A general model for binary cell fate decision gene circuits with degeneracy: indeterminacy and switch behavior in the absence of cooperativity

Systematic analysis and optimization of early warning signals for critical transitions using distribution data

Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.

The generation of the flower by self-organisation

The essence of the Turing-Child theory (Schiffmann, 1991, 2017) is the direct and spontaneous conversion of chemical energy into simultaneous differentiation and morphogenesis, and all localised biological work and localised entropy-reducing processes. This is done via the identification of the Turing instability with cAMP and ATP being the Turing morphogens that mutually fulfil the five Turing inequalities. A flower model like the ABC model is derived from experiments with mutations. But what actually generates the model in real development? That is, how do genes of class A come to be expressed in the sepal and petal whorls, genes of class B in the petal and stamen whorls, and genes of class C in the stamen and carpel whorls. We suggest that the generation of the ABC model occurs via sequential compartmentalisation by Turing-Child eigenfunction patterns similar to the one occurring in Drosophila (Schiffmann, 2012). We also suggest a similar mechanism for the generation of the dorso-lateral-ventral polarity and bilateral symmetry. A mechanism for the generation of the regular location of the floral organs is also suggested. The symmetry and regularity of flowers, which are the source of their attraction and beauty, stem from the symmetry and regularity of the Turing-Child eigenfunctions. The central problem in developmental biology is the endless regress. This endless regress is halted by the Turing-Child pre-patterns and this is illustrated on a central example in flower generation. Both the shape and the chemistry - the steady-state rate of ATP synthesis and hydrolysis - of the Turing-Child pre-patterns are exactly what is required. Art and science meet in flower formation.

Robustness and timing of cellular differentiation through population-based symmetry breaking

During mammalian development and homeostasis, cells often transition from a multilineage primed state to one of several differentiated cell types that are marked by the expression of mutually exclusive genetic markers. These observations have been classically explained by single-cell multistability as the dynamical basis of differentiation, where robust cell-type proportioning relies on pre-existing cell-to-cell differences. We propose a conceptually different dynamical mechanism in which cell types emerge and are maintained collectively by cell-cell communication as a novel inhomogeneous state of the coupled system. Differentiation can be triggered by cell number increase as the population grows in size, through organisation of the initial homogeneous population before the symmetry-breaking bifurcation point. Robust proportioning and reliable recovery of the differentiated cell types following a perturbation is an inherent feature of the inhomogeneous state that is collectively maintained. This dynamical mechanism is valid for systems with steady-state or oscillatory single-cell dynamics. Therefore, our results suggest that timing and subsequent differentiation in robust cell-type proportions can emerge from the cooperative behaviour of growing cell populations during development.

Master regulators as order parameters of gene expression states

Cell type-specific gene expression patterns are represented as memory states of a Hopfield neural network model. It is shown that order parameters of this model can be interpreted as concentrations of master transcription regulators that form concurrent positive feedback loops with a large number of downstream regulated genes. The order parameter free energy then defines an epigenetic landscape in which local minima correspond to stable cell states. The model is applied to gene expression data in the context of hematopoiesis.

Bifurcation and sensitivity analysis reveal key drivers of multistability in a model of macrophage polarization

In this paper, we present and analyze a mathematical model for polarization of a single macrophage which, despite its simplicity, exhibits complex dynamics in terms of multistability. In particular, we demonstrate that an asymmetry in the regulatory mechanisms and parameter values is important for observing multiple phenotypes. Bifurcation and sensitivity analyses show that external signaling cues are necessary for macrophage commitment and emergence to a phenotype, but that the intrinsic macrophage pathways are equally important. Based on our numerical results, we formulate hypotheses that could be further investigated by laboratory experiments to deepen our understanding of macrophage polarization.

A computational model of stem cell molecular mechanism to maintain tissue homeostasis

Stem cells, with their capacity to self-renew and to differentiate to more specialized cell types, play a key role to maintain homeostasis in adult tissues. To investigate how, in the dynamic stochastic environment of a tissue, non-genetic diversity and the precise balance between proliferation and differentiation are achieved, it is necessary to understand the molecular mechanisms of the stem cells in decision making process. By focusing on the impact of stochasticity, we proposed a computational model describing the regulatory circuitry as a tri-stable dynamical system to reveal the mechanism which orchestrate this balance. Our model explains how the distribution of noise in genes, linked to the cell regulatory networks, affects cell decision-making to maintain homeostatic state. The noise effect on tissue homeostasis is achieved by regulating the probability of differentiation and self-renewal through symmetric and/or asymmetric cell divisions. Our model reveals, when mutations due to the replication of DNA in stem cell division, are inevitable, how mutations contribute to either aging gradually or the development of cancer in a short period of time. Furthermore, our model sheds some light on the impact of more complex regulatory networks on the system robustness against perturbations.

Intracellular Energy Variability Modulates Cellular Decision-Making Capacity

Cells generate phenotypic diversity both during development and in response to stressful and changing environments, aiding survival. Functionally vital cell fate decisions from a range of phenotypic choices are made by regulatory networks, the dynamics of which rely on gene expression and hence depend on the cellular energy budget (and particularly ATP levels). However, despite pronounced cell-to-cell ATP differences observed across biological systems, the influence of energy availability on regulatory network dynamics is often overlooked as a cellular decision-making modulator, limiting our knowledge of how energy budgets affect cell behaviour. Here, we consider a mathematical model of a highly generalisable, ATP-dependent, decision-making regulatory network, and show that cell-to-cell ATP variability changes the sets of decisions a cell can make. Our model shows that increasing intracellular energy levels can increase the number of supported stable phenotypes, corresponding to increased decision-making capacity. Model cells with sub-threshold intracellular energy are limited to a singular phenotype, forcing the adoption of a specific cell fate. We suggest that energetic differences between cells may be an important consideration to help explain observed variability in cellular decision-making across biological systems.

