Noise distorts the epigenetic landscape and shapes cell-fate decisions

Living in a noisy world-origins of gene expression noise and its impact on cellular decision-making

The expression level of a gene can vary between genetically identical cells under the same environmental condition-a phenomenon referred to as gene expression noise. Several studies have now elucidated a central role of transcription factors in the generation of expression noise. Transcription factors, as the key components of gene regulatory networks, drive many important cellular decisions in response to cellular and environmental signals. Therefore, a very relevant question is how expression noise impacts gene regulation and influences cellular decision-making. In this Review, we summarize the current understanding of the molecular origins of expression noise, highlighting the role of transcription factors in this process, and discuss the ways in which noise can influence cellular decision-making. As advances in single-cell technologies open new avenues for studying expression noise as well as gene regulatory circuits, a better understanding of the influence of noise on cellular decisions will have important implications for many biological processes.

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

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

Age-related behavioral resilience in smartphone touchscreen interaction dynamics

We experience a life that is full of ups and downs. The ability to bounce back after adverse life events such as the loss of a loved one or serious illness declines with age, and such isolated events can even trigger accelerated aging. How humans respond to common day-to-day perturbations is less clear. Here, we infer the aging status from smartphone behavior by using a decision tree regression model trained to accurately estimate the chronological age based on the dynamics of touchscreen interactions. Individuals (N = 280, 21 to 87 y of age) expressed smartphone behavior that appeared younger on certain days and older on other days through the observation period that lasted up to ~4 y. We captured the essence of these fluctuations by leveraging the mathematical concept of critical transitions and tipping points in complex systems. In most individuals, we find one or more alternative stable aging states separated by tipping points. The older the individual, the lower the resilience to forces that push the behavior across the tipping point into an older state. Traditional accounts of aging based on sparse longitudinal data spanning decades suggest a gradual behavioral decline with age. Taken together with our current results, we propose that the gradual age-related changes are interleaved with more complex dynamics at shorter timescales where the same individual may navigate distinct behavioral aging states from one day to the next. Real-world behavioral data modeled as a complex system can transform how we view and study aging.

Information content and optimization of self-organized developmental systems

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

Feedback between stochastic gene networks and population dynamics enables cellular decision-making

Phenotypic selection occurs when genetically identical cells are subject to different reproductive abilities due to cellular noise. Such noise arises from fluctuations in reactions synthesizing proteins and plays a crucial role in how cells make decisions and respond to stress or drugs. We propose a general stochastic agent-based model for growing populations capturing the feedback between gene expression and cell division dynamics. We devise a finite state projection approach to analyze gene expression and division distributions and infer selection from single-cell data in mother machines and lineage trees. We use the theory to quantify selection in multi-stable gene expression networks and elucidate that the trade-off between phenotypic switching and selection enables robust decision-making essential for synthetic circuits and developmental lineage decisions. Using live-cell data, we demonstrate that combining theory and inference provides quantitative insights into bet-hedging-like response to DNA damage and adaptation during antibiotic exposure in Escherichia coli.

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

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

Unveiling the Dynamics behind Glioblastoma Multiforme Single-Cell Data Heterogeneity

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

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

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

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

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

Repeated Decision Stumping Distils Simple Rules from Single-Cell Data

Single-cell data afford unprecedented insights into molecular processes. But the complexity and size of these data sets have proved challenging and given rise to a large armory of statistical and machine learning approaches. The majority of approaches focuses on either describing features of these data, or making predictions and classifying unlabeled samples. In this study, we introduce repeated decision stumping (ReDX) as a method to distill simple models from single-cell data. We develop decision trees of depth one-hence "stumps"-to identify in an inductive manner, gene products involved in driving cell fate transitions, and in applications to published data we are able to discover the key players involved in these processes in an unbiased manner without prior knowledge. Our algorithm is deliberately targeting the simplest possible candidate hypotheses that can be extracted from complex high-dimensional data. There are three reasons for this: (1) the predictions become straightforwardly testable hypotheses; (2) the identified candidates form the basis for further mechanistic model development, for example, for engineering and synthetic biology interventions; and (3) this approach complements existing descriptive modeling approaches and frameworks. The approach is computationally efficient, has remarkable predictive power, including in simulation studies where the ground truth is known, and yields robust and statistically stable predictors; the same set of candidates is generated by applying the algorithm to different subsamples of experimental data.

