Inferring Cell-State Transition Dynamics from Lineage Trees and Endpoint Single-Cell Measurements

Spatial multi-omics reveals cell-type-specific nuclear compartments

The mammalian nucleus is compartmentalized by diverse subnuclear structures. These subnuclear structures, marked by nuclear bodies and histone modifications, are often cell-type specific and affect gene regulation and 3D genome organization1-3. Understanding their relationships rests on identifying the molecular constituents of subnuclear structures and mapping their associations with specific genomic loci and transcriptional levels in individual cells, all in complex tissues. Here, we introduce two-layer DNA seqFISH+, which enables simultaneous mapping of 100,049 genomic loci, together with the nascent transcriptome for 17,856 genes and subnuclear structures in single cells. These data enable imaging-based chromatin profiling of diverse subnuclear markers and can capture their changes at genomic scales ranging from 100-200 kilobases to approximately 1 megabase, depending on the marker and DNA locus. By using multi-omics datasets in the adult mouse cerebellum, we showed that repressive chromatin regions are more variable by cell type than are active regions across the genome. We also discovered that RNA polymerase II-enriched foci were locally associated with long, cell-type-specific genes (bigger than 200 kilobases) in a manner distinct from that of nuclear speckles. Furthermore, our analysis revealed that cell-type-specific regions of heterochromatin marked by histone H3 trimethylated at lysine 27 (H3K27me3) and histone H4 trimethylated at lysine 20 (H4K20me3) are enriched at specific genes and gene clusters, respectively, and shape radial chromosomal positioning and inter-chromosomal interactions in neurons and glial cells. Together, our results provide a single-cell high-resolution multi-omics view of subnuclear structures, associated genomic loci and their effects on gene regulation, directly within complex tissues.

The lives of cells, recorded

A paradigm for biology is emerging in which cells can be genetically programmed to write their histories into their own genomes. These records can subsequently be read, and the cellular histories reconstructed, which for each cell could include a record of its lineage relationships, extrinsic influences, internal states and physical locations, over time. DNA recording has the potential to transform the way that we study developmental and disease processes. Recent advances in genome engineering are driving the development of systems for DNA recording, and meanwhile single-cell and spatial omics technologies increasingly enable the recovery of the recorded information. Combined with advances in computational and phylogenetic inference algorithms, the DNA recording paradigm is beginning to bear fruit. In this Perspective, we explore the rationale and technical basis of DNA recording, what aspects of cellular biology might be recorded and how, and the types of discovery that we anticipate this paradigm will enable.

Entrainment and multi-stability of the p53 oscillator in human cells

The tumor suppressor p53 responds to cellular stress and activates transcription programs critical for regulating cell fate. DNA damage triggers oscillations in p53 levels with a robust period. Guided by the theory of synchronization and entrainment, we developed a mathematical model and experimental system to test the ability of the p53 oscillator to entrain to external drug pulses of various periods and strengths. We found that the p53 oscillator can be locked and entrained to a wide range of entrainment modes. External periods far from p53's natural oscillations increased the heterogeneity between individual cells whereas stronger inputs reduced it. Single-cell measurements allowed deriving the phase response curves (PRCs) and multiple Arnold tongues of p53. In addition, multi-stability and non-linear behaviors were mathematically predicted and experimentally detected, including mode hopping, period doubling, and chaos. Our work revealed critical dynamical properties of the p53 oscillator and provided insights into understanding and controlling it. A record of this paper's transparent peer review process is included in the supplemental information.

Defining heritability, plasticity, and transition dynamics of cellular phenotypes in somatic evolution

Single-cell sequencing has characterized cell state heterogeneity across diverse healthy and malignant tissues. However, the plasticity or heritability of these cell states remains largely unknown. To address this, we introduce PATH (phylogenetic analysis of trait heritability), a framework to quantify cell state heritability versus plasticity and infer cell state transition and proliferation dynamics from single-cell lineage tracing data. Applying PATH to a mouse model of pancreatic cancer, we observed heritability at the ends of the epithelial-to-mesenchymal transition spectrum, with higher plasticity at more intermediate states. In primary glioblastoma, we identified bidirectional transitions between stem- and mesenchymal-like cells, which use the astrocyte-like state as an intermediary. Finally, we reconstructed a phylogeny from single-cell whole-genome sequencing in B cell acute lymphoblastic leukemia and delineated the heritability of B cell differentiation states linked with genetic drivers. Altogether, PATH replaces qualitative conceptions of plasticity with quantitative measures, offering a framework to study somatic evolution.

Identification of an embryonic differentiation stage marked by Sox1 and FoxA2 co-expression using combined cell tracking and high dimensional protein imaging

Pluripotent mouse embryonic stem cells (ESCs) can differentiate to all germ layers and serve as an in vitro model of embryonic development. To better understand the differentiation paths traversed by ESCs committing to different lineages, we track individual differentiating ESCs by timelapse imaging followed by multiplexed high-dimensional Imaging Mass Cytometry (IMC) protein quantification. This links continuous live single-cell molecular NANOG and cellular dynamics quantification over 5-6 generations to protein expression of 37 different molecular regulators in the same single cells at the observation endpoints. Using this unique data set including kinship history and live lineage marker detection, we show that NANOG downregulation occurs generations prior to, but is not sufficient for neuroectoderm marker Sox1 upregulation. We identify a developmental cell type co-expressing both the canonical Sox1 neuroectoderm and FoxA2 endoderm markers in vitro and confirm the presence of such a population in the post-implantation embryo. RNASeq reveals cells co-expressing SOX1 and FOXA2 to have a unique cell state characterized by expression of both endoderm as well as neuroectoderm genes suggesting lineage potential towards both germ layers.

Dissecting reversible and irreversible single cell state transitions from gene regulatory networks

Understanding cell state transitions and their governing regulatory mechanisms remains one of the fundamental questions in biology. We develop a computational method, state transition inference using cross-cell correlations (STICCC), for predicting reversible and irreversible cell state transitions at single-cell resolution by using gene expression data and a set of gene regulatory interactions. The method is inspired by the fact that the gene expression time delays between regulators and targets can be exploited to infer past and future gene expression states. From applications to both simulated and experimental single-cell gene expression data, we show that STICCC-inferred vector fields capture basins of attraction and irreversible fluxes. By connecting regulatory information with systems' dynamical behaviors, STICCC reveals how network interactions influence reversible and irreversible state transitions. Compared to existing methods that infer pseudotime and RNA velocity, STICCC provides complementary insights into the gene regulation of cell state transitions.

