Towards an understanding of lineage specification in hematopoietic stem cells: a mathematical model for the interaction of transcription factors GATA-1 and PU.1

Inferring structural and dynamical properties of gene networks from data with deep learning

The reconstruction of gene regulatory networks (GRNs) from data is vital in systems biology. Although different approaches have been proposed to infer causality from data, some challenges remain, such as how to accurately infer the direction and type of interactions, how to deal with complex network involving multiple feedbacks, as well as how to infer causality between variables from real-world data, especially single cell data. Here, we tackle these problems by deep neural networks (DNNs). The underlying regulatory network for different systems (gene regulations, ecology, diseases, development) can be successfully reconstructed from trained DNN models. We show that DNN is superior to existing approaches including Boolean network, Random Forest and partial cross mapping for network inference. Further, by interrogating the ensemble DNN model trained from single cell data from dynamical system perspective, we are able to unravel complex cell fate dynamics during preimplantation development. We also propose a data-driven approach to quantify the energy landscape for gene regulatory systems, by combining DNN with the partial self-consistent mean field approximation (PSCA) approach. We anticipate the proposed method can be applied to other fields to decipher the underlying dynamical mechanisms of systems from data.

Computational Methods to Identify Cell-Fate Determinants, Identity Transcription Factors, and Niche-Induced Signaling Pathways for Stem Cell Research

The large-scale development of high-throughput sequencing technologies has not only allowed the generation of reliable omics data related to various regulatory layers but also the development of novel computational models in the field of stem cell research. These computational approaches have enabled the disentangling of a complex interplay between these interrelated layers of regulation by interpreting large quantities of biomedical data in a systematic way. In the context of stem cell research, network modeling of complex gene-gene interactions has been successfully used for understanding the mechanisms underlying stem cell differentiation and cellular conversion. Notably, it has proven helpful for predicting cell-fate determinants and signaling molecules controlling such processes. This chapter will provide an overview of various computational approaches that rely on single-cell and/or bulk RNA sequencing data for elucidating the molecular underpinnings of cell subpopulation identities, lineage specification, and the process of cell-fate decisions. Furthermore, we discuss how these computational methods provide the right framework for computational modeling of biological systems in order to address long-standing challenges in the stem cell field by guiding experimental efforts in stem cell research and regenerative medicine.

A single-cell resolved cell-cell communication model explains lineage commitment in hematopoiesis

Cells do not make fate decisions independently. Arguably, every cell-fate decision occurs in response to environmental signals. In many cases, cell-cell communication alters the dynamics of the internal gene regulatory network of a cell to initiate cell-fate transitions, yet models rarely take this into account. Here, we have developed a multiscale perspective to study the granulocyte-monocyte versus megakaryocyte-erythrocyte fate decisions. This transition is dictated by the GATA1-PU.1 network: a classical example of a bistable cell-fate system. We show that, for a wide range of cell communication topologies, even subtle changes in signaling can have pronounced effects on cell-fate decisions. We go on to show how cell-cell coupling through signaling can spontaneously break the symmetry of a homogenous cell population. Noise, both intrinsic and extrinsic, shapes the decision landscape profoundly, and affects the transcriptional dynamics underlying this important hematopoietic cell-fate decision-making system.

This article has an associated ‘The people behind the papers’ interview.

Summary: Through theory and computational modeling, cell-cell communication is revealed to be a crucial and under-appreciated determinant of cell-fate decision-making during hematopoiesis.

Mechanistic models of blood cell fate decisions in the era of single-cell data

Billions of functionally distinct blood cells emerge from a pool of hematopoietic stem cells in our bodies every day. This progressive differentiation process is hierarchically structured and remarkably robust. We provide an introductory review to mathematical approaches addressing the functional aspects of how lineage choice is potentially implemented on a molecular level. Emerging from studies on the mutual repression of key transcription factors, we illustrate how those simple concepts have been challenged in recent years and subsequently extended. Especially, the analysis of omics data on the single-cell level with computational tools provides descriptive insights on a yet unknown level, while their embedding into a consistent mechanistic and mathematical framework is still incomplete.

Monostability and bistability of biological switches

Cell-fate transition can be modeled by ordinary differential equations (ODEs) which describe the behavior of several molecules in interaction, and for which each stable equilibrium corresponds to a possible phenotype (or 'biological trait'). In this paper, we focus on simple ODE systems modeling two molecules which each negatively (or positively) regulate the other. It is well-known that such models may lead to monostability or multistability, depending on the selected parameters. However, extensive numerical simulations have led systems biologists to conjecture that in the vast majority of cases, there cannot be more than two stable points. Our main result is a proof of this conjecture. More specifically, we provide a criterion ensuring at most bistability, which is indeed satisfied by most commonly used functions. This includes Hill functions, but also a wide family of convex and sigmoid functions. We also determine which parameters lead to monostability, and which lead to bistability, by developing a more general framework encompassing all our results.

Reprogramming multistable monotone systems with application to cell fate control

Multistability is a key property of dynamical systems modeling cellular regulatory networks implicated in cell fate decisions, where, different stable steady states usually represent distinct cell phenotypes. Monotone network motifs are highly represented in these regulatory networks. In this paper, we leverage the properties of monotone dynamical systems to provide theoretical results that guide the selection of inputs that trigger a transition, i.e., reprogram the network, to a desired stable steady state. We first show that monotone dynamical systems with bounded trajectories admit a minimum and a maximum stable steady state. Then, we provide input choices that are guaranteed to reprogram the system to these extreme steady states. For intermediate states, we provide an input space that is guaranteed to contain an input that reprograms the system to the desired state. We then provide implementation guidelines for finite-time procedures that search this space for such an input, along with rules to prune parts of the space during search. We demonstrate these results on simulations of two recurrent regulatory network motifs: self-activation within mutual antagonism and self-activation within mutual cooperation. Our results depend uniquely on the structure of the network and are independent of specific parameter values.

Exploring the mechanisms of cell reprogramming and transdifferentiation via intercellular communication

In the past years, the mechanisms of cell reprogramming and transdifferentiation via the way of gene regulation, stochastic fluctuations, or chemical induction to realize cell type transitions from the perspectives of single cells were explored. In multicellular organisms, intercellular communication plays crucial roles in cell fate decisions. However, the importance of intercellular communication to the processes of cell reprogramming and transdifferentiation is often neglected. In this paper, the mechanisms of cell reprogramming and transdifferentiation by intercellular communication are investigated. A two-gene circuit with mutual inhibition and self-activation as a basic model is selected. Then, a coupling mechanism via intercellular communication by introducing a specific signaling molecule into the gene circuit is considered. Finally, the influence of coupling intensity on the dynamics of the coupled system of two cells is analyzed. Moreover, when the coupling intensity changes with respect to the cell number in a discrete way, the effects of coupling intensity on cell reprogramming and transdifferentiation are discussed. Some theoretical analysis of stability and bifurcation of the systems are also given. Our research shows that cells can realize cell reprogramming and transdifferentiation via intercellular interaction at opportune coupling intensity. These results not only further enrich previous studies but also are beneficial to understand the mechanisms of cell reprogramming and transdifferentiation via intercellular communication in the growth and development of multicellular organisms.

