Universality of clone dynamics during tissue development

Mechanisms that clear mutations drive field cancerization in mammary tissue

Oncogenic mutations are abundant in the tissues of healthy individuals, but rarely form tumours1-3. Yet, the underlying protection mechanisms are largely unknown. To resolve these mechanisms in mouse mammary tissue, we use lineage tracing to map the fate of wild-type and Brca1-/-;Trp53-/- cells, and find that both follow a similar pattern of loss and spread within ducts. Clonal analysis reveals that ducts consist of small repetitive units of self-renewing cells that give rise to short-lived descendants. This offers a first layer of protection as any descendants, including oncogenic mutant cells, are constantly lost, thereby limiting the spread of mutations to a single stem cell-descendant unit. Local tissue remodelling during consecutive oestrous cycles leads to the cooperative and stochastic loss and replacement of self-renewing cells. This process provides a second layer of protection, leading to the elimination of most mutant clones while enabling the minority that by chance survive to expand beyond the stem cell-descendant unit. This leads to fields of mutant cells spanning large parts of the epithelial network, predisposing it for transformation. Eventually, clone expansion becomes restrained by the geometry of the ducts, providing a third layer of protection. Together, these mechanisms act to eliminate most cells that acquire somatic mutations at the expense of driving the accelerated expansion of a minority of cells, which can colonize large areas, leading to field cancerization.

Correspondence between multiple signaling and developmental cellular patterns: a computational perspective

The spatial arrangement of variant phenotypes during stem cell division plays a crucial role in the self-organization of cell tissues. The patterns observed in these cellular assemblies, where multiple phenotypes vie for space and resources, are largely influenced by a mixture of different diffusible chemical signals. This complex process is carried out within a chronological framework of interplaying intracellular and intercellular events. This includes receiving external stimulants, whether secreted by other individuals or provided by the environment, interpreting these environmental signals, and incorporating the information to designate cell fate. Here, given two distinct signaling patterns generated by Turing systems, we investigated the spatial distribution of differentiating cells that use these signals as external cues for modifying the production rates. By proposing a computational map, we show that there is a correspondence between the multiple signaling and developmental cellular patterns. In other words, the model provides an appropriate prediction for the final structure of the differentiated cells in a multi-signal, multi-cell environment. Conversely, when a final snapshot of cellular patterns is given, our algorithm can partially identify the signaling patterns that influenced the formation of the cellular structure, provided that the governing dynamic of the signaling patterns is already known.

Clonal dynamics of surface-driven growing tissues

The self-organization of cells into complex tissues relies on a tight coordination of cell behavior. Identifying the cellular processes driving tissue growth is key to understanding the emergence of tissue forms and devising targeted therapies for aberrant growth, such as in cancer. Inferring the mode of tissue growth, whether it is driven by cells on the surface or by cells in the bulk, is possible in cell culture experiments but difficult in most tissues in living organisms (in vivo). Genetic tracing experiments, where a subset of cells is labeled with inheritable markers, have become important experimental tools to study cell fate in vivo. Here we show that the mode of tissue growth is reflected in the size distribution of the progeny of marked cells. To this end, we derive the clone size distributions using analytical calculations in the limit of negligible cell migration and cell death, and we test our predictions with an agent-based stochastic sampling technique. We show that for surface-driven growth the clone size distribution takes a characteristic power-law form with an exponent determined by fluctuations of the tissue surface. Our results propose a possible way of determining the mode of tissue growth from genetic tracing experiments.