Single-cell expression predicts neuron-specific protein homeostasis networks

The protein homeostasis network keeps proteins in their correct shapes and avoids unwanted aggregation. In turn, the accumulation of aberrantly misfolded proteins has been directly associated with the onset of ageing-associated neurodegenerative diseases such as Alzheimer's and Parkinson's. However, a detailed and rational understanding of how protein homeostasis is achieved in health, and how it can be targeted for therapeutic intervention in diseases remains missing. Here, large-scale single-cell expression data from the Allen Brain Map are analysed to investigate the transcription regulation of the core protein homeostasis network across the human brain. Remarkably, distinct expression profiles suggest specialized protein homeostasis networks with systematic adaptations in excitatory neurons, inhibitory neurons and non-neuronal cells. Moreover, several chaperones and Ubiquitin ligases are found transcriptionally coregulated with genes important for synapse formation and maintenance, thus linking protein homeostasis to the regulation of neuronal function. Finally, evolutionary analyses highlight the conservation of an elevated interaction density in the chaperone network, suggesting that one of the most exciting aspects of chaperone action may yet be discovered in their collective action at the systems level. More generally, our work highlights the power of computational analyses for breaking down complexity and gaining complementary insights into fundamental biological problems.

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

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

Macrophage phenotype transitions in a stochastic gene-regulatory network model

Polarization is the process by which a macrophage cell commits to a phenotype based on external signal stimulation. To know how this process is affected by random fluctuations and events within a cell is of utmost importance to better understand the underlying dynamics and predict possible phenotype transitions. For this purpose, we develop a stochastic modeling approach for the macrophage polarization process. We classify phenotype states using the Robust Perron Cluster Analysis and quantify transition pathways and probabilities by applying Transition Path Theory. Depending on the model parameters, we identify four bistable and one tristable phenotype configuration. We find that bistable transitions are fast but their states less robust. In contrast, phenotype transitions in the tristable situation have a comparatively long time duration, which reflects the robustness of the states. The results indicate parallels in the overall transition behavior of macrophage cells with other heterogeneous and plastic cell types, such as cancer cells. Our approach allows for a probabilistic interpretation of macrophage phenotype transitions and biological inference on phenotype robustness. In general, the methodology can easily be adapted to other systems where random state switches are known to occur.

Studying stochastic systems biology of the cell with single-cell genomics data

Recent experimental developments in genome-wide RNA quantification hold considerable promise for systems biology. However, rigorously probing the biology of living cells requires a unified mathematical framework that accounts for single-molecule biological stochasticity in the context of technical variation associated with genomics assays. We review models for a variety of RNA transcription processes, as well as the encapsulation and library construction steps of microfluidics-based single-cell RNA sequencing, and present a framework to integrate these phenomena by the manipulation of generating functions. Finally, we use simulated scenarios and biological data to illustrate the implications and applications of the approach.

PI3K signaling through a biochemical systems lens

Following 3 decades of extensive research into PI3K signaling, it is now evidently clear that the underlying network does not equate to a simple ON/OFF switch. This is best illustrated by the multifaceted nature of the many diseases associated with aberrant PI3K signaling, including common cancers, metabolic disease, and rare developmental disorders. However, we are still far from a complete understanding of the fundamental control principles that govern the numerous phenotypic outputs that are elicited by activation of this well-characterized biochemical signaling network, downstream of an equally diverse set of extrinsic inputs. At its core, this is a question on the role of PI3K signaling in cellular information processing and decision making. Here, we review the determinants of accurate encoding and decoding of growth factor signals and discuss outstanding questions in the PI3K signal relay network. We emphasize the importance of quantitative biochemistry, in close integration with advances in single-cell time-resolved signaling measurements and mathematical modeling.

Unbalanced response to growth variations reshapes the cell fate decision landscape

The global regulation of cell growth rate on gene expression perturbs the performance of gene networks, which would impose complex variations on the cell-fate decision landscape. Here we use a simple synthetic circuit of mutual repression that allows a bistable landscape to examine how such global regulation would affect the stability of phenotypic landscape and the accompanying dynamics of cell-fate determination. We show that the landscape experiences a growth-rate-induced bifurcation between monostability and bistability. Theoretical and experimental analyses reveal that this bifurcating deformation of landscape arises from the unbalanced response of gene expression to growth variations. The path of growth transition across the bifurcation would reshape cell-fate decisions. These results demonstrate the importance of growth regulation on cell-fate determination processes, regardless of specific molecular signaling or regulation.