A system-level mechanistic explanation for asymmetric stem cell fates: Arabidopsis thaliana root niche as a study system

Asymmetric divisions maintain long-term stem cell populations while producing new cells that proliferate and then differentiate. Recent reports in animal systems show that divisions of stem cells can be uncoupled from their progeny differentiation, and the outcome of a division could be influenced by microenvironmental signals. But the underlying system-level mechanisms, and whether this dynamics also occur in plant stem cell niches (SCN), remain elusive. This article presents a cell fate regulatory network model that contributes to understanding such mechanism and identify critical cues for cell fate transitions in the root SCN. Novel computational and experimental results show that the transcriptional regulator SHR is critical for the most frequent asymmetric division previously described for quiescent centre stem cells. A multi-scale model of the root tip that simulated each cell's intracellular regulatory network, and the dynamics of SHR intercellular transport as a cell-cell coupling mechanism, was developed. It revealed that quiescent centre cell divisions produce two identical cells, that may acquire different fates depending on the feedback between SHR's availability and the state of the regulatory network. Novel experimental data presented here validates our model, which in turn, constitutes the first proposed systemic mechanism for uncoupled SCN cell division and differentiation.

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.

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.

Stochastic multistationarity in a model of the hematopoietic stem cell differentiation network

A central issue in the analysis of multi-stable systems is that of controlling the relative size of the basins of attraction of alternative states through suitable choices of system parameters. We are interested here mainly in the stochastic version of this problem, that of shaping the stationary probability distribution of a Markov chain so that various alternative modes become more likely than others. Although many of our results are more general, we were motivated by an important biological question, that of cell differentiation. In the mathematical modeling of cell differentiation, it is common to think of internal states of cells (quanfitied by activation levels of certain genes) as determining the different cell types. Specifically, we study here the "PU.1/GATA-1 circuit" which is involved in the control of the development of mature blood cells from hematopoietic stem cells (HSCs). All mature, specialized blood cells have been shown to be derived from multipotent HSCs. Our first contribution is to introduce a rigorous chemical reaction network model of the PU.1/GATA-1 circuit, which incorporates current biological knowledge. We then find that the resulting ODE model of these biomolecular reactions is incapable of exhibiting multistability, contradicting the fact that differentiation networks have, by definition, alternative stable steady states. When considering instead the stochastic version of this chemical network, we analytically construct the stationary distribution, and are able to show that this distribution is indeed capable of admitting a multiplicity of modes. Finally, we study how a judicious choice of system parameters serves to bias the probabilities towards different stationary states. We remark that certain changes in system parameters can be physically implemented by a biological feedback mechanism; tuning this feedback gives extra degrees of freedom that allow one to assign higher likelihood to some cell types over others.

Lineage marker synchrony in hematopoietic genealogies refutes the PU.1/GATA1 toggle switch paradigm

Molecular regulation of cell fate decisions underlies health and disease. To identify molecules that are active or regulated during a decision, and not before or after, the decision time point is crucial. However, cell fate markers are usually delayed and the time of decision therefore unknown. Fortunately, dividing cells induce temporal correlations in their progeny, which allow for retrospective inference of the decision time point. We present a computational method to infer decision time points from correlated marker signals in genealogies and apply it to differentiating hematopoietic stem cells. We find that myeloid lineage decisions happen generations before lineage marker onsets. Inferred decision time points are in agreement with data from colony assay experiments. The levels of the myeloid transcription factor PU.1 do not change during, but long after the predicted lineage decision event, indicating  that the PU.1/GATA1 toggle switch paradigm cannot explain the initiation of early myeloid lineage choice.

Exploring intermediate cell states through the lens of single cells

As our catalog of cell states expands, appropriate characterization of these states and the transitions between them is crucial. Here we discuss the roles of intermediate cell states (ICSs) in this growing collection. We begin with definitions and discuss evidence for the existence of ICSs and their relevance in various tissues. We then provide a list of possible functions for ICSs with examples. Finally, we describe means by which ICSs and their functional roles can be identified from single-cell data or predicted from models.

Computational approaches for predicting key transcription factors in targeted cell reprogramming (Review)

There is a need for specific cell types in regenerative medicine and biological research. Frequently, specific cell types may not be easily obtained or the quantity obtained is insufficient for study. Therefore, reprogramming by the direct conversion (transdifferentiation) or re‑induction of induced pluripotent stem cells has been used to obtain cells expressing similar profiles to those of the desired types. Therefore, a specific cocktail of transcription factors (TFs) is required for induction. Nevertheless, identifying the correct combination of TFs is difficult. Although certain computational approaches have been proposed for this task, their methods are complex, and corresponding implementations are difficult to use and generalize for specific source or target cell types. In the present review four computational approaches that have been proposed to obtain likely TFs were compared and discussed. A simplified view of the computational complexity of these methods is provided that consists of three basic ideas: i) The definition of target and non‑target cell types; ii) the estimation of candidate TFs; and iii) filtering candidates. This simplified view was validated by analyzing a well‑documented cardiomyocyte differentiation. Subsequently, these reviewed methods were compared when applied to an unknown differentiation of corneal endothelial cells. The generated results may provide important insights for laboratory assays. Data and computer scripts that may assist with direct conversions in other cell types are also provided.

Kinetic models of hematopoietic differentiation

As cell and molecular biology is becoming increasingly quantitative, there is an upsurge of interest in mechanistic modeling at different levels of resolution. Such models mostly concern kinetics and include gene and protein interactions as well as cell population dynamics. The final goal of these models is to provide experimental predictions, which is now taking on. However, even without matured predictions, kinetic models serve the purpose of compressing a plurality of experimental results into something that can empower the data interpretation, and importantly, suggesting new experiments by turning "knobs" in silico. Once formulated, kinetic models can be executed in terms of molecular rate equations for concentrations or by stochastic simulations when only a limited number of copies are involved. Developmental processes, in particular those of stem and progenitor cell commitments, are not only topical but also particularly suitable for kinetic modeling due to the finite number of key genes involved in cellular decisions. Stem and progenitor cell commitment processes have been subject to intense experimental studies over the last decade with some emphasis on embryonic and hematopoietic stem cells. Gene and protein interactions governing these processes can be modeled by binary Boolean rules or by continuous-valued models with interactions set by binding strengths. Conceptual insights along with tested predictions have emerged from such kinetic models. Here we review kinetic modeling efforts applied to stem cell developmental systems with focus on hematopoiesis. We highlight the future challenges including multi-scale models integrating cell dynamical and transcriptional models. This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Developmental Biology > Stem Cell Biology and Regeneration.