Measures of genetic diversification in somatic tissues at bulk and single-cell resolution

Intra-tissue genetic heterogeneity is universal to both healthy and cancerous tissues. It emerges from the stochastic accumulation of somatic mutations throughout development and homeostasis. By combining population genetics theory and genomic information, genetic heterogeneity can be exploited to infer tissue organization and dynamics in vivo. However, many basic quantities, for example the dynamics of tissue-specific stem cells remain difficult to quantify precisely. Here, we show that single-cell and bulk sequencing data inform on different aspects of the underlying stochastic processes. Bulk-derived variant allele frequency spectra (VAF) show transitions from growing to constant stem cell populations with age in samples of healthy esophagus epithelium. Single-cell mutational burden distributions allow a sample size independent measure of mutation and proliferation rates. Mutation rates in adult hematopietic stem cells are higher compared to inferences during development, suggesting additional proliferation-independent effects. Furthermore, single-cell derived VAF spectra contain information on the number of tissue-specific stem cells. In hematopiesis, we find approximately 2 × 105 HSCs, if all stem cells divide symmetrically. However, the single-cell mutational burden distribution is over-dispersed compared to a model of Poisson distributed random mutations. A time-associated model of mutation accumulation with a constant rate alone cannot generate such a pattern. At least one additional source of stochasticity would be needed. Possible candidates for these processes may be occasional bursts of stem cell divisions, potentially in response to injury, or non-constant mutation rates either through environmental exposures or cell-intrinsic variation.

A computational model of stem cells' internal mechanism to recapitulate spatial patterning and maintain the self-organized pattern in the homeostasis state

The complex functioning of multi-cellular tissue development relies on proper cell production rates to replace dead or differentiated specialized cells. Stem cells are critical for tissue development and maintenance, as they produce specialized cells to meet the tissues' demands. In this study, we propose a computational model to investigate the stem cell's mechanism, which generates the appropriate proportion of specialized cells, and distributes them to their correct position to form and maintain the organized structure in the population through intercellular reactions. Our computational model focuses on early development, where the populations overall behavior is determined by stem cells and signaling molecules. The model does not include complicated factors such as movement of specialized cells or outside signaling sources. The results indicate that in our model, the stem cells can organize the population into a desired spatial pattern, which demonstrates their ability to self-organize as long as the corresponding leading signal is present. We also investigate the impact of stochasticity, which provides desired non-genetic diversity; however, it can also break the proper boundaries of the desired spatial pattern. We further examine the role of the death rate in maintaining the system's steady state. Overall, our study sheds light on the strategies employed by stem cells to organize specialized cells and maintain proper functionality. Our findings provide insight into the complex mechanisms involved in tissue development and maintenance, which could lead to new approaches in regenerative medicine and tissue engineering.

A local polynomial moment approximation for compartmentalized biochemical systems

Compartmentalized biochemical reactions are a ubiquitous building block of biological systems. The interplay between chemical and compartmental dynamics can drive rich and complex dynamical behaviors that are difficult to analyze mathematically - especially in the presence of stochasticity. We have recently proposed an effective moment equation approach to study the statistical properties of compartmentalized biochemical systems. So far, however, this approach is limited to polynomial rate laws and moreover, it relies on suitable moment closure approximations, which can be difficult to find in practice. In this work we propose a systematic method to derive closed moment dynamics for compartmentalized biochemical systems. We show that for the considered class of systems, the moment equations involve expectations over functions that factorize into two parts, one depending on the molecular content of the compartments and one depending on the compartment number distribution. Our method exploits this structure and approximates each function with suitable polynomial expansions, leading to a closed system of moment equations. We demonstrate the method using three systems inspired by cell populations and organelle networks and study its accuracy across different dynamical regimes.

Configurational entropy is an intrinsic driver of tissue structural heterogeneity

Tissues comprise ordered arrangements of cells that can be surprisingly disordered in their details. How the properties of single cells and their microenvironment contribute to the balance between order and disorder at the tissue-scale remains poorly understood. Here, we address this question using the self-organization of human mammary organoids as a model. We find that organoids behave like a dynamic structural ensemble at the steady state. We apply a maximum entropy formalism to derive the ensemble distribution from three measurable parameters - the degeneracy of structural states, interfacial energy, and tissue activity (the energy associated with positional fluctuations). We link these parameters with the molecular and microenvironmental factors that control them to precisely engineer the ensemble across multiple conditions. Our analysis reveals that the entropy associated with structural degeneracy sets a theoretical limit to tissue order and provides new insight for tissue engineering, development, and our understanding of disease progression.