Deciphering cellular heterogeneity in Spodoptera frugiperda midgut cell line through single cell RNA sequencing

Using the 10x Genomics Chromium single-cell RNA sequencing (scRNA-seq) platform, we discovered unexpected heterogeneity in an established cell line developed from the midgut of the Fall armyworm, Spodoptera frugiperda, a major global pest. We analyzed the sequences of 18,794 cells and identified ten unique cellular clusters, including stem cells, enteroblasts, enterocytes and enteroendocrine cells, characterized by the expression of specific marker genes. Additionally, these studies addressed an important knowledge gap by investigating the expression of genes coding for respiratory and midgut membrane insecticide targets classified by the Insecticide Resistance Action Committee. Dual-fluorescence tagging method, fluorescence microscopy and fluorescence-activated cell sorting confirmed the expression of midgut cell type-specific genes. Stem cells were isolated from the heterogeneous population of SfMG-0617 cells. Our results, validated by KEGG and Gene Ontology analyses and supported by Monocle 3.0, advance the fields of midgut cellular biology and establish standards for scRNA-seq studies in non-model organisms.

BANMF-S: a blockwise accelerated non-negative matrix factorization framework with structural network constraints for single cell imputation

MOTIVATION

Single cell RNA sequencing (scRNA-seq) technique enables the transcriptome profiling of hundreds to ten thousands of cells at the unprecedented individual level and provides new insights to study cell heterogeneity. However, its advantages are hampered by dropout events. To address this problem, we propose a Blockwise Accelerated Non-negative Matrix Factorization framework with Structural network constraints (BANMF-S) to impute those technical zeros.

RESULTS

BANMF-S constructs a gene-gene similarity network to integrate prior information from the external PPI network by the Triadic Closure Principle and a cell-cell similarity network to capture the neighborhood structure and temporal information through a Minimum-Spanning Tree. By collaboratively employing these two networks as regularizations, BANMF-S encourages the coherence of similar gene and cell pairs in the latent space, enhancing the potential to recover the underlying features. Besides, BANMF-S adopts a blocklization strategy to solve the traditional NMF problem through distributed Stochastic Gradient Descent method in a parallel way to accelerate the optimization. Numerical experiments on simulations and real datasets verify that BANMF-S can improve the accuracy of downstream clustering and pseudo-trajectory inference, and its performance is superior to seven state-of-the-art algorithms.

AVAILABILITY

All data used in this work are downloaded from publicly available data sources, and their corresponding accession numbers or source URLs are provided in Supplementary File Section 5.1 Dataset Information. The source codes are publicly available in Github repository https://github.com/jiayingzhao/BANMF-S.

Phenotypic noise and plasticity in cancer evolution

Non-genetic alterations can produce changes in a cell's phenotype. In cancer, these phenomena can influence a cell's fitness by conferring access to heritable, beneficial phenotypes. Herein, we argue that current discussions of 'phenotypic plasticity' in cancer evolution ignore a salient feature of the original definition: namely, that it occurs in response to an environmental change. We suggest 'phenotypic noise' be used to distinguish non-genetic changes in phenotype that occur independently from the environment. We discuss the conceptual and methodological techniques used to identify these phenomena during cancer evolution. We propose that the distinction will guide efforts to define mechanisms of phenotype change, accelerate translational work to manipulate phenotypes through treatment, and, ultimately, improve patient outcomes.

Lineage motifs as developmental modules for control of cell type proportions

In multicellular organisms, cell types must be produced and maintained in appropriate proportions. One way this is achieved is through committed progenitor cells or extrinsic interactions that produce specific patterns of descendant cell types on lineage trees. However, cell fate commitment is probabilistic in most contexts, making it difficult to infer these dynamics and understand how they establish overall cell type proportions. Here, we introduce Lineage Motif Analysis (LMA), a method that recursively identifies statistically overrepresented patterns of cell fates on lineage trees as potential signatures of committed progenitor states or extrinsic interactions. Applying LMA to published datasets reveals spatial and temporal organization of cell fate commitment in zebrafish and rat retina and early mouse embryonic development. Comparative analysis of vertebrate species suggests that lineage motifs facilitate adaptive evolutionary variation of retinal cell type proportions. LMA thus provides insight into complex developmental processes by decomposing them into simpler underlying modules.

Identifying critical regulatory interactions in cell fate decision and transition by systematic perturbation analysis

One of the most significant challenges in biology is to elucidate the roles of various regulatory interactions in cell fate decision and transition. However, it remains to be fully clarified how they cooperate and determine fate transition. Here, a general framework based on statistical analysis and bifurcation theory is proposed to identify crucial regulatory interactions and how they play decisive roles in fate transition. More exactly, specific feedback loops determine occurrence of bifurcations by which cell fate transition can be realized. While regulatory interactions in the feedback loops determine the direction of transition. In addition, two-parameter bifurcation analysis further provides detailed understanding of how the fate transition based on statistical analysis occurs. Statistical analysis can also be used to reveal synergistic combinatorial perturbations by which fate transition can be more efficiently realized. The integrative analysis approach can be used to identify critical regulatory interactions in cell fate transition and reveal how specific cell fate transition occurs. To verify feasibility of the approach, the epithelial to mesenchymal transition (EMT) network is chosen as an illustrative example. In agreement with experimental observations, the approach reveals some critical regulatory interactions and underlying mechanisms in cell fate determination and transitions between three states. The approach can also be applied to analyze other regulatory networks related to cell fate decision and transition.

Reconstructing cell lineage trees with genomic barcoding: approaches and applications

In multicellular organisms, developmental history of cell divisions and functional annotation of terminal cells can be organized into a cell lineage tree (CLT). The reconstruction of the CLT has long been a major goal in developmental biology and other related fields. Recent technological advancements, especially those in editable genomic barcodes and single-cell high-throughput sequencing, have sparked a new wave of experimental methods for reconstructing CLTs. Here we review the existing experimental approaches to the reconstruction of CLT, which are broadly categorized as either image-based or DNA barcode-based methods. In addition, we present a summary of the related literature based on the biological insight provided by the obtained CLTs. Moreover, we discuss the challenges that will arise as more and better CLT data become available in the near future. Genomic barcoding-based CLT reconstructions and analyses, due to their wide applicability and high scalability, offer the potential for novel biological discoveries, especially those related to general and systemic properties of the developmental process.

