Cell Fate Decision as High-Dimensional Critical State Transition

Towards a unification of the 2 meanings of "epigenetics"

The notion of epigenetic "marks" used by molecular biologists is conceptually disconnected from the idea of Waddington's epigenetic "landscape" that is used by systems biologists and biophysicists. Recent advances suggest that these 2 distinct schools of thought could be united.

Early enforcement of cell identity by a functional component of the terminally differentiated state

How progenitor cells can attain a distinct differentiated cell identity is a challenging problem given the fluctuating signaling environment in which cells exist and that critical transcription factors are often not unique to a differentiation process. Here, we test the hypothesis that a unique differentiated cell identity can result from a core component of the differentiated state doubling up as a signaling protein that also drives differentiation. Using live single-cell imaging in the adipocyte differentiation system, we show that progenitor fat cells (preadipocytes) can only commit to terminally differentiate after up-regulating FABP4, a lipid buffer that is highly enriched in mature adipocytes. Upon induction of adipogenesis in mouse preadipocyte cells, we show that after a long delay, cells first abruptly start to engage a positive feedback between CEBPA and PPARG before then engaging, after a second delay, a positive feedback between FABP4 and PPARG. These sequential positive feedbacks both need to engage in order to drive PPARG levels past the threshold for irreversible differentiation. In the last step before commitment, PPARG transcriptionally increases FABP4 expression while fatty acid-loaded FABP4 increases PPARG activity. Together, our study suggests a control principle for robust cell identity whereby a core component of the differentiated state also promotes differentiation from its own progenitor state.

Molecular biomarkers, network biomarkers, and dynamic network biomarkers for diagnosis and prediction of rare diseases

The difficulty of converting scientific research findings into novel pharmacological treatments for rare and life-threatening diseases is enormous. Biomarkers related to multiple biological processes involved in cell growth, proliferation, and disease occurrence have been identified in recent years with the development of immunology, molecular biology, and genomics technologies. Biomarkers are capable of reflecting normal physiological processes, pathological processes, and the response to therapeutic intervention; as such, they play vital roles in disease diagnosis, prevention, drug response, and other aspects of biomedicine. The discovery of valuable biomarkers has become a focal point of current research. Numerous studies have identified molecular biomarkers based on the differential expression/concentration of molecules (e.g., genes/proteins) for disease state diagnosis, characterization, and treatment. Although technological breakthroughs in molecular analysis platforms have enabled the identification of a large number of candidate biomarkers for rare diseases, only a small number of these candidates have been properly validated for use in patient treatment. The traditional molecular biomarkers may lose vital information by ignoring molecular associations/interactions, and thus the concept of network biomarkers based on differential associations/correlations of molecule pairs has been established. This approach promises to be more stable and reliable in diagnosing disease states. Furthermore, the newly-emerged dynamic network biomarkers (DNBs) based on differential fluctuations/correlations of molecular groups are able to recognize pre-disease states or critical states instead of disease states, thereby achieving rare disease prediction or predictive/preventative medicine and providing deep insight into the dynamic characteristics of disease initiation and progression.

Multienzyme activity profiling for evaluation of cell-to-cell variability of metabolic state

In solid organs, cells of the same "type" can vary in their molecular phenotype. The basis of this state variation is being revealed by characterizing cell features including the expression pattern of mRNAs and the internal distribution of proteins. Here, the variability of metabolic state between cells is probed by enzyme activity profiling. We study individual cells of types that can be identified during the post-mitotic phase of oogenesis in Xenopus laevis. Whole-cell homogenates of isolated oocytes are used for kinetic analysis of enzymes, with a focus on the initial reaction rate. For each oocyte type studied, the activity signatures of glyceraldehyde 3-phosphate dehydrogenase (GAPDH) and malate dehydrogenase 1 (MDH1) vary more between the homogenates of single oocytes than between repeat samplings of control homogenates. Unexpectedly, the activity signatures of GAPDH and MDH1 strongly co-vary between oocytes of each type and change in strength of correlation during oogenesis. Therefore, variability of the kinetic behavior of these housekeeping enzymes between "identical" cells is physiologically programmed. Based on these findings, we propose that single-cell profiling of enzyme kinetics will improve understanding of how metabolic state heterogeneity is related to heterogeneity revealed by omics methods including proteomics, epigenomics, and metabolomics.

Postnatal state transition of cardiomyocyte as a primary step in heart maturation

Postnatal heart maturation is the basis of normal cardiac function and provides critical insights into heart repair and regenerative medicine. While static snapshots of the maturing heart have provided much insight into its molecular signatures, few key events during postnatal cardiomyocyte maturation have been uncovered. Here, we report that cardiomyocytes (CMs) experience epigenetic and transcriptional decline of cardiac gene expression immediately after birth, leading to a transition state of CMs at postnatal day 7 (P7) that was essential for CM subtype specification during heart maturation. Large-scale single-cell analysis and genetic lineage tracing confirm the presence of transition state CMs at P7 bridging immature state and mature states. Silencing of key transcription factor JUN in P1-hearts significantly repressed CM transition, resulting in perturbed CM subtype proportions and reduced cardiac function in mature hearts. In addition, transplantation of P7-CMs into infarcted hearts exhibited cardiac repair potential superior to P1-CMs. Collectively, our data uncover CM state transition as a key event in postnatal heart maturation, which not only provides insights into molecular foundations of heart maturation, but also opens an avenue for manipulation of cardiomyocyte fate in disease and regenerative medicine.