Hematopoiesis and T-cell specification as a model developmental system

The pathway to generate T cells from hematopoietic stem cells guides progenitors through a succession of fate choices while balancing differentiation progression against proliferation, stage to stage. Many elements of the regulatory system that controls this process are known, but the requirement for multiple, functionally distinct transcription factors needs clarification in terms of gene network architecture. Here, we compare the features of the T-cell specification system with the rule sets underlying two other influential types of gene network models: first, the combinatorial, hierarchical regulatory systems that generate the orderly, synchronized increases in complexity in most invertebrate embryos; second, the dueling 'master regulator' systems that are commonly used to explain bistability in microbial systems and in many fate choices in terminal differentiation. The T-cell specification process shares certain features with each of these prevalent models but differs from both of them in central respects. The T-cell system is highly combinatorial but also highly dose-sensitive in its use of crucial regulatory factors. The roles of these factors are not always T-lineage-specific, but they balance and modulate each other's activities long before any mutually exclusive silencing occurs. T-cell specification may provide a new hybrid model for gene networks in vertebrate developmental systems.

A Generalized Gene-Regulatory Network Model of Stem Cell Differentiation for Predicting Lineage Specifiers

Identification of cell-fate determinants for directing stem cell differentiation remains a challenge. Moreover, little is known about how cell-fate determinants are regulated in functionally important subnetworks in large gene-regulatory networks (i.e., GRN motifs). Here we propose a model of stem cell differentiation in which cell-fate determinants work synergistically to determine different cellular identities, and reside in a class of GRN motifs known as feedback loops. Based on this model, we develop a computational method that can systematically predict cell-fate determinants and their GRN motifs. The method was able to recapitulate experimentally validated cell-fate determinants, and validation of two predicted cell-fate determinants confirmed that overexpression of ESR1 and RUNX2 in mouse neural stem cells induces neuronal and astrocyte differentiation, respectively. Thus, the presented GRN-based model of stem cell differentiation and computational method can guide differentiation experiments in stem cell research and regenerative medicine.

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A network-based method for predicting lineage specifiers and key network motifs

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A computational guidance to stem cell differentiation experiments

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Overexpression of ESR1 in mNSCs induces neuronal differentiation

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Overexpression of RUNX2 in mNSCs induces astrocyte differentiation

Bifurcation-based approach reveals synergism and optimal combinatorial perturbation

Cells accomplish the process of fate decisions and form terminal lineages through a series of binary choices in which cells switch stable states from one branch to another as the interacting strengths of regulatory factors continuously vary. Various combinatorial effects may occur because almost all regulatory processes are managed in a combinatorial fashion. Combinatorial regulation is crucial for cell fate decisions because it may effectively integrate many different signaling pathways to meet the higher regulation demand during cell development. However, whether the contribution of combinatorial regulation to the state transition is better than that of a single one and if so, what the optimal combination strategy is, seem to be significant issue from the point of view of both biology and mathematics. Using the approaches of combinatorial perturbations and bifurcation analysis, we provide a general framework for the quantitative analysis of synergism in molecular networks. Different from the known methods, the bifurcation-based approach depends only on stable state responses to stimuli because the state transition induced by combinatorial perturbations occurs between stable states. More importantly, an optimal combinatorial perturbation strategy can be determined by investigating the relationship between the bifurcation curve of a synergistic perturbation pair and the level set of a specific objective function. The approach is applied to two models, i.e., a theoretical multistable decision model and a biologically realistic CREB model, to show its validity, although the approach holds for a general class of biological systems.

Solution of the chemical master equation by radial basis functions approximation with interface tracking

BACKGROUND

The chemical master equation is the fundamental equation of stochastic chemical kinetics. This differential-difference equation describes temporal evolution of the probability density function for states of a chemical system. A state of the system, usually encoded as a vector, represents the number of entities or copy numbers of interacting species, which are changing according to a list of possible reactions. It is often the case, especially when the state vector is high-dimensional, that the number of possible states the system may occupy is too large to be handled computationally. One way to get around this problem is to consider only those states that are associated with probabilities that are greater than a certain threshold level.

RESULTS

We introduce an algorithm that significantly reduces computational resources and is especially powerful when dealing with multi-modal distributions. The algorithm is built according to two key principles. Firstly, when performing time integration, the algorithm keeps track of the subset of states with significant probabilities (essential support). Secondly, the probability distribution that solves the equation is parametrised with a small number of coefficients using collocation on Gaussian radial basis functions. The system of basis functions is chosen in such a way that the solution is approximated only on the essential support instead of the whole state space.

DISCUSSION

In order to demonstrate the effectiveness of the method, we consider four application examples: a) the self-regulating gene model, b) the 2-dimensional bistable toggle switch, c) a generalisation of the bistable switch to a 3-dimensional tristable problem, and d) a 3-dimensional cell differentiation model that, depending on parameter values, may operate in bistable or tristable modes. In all multidimensional examples the manifold containing the system states with significant probabilities undergoes drastic transformations over time. This fact makes the examples especially challenging for numerical methods.

CONCLUSIONS

The proposed method is a new numerical approach permitting to approximately solve a wide range of problems that have been hard to tackle until now. A full representation of multi-dimensional distributions is recovered. The method is especially attractive when dealing with models that yield solutions of a complex structure, for instance, featuring multi-stability.

Computational Modeling of a Transcriptional Switch Underlying B-Lymphocyte Lineage Commitment of Hematopoietic Multipotent Cells

Despite progresses in identifying the cellular mechanisms at the basis of the differentiation of hematopoietic stem/progenitor cells, little is known about the regulatory circuitry at the basis of lineage commitment of hematopoietic multipotent progenitors. To address this issue, we propose a computational approach to give further insights in the comprehension of this genetic mechanism. Differently from T lymphopoiesis, however, there is at present no mathematical model describing lineage restriction of multipotent progenitors to early B-cell precursors. Here, we provide a first model-constructed on the basis of current experimental evidence from literature and of publicly available microarray datasets-of the genetic regulatory network driving the cellular fate determination at the stage of lymphoid lineage commitment, with particular regard to the multipotent-B-cell progenitor transition. By applying multistability analysis methods, we are able to assess the capability of the model to capture the experimentally observed switch-like commitment behavior. These methods allow us to confirm the central role of zinc finger protein 521 (ZNF521) in this process, that we had previously reported, and to identify a novel putative functional interaction for ZNF521, which is essential to realize such characteristic behavior. Moreover, using the devised model, we are able to rigorously analyze the mechanisms underpinning irreversibility of the physiological commitment step and to devise a possible reprogramming strategy, based on the combined modification of the expression of ZNF521 and EBF1.

