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

Fokker-Planck diffusion maps of microglial transcriptomes reveal radial differentiation into substates associated with Alzheimer's pathology

The identification of microglia subtypes is important for understanding the role of innate immunity in neurodegenerative diseases. Current methods of unsupervised cell type identification assume a small noise-to-signal ratio of transcriptome measurements to produce well-separated cell clusters. However, identification of subtypes can be obscured by gene expression noise, which diminishes the distances in transcriptome space between distinct cell types, blurs boundaries, and reduces reproducibility. Here we use Fokker-Planck (FP) diffusion maps to model cellular differentiation as a stochastic process whereby cells settle into local minima that correspond to cell subtypes, in a potential landscape constructed from transcriptome data using a nearest neighbor graph approach. By applying critical transition fields, we identify individual cells on the verge of transitioning between subtypes, revealing microglial cells in an inactivated, homeostatic state before radially transitioning into various specialized subtypes. Specifically, we show that cells from Alzheimer's disease patients are enriched in a microglia subtype associated to antigen presentation and T-cell recruitment, and are depleted in an anti-inflammatory subtype.

Inference of a three-gene network underpinning epidermal stem cell development in Caenorhabditis elegans

Gene regulatory networks are crucial in cellular decision-making, making the inference of their architecture essential for understanding organismal development. The gene network of Caenorhabditis elegans epidermal stem cells, known as seam cells, remains undefined. Here, we integrate experimental data, mathematical modeling, and statistical inference to investigate this network, focusing on three core transcription factors (TFs), namely ELT-1, EGL-18, and CEH-16. We use single-molecule FISH to quantify TF mRNA levels in single seam cells of wild-type and mutant backgrounds across four early larval stages. Using Modular Response Analysis, we predict TF interactions and uncover a repressive interaction between CEH-16 and egl-18 consistent across time points. We validate its significance at the L1 stage with ordinary differential equations and Bayesian modeling, making testable predictions for a double mutant. Our findings reveal TF regulatory relationships in seam cells and demonstrate a flexible mathematical framework for inferring gene regulatory networks from gene expression data.

Direct Neural Reprogramming in situ: Existing Approaches and Their Optimization

Direct in situ neuronal reprogramming (transdifferentiation) of glial cells (astrocytes and microglia) has attracted a significant interest as a potential approach for the treatment of a wide range of neurodegenerative diseases and damages of the central nervous system (CNS). The nervous system of higher mammals has a very limited capacity for repair. Disruption of CNS functioning due to traumatic injuries or neurodegenerative processes can significantly affect the quality of patients' life, lead to motor and cognitive impairments, and result in disability and, in some cases, death. Restoration of lost neurons in situ via direct reprogramming of glial cells without the intermediate stage of pluripotency seems to be the most attractive approach from the viewpoint of translational biomedicine. The ability of astroglia to actively proliferate in response to the damage of neural tissue supports the idea that these neuron-like cells, which are already present at the lesion site, are good candidates for transdifferentiation into neurons, considering that the possibility of direct neuronal reprogramming of astrocytes both in vitro and in vivo have demonstrated in many independent studies. Overexpression of proneuronal transcription factors, e.g., neurogenic differentiation factors 1-4 (NeuroD1-4), Neurogenin 2 (NeuroG2), Ascl1 (Achaete-Scute homolog 1), and Dlx2 (distal-less homeobox 2), including pioneer transcription factors that recognize target sequences in the compacted chromatin and activate transcription of silent genes, has already been proven as a potential therapeutic strategy. Other strategies, such as microRNA-mediated suppression of activity of PTB and REST transcription factors and application of small molecules or various biomaterials, are also utilized in neuronal reprogramming. However, the efficiency of direct in situ reprogramming is limited by a number of factors, including cell specificity of transgene delivery systems and promoters, brain regions in which transdifferentiation occurs, factors affecting cell metabolism, microenvironment, etc. Reprogramming in situ, which takes place in the presence of a large number of different cell types, requires monitoring and precise phenotypic characterization of subpopulations of cells undergoing transdifferentiation in order to confirm the reprogramming of the astroglia into neurons and subsequent integration of these neurons into the CNS. Here, we discussed the most efficient strategies of neuronal reprogramming and technologies used to visualize the transdifferentiation process, with special focus on the obstacles to efficient neuronal conversion, as well as approaches to overcome them.

Should Artificial Intelligence Play a Durable Role in Biomedical Research and Practice?

During the last decade, artificial intelligence (AI) was applied to nearly all domains of human activity, including scientific research. It is thus warranted to ask whether AI thinking should be durably involved in biomedical research. This problem was addressed by examining three complementary questions (i) What are the major barriers currently met by biomedical investigators? It is suggested that during the last 2 decades there was a shift towards a growing need to elucidate complex systems, and that this was not sufficiently fulfilled by previously successful methods such as theoretical modeling or computer simulation (ii) What is the potential of AI to meet the aforementioned need? it is suggested that recent AI methods are well-suited to perform classification and prediction tasks on multivariate systems, and possibly help in data interpretation, provided their efficiency is properly validated. (iii) Recent representative results obtained with machine learning suggest that AI efficiency may be comparable to that displayed by human operators. It is concluded that AI should durably play an important role in biomedical practice. Also, as already suggested in other scientific domains such as physics, combining AI with conventional methods might generate further progress and new applications, involving heuristic and data interpretation.