Making sense of fragmentation and merging in lineage tracing experiments

Lineage tracing experiments give dynamic information on the functional behaviour of dividing cells. These experiments therefore have become an important tool for studying stem and progenitor cell fate behavior in vivo. When cell proliferation is high or the frequency of induced clones cannot be precisely controlled, the merging and fragmentation of clones renders the retrospective interpretation of clonal fate data highly ambiguous, potentially leading to unguarded interpretations about lineage relationships and fate behaviour. Here, we discuss and generalize statistical strategies to detect, resolve and make use of clonal fragmentation and merging. We first explain how to detect the rates of clonal fragmentation and merging using simple statistical estimates. We then discuss ways to restore the clonal provenance of labelled cells algorithmically and statistically and elaborate on how the process of clonal fragmentation can indirectly inform about cell fate. We generalize and extend results from the context of their original publication.

Resolving morphogenesis into quantifiable cell behaviours

Morphogenesis is extremely diverse, but its systematic quantification to determine the physical mechanisms that produce different phenotypes is possible by quantifying the underlying cell behaviours. These are limited and definable: they consist of cell proliferation, orientation of cell division, cell rearrangement, directional matrix production, cell addition/subtraction and cell size/shape change. Although minor variations in these categories are possible, in sum they capture all possible morphogenetic behaviours. This article summarises these processes, discusses their measurement, and highlights some salient examples.

Phenomenology and dynamics of competitive ecosystems beyond the niche-neutral regimes

Structure, composition, and stability of ecological populations are shaped by the inter- and intraspecies interactions within their communities. It remains to be fully understood how the interplay of these interactions with other factors, such as immigration, controls the structure, the diversity, and the long-term stability of ecological systems in the presence of noise and fluctuations. We address this problem using a minimal model of interacting multispecies ecological communities that incorporates competition, immigration, and demographic noise. We find that a complete phase diagram exhibits rich behavior with multiple regimes that go beyond the classical "niche" and "neutral" regimes, extending and modifying the "rare biosphere" or "niche-like" dichotomy. In particular, we observe regimes that cannot be characterized as either niche or neutral where a multimodal species abundance distribution is observed. We characterize the transitions between the different regimes and show how these arise from the underlying kinetics of the species turnover, extinction, and invasion. Our model serves as a minimal null model of noisy competitive ecological systems, against which more complex models that include factors such as mutations and environmental noise can be compared.

A computational model of stem cells' decision-making mechanism to maintain tissue homeostasis and organization in the presence of stochasticity

The maintenance of multi-cellular developed tissue depends on the proper cell production rate to replace the cells destroyed by the programmed process of cell death. The stem cell is the main source of producing cells in a developed normal tissue. It makes the stem cell the lead role in the scene of a fully formed developed tissue to fulfill its proper functionality. By focusing on the impact of stochasticity, here, we propose a computational model to reveal the internal mechanism of a stem cell, which generates the right proportion of different types of specialized cells, distribute them into their right position, and in the presence of intercellular reactions, maintain the organized structure in a homeostatic state. The result demonstrates that the spatial pattern could be harassed by the population geometries. Besides, it clearly shows that our model with progenitor cells able to recover the stem cell presence could retrieve the initial pattern appropriately in the case of injury. One of the fascinating outcomes of this project is demonstrating the contradictory roles of stochasticity. It breaks the proper boundaries of the initial spatial pattern in the population. While, on the flip side of the coin, it is the exact factor that provides the demanded non-genetic diversity in the tissue. The remarkable characteristic of the introduced model as the stem cells' internal mechanism is that it could control the overall behavior of the population without need for any external factors.