Gene regulatory network analysis reveals differences in site-specific cell fate determination in mammalian brain

Neurogenesis-the generation of new neurons-is an ongoing process that persists in the adult mammalian brain of several species, including humans. In this work we analyze two discrete brain regions: the subventricular zone (SVZ) lining the walls of the lateral ventricles; and the subgranular zone (SGZ) of the dentate gyrus (DG) of the hippocampus in mice and shed light on the SVZ and SGZ specific neurogenesis. We propose a computational model that relies on the construction and analysis of region specific gene regulatory networks (GRNs) from the publicly available data on these two regions. Using this model a number of putative factors involved in neuronal stem cell (NSC) identity and maintenance were identified. We also demonstrate potential gender and niche-derived differences based on cell surface and nuclear receptors via Ar, Hif1a, and Nr3c1. We have also conducted cell fate determinant analysis for SVZ NSC populations to Olfactory Bulb interneurons and SGZ NSC populations to the granule cells of the Granular Cell Layer. We report 31 candidate cell fate determinant gene pairs, ready to be validated. We focus on Ar-Pax6 in SVZ and Sox2-Ncor1 in SGZ. Both pairs are expressed and localized in the suggested anatomical structures as shown by in situ hybridization and found to physically interact. Finally, we conclude that there are fundamental differences between SGZ and SVZ neurogenesis. We argue that these regulatory mechanisms are linked to the observed differential neurogenic potential of these regions. The presence of nuclear and cell surface receptors in the region specific regulatory circuits indicate the significance of niche derived extracellular factors, hormones and region specific factors such as the oxygen sensitivity, dictating SGZ and SVZ specific neurogenesis.

Non-genetic heterogeneity, criticality and cell differentiation

The different cell types in a living organism acquire their identity through the process of cell differentiation in which multipotent progenitor cells differentiate into distinct cell types. Experimental evidence and analysis of large-scale microarray data establish the key role played by a two-gene motif in cell differentiation in a number of cell systems. The two genes express transcription factors which repress each other's expression and autoactivate their own production. A number of theoretical models have recently been proposed based on the two-gene motif to provide a physical understanding of how cell differentiation occurs. In this paper, we study a simple model of cell differentiation which assumes no cooperativity in the regulation of gene expression by the transcription factors. The latter repress each other's activity directly through DNA binding and indirectly through the formation of heterodimers. We specifically investigate how deterministic processes combined with stochasticity contribute in bringing about cell differentiation. The deterministic dynamics of our model give rise to a supercritical pitchfork bifurcation from an undifferentiated stable steady state to two differentiated stable steady states. The stochastic dynamics of our model are studied using the approaches based on the Langevin equations and the linear noise approximation. The simulation results provide a new physical understanding of recent experimental observations. We further propose experimental measurements of quantities like the variance and the lag-1 autocorrelation function in protein fluctuations as the early signatures of an approaching bifurcation point in the cell differentiation process.

Cell commitment motif composed of progenitor-specific transcription factors and mutual-inhibition regulation

Simple mutual-inhibition networks are frequently occurring motifs in transcriptional regulatory networks for cell lineage commitment. Stable attractors represent cell commitment states. However, how progenitor-specific transcription factors stabilise progenitor cells and commit them to different cell fates remains unexplained. In this study, the authors represent the cell commitment motifs composed of mutual-inhibition regulation and progenitor-specific transcription factors, and develop associated mathematical model to understand how specific cell fate decisions are made. Bifurcation analysis and numerical simulation show that the model could exhibit multiple stable steady states corresponding to progenitor and committed cell states. The transitions between different cell states correspond to different commitment processes. Furthermore, the authors demonstrate that different commitment patterns, for example, haematopoietic and neural fate decisions fall within the scope of proposed framework.

A model-based analysis of culture-dependent phenotypes of mESCs

Mouse embryonic stem cells (mESCs) can be maintained in a proliferative and undifferentiated state over many passages (self-renewal) while retaining the potential to give rise to every cell type of the organism (pluripotency). Autocrine FGF4/Erk signalling has been identified as a major stimulus for fate decisions and lineage commitment in these cells. Recent findings on serum-free culture conditions with specific inhibitors (known as 2i) demonstrate that the inhibition of this pathway reduces transcription factor heterogeneity and is vital to maintain ground state pluripotency of mESCs. We suggest a novel mathematical model to explicitly integrate FGF4/Erk signalling into an interaction network of key pluripotency factors (namely Oct4, Sox2, Nanog and Rex1). The envisaged model allows to explore whether and how proposed mechanisms and feedback regulations can account for different expression patterns in mESC cultures. We demonstrate that an FGF4/Erk-mediated negative feedback is sufficient to induce molecular heterogeneity with respect to Nanog and Rex1 expression and thus critically regulates the propensity for differentiation and the loss of pluripotency. Furthermore, we compare simulation results on the transcription factor dynamics in different self-renewing states and during differentiation with experimental data on a Rex1GFPd2 reporter cell line using flow cytometry and qRT-PCR measurements. Concluding from our results we argue that interaction between FGF4/Erk signalling and Nanog expression qualifies as a key mechanism to manipulate mESC pluripotency. In particular, we infer that ground state pluripotency under 2i is achieved by shifting stable expression pattern of Nanog from a bistable into a monostable regulation impeding stochastic state transitions. Furthermore, we derive testable predictions on altering the degree of Nanog heterogeneity and on the frequency of state transitions in LIF/serum conditions to challenge our model assumptions.

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.