Global genome decompaction leads to stochastic activation of gene expression as a first step toward fate commitment in human hematopoietic cells

When human cord blood-derived CD34+ cells are induced to differentiate, they undergo rapid and dynamic morphological and molecular transformations that are critical for fate commitment. In particular, the cells pass through a transitory phase known as "multilineage-primed" state. These cells are characterized by a mixed gene expression profile, different in each cell, with the coexpression of many genes characteristic for concurrent cell lineages. The aim of our study is to understand the mechanisms of the establishment and the exit from this transitory state. We investigated this issue using single-cell RNA sequencing and ATAC-seq. Two phases were detected. The first phase is a rapid and global chromatin decompaction that makes most of the gene promoters in the genome accessible for transcription. It results 24 h later in enhanced and pervasive transcription of the genome leading to the concomitant increase in the cell-to-cell variability of transcriptional profiles. The second phase is the exit from the multilineage-primed phase marked by a slow chromatin closure and a subsequent overall down-regulation of gene transcription. This process is selective and results in the emergence of coherent expression profiles corresponding to distinct cell subpopulations. The typical time scale of these events spans 48 to 72 h. These observations suggest that the nonspecificity of genome decompaction is the condition for the generation of a highly variable multilineage expression profile. The nonspecific phase is followed by specific regulatory actions that stabilize and maintain the activity of key genes, while the rest of the genome becomes repressed again by the chromatin recompaction. Thus, the initiation of differentiation is reminiscent of a constrained optimization process that associates the spontaneous generation of gene expression diversity to subsequent regulatory actions that maintain the activity of some genes, while the rest of the genome sinks back to the repressive closed chromatin state.

Zebrafish neuromesodermal progenitors undergo a critical state transition in vivo

The transition state model of cell differentiation proposes that a transient window of gene expression stochasticity precedes entry into a differentiated state. Here, we assess this theoretical model in zebrafish neuromesodermal progenitors (NMps) in vivo during late somitogenesis stages. We observed an increase in gene expression variability at the 24 somite stage (24ss) before their differentiation into spinal cord and paraxial mesoderm. Analysis of a published 18ss scRNA-seq dataset showed that the NMp population is noisier than its derivatives. By building in silico composite gene expression maps from image data, we assigned an 'NM index' to in silico NMps based on the expression of neural and mesodermal markers and demonstrated that cell population heterogeneity peaked at 24ss. Further examination revealed cells with gene expression profiles incongruent with their prospective fate. Taken together, our work supports the transition state model within an endogenous cell fate decision making event.

Space Biomedicine: A Unique Opportunity to Rethink the Relationships between Physics and Biology

Space biomedicine has provided significant technological breakthroughs by developing new medical devices, diagnostic tools, and health-supporting systems. Many of these products are currently in use onboard the International Space Station and have been successfully translated into clinical practice on Earth. However, biomedical research performed in space has disclosed exciting, new perspectives regarding the relationships between physics and medicine, thus fostering the rethinking of the theoretical basis of biology. In particular, these studies have stressed the critical role that biophysical forces play in shaping the function and pattern formation of living structures. The experimental models investigated under microgravity conditions allow us to appreciate the complexity of living organisms through a very different perspective. Indeed, biological entities should be conceived as a unique magnification of physical laws driven by local energy and order states overlaid by selection history and constraints, in which the source of the inheritance, variation, and process of selection has expanded from the classical Darwinian definition. The very specific nature of the field in which living organisms behave and evolve in a space environment can be exploited to decipher the underlying, basic processes and mechanisms that are not apparent on Earth. In turn, these findings can provide novel opportunities for testing pharmacological countermeasures that can be instrumental for managing a wide array of health problems and diseases on Earth.

Reconstructing data-driven governing equations for cell phenotypic transitions: integration of data science and systems biology

Cells with the same genome can exist in different phenotypes and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming for induced pluripotent stem cells and transdifferentiation, cancer metastasis and fibrosis progression. The regulation and dynamics of cell phenotypic conversion is a fundamental problem in biology, and has a long history of being studied within the formalism of dynamical systems. A main challenge for mechanism-driven modeling studies is acquiring sufficient amount of quantitative information for constraining model parameters. Advances in quantitative experimental approaches, especially high throughput single-cell techniques, have accelerated the emergence of a new direction for reconstructing the governing dynamical equations of a cellular system from quantitative single-cell data, beyond the dominant statistical approaches. Here I review a selected number of recent studies using live- and fixed-cell data and provide my perspective on future development.

Detecting critical transition signals from single-cell transcriptomes to infer lineage-determining transcription factors

Analyzing single-cell transcriptomes promises to decipher the plasticity, heterogeneity, and rapid switches in developmental cellular state transitions. Such analyses require the identification of gene markers for semi-stable transition states. However, there are nontrivial challenges such as unexplainable stochasticity, variable population sizes, and alternative trajectory constructions. By advancing current tipping-point theory-based models with feature selection, network decomposition, accurate estimation of correlations, and optimization, we developed BioTIP to overcome these challenges. BioTIP identifies a small group of genes, called critical transition signal (CTS), to characterize regulated stochasticity during semi-stable transitions. Although methods rooted in different theories converged at the same transition events in two benchmark datasets, BioTIP is unique in inferring lineage-determining transcription factors governing critical transition. Applying BioTIP to mouse gastrulation data, we identify multiple CTSs from one dataset and validated their significance in another independent dataset. We detect the established regulator Etv2 whose expression change drives the haemato-endothelial bifurcation, and its targets together in CTS across three datasets. After comparing to three current methods using six datasets, we show that BioTIP is accurate, user-friendly, independent of pseudo-temporal trajectory, and captures significantly interconnected and reproducible CTSs. We expect BioTIP to provide great insight into dynamic regulations of lineage-determining factors.