Variable cellular decision-making behavior in a constant synthetic network topology

Background

Modules of interacting components arranged in specific network topologies have evolved to perform a diverse array of cellular functions. For a network with a constant topological structure, its function within a cell may still be tuned by changing the number of instances of a particular component (e.g., gene copy number) or by modulating the intrinsic biochemical properties of a component (e.g., binding strength or catalytic efficiency). How such perturbations affect cellular response dynamics remains poorly understood. Here, we explored these effects in a common decision-making motif, cross-antagonism with autoregulation, by synthetically constructing this network in yeast.

Results

We employed the engineering design strategy of reuse to build this topology with a single protein building block, TetR, creating necessary components through TetR mutations and fusion partners. We then studied the impact of several topology-preserving perturbations – strength of cross-antagonism, number of operator sites in a promoter, and gene dosage – on decision-making behavior. We found that reducing TetR repression strength, which hinders cross-antagonism, resulted in a loss of mutually exclusive cell responses. Unexpectedly, increasing the number of operator sites also impeded decision-making exclusivity, which may be a consequence of the averaging effect that arises when multiple transcriptional activators and repressors are accommodated at a given locus. Stochastic simulations of this topology revealed that, even for networks with high TetR repression strength and a low number of operator sites, increasing gene dosage can reduce exclusivity in response dynamics. We further demonstrated this result experimentally by quantifying gene copy numbers in selected yeast clones with differing phenotypic responses.

Conclusions

Our study illustrates how parameters that do not change the topological structure of a decision-making network can nonetheless exert significant influence on its response dynamics. These findings should further inform the study of native motifs, including the effects of topology-preserving mutations, and the robust engineering of synthetic networks.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2866-6) contains supplementary material, which is available to authorized users.

Limit-cycle oscillatory coexpression of cross-inhibitory transcription factors: a model mechanism for lineage promiscuity

Lineage switches are genetic regulatory motifs that govern and maintain the commitment of a developing cell to a particular cell fate. A canonical example of a lineage switch is the pair of transcription factors PU.1 and GATA-1, of which the former is affiliated with the myeloid and the latter with the erythroid lineage within the haematopoietic system. On a molecular level, PU.1 and GATA-1 positively regulate themselves and antagonize each other via direct protein-protein interactions. Here we use mathematical modelling to identify a novel type of dynamic behaviour that can be supported by such a regulatory architecture. Guided by the specifics of the PU.1-GATA-1 interaction, we formulate, using the law of mass action, a system of differential equations for the key molecular concentrations. After a series of systematic approximations, the system is reduced to a simpler one, which is tractable to phase-plane and linearization methods. The reduced system formally resembles, and generalizes, a well-known model for competitive species from mathematical ecology. However, in addition to the qualitative regimes exhibited by a pair of competitive species (exclusivity, bistable exclusivity, stable-node coexpression) it also allows for oscillatory limit-cycle coexpression. A key outcome of the model is that, in the context of cell-fate choice, such oscillations could be harnessed by a differentiating cell to prime alternately for opposite outcomes; a bifurcation-theory approach is adopted to characterize this possibility.

CD4+ T Cell Fate Decisions Are Stochastic, Precede Cell Division, Depend on GITR Co-Stimulation, and Are Associated With Uropodium Development

During an immune response, naïve CD4⁺ T cells proliferate and generate a range of effector, memory, and regulatory T cell subsets, but how these processes are co-ordinated remains unclear. A traditional model suggests that memory cells use mitochondrial respiration and are survivors from a pool of previously proliferating and glycolytic, but short-lived effector cells. A more recent model proposes a binary commitment to either a memory or effector cell lineage during a first, asymmetric cell division, with each lineage able to undergo subsequent proliferation and differentiation. We used improved fixation and staining methods with imaging flow cytometry in an optimized in vitro system that indicates a third model. We found that cell fates result from stochastic decisions that depend on GITR co-stimulation and which take place before any cell division. Effector cell commitment is associated with mTORC2 signaling leading to uropodium development, while developing memory cells lose mitochondria, have a nuclear localization of NFκB and depend on TGFβ for their survival. Induced, T helper subsets and foxp3⁺ regulatory T cells were found in both the effector and memory cell lineages. This in vitro model of T cell differentiation is well suited to testing how manipulation of cytokine, nutrient, and other components of the microenvironment might be exploited for therapeutic purposes.

Inhibitors Alter the Stochasticity of Regulatory Proteins to Force Cells to Switch to the Other State in the Bistable System

The cellular behaviors under the control of genetic circuits are subject to stochastic fluctuations, or noise. The stochasticity in gene regulation, far from a nuisance, has been gradually appreciated for its unusual function in cellular activities. In this work, with Chemical Master Equation (CME), we discovered that the addition of inhibitors altered the stochasticity of regulatory proteins. For a bistable system of a mutually inhibitory network, such a change of noise led to the migration of cells in the bimodal distribution. We proposed that the consumption of regulatory protein caused by the addition of inhibitor is not the only reason for pushing cells to the specific state; the change of the intracellular stochasticity is also the main cause for the redistribution. For the level of the inhibitor capable of driving 99% of cells, if there is no consumption of regulatory protein, 88% of cells were guided to the specific state. It implied that cells were pushed, by the inhibitor, to the specific state due to the change of stochasticity.

Nanog Fluctuations in Embryonic Stem Cells Highlight the Problem of Measurement in Cell Biology

A number of important pluripotency regulators, including the transcription factor Nanog, are observed to fluctuate stochastically in individual embryonic stem cells. By transiently priming cells for commitment to different lineages, these fluctuations are thought to be important to the maintenance of, and exit from, pluripotency. However, because temporal changes in intracellular protein abundances cannot be measured directly in live cells, fluctuations are typically assessed using genetically engineered reporter cell lines that produce a fluorescent signal as a proxy for protein expression. Here, using a combination of mathematical modeling and experiment, we show that there are unforeseen ways in which widely used reporter strategies can systematically disturb the dynamics they are intended to monitor, sometimes giving profoundly misleading results. In the case of Nanog, we show how genetic reporters can compromise the behavior of important pluripotency-sustaining positive feedback loops, and induce a bifurcation in the underlying dynamics that gives rise to heterogeneous Nanog expression patterns in reporter cell lines that are not representative of the wild-type. These findings help explain the range of published observations of Nanog variability and highlight the problem of measurement in live cells.

