Stochastic evolution of four species in cyclic competition

We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios, from single species domination to coexistence between non-interacting species. Using exact results and numerical simulations we discuss the temporal evolution of the system for different values of $N$, for different values of the reaction rates, as well as for different initial conditions. As expected, the stochastic evolution is found to closely follow the mean-field result for large $N$, with notable deviations appearing in proximity of extinction events. Different ways of characterizing and predicting extinction events are discussed.Comment: 19 pages, 6 figures, submitted to J. Stat. Mec

Three-fold way to extinction in populations of cyclically competing species

Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic population model where three species exhibit cyclic competition. The cyclic dynamics reflects the non-equilibrium nature of the species interactions. While previous work focusses on the coarsening process as a mechanism that drives the system to extinction, we found that unexpectedly the dynamics to extinction is much richer. We observed three different types of dynamics. In addition to coarsening, in the evolutionary relevant limit of large times, oscillating traveling waves and heteroclinic orbits play a dominant role. The weight of the different processes depends on the degree of mixing and the system size. By analytical arguments and extensive numerical simulations we provide the full characteristics of scenarios leading to extinction in one of the most surprising models of ecology

Emergence and universality in the regulation of stem cell fate

The mechanisms that control cell fate behaviour during development, and the factors leading to their dysregulation in disease, remain the subject of interest and debate. Lately, advances in single-cell genomics have shifted emphasis towards the elucidation of molecular regulatory programmes and transcriptional cell states. However, quantitative statistical approaches based on cell lineage tracing data have provided fresh insight into stem and progenitor cell behaviour, questioning the role of cell fate stochasticity, transcriptional heterogeneity and state priming. These investigations, which draw upon conceptual insights from statistical physics and mathematics, provide a novel, generic and rigorous framework to resolve and classify stem cell self-renewal strategies, which heavily constrain, but do not seek to define, underlying molecular mechanistic programmes. Here, using epithelial maintenance as an exemplar, we consider the foundation, conceptual basis, utility and limitations of such quantitative approaches in cell biology.B.D.S. acknowledges the support of the Wellcome Trust (grant number 098357/Z/12/Z) and the core funding to the Gurdon Institute by the Wellcome Trust and Cancer Research UK

Neurogenin3 phosphorylation controls reprogramming efficiency of pancreatic ductal organoids into endocrine cells

β-cell replacement has been proposed as an effective treatment for some forms of diabetes, and in vitro methods for β-cell generation are being extensively explored. A potential source of β-cells comes from fate conversion of exocrine pancreatic cells into the endocrine lineage, by overexpression of three regulators of pancreatic endocrine formation and β-cell identity, Ngn3, Pdx1 and MafA. Pancreatic ductal organoid cultures have recently been developed that can be expanded indefinitely, while maintaining the potential to differentiate into the endocrine lineage. Here, using mouse pancreatic ductal organoids, we see that co-expression of Ngn3, Pdx1 and MafA are required and sufficient to generate cells that express insulin and resemble β-cells transcriptome-wide. Efficiency of β-like cell generation can be significantly enhanced by preventing phosphorylation of Ngn3 protein and further augmented by conditions promoting differentiation. Taken together, our new findings underline the potential of ductal organoid cultures as a source material for generation of β-like cells and demonstrate that post-translational regulation of reprogramming factors can be exploited to enhance β-cell generation

Genome-Scale Oscillations in DNA Methylation during Exit from Pluripotency

Pluripotency is accompanied by the erasure of parental epigenetic memory, with naive pluripotent cells exhibiting global DNA hypomethylation both in vitro and in vivo. Exit from pluripotency and priming for differentiation into somatic lineages is associated with genome-wide de novo DNA methylation. We show that during this phase, co-expression of enzymes required for DNA methylation turnover, DNMT3s and TETs, promotes cell-to-cell variability in this epigenetic mark. Using a combination of single- cell sequencing and quantitative biophysical modeling, we show that this variability is associated with coherent, genome-scale oscillations in DNA methylation with an amplitude dependent on CpG density. Analysis of parallel single-cell transcriptional and epigenetic profiling provides evidence for oscillatory dynamics both in vitro and in vivo. These observations provide insights into the emergence of epigenetic heterogeneity during early embryo development, indicating that dynamic changes in DNA methylation might influence early cell fate decisions

