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.

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.

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 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.

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.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12915-021-01046-9.

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.

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More proliferating hippocampal stem cells return to shallow quiescence with age

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Dormant stem cells enter deeper quiescence with age

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These changes drive the transition from developmental to adult neurogenesis

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Increasing degradation of ASCL1 protein by HUWE1 coordinates these changes

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.

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.

Post-Turing tissue pattern formation: Advent of mechanochemistry

Chemical and mechanical pattern formation is fundamental during embryogenesis and tissue development. Yet, the underlying molecular and cellular mechanisms are still elusive in many cases. Most current theories assume that tissue development is driven by chemical processes: either as a sequence of chemical patterns each depending on the previous one, or by patterns spontaneously arising from specific chemical interactions (such as “Turing-patterns”). Within both theories, mechanical patterns are usually regarded as passive by-products of chemical pre-patters. However, several experiments question these theories, and an increasing number of studies shows that tissue mechanics can actively influence chemical patterns during development. In this study, we thus focus on the interplay between chemical and mechanical processes during tissue development. On one hand, based on recent experimental data, we develop new mechanochemical simulation models of evolving tissues, in which the full 3D representation of the tissue appears to be critical for obtaining a realistic mechanochemical behaviour. The presented modelling approach is flexible and numerically studied using state of the art finite element methods. Thus, it may serve as a basis to combine simulations with new experimental methods in tissue development. On the other hand, we apply the developed approach and demonstrate that even simple interactions between tissue mechanics and chemistry spontaneously lead to robust and complex mechanochemical patterns. Especially, we demonstrate that the main contradictions arising in the framework of purely chemical theories are naturally and automatically resolved using the mechanochemical patterning theory.

During embryogenesis, biological tissues gradually increase their complexity by self-organised creation of diverse chemical and mechanical patterns. Detailed mechanisms driving and controlling these patterns are not well understood. Previous theories mostly assume that these patterns are driven by chemical processes. Based on these theories, mechanical patterns are usually considered being mainly determined by chemical pre-patterns. However, experimental evidence for these theories is sparse, and several inconsistencies have been discovered. Furthermore, an increasing amount of data shows that tissue mechanics plays an important role in pattern formation. In this study, we present 3D computer simulations of evolving tissues to investigate the capacity of mechanochemical interactions for pattern formation. We show that even simple interactions between tissue mechanics and tissue chemistry spontaneously lead to robust chemical and mechanical pattern formation. We additionally demonstrate that main contradictions arising in the framework of purely chemical theories are naturally and automatically resolved using the mechanochemical patterning theory. The presented modelling approach can be used to combine simulations with recent experimental developments, to help unravel one of the big mysteries in biology: The mechanisms of self-organised pattern formation during embryogenesis.

Mathematical modeling of the impact of cytokine response of acute myeloid leukemia cells on patient prognosis

Acute myeloid leukemia (AML) is a heterogeneous disease. One reason for the heterogeneity may originate from inter-individual differences in the responses of leukemic cells to endogenous cytokines. On the basis of mathematical modeling, computer simulations and patient data, we have provided evidence that cytokine-independent leukemic cell proliferation may be linked to early relapses and poor overall survival. Depending whether the model of cytokine-dependent or cytokine-independent leukemic cell proliferation fits to the clinical data, patients can be assigned to two groups that differ significantly with respect to overall survival. The modeling approach further enables us to identify parameter constellations that can explain unexpected responses of some patients to external cytokines such as blast crisis or remission without chemotherapy.

Revealing age-related changes of adult hippocampal neurogenesis using mathematical models

New neurons are continuously generated in the dentate gyrus of the adult hippocampus. This continuous supply of newborn neurons is important to modulate cognitive functions. Yet the number of newborn neurons declines with age. Increasing Wnt activity upon loss of dickkopf 1 can counteract both the decline of newborn neurons and the age-related cognitive decline. However, the precise cellular changes underlying the age-related decline or its rescue are fundamentally not understood. The present study combines a mathematical model and experimental data to address features controlling neural stem cell (NSC) dynamics. We show that available experimental data fit a model in which quiescent NSCs may either become activated to divide or may undergo depletion events, such as astrocytic transformation and apoptosis. Additionally, we demonstrate that old NSCs remain quiescent longer and have a higher probability of becoming re-activated than depleted. Finally, our model explains that high NSC-Wnt activity leads to longer time in quiescence while enhancing the probability of activation. Altogether, our study shows that modulation of the quiescent state is crucial to regulate the pool of stem cells throughout the life of an animal.

