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

Information content and optimization of self-organized developmental systems

A key feature of many developmental systems is their ability to self-organize spatial patterns of functionally distinct cell fates. To ensure proper biological function, such patterns must be established reproducibly, by controlling and even harnessing intrinsic and extrinsic fluctuations. While the relevant molecular processes are increasingly well understood, we lack a principled framework to quantify the performance of such stochastic self-organizing systems. To that end, we introduce an information-theoretic measure for self-organized fate specification during embryonic development. We show that the proposed measure assesses the total information content of fate patterns and decomposes it into interpretable contributions corresponding to the positional and correlational information. By optimizing the proposed measure, our framework provides a normative theory for developmental circuits, which we demonstrate on lateral inhibition, cell type proportioning, and reaction-diffusion models of self-organization. This paves a way toward a classification of developmental systems based on a common information-theoretic language, thereby organizing the zoo of implicated chemical and mechanical signaling processes.

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.

The salt-and-pepper pattern in mouse blastocysts is compatible with signaling beyond the nearest neighbors

Embryos develop in a concerted sequence of spatiotemporal arrangements of cells. In the preimplantation mouse embryo, the distribution of the cells in the inner cell mass evolves from a salt-and-pepper pattern to spatial segregation of two distinct cell types. The exact properties of the salt-and-pepper pattern have not been analyzed so far. We investigate the spatiotemporal distribution of NANOG- and GATA6-expressing cells in the ICM of the mouse blastocysts with quantitative three-dimensional single-cell-based neighborhood analyses. A combination of spatial statistics and agent-based modeling reveals that the cell fate distribution follows a local clustering pattern. Using ordinary differential equations modeling, we show that this pattern can be established by a distance-based signaling mechanism enabling cells to integrate information from the whole inner cell mass into their cell fate decision. Our work highlights the importance of longer-range signaling to ensure coordinated decisions in groups of cells to successfully build embryos.

Synthetic symmetry breaking and programmable multicellular structure formation

During development, cells undergo symmetry breaking into differentiated subpopulations that self-organize into complex structures.1,2,3,4,5 However, few tools exist to recapitulate these behaviors in a controllable and coupled manner.6,7,8,9 Here, we engineer a stochastic recombinase genetic switch tunable by small molecules to induce programmable symmetry breaking, commitment to downstream cell fates, and morphological self-organization. Inducers determine commitment probabilities, generating tunable subpopulations as a function of inducer dosage. We use this switch to control the cell-cell adhesion properties of cells committed to each fate.10,11 We generate a wide variety of 3D morphologies from a monoclonal population and develop a computational model showing high concordance with experimental results, yielding new quantitative insights into the relationship between cell-cell adhesion strengths and downstream morphologies. We expect that programmable symmetry breaking, generating precise and tunable subpopulation ratios and coupled to structure formation, will serve as an integral component of the toolbox for complex tissue and organoid engineering.

Adjusting the range of cell-cell communication enables fine-tuning of cell fate patterns from checkerboard to engulfing

During development, spatio-temporal patterns ranging from checkerboard to engulfing occur with precise proportions of the respective cell fates. Key developmental regulators are intracellular transcriptional interactions and intercellular signaling. We present an analytically tractable mathematical model based on signaling that reliably generates different cell type patterns with specified proportions. Employing statistical mechanics, We derived a cell fate decision model for two cell types. A detailed steady state analysis on the resulting dynamical system yielded necessary conditions to generate spatially heterogeneous patterns. This allows the cell type proportions to be controlled by a single model parameter. Cell-cell communication is realized by local and global signaling mechanisms. These result in different cell type patterns. A nearest neighbor signal yields checkerboard patterns. Increasing the signal dispersion, cell fate clusters and an engulfing pattern can be generated. Altogether, the presented model allows us to reliably generate heterogeneous cell type patterns of different kinds as well as desired proportions.

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

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

Self-Regulated Symmetry Breaking Model for Stem Cell Differentiation

In conventional disorder-order phase transitions, a system shifts from a highly symmetric state, where all states are equally accessible (disorder) to a less symmetric state with a limited number of available states (order). This transition may occur by varying a control parameter that represents the intrinsic noise of the system. It has been suggested that stem cell differentiation can be considered as a sequence of such symmetry-breaking events. Pluripotent stem cells, with their capacity to develop into any specialized cell type, are considered highly symmetric systems. In contrast, differentiated cells have lower symmetry, as they can only carry out a limited number of functions. For this hypothesis to be valid, differentiation should emerge collectively in stem cell populations. Additionally, such populations must have the ability to self-regulate intrinsic noise and navigate through a critical point where spontaneous symmetry breaking (differentiation) occurs. This study presents a mean-field model for stem cell populations that considers the interplay of cell-cell cooperativity, cell-to-cell variability, and finite-size effects. By introducing a feedback mechanism to control intrinsic noise, the model can self-tune through different bifurcation points, facilitating spontaneous symmetry breaking. Standard stability analysis showed that the system can potentially differentiate into several cell types mathematically expressed as stable nodes and limit cycles. The existence of a Hopf bifurcation in our model is discussed in light of stem cell differentiation.