Reconstructing data-driven governing equations for cell phenotypic transitions: integration of data science and systems biology

Cells with the same genome can exist in different phenotypes and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming for induced pluripotent stem cells and transdifferentiation, cancer metastasis and fibrosis progression. The regulation and dynamics of cell phenotypic conversion is a fundamental problem in biology, and has a long history of being studied within the formalism of dynamical systems. A main challenge for mechanism-driven modeling studies is acquiring sufficient amount of quantitative information for constraining model parameters. Advances in quantitative experimental approaches, especially high throughput single-cell techniques, have accelerated the emergence of a new direction for reconstructing the governing dynamical equations of a cellular system from quantitative single-cell data, beyond the dominant statistical approaches. Here I review a selected number of recent studies using live- and fixed-cell data and provide my perspective on future development.

Buffering variability in cell regulation motifs close to criticality

Bistable biological regulatory systems need to cope with stochastic noise to fine tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative interactions buffer system variability, hampering noise-induced regime shifts. Our analysis also shows that, in the considered cooperativity range, impending regime shifts can be generically detected by statistical early warning signals from distributional data. Our generic framework, based on minimal models, can be used to extract robustness and variability properties of more complex models and empirical data close to criticality.

A bifurcation concept for B-lymphoid/plasmacytoid dendritic cells with largely fluctuating transcriptome dynamics

Hematopoiesis was considered a hierarchical stepwise process but was revised to a continuous process following single-cell RNA sequencing. However, the uncertainty or fluctuation of single-cell transcriptome dynamics during differentiation was not considered, and the dendritic cell (DC) pathway in the lymphoid context remains unclear. Here, we identify human B-plasmacytoid DC (pDC) bifurcation as large fluctuating transcriptome dynamics in the putative B/NK progenitor region by dry and wet methods. By converting splicing kinetics into diffusion dynamics in a deep generative model, our original computational methodology reveals strong fluctuation at B/pDC bifurcation in IL-7Rα⁺ regions, and LFA-1 fluctuates positively in the pDC direction at the bifurcation. These expectancies are validated by the presence of B/pDC progenitors in the IL-7Rα⁺ fraction and preferential expression of LFA-1 in pDC-biased progenitors with a niche-like culture system. We provide a model of fluctuation-based differentiation, which reconciles continuous and discrete models and is applicable to other developmental systems.

Polyploidy and Myc Proto-Oncogenes Promote Stress Adaptation via Epigenetic Plasticity and Gene Regulatory Network Rewiring

Polyploid cells demonstrate biological plasticity and stress adaptation in evolution; development; and pathologies, including cardiovascular diseases, neurodegeneration, and cancer. The nature of ploidy-related advantages is still not completely understood. Here, we summarize the literature on molecular mechanisms underlying ploidy-related adaptive features. Polyploidy can regulate gene expression via chromatin opening, reawakening ancient evolutionary programs of embryonality. Chromatin opening switches on genes with bivalent chromatin domains that promote adaptation via rapid induction in response to signals of stress or morphogenesis. Therefore, stress-associated polyploidy can activate Myc proto-oncogenes, which further promote chromatin opening. Moreover, Myc proto-oncogenes can trigger polyploidization de novo and accelerate genome accumulation in already polyploid cells. As a result of these cooperative effects, polyploidy can increase the ability of cells to search for adaptive states of cellular programs through gene regulatory network rewiring. This ability is manifested in epigenetic plasticity associated with traits of stemness, unicellularity, flexible energy metabolism, and a complex system of DNA damage protection, combining primitive error-prone unicellular repair pathways, advanced error-free multicellular repair pathways, and DNA damage-buffering ability. These three features can be considered important components of the increased adaptability of polyploid cells. The evidence presented here contribute to the understanding of the nature of stress resistance associated with ploidy and may be useful in the development of new methods for the prevention and treatment of cardiovascular and oncological diseases.

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

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

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CELLoGeNe – Computation of Energy Landscapes of Logical Gene Networks

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Cell states as landscape attractors

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Maintenance and acquisition of cell pluripotency applications

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Single cell stochastic landscape navigation and visualization tool

Lack of Correlation between Landscape Geometry and Transition Rates

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

A Statistical Journey through the Topological Determinants of the β2 Adrenergic Receptor Dynamics

Activation of G-protein-coupled receptors (GPCRs) is mediated by molecular switches throughout the transmembrane region of the receptor. In this work, we continued along the path of a previous computational study wherein energy transport in the β2 Adrenergic Receptor (β2-AR) was examined and allosteric switches were identified in the molecular structure through the reorganization of energy transport networks during activation. In this work, we further investigated the allosteric properties of β2-AR, using Protein Contact Networks (PCNs). In this paper, we report an extensive statistical analysis of the topological and structural properties of β2-AR along its molecular dynamics trajectory to identify the activation pattern of this molecular system. The results show a distinct character to the activation that both helps to understand the allosteric switching previously identified and confirms the relevance of the network formalism to uncover relevant functional features of protein molecules.

From developmental to atavistic bet-hedging: How cancer cells pervert the exploitation of random single-cell phenotypic fluctuations

Stochastic gene expression plays a leading developmental role through its contribution to cell differentiation. It is also proposed to promote phenotypic diversification in malignant cells. However, it remains unclear if these two forms of cellular bet-hedging are identical or rather display distinct features. Here we argue that bet-hedging phenomena in cancer cells are more similar to those occurring in unicellular organisms than to those of normal metazoan cells. We further propose that the atavistic bet-hedging strategies in cancer originate from a hijacking of the normal developmental bet-hedging of metazoans. Finally, we discuss the constraints that may shape the atavistic bet-hedging strategies of cancer cells.

