Stem cell decision making and critical-like exploratory networks

Zebrafish neuromesodermal progenitors undergo a critical state transition in vivo

The transition state model of cell differentiation proposes that a transient window of gene expression stochasticity precedes entry into a differentiated state. Here, we assess this theoretical model in zebrafish neuromesodermal progenitors (NMps) in vivo during late somitogenesis stages. We observed an increase in gene expression variability at the 24 somite stage (24ss) before their differentiation into spinal cord and paraxial mesoderm. Analysis of a published 18ss scRNA-seq dataset showed that the NMp population is noisier than its derivatives. By building in silico composite gene expression maps from image data, we assigned an 'NM index' to in silico NMps based on the expression of neural and mesodermal markers and demonstrated that cell population heterogeneity peaked at 24ss. Further examination revealed cells with gene expression profiles incongruent with their prospective fate. Taken together, our work supports the transition state model within an endogenous cell fate decision making event.

Archetypal Architecture Construction, Patterning, and Scaling Invariance in a 3D Embryoid Body Differentiation Model

Self-organized patterning and architecture construction studying is a priority goal for fundamental developmental and stem cell biology. To study the spatiotemporal patterning of pluripotent stem cells of different origins, we developed a three-dimensional embryoid body (EB) differentiation model quantifying volumetric parameters and investigated how the EB architecture formation, patterning, and scaling depend on the proliferation, cavitation, and differentiation dynamics, external environmental factors, and cell numbers. We identified three similar spatiotemporal patterns in the EB architectures, regardless of cell origin, which constitute the EB archetype and mimick the pre-gastrulation embryonic patterns. We found that the EB patterning depends strongly on cellular positional information, culture media factor/morphogen content, and free diffusion from the external environment and between EB cell layers. However, the EB archetype formation is independent of the EB size and initial cell numbers forming EBs; therefore, it is capable of scaling invariance and patterning regulation. Our findings indicate that the underlying principles of reaction-diffusion and positional information concepts can serve as the basis for EB architecture construction, patterning, and scaling. Thus, the 3D EB differentiation model represents a highly reproducible and reliable platform for experimental and theoretical research on developmental and stem cell biology issues.

When to Be Critical? Performance and Evolvability in Different Regimes of Neural Ising Agents

It has long been hypothesized that operating close to the critical state is beneficial for natural and artificial evolutionary systems. We put this hypothesis to test in a system of evolving foraging agents controlled by neural networks that can adapt the agents' dynamical regime throughout evolution. Surprisingly, we find that all populations that discover solutions evolve to be subcritical. By a resilience analysis, we find that there are still benefits of starting the evolution in the critical regime. Namely, initially critical agents maintain their fitness level under environmental changes (for example, in the lifespan) and degrade gracefully when their genome is perturbed. At the same time, initially subcritical agents, even when evolved to the same fitness, are often inadequate to withstand the changes in the lifespan and degrade catastrophically with genetic perturbations. Furthermore, we find the optimal distance to criticality depends on the task complexity. To test it we introduce a hard task and a simple task: For the hard task, agents evolve closer to criticality, whereas more subcritical solutions are found for the simple task. We verify that our results are independent of the selected evolutionary mechanisms by testing them on two principally different approaches: a genetic algorithm and an evolutionary strategy. In summary, our study suggests that although optimal behaviour in the simple task is obtained in a subcritical regime, initializing near criticality is important to be efficient at finding optimal solutions for new tasks of unknown complexity.