Cyclic competition of four species: domains and interfaces

We study numerically domain growth and interface fluctuations in one- and two-dimensional lattice systems composed of four species that interact in a cyclic way. Particle mobility is implemented through exchanges of particles located on neighboring lattice sites. For the chain we find that domain growth strongly depends on the mobility, with a higher mobility yielding a larger domain growth exponent. In two space dimensions, when also exchanges between mutually neutral particles are possible, both domain growth and interface fluctuations display universal regimes that are independent of the predation and exchange rates.Comment: 14 pages, 7 figures, version accepted for publication in J. Stat. Mec

Metabolic enhancement of mammalian developmental pausing

The quest to model and modulate embryonic development became a recent cornerstone of stem cell and developmental biology. Mammalian developmental timing is adjustable in vivo by preserving preimplantation embryos in a dormant state called diapause. Inhibition of the growth regulator mTOR (mTORi) pauses mouse development in vitro, yet constraints to pause duration are unrecognized. By comparing the response of embryonic and extraembryonic stem cells to mTORi-induced pausing, we identified lipid usage as a bottleneck to developmental pausing. Enhancing fatty acid oxidation (FAO) boosts embryo longevity, while blocking it reduces the pausing capacity. Genomic and metabolic analyses of single embryos point toward a deeper dormant state in FAO-enhanced pausing and reveal a link between lipid metabolism and embryo morphology. Our results lift a constraint on in vitro embryo survival and suggest that lipid metabolism may be a critical metabolic transition relevant for longevity and stem cell function across tissues

Defining Lineage Potential and Fate Behavior of Precursors during Pancreas Development

Pancreas development involves a coordinated process in which an early phase of cell segregation is followed by a longer phase of lineage restriction, expansion, and tissue remodeling. By combining clonal tracing and whole-mount reconstruction with proliferation kinetics and single-cell transcriptional profiling, we define the functional basis of pancreas morphogenesis. We show that the large-scale organization of mouse pancreas can be traced to the activity of self-renewing precursors positioned at the termini of growing ducts, which act collectively to drive serial rounds of stochastic ductal bifurcation balanced by termination. During this phase of branching morphogenesis, multipotent precursors become progressively fate-restricted, giving rise to self-renewing acinar-committed precursors that are conveyed with growing ducts, as well as ductal progenitors that expand the trailing ducts and give rise to delaminating endocrine cells. These findings define quantitatively how the functional behavior and lineage progression of precursor pools determine the large-scale patterning of pancreatic sub-compartments

Range expansion with mutation and selection: dynamical phase transition in a two-species Eden model

The colonization of unoccupied territory by invading species, known as range expansion, is a spatially heterogeneous non-equilibrium growth process. We introduce a two-species Eden growth model to analyze the interplay between uni-directional (irreversible) mutations and selection at the expanding front. While the evolutionary dynamics leads to coalescence of both wild-type and mutant clusters, the non-homogeneous advance of the colony results in a rough front. We show that roughening and domain dynamics are strongly coupled, resulting in qualitatively altered bulk and front properties. For beneficial mutations the front is quickly taken over by mutants and growth proceeds Eden-like. In contrast, if mutants grow slower than wild-types, there is an antagonism between selection pressure against mutants and growth by the merging of mutant domains with an ensuing absorbing state phase transition to an all-mutant front. We find that surface roughening has a marked effect on the critical properties of the absorbing state phase transition. While reference models, which keep the expanding front flat, exhibit directed percolation critical behavior, the exponents of the two-species Eden model strongly deviate from it. In turn, the mutation-selection process induces an increased surface roughness with exponents distinct from that of the classical Eden model

Universality of clone dynamics during tissue development.

The emergence of complex organs is driven by the coordinated proliferation, migration and differentiation of precursor cells. The fate behaviour of these cells is reflected in the time evolution their progeny, termed clones, which serve as a key experimental observable. In adult tissues, where cell dynamics is constrained by the condition of homeostasis, clonal tracing studies based on transgenic animal models have advanced our understanding of cell fate behaviour and its dysregulation in disease (1, 2). But what can be learned from clonal dynamics in development, where the spatial cohesiveness of clones is impaired by tissue deformations during tissue growth? Drawing on the results of clonal tracing studies, we show that, despite the complexity of organ development, clonal dynamics may converge to a critical state characterized by universal scaling behaviour of clone sizes. By mapping clonal dynamics onto a generalization of the classical theory of aerosols, we elucidate the origin and range of scaling behaviours and show how the identification of universal scaling dependences may allow lineage-specific information to be distilled from experiments. Our study shows the emergence of core concepts of statistical physics in an unexpected context, identifying cellular systems as a laboratory to study non-equilibrium statistical physics.Wellcome Trus