Evidence for close molecular proximity between reverting and undifferentiated cells

BACKGROUND

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

RESULTS

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

CONCLUSIONS

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

NANOG initiates epiblast fate through the coordination of pluripotency genes expression

The epiblast is the source of all mammalian embryonic tissues and of pluripotent embryonic stem cells. It differentiates alongside the primitive endoderm in a “salt and pepper” pattern from inner cell mass (ICM) progenitors during the preimplantation stages through the activity of NANOG, GATA6 and the FGF pathway. When and how epiblast lineage specification is initiated is still unclear. Here, we show that the coordinated expression of pluripotency markers defines epiblast identity. Conversely, ICM progenitor cells display random cell-to-cell variability in expression of various pluripotency markers, remarkably dissimilar from the epiblast signature and independently from NANOG, GATA6 and FGF activities. Coordination of pluripotency markers expression fails in Nanog and Gata6 double KO (DKO) embryos. Collectively, our data suggest that NANOG triggers epiblast specification by ensuring the coordinated expression of pluripotency markers in a subset of cells, implying a stochastic mechanism. These features are likely conserved, as suggested by analysis of human embryos.

Pluripotent epiblast cells segregate from primitive endoderm in the blastocyst inner cell mass (ICM). Here the authors show that mosaic epiblast differentiation during mouse and human preimplantation development initiates stochastically in ICM progenitors, independently of the FGF pathway, and requires NANOG activity

Dynamical landscapes of cell fate decisions

The generation of cellular diversity during development involves differentiating cells transitioning between discrete cell states. In the 1940s, the developmental biologist Conrad Waddington introduced a landscape metaphor to describe this process. The developmental path of a cell was pictured as a ball rolling through a terrain of branching valleys with cell fate decisions represented by the branch points at which the ball decides between one of two available valleys. Here we discuss progress in constructing quantitative dynamical models inspired by this view of cellular differentiation. We describe a framework based on catastrophe theory and dynamical systems methods that provides the foundations for quantitative geometric models of cellular differentiation. These models can be fit to experimental data and used to make quantitative predictions about cellular differentiation. The theory indicates that cell fate decisions can be described by a small number of decision structures, such that there are only two distinct ways in which cells make a binary choice between one of two fates. We discuss the biological relevance of these mechanisms and suggest the approach is broadly applicable for the quantitative analysis of differentiation dynamics and for determining principles of developmental decisions.

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.

Profiling intermediate cell states in high resolution

Kong et al. present Capybara, a computational method to identify cell states from single-cell gene expression data. Notably, Capybara can identify intermediate cell states and cell state transitions, offering biologists new means with which to interrogate the states and fates of cells.

Dynamic patterns of microRNA expression during acute myeloid leukemia state-transition

MicroRNAs (miRNAs) have been shown to hold prognostic value in acute myeloid leukemia (AML); however, the temporal dynamics of miRNA expression in AML are poorly understood. Using serial samples from a mouse model of AML to generate time-series miRNA sequencing data, we are the first to show that the miRNA transcriptome undergoes state-transition during AML initiation and progression. We modeled AML state-transition as a particle undergoing Brownian motion in a quasi-potential and validated the AML state-space and state-transition model to accurately predict time to AML in an independent cohort of mice. The critical points of the model provided a framework to align samples from mice that developed AML at different rates. Our mathematical approach allowed discovery of dynamic processes involved during AML development and, if translated to humans, has the potential to predict an individual's disease trajectory.

Roadmap on plasticity and epigenetics in cancer

The role of plasticity and epigenetics in shaping cancer evolution and response to therapy has taken center stage with recent technological advances including single cell sequencing. This roadmap article is focused on state-of-the-art mathematical and experimental approaches to interrogate plasticity in cancer, and addresses the following themes and questions: is there a formal overarching framework that encompasses both non-genetic plasticity and mutation-driven somatic evolution? How do we measure and model the role of the microenvironment in influencing/controlling non-genetic plasticity? How can we experimentally study non-genetic plasticity? Which mathematical techniques are required or best suited? What are the clinical and practical applications and implications of these concepts?

A robust method for designing multistable systems by embedding bistable subsystems

Although multistability is an important dynamic property of a wide range of complex systems, it is still a challenge to develop mathematical models for realising high order multistability using realistic regulatory mechanisms. To address this issue, we propose a robust method to develop multistable mathematical models by embedding bistable models together. Using the GATA1-GATA2-PU.1 module in hematopoiesis as the test system, we first develop a tristable model based on two bistable models without any high cooperative coefficients, and then modify the tristable model based on experimentally determined mechanisms. The modified model successfully realises four stable steady states and accurately reflects a recent experimental observation showing four transcriptional states. In addition, we develop a stochastic model, and stochastic simulations successfully realise the experimental observations in single cells. These results suggest that the proposed method is a general approach to develop mathematical models for realising multistability and heterogeneity in complex systems.

Determination of tipping point in course of PM2.5 organic extracts-induced malignant transformation by dynamic network biomarkers

The dynamic network biomarkers (DNBs) are designed to identify the tipping point and specific molecules in initiation of PM_2.5-induced lung cancers. To discover early-warning signals, we analyzed time-series gene expression datasets over a course of PM_2.5 organic extraction-induced human bronchial epithelial (HBE) cell transformation (0^th~16^th week). A composition index of DNB (CI_DNB) was calculated to determine correlations and fluctuations in molecule clusters at each timepoint. We identified a group of genes with the highest CI_DNB at the 10^th week, implicating a tipping point and corresponding DNBs. Functional experiments revealed that manipulating respective DNB genes at the tipping point led to remarkable changes in malignant phenotypes, including four promoters (GAB2, NCF1, MMP25, LAPTM5) and three suppressors (BATF2, DOK3, DAP3). Notably, co-altered expression of seven core DNB genes resulted in an enhanced activity of malignant transformation compared to effects of single-gene manipulation. Perturbation of pathways (EMT, HMGB1, STAT3, NF-κB, PTEN) appeared in HBE cells at the tipping point. The core DNB genes were involved in regulating lung cancer cell growth and associated with poor survival, indicating their synergistic effects in initiation and development of lung cancers. These findings provided novel insights into the mechanism of dynamic networks attributable to PM_2.5-induced cell transformation.