Systems hematology: an introduction

Hematologists have traditionally studied blood and its components by simplifying it into its components and functions. A variety of new techniques have generated large and complex datasets. Coupled to an appreciation of blood as a dynamic system, a new approach in systems hematology is needed. Systems hematology embraces the multi-scale complexity with a combination of mathematical, engineering, and computational tools for constructing and validating models of biological phenomena. The validity of mathematical modeling in hematopoiesis was established early by the pioneering work of Till and McCulloch. This volume seeks to introduce to the various scientists and physicians to the multi-faceted field of hematology by highlighting recent works in systems biology. Deterministic, stochastic, statistical, and network-based models have been used to better understand a range of topics in hematopoiesis, including blood cell production, the periodicity of cyclical neutropenia, stem cell production in response to cytokine administration, and the emergence of drug resistance. Future advances require technological improvements in computing power, imaging, and proteomics as well as greater collaboration between experimentalists and modelers. Altogether, systems hematology will improve our understanding of normal and abnormal hematopoiesis, better define stem cells and their daughter cells, and potentially lead to more effective therapies.

Hard-wired heterogeneity in blood stem cells revealed using a dynamic regulatory network model

Motivation: Combinatorial interactions of transcription factors with cis-regulatory elements control the dynamic progression through successive cellular states and thus underpin all metazoan development. The construction of network models of cis-regulatory elements, therefore, has the potential to generate fundamental insights into cellular fate and differentiation. Haematopoiesis has long served as a model system to study mammalian differentiation, yet modelling based on experimentally informed cis-regulatory interactions has so far been restricted to pairs of interacting factors. Here, we have generated a Boolean network model based on detailed cis-regulatory functional data connecting 11 haematopoietic stem/progenitor cell (HSPC) regulator genes.

Results: Despite its apparent simplicity, the model exhibits surprisingly complex behaviour that we charted using strongly connected components and shortest-path analysis in its Boolean state space. This analysis of our model predicts that HSPCs display heterogeneous expression patterns and possess many intermediate states that can act as ‘stepping stones’ for the HSPC to achieve a final differentiated state. Importantly, an external perturbation or ‘trigger’ is required to exit the stem cell state, with distinct triggers characterizing maturation into the various different lineages. By focusing on intermediate states occurring during erythrocyte differentiation, from our model we predicted a novel negative regulation of Fli1 by Gata1, which we confirmed experimentally thus validating our model. In conclusion, we demonstrate that an advanced mammalian regulatory network model based on experimentally validated cis-regulatory interactions has allowed us to make novel, experimentally testable hypotheses about transcriptional mechanisms that control differentiation of mammalian stem cells.

Contact:j.heringa@vu.nl or ioannis.xenarios@isb-sib.ch or bg200@cam.ac.uk

Supplementary information:Supplementary data are available at Bioinformatics online.

Dynamic analysis of gene expression and genome-wide transcription factor binding during lineage specification of multipotent progenitors

We used the paradigmatic GATA-PU.1 axis to explore, at the systems level, dynamic relationships between transcription factor (TF) binding and global gene expression programs as multipotent cells differentiate. We combined global ChIP-seq of GATA1, GATA2, and PU.1 with expression profiling during differentiation to erythroid and neutrophil lineages. Our analysis reveals (1) differential complexity of sequence motifs bound by GATA1, GATA2, and PU.1; (2) the scope and interplay of GATA1 and GATA2 programs within, and during transitions between, different cell compartments, and the extent of their hard-wiring by DNA motifs; (3) the potential to predict gene expression trajectories based on global associations between TF-binding data and target gene expression; and (4) how dynamic modeling of DNA-binding and gene expression data can be used to infer regulatory logic of TF circuitry. This rubric exemplifies the utility of this cross-platform resource for deconvoluting the complexity of transcriptional programs controlling stem/progenitor cell fate in hematopoiesis.

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Cross-platform resource for TF-network regulation of multipotent blood cell fate

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DNA motif dependence and changing specificity of GATA factors in lineage choice

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Modeling-based inference identifies GATA2 repression of PU.1 in multipotent cells

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Priming, recruitment, and switching modes of GATA interplay during differentiation

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.

Transcriptional hierarchies regulating early blood cell development

Hematopoiesis represents one of the paradigmatic systems for studying stem cell biology, but our understanding of how the hematopoietic system develops during embryogenesis is still incomplete. While many lessons have been learned from studying the mouse embryo, embryonic stem cells have come to the fore as an alternative and more tractable model to recapitulate hematopoietic development. Here we review what is known about the embryonic origin of blood from these complementary systems and how transcription factor networks regulate the emergence of hematopoietic tissue from the mesoderm. Furthermore, we have performed an integrated analysis of genome-wide microarray and ChIP-seq data sets from mouse embryos and embryonic stem (ES) cell lines deficient in key regulators and demonstrate how this type of analysis can be used to reconstruct regulatory hierarchies that both confirm existing regulatory linkages and suggest additional interactions.

Mapping differentiation under mixed culture conditions reveals a tunable continuum of T cell fates

An experimental and theoretical study of T cell differentiation in response to mixed-input conditions reveals that cells can tune between Th1 and Th2 states through a continuum of mixed phenotypes.

Cell differentiation is typically directed by external signals that drive opposing regulatory pathways. Studying differentiation under polarizing conditions, with only one input signal provided, is limited in its ability to resolve the logic of interactions between opposing pathways. Dissection of this logic can be facilitated by mapping the system's response to mixtures of input signals, which are expected to occur in vivo, where cells are simultaneously exposed to various signals with potentially opposing effects. Here, we systematically map the response of naïve T cells to mixtures of signals driving differentiation into the Th1 and Th2 lineages. We characterize cell state at the single cell level by measuring levels of the two lineage-specific transcription factors (T-bet and GATA3) and two lineage characteristic cytokines (IFN-γ and IL-4) that are driven by these transcription regulators. We find a continuum of mixed phenotypes in which individual cells co-express the two lineage-specific master regulators at levels that gradually depend on levels of the two input signals. Using mathematical modeling we show that such tunable mixed phenotype arises if autoregulatory positive feedback loops in the gene network regulating this process are gradual and dominant over cross-pathway inhibition. We also find that expression of the lineage-specific cytokines follows two independent stochastic processes that are biased by expression levels of the master regulators. Thus, cytokine expression is highly heterogeneous under mixed conditions, with subpopulations of cells expressing only IFN-γ, only IL-4, both cytokines, or neither. The fraction of cells in each of these subpopulations changes gradually with input conditions, reproducing the continuous internal state at the cell population level. These results suggest a differentiation scheme in which cells reflect uncertainty through a continuously tuneable mixed phenotype combined with a biased stochastic decision rather than a binary phenotype with a deterministic decision.

