During development, cells from a population of common progenitors evolve towards different fates characterized by distinct levels of specific transcription factors, a process known as cell differentiation. This evolution is governed by gene regulatory networks modulated by intercellular signalling. In order to evolve towards distinct fates, cells forming the population of common progenitors must display some heterogeneity. We applied a modelling approach to obtain insights into the possible sources of cell-to-cell variability initiating the specification of cells of the inner cell mass into epiblast or primitive endoderm cells in early mammalian embryo. At the single-cell level, these cell fates correspond to three possible steady states of the model. A combination of numerical simulations and bifurcation analyses predicts that the behaviour of the model is preserved with respect to the source of variability and that cell–cell coupling induces the emergence of multiple steady states associated with various cell fate configurations, and to a distribution of the levels of expression of key transcription factors. Statistical analysis of these time-dependent distributions reveals differences in the evolutions of the variance-to-mean ratios of key variables of the system, depending on the simulated source of variability, and, by comparison with experimental data, points to the rate of synthesis of the key transcription factor NANOG as a likely initial source of heterogeneity.

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Initial source of heterogeneity in a model for cell fate decision in the early mammalian embryo

Department of Biological Sciences, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061, USA Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, 1088 Budapest, Hungary Unit of Theoretical Chronobiology, Université Libre de Bruxelles, 1050 Brussels, Belgium Department of Mathematical Sciences, KAIST, Daejeon 34141, South Korea Biomedical Mathematics Group, Institute for Basic Science, Daejeon 34126, South Korea Quantitative Stem Cell Biology Laboratory, The Francis Crick Institute, London NW1 1AT, UK Mathematical Modeling of Cellular Processes, Max Delbrück Center for Molecular Medicine, 13125 Berlin, Germany Department of Mathematics and Computer Science, Free University, 14195 Berlin, Germany

Time-keeping and decision-making in living cells: Part II

Robust cell identity specifications through transitions in the collective state of growing developmental systems

Understanding how multicellular organisms reliably orchestrate cell-fate decisions is a central challenge in developmental biology, particularly in early mammalian development, where tissue-level differentiation arises from seemingly cell-autonomous mechanisms. In this study, we present a multi-scale, spatial-stochastic simulation framework for mouse embryogenesis, focusing on inner cell mass (ICM) differentiation into epiblast (EPI) and primitive endoderm (PRE) at the blastocyst stage. Our framework models key regulatory and tissue-scale interactions in a biophysically realistic fashion, capturing the inherent stochasticity of intracellular gene expression and intercellular signaling, while efficiently simulating these processes by advancing event-driven simulation techniques. Leveraging the power of Simulation-Based Inference (SBI) through the AI-driven Sequential Neural Posterior Estimation (SNPE) algorithm, we conduct a large-scale Bayesian inferential analysis to identify parameter sets that faithfully reproduce experimentally observed features of ICM specification. Our results reveal mechanistic insights into how the combined action of autocrine and paracrine FGF4 signaling coordinates stochastic gene expression at the cellular scale to achieve robust and reproducible ICM patterning at the tissue scale. We further demonstrate that the ICM exhibits a specific time window of sensitivity to exogenous FGF4, enabling lineage proportions to be adjusted based on timing and dosage, thereby extending current experimental findings and providing quantitative predictions for both mutant and wild-type ICM systems. Notably, FGF4 signaling not only ensures correct EPI-PRE lineage proportions but also enhances ICM resilience to perturbations, reducing fate-proportioning errors by 10-20% compared to a purely cell-autonomous system. Additionally, we uncover a surprising role for variability in intracellular initial conditions, showing that high gene-expression heterogeneity can improve both the accuracy and precision of cell-fate proportioning, which remains robust when fewer than 25% of the ICM population experiences perturbed initial conditions. Our work offers a comprehensive, spatial-stochastic description of the biochemical processes driving ICM differentiation and identifies the necessary conditions for its robust unfolding. It also provides a framework for future exploration of similar spatial-stochastic systems in developmental biology. 

AI-powered simulation-based inference of a genuinely spatial-stochastic gene regulation model of early mouse embryogenesis

The paper assumed that Nf2-Amot complex regulates the phosphorylation cascade so that each cell in the early mammalian embryo differentiates properly in silico. To confirm the validity of the assumption, it was necessary to verify whether Nf2-Amot complex has an impact on the resulting differentiation. The living embryo is unsuitable for the confirmation since the early mammalian embryo is too small to observe and too ethically sensitive to invade. In such cases, computational models can be used as experimental subjects for operations that cannot be applied to the living embryo. Previous models on the embryo, however, could not verify the assumption because they had not modeled Nf2-Amot complex, and they seldom modeled the Hippo signaling pathway. Therefore, the paper introduced a model of Nf2-Amot complex to the previous study that had modeled the Hippo signaling pathway. Testing the model under diverse conditions revealed that the existence of Nf2-Amot complex reproduces the ideal cell differentiation observed in the living embryo. In this sense, the validity of the model was confirmed. Furthermore, diverse cell-cell contacts that induce various concentrations of Nf2-Amot complex also resulted in ideal cell differentiation. These results suggested the correctness of the assumption in silico.

An Assumption of The Regulatory Function of Nf2-Amot Complex in Early Mammalian Embryos with A Computational Model

In the preimplantation mammalian embryo, stochastic cell-to-cell expression heterogeneity is followed by signal reinforcement to initiate the specification of Inner Cell Mass (ICM) cells into Epiblast (Epi). The expression of NANOG, the key transcription factor for the Epi fate, is necessary but not sufficient: coincident expression of other factors is required. To identify possible Nanog-helper genes, we analyzed gene expression variability in five time-stamped single-cell transcriptomic datasets using differential entropy, a quantitative measure of cell-to-cell heterogeneity. The entropy of Nanog displays a peak-shaped temporal pattern from the 16-cell to the 64-cell stage, consistent with its key role in Epi specification. By estimating the entropy profiles of the 21 genes common to all five datasets, we identified three genes - Pecam1, Sox2, and Hnf4a - whose variability in expression patterns mirrors that of Nanog. We further performed gene regulatory network inference using CARDAMOM, an algorithm that exploits temporal dynamics and transcriptional bursting. The results revealed that these three genes exhibit reciprocal activation with Nanog at the 32-cell stage. This regulatory motif reinforces fate-switching decisions and co-expression states. Our innovative analysis of single-cell transcriptomic data thus uncovers a likely role for Pecam1, Sox2, and Hnf4a as key genes that, when coincidentally expressed with Nanog, initiate ICM differentiation.

Uncovering candidate Nanog-Helper genes in early mouse embryo differentiation using differential entropy and network inference

Role of tristability in the robustness of the differentiation mechanism

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Initial source of heterogeneity in a model for cell fate decision in the early mammalian embryo

Uncovering candidate Nanog-Helper genes in early mouse embryo differentiation using differential entropy and network inference

Role of tristability in the robustness of the differentiation mechanism