Studying stochastic systems biology of the cell with single-cell genomics data

Recent experimental developments in genome-wide RNA quantification hold considerable promise for systems biology. However, rigorously probing the biology of living cells requires a unified mathematical framework that accounts for single-molecule biological stochasticity in the context of technical variation associated with genomics assays. We review models for a variety of RNA transcription processes, as well as the encapsulation and library construction steps of microfluidics-based single-cell RNA sequencing, and present a framework to integrate these phenomena by the manipulation of generating functions. Finally, we use simulated scenarios and biological data to illustrate the implications and applications of the approach.

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

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

Open problems in mathematical biology

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

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

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

The chemical Langevin equation for biochemical systems in dynamic environments

Modelling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly stem from the interplay of the network with many other - and mostly unknown - fluctuating processes, as well as with various random signals arising from the extracellular world; these sources contribute extrinsic noise. Here we provide a computational simulation method to probe the stochastic dynamics of biochemical systems subject to both intrinsic and extrinsic noise. We develop an extrinsic chemical Langevin equation-a physically motivated extension of the chemical Langevin equation- to model intrinsically noisy reaction networks embedded in a stochastically fluctuating environment. The extrinsic CLE is a continuous approximation to the Chemical Master Equation (CME) with time-varying propensities. In our approach, noise is incorporated at the level of the CME, and can account for the full dynamics of the exogenous noise process, irrespective of timescales and their mismatches. We show that our method accurately captures the first two moments of the stationary probability density when compared with exact stochastic simulation methods, while reducing the computational runtime by several orders of magnitude. Our approach provides a method that is practical, computationally efficient and physically accurate to study systems that are simultaneously subject to a variety of noise sources.

Nonmodular oscillator and switch based on RNA decay drive regeneration of multimodal gene expression

Periodic gene expression dynamics are key to cell and organism physiology. Studies of oscillatory expression have focused on networks with intuitive regulatory negative feedback loops, leaving unknown whether other common biochemical reactions can produce oscillations. Oscillation and noise have been proposed to support mammalian progenitor cells’ capacity to restore heterogenous, multimodal expression from extreme subpopulations, but underlying networks and specific roles of noise remained elusive. We use mass-action-based models to show that regulated RNA degradation involving as few as two RNA species—applicable to nearly half of human protein-coding genes—can generate sustained oscillations without explicit feedback. Diverging oscillation periods synergize with noise to robustly restore cell populations’ bimodal expression on timescales of days. The global bifurcation organizing this divergence relies on an oscillator and bistable switch which cannot be decomposed into two structural modules. Our work reveals surprisingly rich dynamics of post-transcriptional reactions and a potentially widespread mechanism underlying development, tissue regeneration, and cancer cell heterogeneity.

A single-cell resolved cell-cell communication model explains lineage commitment in hematopoiesis

Cells do not make fate decisions independently. Arguably, every cell-fate decision occurs in response to environmental signals. In many cases, cell-cell communication alters the dynamics of the internal gene regulatory network of a cell to initiate cell-fate transitions, yet models rarely take this into account. Here, we have developed a multiscale perspective to study the granulocyte-monocyte versus megakaryocyte-erythrocyte fate decisions. This transition is dictated by the GATA1-PU.1 network: a classical example of a bistable cell-fate system. We show that, for a wide range of cell communication topologies, even subtle changes in signaling can have pronounced effects on cell-fate decisions. We go on to show how cell-cell coupling through signaling can spontaneously break the symmetry of a homogenous cell population. Noise, both intrinsic and extrinsic, shapes the decision landscape profoundly, and affects the transcriptional dynamics underlying this important hematopoietic cell-fate decision-making system.

This article has an associated ‘The people behind the papers’ interview.

Summary: Through theory and computational modeling, cell-cell communication is revealed to be a crucial and under-appreciated determinant of cell-fate decision-making during hematopoiesis.