Operating principles of tristable circuits regulating cellular differentiation

Many cell-fate decisions during embryonic development are governed by a motif comprised of two transcription factors (TFs) A and B that mutually inhibit each other and may self-activate. This motif, called as a self-activating toggle switch (SATS), can typically have three stable states (phenotypes)-two corresponding to differentiated cell fates, each of which has a much higher level of one TF than the other-[Formula: see text] or [Formula: see text]-and the third state corresponding to an 'undecided' stem-like state with similar levels of both A and B-[Formula: see text]. Furthermore, two or more SATSes can be coupled together in various topologies in different contexts, thereby affecting the coordination between multiple cellular decisions. However, two questions remain largely unanswered: (a) what governs the co-existence and relative stability of these three stable states? (b) What orchestrates the decision-making of coupled SATSes? Here, we first demonstrate that the co-existence and relative stability of the three stable states in an individual SATS can be governed by the relative strength of self-activation, external signals activating and/or inhibiting A and B, and mutual degradation between A and B. Simultaneously, we investigate the effects of these factors on the decision-making of two coupled SATSes. Our results offer novel understanding into the operating principles of individual and coupled tristable self-activating toggle switches (SATSes) regulating cellular differentiation and can yield insights into synthesizing three-way genetic circuits and understanding of cellular reprogramming.

Driving Cells to the Desired State in a Bimodal Distribution through Manipulation of Internal Noise with Biologically Practicable Approaches

The stochastic nature of gene regulatory networks described by Chemical Master Equation (CME) leads to the distribution of proteins. A deterministic bistability is usually reflected as a bimodal distribution in stochastic simulations. Within a certain range of the parameter space, a bistable system exhibits two stable steady states, one at the low end and the other at the high end. Consequently, it appears to have a bimodal distribution with one sub-population (mode) around the low end and the other around the high end. In most cases, only one mode is favorable, and guiding cells to the desired state is valuable. Traditionally, the population was redistributed simply by adjusting the concentration of the inducer or the stimulator. However, this method has limitations; for example, the addition of stimulator cannot drive cells to the desired state in a common bistable system studied in this work. In fact, it pushes cells only to the undesired state. In addition, it causes a position shift of the modes, and this shift could be as large as the value of the mode itself. Such a side effect might damage coordination, and this problem can be avoided by applying a new method presented in this work. We illustrated how to manipulate the intensity of internal noise by using biologically practicable methods and utilized it to prompt the population to the desired mode. As we kept the deterministic behavior untouched, the aforementioned drawback was overcome. Remarkably, more than 96% of cells has been driven to the desired state. This method is genetically applicable to biological systems exhibiting a bimodal distribution resulting from bistability. Moreover, the reaction network studied in this work can easily be extended and applied to many other systems.

BTR: training asynchronous Boolean models using single-cell expression data

Background

Rapid technological innovation for the generation of single-cell genomics data presents new challenges and opportunities for bioinformatics analysis. One such area lies in the development of new ways to train gene regulatory networks. The use of single-cell expression profiling technique allows the profiling of the expression states of hundreds of cells, but these expression states are typically noisier due to the presence of technical artefacts such as drop-outs. While many algorithms exist to infer a gene regulatory network, very few of them are able to harness the extra expression states present in single-cell expression data without getting adversely affected by the substantial technical noise present.

Results

Here we introduce BTR, an algorithm for training asynchronous Boolean models with single-cell expression data using a novel Boolean state space scoring function. BTR is capable of refining existing Boolean models and reconstructing new Boolean models by improving the match between model prediction and expression data. We demonstrate that the Boolean scoring function performed favourably against the BIC scoring function for Bayesian networks. In addition, we show that BTR outperforms many other network inference algorithms in both bulk and single-cell synthetic expression data. Lastly, we introduce two case studies, in which we use BTR to improve published Boolean models in order to generate potentially new biological insights.

Conclusions

BTR provides a novel way to refine or reconstruct Boolean models using single-cell expression data. Boolean model is particularly useful for network reconstruction using single-cell data because it is more robust to the effect of drop-outs. In addition, BTR does not assume any relationship in the expression states among cells, it is useful for reconstructing a gene regulatory network with as few assumptions as possible. Given the simplicity of Boolean models and the rapid adoption of single-cell genomics by biologists, BTR has the potential to make an impact across many fields of biomedical research.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1235-y) contains supplementary material, which is available to authorized users.

Coupling the modules of EMT and stemness: A tunable 'stemness window' model

Metastasis of carcinoma involves migration of tumor cells to distant organs and initiate secondary tumors. Migration requires a complete or partial Epithelial-to-Mesenchymal Transition (EMT), and tumor-initiation requires cells possessing stemness. Epithelial cells (E) undergoing a complete EMT to become mesenchymal (M) have been suggested to be more likely to possess stemness. However, recent studies suggest that stemness can also be associated with cells undergoing a partial EMT (hybrid E/M phenotype). Therefore, the correlation between EMT and stemness remains elusive. Here, using a theoretical framework that couples the core EMT and stemness modules (miR-200/ZEB and LIN28/let-7), we demonstrate that the positioning of ‘stemness window’ on the ‘EMT axis’ need not be universal; rather it can be fine-tuned. Particularly, we present OVOL as an example of a modulating factor that, due to its coupling with miR-200/ZEB/LIN28/let-7 circuit, fine-tunes the EMT-stemness interplay. Coupling OVOL can inhibit the stemness likelihood of M and elevate that of the hybrid E/M (partial EMT) phenotype, thereby pulling the ‘stemness window’ away from the M end of ‘EMT axis’. Our results unify various apparently contradictory experimental findings regarding the interconnection between EMT and stemness, corroborate the emerging notion that partial EMT associates with stemness, and offer new testable predictions.