During cell differentiation, progenitor cells respond to external signals that drive the expression of genes that are characteristic of the differentiated cell states. This process is controlled by gene regulatory networks that typically involve positive autoregulation and cross-inhibition between master regulators of the two differentiated states. Mapping the system's response to mixtures of external signals can help us to understand the operational logic of these binary cell fate decisions. Here, we study differentiation of CD4⁺ T cells into Th1 and Th2 lineages under mixed-input conditions, at the single cell level. We reveal that cell state is not restricted to a small number of well-defined phenotypes, but rather tunes through a continuum of mixed-phenotype states in which levels of lineage-specifying transcription factors gradually change with the levels of the two inputs. Using mathematical modeling we establish the conditions under which the system has one stable steady state that continuously tunes in response to changes in levels of the inputs. Results of this model qualitatively explain our experimental observations. We further characterize expression patterns of downstream lineage-specific genes—cytokines that are driven by the two master regulators upon cell re-stimulation. We find a highly heterogeneous population with cells expressing either one of the cytokines, both cytokines, or neither. Of note, the fraction of cells in these subpopulations continuously tunes with input levels, thus reproducing a tunable state at the cell population level. Our results can be explained by a two-stage scheme in which the gene regulatory network is responsible for a continuously tunable cell state, which is translated into a heterogeneous cytokine expression pattern through uncorrelated and biased stochastic processes.

A minimal transcriptional controlling network of regulatory T cell development

Regulatory T cells (Treg) are a subpopulation of T cells that are central to immune homeostasis and develop under the control of a complex regulatory network consisting of FoxP3 and its partner factors. A central question about this network is how does it enable T cells to robustly specify and stably maintain their states despite intrinsic and environmental fluctuations. Inspired by recent experimental advances, we propose here a minimal transcriptional controlling network and use it to illustrate the robustness and dynamic features of Treg development. Our study shows that the controlling network may exhibit distinct dynamics depending on its parameter regimes and that the maintenance of multistability requires the orchestration of both its positive and negative feedback loops. In addition, system volume contributes monotonically to the increase in the network's robustness. We further show that the dynamics of our model varies with the alteration of FoxP3-DNA binding affinity, consistent with recent experimental findings. This minimal model thereby offers new insights into the dynamics and robustness of Treg development and may serve as a platform for future exploration toward a more quantitative and systematic understanding of the immune system.

An in silico erythropoiesis model rationalizing synergism between stem cell factor and erythropoietin

Stem cell factor (SCF) and erythropoietin (EPO) are two most recognized growth factors that play in concert to control in vitro erythropoiesis. However, exact mechanisms underlying the interplay of these growth factors in vitro remain unclear. We developed a mathematical model to study co-signaling effects of SCF and EPO utilizing the ERK1/2 and GATA-1 pathways (activated by SCF and EPO) that drive the proliferation and differentiation of erythroid progenitors. The model was simplified and formulated based on three key features: synergistic contribution of SCF and EPO on ERK1/2 activation, positive feedback effects on proliferation and differentiation, and cross-inhibition effects of activated ERK1/2 and GATA-1. The model characteristics were developed to correspond with biological observations made known thus far. Our simulation suggested that activated GATA-1 has a more dominant cross-inhibition effect and stronger positive feedback response on differentiation than the proliferation pathway, while SCF contributed more to the activation of ERK1/2 than EPO. A sensitivity analysis performed to gauge the dynamics of the system was able to identify the most sensitive model parameters and illustrated a contribution of transient activity in EPO ligand to growth factor synergism. Based on theoretical arguments, we have successfully developed a model that can simulate growth factor synergism observed in vitro for erythropoiesis. This hypothesized model can be applied to further computational studies in biological systems where synergistic effects of two ligands are seen.

A stochastic model of epigenetic dynamics in somatic cell reprogramming

Somatic cell reprogramming has dramatically changed stem cell research in recent years. The high pace of new findings in the field and an ever increasing amount of data from new high throughput techniques make it challenging to isolate core principles of the process. In order to analyze such mechanisms, we developed an abstract mechanistic model of a subset of the known regulatory processes during cell differentiation and production of induced pluripotent stem cells. This probabilistic Boolean network describes the interplay between gene expression, chromatin modifications, and DNA methylation. The model incorporates recent findings in epigenetics and partially reproduces experimentally observed reprogramming efficiencies and changes in methylation and chromatin remodeling. It enables us to investigate, how the temporal progression of the process is regulated. It also explicitly includes the transduction of factors using viral vectors and their silencing in reprogrammed cells, since this is still a standard procedure in somatic cell reprogramming. Based on the model we calculate an epigenetic landscape for probabilities of cell states. Simulation results show good reproduction of experimental observations during reprogramming, despite the simple structure of the model. An extensive analysis and introduced variations hint toward possible optimizations of the process that could push the technique closer to clinical applications. Faster changes in DNA methylation increase the speed of reprogramming at the expense of efficiency, while accelerated chromatin modifications moderately improve efficiency.

Progress and prospects for stem cell engineering

Stem cells offer tremendous biomedical potential owing to their abilities to self-renew and differentiate into cell types of multiple adult tissues. Researchers and engineers have increasingly developed novel discovery technologies, theoretical approaches, and cell culture systems to investigate microenvironmental cues and cellular signaling events that control stem cell fate. Many of these technologies facilitate high-throughput investigation of microenvironmental signals and the intracellular signaling networks and machinery processing those signals into cell fate decisions. As our aggregate empirical knowledge of stem cell regulation grows, theoretical modeling with systems and computational biology methods has and will continue to be important for developing our ability to analyze and extract important conceptual features of stem cell regulation from complex data. Based on this body of knowledge, stem cell engineers will continue to develop technologies that predictably control stem cell fate with the ultimate goal of being able to accurately and economically scale up these systems for clinical-grade production of stem cell therapeutics.

Stability and multiattractor dynamics of a toggle switch based on a two-stage model of stochastic gene expression

A toggle switch consists of two genes that mutually repress each other. This regulatory motif is active during cell differentiation and is thought to act as a memory device, being able to choose and maintain cell fate decisions. Commonly, this switch has been modeled in a deterministic framework where transcription and translation are lumped together. In this description, bistability occurs for transcription factor cooperativity, whereas autoactivation leads to a tristable system with an additional undecided state. In this contribution, we study the stability and dynamics of a two-stage gene expression switch within a probabilistic framework inspired by the properties of the Pu/Gata toggle switch in myeloid progenitor cells. We focus on low mRNA numbers, high protein abundance, and monomeric transcription-factor binding. Contrary to the expectation from a deterministic description, this switch shows complex multiattractor dynamics without autoactivation and cooperativity. Most importantly, the four attractors of the system, which only emerge in a probabilistic two-stage description, can be identified with committed and primed states in cell differentiation. To begin, we study the dynamics of the system and infer the mechanisms that move the system between attractors using both the quasipotential and the probability flux of the system. Next, we show that the residence times of the system in one of the committed attractors are geometrically distributed. We derive an analytical expression for the parameter of the geometric distribution, therefore completely describing the statistics of the switching process and elucidate the influence of the system parameters on the residence time. Moreover, we find that the mean residence time increases linearly with the mean protein level. This scaling also holds for a one-stage scenario and for autoactivation. Finally, we study the implications of this distribution for the stability of a switch and discuss the influence of the stability on a specific cell differentiation mechanism. Our model explains lineage priming and proposes the need of either high protein numbers or long-term modifications such as chromatin remodeling to achieve stable cell fate decisions. Notably, we present a system with high protein abundance that nevertheless requires a probabilistic description to exhibit multistability, complex switching dynamics, and lineage priming.