Summary: New deterministic and stochastic mathematical models are proposed to investigate adult neurogenesis in young, old and perturbed hippocampus, and quantified using population-level and clonal experimental data.

Quantification of plasma cell dynamics using mathematical modelling

Plasma cells (PCs) are the main antibody-producing cells in humans. They are long-lived so that specific antibodies against either pathogens or vaccines are produced for decades. PC longevity is attributed to specific areas within the bone marrow micro-environment, the so-called 'niche', providing the cells with required growth and survival factors. With antigen encounters, e.g. infection or vaccination, new PCs are generated and home to the bone marrow where they compete with resident PCs for the niche. We propose a parametrized mathematical model describing healthy PC dynamics in the bone marrow. The model accounts for competition for the niche between newly produced PCs owing to vaccination and resident PCs. Mathematical analysis and numerical simulations of the model allow explanation of the recovery of PC homoeostasis after a vaccine-induced perturbation, and the fraction of vaccine-specific PCs inside the niche. The model enables quantification of the niche-related dynamics of PCs, i.e. the duration of PC transition into the niche and the impact of different rates for PC transitions into and out of the niche on the observed cell dynamics. Ultimately, it provides a potential basis for further investigations in health and disease.

Control of plant cell fate transitions by transcriptional and hormonal signals

Plant meristems carry pools of continuously active stem cells, whose activity is controlled by developmental and environmental signals. After stem cell division, daughter cells that exit the stem cell domain acquire transit amplifying cell identity before they are incorporated into organs and differentiate. In this study, we used an integrated approach to elucidate the role of HECATE (HEC) genes in regulating developmental trajectories of shoot stem cells in Arabidopsis thaliana. Our work reveals that HEC function stabilizes cell fate in distinct zones of the shoot meristem thereby controlling the spatio-temporal dynamics of stem cell differentiation. Importantly, this activity is concomitant with the local modulation of cellular responses to cytokinin and auxin, two key phytohormones regulating cell behaviour. Mechanistically, we show that HEC factors transcriptionally control and physically interact with MONOPTEROS (MP), a key regulator of auxin signalling, and modulate the autocatalytic stabilization of auxin signalling output.

Unlike animals, plants continuously generate new organs that make up their body. At the core of this amazing capacity lie tissues called meristems, which are found at the growing tips of all plants. Meristems contain dividing stem cells. The daughters of these stem cells pass through nearby regions called transition domains. Over time, they change – or differentiate – to go on to become part of tissues like leaves, roots, stems, shoots, flowers or fruits.

Stem cell differentiation has a direct impact on a plant’s architecture and eventually its reproductive success. For crops, these factors determine yield. This means that understanding this aspect of plant development is central to basic and applied plant biology. Many factors required for shoot meristem activity have been identified, with a focus so far on the processes that control the identity of the cells produced.

Now, Gaillochet et al. have asked which genes are responsible for controlling when stem cells in meristems differentiate. The analysis focused on the meristem that makes all the above ground parts of model plant Arabidopsis thaliana – the shoot apical meristem. Gaillochet et al. found that HECATE genes (or HEC for short) control the timing of stem cell differentiation by regulating the balance between the activities of two plant hormones: cytokinin and auxin. These genes promote cytokinin signals at the centre of the meristem, and dampen auxin response at the edges. This acts to slow down cell differentiation in two key transition domains of the shoot meristem.

These new findings provide a molecular framework that now can be further investigated in crop plants to try to improve their yield. The findings also lay the foundation for studies of animals that may define common principles shared among stem cell systems in organisms that diverged over a billion years ago.

