Analysis of Cell Lineage Trees by Exact Bayesian Inference Identifies Negative Autoregulation of Nanog in Mouse Embryonic Stem Cells

Inference on autoregulation in gene expression with variance-to-mean ratio

Some genes can promote or repress their own expressions, which is called autoregulation. Although gene regulation is a central topic in biology, autoregulation is much less studied. In general, it is extremely difficult to determine the existence of autoregulation with direct biochemical approaches. Nevertheless, some papers have observed that certain types of autoregulations are linked to noise levels in gene expression. We generalize these results by two propositions on discrete-state continuous-time Markov chains. These two propositions form a simple but robust method to infer the existence of autoregulation from gene expression data. This method only needs to compare the mean and variance of the gene expression level. Compared to other methods for inferring autoregulation, our method only requires non-interventional one-time data, and does not need to estimate parameters. Besides, our method has few restrictions on the model. We apply this method to four groups of experimental data and find some genes that might have autoregulation. Some inferred autoregulations have been verified by experiments or other theoretical works.

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.

Bioimaging approaches for quantification of individual cell behavior during cell fate decisions

Tracking individual cells has allowed a new understanding of cellular behavior in human health and disease by adding a dynamic component to the already complex heterogeneity of single cells. Technically, despite countless advances, numerous experimental variables can affect data collection and interpretation and need to be considered. In this review, we discuss the main technical aspects and biological findings in the analysis of the behavior of individual cells. We discuss the most relevant contributions provided by these approaches in clinically relevant human conditions like embryo development, stem cells biology, inflammation, cancer and microbiology, along with the cellular mechanisms and molecular pathways underlying these conditions. We also discuss the key technical aspects to be considered when planning and performing experiments involving the analysis of individual cells over long periods. Despite the challenges in automatic detection, features extraction and long-term tracking that need to be tackled, the potential impact of single-cell bioimaging is enormous in understanding the pathogenesis and development of new therapies in human pathophysiology.

Imaging developmental cell cycles

The last decade has seen a major expansion in development of live biosensors, the tools needed to genetically encode them into model organisms, and the microscopic techniques used to visualize them. When combined, these offer us powerful tools with which to make fundamental discoveries about complex biological processes. In this review, we summarize the availability of biosensors to visualize an essential cellular process, the cell cycle, and the techniques for single-cell tracking and quantification of these reporters. We also highlight studies investigating the connection of cellular behavior to the cell cycle, particularly through live imaging, and anticipate exciting discoveries with the combination of these technologies in developmental contexts.

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.

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.

Promoters adopt distinct dynamic manifestations depending on transcription factor context

Cells respond to external signals and stresses by activating transcription factors (TF), which induce gene expression changes. Prior work suggests that signal-specific gene expression changes are partly achieved because different gene promoters exhibit distinct induction dynamics in response to the same TF input signal. Here, using high-throughput quantitative single-cell measurements and a novel statistical method, we systematically analyzed transcriptional responses to a large number of dynamic TF inputs. In particular, we quantified the scaling behavior among different transcriptional features extracted from the measured trajectories such as the gene activation delay or duration of promoter activity. Surprisingly, we found that even the same gene promoter can exhibit qualitatively distinct induction and scaling behaviors when exposed to different dynamic TF contexts. While it was previously known that promoters fall into distinct classes, here we show that the same promoter can switch between different classes depending on context. Thus, promoters can adopt context-dependent "manifestations". Our analysis suggests that the full complexity of signal processing by genetic circuits may be significantly underestimated when studied in only specific contexts.

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.

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.

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.

Statistical and Mathematical Modeling of Spatiotemporal Dynamics of Stem Cells

Statistical and mathematical modeling are crucial to describe, interpret, compare, and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment. The current prominence of high-resolution and live-cell imaging data provides an unprecedented opportunity to study the spatiotemporal dynamics of these cells within their stem cell niche and learn more about aberrant, but also unperturbed, normal hematopoiesis. However, this requires careful quantitative statistical analysis of the spatial and temporal behavior of cells and the interaction with their microenvironment. Moreover, such quantification is a prerequisite for the construction of hypothesis-driven mathematical models that can provide mechanistic explanations by generating spatiotemporal dynamics that can be directly compared to experimental observations. Here, we provide a brief overview of statistical methods in analyzing spatial distribution of cells, cell motility, cell shapes, and cellular genealogies. We also describe cell-based modeling formalisms that allow researchers to simulate emergent behavior in a multicellular system based on a set of hypothesized mechanisms. Together, these methods provide a quantitative workflow for the analytic and synthetic study of the spatiotemporal behavior of hematopoietic stem and progenitor cells.