A review on gene regulatory network reconstruction algorithms based on single cell RNA sequencing

BACKGROUND

Understanding gene regulatory networks (GRNs) is essential for unraveling the molecular mechanisms governing cellular behavior. With the advent of high-throughput transcriptome measurement technology, researchers have aimed to reverse engineer the biological systems, extracting gene regulatory rules from their outputs, which represented by gene expression data. Bulk RNA sequencing, a widely used method for measuring gene expression, has been employed for GRN reconstruction. However, it falls short in capturing dynamic changes in gene expression at the level of individual cells since it averages gene expression across mixed cell populations.

OBJECTIVE

In this review, we provide an overview of 15 GRN reconstruction tools and discuss their respective strengths and limitations, particularly in the context of single cell RNA sequencing (scRNA-seq).

METHODS

Recent advancements in scRNA-seq break new ground of GRN reconstruction. They offer snapshots of the individual cell transcriptomes and capturing dynamic changes. We emphasize how these technological breakthroughs have enhanced GRN reconstruction.

CONCLUSION

GRN reconstructors can be classified based on their requirement for cellular trajectory, which represents a dynamical cellular process including differentiation, aging, or disease progression. Benchmarking studies support the superiority of GRN reconstructors that do not require trajectory analysis in identifying regulator-target relationships. However, methods equipped with trajectory analysis demonstrate better performance in identifying key regulatory factors. In conclusion, researchers should select a suitable GRN reconstructor based on their specific research objectives.

Constructing maps between distinct cell fates and parametric conditions by systematic perturbations

MOTIVATION

Cell fate transitions are common in many developmental processes. Therefore, identifying the mechanisms behind them is crucial. Traditionally, due to complexity of networks and existence of plenty of kinetic parameters, dynamical analysis of biomolecular networks can only be performed by simultaneously perturbing a small number of parameters. Although many efforts have focused on how cell states change under specific perturbations, conversely, how to infer parametric conditions underlying distinct cell fates by systematic perturbations is less clear and needs to be further investigated.

RESULTS

In this article, we present a general computational method by integrating systematic perturbations, unsupervised clustering, principal component analysis, and fitting analysis. The method can be used to to construct maps between distinct cell fates and parametric conditions by systematic perturbations. In particular, there are no needs of accurate parameter measurements and occurrence of bifurcations to establish the maps. To validate feasibility and inference performance of the method, we use toggle switch, inner cell mass, and epithelial mesenchymal transition as model systems to show how the maps are constructed and how system parameters encode essential information on cell fates. The maps tell us how systematic perturbations drive cell fate decisions and transitions, and allow us to purposefully predict, manipulate, and even control cell states. The approach is especially helpful in understanding crucial roles of certain parameter combinations during fate transitions. We hope that the approach can provide us valuable information on parametric or perturbation conditions so some specific targets, e.g. directional differentiation, can be realized.

AVAILABILITY AND IMPLEMENTATION

No public data are used. The data we used are generated by randomly chosen values of model parameters in certain ranges, and the corresponding parameters are already attached in supplementary materials.

Transcription factor fluctuations underlie cell-to-cell variability in a signaling pathway response

Stochastic differences among clonal cells can initiate cell fate decisions in development or cause cell-to-cell differences in the responses to drugs or extracellular ligands. One hypothesis is that some of this phenotypic variability is caused by stochastic fluctuations in the activities of transcription factors (TFs). We tested this hypothesis in NIH3T3-CG cells using the response to Hedgehog signaling as a model cellular response. Here, we present evidence for the existence of distinct fast- and slow-responding substates in NIH3T3-CG cells. These two substates have distinct expression profiles, and fluctuations in the Prrx1 TF underlie some of the differences in expression and responsiveness between fast and slow cells. Our results show that fluctuations in TFs can contribute to cell-to-cell differences in Hedgehog signaling.

Multiplex Protein Imaging through PACIFIC: Photoactive Immunofluorescence with Iterative Cleavage

Multiplex protein imaging technologies enable deep phenotyping and provide rich spatial information about biological samples. Existing methods have shown great success but also harbored trade-offs between various pros and cons, underscoring the persisting necessity to expand the imaging toolkits. Here we present PACIFIC: photoactive immunofluorescence with iterative cleavage, a new modality of multiplex protein imaging methods. PACIFIC achieves iterative multiplexing by implementing photocleavable fluorophores for antibody labeling with one-step spin-column purification. PACIFIC requires no specialized instrument, no DNA encoding, or chemical treatments. We demonstrate that PACIFIC can resolve cellular heterogeneity in both formalin-fixed paraffin-embedded (FFPE) samples and fixed cells. To further highlight how PACIFIC assists discovery, we integrate PACIFIC with live-cell tracking and identify phosphor-p70S6K as a critical driver that governs U87 cell mobility. Considering the cost, flexibility, and compatibility, we foresee that PACIFIC can confer deep phenotyping capabilities to anyone with access to traditional immunofluorescence platforms.

Lineage motifs: developmental modules for control of cell type proportions

In multicellular organisms, cell types must be produced and maintained in appropriate proportions. One way this is achieved is through committed progenitor cells that produce specific sets of descendant cell types. However, cell fate commitment is probabilistic in most contexts, making it difficult to infer progenitor states and understand how they establish overall cell type proportions. Here, we introduce Lineage Motif Analysis (LMA), a method that recursively identifies statistically overrepresented patterns of cell fates on lineage trees as potential signatures of committed progenitor states. Applying LMA to published datasets reveals spatial and temporal organization of cell fate commitment in zebrafish and rat retina and early mouse embryo development. Comparative analysis of vertebrate species suggests that lineage motifs facilitate adaptive evolutionary variation of retinal cell type proportions. LMA thus provides insight into complex developmental processes by decomposing them into simpler underlying modules.

Optogenetic manipulation identifies the roles of ERK and AKT dynamics in controlling mouse embryonic stem cell exit from pluripotency

ERK and AKT signaling control pluripotent cell self-renewal versus differentiation. ERK pathway activity over time (i.e., dynamics) is heterogeneous between individual pluripotent cells, even in response to the same stimuli. To analyze potential functions of ERK and AKT dynamics in controlling mouse embryonic stem cell (ESC) fates, we developed ESC lines and experimental pipelines for the simultaneous long-term manipulation and quantification of ERK or AKT dynamics and cell fates. We show that ERK activity duration or amplitude or the type of ERK dynamics (e.g., transient, sustained, or oscillatory) alone does not influence exit from pluripotency, but the sum of activity over time does. Interestingly, cells retain memory of previous ERK pulses, with duration of memory retention dependent on duration of previous pulse length. FGF receptor/AKT dynamics counteract ERK-induced pluripotency exit. These findings improve our understanding of how cells integrate dynamics from multiple signaling pathways and translate them into cell fate cues.