Systems biology of stem cells: three useful perspectives to help overcome the paradigm of linear pathways

Stem cell behaviours, such as stabilization of the undecided state of pluripotency or multipotency, the priming towards a prospective fate, binary fate decisions and irreversible commitment, must all somehow emerge from a genome-wide gene-regulatory network. Its unfathomable complexity defies the standard mode of explanation that is deeply rooted in molecular biology thinking: the reduction of observables to linear deterministic molecular pathways that are tacitly taken as chains of causation. Such culture of proximate explanation that uses qualitative arguments, simple arrow-arrow schemes or metaphors persists despite the ceaseless accumulation of 'omics' data and the rise of systems biology that now offers precise conceptual tools to explain emergent cell behaviours from gene networks. To facilitate the embrace of the principles of physics and mathematics that underlie such systems and help to bridge the gap between the formal description of theorists and the intuition of experimental biologists, we discuss in qualitative terms three perspectives outside the realm of their familiar linear-deterministic view: (i) state space (ii), high-dimensionality and (iii) heterogeneity. These concepts jointly offer a new vista on stem cell regulation that naturally explains many novel, counterintuitive observations and their inherent inevitability, obviating the need for ad hoc explanations of their existence based on natural selection. Hopefully, this expanded view will stimulate novel experimental designs.

Hierarchical differentiation of myeloid progenitors is encoded in the transcription factor network

Hematopoiesis is an ideal model system for stem cell biology with advanced experimental access. A systems view on the interactions of core transcription factors is important for understanding differentiation mechanisms and dynamics. In this manuscript, we construct a Boolean network to model myeloid differentiation, specifically from common myeloid progenitors to megakaryocytes, erythrocytes, granulocytes and monocytes. By interpreting the hematopoietic literature and translating experimental evidence into Boolean rules, we implement binary dynamics on the resulting 11-factor regulatory network. Our network contains interesting functional modules and a concatenation of mutual antagonistic pairs. The state space of our model is a hierarchical, acyclic graph, typifying the principles of myeloid differentiation. We observe excellent agreement between the steady states of our model and microarray expression profiles of two different studies. Moreover, perturbations of the network topology correctly reproduce reported knockout phenotypes in silico. We predict previously uncharacterized regulatory interactions and alterations of the differentiation process, and line out reprogramming strategies.

Cellular aging leads to functional heterogeneity of hematopoietic stem cells: a modeling perspective

Hematopoietic stem cells (HSCs) are the source for the life-long supply of functional cells in peripheral blood while they simultaneously maintain their own reserve pool. However, there is accumulating evidence that HSCs are themselves subject to quantitative and qualitative exhaustion. Although several processes linked to mitotic activity can potentially account for the observed aging phenomena (e.g., DNA damage, telomere shortening, epigenetic modification), a precise understanding of HSC exhaustion is still missing. It is particularly unclear how individual aging processes on the single-cell level translate on the phenotypic level of the overall tissue and whether there is a functional implication of an age-structured HSC population. We address these issues by applying a novel mathematical model of HSC organization in which division-specific, cumulative alterations of stem cell quality determine the phenotypic and functional appearance of the overall cell population. Adapting the model to a number of basic experimental findings, we quantify the level of additional heterogeneity that is introduced by a population of individually aging cells. Based on this model, we are able to conclude that division-dependent processes of cellular aging explain a wide range of phenomena on HSC exhaustion and that HSC aging needs to be considered as a highly heterogeneous process. We furthermore report that functional heterogeneity between young and old HSCs appears closely similar to the phenomena described for long- and short-term repopulating cells. We speculate whether differential, division-coupled stem cell aging introduces an intra-animal variability that also accounts for heterogeneity with respect to the repopulation ability of HSCs.

A deterministic map of Waddington's epigenetic landscape for cell fate specification

Background

The image of the "epigenetic landscape", with a series of branching valleys and ridges depicting stable cellular states and the barriers between those states, has been a popular visual metaphor for cell lineage specification - especially in light of the recent discovery that terminally differentiated adult cells can be reprogrammed into pluripotent stem cells or into alternative cell lineages. However the question of whether the epigenetic landscape can be mapped out quantitatively to provide a predictive model of cellular differentiation remains largely unanswered.

Results

Here we derive a simple deterministic path-integral quasi-potential, based on the kinetic parameters of a gene network regulating cell fate, and show that this quantity is minimized along a temporal trajectory in the state space of the gene network, thus providing a marker of directionality for cell differentiation processes. We then use the derived quasi-potential as a measure of "elevation" to quantitatively map the epigenetic landscape, on which trajectories flow "downhill" from any location. Stochastic simulations confirm that the elevation of this computed landscape correlates to the likelihood of occurrence of particular cell fates, with well-populated low-lying "valleys" representing stable cellular states and higher "ridges" acting as barriers to transitions between the stable states.

Conclusions

This quantitative map of the epigenetic landscape underlying cell fate choice provides mechanistic insights into the "forces" that direct cellular differentiation in the context of physiological development, as well as during artificially induced cell lineage reprogramming. Our generalized approach to mapping the landscape is applicable to non-gradient gene regulatory systems for which an analytical potential function cannot be derived, and also to high-dimensional gene networks. Rigorous quantification of the gene regulatory circuits that govern cell lineage choice and subsequent mapping of the epigenetic landscape can potentially help identify optimal routes of cell fate reprogramming.

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

Background

The gene regulatory circuit motif in which two opposing fate-determining transcription factors inhibit each other but activate themselves has been used in mathematical models of binary cell fate decisions in multipotent stem or progenitor cells. This simple circuit can generate multistability and explains the symmetric “poised” precursor state in which both factors are present in the cell at equal amounts as well as the resolution of this indeterminate state as the cell commits to either cell fate characterized by an asymmetric expression pattern of the two factors. This establishes the two alternative stable attractors that represent the two fate options. It has been debated whether cooperativity of molecular interactions is necessary to produce such multistability.