A Unified Genomic Mechanism of Cell-Fate Change

The purpose of our studies is to elucidate the nature of massive control of the whole genome expression with a particular emphasis on cell-fate change. The whole genome expression is coordinated by the emergence of a critical point (CP: a peculiar set of biphasic genes) with the genome acting as an integrated dynamical system. In response to stimuli, the genome expression self-organizes into local sub-, near-, and super-critical states, each exhibiting distinct collective behaviors with its center of mass acting as a local attractor, coexisting with the whole genome attractor (GA). The CP serves as the organizing center of cell-fate change, and its activation makes local perturbation to spread over the genome affecting GA. The activation of CP is in turn elicited by genes with elevated temporal variance (oscillating-mode genes), normally in charge to keep genome expression at pace with microenvironment fluctuations. When oscillation exceeds a given threshold, the CP synchronizes with the GA driving genome expression state transition. The expression synchronization wave invading the entire genome is fostered by the fusion-splitting dynamics of silencing pericentromere-associated heterochromatin domains and the consequent folding-unfolding transitions of transcribing euchromatin domains. The proposed mechanism is a unified step toward a time-evolutional transition theory of biological regulation.

Cell-Fate Determination from Embryo to Cancer Development: Genomic Mechanism Elucidated

Elucidation of the genomic mechanism that guides the cell-fate change is one of the fundamental issues of biology. We previously demonstrated that whole genome expression is coordinated by the emergence of a critical point at both the cell-population and single-cell levels through the physical principle of self-organized criticality. In this paper, we further examine the genomic mechanism that determines the cell-fate changes from embryo to cancer development. The state of the critical point, acting as the organizing center of the cell fate, determines whether the genome resides in a super- or sub-critical state. In the super-critical state, a specific stochastic perturbation can spread over the entire system through the "genome engine", an autonomous critical-control genomic system, whereas in the sub-critical state, the perturbation remains at a local level. The cell-fate changes when the genome becomes super-critical. We provide a consistent framework to develop a time-evolutional transition theory for the biological regulation of the cell-fate change.

Self-Organization of Genome Expression from Embryo to Terminal Cell Fate: Single-Cell Statistical Mechanics of Biological Regulation

A statistical mechanical mean-field approach to the temporal development of biological regulation provides a phenomenological, but basic description of the dynamical behavior of genome expression in terms of autonomous self-organization with a critical transition (Self-Organized Criticality: SOC). This approach reveals the basis of self-regulation/organization of genome expression, where the extreme complexity of living matter precludes any strict mechanistic approach. The self-organization in SOC involves two critical behaviors: scaling-divergent behavior (genome avalanche) and sandpile-type critical behavior. Genome avalanche patterns-competition between order (scaling) and disorder (divergence) reflect the opposite sequence of events characterizing the self-organization process in embryo development and helper T17 terminal cell differentiation, respectively. On the other hand, the temporal development of sandpile-type criticality (the degree of SOC control) in mouse embryo suggests the existence of an SOC control landscape with a critical transition state (i.e., the erasure of zygote-state criticality). This indicates that a phase transition of the mouse genome before and after reprogramming (immediately after the late 2-cell state) occurs through a dynamical change in a control parameter. This result provides a quantitative open-thermodynamic appreciation of the still largely qualitative notion of the epigenetic landscape. Our results suggest: (i) the existence of coherent waves of condensation/de-condensation in chromatin, which are transmitted across regions of different gene-expression levels along the genome; and (ii) essentially the same critical dynamics we observed for cell-differentiation processes exist in overall RNA expression during embryo development, which is particularly relevant because it gives further proof of SOC control of overall expression as a universal feature.

A conceptual and computational framework for modelling and understanding the non-equilibrium gene regulatory networks of mouse embryonic stem cells