Estimation methods for heterogeneous cell population models in systems biology

Heterogeneity among individual cells is a characteristic and relevant feature of living systems. A range of experimental techniques to investigate this heterogeneity is available, and multiple modelling frameworks have been developed to describe and simulate the dynamics of heterogeneous populations. Measurement data are used to adjust computational models, which results in parameter and state estimation problems. Methods to solve these estimation problems need to take the specific properties of data and models into account. The aim of this review is to give an overview on the state of the art in estimation methods for heterogeneous cell population data and models. The focus is on models based on the population balance equation, but stochastic and individual-based models are also discussed. It starts with a brief discussion of common experimental approaches and types of measurement data that can be obtained in this context. The second part describes computational modelling frameworks for heterogeneous populations and the types of estimation problems occurring for these models. The third part starts with a discussion of observability and identifiability properties, after which the computational methods to solve the various estimation problems are described.

Making lineage decisions with biological noise: Lessons from the early mouse embryo

Understanding how individual cells make fate decisions that lead to the faithful formation and homeostatic maintenance of tissues is a fundamental goal of contemporary developmental and stem cell biology. Seemingly uniform populations of stem cells and multipotent progenitors display a surprising degree of heterogeneity, primarily originating from the inherent stochastic nature of molecular processes underlying gene expression. Despite this heterogeneity, lineage decisions result in tissues of a defined size and with consistent proportions of differentiated cell types. Using the early mouse embryo as a model we review recent developments that have allowed the quantification of molecular intercellular heterogeneity during cell differentiation. We first discuss the relationship between these heterogeneities and developmental cellular potential. We then review recent theoretical approaches that formalize the mechanisms underlying fate decisions in the inner cell mass of the blastocyst stage embryo. These models build on our extensive knowledge of the genetic control of fate decisions in this system and will become essential tools for a rigorous understanding of the connection between noisy molecular processes and reproducible outcomes at the multicellular level. We conclude by suggesting that cell-to-cell communication provides a mechanism to exploit and buffer intercellular variability in a self-organized process that culminates in the reproducible formation of the mature mammalian blastocyst stage embryo that is ready for implantation into the maternal uterus. This article is categorized under: Gene Expression and Transcriptional Hierarchies > Cellular Differentiation Establishment of Spatial and Temporal Patterns > Regulation of Size, Proportion, and Timing Gene Expression and Transcriptional Hierarchies > Gene Networks and Genomics Gene Expression and Transcriptional Hierarchies > Quantitative Methods and Models.

A stochastic and dynamical view of pluripotency in mouse embryonic stem cells

Pluripotent embryonic stem cells are of paramount importance for biomedical sciences because of their innate ability for self-renewal and differentiation into all major cell lines. The fateful decision to exit or remain in the pluripotent state is regulated by complex genetic regulatory networks. The rapid growth of single-cell sequencing data has greatly stimulated applications of statistical and machine learning methods for inferring topologies of pluripotency regulating genetic networks. The inferred network topologies, however, often only encode Boolean information while remaining silent about the roles of dynamics and molecular stochasticity inherent in gene expression. Herein we develop a framework for systematically extending Boolean-level network topologies into higher resolution models of networks which explicitly account for the promoter architectures and gene state switching dynamics. We show the framework to be useful for disentangling the various contributions that gene switching, external signaling, and network topology make to the global heterogeneity and dynamics of transcription factor populations. We find the pluripotent state of the network to be a steady state which is robust to global variations of gene switching rates which we argue are a good proxy for epigenetic states of individual promoters. The temporal dynamics of exiting the pluripotent state, on the other hand, is significantly influenced by the rates of genetic switching which makes cells more responsive to changes in extracellular signals.