Principal Findings

Here we take a general modeling approach and argue that this question is not relevant. We show that non-linearity can arise in two distinct models in which no explicit interaction between the two factors is assumed and that distinct chemical reaction kinetic formalisms can lead to the same (generic) dynamical system form. Moreover, we describe a novel type of bifurcation that produces a degenerate steady state that can explain the metastable state of indeterminacy prior to cell fate decision-making and is consistent with biological observations.

Conclusion

The general model presented here thus offers a novel principle for linking regulatory circuits with the state of indeterminacy characteristic of multipotent (stem) cells.

Mathematical modelling of stem cell differentiation: the PU.1-GATA-1 interaction

The transcription factors PU.1 and GATA-1 are known to be important in the development of blood progenitor cells. Specifically they are thought to regulate the differentiation of progenitor cells into the granulocyte/macrophage lineage and the erythrocyte/megakaryocite lineage. While several mathematical models have been proposed to investigate the interaction between the transcription factors in recent years, there is still debate about the nature of the progenitor state in the dynamical system, and whether the existing models adequately capture new knowledge about the interactions gleaned from experimental data. Further, the models utilise different formalisms to represent the genetic regulation, and it appears that the resulting dynamical system depends upon which formalism is adopted. In this paper we analyse the four existing models, and propose an alternative model which is shown to demonstrate a rich variety of dynamical systems behaviours found across the existing models, including both bistability and tristability required for modelling the undifferentiated progenitors.

Dynamic stabilization in the PU1-GATA1 circuit using a model with time-dependent kinetic change

The PU.1 and GATA1 genes play an important role in the differentiation of blood stem cells. The protein levels expressed by these genes are thought to be regulated by a self-excitatory feedback loop for each gene and a cross-inhibitory feedback loop between the two genes. A mathematical model that captures the dynamical interaction between these two genes reveals that constant levels of self-excitation and cross-inhibition allow the most self-exciting or cross-inhibiting gene to dominate the system. However, since biological systems rarely exist in an unchanging equilibrium, we modeled this gene circuit using discrete time-dependent changes in the parameters in lieu of steady state parameters. These time-dependent parameters lead to new phenomena, including the development of new limit cycles and basins of attraction. These phenomena are not present in models using constant parameter values. Our findings suggest that even small perturbations in the PU.1 and GATA1 feedback loops may substantially alter the gene expression and therefore the cell phenotype. These time-dependent parameter models may also have implications for other gene systems and provide new ways to understand the mechanisms of cellular differentiation.

The ARID family transcription factor bright is required for both hematopoietic stem cell and B lineage development

Bright/Arid3a has been characterized both as an activator of immunoglobulin heavy-chain transcription and as a proto-oncogene. Although Bright expression is highly B lineage stage restricted in adult mice, its expression in the earliest identifiable hematopoietic stem cell (HSC) population suggests that Bright might have additional functions. We showed that >99% of Bright(-/-) embryos die at midgestation from failed hematopoiesis. Bright(-/-) embryonic day 12.5 (E12.5) fetal livers showed an increase in the expression of immature markers. Colony-forming assays indicated that the hematopoietic potential of Bright(-/-) mice is markedly reduced. Rare survivors of lethality, which were not compensated by the closely related paralogue Bright-derived protein (Bdp)/Arid3b, suffered HSC deficits in their bone marrow as well as B lineage-intrinsic developmental and functional deficiencies in their peripheries. These include a reduction in a natural antibody, B-1 responses to phosphocholine, and selective T-dependent impairment of IgG1 class switching. Our results place Bright/Arid3a on a select list of transcriptional regulators required to program both HSC and lineage-specific differentiation.

Understanding gene circuits at cell-fate branch points for rational cell reprogramming

Cell-type reprogramming, the artificial induction of a switch of cell lineage and developmental stage, holds great promise for regenerative medicine. However, how does the metazoan body itself 'program' the various cell lineages in the first place? Knowledge of how multipotent cells make cell-fate decisions and commit to a particular lineage is crucial for a rational reprogramming strategy and to avoid trial-and-error approaches in choosing the appropriate set of transcription factors to use. In the past few years, a general principle has emerged in which small gene circuits of cross-inhibition and self-activation govern the decision at branch points of cell development. A formal theoretical treatment of such circuits that deal with their dynamics on the 'epigenetic landscape' could offer some guidance to find the optimal way of cell reprogramming.

Cell differentiation modeled via a coupled two-switch regulatory network

Mesenchymal stem cells can give rise to bone and other tissue cells, but their differentiation still escapes full control. In this paper we address this issue by mathematical modeling. We present a model for a genetic switch determining the cell fate of progenitor cells which can differentiate into osteoblasts (bone cells) or chondrocytes (cartilage cells). The model consists of two switch mechanisms and reproduces the experimentally observed three stable equilibrium states: a progenitor, an osteogenic, and a chondrogenic state. Conventionally, the loss of an intermediate (progenitor) state and the entailed attraction to one of two opposite (differentiated) states is modeled as a result of changing parameters. In our model in contrast, we achieve this by distributing the differentiation process to two functional switch parts acting in concert: one triggering differentiation and the other determining cell fate. Via stability and bifurcation analysis, we investigate the effects of biochemical stimuli associated with different system inputs. We employ our model to generate differentiation scenarios on the single cell as well as on the cell population level. The single cell scenarios allow to reconstruct the switching upon extrinsic signals, whereas the cell population scenarios provide a framework to identify the impact of intrinsic properties and the limiting factors for successful differentiation.

The potential landscape of genetic circuits imposes the arrow of time in stem cell differentiation

Differentiation from a multipotent stem or progenitor state to a mature cell is an essentially irreversible process. The associated changes in gene expression patterns exhibit time-directionality. This "arrow of time" in the collective change of gene expression across multiple stable gene expression patterns (attractors) is not explained by the regulated activation, the suppression of individual genes which are bidirectional molecular processes, or by the standard dynamical models of the underlying gene circuit which only account for local stability of attractors. To capture the global dynamics of this nonequilibrium system and gain insight in the time-asymmetry of state transitions, we computed the quasipotential landscape of the stochastic dynamics of a canonical gene circuit that governs branching cell fate commitment. The potential landscape reveals the global dynamics and permits the calculation of potential barriers between cell phenotypes imposed by the circuit architecture. The generic asymmetry of barrier heights indicates that the transition from the uncommitted multipotent state to differentiated states is inherently unidirectional. The model agrees with observations and predicts the extreme conditions for reprogramming cells back to the undifferentiated state.