Genetic interference with HvNotch provides new insights into the role of the Notch-signalling pathway for developmental pattern formation in Hydra.

The Notch-signalling pathway plays an important role in pattern formation in Hydra. Using pharmacological Notch inhibitors (DAPT and SAHM1), it has been demonstrated that HvNotch is required for head regeneration and tentacle patterning in Hydra. HvNotch is also involved in establishing the parent-bud boundary and instructing buds to develop feet and detach from the parent. To further investigate the functions of HvNotch, we successfully constructed NICD (HvNotch intracellular domain)-overexpressing and HvNotch-knockdown transgenic Hydra strains. NICD-overexpressing transgenic Hydra showed a pronounced inhibition on the expression of predicted HvNotch-target genes, suggesting a dominant negative effect of ectopic NICD. This resulted in a "Y-shaped" phenotype, which arises from the parent-bud boundary defect seen in polyps treated with DAPT. Additionally, "multiple heads", "two-headed" and "ectopic tentacles" phenotypes were observed. The HvNotch-knockdown transgenic Hydra with reduced expression of HvNotch exhibited similar, but not identical phenotypes, with the addition of a "two feet" phenotype. Furthermore, we observed regeneration defects in both, overexpression and knockdown strains. We integrated these findings into a mathematical model based on long-range gradients of signalling molecules underlying sharply defined positions of HvNotch-signalling cells at the Hydra tentacle and bud boundaries.

Mathematics of neural stem cells: Linking data and processes.

Adult stem cells are described as a discrete population of cells that stand at the top of a hierarchy of progressively differentiating cells. Through their unique ability to self-renew and differentiate, they regulate the number of end-differentiated cells that contribute to tissue physiology. The question of how discrete, continuous, or reversible the transitions through these hierarchies are and the precise parameters that determine the ultimate performance of stem cells in adulthood are the subject of intense research. In this review, we explain how mathematical modelling has improved the mechanistic understanding of stem cell dynamics in the adult brain. We also discuss how single-cell sequencing has influenced the understanding of cell states or cell types. Finally, we discuss how the combination of single-cell sequencing technologies and mathematical modelling provides a unique opportunity to answer some burning questions in the field of stem cell biology.

Non-muscle myosin II drives critical steps of nematocyst morphogenesis.

Nematocysts are generated by secretion of proteins into a post-Golgi compartment. They consist of a capsule that elongates into a long tube, which is coiled inside the capsule matrix and expelled during its nano-second discharge deployed for prey capture. The driving force for discharge is an extreme osmotic pressure of 150 bar. The complex processes of tube elongation and invagination under these biomechanical constraints have so far been elusive. Here, we show that a non-muscle myosin II homolog (HyNMII) is essential for nematocyst formation in Hydra. In early nematocysts, HyNMII assembles to a collar around the neck of the protruding tube. HyNMII then facilitates tube outgrowth by compressing it along the longitudinal axis as evidenced by inhibitor treatment and genetic knockdown. In addition, live imaging of a NOWA::NOWA-GFP transgenic line, which re-defined NOWA as a tube component facilitating invagination, allowed us to analyze the impact of HyNMII on tube maturation.

Interferon regulates neural stem cell function at all ages by orchestrating mTOR and cell cycle.

Stem cells show intrinsic interferon signalling, which protects them from viral infections at all ages. In the ageing brain, interferon signalling also reduces the ability of stem cells to activate. Whether these functions are linked and at what time interferons start taking on a role in stem cell functioning is unknown. Additionally, the molecular link between interferons and activation in neural stem cells and how this relates to progenitor production is not well understood. Here we combine single-cell transcriptomics, RiboSeq and mathematical models of interferon to show that this pathway is important for proper stem cell function at all ages in mice. Interferon orchestrates cell cycle and mTOR activity to post-transcriptionally repress Sox2 and induces quiescence. The interferon response then decreases in the subsequent maturation states. Mathematical simulations indicate that this regulation is beneficial for the young and harmful for the old brain. Our study establishes molecular mechanisms of interferon in stem cells and interferons as genuine regulators of stem cell homeostasis and a potential therapeutic target to repair the ageing brain.

Injury-induced MAPK activation triggers body axis formation in Hydra by default Wnt signaling.