Dynamics of Epithelial-Mesenchymal Plasticity: What Have Single-Cell Investigations Elucidated So Far?

Epithelial-mesenchymal plasticity (EMP) is a key driver of cancer metastasis and therapeutic resistance, through which cancer cells can reversibly and dynamically alter their molecular and functional traits along the epithelial-mesenchymal spectrum. While cells in the epithelial phenotype are usually tightly adherent, less metastatic, and drug-sensitive, those in the hybrid epithelial/mesenchymal and/or mesenchymal state are more invasive, migratory, drug-resistant, and immune-evasive. Single-cell studies have emerged as a powerful tool in gaining new insights into the dynamics of EMP across various cancer types. Here, we review many recent studies that employ single-cell analysis techniques to better understand the dynamics of EMP in cancer both in vitro and in vivo. These single-cell studies have underlined the plurality of trajectories cells can traverse during EMP and the consequent heterogeneity of hybrid epithelial/mesenchymal phenotypes seen at both preclinical and clinical levels. They also demonstrate how diverse EMP trajectories may exhibit hysteretic behavior and how the rate of such cell-state transitions depends on the genetic/epigenetic background of recipient cells, as well as the dose and/or duration of EMP-inducing growth factors. Finally, we discuss the relationship between EMP and patient survival across many cancer types. We also present a next set of questions related to EMP that could benefit much from single-cell observations and pave the way to better tackle phenotypic switching and heterogeneity in clinic.

Probing transient memory of cellular states using single-cell lineages

The inherent stochasticity in the gene product levels can drive single cells within an isoclonal population to different phenotypic states. The dynamic nature of this intercellular variation, where individual cells can transition between different states over time, makes it a particularly hard phenomenon to characterize. We reviewed recent progress in leveraging the classical Luria-Delbrück experiment to infer the transient heritability of the cellular states. Similar to the original experiment, individual cells were first grown into cell colonies, and then, the fraction of cells residing in different states was assayed for each colony. We discuss modeling approaches for capturing dynamic state transitions in a growing cell population and highlight formulas that identify the kinetics of state switching from the extent of colony-to-colony fluctuations. The utility of this method in identifying multi-generational memory of the both expression and phenotypic states is illustrated across diverse biological systems from cancer drug resistance, reactivation of human viruses, and cellular immune responses. In summary, this fluctuation-based methodology provides a powerful approach for elucidating cell-state transitions from a single time point measurement, which is particularly relevant in situations where measurements lead to cell death (as in single-cell RNA-seq or drug treatment) or cause an irreversible change in cell physiology.

Quantitative fate mapping: A general framework for analyzing progenitor state dynamics via retrospective lineage barcoding

Natural and induced somatic mutations that accumulate in the genome during development record the phylogenetic relationships of cells; whether these lineage barcodes capture the complex dynamics of progenitor states remains unclear. We introduce quantitative fate mapping, an approach to reconstruct the hierarchy, commitment times, population sizes, and commitment biases of intermediate progenitor states during development based on a time-scaled phylogeny of their descendants. To reconstruct time-scaled phylogenies from lineage barcodes, we introduce Phylotime, a scalable maximum likelihood clustering approach based on a general barcoding mutagenesis model. We validate these approaches using realistic in silico and in vitro barcoding experiments. We further establish criteria for the number of cells that must be analyzed for robust quantitative fate mapping and a progenitor state coverage statistic to assess the robustness. This work demonstrates how lineage barcodes, natural or synthetic, enable analyzing progenitor fate and dynamics long after embryonic development in any organism.

Network inference from perturbation time course data

Networks underlie much of biology from subcellular to ecological scales. Yet, understanding what experimental data are needed and how to use them for unambiguously identifying the structure of even small networks remains a broad challenge. Here, we integrate a dynamic least squares framework into established modular response analysis (DL-MRA), that specifies sufficient experimental perturbation time course data to robustly infer arbitrary two and three node networks. DL-MRA considers important network properties that current methods often struggle to capture: (i) edge sign and directionality; (ii) cycles with feedback or feedforward loops including self-regulation; (iii) dynamic network behavior; (iv) edges external to the network; and (v) robust performance with experimental noise. We evaluate the performance of and the extent to which the approach applies to cell state transition networks, intracellular signaling networks, and gene regulatory networks. Although signaling networks are often an application of network reconstruction methods, the results suggest that only under quite restricted conditions can they be robustly inferred. For gene regulatory networks, the results suggest that incomplete knockdown is often more informative than full knockout perturbation, which may change experimental strategies for gene regulatory network reconstruction. Overall, the results give a rational basis to experimental data requirements for network reconstruction and can be applied to any such problem where perturbation time course experiments are possible.

Cost-efficient boundary-free surface patterning achieves high effective-throughput of time-lapse microscopy experiments

Time-lapse microscopy plays critical roles in the studies of cellular dynamics. However, setting up a time-lapse movie experiments is not only laborious but also with low output, mainly due to the cell-losing problem (i.e., cells moving out of limited field of view), especially in a long-time recording. To overcome this issue, we have designed a cost-efficient way that enables cell patterning on the imaging surfaces without any physical boundaries. Using mouse embryonic stem cells as an example system, we have demonstrated that our boundary-free patterned surface solves the cell-losing problem without disturbing their cellular phenotype. Statistically, the presented system increases the effective-throughput of time-lapse microscopy experiments by an order of magnitude.

Control of cell state transitions

Understanding cell state transitions and purposefully controlling them is a longstanding challenge in biology. Here we present cell state transition assessment and regulation (cSTAR), an approach for mapping cell states, modelling transitions between them and predicting targeted interventions to convert cell fate decisions. cSTAR uses omics data as input, classifies cell states, and develops a workflow that transforms the input data into mechanistic models that identify a core signalling network, which controls cell fate transitions by influencing whole-cell networks. By integrating signalling and phenotypic data, cSTAR models how cells manoeuvre in Waddington's landscape1 and make decisions about which cell fate to adopt. Notably, cSTAR devises interventions to control the movement of cells in Waddington's landscape. Testing cSTAR in a cellular model of differentiation and proliferation shows a high correlation between quantitative predictions and experimental data. Applying cSTAR to different types of perturbation and omics datasets, including single-cell data, demonstrates its flexibility and scalability and provides new biological insights. The ability of cSTAR to identify targeted perturbations that interconvert cell fates will enable designer approaches for manipulating cellular development pathways and mechanistically underpinned therapeutic interventions.

