Global attractors and extinction dynamics of cyclically competing species

Transitions to absorbing states are of fundamental importance in nonequilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three cyclically interacting species. The interaction scheme comprises both direct competition between species as in the cyclic Lotka-Volterra model, and separated selection and reproduction processes as in the May-Leonard model. We show that the dynamic processes leading to the transient maintenance of biodiversity are closely linked to attractors of the nonlinear dynamics for the overall species' concentrations. The characteristics of these global attractors change qualitatively at certain threshold values of the mobility and depend on the relative strength of the different types of competition between species. They give information about the scaling of extinction times with the system size and thereby the stability of biodiversity. We define an effective free energy as the negative logarithm of the probability to find the system in a specific global state before reaching one of the absorbing states. The global attractors then correspond to minima of this effective energy landscape and determine the most probable values for the species' global concentrations. As in equilibrium thermodynamics, qualitative changes in the effective free energy landscape indicate and characterize the underlying nonequilibrium phase transitions. We provide the complete phase diagrams for the population dynamics and give a comprehensive analysis of the spatio-temporal dynamics and routes to extinction in the respective phases

Stability of Localized Wave Fronts in Bistable Systems

Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation, and spatially inhomogeneous activating agents. We determine the conditions under which wave-front localization is possible and analyze the stability thereof with respect to extrinsic perturbations and internal noise. It is found that stability is enhanced upon regulating a positional signal and, surprisingly, also for a low degree of binding cooperativity. We further show a contrasting impact of self-activation to the stability of these two sources of destabilization. DOI: 10.1103/PhysRevLett.110.03810

Field theory of enzyme-substrate systems with restricted long-range interactions

Enzyme-substrate kinetics form the basis of many biomolecular processes. The interplay between substrate binding and substrate geometry can give rise to long-range interactions between enzyme binding events. Here, we study a general model of enzyme-substrate kinetics with restricted long-range interactions described by an exponent $-\lambda$. We employ a coherent-state path integral and renormalization group approach to calculate the first moment and two-point correlation function of the enzyme-binding profile. We show that starting from an empty substrate the average occupancy follows a power law with an exponent $1/(1-\lambda)$ over time. The correlation function decays algebraically with two distinct spatial regimes characterized by exponents $-\lambda$ on short distances and $-(2/3)(2-\lambda)$ on long distances. The crossover between both regimes scales inversely with the average substrate occupancy. Our work allows to associate experimental measurements of bound enzyme locations with their binding kinetics and the spatial confirmation of the substrate

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

Tracing cellular dynamics in tissue development, maintenance and disease.

The coordination of cell proliferation and differentiation is central to the development and maintenance of tissues, while its dysregulation underlies the transition to diseased states. By combining lineage tracing with transcriptional profiling and marker-based assays, statistical methods are delivering insights into the dynamics of stem cells and their developmental precursors. These studies have provided evidence for molecular heterogeneity and fate priming, and have revealed a role for stochasticity in stem cell fate, refocusing the search for regulatory mechanisms. At the same time, they present a quantitative platform to study the initiation and progression of disease. Here, we review how quantitative lineage tracing strategies are shaping our understanding of the cellular mechanisms of tissue development, maintenance and disease

The ciliary marginal zone of the zebrafish retina: clonal and time-lapse analysis of a continuously growing tissue.

Clonal analysis is helping us understand the dynamics of cell replacement in homeostatic adult tissues (Simons and Clevers, 2011). Such an analysis, however, has not yet been achieved for continuously growing adult tissues, but is essential if we wish to understand the architecture of adult organs. The retinas of lower vertebrates grow throughout life from retinal stem cells (RSCs) and retinal progenitor cells (RPCs) at the rim of the retina, called the ciliary marginal zone (CMZ). Here, we show that RSCs reside in a niche at the extreme periphery of the CMZ and divide asymmetrically along a radial (peripheral to central) axis, leaving one daughter in the peripheral RSC niche and the other more central where it becomes an RPC. We also show that RPCs of the CMZ have clonal sizes and compositions that are statistically similar to progenitor cells of the embryonic retina and fit the same stochastic model of proliferation. These results link embryonic and postembryonic cell behaviour, and help to explain the constancy of tissue architecture that has been generated over a lifetime.This work was supported by a Wellcome Trust Senior Investigator Awards [100329/Z/12/Z to W.A.H.] and [098357/Z/12/Z to B.D.S].This is the final version of the article. It first appeared from The Company of Biologists via https://doi.org/10.1242/dev.13331

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.M.H. is a Wellcome Trust Sir Henry Dale Fellow and is jointly funded by the Wellcome Trust and the Royal Society (104151/Z/14/Z); M.H. and N.P. are funded by a Horizon 2020 grant (LSFM4LIFE). C.H. was funded by a Cambridge Stem Cell Institute Seed funding for interdisciplinary research awarded to M.H. and B.D.S., B.D.S acknowledges funding from the Royal Society E.P. Abraham Research Professorship (RP\R1\180165) and Wellcome Trust (098357/Z/12/Z). W.L. and B.G. were supported by programmatic funding from the Wellcome Trust, CRUK and Bloodwise, core infrastructure support from the Wellcome and MRC to the Wellcome & MRC Cambridge Stem Cell Institute, and an MRC Clinical Research Infrastructure grant supporting single cell molecular analysis. S.R. was funded on a Herchel-Smith Fellowship. The authors acknowledge core funding to the Gurdon Institute from the Wellcome Trust (092096) and CRUK (C6946/A14492)

Defining stem cell dynamics and migration during wound healing in mouse skin epidermis.

Wound healing is essential to repair the skin after injury. In the epidermis, distinct stem cells (SCs) populations contribute to wound healing. However, how SCs balance proliferation, differentiation and migration to repair a wound remains poorly understood. Here, we show the cellular and molecular mechanisms that regulate wound healing in mouse tail epidermis. Using a combination of proliferation kinetics experiments and molecular profiling, we identify the gene signatures associated with proliferation, differentiation and migration in different regions surrounding the wound. Functional experiments show that SC proliferation, migration and differentiation can be uncoupled during wound healing. Lineage tracing and quantitative clonal analysis reveal that, following wounding, progenitors divide more rapidly, but conserve their homoeostatic mode of division, leading to their rapid depletion, whereas SCs become active, giving rise to new progenitors that expand and repair the wound. These results have important implications for tissue regeneration, acute and chronic wound disorders.This work was supported by the FNRS, TELEVIE, the PAI programme, a research grant from the Fondation contre le Cancer, the ULB fondation, the foundation Bettencourt Schueller, the foundation Baillet Latour and a consolidator grant the European Research Council (ERC-EXPAND)