Branching structure of genealogies in spatially growing populations and its implications for population genetics inference

Spatial models where growth is limited to the population edge have been instrumental to understanding the population dynamics and the clone size distribution in growing cellular populations, such as microbial colonies and avascular tumours. A complete characterization of the coalescence process generated by spatial growth is still lacking, limiting our ability to apply classic population genetics inference to spatially growing populations. Here, we start filling this gap by investigating the statistical properties of the cell lineages generated by the two dimensional Eden model, leveraging their physical analogy with directed polymers. Our analysis provides quantitative estimates for population measurements that can easily be assessed via sequencing, such as the average number of segregating sites and the clone size distribution of a subsample of the population. Our results not only reveal remarkable features of the genealogies generated during growth, but also highlight new properties that can be misinterpreted as signs of selection if non-spatial models are inappropriately applied.

Role of Delta-Notch signalling molecules on cell-cell adhesion in determining heterogeneous chemical and cell morphological patterning

Cell mechanics and motility are responsible for collective motion of cells that result in overall deformation of epithelial tissues. On the other hand, contact-dependent cell-cell signalling is responsible for generating a large variety of intricate, self-organized, spatial patterns of the signalling molecules. Moreover, it is becoming increasingly clear that the combined mechanochemical patterns of cell shape/size and signalling molecules in the tissues, for example, in cancerous and sensory epithelium, are governed by mechanochemical coupling between chemical signalling and cell mechanics. However, a clear quantitative picture of how these two aspects of tissue dynamics, i.e., signalling and mechanics, lead to pattern and form is still emerging. Although, a number of recent experiments demonstrate that cell mechanics, cell motility, and cell-cell signalling are tightly coupled in many morphogenetic processes, relatively few modeling efforts have focused on an integrated approach. We extend the vertex model of an epithelial monolayer to account for contact-dependent signalling between adjacent cells and between non-adjacent neighbors through long protrusional contacts with a feedback mechanism wherein the adhesive strength between adjacent cells is controlled by the expression of the signalling molecules in those cells. Local changes in cell-cell adhesion lead to changes in cell shape and size, which in turn drives changes in the levels of signalling molecules. Our simulations show that even this elementary two-way coupling of chemical signalling and cell mechanics is capable of giving rise to a rich variety of mechanochemical patterns in epithelial tissues. In particular, under certain parametric conditions, bimodal distributions in cell size and shape are obtained, which resemble experimental observations in cancerous and sensory tissues.

Inflation-collapse dynamics drive patterning and morphogenesis in intestinal organoids

How stem cells self-organize to form structured tissues is an unsolved problem. Intestinal organoids offer a model of self-organization as they generate stem cell zones (SCZs) of typical size even without a spatially structured environment. Here we examine processes governing the size of SCZs. We improve the viability and homogeneity of intestinal organoid cultures to enable long-term time-lapse imaging of multiple organoids in parallel. We find that SCZs are shaped by fission events under strong control of ion channel-mediated inflation and mechanosensitive Piezo-family channels. Fission occurs through stereotyped modes of dynamic behavior that differ in their coordination of budding and differentiation. Imaging and single-cell transcriptomics show that inflation drives acute stem cell differentiation and induces a stretch-responsive cell state characterized by large transcriptional changes, including upregulation of Piezo1. Our results reveal an intrinsic capacity of the intestinal epithelium to self-organize by modulating and then responding to its mechanical state.

Tracing the cellular basis of islet specification in mouse pancreas

Pancreatic islets play an essential role in regulating blood glucose level. Although the molecular pathways underlying islet cell differentiation are beginning to be resolved, the cellular basis of islet morphogenesis and fate allocation remain unclear. By combining unbiased and targeted lineage tracing, we address the events leading to islet formation in the mouse. From the statistical analysis of clones induced at multiple embryonic timepoints, here we show that, during the secondary transition, islet formation involves the aggregation of multiple equipotent endocrine progenitors that transition from a phase of stochastic amplification by cell division into a phase of sublineage restriction and limited islet fission. Together, these results explain quantitatively the heterogeneous size distribution and degree of polyclonality of maturing islets, as well as dispersion of progenitors within and between islets. Further, our results show that, during the secondary transition, α- and β-cells are generated in a contemporary manner. Together, these findings provide insight into the cellular basis of islet development.