Transition paths across the EMT landscape are dictated by network logic

During development and cancer metastasis, cells transition reversibly from epithelial to mesenchymal via intermediate cell states during epithelial-mesenchymal transition (EMT). EMT is controlled by gene regulatory networks (GRNs) and can be described by a three-node GRN that permits tristable EMT landscapes. In this GRN, multiple inputs regulate the transcription factor ZEB that induces EMT. It is unknown how to choose the network logic for such regulation. Here we explore the effects of network logic on a tristable EMT network. We discover that the choice of additive vs multiplicative logic affects EMT phenotypes, leading to opposing predictions regarding the factors controlling EMT transition paths. We show that strong inhibition of miR-200 destabilizes the epithelial state and initiates EMT for multiplicative (AND) but not additive (OR) logic, suggesting that AND logic is in better agreement with experimental measurements of the effects of miR-200 regulation on EMT. Using experimental single-cell data, stochastic simulations, and perturbation analysis, we demonstrate how our results can be used to design experiments to infer the network logic of an EMT GRN in live cells. Our results explain how the manipulation of molecular interactions can stabilize or destabilize EMT hybrid states, of relevance during cancer progression and metastasis. More generally, we highlight the importance of the choice of network logic in GRN models in the presence of biological noise and multistability.

Statistical inference with a manifold-constrained RNA velocity model uncovers cell cycle speed modulations

Across biological systems, cells undergo coordinated changes in gene expression, resulting in transcriptome dynamics that unfold within a low-dimensional manifold. While low-dimensional dynamics can be extracted using RNA velocity, these algorithms can be fragile and rely on heuristics lacking statistical control. Moreover, the estimated vector field is not dynamically consistent with the traversed gene expression manifold. To address these challenges, we introduce a Bayesian model of RNA velocity that couples velocity field and manifold estimation in a reformulated, unified framework, identifying the parameters of an explicit dynamical system. Focusing on the cell cycle, we implement VeloCycle to study gene regulation dynamics on one-dimensional periodic manifolds and validate its ability to infer cell cycle periods using live imaging. We also apply VeloCycle to reveal speed differences in regionally defined progenitors and Perturb-seq gene knockdowns. Overall, VeloCycle expands the single-cell RNA sequencing analysis toolkit with a modular and statistically consistent RNA velocity inference framework.

Inertial effect of cell state velocity on the quiescence-proliferation fate decision

Energy landscapes can provide intuitive depictions of population heterogeneity and dynamics. However, it is unclear whether individual cell behavior, hypothesized to be determined by initial position and noise, is faithfully recapitulated. Using the p21-/Cdk2-dependent quiescence-proliferation decision in breast cancer dormancy as a testbed, we examined single-cell dynamics on the landscape when perturbed by hypoxia, a dormancy-inducing stress. Combining trajectory-based energy landscape generation with single-cell time-lapse microscopy, we found that a combination of initial position and velocity on a p21/Cdk2 landscape, but not position alone, was required to explain the observed cell fate heterogeneity under hypoxia. This is likely due to additional cell state information such as epigenetic features and/or other species encoded in velocity but missing in instantaneous position determined by p21 and Cdk2 levels alone. Here, velocity dependence manifested as inertia: cells with higher cell cycle velocities prior to hypoxia continued progressing along the cell cycle under hypoxia, resisting the change in landscape towards cell cycle exit. Such inertial effects may markedly influence cell fate trajectories in tumors and other dynamically changing microenvironments where cell state transitions are governed by coordination across several biochemical species.

EnhancerNet: a predictive model of cell identity dynamics through enhancer selection

Understanding how cell identity is encoded by the genome and acquired during differentiation is a central challenge in cell biology. I have developed a theoretical framework called EnhancerNet, which models the regulation of cell identity through the lens of transcription factor-enhancer interactions. I demonstrate that autoregulation in these interactions imposes a constraint on the model, resulting in simplified dynamics that can be parameterized from observed cell identities. Despite its simplicity, EnhancerNet recapitulates a broad range of experimental observations on cell identity dynamics, including enhancer selection, cell fate induction, hierarchical differentiation through multipotent progenitor states and direct reprogramming by transcription factor overexpression. The model makes specific quantitative predictions, reproducing known reprogramming recipes and the complex haematopoietic differentiation hierarchy without fitting unobserved parameters. EnhancerNet provides insights into how new cell types could evolve and highlights the functional importance of distal regulatory elements with dynamic chromatin in multicellular evolution.

Nonreciprocal synchronization in embryonic oscillator ensembles

Synchronization of coupled oscillators is a universal phenomenon encountered across different scales and contexts, e.g., chemical wave patterns, superconductors, and the unison applause we witness in concert halls. The existence of common underlying coupling rules defines universality classes, revealing a fundamental sameness between seemingly distinct systems. Identifying rules of synchronization in any particular setting is hence of paramount relevance. Here, we address the coupling rules within an embryonic oscillator ensemble linked to vertebrate embryo body axis segmentation. In vertebrates, the periodic segmentation of the body axis involves synchronized signaling oscillations in cells within the presomitic mesoderm (PSM), from which somites, the prevertebrae, form. At the molecular level, it is known that intact Notch-signaling and cell-to-cell contact are required for synchronization between PSM cells. However, an understanding of the coupling rules is still lacking. To identify these, we develop an experimental assay that enables direct quantification of synchronization dynamics within mixtures of oscillating cell ensembles, for which the initial input frequency and phase distribution are known. Our results reveal a "winner-takes-it-all" synchronization outcome, i.e., the emerging collective rhythm matches one of the input rhythms. Using a combination of theory and experimental validation, we develop a coupling model, the "Rectified Kuramoto" (ReKu) model, characterized by a phase-dependent, nonreciprocal interaction in the coupling of oscillatory cells. Such nonreciprocal synchronization rules reveal fundamental similarities between embryonic oscillators and a class of collective behaviors seen in neurons and fireflies, where higher-level computations are performed and linked to nonreciprocal synchronization.