Reduced hematopoietic stem cell frequency predicts outcome in acute myeloid leukemia

In patients with acute myeloid leukemia and low percentages of aldehyde-dehydrogenase-positive cells, non-leukemic hematopoietic stem cells can be separated from leukemic cells. By relating hematopoietic stem cell frequencies to outcome we detected poor overall- and disease-free survival of patients with low hematopoietic stem cell frequencies. Serial analysis of matched diagnostic and follow-up samples further demonstrated that hematopoietic stem cells increased after chemotherapy in patients who achieved durable remissions. However, in patients who eventually relapsed, hematopoietic stem cell numbers decreased dramatically at the time of molecular relapse demonstrating that hematopoietic stem cell levels represent an indirect marker of minimal residual disease, which heralds leukemic relapse. Upon transplantation in immune-deficient mice cases with low percentages of hematopoietic stem cells of our cohort gave rise to leukemic or no engraftment, whereas cases with normal hematopoietic stem cell levels mostly resulted in multi-lineage engraftment. Based on our experimental data, we propose that leukemic stem cells have increased niche affinity in cases with low percentages of hematopoietic stem cells. To validate this hypothesis, we developed new mathematical models describing the dynamics of healthy and leukemic cells under different regulatory scenarios. These models suggest that the mechanism leading to decreases in hematopoietic stem cell frequencies before leukemic relapse must be based on expansion of leukemic stem cells with high niche affinity and the ability to dislodge hematopoietic stem cells. Thus, our data suggest that decreasing numbers of hematopoietic stem cells indicate leukemic stem cell persistence and the emergence of leukemic relapse.

Emergence of heterogeneity in acute leukemias

BACKGROUND

Leukemias are malignant proliferative disorders of the blood forming system. Sequencing studies demonstrate that the leukemic cell population consists of multiple clones. The genetic relationship between the different clones, referred to as the clonal hierarchy, shows high interindividual variability. So far, the source of this heterogeneity and its clinical relevance remain unknown. We propose a mathematical model to study the emergence and evolution of clonal heterogeneity in acute leukemias. The model allows linking properties of leukemic clones in terms of self-renewal and proliferation rates to the structure of the clonal hierarchy.

RESULTS

Computer simulations imply that the self-renewal potential of the first emerging leukemic clone has a major impact on the total number of leukemic clones and on the structure of their hierarchy. With increasing depth of the clonal hierarchy the self-renewal of leukemic clones increases, whereas the proliferation rates do not change significantly. The emergence of deep clonal hierarchies is a complex process that is facilitated by a cooperativity of different mutations.

CONCLUSION

Comparison of patient data and simulation results suggests that the self-renewal of leukemic clones increases with the emergence of clonal heterogeneity. The structure of the clonal hierarchy may serve as a marker for patient prognosis.

REVIEWERS

This article was reviewed by Marek Kimmel, Tommaso Lorenzi and Tomasz Lipniacki.

Instability of turing patterns in reaction-diffusion-ODE systems

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

Beyond Turing: mechanochemical pattern formation in biological tissues

Background

During embryogenesis, chemical (morphogen) and mechanical patterns develop within tissues in a self-organized way. More than 60 years ago, Turing proposed his famous reaction-diffusion model for such processes, assuming chemical interactions as the main driving force in tissue patterning. However, experimental identification of corresponding molecular candidates is still incomplete. Recent results suggest that beside morphogens, also tissue mechanics play a significant role in these patterning processes.

Results

Combining continuous finite strain with discrete cellular tissue models, we present and numerically investigate mechanochemical processes, in which morphogen dynamics and tissue mechanics are coupled by feedback loops. We consider three different mechanical cues involved in such feedbacks: strain, stress, and compression. Based on experimental results, for each case, we present a feedback loop spontaneously creating robust mechanochemical patterns. In contrast to Turing-type models, simple mechanochemical interaction terms are sufficient to create de novo patterns.

Conclusions

Our results emphasize mechanochemical processes as possible candidates controlling different steps of embryogenesis. To motivate further experimental research discovering related mechanisms in living tissues, we also present predictive in silicio experiments.

Reviewers

Reviewer 1 - Marek Kimmel; Reviewer 2 - Konstantin Doubrovinski (nominated by Ned Wingreen); Reviewer 3 - Jun Allard (nominated by William Hlavacek).