Tipping the Balance: A Criticality Perspective

Cell populations are often characterised by phenotypic heterogeneity in the form of two distinct subpopulations. We consider a model of tumour cells consisting of two subpopulations: non-cancer promoting (NCP) and cancer-promoting (CP). Under steady state conditions, the model has similarities with a well-known model of population genetics which exhibits a purely noise-induced transition from unimodality to bimodality at a critical value of the noise intensity σ2. The noise is associated with the parameter λ representing the system-environment coupling. In the case of the tumour model, λ has a natural interpretation in terms of the tissue microenvironment which has considerable influence on the phenotypic composition of the tumour. Oncogenic transformations give rise to considerable fluctuations in the parameter. We compute the λ−σ2 phase diagram in a stochastic setting, drawing analogies between bifurcations and phase transitions. In the region of bimodality, a transition from a state of balance to a state of dominance, in terms of the competing subpopulations, occurs at λ = 0. Away from this point, the NCP (CP) subpopulation becomes dominant as λ changes towards positive (negative) values. The variance of the steady state probability density function as well as two entropic measures provide characteristic signatures at the transition point.

Hematopoietic differentiation is characterized by a transient peak of entropy at a single-cell level

Background

Mature blood cells arise from hematopoietic stem cells in the bone marrow by a process of differentiation along one of several different lineage trajectories. This is often represented as a series of discrete steps of increasing progenitor cell commitment to a given lineage, but as for differentiation in general, whether the process is instructive or stochastic remains controversial. Here, we examine this question by analyzing single-cell transcriptomic data from human bone marrow cells, assessing cell-to-cell variability along the trajectories of hematopoietic differentiation into four different types of mature blood cells. The instructive model predicts that cells will be following the same sequence of instructions and that there will be minimal variability of gene expression between them throughout the process, while the stochastic model predicts a role for cell-to-cell variability when lineage commitments are being made.

Results

Applying Shannon entropy to measure cell-to-cell variability among human hematopoietic bone marrow cells at the same stage of differentiation, we observed a transient peak of gene expression variability occurring at characteristic points in all hematopoietic differentiation pathways. Strikingly, the genes whose cell-to-cell variation of expression fluctuated the most over the course of a given differentiation trajectory are pathway-specific genes, whereas genes which showed the greatest variation of mean expression are common to all pathways. Finally, we showed that the level of cell-to-cell variation is increased in the most immature compartment of hematopoiesis in myelodysplastic syndromes.

Conclusions

These data suggest that human hematopoietic differentiation could be better conceptualized as a dynamical stochastic process with a transient stage of cellular indetermination, and strongly support the stochastic view of differentiation. They also highlight the need to consider the role of stochastic gene expression in complex physiological processes and pathologies such as cancers, paving the way for possible noise-based therapies through epigenetic regulation.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12915-022-01264-9.

Development of a dynamic network biomarkers method and its application for detecting the tipping point of prior disease development

The dynamic network biomarker (DNB) method has advanced since it was first proposed. This review discusses advances in the DNB method that can identify the dynamic change in the expression signature related to the critical time point of disease progression by utilizing different kinds of transcriptome data. The DNB method is good at identifying potential biomarkers for cancer and other disease development processes that are represented by a limited molecular profile change between the normal and critical stages. We highlight that the cancer tipping point or premalignant state has been widely discovered for different types of cancer by using the DNB method that utilizes bulk or single-cell RNA sequencing data. This method could also be applied to other dynamic research studies and help identify early warning signals, such as the prediction of a pre-outbreak of COVID-19. We also discuss how the identification of reliable biomarkers of cancer and the development of new methods can be utilized for early detection and intervention and provide insights into emerging paths of the widespread biomarker candidate pool for further validation and disease/health management.

Epithelial-to-mesenchymal transition proceeds through directional destabilization of multidimensional attractor

How a cell changes from one stable phenotype to another one is a fundamental problem in developmental and cell biology. Mathematically, a stable phenotype corresponds to a stable attractor in a generally multi-dimensional state space, which needs to be destabilized so the cell relaxes to a new attractor. Two basic mechanisms for destabilizing a stable fixed point, pitchfork and saddle-node bifurcations, have been extensively studied theoretically; however, direct experimental investigation at the single-cell level remains scarce. Here, we performed live cell imaging studies and analyses in the framework of dynamical systems theories on epithelial-to-mesenchymal transition (EMT). While some mechanistic details remain controversial, EMT is a cell phenotypic transition (CPT) process central to development and pathology. Through time-lapse imaging we recorded single cell trajectories of human A549/Vim-RFP cells undergoing EMT induced by different concentrations of exogenous TGF-β in a multi-dimensional cell feature space. The trajectories clustered into two distinct groups, indicating that the transition dynamics proceeds through parallel paths. We then reconstructed the reaction coordinates and the corresponding quasi-potentials from the trajectories. The potentials revealed a plausible mechanism for the emergence of the two paths where the original stable epithelial attractor collides with two saddle points sequentially with increased TGF-β concentration, and relaxes to a new one. Functionally, the directional saddle-node bifurcation ensures a CPT proceeds towards a specific cell type, as a mechanistic realization of the canalization idea proposed by Waddington.

Cells with the same genetic code can take on many different formss, or phenotypes, which have distinct roles and appearances. Sometimes cells switch from one phenotype to another as part of healthy growth or during disease. One such change is the epithelial-to-mesenchymal transition (EMT), which is involved in fetal development, wound healing and the spread of cancer cells.

During EMT, closely connected epithelial cells detach from one another and change into mesenchymal cells that are able to migrate. Cells undergo a number of changes during this transition; however, the path they take to reach their new form is not entirely clear. For instance, do all cells follow the same route, or are there multiple ways that cells can shift from one state to the next?