TrajectoryGeometry suggests cell fate decisions can involve branches rather than bifurcations

Differentiation of multipotential progenitor cells is a key process in the development of any multi-cellular organism and often continues throughout its life. It is often assumed that a bi-potential progenitor develops along a (relatively) straight trajectory until it reaches a decision point where the trajectory bifurcates. At this point one of two directions is chosen, each direction representing the unfolding of a new transcriptional programme. However, we have lacked quantitative means for testing this model. Accordingly, we have developed the R package TrajectoryGeometry. Applying this to published data we find several examples where, rather than bifurcate, developmental pathways branch. That is, the bipotential progenitor develops along a relatively straight trajectory leading to one of its potential fates. A second relatively straight trajectory branches off from this towards the other potential fate. In this sense only cells that branch off to follow the second trajectory make a 'decision'. Our methods give precise descriptions of the genes and cellular pathways involved in these trajectories. We speculate that branching may be the more common behaviour and may have advantages from a control-theoretic viewpoint.

Fokker-Planck diffusion maps of multiple single cell microglial transcriptomes reveals radial differentiation into substates associated with Alzheimer's pathology

The identification of microglia subtypes is important for understanding the role of innate immunity in neurodegenerative diseases. Current methods of unsupervised cell type identification assume a small noise-to-signal ratio of transcriptome measurements that would produce well-separated cell clusters. However, identification of subtypes is obscured by gene expression noise, diminishing the distances in transcriptome space between distinct cell types and blurring boundaries. Here we use Fokker-Planck (FP) diffusion maps to model cellular differentiation as a stochastic process whereby cells settle into local minima, corresponding to cell subtypes, in a potential landscape constructed from transcriptome data using a nearest neighbor graph approach. By applying critical transition fields, we identify individual cells on the verge of transitioning between subtypes, revealing microglial cells in inactivated, homeostatic state before radially transitioning into various specialized subtypes. Specifically, we show that cells from Alzheimer's disease patients are enriched in a microglia subtype associated to antigen presentation and T-cell recruitment.

Establishing a conceptual framework for holistic cell states and state transitions

Cell states were traditionally defined by how they looked, where they were located, and what functions they performed. In this post-genomic era, the field is largely focused on a molecular view of cell state. Moving forward, we anticipate that the observables used to define cell states will evolve again as single-cell imaging and analytics are advancing at a breakneck pace via the collection of large-scale, systematic cell image datasets and the application of quantitative image-based data science methods. This is, therefore, a key moment in the arc of cell biological research to develop approaches that integrate the spatiotemporal observables of the physical structure and organization of the cell with molecular observables toward the concept of a holistic cell state. In this perspective, we propose a conceptual framework for holistic cell states and state transitions that is data-driven, practical, and useful to enable integrative analyses and modeling across many data types.

Combinatorial interpretation of BMP and WNT controls the decision between primitive streak and extraembryonic fates

BMP signaling is essential for mammalian gastrulation, as it initiates a cascade of signals that control self-organized patterning. As development is highly dynamic, it is crucial to understand how time-dependent combinatorial signaling affects cellular differentiation. Here, we show that BMP signaling duration is a crucial control parameter that determines cell fates upon the exit from pluripotency through its interplay with the induced secondary signal WNT. BMP signaling directly converts cells from pluripotent to extraembryonic fates while simultaneously upregulating Wnt signaling, which promotes primitive streak and mesodermal specification. Using live-cell imaging of signaling and cell fate reporters together with a simple mathematical model, we show that this circuit produces a temporal morphogen effect where, once BMP signal duration is above a threshold for differentiation, intermediate and long pulses of BMP signaling produce specification of mesoderm and extraembryonic fates, respectively. Our results provide a systems-level picture of how these signaling pathways control the landscape of early human development.

Unveiling the Dynamics behind Glioblastoma Multiforme Single-Cell Data Heterogeneity

Glioblastoma Multiforme is a brain tumor distinguished by its aggressiveness. We suggested that this aggressiveness leads single-cell RNA-sequence data (scRNA-seq) to span a representative portion of the cancer attractors domain. This conjecture allowed us to interpret the scRNA-seq heterogeneity as reflecting a representative trajectory within the attractor's domain. We considered factors such as genomic instability to characterize the cancer dynamics through stochastic fixed points. The fixed points were derived from centroids obtained through various clustering methods to verify our method sensitivity. This methodological foundation is based upon sample and time average equivalence, assigning an interpretative value to the data cluster centroids and supporting parameters estimation. We used stochastic simulations to reproduce the dynamics, and our results showed an alignment between experimental and simulated dataset centroids. We also computed the Waddington landscape, which provided a visual framework for validating the centroids and standard deviations as characterizations of cancer attractors. Additionally, we examined the stability and transitions between attractors and revealed a potential interplay between subtypes. These transitions might be related to cancer recurrence and progression, connecting the molecular mechanisms of cancer heterogeneity with statistical properties of gene expression dynamics. Our work advances the modeling of gene expression dynamics and paves the way for personalized therapeutic interventions.

