A geometrical model of cell fate specification in the mouse blastocyst

The lineage decision that generates the epiblast and primitive endoderm from the inner cell mass (ICM) is a paradigm for cell fate specification. Recent mathematics has formalized Waddington's landscape metaphor and proven that lineage decisions in detailed gene network models must conform to a small list of low-dimensional stereotypic changes called bifurcations. The most plausible bifurcation for the ICM is the so-called heteroclinic flip that we define and elaborate here. Our re-analysis of recent data suggests that there is sufficient cell movement in the ICM so the FGF signal, which drives the lineage decision, can be treated as spatially uniform. We thus extend the bifurcation model for a single cell to the entire ICM by means of a self-consistently defined time-dependent FGF signal. This model is consistent with available data and we propose additional dynamic experiments to test it further. This demonstrates that simplified, quantitative and intuitively transparent descriptions are possible when attention is shifted from specific genes to lineages. The flip bifurcation is a very plausible model for any situation where the embryo needs control over the relative proportions of two fates by a morphogen feedback.

Dynamics of cell-type transition mediated by epigenetic modifications

Maintaining tissue homeostasis requires appropriate regulation of stem cell differentiation. The Waddington landscape posits that gene circuits in a cell form a potential landscape of different cell types, wherein cells follow attractors of the probability landscape to develop into distinct cell types. However, how adult stem cells achieve a delicate balance between self-renewal and differentiation remains unclear. We propose that random inheritance of epigenetic states plays a pivotal role in stem cell differentiation and present a hybrid model of stem cell differentiation induced by epigenetic modifications. Our comprehensive model integrates gene regulation networks, epigenetic state inheritance, and cell regeneration, encompassing multi-scale dynamics ranging from transcription regulation to cell population. Through model simulations, we demonstrate that random inheritance of epigenetic states during cell divisions can spontaneously induce cell differentiation, dedifferentiation, and transdifferentiation. Furthermore, we investigate the influences of interfering with epigenetic modifications and introducing additional transcription factors on the probabilities of dedifferentiation and transdifferentiation, revealing the underlying mechanism of cell reprogramming. This in silico model provides valuable insights into the intricate mechanism governing stem cell differentiation and cell reprogramming and offers a promising path to enhance the field of regenerative medicine.

Uncovering the Quantitative Relationships Among Chromosome Fluctuations, Epigenetics, and Gene Expressions of Transdifferentiation on Waddington Landscape

The 3D spatial organization of the chromosomes appears to be linked to the gene function, which is cell type-specific. The chromosome structural ensemble switching model (CSESM) is developed by employing a heteropolymer model on different cell types and the important quantitative relationships among the chromosome ensemble, the epigenetic marks, and the gene expressions are uncovered, that both chromosome fluctuation and epigenetic marks have strong linear correlations with the gene expressions. The results support that the two compartments have different behaviors, corresponding to the relatively sparse and fluctuating phase (compartment A) and the relatively dense and stable phase (compartment B). Importantly, through the investigation of the transdifferentiation processes between the peripheral blood mononuclear cell (PBMC) and the bipolar neuron (BN), a quantitative description for the transdifferentiation is provided, which can be linked to the Waddington landscape. In addition, compared to the direct transdifferentiation between PBMC and BN, the transdifferentiation via the intermediate state neural progenitor cell (NPC) follows a different path (an "uphill" followed by a "downhill"). These theoretical studies bridge the gap among the chromosome fluctuations/ensembles, the epigenetics, and gene expressions in determining the cell fate.

Statistically derived geometrical landscapes capture principles of decision-making dynamics during cell fate transitions

Fate decisions in developing tissues involve cells transitioning between discrete cell states, each defined by distinct gene expression profiles. The Waddington landscape, in which the development of a cell is viewed as a ball rolling through a valley filled terrain, is an appealing way to describe differentiation. To construct and validate accurate landscapes, quantitative methods based on experimental data are necessary. We combined principled statistical methods with a framework based on catastrophe theory and approximate Bayesian computation to formulate a quantitative dynamical landscape that accurately predicts cell fate outcomes of pluripotent stem cells exposed to different combinations of signaling factors. Analysis of the landscape revealed two distinct ways in which cells make a binary choice between one of two fates. We suggest that these represent archetypal designs for developmental decisions. The approach is broadly applicable for the quantitative analysis of differentiation and for determining the logic of developmental decisions.