Towards elucidating the connection between epithelial-mesenchymal transitions and stemness

Epithelial cells undergoing epithelial-to-mesenchymal transitions have often been shown to behave as cancer stem cells, but the precise molecular connection remains elusive. At the genetic level, stemness is governed by LIN28/let-7 double inhibition switch, whereas EMT/MET is controlled by miR-200/ZEB double inhibition circuit and LIN28 is inhibited by miR-200, coupling the two modules. Here, using a specially devised theoretical framework to investigate the dynamics of the LIN28/let-7 system, we show that it can operate as a three-way switch (between low, high and intermediate LIN28 levels termed the D, U and hybrid D/U states) similar to the three-way operation of the miR-200/ZEB circuit that allows for the existence of a hybrid epithelial/mesenchymal (E/M) phenotype. We find significant correspondence between the existence of the three states of the two circuits: E-D, M-U and E/M-D/U. Incorporating the activation of OCT4 by LIN28, we find that the hybrid E/M phenotype has high likelihood (when compared with either the E or M states) to gain stemness. Combining the LIN28/let-7 regulation by NF-κB and c-MYC, we find that NF-κB, but not c-MYC, elevates the likelihood of E/M phenotype to gain stemness. Our results are consistent with emerging concept that partial EMT can lead to stemness.

Pluripotency, Differentiation, and Reprogramming: A Gene Expression Dynamics Model with Epigenetic Feedback Regulation

Embryonic stem cells exhibit pluripotency: they can differentiate into all types of somatic cells. Pluripotent genes such as Oct4 and Nanog are activated in the pluripotent state, and their expression decreases during cell differentiation. Inversely, expression of differentiation genes such as Gata6 and Gata4 is promoted during differentiation. The gene regulatory network controlling the expression of these genes has been described, and slower-scale epigenetic modifications have been uncovered. Although the differentiation of pluripotent stem cells is normally irreversible, reprogramming of cells can be experimentally manipulated to regain pluripotency via overexpression of certain genes. Despite these experimental advances, the dynamics and mechanisms of differentiation and reprogramming are not yet fully understood. Based on recent experimental findings, we constructed a simple gene regulatory network including pluripotent and differentiation genes, and we demonstrated the existence of pluripotent and differentiated states from the resultant dynamical-systems model. Two differentiation mechanisms, interaction-induced switching from an expression oscillatory state and noise-assisted transition between bistable stationary states, were tested in the model. The former was found to be relevant to the differentiation process. We also introduced variables representing epigenetic modifications, which controlled the threshold for gene expression. By assuming positive feedback between expression levels and the epigenetic variables, we observed differentiation in expression dynamics. Additionally, with numerical reprogramming experiments for differentiated cells, we showed that pluripotency was recovered in cells by imposing overexpression of two pluripotent genes and external factors to control expression of differentiation genes. Interestingly, these factors were consistent with the four Yamanaka factors, Oct4, Sox2, Klf4, and Myc, which were necessary for the establishment of induced pluripotent stem cells. These results, based on a gene regulatory network and expression dynamics, contribute to our wider understanding of pluripotency, differentiation, and reprogramming of cells, and they provide a fresh viewpoint on robustness and control during development.

Characterization of pluripotent states, in which cells can both self-renew and differentiate, and the irreversible loss of pluripotency are important research areas in developmental biology. In particular, an understanding of these processes is essential to the reprogramming of cells for biomedical applications, i.e., the experimental recovery of pluripotency in differentiated cells. Based on recent advances in dynamical-systems theory for gene expression, we propose a gene-regulatory-network model consisting of several pluripotent and differentiation genes. Our results show that cellular-state transition to differentiated cell types occurs as the number of cells increases, beginning with the pluripotent state and oscillatory expression of pluripotent genes. Cell-cell signaling mediates the differentiation process with robustness to noise, while epigenetic modifications affecting gene expression dynamics fix the cellular state. These modifications ensure the cellular state to be protected against external perturbation, but they also work as an epigenetic barrier to recovery of pluripotency. We show that overexpression of several genes leads to the reprogramming of cells, consistent with the methods for establishing induced pluripotent stem cells. Our model, which involves the inter-relationship between gene expression dynamics and epigenetic modifications, improves our basic understanding of cell differentiation and reprogramming.

Implications of the Hybrid Epithelial/Mesenchymal Phenotype in Metastasis

Transitions between epithelial and mesenchymal phenotypes – the epithelial to ­mesenchymal transition (EMT) and its reverse the mesenchymal to epithelial transition (MET) – are hallmarks of cancer metastasis. While transitioning between the epithelial and mesenchymal phenotypes, cells can also attain a hybrid epithelial/mesenchymal (E/M) (i.e., partial or intermediate EMT) phenotype. Cells in this phenotype have mixed epithelial (e.g., adhesion) and mesenchymal (e.g., migration) properties, thereby allowing them to move collectively as clusters. If these clusters reach the bloodstream intact, they can give rise to clusters of circulating tumor cells (CTCs), as have often been seen experimentally. Here, we review the operating principles of the core regulatory network for EMT/MET that acts as a “three-way” switch giving rise to three distinct phenotypes – E, M and hybrid E/M – and present a theoretical framework that can elucidate the role of many other players in regulating epithelial plasticity. Furthermore, we highlight recent studies on partial EMT and its association with drug resistance and tumor-initiating potential; and discuss how cell–cell communication between cells in a partial EMT phenotype can enable the formation of clusters of CTCs. These clusters can be more apoptosis-resistant and have more tumor-initiating potential than singly moving CTCs with a wholly mesenchymal (complete EMT) phenotype. Also, more such clusters can be formed under inflammatory conditions that are often generated by various therapies. Finally, we discuss the multiple advantages that the partial EMT or hybrid E/M phenotype have as compared to a complete EMT phenotype and argue that these collectively migrating cells are the primary “bad actors” of metastasis.