Mass concentration in a nonlocal model of clonal selection

Self-renewal is a constitutive property of stem cells. Testing the cancer stem cell hypothesis requires investigation of the impact of self-renewal on cancer expansion. To better understand this impact, we propose a mathematical model describing the dynamics of a continuum of cell clones structured by the self-renewal potential. The model is an extension of the finite multi-compartment models of interactions between normal and cancer cells in acute leukemias. It takes a form of a system of integro-differential equations with a nonlinear and nonlocal coupling which describes regulatory feedback loops of cell proliferation and differentiation. We show that this coupling leads to mass concentration in points corresponding to the maxima of the self-renewal potential and the solutions of the model tend asymptotically to Dirac measures multiplied by positive constants. Furthermore, using a Lyapunov function constructed for the finite dimensional counterpart of the model, we prove that the total mass of the solution converges to a globally stable equilibrium. Additionally, we show stability of the model in the space of positive Radon measures equipped with the flat metric (bounded Lipschitz distance). Analytical results are illustrated by numerical simulations.

Mechanochemical symmetry breaking in Hydra aggregates

Tissue morphogenesis comprises the self-organized creation of various patterns and shapes. Although detailed underlying mechanisms are still elusive in many cases, an increasing amount of experimental data suggests that chemical morphogen and mechanical processes are strongly coupled. Here, we develop and test a minimal model of the axis-defining step (i.e., symmetry breaking) in aggregates of the Hydra polyp. Based on previous findings, we combine osmotically driven shape oscillations with tissue mechanics and morphogen dynamics. We show that the model incorporating a simple feedback loop between morphogen patterning and tissue stretch reproduces a wide range of experimental data. Finally, we compare different hypothetical morphogen patterning mechanisms (Turing, tissue-curvature, and self-organized criticality). Our results suggest the experimental investigation of bigger (i.e., multiple head) aggregates as a key step for a deeper understanding of mechanochemical symmetry breaking in Hydra.

Cell division patterns in acute myeloid leukemia stem-like cells determine clinical course: a model to predict patient survival

Acute myeloid leukemia (AML) is a heterogeneous disease in which a variety of distinct genetic alterations might occur. Recent attempts to identify the leukemia stem-like cells (LSC) have also indicated heterogeneity of these cells. On the basis of mathematical modeling and computer simulations, we have provided evidence that proliferation and self-renewal rates of the LSC population have greater impact on the course of disease than proliferation and self-renewal rates of leukemia blast populations, that is, leukemia progenitor cells. The modeling approach has enabled us to estimate the LSC properties of 31 individuals with relapsed AML and to link them to patient survival. On the basis of the estimated LSC properties, the patients can be divided into two prognostic groups that differ significantly with respect to overall survival after first relapse. The results suggest that high LSC self-renewal and proliferation rates are indicators of poor prognosis. Nevertheless, high LSC self-renewal rate may partially compensate for slow LSC proliferation and vice versa. Thus, model-based interpretation of clinical data allows estimation of prognostic factors that cannot be measured directly. This may have clinical implications for designing treatment strategies.

Mathematical Modelling as a Tool to Understand Cell Self-renewal and Differentiation

Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.

Feedback signals in myelodysplastic syndromes: increased self-renewal of the malignant clone suppresses normal hematopoiesis

Myelodysplastic syndromes (MDS) are triggered by an aberrant hematopoietic stem cell (HSC). It is, however, unclear how this clone interferes with physiologic blood formation. In this study, we followed the hypothesis that the MDS clone impinges on feedback signals for self-renewal and differentiation and thereby suppresses normal hematopoiesis. Based on the theory that the MDS clone affects feedback signals for self-renewal and differentiation and hence suppresses normal hematopoiesis, we have developed a mathematical model to simulate different modifications in MDS-initiating cells and systemic feedback signals during disease development. These simulations revealed that the disease initiating cells must have higher self-renewal rates than normal HSCs to outcompete normal hematopoiesis. We assumed that self-renewal is the default pathway of stem and progenitor cells which is down-regulated by an increasing number of primitive cells in the bone marrow niche – including the premature MDS cells. Furthermore, the proliferative signal is up-regulated by cytopenia. Overall, our model is compatible with clinically observed MDS development, even though a single mutation scenario is unlikely for real disease progression which is usually associated with complex clonal hierarchy. For experimental validation of systemic feedback signals, we analyzed the impact of MDS patient derived serum on hematopoietic progenitor cells in vitro: in fact, MDS serum slightly increased proliferation, whereas maintenance of primitive phenotype was reduced. However, MDS serum did not significantly affect colony forming unit (CFU) frequencies indicating that regulation of self-renewal may involve local signals from the niche. Taken together, we suggest that initial mutations in MDS particularly favor aberrant high self-renewal rates. Accumulation of primitive MDS cells in the bone marrow then interferes with feedback signals for normal hematopoiesis – which then results in cytopenia.