Comparison of cell state models derived from single-cell RNA sequencing data: graph versus multi-dimensional space

Single-cell sequencing technologies have revolutionized molecular and cellular biology and stimulated the development of computational tools to analyze the data generated from these technology platforms. However, despite the recent explosion of computational analysis tools, relatively few mathematical models have been developed to utilize these data. Here we compare and contrast two cell state geometries for building mathematical models of cell state-transitions with single-cell RNA-sequencing data with hematopoeisis as a model system; (i) by using partial differential equations on a graph representing intermediate cell states between known cell types, and (ii) by using the equations on a multi-dimensional continuous cell state-space. As an application of our approach, we demonstrate how the calibrated models may be used to mathematically perturb normal hematopoeisis to simulate, predict, and study the emergence of novel cell states during the pathogenesis of acute myeloid leukemia. We particularly focus on comparing the strength and weakness of the graph model and multi-dimensional model.

Heritable changes in division speed accompany the diversification of single T cell fate

Rapid clonal expansion of antigen-specific T cells is a fundamental feature of adaptive immune responses. Here, we utilize continuous live-cell imaging in vitro to track the division speed and genealogical connections of all descendants derived from a single naive CD8⁺ T cell throughout up to ten divisions of activation-induced proliferation. Bayesian inference of tree-structured data reveals that clonal expansion is divided into a homogenously fast burst phase encompassing two to three divisions and a subsequent diversification phase during which T cells segregate into quickly dividing effector T cells and more slowly cycling memory precursors. Our work highlights cell cycle speed as a major heritable property that is regulated in parallel to key lineage decisions of activated T cells.

Rapid clonal expansion of antigen-specific T cells is a fundamental feature of adaptive immune responses. It enables the outgrowth of an individual T cell into thousands of clonal descendants that diversify into short-lived effectors and long-lived memory cells. Clonal expansion is thought to be programmed upon priming of a single naive T cell and then executed by homogenously fast divisions of all of its descendants. However, the actual speed of cell divisions in such an emerging “T cell family” has never been measured with single-cell resolution. Here, we utilize continuous live-cell imaging in vitro to track the division speed and genealogical connections of all descendants derived from a single naive CD8⁺ T cell throughout up to ten divisions of activation-induced proliferation. This comprehensive mapping of T cell family trees identifies a short burst phase, in which division speed is homogenously fast and maintained independent of external cytokine availability or continued T cell receptor stimulation. Thereafter, however, division speed diversifies, and model-based computational analysis using a Bayesian inference framework for tree-structured data reveals a segregation into heritably fast- and slow-dividing branches. This diversification of division speed is preceded already during the burst phase by variable expression of the interleukin-2 receptor alpha chain. Later it is accompanied by selective expression of memory marker CD62L in slower dividing branches. Taken together, these data demonstrate that T cell clonal expansion is structured into subsequent burst and diversification phases, the latter of which coincides with specification of memory versus effector fate.

Gene expression at a single-molecule level: implications for myelodysplastic syndromes and acute myeloid leukemia

Nongenetic heterogeneity, or gene expression stochasticity, is an important source of variability in biological systems. With the advent and improvement of single molecule resolution technologies, it has been shown that transcription dynamics and resultant transcript number fluctuations generate significant cell-to-cell variability that has important biological effects and may contribute substantially to both tissue homeostasis and disease. In this respect, the pathophysiology of stem cell-derived malignancies such as acute myeloid leukemia and myelodysplastic syndromes, which has historically been studied at the ensemble level, may require reevaluation. To that end, it is our aim in this review to highlight the results of recent single-molecule, biophysical, and systems studies of gene expression dynamics, with the explicit purpose of demonstrating how the insights from these basic science studies may help inform and progress the field of leukemia biology and, ultimately, research into novel therapies.

Lineages of embryonic stem cells show non-Markovian state transitions

Pluripotent embryonic stem cells (ESCs) constitute the cell types of the adult vertebrate through a series of developmental state transitions. These states can be defined by expression levels of marker genes, such as Nanog and Sox2. In culture, ESCs reversibly transition between states. However, whether ESCs retain memory of their previous states or transition in a memoryless (Markovian) process remains relatively unknown. Here, we show some highly dynamic lineages of ESCs do not exhibit the Markovian property: their previous states and kin relations influence future choices. Unexpectedly, the distribution of lineages across their composition between states is constant over time, contrasting with the predictions of a Markov model. Additionally, highly dynamic ESC lineages show skewed cell fate distributions after retinoic acid differentiation. Together, these data suggest ESC lineage is an important variable governing future cell states, with implications for stem cell function and development.

Decoding the dynamics of multilayered stochastic antiviral IFN-I responses

Type I Interferon (IFN-I) responses were first recognized for their role in antiviral immunity, but it is now widely appreciated that IFN-Is have many immunomodulatory functions, influencing antitumor responses, autoimmune manifestations, and antimicrobial defenses. Given these pivotal roles, it may be surprising that multilayered stochastic events create highly heterogeneous, but tightly regulated, all-or-nothing cellular decisions. Recently, mathematical models have provided crucial insights into the stochastic nature of antiviral IFN-I responses, which we critically evaluate in this review. In this context, we emphasize the need for innovative single-cell technologies combined with mathematical models to further reveal, understand, and predict the complexity of the IFN-I system in physiological and pathological conditions that may be relevant to a plethora of diseases.

Single-cell image analysis to explore cell-to-cell heterogeneity in isogenic populations

Single-cell image analysis provides a powerful approach for studying cell-to-cell heterogeneity, which is an important attribute of isogenic cell populations, from microbial cultures to individual cells in multicellular organisms. This phenotypic variability must be explained at a mechanistic level if biologists are to fully understand cellular function and address the genotype-to-phenotype relationship. Variability in single-cell phenotypes is obscured by bulk readouts or averaging of phenotypes from individual cells in a sample; thus, single-cell image analysis enables a higher resolution view of cellular function. Here, we consider examples of both small- and large-scale studies carried out with isogenic cell populations assessed by fluorescence microscopy, and we illustrate the advantages, challenges, and the promise of quantitative single-cell image analysis.