A logic-incorporated gene regulatory network deciphers principles in cell fate decisions

Organisms utilize gene regulatory networks (GRN) to make fate decisions, but the regulatory mechanisms of transcription factors (TF) in GRNs are exceedingly intricate. A longstanding question in this field is how these tangled interactions synergistically contribute to decision-making procedures. To comprehensively understand the role of regulatory logic in cell fate decisions, we constructed a logic-incorporated GRN model and examined its behavior under two distinct driving forces (noise-driven and signal-driven). Under the noise-driven mode, we distilled the relationship among fate bias, regulatory logic, and noise profile. Under the signal-driven mode, we bridged regulatory logic and progression-accuracy trade-off, and uncovered distinctive trajectories of reprogramming influenced by logic motifs. In differentiation, we characterized a special logic-dependent priming stage by the solution landscape. Finally, we applied our findings to decipher three biological instances: hematopoiesis, embryogenesis, and trans-differentiation. Orthogonal to the classical analysis of expression profile, we harnessed noise patterns to construct the GRN corresponding to fate transition. Our work presents a generalizable framework for top-down fate-decision studies and a practical approach to the taxonomy of cell fate decisions.

A dynamical perspective: moving towards mechanism in single-cell transcriptomics

As the field of single-cell transcriptomics matures, research is shifting focus from phenomenological descriptions of cellular phenotypes to a mechanistic understanding of the gene regulation underneath. This perspective considers the value of capturing dynamical information at single-cell resolution for gaining mechanistic insight; reviews the available technologies for recording and inferring temporal information in single cells; and explores whether better dynamical resolution is sufficient to adequately capture the causal relationships driving complex biological systems. This article is part of a discussion meeting issue 'Causes and consequences of stochastic processes in development and disease'.

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.

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

Extended culture of 2D gastruloids to model human mesoderm development

Micropatterned human pluripotent stem cells (hPSCs) treated with BMP4 (2D gastruloids) are among the most widely used stem cell models for human gastrulation. Due to its simplicity and reproducibility, this system is ideal for high throughput quantitative studies of tissue patterning and has led to many insights into the mechanisms of mammalian gastrulation. However, 2D gastruloids have only been studied up to 48h. Here we extended this system to 96h. We discovered a phase of highly reproducible morphogenesis during which directed migration from the primitive streak-like region gives rise to a mesodermal layer beneath an epiblast-like layer. Multiple types of mesoderm arise with striking spatial organization including lateral mesoderm-like cells on the colony border and paraxial mesoderm-like further inside the colony. Single cell transcriptomics showed strong similarity of these cells to mesoderm in human and non-human primate embryos. However, our data suggest that the annotation of the reference human embryo may need to be revised. This illustrates that extended culture of 2D gastruloids provides a powerful model for human mesoderm differentiation and morphogenesis.

A neural network-based model framework for cell-fate decisions and development

Gene regulatory networks (GRNs) fulfill the essential function of maintaining the stability of cellular differentiation states by sustaining lineage-specific gene expression, while driving the progression of development. However, accounting for the relative stability of intermediate differentiation stages and their divergent trajectories remains a major challenge for models of developmental biology. Here, we develop an empirical data-based associative GRN model (AGRN) in which regulatory networks store multilineage stage-specific gene expression profiles as associative memory patterns. These networks are capable of responding to multiple instructive signals and, depending on signal timing and identity, can dynamically drive the differentiation of multipotent cells toward different cell state attractors. The AGRN dynamics can thus generate diverse lineage-committed cell populations in a robust yet flexible manner, providing an attractor-based explanation for signal-driven cell fate decisions during differentiation and offering a readily generalizable modelling tool that can be applied to a wide variety of cell specification systems.

Charting cellular differentiation trajectories with Ricci flow

Complex biological processes, such as cellular differentiation, require intricate rewiring of intra-cellular signalling networks. Previous characterisations revealed a raised network entropy underlies less differentiated and malignant cell states. A connection between entropy and Ricci curvature led to applications of discrete curvatures to biological networks. However, predicting dynamic biological network rewiring remains an open problem. Here we apply Ricci curvature and Ricci flow to biological network rewiring. By investigating the relationship between network entropy and Forman-Ricci curvature, theoretically and empirically on single-cell RNA-sequencing data, we demonstrate that the two measures do not always positively correlate, as previously suggested, and provide complementary rather than interchangeable information. We next employ Ricci flow to derive network rewiring trajectories from stem cells to differentiated cells, accurately predicting true intermediate time points in gene expression time courses. In summary, we present a differential geometry toolkit for understanding dynamic network rewiring during cellular differentiation and cancer.

Inference of differentiation trajectories by transfer learning across biological processes

Stem cells differentiate into distinct fates by transitioning through a series of transcriptional states. Current computational approaches allow reconstruction of differentiation trajectories from single-cell transcriptomics data, but it remains unknown to what degree differentiation can be predicted across biological processes. Here, we use transfer learning to infer differentiation processes and quantify predictability in early embryonic development and adult hematopoiesis. Overall, we find that non-linear methods outperform linear approaches, and we achieved the best predictions with a custom variational autoencoder that explicitly models changes in transcriptional variance. We observed a high accuracy of predictions in embryonic development, but we found somewhat lower agreement with the real data in adult hematopoiesis. We demonstrate that this discrepancy can be explained by a higher degree of concordant transcriptional processes along embryonic differentiation compared with adult homeostasis. In summary, we establish a framework for quantifying and exploiting predictability of cellular differentiation trajectories.

Quantitative Modelling in Stem Cell Biology and Beyond: How to Make Best Use of It

Purpose of Review

This article gives a broad overview of quantitative modelling approaches in biology and provides guidance on how to employ them to boost stem cell research, by helping to answer biological questions and to predict the outcome of biological processes.

Recent Findings

The twenty-first century has seen a steady increase in the proportion of cell biology publications employing mathematical modelling to aid experimental research. However, quantitative modelling is often used as a rather decorative element to confirm experimental findings, an approach which often yields only marginal added value, and is in many cases scientifically questionable.

Summary

Quantitative modelling can boost biological research in manifold ways, but one has to take some careful considerations before embarking on a modelling campaign, in order to maximise its added value, to avoid pitfalls that may lead to wrong results, and to be aware of its fundamental limitations, imposed by the risks of over-fitting and "universality".