The cellular basis of islet morphogenesis and fate allocation remain unclear. Here, the authors use a R26-CreER-R26R-Confetti mouse line to follow quantitatively the clonal dynamics of islet formation showing how, during the secondary transition, islet progenitors amplify through rounds of stochastic cell division before becoming restricted to α and β cell sublineages.

Stochastic reaction networks in dynamic compartment populations

Many biochemical processes in living systems take place in compartmentalized environments, where individual compartments can interact with each other and undergo dynamic remodeling. Studying such processes through mathematical models poses formidable challenges because the underlying dynamics involve a large number of states, which evolve stochastically with time. Here we propose a mathematical framework to study stochastic biochemical networks in compartmentalized environments. We develop a generic population model, which tracks individual compartments and their molecular composition. We then show how the time evolution of this system can be studied effectively through a small number of differential equations, which track the statistics of the population. Our approach is versatile and renders an important class of biological systems computationally accessible.

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress toward addressing this problem in the context of specific biological systems, but a general and sufficiently effective approach remains lacking. In this work, we propose a mathematical framework based on counting processes that allows us to study dynamic compartment populations with arbitrary interactions and internal biochemistry. We derive an efficient description of the dynamics in terms of differential equations which capture the statistics of the population. We demonstrate the relevance of our approach by analyzing models inspired by different biological processes, including subcellular compartmentalization and tissue homeostasis.

A computational model of stem cell molecular mechanism to maintain tissue homeostasis

Stem cells, with their capacity to self-renew and to differentiate to more specialized cell types, play a key role to maintain homeostasis in adult tissues. To investigate how, in the dynamic stochastic environment of a tissue, non-genetic diversity and the precise balance between proliferation and differentiation are achieved, it is necessary to understand the molecular mechanisms of the stem cells in decision making process. By focusing on the impact of stochasticity, we proposed a computational model describing the regulatory circuitry as a tri-stable dynamical system to reveal the mechanism which orchestrate this balance. Our model explains how the distribution of noise in genes, linked to the cell regulatory networks, affects cell decision-making to maintain homeostatic state. The noise effect on tissue homeostasis is achieved by regulating the probability of differentiation and self-renewal through symmetric and/or asymmetric cell divisions. Our model reveals, when mutations due to the replication of DNA in stem cell division, are inevitable, how mutations contribute to either aging gradually or the development of cancer in a short period of time. Furthermore, our model sheds some light on the impact of more complex regulatory networks on the system robustness against perturbations.

Stem cell lineage survival as a noisy competition for niche access

Understanding to what extent stem cell potential is a cell-intrinsic property or an emergent behavior coming from global tissue dynamics and geometry is a key outstanding question of systems and stem cell biology. Here, we propose a theory of stem cell dynamics as a stochastic competition for access to a spatially localized niche, giving rise to a stochastic conveyor-belt model. Cell divisions produce a steady cellular stream which advects cells away from the niche, while random rearrangements enable cells away from the niche to be favorably repositioned. Importantly, even when assuming that all cells in a tissue are molecularly equivalent, we predict a common ("universal") functional dependence of the long-term clonal survival probability on distance from the niche, as well as the emergence of a well-defined number of functional stem cells, dependent only on the rate of random movements vs. mitosis-driven advection. We test the predictions of this theory on datasets of pubertal mammary gland tips and embryonic kidney tips, as well as homeostatic intestinal crypts. Importantly, we find good agreement for the predicted functional dependency of the competition as a function of position, and thus functional stem cell number in each organ. This argues for a key role of positional fluctuations in dictating stem cell number and dynamics, and we discuss the applicability of this theory to other settings.