Cell Tracking for Organoids: Lessons From Developmental Biology

Organoids have emerged as powerful model systems to study organ development and regeneration at the cellular level. Recently developed microscopy techniques that track individual cells through space and time hold great promise to elucidate the organizational principles of organs and organoids. Applied extensively in the past decade to embryo development and 2D cell cultures, cell tracking can reveal the cellular lineage trees, proliferation rates, and their spatial distributions, while fluorescent markers indicate differentiation events and other cellular processes. Here, we review a number of recent studies that exemplify the power of this approach, and illustrate its potential to organoid research. We will discuss promising future routes, and the key technical challenges that need to be overcome to apply cell tracking techniques to organoid biology.

Quantitative measurements of early alphaviral replication dynamics in single cells reveals the basis for superinfection exclusion

While decades of research have elucidated many steps of the alphavirus lifecycle, the earliest replication dynamics have remained unclear. This missing time window has obscured early replicase strand-synthesis behavior and prevented elucidation of how the first events of infection might influence subsequent viral competition. Using quantitative live-cell and single-molecule imaging, we observed the initial replicase activity and its strand preferences in situ and measured the trajectory of replication over time. Under this quantitative framework, we investigated viral competition, where one alphavirus is able to exclude superinfection by a second homologous virus. We show that this appears as an indirect phenotypic consequence of a bidirectional competition between the two species, coupled with the rapid onset of viral replication and a limited total cellular carrying capacity. Together, these results emphasize the utility of analyzing viral kinetics within single cells.

Phylodynamics for cell biologists

Multicellular organisms are composed of cells connected by ancestry and descent from progenitor cells. The dynamics of cell birth, death, and inheritance within an organism give rise to the fundamental processes of development, differentiation, and cancer. Technical advances in molecular biology now allow us to study cellular composition, ancestry, and evolution at the resolution of individual cells within an organism or tissue. Here, we take a phylogenetic and phylodynamic approach to single-cell biology. We explain how "tree thinking" is important to the interpretation of the growing body of cell-level data and how ecological null models can benefit statistical hypothesis testing. Experimental progress in cell biology should be accompanied by theoretical developments if we are to exploit fully the dynamical information in single-cell data.

Integrated spatial genomics reveals global architecture of single nuclei

Identifying the relationships between chromosome structures, nuclear bodies, chromatin states, and gene expression is an overarching goal of nuclear organization studies^1–4. Because individual cells appear to be highly variable at all these levels⁵, it is essential to map different modalities in the same cells. Here, we report the imaging of 3,660 chromosomal loci in single mouse embryonic stem cells (mESCs) by DNA seqFISH+, along with 17 chromatin marks and subnuclear structures by sequential immunofluorescence (IF) and the expression profile of 70 RNAs. We found many loci were invariantly associated with IF marks in single mESCs. These loci form “fixed points” in the nuclear organizations in single cells and often appear on the surfaces of nuclear bodies and zones defined by combinatorial chromatin marks. Furthermore, highly expressed genes appear to be pre-positioned to active nuclear zones, independent of bursting dynamics in single cells. Our analysis also uncovered several distinct mESCs subpopulations with characteristic combinatorial chromatin states. Using clonal analysis, we show that the global levels of some chromatin marks, such as H3K27me3 and macroH2A1 (mH2A1), are heritable over at least 3–4 generations, whereas other marks fluctuate on a faster time scale. This seqFISH+ based spatial multimodal approach can be used to explore nuclear organization and cell states in diverse biological systems.

TENET: gene network reconstruction using transfer entropy reveals key regulatory factors from single cell transcriptomic data

Accurate prediction of gene regulatory rules is important towards understanding of cellular processes. Existing computational algorithms devised for bulk transcriptomics typically require a large number of time points to infer gene regulatory networks (GRNs), are applicable for a small number of genes and fail to detect potential causal relationships effectively. Here, we propose a novel approach 'TENET' to reconstruct GRNs from single cell RNA sequencing (scRNAseq) datasets. Employing transfer entropy (TE) to measure the amount of causal relationships between genes, TENET predicts large-scale gene regulatory cascades/relationships from scRNAseq data. TENET showed better performance than other GRN reconstructors, in identifying key regulators from public datasets. Specifically from scRNAseq, TENET identified key transcriptional factors in embryonic stem cells (ESCs) and during direct cardiomyocytes reprogramming, where other predictors failed. We further demonstrate that known target genes have significantly higher TE values, and TENET predicted higher TE genes were more influenced by the perturbation of their regulator. Using TENET, we identified and validated that Nme2 is a culture condition specific stem cell factor. These results indicate that TENET is uniquely capable of identifying key regulators from scRNAseq data.

Memory Sequencing Reveals Heritable Single-Cell Gene Expression Programs Associated with Distinct Cellular Behaviors

Non-genetic factors can cause individual cells to fluctuate substantially in gene expression levels over time. It remains unclear whether these fluctuations can persist for much longer than the time of one cell division. Current methods for measuring gene expression in single cells mostly rely on single time point measurements, making the duration of gene expression fluctuations or cellular memory difficult to measure. Here, we combined Luria and Delbrück's fluctuation analysis with population-based RNA sequencing (MemorySeq) for identifying genes transcriptome-wide whose fluctuations persist for several divisions. MemorySeq revealed multiple gene modules that expressed together in rare cells within otherwise homogeneous clonal populations. These rare cell subpopulations were associated with biologically distinct behaviors like proliferation in the face of anti-cancer therapeutics. The identification of non-genetic, multigenerational fluctuations can reveal new forms of biological memory in single cells and suggests that non-genetic heritability of cellular state may be a quantitative property.

State-Transition Analysis of Time-Sequential Gene Expression Identifies Critical Points That Predict Development of Acute Myeloid Leukemia

Temporal dynamics of gene expression inform cellular and molecular perturbations associated with disease development and evolution. Given the complexity of high-dimensional temporal genomic data, an analytic framework guided by a robust theory is needed to interpret time-sequential changes and to predict system dynamics. Here we model temporal dynamics of the transcriptome of peripheral blood mononuclear cells in a two-dimensional state-space representing states of health and leukemia using time-sequential bulk RNA-seq data from a murine model of acute myeloid leukemia (AML). The state-transition model identified critical points that accurately predict AML development and identifies stepwise transcriptomic perturbations that drive leukemia progression. The geometry of the transcriptome state-space provided a biological interpretation of gene dynamics, aligned gene signals that are not synchronized in time across mice, and allowed quantification of gene and pathway contributions to leukemia development. Our state-transition model synthesizes information from multiple cell types in the peripheral blood and identifies critical points in the transition from health to leukemia to guide interpretation of changes in the transcriptome as a whole to predict disease progression. SIGNIFICANCE: These findings apply the theory of state transitions to model the initiation and development of acute myeloid leukemia, identifying transcriptomic perturbations that accurately predict time to disease development.See related commentary by Kuijjer, p. 3072 GRAPHICAL ABSTRACT: http://cancerres.aacrjournals.org/content/canres/80/15/3157/F1.large.jpg.