From signalling to form: the coordination of neural tube patterning

The development of the vertebrate spinal cord involves the formation of the neural tube and the generation of multiple distinct cell types. The process starts during gastrulation, combining axial elongation with specification of neural cells and the formation of the neuroepithelium. Tissue movements produce the neural tube which is then exposed to signals that provide patterning information to neural progenitors. The intracellular response to these signals, via a gene regulatory network, governs the spatial and temporal differentiation of progenitors into specific cell types, facilitating the assembly of functional neuronal circuits. The interplay between the gene regulatory network, cell movement, and tissue mechanics generates the conserved neural tube pattern observed across species. In this review we offer an overview of the molecular and cellular processes governing the formation and patterning of the neural tube, highlighting how the remarkable complexity and precision of vertebrate nervous system arises. We argue that a multidisciplinary and multiscale understanding of the neural tube development, paired with the study of species-specific strategies, will be crucial to tackle the open questions.

Collective signalling drives rapid jumping between cell states

Development can proceed in 'fits and starts', with rapid transitions between cell states involving concerted transcriptome-wide changes in gene expression. However, it is not clear how these transitions are regulated in complex cell populations, in which cells receive multiple inputs. We address this issue using Dictyostelium cells undergoing development in their physiological niche. A continuous single cell transcriptomics time series identifies a sharp 'jump' in global gene expression marking functionally different cell states. By simultaneously imaging the physiological dynamics of transcription and signalling, we show the jump coincides with the onset of collective oscillations of cAMP. Optogenetic control of cAMP pulses shows that different jump genes respond to distinct dynamic features of signalling. Late jump gene expression changes are almost completely dependent on cAMP, whereas transcript changes at the onset of the jump require additional input. The coupling of collective signalling with gene expression is a potentially powerful strategy to drive robust cell state transitions in heterogeneous signalling environments. Based on the context of the jump, we also conclude that sharp gene expression transitions may not be sufficient for commitment.

Optimal control of gene regulatory networks for morphogen-driven tissue patterning

The generation of distinct cell types in developing tissues depends on establishing spatial patterns of gene expression. Often, this is directed by spatially graded chemical signals-known as morphogens. In the "French Flag model," morphogen concentration instructs cells to acquire specific fates. How this mechanism produces timely and organized cell-fate decisions, despite the presence of changing morphogen levels, molecular noise, and individual variability, is unclear. Moreover, feedback is present at various levels in developing tissues, breaking the link between morphogen concentration, signaling activity, and position. Here, we develop an alternative framework using optimal control theory to tackle the problem of morphogen-driven patterning: intracellular signaling is derived as the control strategy that guides cells to the correct fate while minimizing a combination of signaling levels and time. This approach recovers experimentally observed properties of patterning strategies and offers insight into design principles that produce timely, precise, and reproducible morphogen patterning.

A two-galectin network establishes mesenchymal condensation phenotype in limb development

Previous work showed that Gal-1A and Gal-8, two proteins belonging to the galactoside-binding galectin family, are the earliest determinants of the patterning of the skeletal elements of embryonic chicken limbs, and further, that their experimentally determined interactions in the embryonic limb bud can be interpreted via a reaction-diffusion-adhesion (2GL: two galectin plus ligands) model. Here, we use an ordinary differential equation-based approach to analyze the intrinsic switching modality of the 2GL network and characterize the network behavior independent of the diffusive and adhesive arms of the patterning mechanism. We identify two states: where the concentrations of both the galectins are respectively, negligible, and very high. This bistable switch-like system arises via a saddle-node bifurcation from a monostable state. For the case of mass-action production terms, we provide an explicit Lyapunov function for the system, which shows that it has no periodic solutions. Our model therefore predicts that the galectin network may exist in low expression and high expression states separated in space or time, without any intermediate states. We test these predictions in experiments performed with high density cultures of chick limb mesenchymal cells and observe that cells inside precartilage protocondensations express Gal-1A at a much higher rate than those outside, for which it was negligible. The Gal-1A and -8-based patterning network is therefore sufficient to partition the mesenchymal cell population into two discrete cell states with different developmental (chondrogenic vs. non-chondrogenic) fates. When incorporated into an adhesion and diffusion-enabled framework this system can generate a spatially patterned limb skeleton.

A bistable autoregulatory module in the developing embryo commits cells to binary expression fates

Bistable autoactivation has been proposed as a mechanism for cells to adopt binary fates during embryonic development. However, it is unclear whether the autoactivating modules found within developmental gene regulatory networks are bistable, unless their parameters are quantitatively determined. Here, we combine in vivo live imaging with mathematical modeling to dissect the binary cell fate dynamics of the fruit fly pair-rule gene fushi tarazu (ftz), which is regulated by two known enhancers: the early (non-autoregulating) element and the autoregulatory element. Live imaging of transcription and protein concentration in the blastoderm revealed that binary Ftz fates are achieved as Ftz expression rapidly transitions from being dictated by the early element to the autoregulatory element. Moreover, we discovered that Ftz concentration alone is insufficient to activate the autoregulatory element, and that this element only becomes responsive to Ftz at a prescribed developmental time. Based on these observations, we developed a dynamical systems model and quantitated its kinetic parameters directly from experimental measurements. Our model demonstrated that the ftz autoregulatory module is indeed bistable and that the early element transiently establishes the content of the binary cell fate decision to which the autoregulatory module then commits. Further in silico analysis revealed that the autoregulatory element locks the Ftz fate quickly, within 35 min of exposure to the transient signal of the early element. Overall, our work confirms the widely held hypothesis that autoregulation can establish developmental fates through bistability and, most importantly, provides a framework for the quantitative dissection of cellular decision-making.