Modeling signaling-dependent pluripotency with Boolean logic to predict cell fate transitions

Pluripotent stem cells (PSCs) exist in multiple stable states, each with specific cellular properties and molecular signatures. The mechanisms that maintain pluripotency, or that cause its destabilization to initiate development, are complex and incompletely understood. We have developed a model to predict stabilized PSC gene regulatory network (GRN) states in response to input signals. Our strategy used random asynchronous Boolean simulations (R-ABS) to simulate single-cell fate transitions and strongly connected components (SCCs) strategy to represent population heterogeneity. This framework was applied to a reverse-engineered and curated core GRN for mouse embryonic stem cells (mESCs) and used to simulate cellular responses to combinations of five signaling pathways. Our simulations predicted experimentally verified cell population compositions and input signal combinations controlling specific cell fate transitions. Extending the model to PSC differentiation, we predicted a combination of signaling activators and inhibitors that efficiently and robustly generated a Cdx2⁺Oct4^- cells from naïve mESCs. Overall, this platform provides new strategies to simulate cell fate transitions and the heterogeneity that typically occurs during development and differentiation.

Leveraging and coping with uncertainty in the response of individual cells to therapy

Non-genetic heterogeneity fluctuates over diverse timescales, ranging from hours to months. In specific cases, such variability can profoundly impact the response of cell populations to therapy, in both antibiotic treatments in bacteria and chemotherapy in cancer. It is thus critical to understand the way phenotypes fluctuate in cell populations and the molecular sources of phenotypic diversity. Technical and analytical breakthroughs in the study of single cells have leveraged cellular heterogeneity to gain phenomenological and mechanistic insights of the phenotypic transitions that occur within isogenic cell populations over time. Such an understanding moves forward our ability to design therapeutic strategies with the explicit goal of preventing and controlling the selective expansion and stabilization of drug-tolerant phenotypic states.

Time-dependent propagators for stochastic models of gene expression: an analytical method

The inherent stochasticity of gene expression in the context of regulatory networks profoundly influences the dynamics of the involved species. Mathematically speaking, the propagators which describe the evolution of such networks in time are typically defined as solutions of the corresponding chemical master equation (CME). However, it is not possible in general to obtain exact solutions to the CME in closed form, which is due largely to its high dimensionality. In the present article, we propose an analytical method for the efficient approximation of these propagators. We illustrate our method on the basis of two categories of stochastic models for gene expression that have been discussed in the literature. The requisite procedure consists of three steps: a probability-generating function is introduced which transforms the CME into (a system of) partial differential equations (PDEs); application of the method of characteristics then yields (a system of) ordinary differential equations (ODEs) which can be solved using dynamical systems techniques, giving closed-form expressions for the generating function; finally, propagator probabilities can be reconstructed numerically from these expressions via the Cauchy integral formula. The resulting ‘library’ of propagators lends itself naturally to implementation in a Bayesian parameter inference scheme, and can be generalised systematically to related categories of stochastic models beyond the ones considered here.

Parameter inference for stochastic single-cell dynamics from lineage tree data

Background

With the advance of experimental techniques such as time-lapse fluorescence microscopy, the availability of single-cell trajectory data has vastly increased, and so has the demand for computational methods suitable for parameter inference with this type of data. Most of currently available methods treat single-cell trajectories independently, ignoring the mother-daughter relationships and the information provided by the population structure. However, this information is essential if a process of interest happens at cell division, or if it evolves slowly compared to the duration of the cell cycle.

Results

In this work, we propose a Bayesian framework for parameter inference on single-cell time-lapse data from lineage trees. Our method relies on a combination of Sequential Monte Carlo for approximating the parameter likelihood function and Markov Chain Monte Carlo for parameter exploration. We demonstrate our inference framework on two simple examples in which the lineage tree information is crucial: one in which the cell phenotype can only switch at cell division and another where the cell state fluctuates slowly over timescales that extend well beyond the cell-cycle duration.

Conclusion

There exist several examples of biological processes, such as stem cell fate decisions or epigenetically controlled phase variation in bacteria, where the cell ancestry is expected to contain important information about the underlying system dynamics. Parameter inference methods that discard this information are expected to perform poorly for such type of processes. Our method provides a simple and computationally efficient way to take into account single-cell lineage tree data for the purpose of parameter inference and serves as a starting point for the development of more sophisticated and powerful approaches in the future.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0425-1) contains supplementary material, which is available to authorized users.

Cell Lineage Trees Bear Fruit

Two inference approaches harness the information present in cell lineage trees to better understand the dynamic transitions between cell states.