To address this question, Wang et al. studied individual lung cancer cells that had been treated with a protein that drives EMT. The cells were then imaged at regular intervals over the course of two to three days to see how they changed in response to different concentrations of protein. Using a mathematical analysis designed to study chemical reactions, Wang et al. showed that the cells transform into the mesenchymal phenotype through two main routes.

This result suggests that attempts to prevent EMT, in cancer treatment for instance, would require blocking both paths taken by the cells. This information could be useful for biomedical researchers trying to regulate the EMT process. The quantitative approach of this study could also help physicists and mathematicians study other types of transition that occur in biology.

Slow nucleosome dynamics set the transcriptional speed limit and induce RNA polymerase II traffic jams and bursts

Nucleosomes are recognized as key regulators of transcription. However, the relationship between slow nucleosome unwrapping dynamics and bulk transcriptional properties has not been thoroughly explored. Here, an agent-based model that we call the dynamic defect Totally Asymmetric Simple Exclusion Process (ddTASEP) was constructed to investigate the effects of nucleosome-induced pausing on transcriptional dynamics. Pausing due to slow nucleosome dynamics induced RNAPII convoy formation, which would cooperatively prevent nucleosome rebinding leading to bursts of transcription. The mean first passage time (MFPT) and the variance of first passage time (VFPT) were analytically expressed in terms of the nucleosome rate constants, allowing for the direct quantification of the effects of nucleosome-induced pausing on pioneering polymerase dynamics. The mean first passage elongation rate γ(h_c, h_o) is inversely proportional to the MFPT and can be considered to be a new axis of the ddTASEP phase diagram, orthogonal to the classical αβ-plane (where α and β are the initiation and termination rates). Subsequently, we showed that, for β = 1, there is a novel jamming transition in the αγ-plane that separates the ddTASEP dynamics into initiation-limited and nucleosome pausing-limited regions. We propose analytical estimates for the RNAPII density ρ, average elongation rate v, and transcription flux J and verified them numerically. We demonstrate that the intra-burst RNAPII waiting times t_in follow the time-headway distribution of a max flux TASEP and that the average inter-burst interval tIBI¯ correlates with the index of dispersion D_e. In the limit γ→0, the average burst size reaches a maximum set by the closing rate h_c. When α≪1, the burst sizes are geometrically distributed, allowing large bursts even while the average burst size NB¯ is small. Last, preliminary results on the relative effects of static and dynamic defects are presented to show that dynamic defects can induce equal or greater pausing than static bottle necks.

To perform specific functions, cells must express specific genes by copying the information in DNA into RNA via transcription. Structural proteins called nucleosomes are spaced every 200 base pairs along the length of a strand of DNA and play a crucial function in the regulation of gene activity by tightly binding DNA strands and condensing them into heterochromatin, preventing transcription by RNA polymerase II (RNAPII). Even on active genes where nucleosomes are loosely attached to DNA strands, the wrapping and unwrapping of nucleosomes pause transcription as RNAPII passes by. Previous mathematical models of transcription have compared this biological process to traffic on a one lane highway without obstructions. In contrast, our proposed model simulates transcription like traffic in a grid system where nucleosomes can be thought of as pedestrians or other vehicles crossing the road at regularly spaced intersections. Just as side street traffic and pedestrian crossings can cause cars to form convoys and cause jams limiting the max speed in an area, nucleosomes can cause RNAPII to form convoys that lead to bursts of mRNA production and limit the average polymerase flux through the gene.

Detect the early-warning signals of diseases based on signaling pathway perturbations on a single sample

BACKGROUND

During the pathogenesisof complex diseases, a sudden health deterioration will occur as results of the cumulative effect of various internal or external factors. The prediction of an early warning signal (pre-disease state) before such deterioration is very important in clinical practice, especially for a single sample. The single-sample landscape entropy (SLE) was proposed to tackle this issue. However, the PPI used in SLE was lack of definite biological meanings. Besides, the calculation of multiple correlations based on limited reference samples in SLE is time-consuming and suspect.

RESULTS

Abnormal signals generally exert their effect through the static definite biological functions in signaling pathways across the development of diseases. Thus, it is a natural way to study the propagation of the early-warning signals based on the signaling pathways in the KEGG database. In this paper, we propose a signaling perturbation method named SSP, to study the early-warning signal in signaling pathways for single dynamic time-series data. Results in three real datasets including the influenza virus infection, lung adenocarcinoma, and acute lung injury show that the proposed SSP outperformed the SLE. Moreover, the early-warning signal can be detected by one important signaling pathway PI3K-Akt.

CONCLUSIONS

These results all indicate that the static model in pathways could simplify the detection of the early-warning signals.

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

Fate decisions in developing tissues involve cells transitioning between discrete cell states, each defined by distinct gene expression profiles. The Waddington landscape, in which the development of a cell is viewed as a ball rolling through a valley filled terrain, is an appealing way to describe differentiation. To construct and validate accurate landscapes, quantitative methods based on experimental data are necessary. We combined principled statistical methods with a framework based on catastrophe theory and approximate Bayesian computation to formulate a quantitative dynamical landscape that accurately predicts cell fate outcomes of pluripotent stem cells exposed to different combinations of signaling factors. Analysis of the landscape revealed two distinct ways in which cells make a binary choice between one of two fates. We suggest that these represent archetypal designs for developmental decisions. The approach is broadly applicable for the quantitative analysis of differentiation and for determining the logic of developmental decisions.

Dynamical network biomarkers: Theory and applications

This paper reviews theory of DNB (Dynamical Network Biomarkers) and its applications including both modern medicine and traditional medicine. We show that omics data such as gene/protein expression profiles can be effectively used to detect pre-disease states before critical transitions from healthy states to disease states by using the DNB theory. The DNB theory with big biological data is expected to lead to ultra-early precision and preventive medicine.