The capacity of pluripotent embryonic stem cells to differentiate into any cell type in the body makes them invaluable in the field of regenerative medicine. However, because of the complexity of both the core pluripotency network and the process of cell fate computation it is not yet possible to control the fate of stem cells. We present a theoretical model of stem cell fate computation that is based on Halley and Winkler’s Branching Process Theory (BPT) and on Greaves et al.’s agent-based computer simulation derived from that theoretical model. BPT abstracts the complex production and action of a Transcription Factor (TF) into a single critical branching process that may dissipate, maintain, or become supercritical. Here we take the single TF model and extend it to multiple interacting TFs, and build an agent-based simulation of multiple TFs to investigate the dynamics of such coupled systems. We have developed the simulation and the theoretical model together, in an iterative manner, with the aim of obtaining a deeper understanding of stem cell fate computation, in order to influence experimental efforts, which may in turn influence the outcome of cellular differentiation. The model used is an example of self-organization and could be more widely applicable to the modelling of other complex systems. The simulation based on this model, though currently limited in scope in terms of the biology it represents, supports the utility of the Halley and Winkler branching process model in describing the behaviour of stem cell gene regulatory networks. Our simulation demonstrates three key features: (i) the existence of a critical value of the branching process parameter, dependent on the details of the cistrome in question; (ii) the ability of an active cistrome to “ignite” an otherwise fully dissipated cistrome, and drive it to criticality; (iii) how coupling cistromes together can reduce their critical branching parameter values needed to drive them to criticality.

Pluripotent stem cells possess the capacity both to renew themselves indefinitely and to differentiate to any cell type in the body. Thus the ability to direct stem cell differentiation would have immense potential in regenerative medicine. There is a massive amount of biological data relevant to stem cells; here we exploit data relating to stem cell differentiation to help understand cell behaviour and complexity. These cells contain a dynamic, non-equilibrium network of genes regulated in part by transcription factors expressed by the network itself. Here we take an existing theoretical framework, Transcription Factor Branching Processes, which explains how these genetic networks can have critical behaviour, and can tip between low and full expression. We use this theory as the basis for the design and implementation of a computational simulation platform, which we then use to run a variety of simulation experiments, to gain a better understanding how these various transcription factors can combine, interact, and influence each other. The simulation parameters are derived from experimental data relating to the core factors in pluripotent stem cell differentiation. The simulation results determine the critical values of branching process parameters, and how these are modulated by the various interacting transcription factors.

Nanog Dynamics in Mouse Embryonic Stem Cells: Results from Systems Biology Approaches

Mouse embryonic stem cells (mESCs), derived from the inner cell mass of the blastocyst, are pluripotent stem cells having self-renewal capability and the potential of differentiating into every cell type under the appropriate culture conditions. An increasing number of reports have been published to uncover the molecular mechanisms that orchestrate pluripotency and cell fate specification using combined computational and experimental methodologies. Here, we review recent systems biology approaches to describe the causes and functions of gene expression heterogeneity and complex temporal dynamics of pluripotency markers in mESCs under uniform culture conditions. In particular, we focus on the dynamics of Nanog, a key regulator of the core pluripotency network and of mESC fate. We summarize the strengths and limitations of different experimental and modeling approaches and discuss how various strategies could be used.

Self-Organizing Global Gene Expression Regulated through Criticality: Mechanism of the Cell-Fate Change

BACKGROUND

A fundamental issue in bioscience is to understand the mechanism that underlies the dynamic control of genome-wide expression through the complex temporal-spatial self-organization of the genome to regulate the change in cell fate. We address this issue by elucidating a physically motivated mechanism of self-organization.

PRINCIPAL FINDINGS

Building upon transcriptome experimental data for seven distinct cell fates, including early embryonic development, we demonstrate that self-organized criticality (SOC) plays an essential role in the dynamic control of global gene expression regulation at both the population and single-cell levels. The novel findings are as follows: i) Mechanism of cell-fate changes: A sandpile-type critical transition self-organizes overall expression into a few transcription response domains (critical states). A cell-fate change occurs by means of a dissipative pulse-like global perturbation in self-organization through the erasure of initial-state critical behaviors (criticality). Most notably, the reprogramming of early embryo cells destroys the zygote SOC control to initiate self-organization in the new embryonal genome, which passes through a stochastic overall expression pattern. ii) Mechanism of perturbation of SOC controls: Global perturbations in self-organization involve the temporal regulation of critical states. Quantitative evaluation of this perturbation in terminal cell fates reveals that dynamic interactions between critical states determine the critical-state coherent regulation. The occurrence of a temporal change in criticality perturbs this between-states interaction, which directly affects the entire genomic system. Surprisingly, a sub-critical state, corresponding to an ensemble of genes that shows only marginal changes in expression and consequently are considered to be devoid of any interest, plays an essential role in generating a global perturbation in self-organization directed toward the cell-fate change.

