writer domain that recognize and create the same modification state should allow nucleosomes in a particular modification state to recruit enzymes that create that modification state on nearby nucleosomes. This positive feedback has the potential to provide the alternative stable and heritable states required for epigenetic memory. However, analysis of simple histone codes involving interconversions between only two or three types of modified nucleosomes has revealed only a few circuit designs that allow heritable bistability. Here we show by computer simulations that a histone code involving alternative modifications at two histone positions, producing four modification states, combined with reader-writer proteins able to distinguish these states, allows for hundreds of different circuits capable of heritable bistability. These expanded possibilities result from multiple ways of generating two-step cooperativity in the positive feedback - through alternative pathways and an additional, novel cooperativity motif. Our analysis reveals other properties of such epigenetic circuits. They are most robust when the dominant nucleosome types are different at both modification positions and are not the type inserted after DNA replication. The dominant nucleosome types often recruit enzymes that create their own type or destroy the opposing type, but never catalyze their own destruction. The circuits appear to be evolutionary accessible; most circuits can be changed stepwise into almost any other circuit without losing heritable bistability. Thus, our analysis indicates that systems that utilize an expanded histone code have huge potential for generating stable and heritable nucleosome modification states and identifies the critical features of such systems.     

Breaking an Epigenetic Chromatin Switch: Curious Features of Hysteresis in Saccharomyces cerevisiae Telomeric Silencing

In addition to gene network switches, local epigenetic modifications to DNA and histones play an important role in all-or-none cellular decision-making. Here, we study the dynamical design of a well-characterized epigenetic chromatin switch: the yeast SIR system, in order to understand the origin of the stability of epigenetic states. We study hysteresis in this system by perturbing it with a histone deacetylase inhibitor. We find that SIR silencing has many characteristics of a non-linear bistable system, as observed in conventional genetic switches, which are based on activities of a few promoters affecting each other through the abundance of their gene products. Quite remarkably, our experiments in yeast telomeric silencing show a very distinctive pattern when it comes to the transition from bistability to monostability. In particular, the loss of the stable silenced state, upon increasing the inhibitor concentration, does not seem to show the expected saddle node behavior, instead looking like a supercritical pitchfork bifurcation. In other words, the ‘off’ state merges with the ‘on’ state at a threshold concentration leading to a single state, as opposed to the two states remaining distinct up to the threshold and exhibiting a discontinuous jump from the ‘off’ to the ‘on’ state. We argue that this is an inevitable consequence of silenced and active regions coexisting with dynamic domain boundaries. The experimental observations in our study therefore have broad implications for the understanding of chromatin silencing in yeast and beyond.     

Akt versus p53 in a network of oncogenes and tumor suppressor genes regulating cell survival and death

The tumor suppressor protein, p53, and the oncoprotein, Akt, are involved in a cross talk that could be at the core of a cell's control machinery for switching between survival and death. This cross talk is a combination of reciprocally antagonistic pathways emanating from p53 and Akt, and also involves another tumor suppressor gene, PTEN, and another oncogene, Mdm2; such a connected network of cancer-relevant genes must be significant and demands a critical study. The p53-Akt network is shown in this report to possess the potential to exhibit bistability, a phenomenon in which two stable steady states of the system coexist for a fixed set of control parameter values. A hierarchy of qualitative networks and abstract kinetic models are analyzed and simulated on a computer to demonstrate the robustness of the bistable behavior, which, as argued in this study, is a likely candidate mechanism for a cellular survival-death switch. The analysis applies to cells that are neither p53-null nor Akt-null. The models presented here offer experimental predictions on the identity of control parameters of apoptotic thresholds and on network perturbations (including DNA damage and Akt inhibition) that are sufficient to generate switching between pro-survival and pro-death cellular states.     

Dual selection of a genetic switch by a single selection marker

Forward engineering of synthetic genetic circuits in living cells is expected to deliver various applications in biotechnology and medicine and to provide valuable insights into the design principles of natural gene networks. However, lack of biochemical data and complexity of biological environment complicate rational design of such circuits based on quantitative simulation. Previously, we have shown that directed evolution can complement our weakness in designing genetic circuits by screening or selecting functional circuits from a large pool of nonfunctional ones. Here we describe a dual selection strategy that allows selection of both ON and OFF states of genetic circuits using tetA as a single selection marker. We also describe a successful demonstration of a genetic switch selection from a 2000-fold excess background of nonfunctional switches in three rounds of iterative selection. The dual selection system is more robust than the previously reported selection system employing three genes, with no observed false positive mutants during the simulated selections.     

Dynamic bistable switches enhance robustness and accuracy of cell cycle transitions

Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies have uncovered mechanisms that can make the shape of the bistable response curve change dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time. Our results are not specific to cell cycle models and may apply to other bistable systems in which the bistable response curve is time-dependent.     