Increased robustness of early embryogenesis through collective decision-making by key transcription factors

Background

Understanding the mechanisms by which hundreds of diverse cell types develop from a single mammalian zygote has been a central challenge of developmental biology. Conrad H. Waddington, in his metaphoric “epigenetic landscape” visualized the early embryogenesis as a hierarchy of lineage bifurcations. In each bifurcation, a single progenitor cell type produces two different cell lineages. The tristable dynamical systems are used to model the lineage bifurcations. It is also shown that a genetic circuit consisting of two auto-activating transcription factors (TFs) with cross inhibitions can form a tristable dynamical system.

Results

We used gene expression profiles of pre-implantation mouse embryos at the single cell resolution to visualize the Waddington landscape of the early embryogenesis. For each lineage bifurcation we identified two clusters of TFs – rather than two single TFs as previously proposed – that had opposite expression patterns between the pair of bifurcated cell types. The regulatory circuitry among each pair of TF clusters resembled a genetic circuit of a pair of single TFs; it consisted of positive feedbacks among the TFs of the same cluster, and negative interactions among the members of the opposite clusters. Our analyses indicated that the tristable dynamical system of the two-cluster regulatory circuitry is more robust than the genetic circuit of two single TFs.

Conclusions

We propose that a modular hierarchy of regulatory circuits, each consisting of two mutually inhibiting and auto-activating TF clusters, can form hierarchical lineage bifurcations with improved safeguarding of critical early embryogenesis against biological perturbations. Furthermore, our computationally fast framework for modeling and visualizing the epigenetic landscape can be used to obtain insights from experimental data of development at the single cell resolution.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0169-8) contains supplementary material, which is available to authorized users.

Reshaping the epigenetic landscape during early flower development: induction of attractor transitions by relative differences in gene decay rates

BACKGROUND

Gene regulatory network (GRN) dynamical models are standard systems biology tools for the mechanistic understanding of developmental processes and are enabling the formalization of the epigenetic landscape (EL) model.

METHODS

In this work we propose a modeling framework which integrates standard mathematical analyses to extend the simple GRN Boolean model in order to address questions regarding the impact of gene specific perturbations in cell-fate decisions during development.

RESULTS

We systematically tested the propensity of individual genes to produce qualitative changes to the EL induced by modification of gene characteristic decay rates reflecting the temporal dynamics of differentiation stimuli. By applying this approach to the flower specification GRN (FOS-GRN) we uncovered differences in the functional (dynamical) role of their genes. The observed dynamical behavior correlates with biological observables. We found a relationship between the propensity of undergoing attractor transitions between attraction basins in the EL and the direction of differentiation during early flower development - being less likely to induce up-stream attractor transitions as the course of development progresses. Our model also uncovered a potential mechanism at play during the transition from EL basins defining inflorescence meristem to those associated to flower organs meristem. Additionally, our analysis provided a mechanistic interpretation of the homeotic property of the ABC genes, being more likely to produce both an induced inter-attractor transition and to specify a novel attractor. Finally, we found that there is a close relationship between a gene's topological features and its propensity to produce attractor transitions.

CONCLUSIONS

The study of how the state-space associated with a dynamical model of a GRN can be restructured by modulation of genes' characteristic expression times is an important aid for understanding underlying mechanisms occurring during development. Our contribution offers a simple framework to approach such problem, as exemplified here by the case of flower development. Different GRN models and the effect of diverse inductive signals can be explored within the same framework. We speculate that the dynamical role of specific genes within a GRN, as uncovered here, might give information about which genes are more likely to link a module to other regulatory circuits and signaling transduction pathways.

The AhR agonist VAF347 augments retinoic acid-induced differentiation in leukemia cells

In binary cell-fate decisions, driving one lineage and suppressing the other are conjoined. We have previously reported that aryl hydrocarbon receptor (AhR) promotes retinoic acid (RA)-induced granulocytic differentiation of lineage bipotent HL-60 myeloblastic leukemia cells. VAF347, an AhR agonist, impairs the development of CD14(+)CD11b(+) monocytes from granulo-monocytic (GM) stage precursors. We thus hypothesized that VAF347 propels RA-induced granulocytic differentiation and impairs D3-induced monocytic differentiation of HL-60 cells. Our results show that VAF347 enhanced RA-induced cell cycle arrest, CD11b integrin expression and neutrophil respiratory burst. Granulocytic differentiation is known to be driven by MAPK signaling events regulated by Fgr and Lyn Src-family kinases, the CD38 cell membrane receptor, the Vav1 GEF, the c-Cbl adaptor, as well as AhR, all of which are embodied in a putative signalsome. We found that the VAF347 AhR ligand regulates the signalsome. VAF347 augments RA-induced expression of AhR, Lyn, Vav1, and c-Cbl as well as p47(phox). Several interactions of partners in the signalsome appear to be enhanced: Fgr interaction with c-Cbl, CD38, and with pS259c-Raf and AhR interaction with c-Cbl and Lyn. Thus, we report that, while VAF347 impedes monocytic differentiation induced by 1,25-dihydroxyvitamin D3, VAF347 promotes RA-induced differentiation. This effect seems to involve but not to be limited to Lyn, Vav1, c-Cbl, AhR, and Fgr.

Toward decoding the principles of cancer metastasis circuits

Understanding epithelial-mesenchymal transitions (EMT) during cancer metastasis remains a major challenge in modern biology. Recent observations of cell behavior together with progress in mapping the underlying regulatory genetic networks led to new understandings of carcinoma metastasis. It is now established that the genetic network that regulates the EMT also enables an epithelial-mesenchymal hybrid phenotype. These hybrid cells possess mixed carcinoma epithelial and mesenchymal characteristics that enable specialized capabilities such as collective cell migration. On the gene network perspective, a four-component decision unit composed of two highly interconnected chimeric modules--the miR34/SNAIL and the miR200/ZEB mutual-inhibition feedback circuits--regulates the coexistence of and transitions between the different phenotypes. Here, we present a new tractable theoretical framework to model and decode the underlying principles governing the operation of the regulatory unit. Our approach connects the knowledge about intracellular pathways with observations of cellular behavior and advances toward understanding the logic of cancer decision-making. We found that the miR34/SNAIL module acts as an integrator while the miR200/ZEB module acts as a three-way switch. Consequently, the combined unit can give rise to three phenotypes (stable states): (i) a high miR200 and low ZEB, or (1, 0) state; (ii) a low miR200 and high ZEB, or (0, 1) state; and (iii) a medium miR200 and medium ZEB, or (½, ½) state. We associate these states with the epithelial, mesenchymal, and hybrid phenotypes, respectively. We reflect on the consistency between our theoretical predictions and recent observations in several types of carcinomas and suggest new testable predictions. See all articles in this Cancer Research section,