Single-cell transcriptional uncertainty landscape of cell differentiation

Background: Single-cell studies have demonstrated the presence of significant cell-to-cell heterogeneity in gene expression. Whether such heterogeneity is only a bystander or has a functional role in the cell differentiation process is still hotly debated. Methods: In this study, we quantified and followed single-cell transcriptional uncertainty - a measure of gene transcriptional stochasticity in single cells - in 10 cell differentiation systems of varying cell lineage progressions, from single to multi-branching trajectories, using the stochastic two-state gene transcription model. Results: By visualizing the transcriptional uncertainty as a landscape over a two-dimensional representation of the single-cell gene expression data, we observed universal features in the cell differentiation trajectories that include: (i) a peak in single-cell uncertainty during transition states, and in systems with bifurcating differentiation trajectories, each branching point represents a state of high transcriptional uncertainty; (ii) a positive correlation of transcriptional uncertainty with transcriptional burst size and frequency; (iii) an increase in RNA velocity preceding the increase in the cell transcriptional uncertainty. Conclusions: Our findings suggest a possible universal mechanism during the cell differentiation process, in which stem cells engage stochastic exploratory dynamics of gene expression at the start of the cell differentiation by increasing gene transcriptional bursts, and disengage such dynamics once cells have decided on a particular terminal cell identity. Notably, the peak of single-cell transcriptional uncertainty signifies the decision-making point in the cell differentiation process.

Inertial effect of cell state velocity on the quiescence-proliferation fate decision in breast cancer

Energy landscapes can provide intuitive depictions of population heterogeneity and dynamics. However, it is unclear whether individual cell behavior, hypothesized to be determined by initial position and noise, is faithfully recapitulated. Using the p21-/Cdk2-dependent quiescence-proliferation decision in breast cancer dormancy as a testbed, we examined single-cell dynamics on the landscape when perturbed by hypoxia, a dormancy-inducing stress. Combining trajectory-based energy landscape generation with single-cell time-lapse microscopy, we found that initial position on a p21/Cdk2 landscape did not fully explain the observed cell-fate heterogeneity under hypoxia. Instead, cells with higher cell state velocities prior to hypoxia, influenced by epigenetic parameters, tended to remain proliferative under hypoxia. Thus, the fate decision on this landscape is significantly influenced by "inertia", a velocity-dependent ability to resist directional changes despite reshaping of the underlying landscape, superseding positional effects. Such inertial effects may markedly influence cell-fate trajectories in tumors and other dynamically changing microenvironments.

Predicting anti-cancer drug combination responses with a temporal cell state network model

Cancer chemotherapy combines multiple drugs, but predicting the effects of drug combinations on cancer cell proliferation remains challenging, even for simple in vitro systems. We hypothesized that by combining knowledge of single drug dose responses and cell state transition network dynamics, we could predict how a population of cancer cells will respond to drug combinations. We tested this hypothesis here using three targeted inhibitors of different cell cycle states in two different cell lines in vitro. We formulated a Markov model to capture temporal cell state transitions between different cell cycle phases, with single drug data constraining how drug doses affect transition rates. This model was able to predict the landscape of all three different pairwise drug combinations across all dose ranges for both cell lines with no additional data. While further application to different cell lines, more drugs, additional cell state networks, and more complex co-culture or in vivo systems remain, this work demonstrates how currently available or attainable information could be sufficient for prediction of drug combination response for single cell lines in vitro.

Ratiometric sensing of Pnt and Yan transcription factor levels confers ultrasensitivity to photoreceptor fate transitions in Drosophila

Cell state transitions are often triggered by large changes in the concentrations of transcription factors and therefore large differences in their stoichiometric ratios. Whether cells can elicit transitions using modest changes in the ratios of co-expressed factors is unclear. Here, we investigate how cells in the Drosophila eye resolve state transitions by quantifying the expression dynamics of the ETS transcription factors Pnt and Yan. Eye progenitor cells maintain a relatively constant ratio of Pnt/Yan protein, despite expressing both proteins with pulsatile dynamics. A rapid and sustained twofold increase in the Pnt/Yan ratio accompanies transitions to photoreceptor fates. Genetic perturbations that modestly disrupt the Pnt/Yan ratio produce fate transition defects consistent with the hypothesis that transitions are normally driven by a twofold shift in the ratio. A biophysical model based on cooperative Yan-DNA binding coupled with non-cooperative Pnt-DNA binding illustrates how twofold ratio changes could generate ultrasensitive changes in target gene transcription to drive fate transitions. Thus, coupling cell state transitions to the Pnt/Yan ratio sensitizes the system to modest fold-changes, conferring robustness and ultrasensitivity to the developmental program.

Cell state transitions: catch them if you can

The Company of Biologists' 2022 workshop on 'Cell State Transitions: Approaches, Experimental Systems and Models' brought together an international and interdisciplinary team of investigators spanning the fields of cell and developmental biology, stem cell biology, physics, mathematics and engineering to tackle the question of how cells precisely navigate between distinct identities and do so in a dynamic manner. This second edition of the workshop was organized after a successful virtual workshop on the same topic that took place in 2021.