Hydra's almost unlimited regenerative potential is based on Wnt signaling, but so far it is unknown how the injury stimulus is transmitted to discrete patterning fates in head and foot regenerates. We previously identified mitogen-activated protein kinases (MAPKs) among the earliest injury response molecules in Hydra head regeneration. Here, we show that three MAPKs-p38, c-Jun N-terminal kinases (JNKs), and extracellular signal-regulated kinases (ERKs)-are essential to initiate regeneration in Hydra, independent of the wound position. Their activation occurs in response to any injury and requires calcium and reactive oxygen species (ROS) signaling. Phosphorylated MAPKs hereby exhibit cross talk with mutual antagonism between the ERK pathway and stress-induced MAPKs, orchestrating a balance between cell survival and apoptosis. Importantly, Wnt3 and Wnt9/10c, which are induced by MAPK signaling, can partially rescue regeneration in tissues treated with MAPK inhibitors. Also, foot regenerates can be reverted to form head tissue by a pharmacological increase of ß-catenin signaling or the application of recombinant Wnts. We propose a model in which a ß-catenin-based stable gradient of head-forming capacity along the primary body axis, by differentially integrating an indiscriminate injury response, determines the fate of the regenerating tissue. Hereby, Wnt signaling acquires sustained activation in the head regenerate, while it is transient in the presumptive foot tissue. Given the high level of evolutionary conservation of MAPKs and Wnts, we assume that this mechanism is deeply embedded in our genome.

Identifying stem cell numbers and functional heterogeneities during postembryonic organ growth.

Uncovering the number of stem cells necessary for organ growth has been challenging in vertebrate systems. Here, we developed a mathematical model characterizing stem cells in the fish gill, an organ displaying non-exhaustive growth. We employ a Markov model, stochastically simulated via an adapted Gillespie algorithm, and further improved through probability theory. The stochastic algorithm produces a simulated dataset for comparison with experimental clonal data by inspecting quantifiable properties. The analytical approach skips the step of artificial data generation and goes directly to the quantification, being more abstract and efficient. We report that a reduced number of stem cells actively contribute to growing and maintaining the gills. The model also highlights a functional heterogeneity among the stem cells involved, where activation and quiescence phases determine their relative growth contribution. Overall, our work presents a method for inferring the number and properties of stem cells required in a lifelong growing system.

Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation.

In this paper we consider a system of non-linear integro-differential equations (IDEs) describing evolution of a clonally heterogeneous population of malignant white blood cells (leukemic cells) undergoing mutation and clonal selection. We prove existence and uniqueness of non-trivial steady states and study their asymptotic stability. The results are compared to those of the system without mutation. Existence of equilibria is proved by formulating the steady state problem as an eigenvalue problem and applying a version of the Krein-Rutmann theorem for Banach lattices. The stability at equilibrium is analysed using linearisation and the Weinstein-Aronszajn determinant which allows to conclude local asymptotic stability.

Computational modelling of nephron progenitor cell movement and aggregation during kidney organogenesis.

During early kidney organogenesis, nephron progenitor (NP) cells move from the tip to the corner region of the ureteric bud (UB) branches in order to form the pretubular aggregate, the early structure giving rise to nephron formation. NP cells derive from metanephric mesenchymal cells and physically interact with them during the movement. Chemotaxis and cell-cell adhesion differences are believed to drive the cell patterning during this critical period of organogenesis. However, the effect of these forces to the cell patterns and their respective movements are known in limited details. We applied a Cellular Potts Model to explore how these forces and organizations contribute to directed cell movement and aggregation. Model parameters were estimated based on fitting to experimental data obtained in ex vivo kidney explant and dissociation-reaggregation organoid culture studies. Our simulations indicated that optimal enrichment and aggregation of NP cells in the UB corner niche requires chemoattractant secretion from both the UB epithelial cells and the NP cells themselves, as well as differences in cell-cell adhesion energies. Furthermore, NP cells were observed, both experimentally and by modelling, to move at higher speed in the UB corner as compared to the tip region where they originated. The existence of different cell speed domains along the UB was confirmed using self-organizing map analysis. In summary, we saw faster NP cell movements near aggregation. The applicability of Cellular Potts Model approach to simulate cell movement and patterning was found to be good during for this early nephrogenesis process. Further refinement of the model should allow us to recapitulate the effects of developmental changes of cell phenotypes and molecular crosstalk during further organ development.