Modulating mesendoderm competence during human germ layer differentiation

As pluripotent human embryonic stem cells progress toward one germ layer fate, they lose the ability to adopt alternative fates. Using a low-dimensional reaction coordinate to monitor progression toward ectoderm, we show that a differentiating stem cell's probability of adopting a mesendodermal fate given appropriate signals falls sharply at a point along the ectoderm trajectory. We use this reaction coordinate to prospectively isolate and profile differentiating cells based on their mesendoderm competence and analyze their RNA sequencing (RNA-seq) and assay for transposase-accessible chromatin using sequencing (ATAC-seq) profiles to identify transcription factors that control the cell's mesendoderm competence. By modulating these key transcription factors, we can expand or contract the window of competence to adopt the mesendodermal fate along the ectodermal differentiation trajectory. The ability of the underlying gene regulatory network to modulate competence is essential for understanding human development and controlling the fate choices of stem cells in vitro.

A pan-metazoan concept for adult stem cells: the wobbling Penrose landscape

Adult stem cells (ASCs) in vertebrates and model invertebrates (e.g. Drosophila melanogaster) are typically long‐lived, lineage‐restricted, clonogenic and quiescent cells with somatic descendants and tissue/organ‐restricted activities. Such ASCs are mostly rare, morphologically undifferentiated, and undergo asymmetric cell division. Characterized by ‘stemness’ gene expression, they can regulate tissue/organ homeostasis, repair and regeneration. By contrast, analysis of other animal phyla shows that ASCs emerge at different life stages, present both differentiated and undifferentiated phenotypes, and may possess amoeboid movement. Usually pluri/totipotent, they may express germ‐cell markers, but often lack germ‐line sequestering, and typically do not reside in discrete niches. ASCs may constitute up to 40% of animal cells, and participate in a range of biological phenomena, from whole‐body regeneration, dormancy, and agametic asexual reproduction, to indeterminate growth. They are considered legitimate units of selection. Conceptualizing this divergence, we present an alternative stemness metaphor to the Waddington landscape: the ‘wobbling Penrose’ landscape. Here, totipotent ASCs adopt ascending/descending courses of an ‘Escherian stairwell’, in a lifelong totipotency pathway. ASCs may also travel along lower stemness echelons to reach fully differentiated states. However, from any starting state, cells can change their stemness status, underscoring their dynamic cellular potencies. Thus, vertebrate ASCs may reflect just one metazoan ASC archetype.

Geometry of gene regulatory dynamics

Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types that elaborate this complexity results from the activity of gene networks and was likened by Waddington to a flow through a landscape in which valleys represent alternative fates. Geometric methods allow the formal representation of such landscapes and codify the types of behaviors that result from systems of differential equations. Results from Smale and coworkers imply that systems encompassing gene network models can be represented as potential gradients with a Riemann metric, justifying the Waddington metaphor. Here, we extend this representation to include parameter dependence and enumerate all three-way cellular decisions realizable by tuning at most two parameters, which can be generalized to include spatial coordinates in a tissue. All diagrams of cell states vs. model parameters are thereby enumerated. We unify a number of standard models for spatial pattern formation by expressing them in potential form (i.e., as topographic elevation). Turing systems appear nonpotential, yet in suitable variables the dynamics are low dimensional and potential. A time-independent embedding recovers the original variables. Lateral inhibition is described by a saddle point with many unstable directions. A model for the patterning of the Drosophila eye appears as relaxation in a bistable potential. Geometric reasoning provides intuitive dynamic models for development that are well adapted to fit time-lapse data.

On the origins and conceptual frameworks of natural plasticity-Lessons from single-cell models in C. elegans

How flexible are cell identities? This problem has fascinated developmental biologists for several centuries and can be traced back to Abraham Trembley's pioneering manipulations of Hydra to test its regeneration abilities in the 1700s. Since the cell theory in the mid-19th century, developmental biology has been dominated by a single framework in which embryonic cells are committed to specific cell fates, progressively and irreversibly acquiring their differentiated identities. This hierarchical, unidirectional and irreversible view of cell identity has been challenged in the past decades through accumulative evidence that many cell types are more plastic than previously thought, even in intact organisms. The paradigm shift introduced by such plasticity calls into question several other key traditional concepts, such as how to define a differentiated cell or more generally cellular identity, and has brought new concepts, such as distinct cellular states. In this review, we want to contribute to this representation by attempting to clarify the conceptual and theoretical frameworks of cell plasticity and identity. In the context of these new frameworks we describe here an atlas of natural plasticity of cell identity in C. elegans, including our current understanding of the cellular and molecular mechanisms at play. The worm further provides interesting cases at the borderlines of cellular plasticity that highlight the conceptual challenges still ahead. We then discuss a set of future questions and perspectives arising from the studies of natural plasticity in the worm that are shared with other reprogramming and plasticity events across phyla.