Lineage hierarchies and stochasticity ensure the long-term maintenance of adult neural stem cells

The cellular basis and extent of neural stem cell (NSC) self-renewal in adult vertebrates, and their heterogeneity, remain controversial. To explore the functional behavior and dynamics of individual NSCs, we combined genetic lineage tracing, quantitative clonal analysis, intravital imaging, and global population assessments in the adult zebrafish telencephalon. Our results are compatible with a model where adult neurogenesis is organized in a hierarchy in which a subpopulation of deeply quiescent reservoir NSCs with long-term self-renewal potential generate, through asymmetric divisions, a pool of operational NSCs activating more frequently and taking stochastic fates biased toward neuronal differentiation. Our data further suggest the existence of an additional, upstream, progenitor population that supports the continuous generation of new reservoir NSCs, thus contributing to their overall expansion. Hence, we propose that the dynamics of vertebrate neurogenesis relies on a hierarchical organization where growth, self-renewal, and neurogenic functions are segregated between different NSC types.

Phenomics-Based Quantification of CRISPR-Induced Mosaicism in Zebrafish

Genetic mosaicism can manifest as spatially variable phenotypes that vary from site to site within an organism. Here, we use imaging-based phenomics to quantitate phenotypes at many sites within the axial skeleton of CRISPR-edited G0 zebrafish. Through characterization of loss-of-function cell clusters in the developing skeleton, we identify a distinctive size distribution shown to arise from clonal fragmentation and merger events. We quantitate the phenotypic mosaicism produced by somatic mutations of two genes, plod2 and bmp1a, implicated in human osteogenesis imperfecta. Comparison of somatic, CRISPR-generated G0 mutants to homozygous germline mutants reveals phenotypic convergence, suggesting that CRISPR screens of G0 animals can faithfully recapitulate the biology of inbred disease models. We describe statistical frameworks for phenomic analysis of spatial phenotypic variation present in somatic G0 mutants. In sum, this study defines an approach for decoding spatially variable phenotypes generated during CRISPR-based screens.

Cell-Size Pleomorphism Drives Aberrant Clone Dispersal in Proliferating Epithelia

As epithelial tissues develop, groups of cells related by descent tend to associate in clonal populations rather than dispersing within the cell layer. While this is frequently assumed to be a result of differential adhesion, precise mechanisms controlling clonal cohesiveness remain unknown. Here we employ computational simulations to modulate epithelial cell size in silico and show that junctions between small cells frequently collapse, resulting in clone-cell dispersal among larger neighbors. Consistent with similar dynamics in vivo, we further demonstrate that mosaic disruption of Drosophila Tor generates small cells and results in aberrant clone dispersal in developing wing disc epithelia. We propose a geometric basis for this phenomenon, supported in part by the observation that soap-foam cells exhibit similar size-dependent junctional rearrangements. Combined, these results establish a link between cell-size pleomorphism and the control of epithelial cell packing, with potential implications for understanding tumor cell dispersal in human disease.

A marker-independent lineage-tracing system to quantify clonal dynamics and stem cell functionality in cancer tissue

Lineage tracing is a powerful tool that can be used to uncover cell fates. Here, we describe a novel method for the quantitative analysis of clonal dynamics in grafted cancer tissues. The protocol involves the preparation and validation of cells for lineage tracing, establishment of grafts and label induction, analysis of clone-size distribution and fitting of the experimental data to a mathematical tumor growth model. In contrast to other lineage-tracing strategies, the method described here assesses stem cell functionality and infers tumor expansion dynamics independently of molecular markers such as putative cancer stem cell (CSC)-specific genes. The experimental system and analytical framework presented can be used to quantify clonal advantages that specific mutations provide, in both the absence and presence of (targeted) therapeutic agents. This protocol typically takes ~20 weeks to complete from cell line selection to inference of growth dynamics, depending on the grafted cancer growth rate.