Beyond Turing: far-from-equilibrium patterns and mechano-chemical feedback.

Turing patterns are commonly understood as specific instabilities of a spatially homogeneous steady state, resulting from activator-inhibitor interaction destabilized by diffusion. We argue that this view is restrictive and its agreement with biological observations is problematic. We present two alternatives to the classical Turing analysis of patterns. First, we employ the abstract framework of evolution equations to enable the study of far-from-equilibrium patterns. Second, we introduce a mechano-chemical model, with the surface on which the pattern forms being dynamic and playing an active role in the pattern formation, effectively replacing the inhibitor. We highlight the advantages of these two alternatives vis-à-vis the classical Turing analysis, and give an overview of recent results and future challenges for both approaches. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

High throughput screening of novel AAV capsids identifies variants for transduction of adult NSCs within the subventricular zone.

The adult mammalian brain entails a reservoir of neural stem cells (NSCs) generating glial cells and neurons. However, NSCs become increasingly quiescent with age, which hampers their regenerative capacity. New means are therefore required to genetically modify adult NSCs for re-enabling endogenous brain repair. Recombinant adeno-associated viruses (AAVs) are ideal gene-therapy vectors due to an excellent safety profile and high transduction efficiency. We thus conducted a high-throughput screening of 177 intraventricularly injected barcoded AAV variants profiled by RNA sequencing. Quantification of barcoded AAV mRNAs identified two synthetic capsids, peptide-modified derivative of wild-type AAV9 (AAV9_A2) and peptide-modified derivative of wild-type AAV1 (AAV1_P5), both of which transduce active and quiescent NSCs. Further optimization of AAV1_P5 by judicious selection of the promoter and dose of injected viral genomes enabled labeling of 30%-60% of the NSC compartment, which was validated by fluorescence-activated cell sorting (FACS) analyses and single-cell RNA sequencing. Importantly, transduced NSCs readily produced neurons. The present study identifies AAV variants with a high regional tropism toward the ventricular-subventricular zone (v-SVZ) with high efficiency in targeting adult NSCs, thereby paving the way for preclinical testing of regenerative gene therapy.

Computational Reconstruction of Clonal Hierarchies From Bulk Sequencing Data of Acute Myeloid Leukemia Samples.

Acute myeloid leukemia is an aggressive cancer of the blood forming system. The malignant cell population is composed of multiple clones that evolve over time. Clonal data reflect the mechanisms governing treatment response and relapse. Single cell sequencing provides most direct insights into the clonal composition of the leukemic cells, however it is still not routinely available in clinical practice. In this work we develop a computational algorithm that allows identifying all clonal hierarchies that are compatible with bulk variant allele frequencies measured in a patient sample. The clonal hierarchies represent descendance relations between the different clones and reveal the order in which mutations have been acquired. The proposed computational approach is tested using single cell sequencing data that allow comparing the outcome of the algorithm with the true structure of the clonal hierarchy. We investigate which problems occur during reconstruction of clonal hierarchies from bulk sequencing data. Our results suggest that in many cases only a small number of possible hierarchies fits the bulk data. This implies that bulk sequencing data can be used to obtain insights in clonal evolution.

The Wnt-specific astacin proteinase HAS-7 restricts head organizer formation in Hydra.

BACKGROUND: The Hydra head organizer acts as a signaling center that initiates and maintains the primary body axis in steady state polyps and during budding or regeneration. Wnt/beta-Catenin signaling functions as a primary cue controlling this process, but how Wnt ligand activity is locally restricted at the protein level is poorly understood. Here we report a proteomic analysis of Hydra head tissue leading to the identification of an astacin family proteinase as a Wnt processing factor. RESULTS: Hydra astacin-7 (HAS-7) is expressed from gland cells as an apical-distal gradient in the body column, peaking close beneath the tentacle zone. HAS-7 siRNA knockdown abrogates HyWnt3 proteolysis in the head tissue and induces a robust double axis phenotype, which is rescued by simultaneous HyWnt3 knockdown. Accordingly, double axes are also observed in conditions of increased Wnt activity as in transgenic actin::HyWnt3 and HyDkk1/2/4 siRNA treated animals. HyWnt3-induced double axes in Xenopus embryos could be rescued by coinjection of HAS-7 mRNA. Mathematical modelling combined with experimental promotor analysis indicate an indirect regulation of HAS-7 by beta-Catenin, expanding the classical Turing-type activator-inhibitor model. CONCLUSIONS: We show the astacin family protease HAS-7 maintains a single head organizer through proteolysis of HyWnt3. Our data suggest a negative regulatory function of Wnt processing astacin proteinases in the global patterning of the oral-aboral axis in Hydra.