CONCLUSION AND SIGNIFICANCE

'Whole-genome' regulation of gene expression through self-regulatory SOC control complements gene-by-gene fine tuning and represents a still largely unexplored non-equilibrium statistical mechanism that is responsible for the massive reprogramming of genome expression.

The function of chromatin modifiers in lineage commitment and cell fate specification

Proteins that modify the structure of chromatin are known to be important for various aspects of metazoan biology including development, disease and possibly ageing. Yet functional details of why these proteins are important, i.e. how their action influences a given biological process, are lacking. While it is now possible to describe the biochemistry of how these proteins remodel chromatin, their chromatin binding profiles in cell lines, or gene expression changes upon loss of a given protein, in very few cases has this easily translated into an understanding of how the function of that protein actually influences a developmental process. Given that many chromatin modifying proteins will largely exert their influence through control of gene expression, it is useful to consider developmental processes as changes in the gene regulatory network (GRN), with each cell type exhibiting a unique gene expression profile. In this essay we consider the impact of two abundant and highly conserved chromatin modifying complexes, namely the nucleosome remodelling and deacetylation (NuRD) complex and the polycomb repressive complex 2 (PRC2), on the change in GRNs associated with lineage commitment during early mammalian development. We propose that while the NuRD complex limits the stability of cell states and defines the developmental trajectory between two stable states, PRC2 activity is important for stabilizing a new GRN once established. Although these two complexes display different biochemical activities, chromatin binding profiles and mutant phenotypes, we propose a model to explain how they cooperate to facilitate the transition through cell states that is development.

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.

Critical behavior and axis defining symmetry breaking in Hydra embryonic development

The formation of a hollow cellular sphere is often one of the first steps of multicellular embryonic development. In the case of Hydra, the sphere breaks its initial symmetry to form a foot-head axis. During this process a gene, ks1, is increasingly expressed in localized cell domains whose size distribution becomes scale-free at the axis-locking moment. We show that a physical model based solely on the production and exchange of ks1-promoting factors among neighboring cells robustly reproduces the scaling behavior as well as the experimentally observed spontaneous and temperature-directed symmetry breaking.

Self-organizing circuitry and emergent computation in mouse embryonic stem cells

Pluripotency is a cellular state of multiple options. Here, we highlight the potential for self-organization to contribute to stem cell fate computation. A new way of considering regulatory circuitry is presented that describes the expression of each transcription factor (TF) as a branching process that propagates through time, interacting and competing with others. In a single cell, the interactions between multiple branching processes generate a collective process called 'critical-like self-organization'. We explain how this phenomenon provides a valid description of whole genome regulatory circuit dynamics. The hypothesis of exploratory stem cell decision-making proposes that critical-like self-organization (also called rapid self-organized criticality) provides the backbone for cell fate computation in regulative embryos and pluripotent stem cells. Unspecific amplification of TF expression is predicted to initiate this self-organizing circuitry, where cascades of gene expression propagate and may interact either synergistically or antagonistically. The emergent and highly dynamic circuitry is affected by various sources of selection pressure, such as the expression of TFs with disproportionate influence over other genes, and extrinsic biological and physical stimuli that differentially modulate particular gene expression cascades. Extrinsic conditions continuously trigger waves of transcription that ripple throughout regulatory networks on multiple spatiotemporal scales, providing the context within which circuitry self-organizes. In this framework, a distinction between instructive and selective mechanisms of fate determination is misleading because it is the 'interference pattern', rather than any single instructing or selecting factor, that is ultimately responsible for computing and directing cell fate. Using this framework, we consider whether the idea of a naïve ground state of pluripotency and that of a fluctuating transcriptome are compatible, and whether a ground state like that captured in vitro could exist in vivo.

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.