Boolean network model for GPR142 against Type 2 diabetes and relative dynamic change ratio analysis using systems and biological circuits approach

Systems biology addresses challenges in the analysis of genomics data, especially for complex genes and protein interactions using Meta data approach on various signaling pathways. In this paper, we report systems biology and biological circuits approach to construct pathway and identify early gene and protein interactions for predicting GPR142 responses in Type 2 diabetes. The information regarding genes, proteins and other molecules involved in Type 2 diabetes were retrieved from literature and kinetic simulation of GPR142 was carried out in order to determine the dynamic interactions. The major objective of this work was to design a GPR142 biochemical pathway using both systems biology as well as biological circuits synthetically. The term 'synthetically' refers to building biological circuits for cell signaling pathway especially for hormonal pathway disease. The focus of the paper is on logical components and logical circuits whereby using these applications users can create complex virtual circuits. Logic gates process represents only true or false and investigates whether biological regulatory circuits are active or inactive. The basic gates used are AND, NAND, OR, XOR and NOT gates and Integrated circuit composition of many such basic gates and some derived gates. Biological circuits may have a futuristic application in biomedical sciences which may involve placing a micro chip in human cells to modulate the down or up regulation of hormonal disease.

Bifurcation dynamics and determination of alternate cell fates in bipotent progenitor cells

The gene regulatory networks in which two lineage-affiliated transcription factors, such as GATA1 and PU.1, inhibit each other but activate themselves so as to regulate the choice between alternative cell fates have been extensively studied. These simple networks can generate bistability and explain the transitions between the alternative cell fates. The commitment of a progenitor cell to a new fate corresponds to the occurrence of different types of bifurcations, depending on if a system is symmetrical and how perturbations affect the system. Here we take a general modeling and analyzing approach and show that the lateral inhibition with symmetry and asymmetry can lead to different bifurcation dynamics. Especially, if cell fate decision-making is initiated with asymmetry or symmetry-breaking perturbations, a progenitor cell pre-patterns itself into a polarized cell, depending on the asymmetry or symmetry-breaking perturbations. This study may help us understand the fundamental features of binary cell fate decisions more clearly and further apply to a wider range of decision-making processes.

Single-cell transcriptional analysis to uncover regulatory circuits driving cell fate decisions in early mouse development

MOTIVATION

Transcriptional regulatory networks controlling cell fate decisions in mammalian embryonic development remain elusive despite a long time of research. The recent emergence of single-cell RNA profiling technology raises hope for new discovery. Although experimental works have obtained intriguing insights into the mouse early development, a holistic and systematic view is still missing. Mathematical models of cell fates tend to be concept-based, not designed to learn from real data. To elucidate the regulatory mechanisms behind cell fate decisions, it is highly desirable to synthesize the data-driven and knowledge-driven modeling approaches.

RESULTS

We propose a novel method that integrates the structure of a cell lineage tree with transcriptional patterns from single-cell data. This method adopts probabilistic Boolean network (PBN) for network modeling, and genetic algorithm as search strategy. Guided by the 'directionality' of cell development along branches of the cell lineage tree, our method is able to accurately infer the regulatory circuits from single-cell gene expression data, in a holistic way. Applied on the single-cell transcriptional data of mouse preimplantation development, our algorithm outperforms conventional methods of network inference. Given the network topology, our method can also identify the operational interactions in the gene regulatory network (GRN), corresponding to specific cell fate determination. This is one of the first attempts to infer GRNs from single-cell transcriptional data, incorporating dynamics of cell development along a cell lineage tree.

AVAILABILITY AND IMPLEMENTATION

Implementation of our algorithm is available from the authors upon request.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A bistable genetic switch based on designable DNA-binding domains

Bistable switches are fundamental regulatory elements of complex systems, ranging from electronics to living cells. Designed genetic toggle switches have been constructed from pairs of natural transcriptional repressors wired to inhibit one another. The complexity of the engineered regulatory circuits can be increased using orthogonal transcriptional regulators based on designed DNA-binding domains. However, a mutual repressor-based toggle switch comprising DNA-binding domains of transcription-activator-like effectors (TALEs) did not support bistability in mammalian cells. Here, the challenge of engineering a bistable switch based on monomeric DNA-binding domains is solved via the introduction of a positive feedback loop composed of activators based on the same TALE domains as their opposing repressors and competition for the same DNA operator site. This design introduces nonlinearity and results in epigenetic bistability. This principle could be used to employ other monomeric DNA-binding domains such as CRISPR for applications ranging from reprogramming cells to building digital biological memory.

The three-way switch operation of Rac1/RhoA GTPase-based circuit controlling amoeboid-hybrid-mesenchymal transition

Metastatic carcinoma cells exhibit at least two different phenotypes of motility and invasion - amoeboid and mesenchymal. This plasticity poses a major clinical challenge for treating metastasis, while its underlying mechanisms remain enigmatic. Transitions between these phenotypes are mediated by the Rac1/RhoA circuit that responds to external signals such as HGF/SF via c-MET pathway. Using detailed modeling of GTPase-based regulation to study the Rac1/RhoA circuit's dynamics, we found that it can operate as a three-way switch. We propose to associate the circuit's three possible states to the amoeboid, mesenchymal and amoeboid/mesenchymal hybrid phenotype. In particular, we investigated the range of existence of, and the transition between, the three states (phenotypes) in response to Grb2 and Gab1 - two downstream adaptors of c-MET. The results help to explain the regulation of metastatic cells by c-MET pathway and hence can contribute to the assessment of possible clinical interventions.