Single-molecule imaging of transcription dynamics in somatic stem cells

Molecular noise is a natural phenomenon that is inherent to all biological systems1,2. How stochastic processes give rise to the robust outcomes that support tissue homeostasis remains unclear. Here we use single-molecule RNA fluorescent in situ hybridization (smFISH) on mouse stem cells derived from haematopoietic tissue to measure the transcription dynamics of three key genes that encode transcription factors: PU.1 (also known as Spi1), Gata1 and Gata2. We find that infrequent, stochastic bursts of transcription result in the co-expression of these antagonistic transcription factors in the majority of haematopoietic stem and progenitor cells. Moreover, by pairing smFISH with time-lapse microscopy and the analysis of pedigrees, we find that although individual stem-cell clones produce descendants that are in transcriptionally related states-akin to a transcriptional priming phenomenon-the underlying transition dynamics between states are best captured by stochastic and reversible models. As such, a stochastic process can produce cellular behaviours that may be incorrectly inferred to have arisen from deterministic dynamics. We propose a model whereby the intrinsic stochasticity of gene expression facilitates, rather than impedes, the concomitant maintenance of transcriptional plasticity and stem cell robustness.

Advancing Stem Cell Research through Multimodal Single-Cell Analysis

Technological advances play a key role in furthering our understanding of stem cell biology, and advancing the prospects of regenerative therapies. Highly parallelized methods, developed in the last decade, can profile DNA, RNA, or proteins in thousands of cells and even capture data across two or more modalities (multiomics). This allows unbiased and precise definition of molecular cell states, thus allowing classification of cell types, tracking of differentiation trajectories, and discovery of underlying mechanisms. Despite being based on destructive techniques, novel experimental and bioinformatic approaches enable embedding and extraction of temporal information, which is essential for deconvolution of complex data and establishing cause and effect relationships. Here, we provide an overview of recent studies pertinent to stem cell biology, followed by an outlook on how further advances in single-cell molecular profiling and computational analysis have the potential to shape the future of both basic and translational research.

Inheritance and variability of kinetic gene expression parameters in microbial cells: modeling and inference from lineage tree data

Motivation

Modern experimental technologies enable monitoring of gene expression dynamics in individual cells and quantification of its variability in isogenic microbial populations. Among the sources of this variability is the randomness that affects inheritance of gene expression factors at cell division. Known parental relationships among individually observed cells provide invaluable information for the characterization of this extrinsic source of gene expression noise. Despite this fact, most existing methods to infer stochastic gene expression models from single-cell data dedicate little attention to the reconstruction of mother–daughter inheritance dynamics.

Results

Starting from a transcription and translation model of gene expression, we propose a stochastic model for the evolution of gene expression dynamics in a population of dividing cells. Based on this model, we develop a method for the direct quantification of inheritance and variability of kinetic gene expression parameters from single-cell gene expression and lineage data. We demonstrate that our approach provides unbiased estimates of mother–daughter inheritance parameters, whereas indirect approaches using lineage information only in the post-processing of individual-cell parameters underestimate inheritance. Finally, we show on yeast osmotic shock response data that daughter cell parameters are largely determined by the mother, thus confirming the relevance of our method for the correct assessment of the onset of gene expression variability and the study of the transmission of regulatory factors.

Availability and implementation

Software code is available at https://github.com/almarguet/IdentificationWithARME. Lineage tree data is available upon request.

Supplementary information

Supplementary material is available at Bioinformatics online.

Lineage EM algorithm for inferring latent states from cellular lineage trees

SUMMARY

Phenotypic variability in a population of cells can work as the bet-hedging of the cells under an unpredictably changing environment, the typical example of which is the bacterial persistence. To understand the strategy to control such phenomena, it is indispensable to identify the phenotype of each cell and its inheritance. Although recent advancements in microfluidic technology offer us useful lineage data, they are insufficient to directly identify the phenotypes of the cells. An alternative approach is to infer the phenotype from the lineage data by latent-variable estimation. To this end, however, we must resolve the bias problem in the inference from lineage called survivorship bias. In this work, we clarify how the survivorship bias distorts statistical estimations. We then propose a latent-variable estimation algorithm without the survivorship bias from lineage trees based on an expectation-maximization (EM) algorithm, which we call lineage EM algorithm (LEM). LEM provides a statistical method to identify the traits of the cells applicable to various kinds of lineage data.

AVAILABILITY AND IMPLEMENTATION

An implementation of LEM is available at https://github.com/so-nakashima/Lineage-EM-algorithm.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

From observing to predicting single-cell structure and function with high-throughput/high-content microscopy

In the past 15 years, cell-based microscopy has evolved its focus from observing cell function to aiming to predict it. In particular-powered by breakthroughs in computer vision, large-scale image analysis and machine learning-high-throughput and high-content microscopy imaging have enabled to uniquely harness single-cell information to systematically discover and annotate genes and regulatory pathways, uncover systems-level interactions and causal links between cellular processes, and begin to clarify and predict causal cellular behaviour and decision making. Here we review these developments, discuss emerging trends in the field, and describe how single-cell 'omics and single-cell microscopy are imminently in an intersecting trajectory. The marriage of these two fields will make possible an unprecedented understanding of cell and tissue behaviour and function.

Stem Cell Differentiation as a Non-Markov Stochastic Process

Pluripotent stem cells can self-renew in culture and differentiate along all somatic lineages in vivo. While much is known about the molecular basis of pluripotency, the mechanisms of differentiation remain unclear. Here, we profile individual mouse embryonic stem cells as they progress along the neuronal lineage. We observe that cells pass from the pluripotent state to the neuronal state via an intermediate epiblast-like state. However, analysis of the rate at which cells enter and exit these observed cell states using a hidden Markov model indicates the presence of a chain of unobserved molecular states that each cell transits through stochastically in sequence. This chain of hidden states allows individual cells to record their position on the differentiation trajectory, thereby encoding a simple form of cellular memory. We suggest a statistical mechanics interpretation of these results that distinguishes between functionally distinct cellular “macrostates” and functionally similar molecular “microstates” and propose a model of stem cell differentiation as a non-Markov stochastic process.