Soft Statistical Mechanics for Biology

The multilevel organization of nature is self-evident: proteins do interact among them to give rise to an organized metabolism and the same hierarchical organization is in action for gene expression, tissue and organ architectures, and ecological systems.The still more common approach to such state of affairs is to think that causally relevant events originate from the lower level in the form of perturbations, that climb up the hierarchy reaching the ultimate layer of macroscopic behavior (e.g., causing a specific disease). Such rigid bottom-up causative model is unable to offer realistic models of many biological phenomena.Complex network approach allows to uncover the nature of multilevel organization, but in order to operationally define the organization principles of biological systems, we need to go further and complement network approach with sensible measures of order and organization. These measures, while keeping their original physical meaning, must not impose theoretical premises not verifiable in biological frameworks. We will show here how relatively simple and largely hypothesis-free multidimensional statistics tools can satisfactorily meet these criteria.

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.

Identifying toggle genes from transcriptome-wide scatter: A new perspective for biological regulation

The study of gene expression variability, especially for cancer and cell differentiation studies, has become important. Here, we investigate transcriptome-wide scatter of 23 cell types and conditions across different levels of biological complexity. We focused on genes that act like toggle switches between pairwise replicates of the same cell type, i.e. genes expressed in one replicate and not expressed in the other, sometimes also referred as ON/OFF genes. The proportion of these toggle genes dramatically increases from unicellular to multicellular organization, especially for development and cancer cells. A relevant portion of toggle switches are non-coding genes: in unicellular systems the most represented classes are tRNA and rRNA, while multicellular systems more frequently show lncRNA, sncRNA and pseudogenes. Notably, disease associated microRNAs (miRNAs), pseudogenes and numerous uncharacterized transcripts are present in both development and cancer cells. On top of the known intrinsic and extrinsic factors, our work indicates toggle genes as a novel collective component creating transcriptome-wide variability. This requires further investigation for elucidating both evolutionary and disease processes.

Human Synchronization Maps-The Hybrid Consciousness of the Embodied Mind

We examine the theoretical implications of empirical studies developed over recent years. These experiments have explored the biosemiotic nature of communication streams from emotional neuroscience and embodied mind perspectives. Information combinatorics analysis enabled a deeper understanding of the coupling and decoupling dynamics of biosemiotics streams. We investigated intraindividual and interpersonal relations as coevolution dynamics of hybrid couplings, synchronizations, and desynchronizations. Cluster analysis and Markov chains produced evidence of chimaera states and phase transitions. A probabilistic and nondeterministic approach clarified the properties of these hybrid dynamics. Thus, multidimensional theoretical models can represent the hybrid nature of human interactions.

Reduction of a stochastic model of gene expression: Lagrangian dynamics gives access to basins of attraction as cell types and metastabilty

Differentiation is the process whereby a cell acquires a specific phenotype, by differential gene expression as a function of time. This is thought to result from the dynamical functioning of an underlying Gene Regulatory Network (GRN). The precise path from the stochastic GRN behavior to the resulting cell state is still an open question. In this work we propose to reduce a stochastic model of gene expression, where a cell is represented by a vector in a continuous space of gene expression, to a discrete coarse-grained model on a limited number of cell types. We develop analytical results and numerical tools to perform this reduction for a specific model characterizing the evolution of a cell by a system of piecewise deterministic Markov processes (PDMP). Solving a spectral problem, we find the explicit variational form of the rate function associated to a large deviations principle, for any number of genes. The resulting Lagrangian dynamics allows us to define a deterministic limit of which the basins of attraction can be identified to cellular types. In this context the quasipotential, describing the transitions between these basins in the weak noise limit, can be defined as the unique solution of an Hamilton-Jacobi equation under a particular constraint. We develop a numerical method for approximating the coarse-grained model parameters, and show its accuracy for a symmetric toggle-switch network. We deduce from the reduced model an approximation of the stationary distribution of the PDMP system, which appears as a Beta mixture. Altogether those results establish a rigorous frame for connecting GRN behavior to the resulting cellular behavior, including the calculation of the probability of jumps between cell types.

Cell state transitions: definitions and challenges

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

Personalization of medical treatments in oncology: time for rethinking the disease concept to improve individual outcomes

The agenda of pharmacology discovery in the field of personalized oncology was dictated by the search of molecular targets assumed to deterministically drive tumor development. In this perspective, genes play a fundamental "causal" role while cells simply act as causal proxies, i.e., an intermediate between the molecular input and the organismal output. However, the ceaseless genomic change occurring across time within the same primary and metastatic tumor has broken the hope of a personalized treatment based only upon genomic fingerprint. Indeed, current models are unable in capturing the unfathomable complexity behind the outbreak of a disease, as they discard the contribution of non-genetic factors, environment constraints, and the interplay among different tiers of organization. Herein, we posit that a comprehensive personalized model should view at the disease as a "historical" process, in which different spatially and timely distributed factors interact with each other across multiple levels of organization, which collectively interact with a dynamic gene-expression pattern. Given that a disease is a dynamic, non-linear process - and not a static-stable condition - treatments should be tailored according to the "timing-frame" of each condition. This approach can help in detecting those critical transitions through which the system can access different attractors leading ultimately to diverse outcomes - from a pre-disease state to an overt illness or, alternatively, to recovery. Identification of such tipping points can substantiate the predictive and the preventive ambition of the Predictive, Preventive and Personalized Medicine (PPPM/3PM). However, an unusual effort is required to conjugate multi-omics approaches, data collection, and network analysis reconstruction (eventually involving innovative Artificial Intelligent tools) to recognize the critical phases and the relevant targets, which could help in patient stratification and therapy personalization.