Why are cellular switches Boolean? General conditions for multistable genetic circuits

The logic of cellular decision-making is largely controlled by regulatory circuits defining molecular switches. Such switching elements allow to turn a graded input signal into an all-or-nothing output. Traditional studies have focused on this bistable picture of regulation, but higher-order scenarios involving tristable and tetrastable states are possible too. Are these multiswitches allowed in simple gene regulatory networks? Are they likely to be observed? If not, why not? In this paper we present the examination of this question by means of a simple but powerful geometric approach. We examine the relation between multistability, the degree of multimerization of the regulators and the role of autoloops within a deterministic setting, finding that N-stable circuits are possible, although their likelihood to occur rapidly decays with the order of the switch. Our work indicates that, despite two-component circuits are able to implement multistability, they are optimal for Boolean switches. The evolutionary implications are outlined.     

Synchrony and Asynchrony in a Fully Stochastic Neural Network

We describe and analyze a model for a stochastic pulse-coupled neural network, in which the randomness in the model corresponds to synaptic failure and random external input. We show that the network can exhibit both synchronous and asynchronous behavior, and surprisingly, that there exists a range of parameters for which the network switches spontaneously between synchrony and asynchrony. We analyze the associated mean-field model and show that the switching parameter regime corresponds to a bistability in the mean field, and that the switches themselves correspond to rare events in the stochastic system.     

Signaling in small subcellular volumes. II. Stochastic and diffusion effects on synaptic network properties

The synaptic signaling network is capable of sophisticated cellular computations. These include the ability to respond selectively to different patterns of input, and to sustain changes in response over long periods. The small volume of the synapse complicates the analysis of signaling because the chemical environment is strongly affected by diffusion and stochasticity. This study is based on an updated version of a previously proposed synaptic signaling circuit (Bhalla and Iyengar, 1999) and analyzes three network computation properties in small volumes: bistability, thresholding, and pattern selectivity. Simulations show that although there are diffusive regimes in which bistability may persist, chemical noise at small volumes overwhelms bistability. In the deterministic situation, the network exhibits a sharp threshold for transition between lower and upper stable states. This transition is broadened and individual runs partition between lower and upper states, when stochasticity is considered. The third network property, pattern selectivity, is severely degraded at synaptic volumes. However, there are regimes in which a process similar to stochastic resonance operates and amplifies pattern selectivity. These results imply that simple scaling of signaling conditions to femtoliter volumes is unlikely, and microenvironments, such as reaction complex formation, may be essential for reliable small-volume signaling.     

Programming microbial population dynamics by engineered cell-cell communication

A major aim of synthetic biology is to program novel cellular behavior using engineered gene circuits. Early endeavors focused on building simple circuits that fulfill simple functions, such as logic gates, bistable toggle switches, and oscillators. These gene circuits have primarily focused on single-cell behaviors since they operate intracellularly. Thus, they are often susceptible to cell-cell variations due to stochastic gene expression. Cell-cell communication offers an efficient strategy to coordinate cellular behavior at the population level. To this end, we review recent advances in engineering cell-cell communication to achieve reliable population dynamics, spanning from communication within single species to multispecies, from one-way sender-receiver communication to two-way communication in synthetic microbial ecosystems. These engineered systems serve as well-defined model systems to better understand design principles of their naturally occurring counterparts and to facilitate novel biotechnology applications.     

Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades

Mitogen-activated protein kinase (MAPK) cascades can operate as bistable switches residing in either of two different stable states. MAPK cascades are often embedded in positive feedback loops, which are considered to be a prerequisite for bistable behavior. Here we demonstrate that in the absence of any imposed feedback regulation, bistability and hysteresis can arise solely from a distributive kinetic mechanism of the two-site MAPK phosphorylation and dephosphorylation. Importantly, the reported kinetic properties of the kinase (MEK) and phosphatase (MKP3) of extracellular signal-regulated kinase (ERK) fulfill the essential requirements for generating a bistable switch at a single MAPK cascade level. Likewise, a cycle where multisite phosphorylations are performed by different kinases, but dephosphorylation reactions are catalyzed by the same phosphatase, can also exhibit bistability and hysteresis. Hence, bistability induced by multisite covalent modification may be a widespread mechanism of the control of protein activity.     

New directions in incidence-dose modeling

Many cellular responses are quantal; that is, they either take place or they do not. Examples of "either-or" responses include cell replication, differentiation and apoptosis. Surprisingly, induction of suites of genes and coordinated phenotypic changes in cells are also often quantal, where embedded molecular circuitry creates on-off switches. Mechanistic incidence-dose (ID) models need to account for the quantal characteristics of cellular switches that contribute, in turn, to dose thresholds and to the incidence of biological responses in individuals. Interdisciplinary systems biology approaches create mechanistic ID models based on: (i) detailed knowledge of the cellular circuitry controlling signal transduction; (ii) evolving biological modeling tools describing cellular circuits and their perturbations by chemicals and (iii) high throughput, high coverage "omic" screens for examining cell signaling pathways and biological responses. These interdisciplinary approaches should produce novel, quantitative ID models for biological responses and greatly improve the biological basis of safety and risk assessments.