Regulatory Dynamics of Cell Differentiation Revealed by True Time Series From Multinucleate Single Cells

Dynamics of cell fate decisions are commonly investigated by inferring temporal sequences of gene expression states by assembling snapshots of individual cells where each cell is measured once. Ordering cells according to minimal differences in expression patterns and assuming that differentiation occurs by a sequence of irreversible steps, yields unidirectional, eventually branching Markov chains with a single source node. In an alternative approach, we used multi-nucleate cells to follow gene expression taking true time series. Assembling state machines, each made from single-cell trajectories, gives a network of highly structured Markov chains of states with different source and sink nodes including cycles, revealing essential information on the dynamics of regulatory events. We argue that the obtained networks depict aspects of the Waddington landscape of cell differentiation and characterize them as reachability graphs that provide the basis for the reconstruction of the underlying gene regulatory network.

The Basal Level of Gene Expression Associated with Chromatin Loosening Shapes Waddington Landscapes and Controls Cell Differentiation

The baseline level of transcription, which is variable and difficult to quantify, seriously complicates the normalization of comparative transcriptomic data, but its biological importance remains unappreciated. We show that this currently neglected ingredient is essential for controlling gene network multistability and therefore cellular differentiation. Basal expression is correlated to the degree of chromatin loosening measured by DNA accessibility and systematically leads to cellular dedifferentiation as assessed by transcriptomic signatures, irrespective of the molecular and cellular tools used. Modeling gene network motifs formally involved in developmental bifurcations reveals that the epigenetic landscapes of Waddington are restructured by the level of nonspecific expression, such that the attractors of progenitor and differentiated cells can be mutually exclusive. This mechanism is universal and holds beyond the particular nature of the genes involved, provided the multistable circuits are correctly described with autonomous basal expression. These results explain the relationships long established between gene expression noise, chromatin decondensation and cellular dedifferentiation, and highlight how heterochromatin maintenance is essential for preventing pathological cellular reprogramming, age-related diseases, and cancer.

Buffering and Amplifying Transcriptional Noise During Cell Fate Specification

The molecular processes that drive gene transcription are inherently noisy. This noise often manifests in the form of transcriptional bursts, producing fluctuations in gene activity over time. During cell fate specification, this noise is often buffered to ensure reproducible developmental outcomes. However, sometimes noise is utilized as a “bet-hedging” mechanism to diversify functional roles across a population of cells. Studies of bacteria, yeast, and cultured cells have provided insights into the nature and roles of noise in transcription, yet we are only beginning to understand the mechanisms by which noise influences the development of multicellular organisms. Here we discuss the sources of transcriptional noise and the mechanisms that either buffer noise to drive reproducible fate choices or amplify noise to randomly specify fates.

Developmental History Provides a Roadmap for the Emergence of Tumor Plasticity

We show that the loss or gain of transcription factor programs that govern embryonic cell-fate specification is associated with a form of tumor plasticity characterized by the acquisition of alternative cell fates normally characteristic of adjacent organs. In human non-small cell lung cancers, downregulation of the lung lineage-specifying TF NKX2-1 is associated with tumors bearing features of various gut tissues. Loss of Nkx2-1 from murine alveolar, but not airway, epithelium results in conversion of lung cells to gastric-like cells. Superimposing oncogenic Kras activation enables further plasticity in both alveolar and airway epithelium, producing tumors that adopt midgut and hindgut fates. Conversely, coupling Nkx2-1 loss with foregut lineage-specifying SOX2 overexpression drives the formation of squamous cancers with features of esophageal differentiation. These findings demonstrate that elements of pathologic tumor plasticity mirror the normal developmental history of organs in that cancer cells acquire cell fates associated with developmentally related neighboring organs.

Physical constraints in cell fate specification. A case in point: Microgravity and phenotypes differentiation

Data obtained by studying mammalian cells in absence of gravity strongly support the notion that cell fate specification cannot be understood according to the current molecular model. A paradigmatic case in point is provided by studying cell populations growing in absence of gravity. When the physical constraint (gravity) is 'experimentally removed', cells spontaneously allocate into two morphologically different phenotypes. Such phenomenon is likely enacted by the intrinsic stochasticity, which, in turn, is successively 'canalized' by a specific gene regulatory network. Both phenotypes are thermodynamically and functionally 'compatibles' with the new, modified environment. However, when the two cell subsets are reseeded into the 1g gravity field the two phenotypes collapse into one. Gravity constraints the system in adopting only one phenotype, not by selecting a pre-existing configuration, but more precisely shaping it de-novo through the modification of the cytoskeleton three-dimensional structure. Overall, those findings highlight how macro-scale features are irreducible to lower-scale explanations. The identification of macroscale control parameters - as those depending on the field (gravity, electromagnetic fields) or emerging from the cooperativity among the field's components (tissue stiffness, cell-to-cell connectivity) - are mandatory for assessing boundary conditions for models at lower scales, thus providing a concrete instantiation of top-down effects.