Dynamical properties of feedback signalling in B lymphopoiesis: A mathematical modelling approach.

Haematopoiesis is the process of generation of blood cells. Lymphopoiesis generates lymphocytes, the cells in charge of the adaptive immune response. Disruptions of this process are associated with diseases like leukaemia, which is especially incident in children. The characteristics of self-regulation of this process make them suitable for a mathematical study. In this paper we develop mathematical models of lymphopoiesis using currently available data. We do this by drawing inspiration from existing structured models of cell lineage development and integrating them with paediatric bone marrow data, with special focus on regulatory mechanisms. A formal analysis of the models is carried out, giving steady states and their stability conditions. We use this analysis to obtain biologically relevant regions of the parameter space and to understand the dynamical behaviour of B-cell renovation. Finally, we use numerical simulations to obtain further insight into the influence of proliferation and maturation rates on the reconstitution of the cells in the B line. We conclude that a model including feedback regulation of cell proliferation represents a biologically plausible depiction for B-cell reconstitution in bone marrow. Research into haematological disorders could benefit from a precise dynamical description of B lymphopoiesis.

Coordinated changes in cellular behavior ensure the lifelong maintenance of the hippocampal stem cell population.

Neural stem cell numbers fall rapidly in the hippocampus of juvenile mice but stabilize during adulthood, ensuring lifelong hippocampal neurogenesis. We show that this stabilization of stem cell numbers in young adults is the result of coordinated changes in stem cell behavior. Although proliferating neural stem cells in juveniles differentiate rapidly, they increasingly return to a resting state of shallow quiescence and progress through additional self-renewing divisions in adulthood. Single-cell transcriptomics, modeling, and label retention analyses indicate that resting cells have a higher activation rate and greater contribution to neurogenesis than dormant cells, which have not left quiescence. These changes in stem cell behavior result from a progressive reduction in expression of the pro-activation protein ASCL1 because of increased post-translational degradation. These cellular mechanisms help reconcile current contradictory models of hippocampal neural stem cell (NSC) dynamics and may contribute to the different rates of decline of hippocampal neurogenesis in mammalian species, including humans.

Mathematical Modeling Provides Evidence for Niche Competition in Human AML and Serves as a Tool to Improve Risk Stratification.

Acute myeloid leukemia (AML) is a stem cell-driven malignant disease. There is evidence that leukemic stem cells (LSC) interact with stem cell niches and outcompete hematopoietic stem cells (HSC). The impact of this interaction on the clinical course of the disease remains poorly understood. We developed and validated a mathematical model of stem cell competition in the human HSC niche. Model simulations predicted how processes in the stem cell niche affect the speed of disease progression. Combining the mathematical model with data of individual patients, we quantified the selective pressure LSCs exert on HSCs and demonstrated the model's prognostic significance. A novel model-based risk-stratification approach allowed extraction of prognostic information from counts of healthy and malignant cells at the time of diagnosis. This model's feasibility was demonstrable based on a cohort of patients with ALDH-rare AML and shows that the model-based risk stratification is an independent predictor of disease-free and overall survival. This proof-of-concept study shows how model-based interpretation of patient data can improve prognostic scoring and contribute to personalized medicine. SIGNIFICANCE: Combining a novel mathematical model of the human hematopoietic stem cell niche with individual patient data enables quantification of properties of leukemic stem cells and improves risk stratification in acute myeloid leukemia.

Mathematical modeling of plant cell fate transitions controlled by hormonal signals.