Universal dynamics of biological pattern formation in spatio-temporal morphogen variations

In biological systems, chemical signals termed morphogens self-organize into patterns that are vital for many physiological processes. As observed by Turing in 1952, these patterns are in a state of continual development, and are usually transitioning from one pattern into another. How do cells robustly decode these spatio-temporal patterns into signals in the presence of confounding effects caused by unpredictable or heterogeneous environments? Here, we answer this question by developing a general theory of pattern formation in spatio-temporal variations of ‘pre-pattern’ morphogens, which determine gene-regulatory network parameters. Through mathematical analysis, we identify universal dynamical regimes that apply to wide classes of biological systems. We apply our theory to two paradigmatic pattern-forming systems, and predict that they are robust with respect to non-physiological morphogen variations. More broadly, our theoretical framework provides a general approach to classify the emergent dynamics of pattern-forming systems based on how the bifurcations in their governing equations are traversed.

Understanding How Cells Probe the World: A Preliminary Step towards Modeling Cell Behavior?

Cell biologists have long aimed at quantitatively modeling cell function. Recently, the outstanding progress of high-throughput measurement methods and data processing tools has made this a realistic goal. The aim of this paper is twofold: First, to suggest that, while much progress has been done in modeling cell states and transitions, current accounts of environmental cues driving these transitions remain insufficient. There is a need to provide an integrated view of the biochemical, topographical and mechanical information processed by cells to take decisions. It might be rewarding in the near future to try to connect cell environmental cues to physiologically relevant outcomes rather than modeling relationships between these cues and internal signaling networks. The second aim of this paper is to review exogenous signals that are sensed by living cells and significantly influence fate decisions. Indeed, in addition to the composition of the surrounding medium, cells are highly sensitive to the properties of neighboring surfaces, including the spatial organization of anchored molecules and substrate mechanical and topographical properties. These properties should thus be included in models of cell behavior. It is also suggested that attempts at cell modeling could strongly benefit from two research lines: (i) trying to decipher the way cells encode the information they retrieve from environment analysis, and (ii) developing more standardized means of assessing the quality of proposed models, as was done in other research domains such as protein structure prediction.

Stem cell biology needs a theory

Stem cell biologists are increasingly making use of computational models to decipher their data. However, there is sometimes uncertainty about what makes a "good" model. The purpose of this commentary is to argue for closer integration of experiment and theory in stem cell research and propose guidelines for good theory.

Colour patterns: Predicting patterns without knowing the details

A bewildering array of colour patterns occurs across animals. New work studying five lizard species reveals that reaction-diffusion models can be remarkably predictive of future adult skin patterning, even though molecular details are unknown. This has implications for understanding how complex patterns evolve.

Open problems in mathematical biology

Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life- and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.

Hematopoietic and Chronic Myeloid Leukemia Stem Cells: Multi-Stability versus Lineage Restriction

There is compelling evidence to support the view that the cell-of-origin for chronic myeloid leukemia is a hematopoietic stem cell. Unlike normal hematopoietic stem cells, the progeny of the leukemia stem cells are predominantly neutrophils during the disease chronic phase and there is a mild anemia. The hallmark oncogene for chronic myeloid leukemia is the BCR-ABLp210 fusion gene. Various studies have excluded a role for BCR-ABLp210 expression in maintaining the population of leukemia stem cells. Studies of BCR-ABLp210 expression in embryonal stem cells that were differentiated into hematopoietic stem cells and of the expression in transgenic mice have revealed that BCR-ABLp210 is able to veer hematopoietic stem and progenitor cells towards a myeloid fate. For the transgenic mice, global changes to the epigenetic landscape were observed. In chronic myeloid leukemia, the ability of the leukemia stem cells to choose from the many fates that are available to normal hematopoietic stem cells appears to be deregulated by BCR-ABLp210 and changes to the epigenome are also important. Even so, we still do not have a precise picture as to why neutrophils are abundantly produced in chronic myeloid leukemia.

Landscape of epithelial-mesenchymal plasticity as an emergent property of coordinated teams in regulatory networks

Elucidating the design principles of regulatory networks driving cellular decision-making has fundamental implications in mapping and eventually controlling cell-fate decisions. Despite being complex, these regulatory networks often only give rise to a few phenotypes. Previously, we identified two 'teams' of nodes in a small cell lung cancer regulatory network that constrained the phenotypic repertoire and aligned strongly with the dominant phenotypes obtained from network simulations (Chauhan et al., 2021). However, it remained elusive whether these 'teams' exist in other networks, and how do they shape the phenotypic landscape. Here, we demonstrate that five different networks of varying sizes governing epithelial-mesenchymal plasticity comprised of two 'teams' of players - one comprised of canonical drivers of epithelial phenotype and the other containing the mesenchymal inducers. These 'teams' are specific to the topology of these regulatory networks and orchestrate a bimodal phenotypic landscape with the epithelial and mesenchymal phenotypes being more frequent and dynamically robust to perturbations, relative to the intermediary/hybrid epithelial/mesenchymal ones. Our analysis reveals that network topology alone can contain information about corresponding phenotypic distributions, thus obviating the need to simulate them. We propose 'teams' of nodes as a network design principle that can drive cell-fate canalization in diverse decision-making processes.

CELLoGeNe - An energy landscape framework for logical networks controlling cell decisions

Experimental and computational efforts are constantly made to elucidate mechanisms controlling cell fate decisions during development and reprogramming. One powerful computational method is to consider cell commitment and reprogramming as movements in an energy landscape. Here, we develop Computation of Energy Landscapes of Logical Gene Networks (CELLoGeNe), which maps Boolean implementation of gene regulatory networks (GRNs) into energy landscapes. CELLoGeNe removes inadvertent symmetries in the energy landscapes normally arising from standard Boolean operators. Furthermore, CELLoGeNe provides tools to visualize and stochastically analyze the shapes of multi-dimensional energy landscapes corresponding to epigenetic landscapes for development and reprogramming. We demonstrate CELLoGeNe on two GRNs governing different aspects of induced pluripotent stem cells, identifying experimentally validated attractors and revealing potential reprogramming roadblocks. CELLoGeNe is a general framework that can be applied to various biological systems offering a broad picture of intracellular dynamics otherwise inaccessible with existing methods.