Myelodysplastic syndromes are diseases which are characterized by ineffective blood formation. There is accumulating evidence that they are caused by an aberrant hematopoietic stem cell. However, it is yet unclear how this malignant clone suppresses normal hematopoiesis. To this end, we generated mathematical models under the assumption that feedback signals regulate self-renewal and proliferation of normal and diseased stem cells. The simulations demonstrate that the malignant cells must have particularly higher self-renewal rates than normal stem cells – rather than higher proliferation rates. On the other hand, down-regulation of self-renewal by the increasing number of malignant cells in the bone marrow niche can explain impairment of normal blood formation. In fact, we show that serum of patients with myelodysplastic syndrome, as compared to serum of healthy donors, stimulates proliferation and moderately impacts on maintenance of hematopoietic stem and progenitor cells in vitro. Thus, aberrant high self-renewal rates of the malignant clone seem to initiate disease development; suppression of normal blood formation is then caused by a rebound effect of feedback signals which down-regulate self-renewal of normal stem and progenitor cells as well.

Clonal selection and therapy resistance in acute leukaemias: mathematical modelling explains different proliferation patterns at diagnosis and relapse

Recent experimental evidence suggests that acute myeloid leukaemias may originate from multiple clones of malignant cells. Nevertheless, it is not known how the observed clones may differ with respect to cell properties, such as proliferation and self-renewal. There are scarcely any data on how these cell properties change due to chemotherapy and relapse. We propose a new mathematical model to investigate the impact of cell properties on the multi-clonal composition of leukaemias. Model results imply that enhanced self-renewal may be a key mechanism in the clonal selection process. Simulations suggest that fast proliferating and highly self-renewing cells dominate at primary diagnosis, while relapse following therapy-induced remission is triggered mostly by highly self-renewing but slowly proliferating cells. Comparison of simulation results to patient data demonstrates that the proposed model is consistent with clinically observed dynamics based on a clonal selection process.

Mathematical modelling of adult hippocampal neurogenesis: effects of altered stem cell dynamics on cell counts and bromodeoxyuridine-labelled cells

In the adult hippocampus, neurogenesis—the process of generating mature granule cells from adult neural stem cells—occurs throughout the entire lifetime. In order to investigate the involved regulatory mechanisms, knockout (KO) experiments, which modify the dynamic behaviour of this process, were conducted in the past. Evaluating these KOs is a non-trivial task owing to the complicated nature of the hippocampal neurogenic niche. In this study, we model neurogenesis as a multicompartmental system of ordinary differential equations based on experimental data. To analyse the results of KO experiments, we investigate how changes of cell properties, reflected by model parameters, influence the dynamics of cell counts and of the experimentally observed counts of cells labelled by the cell division marker bromodeoxyuridine (BrdU). We find that changing cell proliferation rates or the fraction of self-renewal, reflecting the balance between symmetric and asymmetric cell divisions, may result in multiple time phases in the response of the system, such as an initial increase in cell counts followed by a decrease. Furthermore, these phases may be qualitatively different in cells at different differentiation stages and even between mitotically labelled cells and all cells existing in the system.

Assessing hematopoietic (stem-) cell behavior during regenerative pressure

Hematopoiesis is a complex and strongly regulated process. In case of regenerative pressure, efficient recovery of blood cell counts is crucial for survival of an individual. We propose a quantitative mathematical model of white blood cell formation based on the following cell parameters: (1) proliferation rate, (2) self-renewal, and (3) cell death. Simulating this model we assess the change of these parameters under regenerative pressure. The proposed model allows to quantitatively describe the impact of these cell parameters on engraftment time after stem cell transplantation. Results indicate that enhanced self-renewal during the posttransplant period is crucial for efficient regeneration of blood cell counts while constant or reduced self-renewal leads to delayed recovery or graft failure. Increased cell death in the posttransplant period has a similar impact. In contrast, reduced proliferation or pre-homing cell death causes only mild delays in blood cell recovery which can be compensated sufficiently by increasing the dose of transplanted cells.