Engineering of a synthetic quadrastable gene network to approach Waddington landscape and cell fate determination

The process of cell fate determination has been depicted intuitively as cells travelling and resting on a rugged landscape, which has been probed by various theoretical studies. However, few studies have experimentally demonstrated how underlying gene regulatory networks shape the landscape and hence orchestrate cellular decision-making in the presence of both signal and noise. Here we tested different topologies and verified a synthetic gene circuit with mutual inhibition and auto-activations to be quadrastable, which enables direct study of quadruple cell fate determination on an engineered landscape. We show that cells indeed gravitate towards local minima and signal inductions dictate cell fates through modulating the shape of the multistable landscape. Experiments, guided by model predictions, reveal that sequential inductions generate distinct cell fates by changing landscape in sequence and hence navigating cells to different final states. This work provides a synthetic biology framework to approach cell fate determination and suggests a landscape-based explanation of fixed induction sequences for targeted differentiation.

DOI:http://dx.doi.org/10.7554/eLife.23702.001

Cells in animals use a process called differentiation to specialize into specific cell types such as skin cells and liver cells. Proteins called transcription factors drive particular steps in differentiation by controlling the activity of specific genes. Many transcription factors interact with each other to form complex networks that regulate gene activity to determine the fate of a cell and control the whole differentiation process. Some individual gene networks can program cells to become any one of several different cell fates, a feature known as multistability.

In the 1950s, a scientist called Conrad Waddington proposed the concept of an “epigenetic landscape” to describe how the fate of a cell is decided as an animal develops. The cell, depicted as a ball, rolls down a rugged landscape and has the option of taking several different routes. Each route will eventually lead to a distinct cell fate. As the ball moves down the hill, the choice of routes and final destinations becomes more limited. Theoretical approaches have been used to understand how gene regulatory networks shape the epigenetic landscape of an animal. However, few studies have experimentally tested the findings of the theoretical approaches and it is not clear how environmental inputs help to determine which path a cell will take.

Although bacteria cells do not generally specialize into particular cell types, bacteria cells can use multistability in transcription factor networks to switch between different behaviors or “states” in response to cues from the environment. Wu et al. used a bacterium called E. coli as a model to investigate how a gene network called MINPA from mammals, which is involved in differentiation and is believed to show multistability, can guide cells to adopt different states. The work combined experimental and mathematical approaches to design, construct and test an artificial version of the MINPA gene network in E. coli.

The experiments showed that MINPA could direct the cells to adopt four different stable states in which the cells produced fluorescent proteins of different colors. With the help of mathematical modeling, Wu et al. charted how the landscape of cell states changed when external chemical cues were applied. Exposing the cells to several cues in particular orders guided the cells to different final states.

The findings of Wu et al. shed new light on how the fate of a cell is determined and provide a theoretical framework for understanding the complex networks that control cell differentiation. This could help develop new ways of directing cell fate that could ultimately be used to generate cells to treat human diseases.

DOI:http://dx.doi.org/10.7554/eLife.23702.002

Mathematical approaches to modeling development and reprogramming

Induced pluripotent stem cells (iPSCs) are created by the reprogramming of somatic cells via overexpression of certain transcription factors, such as the originally described Yamanaka factors: Oct4, Sox2, Klf4, and c-Myc (OSKM). Here we discuss recent advancements in iPSC reprogramming and introduce mathematical approaches to help map the landscape between cell states during reprogramming. Our modelization indicates that OSKM expression diminishes and/or changes potential barriers between cell states and that epigenetic remodeling facilitate these transitions. From a practical perspective, the modeling approaches outlined here allow us to predict the time necessary to create a given number of iPSC colonies or the number of reprogrammed cells generated in a given time. Additional investigations will help to further refine modeling strategies, rendering them applicable toward the study of the development and stability of cancer cells or even other reprogramming processes such as lineage conversion. Ultimately, a quantitative understanding of cell state transitions might facilitate the establishment of regenerative medicine strategies and enhance the translation of reprogramming technologies into the clinic.