Classification of transient behaviours in a time-dependent toggle switch model

BACKGROUND

Waddington's epigenetic landscape is an intuitive metaphor for the developmental and evolutionary potential of biological regulatory processes. It emphasises time-dependence and transient behaviour. Nowadays, we can derive this landscape by modelling a specific regulatory network as a dynamical system and calculating its so-called potential surface. In this sense, potential surfaces are the mathematical equivalent of the Waddingtonian landscape metaphor. In order to fully capture the time-dependent (non-autonomous) transient behaviour of biological processes, we must be able to characterise potential landscapes and how they change over time. However, currently available mathematical tools focus on the asymptotic (steady-state) behaviour of autonomous dynamical systems, which restricts how biological systems are studied.

RESULTS

We present a pragmatic first step towards a methodology for dealing with transient behaviours in non-autonomous systems. We propose a classification scheme for different kinds of such dynamics based on the simulation of a simple genetic toggle-switch model with time-variable parameters. For this low-dimensional system, we can calculate and explicitly visualise numerical approximations to the potential landscape. Focussing on transient dynamics in non-autonomous systems reveals a range of interesting and biologically relevant behaviours that would be missed in steady-state analyses of autonomous systems. Our simulation-based approach allows us to identify four qualitatively different kinds of dynamics: transitions, pursuits, and two kinds of captures. We describe these in detail, and illustrate the usefulness of our classification scheme by providing a number of examples that demonstrate how it can be employed to gain specific mechanistic insights into the dynamics of gene regulation.

CONCLUSIONS

The practical aim of our proposed classification scheme is to make the analysis of explicitly time-dependent transient behaviour tractable, and to encourage the wider use of non-autonomous models in systems biology. Our method is applicable to a large class of biological processes.

Mathematical modeling of GATA-switching for regulating the differentiation of hematopoietic stem cell

Background

Hematopoiesis is a highly orchestrated developmental process that comprises various developmental stages of the hematopoietic stem cells (HSCs). During development, the decision to leave the self-renewing state and selection of a differentiation pathway is regulated by a number of transcription factors. Among them, genes GATA-1 and PU.1 form a core negative feedback module to regulate the genetic switching between the cell fate choices of HSCs. Although extensive experimental studies have revealed the mechanisms to regulate the expression of these two genes, it is still unclear how this simple module regulates the genetic switching.

Methods

In this work we proposed a mathematical model to study the mechanisms of the GATA-PU.1 gene network in the determination of HSC differentiation pathways. We incorporated the mechanisms of GATA switch into the module, and developed a mathematical model that comprises three genes GATA-1, GATA-2 and PU.1. In addition, a novel multiple-objective optimization method was designed to infer unknown parameters in the proposed model by realizing different experimental observations. A stochastic model was also designed to describe the critical function of noise, due to the small copy numbers of molecular species, in determining the differentiation pathways.

Results

The proposed deterministic model has successfully realized three stable steady states representing the priming and different progenitor cells as well as genetic switching between the genetic states under various experimental conditions. Using different values of GATA-1 synthesis rate for the GATA-1 protein availability in the chromatin sites during the time period of GATA switch, stochastic simulations for the first time have realized different proportions of cells leading to different developmental pathways under various experimental conditions.

Conclusions

Mathematical models provide testable predictions regarding the mechanisms and conditions for realizing different differentiation pathways of hematopoietic stem cells. This work represents the first attempt at using a discrete stochastic model to realize the decision of HSC differentiation pathways showing a multimodal distribution.

MicroRNA-based regulation of epithelial-hybrid-mesenchymal fate determination

Forward and backward transitions between epithelial and mesenchymal phenotypes play crucial roles in embryonic development and tissue repair. Aberrantly regulated transitions are also a hallmark of cancer metastasis. The genetic network that regulates these transitions appears to allow for the existence of a hybrid phenotype (epithelial/mesenchymal). Hybrid cells are endowed with mixed epithelial and mesenchymal characteristics, enabling specialized capabilities such as collective cell migration. Cell-fate determination between the three phenotypes is in fact regulated by a circuit composed of two highly interconnected chimeric modules--the miR-34/SNAIL and the miR-200/ZEB mutual-inhibition feedback circuits. Here, we used detailed modeling of microRNA-based regulation to study this core unit. More specifically, we investigated the functions of the two isolated modules and subsequently of the combined unit when the two modules are integrated into the full regulatory circuit. We found that miR-200/ZEB forms a tristable circuit that acts as a ternary switch, driven by miR-34/SNAIL, that is a monostable module that acts as a noise-buffering integrator of internal and external signals. We propose to associate the three stable states--(1,0), (high miR-200)/(low ZEB); (0,1), (low miR-200)/(high ZEB); and (1/2,1/2), (medium miR-200)/(medium ZEB)--with the epithelial, mesenchymal, and hybrid phenotypes, respectively. Our (1/2,1/2) state hypothesis is consistent with recent experimental studies (e.g., ZEB expression measurements in collectively migrating cells) and explains the lack of observed mesenchymal-to-hybrid transitions in metastatic cells and in induced pluripotent stem cells. Testable predictions of dynamic gene expression during complete and partial transitions are presented.

Hybrid T-helper cells: stabilizing the moderate center in a polarized system

Polarization of cell phenotypes, a common strategy to achieve cell type diversity in metazoa, results from binary cell-fate decisions in the branching pedigree of development. Such "either-or" fate decisions are controlled by two opposing cell fate-determining transcription factors. Each of the two distinct "master regulators" promotes differentiation of its respective sister lineage. But they also suppress one other, leading to their mutually exclusive expression in the two ensuing lineages. Thus, promiscuous coexistence of the antagonist regulators in the same cell, the hallmark of the common "undecided" progenitor of two sister lineages, is considered unstable. This antagonism ensures robust polarization into two discretely distinct cell types. But now the immune system's T-helper (Th) cells and their two canonical subtypes, Th1 and Th2 cells, tell a different story, as revealed in three papers recently published in PLOS Biology. The intermediate state that co-expresses the two opposing master regulators of the Th1 and Th2 subtypes, T-bet and Gata3, is highly stable and is not necessarily an undecided precursor. Instead, the Th1/Th2 hybrid cell is a robust new type with properties of both Th1 and Th2 cells. These hybrid cells are functionally active and possess the benefit of moderation: self-limitation of effector T cell function to prevent excessive inflammation, a permanent risk in host defense that can cause tissue damage or autoimmunity. Gene regulatory network analysis suggests that stabilization of the intermediate center in a polarizing system can be achieved by minor tweaking of the architecture of the mutual suppression gene circuit, and thus is a design option readily available to evolution.