Receptor-Based Models with Diffusion-Driven Instability for Pattern Formation in Hydra

The aim of this paper is to show under which conditions a receptor-based model can produce and regulate patterns. Such model is applied to the pattern formation and regulation in a fresh water polyp, hydra. The model is based on the idea that both head and foot formation could be controlled by receptor-ligand binding. Positional value is determined by the density of bound receptors. The model is defined in the form of reaction-diffusion equations coupled with ordinary differential equations. The objective is to check what minimal processes are sufficient to produce patterns in the framework of a diffusion-driven (Turing-type) instability. Three-variable (describing the dynamics of ligands, free and bound receptors) and four-variable models (including also an enzyme cleaving the ligand) are analyzed and compared. The minimal three-variable model takes into consideration the density of free receptors, bound receptors and ligands. In such model patterns can evolve only if self-enhancement of free receptors, i.e., a positive feedback loop between the production of new free receptors and their present density, is assumed. The final pattern strongly depends on initial conditions. In the four-variable model a diffusion-driven instability occurs without the assumption that free receptors stimulate their own synthesis. It is shown that gradient in the density of bound receptors occurs if there is also a second diffusible substance, an enzyme, which degrades ligands. Numerical simulations are done to illustrate the analysis. The four-variable model is able to capture some results from cutting experiments and reflects de novo pattern formation from dissociated cells.

Stability analysis of multi-compartment models for cell production systems

We study two- and three-compartment models of a hierarchical cell production system with cell division regulated by the level of mature cells. We investigate the structure of equilibria with respect to parameters as well as local stability properties for the equilibria. To interpret the results we adapt the concept of reproduction numbers, which is well known in ecology, to stem cell population dynamics. In the two-compartment model, the positive equilibrium is stable wherever it exists. In the three-compartment model, we find that the intermediate stage of differentiation is responsible for the emergence of an instability region in the parameter plane. Moreover, we prove that this region shrinks as the mortality rate for mature cells increases and discuss this result.

Expansion of adipose mesenchymal stromal cells is affected by human platelet lysate and plating density

The composition of mesenchymal stromal cells (MSCs) changes in the course of in vitro culture expansion. Little is known how these cell preparations are influenced by culture media, plating density, or passaging. In this study, we have isolated MSCs from human adipose tissue in culture medium supplemented with either fetal calf serum (FCS) or human platelet lysate (HPL). In addition, culture expansion was simultaneously performed at plating densities of 10 or 10,000 cells/cm(2). The use of FCS resulted in larger cells, whereas HPL significantly enhanced proliferation. Notably, HPL also facilitated expansion for more population doublings than FCS (43 ± 3 vs. 22 ± 4 population doubling; p < 0.001), while plating density did not have a significant effect on long-term growth curves. To gain further insight into population dynamics, we conceived a cellular automaton model to simulate expansion of MSCS. It is based on the assumptions that the number of cell divisions is limited and that due to contact inhibition proliferation occurs only at the rim of colonies. The model predicts that low plating densities result in more heterogeneity with regard to cell division history, and favor subpopulations of higher migratory activity. In summary, HPL is a suitable serum supplement for isolation of MSC from adipose tissue and facilitates more population doublings than FCS. Cellular automaton computer simulations provided additional insights into how complex population dynamics during long-term expansion are affected by plating density and migration.

Modeling of replicative senescence in hematopoietic development

Hematopoietic stem cells (HSC) give rise to an enormous number of blood cells throughout our life. In contrast their number of cell divisions preceding senescence is limited underin vitro culture conditions. Here we consider the question whether HSC can rejuvenate indefinitely or if the number of cell divisions is restricted. We have developed a multi-compartmental model for hematopoietic differentiation based on ordinary differential equations. The model is based on the hypothesis that in each step of maturation, the percentage of self-renewal versus differentiation is regulated by a single external feedback mechanism. We simulate the model under the assumption that hematopoietic differentiation precedes the six steps of maturation and the cells ultimately cease to proliferate after 50 divisions. Our results demonstrate that it is conceivable to maintain hematopoiesis over a life-time if HSC have a slow division rate and a high self-renewal rate. With age, the feedback signal increases and this enhances self-renewal, which results in the increase of the number of stem and progenitor cells. This study demonstrates that replicative senescence is compatible with life-long hematopoiesis and that model predictions are in line with experimental observations. Thus, HSC might not divide indefinitely with potentially important clinical implications.