Lgr5+ stem and progenitor cells reside at the apex of a heterogeneous embryonic hepatoblast pool

During mouse embryogenesis, progenitors within the liver known as hepatoblasts give rise to adult hepatocytes and cholangiocytes. Hepatoblasts, which are specified at E8.5-E9.0, have been regarded as a homogeneous progenitor population that initiate differentiation from E13.5. Recently, scRNA-seq analysis has identified sub-populations of transcriptionally distinct hepatoblasts at E11.5. Here, we show that hepatoblasts are not only transcriptionally but also functionally heterogeneous, and that a subpopulation of E9.5-E10.0 hepatoblasts exhibit a previously unidentified early commitment to cholangiocyte fate. Importantly, we also identify a subpopulation constituting 2% of E9.5-E10.0 hepatoblasts that express the adult stem cell marker Lgr5, and generate both hepatocyte and cholangiocyte progeny that persist for the lifespan of the mouse. Combining lineage tracing and scRNA-seq, we show that Lgr5 marks E9.5-E10.0 bipotent liver progenitors residing at the apex of a hepatoblast hierarchy. Furthermore, isolated Lgr5⁺ hepatoblasts can be clonally expanded in vitro into embryonic liver organoids, which can commit to either hepatocyte or cholangiocyte fates. Our study demonstrates functional heterogeneity within E9.5 hepatoblasts and identifies Lgr5 as a marker for a subpopulation of bipotent liver progenitors.

Statistics of noisy growth with mechanical feedback in elastic tissues

Tissue growth is a fundamental aspect of development and is intrinsically noisy. Stochasticity has important implications for morphogenesis, precise control of organ size, and regulation of tissue composition and heterogeneity. However, the basic statistical properties of growing tissues, particularly when growth induces mechanical stresses that can in turn affect growth rates, have received little attention. Here, we study the noisy growth of elastic sheets subject to mechanical feedback. Considering both isotropic and anisotropic growth, we find that the density-density correlation function shows power law scaling. We also consider the dynamics of marked, neutral clones of cells. We find that the areas (but not the shapes) of two clones are always statistically independent, even when they are adjacent. For anisotropic growth, we show that clone size variance scales like the average area squared and that the mode amplitudes characterizing clone shape show a slow [Formula: see text] decay, where n is the mode index. This is in stark contrast to the isotropic case, where relative variations in clone size and shape vanish at long times. The high variability in clone statistics observed in anisotropic growth is due to the presence of two soft modes-growth modes that generate no stress. Our results lay the groundwork for more in-depth explorations of the properties of noisy tissue growth in specific biological contexts.

Stem cell functionality is microenvironmentally defined during tumour expansion and therapy response in colon cancer

Solid malignancies have been speculated to depend on cancer stem cells (CSCs) for expansion and relapse after therapy. Here we report on quantitative analyses of lineage tracing data from primary colon cancer xenograft tissue to assess CSC functionality in a human solid malignancy. The temporally obtained clone size distribution data support a model in which stem cell function in established cancers is not intrinsically, but is entirely spatiotemporally orchestrated. Functional stem cells that drive tumour expansion predominantly reside at the tumour edge, close to cancer-associated fibroblasts. Hence, stem cell properties change in time depending on the cell location. Furthermore, although chemotherapy enriches for cells with a CSC phenotype, in this context functional stem cell properties are also fully defined by the microenvironment. To conclude, we identified osteopontin as a key cancer-associated fibroblast-produced factor that drives in situ clonogenicity in colon cancer.

Effective models and the search for quantitative principles in microbial evolution

Microbes evolve rapidly. Yet they do so in idiosyncratic ways, which depend on the specific mutations that are beneficial or deleterious in a given situation. At the same time, some population-level patterns of adaptation are strikingly similar across different microbial systems, suggesting that there may also be simple, quantitative principles that unite these diverse scenarios. We review the search for simple principles in microbial evolution, ranging from the biophysical level to emergent evolutionary dynamics. A key theme has been the use of effective models, which coarse-grain over molecular and cellular details to obtain a simpler description in terms of a few effective parameters. Collectively, these theoretical approaches provide a set of quantitative principles that facilitate understanding, prediction, and potentially control of evolutionary phenomena, though formidable challenges remain due to the ecological complexity of natural populations.