Tristability in cancer-associated microRNA-TF chimera toggle switch

Cell fate decisions during embryonic development and tumorigenesis pose a major research challenge in modern developmental and cancer biology. Binary cell fate decisions are usually regulated by gene circuits incorporating either classical toggle switches with two mutually inhibiting transcription factor (TF) genes or chimera toggle switches with a mutually inhibiting pair of microRNA (miRNA) and TF gene. These circuits can explain binary cell fate decisions. Importantly, intermediate cell types can exist during the differentiation of both stem cells and cancer cells. It has been shown that TF-TF self-activating toggle switches (SATS) can have coexistence of three metastable states (tristability), yet the role of chimera toggle switches in opening these additional states remains elusive. Here we present a generalized framework for both the TF-TF SATS and miRNA-TF chimera SATS, starting from the TF-promoter and miRNA-mRNA binding/unbinding dynamics. We show that the chimera SATSs can also have tristability. We demonstrate that the dynamics of miRNA-TF SATS is qualitatively different from that of the TF-TF SATS because the nonlinear effects of translational silencing by miRNA are distinct from those of transcriptional repression. We discuss the possible relevance of these findings to fate decisions by cancer cells.

Transcriptional bursting diversifies the behaviour of a toggle switch: hybrid simulation of stochastic gene expression

Hybrid models for gene expression combine stochastic and deterministic representations of the underlying biophysical mechanisms. According to one of the simplest hybrid formalisms, protein molecules are produced in randomly occurring bursts of a randomly distributed size while they are degraded deterministically. Here, we use this particular formalism to study two key regulatory motifs-the autoregulation loop and the toggle switch. The distribution of burst times is determined and used as a basis for the development of exact simulation algorithms for gene expression dynamics. For the autoregulation loop, the simulations are compared to an analytic solution of a master equation. Simulations of the toggle switch reveal a number of qualitatively distinct scenarios with implications for the modelling of cell-fate selection.

From understanding the development landscape of the canonical fate-switch pair to constructing a dynamic landscape for two-step neural differentiation

Recent progress in stem cell biology, notably cell fate conversion, calls for novel theoretical understanding for cell differentiation. The existing qualitative concept of Waddington’s “epigenetic landscape” has attracted particular attention because it captures subsequent fate decision points, thus manifesting the hierarchical (“tree-like”) nature of cell fate diversification. Here, we generalized a recent work and explored such a developmental landscape for a two-gene fate decision circuit by integrating the underlying probability landscapes with different parameters (corresponding to distinct developmental stages). The change of entropy production rate along the parameter changes indicates which parameter changes can represent a normal developmental process while other parameters’ change can not. The transdifferentiation paths over the landscape under certain conditions reveal the possibility of a direct and reversible phenotypic conversion. As the intensity of noise increases, we found that the landscape becomes flatter and the dominant paths more straight, implying the importance of biological noise processing mechanism in development and reprogramming. We further extended the landscape of the one-step fate decision to that for two-step decisions in central nervous system (CNS) differentiation. A minimal network and dynamic model for CNS differentiation was firstly constructed where two three-gene motifs are coupled. We then implemented the SDEs (Stochastic Differentiation Equations) simulation for the validity of the network and model. By integrating the two landscapes for the two switch gene pairs, we constructed the two-step development landscape for CNS differentiation. Our work provides new insights into cellular differentiation and important clues for better reprogramming strategies.

A transcriptional dynamic network during Arabidopsis thaliana pollen development

Background

To understand transcriptional regulatory networks (TRNs), especially the coordinated dynamic regulation between transcription factors (TFs) and their corresponding target genes during development, computational approaches would represent significant advances in the genome-wide expression analysis. The major challenges for the experiments include monitoring the time-specific TFs' activities and identifying the dynamic regulatory relationships between TFs and their target genes, both of which are currently not yet available at the large scale. However, various methods have been proposed to computationally estimate those activities and regulations. During the past decade, significant progresses have been made towards understanding pollen development at each development stage under the molecular level, yet the regulatory mechanisms that control the dynamic pollen development processes remain largely unknown. Here, we adopt Networks Component Analysis (NCA) to identify TF activities over time couse, and infer their regulatory relationships based on the coexpression of TFs and their target genes during pollen development.

Results

We carried out meta-analysis by integrating several sets of gene expression data related to Arabidopsis thaliana pollen development (stages range from UNM, BCP, TCP, HP to 0.5 hr pollen tube and 4 hr pollen tube). We constructed a regulatory network, including 19 TFs, 101 target genes and 319 regulatory interactions. The computationally estimated TF activities were well correlated to their coordinated genes' expressions during the development process. We clustered the expression of their target genes in the context of regulatory influences, and inferred new regulatory relationships between those TFs and their target genes, such as transcription factor WRKY34, which was identified that specifically expressed in pollen, and regulated several new target genes. Our finding facilitates the interpretation of the expression patterns with more biological relevancy, since the clusters corresponding to the activity of specific TF or the combination of TFs suggest the coordinated regulation of TFs to their target genes.

Conclusions

Through integrating different resources, we constructed a dynamic regulatory network of Arabidopsis thaliana during pollen development with gene coexpression and NCA. The network illustrated the relationships between the TFs' activities and their target genes' expression, as well as the interactions between TFs, which provide new insight into the molecular mechanisms that control the pollen development.