Morphogen-directed cell fate boundaries: slow passage through bifurcation and the role of folded saddles

One of the fundamental mechanisms in embryogenesis is the process by which cells differentiate and create tissues and structures important for functioning as a multicellular organism. Morphogenesis involves diffusive process of chemical signalling involving morphogens that pre-pattern the tissue. These morphogens influence cell fate through a highly nonlinear process of transcriptional signalling. In this paper, we consider this multiscale process in an idealised model for a growing domain. We focus on intracellular processes that lead to robust differentiation into two cell lineages through interaction of a single morphogen species with a cell fate variable that undergoes a bifurcation from monostability to bistability. In particular, we investigate conditions that result in successful and robust pattern formation into two well-separated domains, as well as conditions where this fails and produces a pinned boundary wave where only one part of the domain grows. We show that successful and unsuccessful patterning scenarios can be characterised in terms of presence or absence of a folded saddle singularity for a system with two slow variables and one fast variable; this models the interaction of slow morphogen diffusion, slow parameter drift through bifurcation and fast transcription dynamics. We illustrate how this approach can successfully model acquisition of three cell fates to produce three-domain "French flag" patterning, as well as for a more realistic model of the cell fate dynamics in terms of two mutually inhibiting transcription factors.

Dynamical landscapes of cell fate decisions

The generation of cellular diversity during development involves differentiating cells transitioning between discrete cell states. In the 1940s, the developmental biologist Conrad Waddington introduced a landscape metaphor to describe this process. The developmental path of a cell was pictured as a ball rolling through a terrain of branching valleys with cell fate decisions represented by the branch points at which the ball decides between one of two available valleys. Here we discuss progress in constructing quantitative dynamical models inspired by this view of cellular differentiation. We describe a framework based on catastrophe theory and dynamical systems methods that provides the foundations for quantitative geometric models of cellular differentiation. These models can be fit to experimental data and used to make quantitative predictions about cellular differentiation. The theory indicates that cell fate decisions can be described by a small number of decision structures, such that there are only two distinct ways in which cells make a binary choice between one of two fates. We discuss the biological relevance of these mechanisms and suggest the approach is broadly applicable for the quantitative analysis of differentiation dynamics and for determining principles of developmental decisions.

Cell-cell communication through FGF4 generates and maintains robust proportions of differentiated cell types in embryonic stem cells

During embryonic development and tissue homeostasis, reproducible proportions of differentiated cell types are specified from populations of multipotent precursor cells. Molecular mechanisms that enable both robust cell-type proportioning despite variable initial conditions in the precursor cells, and the re-establishment of these proportions upon perturbations in a developing tissue remain to be characterized. Here, we report that the differentiation of robust proportions of epiblast-like and primitive endoderm-like cells in mouse embryonic stem cell cultures emerges at the population level through cell-cell communication via a short-range fibroblast growth factor 4 (FGF4) signal. We characterize the molecular and dynamical properties of the communication mechanism and show how it controls both robust cell-type proportioning from a wide range of experimentally controlled initial conditions, as well as the autonomous re-establishment of these proportions following the isolation of one cell type. The generation and maintenance of reproducible proportions of discrete cell types is a new function for FGF signaling that might operate in a range of developing tissues.

Intercellular communication and the organization of simple multicellular animals

Animal cells are amazing examples of decentralized systems: By interchanging information about their position and internal state, cells coordinate their behavior and organize themselves in time and space. Examples of this behavior are the development of an embryo or of an organoid. In this work we have asked which are the "rules of intercellular relationship" that allow the organization of an abstract cell collective into structures similar to simple metazoans, without being specific about the (molecular, cellular or physical) nature of the processes involved. To do so, we have used a computational modeling approach following a modified version of the "Swarmalator" concept introduced by O'Keeffe, Hong and Strogatz (2017): a collection of interacting particles ("swarmalators"), each of which defined by a position in space and an internal state (a phase). The key feature is that swarmalators are coupled, so that their position and internal state are both affected by the position and state of all other swarmalators. This model can be easily analogized to biological systems, with "cells" being the swarmalators, and their phase the cell's internal state or "cell type". With this model we explore the conditions (represented by the coupling parameters) that would allow the organization of a multicellular "bioswarmer" and its dynamics along a sort of life cycle. Originally developed in 2D, we implement the model in 3D as well. We describe how changing the strength of intercellular communication can alter the structure and differentiation state of the bioswarmer, how internal polarization can arise and trigger collective directed migration, or how partly erasing the cellular memory of cell state is critical to allow bioswarmers to transit through different states. In addition, we show that the size of a multicellular ensemble might control the differentiation of its constituent cells without changing its rules of relationship.