Noise distorts the epigenetic landscape and shapes cell-fate decisions

The Waddington epigenetic landscape has become an iconic representation of the cellular differentiation process. Recent single-cell transcriptomic data provide new opportunities for quantifying this originally conceptual tool, offering insight into the gene regulatory networks underlying cellular development. While many methods for constructing the landscape have been proposed, by far the most commonly employed approach is based on computing the landscape as the negative logarithm of the steady-state probability distribution. Here, we use simple models to highlight the complexities and limitations that arise when reconstructing the potential landscape in the presence of stochastic fluctuations. We consider how the landscape changes in accordance with different stochastic systems and show that it is the subtle interplay between the deterministic and stochastic components of the system that ultimately shapes the landscape. We further discuss how the presence of noise has important implications for the identifiability of the regulatory dynamics from experimental data. A record of this paper's transparent peer review process is included in the supplemental information.

Spatial control over near-critical-point operation ensures fidelity of ParABS-mediated DNA partition

In bacteria, most low-copy-number plasmid and chromosomally encoded partition systems belong to the tripartite ParABS partition machinery. Despite the importance in genetic inheritance, the mechanisms of ParABS-mediated genome partition are not well understood. Combining theory and experiment, we provided evidence that the ParABS system-DNA partitioning in vivo via the ParA-gradient-based Brownian ratcheting-operates near a transition point in parameter space (i.e., a critical point), across which the system displays qualitatively different motile behaviors. This near-critical-point operation adapts the segregation distance of replicated plasmids to the half length of the elongating nucleoid, ensuring both cell halves to inherit one copy of the plasmids. Further, we demonstrated that the plasmid localizes the cytoplasmic ParA to buffer the partition fidelity against the large cell-to-cell fluctuations in ParA level. The spatial control over the near-critical-point operation not only ensures both sensitive adaptation and robust execution of partitioning but also sheds light on the fundamental question in cell biology: how do cells faithfully measure cellular-scale distance by only using molecular-scale interactions?

Self-organization of whole-gene expression through coordinated chromatin structural transition

The human DNA molecule is a 2-m-long polymer collapsed into the micrometer space of the cell nucleus. This simple consideration rules out any "Maxwell demon"-like explanation of regulation in which a single regulatory molecule (e.g., a transcription factor) finds autonomously its way to the particular target gene whose expression must be repressed or enhanced. A gene-by-gene regulation is still more contrasting with the physical reality when in the presence of cell state transitions involving the contemporary expression change of thousands of genes. This state of affair asks for a statistical mechanics inspired approach where specificity arises from a selective unfolding of chromatin driving the rewiring of gene expression pattern. The arising of "expression waves" marking state transitions related to chromatin structural reorganization through self-organized critical control of whole-genome expression will be described in the present paper. We adopt as a model system the gene expression time course of a cancer cell (MCF-7) population exposed to an efficient stimulus causing a state transition in comparison with an ineffective stimulus. The obtained results will be put into the perspective of biological adaptive systems living on the edge of chaos.

A DNA repair pathway can regulate transcriptional noise to promote cell fate transitions

Stochastic fluctuations in gene expression ("noise") are often considered detrimental, but fluctuations can also be exploited for benefit (e.g., dither). We show here that DNA base excision repair amplifies transcriptional noise to facilitate cellular reprogramming. Specifically, the DNA repair protein Apex1, which recognizes both naturally occurring and unnatural base modifications, amplifies expression noise while homeostatically maintaining mean expression levels. This amplified expression noise originates from shorter-duration, higher-intensity transcriptional bursts generated by Apex1-mediated DNA supercoiling. The remodeling of DNA topology first impedes and then accelerates transcription to maintain mean levels. This mechanism, which we refer to as "discordant transcription through repair" ("DiThR," which is pronounced "dither"), potentiates cellular reprogramming and differentiation. Our study reveals a potential functional role for transcriptional fluctuations mediated by DNA base modifications in embryonic development and disease.

Close to Optimal Cell Sensing Ensures the Robustness of Tissue Differentiation Process: The Avian Photoreceptor Mosaic Case

The way that progenitor cell fate decisions and the associated environmental sensing are regulated to ensure the robustness of the spatial and temporal order in which cells are generated towards a fully differentiating tissue still remains elusive. Here, we investigate how cells regulate their sensing intensity and radius to guarantee the required thermodynamic robustness of a differentiated tissue. In particular, we are interested in finding the conditions where dedifferentiation at cell level is possible (microscopic reversibility), but tissue maintains its spatial order and differentiation integrity (macroscopic irreversibility). In order to tackle this, we exploit the recently postulated Least microEnvironmental Uncertainty Principle (LEUP) to develop a theory of stochastic thermodynamics for cell differentiation. To assess the predictive and explanatory power of our theory, we challenge it against the avian photoreceptor mosaic data. By calibrating a single parameter, the LEUP can predict the cone color spatial distribution in the avian retina and, at the same time, suggest that such a spatial pattern is associated with quasi-optimal cell sensing. By means of the stochastic thermodynamics formalism, we find out that thermodynamic robustness of differentiated tissues depends on cell metabolism and cell sensing properties. In turn, we calculate the limits of the cell sensing radius that ensure the robustness of differentiated tissue spatial order. Finally, we further constrain our model predictions to the avian photoreceptor mosaic.

Statistical mechanics meets single-cell biology

Single-cell omics is transforming our understanding of cell biology and disease, yet the systems-level analysis and interpretation of single-cell data faces many challenges. In this Perspective, we describe the impact that fundamental concepts from statistical mechanics, notably entropy, stochastic processes and critical phenomena, are having on single-cell data analysis. We further advocate the need for more bottom-up modelling of single-cell data and to embrace a statistical mechanics analysis paradigm to help attain a deeper understanding of single-cell systems biology.