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CELLoGeNe – Computation of Energy Landscapes of Logical Gene Networks

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Cell states as landscape attractors

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Maintenance and acquisition of cell pluripotency applications

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Single cell stochastic landscape navigation and visualization tool

Lack of Correlation between Landscape Geometry and Transition Rates

Biological cells can exist in a variety of distinct phenotypes, determined by the steady-state solutions of genetic networks governing their cell fate. A popular way of representing these states relies on the creation of landscape related to the relative occupation of these states. It is often assumed that this landscape offers direct information regarding the state-to-state transition rates, suggesting that these are related to barrier heights separating landscape minima. Here, we study a toggle triad network exhibiting multistability and directly demonstrate the lack of any direct correlation between properties of the landscape and corresponding transition rates.

Evidence for close molecular proximity between reverting and undifferentiated cells

BACKGROUND

According to Waddington's epigenetic landscape concept, the differentiation process can be illustrated by a cell akin to a ball rolling down from the top of a hill (proliferation state) and crossing furrows before stopping in basins or "attractor states" to reach its stable differentiated state. However, it is now clear that some committed cells can retain a certain degree of plasticity and reacquire phenotypical characteristics of a more pluripotent cell state. In line with this dynamic model, we have previously shown that differentiating cells (chicken erythrocytic progenitors (T2EC)) retain for 24 h the ability to self-renew when transferred back in self-renewal conditions. Despite those intriguing and promising results, the underlying molecular state of those "reverting" cells remains unexplored. The aim of the present study was therefore to molecularly characterize the T2EC reversion process by combining advanced statistical tools to make the most of single-cell transcriptomic data. For this purpose, T2EC, initially maintained in a self-renewal medium (0H), were induced to differentiate for 24H (24H differentiating cells); then, a part of these cells was transferred back to the self-renewal medium (48H reverting cells) and the other part was maintained in the differentiation medium for another 24H (48H differentiating cells). For each time point, cell transcriptomes were generated using scRT-qPCR and scRNAseq.

RESULTS

Our results showed a strong overlap between 0H and 48H reverting cells when applying dimensional reduction. Moreover, the statistical comparison of cell distributions and differential expression analysis indicated no significant differences between these two cell groups. Interestingly, gene pattern distributions highlighted that, while 48H reverting cells have gene expression pattern more similar to 0H cells, they are not completely identical, which suggest that for some genes a longer delay may be required for the cells to fully recover. Finally, sparse PLS (sparse partial least square) analysis showed that only the expression of 3 genes discriminates 48H reverting and 0H cells.

CONCLUSIONS

Altogether, we show that reverting cells return to an earlier molecular state almost identical to undifferentiated cells and demonstrate a previously undocumented physiological and molecular plasticity during the differentiation process, which most likely results from the dynamic behavior of the underlying molecular network.

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.

Reprogramming cellular identity in vivo

Cellular identity is established through complex layers of genetic regulation, forged over a developmental lifetime. An expanding molecular toolbox is allowing us to manipulate these gene regulatory networks in specific cell types in vivo. In principle, if we found the right molecular tricks, we could rewrite cell identity and harness the rich repertoire of possible cellular functions and attributes. Recent work suggests that this rewriting of cell identity is not only possible, but that newly induced cells can mitigate disease phenotypes in animal models of major human diseases. So, is the sky the limit, or do we need to keep our feet on the ground? This Spotlight synthesises key concepts emerging from recent efforts to reprogramme cellular identity in vivo. We provide our perspectives on recent controversies in the field of glia-to-neuron reprogramming and identify important gaps in our understanding that present barriers to progress.

Dissecting the Complexity of Early Heart Progenitor Cells

Early heart development depends on the coordinated participation of heterogeneous cell sources. As pioneer work from Adriana C. Gittenberger-de Groot demonstrated, characterizing these distinct cell sources helps us to understand congenital heart defects. Despite decades of research on the segregation of lineages that form the primitive heart tube, we are far from understanding its full complexity. Currently, single-cell approaches are providing an unprecedented level of detail on cellular heterogeneity, offering new opportunities to decipher its functional role. In this review, we will focus on three key aspects of early heart morphogenesis: First, the segregation of myocardial and endocardial lineages, which yields an early lineage diversification in cardiac development; second, the signaling cues driving differentiation in these progenitor cells; and third, the transcriptional heterogeneity of cardiomyocyte progenitors of the primitive heart tube. Finally, we discuss how single-cell transcriptomics and epigenomics, together with live imaging and functional analyses, will likely transform the way we delve into the complexity of cardiac development and its links with congenital defects.

Cell state transitions: definitions and challenges

A fundamental challenge when studying biological systems is the description of cell state dynamics. During transitions between cell states, a multitude of parameters may change - from the promoters that are active, to the RNAs and proteins that are expressed and modified. Cells can also adopt different shapes, alter their motility and change their reliance on cell-cell junctions or adhesion. These parameters are integral to how a cell behaves and collectively define the state a cell is in. Yet, technical challenges prevent us from measuring all of these parameters simultaneously and dynamically. How, then, can we comprehend cell state transitions using finite descriptions? The recent virtual workshop organised by The Company of Biologists entitled 'Cell State Transitions: Approaches, Experimental Systems and Models' attempted to address this question. Here, we summarise some of the main points that emerged during the workshop's themed discussions. We also present examples of cell state transitions and describe models and systems that are pushing forward our understanding of how cells rewire their state.