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We profile individual stem cells as they differentiate along the neural lineage

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Regulatory network changes and increased cell variability accompany differentiation

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Analysis of dynamics with a hidden Markov model reveals unobserved molecular states

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We propose a model of stem cell differentiation as a non-Markov stochastic process

Exploring single cells in space and time during tissue development, homeostasis and regeneration

Complex 3D tissues arise during development following tightly organized events in space and time. In particular, gene regulatory networks and local interactions between single cells lead to emergent properties at the tissue and organism levels. To understand the design principles of tissue organization, we need to characterize individual cells at given times, but we also need to consider the collective behavior of multiple cells across different spatial and temporal scales. In recent years, powerful single cell methods have been developed to characterize cells in tissues and to address the challenging questions of how different tissues are formed throughout development, maintained in homeostasis, and repaired after injury and disease. These approaches have led to a massive increase in data pertaining to both mRNA and protein abundances in single cells. As we review here, these new technologies, in combination with in toto live imaging, now allow us to bridge spatial and temporal information quantitatively at the single cell level and generate a mechanistic understanding of tissue development.

Morphological State Transition Dynamics in EGF-Induced Epithelial to Mesenchymal Transition

Epithelial to Mesenchymal Transition (EMT) is a multi-state process. Here, we investigated phenotypic state transition dynamics of Epidermal Growth Factor (EGF)-induced EMT in a breast cancer cell line MDA-MB-468. We have defined phenotypic states of these cells in terms of their morphologies and have shown that these cells have three distinct morphological states-cobble, spindle, and circular. The spindle and circular states are the migratory phenotypes. Using quantitative image analysis and mathematical modeling, we have deciphered state transition trajectories in different experimental conditions. This analysis shows that the phenotypic state transition during EGF-induced EMT in these cells is reversible, and depends upon the dose of EGF and level of phosphorylation of the EGF receptor (EGFR). The dominant reversible state transition trajectory in this system was cobble to circular to spindle to cobble. We have observed that there exists an ultrasensitive on/off switch involving phospho-EGFR that decides the transition of cells in and out of the circular state. In general, our observations can be explained by the conventional quasi-potential landscape model for phenotypic state transition. As an alternative to this model, we have proposed a simpler discretized energy-level model to explain the observed state transition dynamics.

Memory and relatedness of transcriptional activity in mammalian cell lineages

Phenotypically identical mammalian cells often display considerable variability in transcript levels of individual genes. How transcriptional activity propagates in cell lineages, and how this varies across genes is poorly understood. Here we combine live-cell imaging of short-lived transcriptional reporters in mouse embryonic stem cells with mathematical modelling to quantify the propagation of transcriptional activity over time and across cell generations in phenotypically homogenous cells. In sister cells we find mean transcriptional activity to be strongly correlated and transcriptional dynamics tend to be synchronous; both features control how quickly transcriptional levels in sister cells diverge in a gene-specific manner. Moreover, mean transcriptional activity is transmitted from mother to daughter cells, leading to multi-generational transcriptional memory and causing inter-family heterogeneity in gene expression.

Maps of variability in cell lineage trees

New approaches to lineage tracking have allowed the study of differentiation in multicellular organisms over many generations of cells. Understanding the phenotypic variability observed in these lineage trees requires new statistical methods. Whereas an invariant cell lineage, such as that for the nematode Caenorhabditis elegans, can be described by a lineage map, defined as the pattern of phenotypes overlaid onto the binary tree, a traditional lineage map is static and does not describe the variability inherent in the cell lineages of higher organisms. Here, we introduce lineage variability maps which describe the pattern of second-order variation in lineage trees. These maps can be undirected graphs of the partial correlations between every lineal position, or directed graphs showing the dynamics of bifurcated patterns in each subtree. We show how to infer these graphical models for lineages of any depth from sample sizes of only a few pedigrees. This required developing the generalized spectral analysis for a binary tree, the natural framework for describing tree-structured variation. When tested on pedigrees from C. elegans expressing a marker for pharyngeal differentiation potential, the variability maps recover essential features of the known lineage map. When applied to highly-variable pedigrees monitoring cell size in T lymphocytes, the maps show that most of the phenotype is set by the founder naive T cell. Lineage variability maps thus elevate the concept of the lineage map to the population level, addressing questions about the potency and dynamics of cell lineages and providing a way to quantify the progressive restriction of cell fate with increasing depth in the tree.

A stochastic epigenetic switch controls the dynamics of T-cell lineage commitment

Cell fate decisions occur through the switch-like, irreversible activation of fate-specifying genes. These activation events are often assumed to be tightly coupled to changes in upstream transcription factors, but could also be constrained by cis-epigenetic mechanisms at individual gene loci. Here, we studied the activation of Bcl11b, which controls T-cell fate commitment. To disentangle cis and trans effects, we generated mice where two Bcl11b copies are tagged with distinguishable fluorescent proteins. Quantitative live microscopy of progenitors from these mice revealed that Bcl11b turned on after a stochastic delay averaging multiple days, which varied not only between cells but also between Bcl11b alleles within the same cell. Genetic perturbations, together with mathematical modeling, showed that a distal enhancer controls the rate of epigenetic activation, while a parallel Notch-dependent trans-acting step stimulates expression from activated loci. These results show that developmental fate transitions can be controlled by stochastic cis-acting events on individual loci.

Transition state characteristics during cell differentiation

Models describing the process of stem-cell differentiation are plentiful, and may offer insights into the underlying mechanisms and experimentally observed behaviour. Waddington's epigenetic landscape has been providing a conceptual framework for differentiation processes since its inception. It also allows, however, for detailed mathematical and quantitative analyses, as the landscape can, at least in principle, be related to mathematical models of dynamical systems. Here we focus on a set of dynamical systems features that are intimately linked to cell differentiation, by considering exemplar dynamical models that capture important aspects of stem cell differentiation dynamics. These models allow us to map the paths that cells take through gene expression space as they move from one fate to another, e.g. from a stem-cell to a more specialized cell type. Our analysis highlights the role of the transition state (TS) that separates distinct cell fates, and how the nature of the TS changes as the underlying landscape changes-change that can be induced by e.g. cellular signaling. We demonstrate that models for stem cell differentiation may be interpreted in terms of either a static or transitory landscape. For the static case the TS represents a particular transcriptional profile that all cells approach during differentiation. Alternatively, the TS may refer to the commonly observed period of heterogeneity as cells undergo stochastic transitions.