Coordination of fate transition and cell division is crucial to maintain the plant architecture and to achieve efficient production of plant organs. In this paper, we analysed the stem cell dynamics at the shoot apical meristem (SAM) that is one of the plant stem cells locations. We designed a mathematical model to elucidate the impact of hormonal signaling on the fate transition rates between different zones corresponding to slowly dividing stem cells and fast dividing transit amplifying cells. The model is based on a simplified two-dimensional disc geometry of the SAM and accounts for a continuous displacement towards the periphery of cells produced in the central zone. Coupling growth and hormonal signaling results in a nonlinear system of reaction-diffusion equations on a growing domain with the growth rate depending on the model components. The model is tested by simulating perturbations in the level of key transcription factors that maintain SAM homeostasis. The model provides new insights on how the transcription factor HECATE is integrated in the regulatory network that governs stem cell differentiation.

Oscillations in a white blood cell production model with multiple differentiation stages.

In this work we prove occurrence of a super-critical Hopf bifurcation in a model of white blood cell formation structured by three maturation stages. We provide an explicit analytical expression for the bifurcation point depending on model parameters. The Hopf bifurcation is a unique feature of the multi-compartment structure as it does not exist in the corresponding two-compartment model. It appears for a parameter set different from the parameters identified for healthy hematopoiesis and requires changes in at least two cell properties. Model analysis allows identifying a range of biologically plausible parameter sets that can explain persistent oscillations of white blood cell counts observed in some hematopoietic diseases. Relating the identified parameter sets to recent experimental and clinical findings provides insights into the pathological mechanisms leading to oscillating blood cell counts.

A structured population model of clonal selection in acute leukemias with multiple maturation stages.

Recent progress in genetic techniques has shed light on the complex co-evolution of malignant cell clones in leukemias. However, several aspects of clonal selection still remain unclear. In this paper, we present a multi-compartmental continuously structured population model of selection dynamics in acute leukemias, which consists of a system of coupled integro-differential equations. Our model can be analysed in a more efficient way than classical models formulated in terms of ordinary differential equations. Exploiting the analytical tractability of this model, we investigate how clonal selection is shaped by the self-renewal fraction and the proliferation rate of leukemic cells at different maturation stages. We integrate analytical results with numerical solutions of a calibrated version of the model based on real patient data. In summary, our mathematical results formalise the biological notion that clonal selection is driven by the self-renewal fraction of leukemic stem cells and the clones that possess the highest value of this parameter are ultimately selected. Moreover, we demonstrate that the self-renewal fraction and the proliferation rate of non-stem cells do not have a substantial impact on clonal selection. Taken together, our results indicate that interclonal variability in the self-renewal fraction of leukemic stem cells provides the necessary substrate for clonal selection to act upon.

Stem cell topography splits growth and homeostatic functions in the fish gill.

While lower vertebrates contain adult stem cells (aSCs) that maintain homeostasis and drive un-exhaustive organismal growth, mammalian aSCs display mainly the homeostatic function. Here, we use lineage analysis in the medaka fish gill to address aSCs and report separate stem cell populations for homeostasis and growth. These aSCs are fate-restricted during the entire post-embryonic life and even during re-generation paradigms. We use chimeric animals to demonstrate that p53 mediates growth coordination among fate-restricted aSCs, suggesting a hierarchical organisation among lineages in composite organs like the fish gill. Homeostatic and growth aSCs are clonal but differ in their topology; modifications in tissue architecture can convert the homeostatic zone into a growth zone, indicating a leading role for the physical niche defining stem cell output. We hypothesise that physical niches are main players to restrict aSCs to a homeostatic function in animals with fixed adult size.

Quiescence Modulates Stem Cell Maintenance and Regenerative Capacity in the Aging Brain.

The function of somatic stem cells declines with age. Understanding the molecular underpinnings of this decline is key to counteract age-related disease. Here, we report a dramatic drop in the neural stem cells (NSCs) number in the aging murine brain. We find that this smaller stem cell reservoir is protected from full depletion by an increase in quiescence that makes old NSCs more resistant to regenerate the injured brain. Once activated, however, young and old NSCs show similar proliferation and differentiation capacity. Single-cell transcriptomics of NSCs indicate that aging changes NSCs minimally. In the aging brain, niche-derived inflammatory signals and the Wnt antagonist sFRP5 induce quiescence. Indeed, intervention to neutralize them increases activation of old NSCs during homeostasis and following injury. Our study identifies quiescence as a key feature of old NSCs imposed by the niche and uncovers ways to activate NSCs to repair the aging brain.