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Purpose of review Hematopoietic stem cells (HSCs) drive blood-cell production (hematopoiesis). Out-competition of HSCs by malignant cells occurs in many hematologic malignancies like acute myeloid leukemia (AML). Through mathematical modelling, HSC dynamics and their impact on healthy blood cell formation can be studied, using mathematical analysis and computer simulations. We review important work within this field and discuss mathematical modelling as a tool for attaining biological insight. Recent findings Various mechanism-based models of HSC dynamics have been proposed in recent years. Key properties of such models agree with observations and medical knowledge and suggest relations between stem cell properties, e.g., rates of division and the temporal evolution of the HSC population. This has made it possible to study how HSC properties shape clinically relevant processes, including engraftment following an HSC transplantation and the response to different treatment. Summary Understanding how properties of HSCs affect hematopoiesis is important for efficient treatment of diseases. Mathematical modelling can contribute significantly to these efforts.

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.

Supplementary Methods, Supplementary Figures 1-7 and Supplementary Tables 1-3.

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. Cancer Res; 75(6); 940–9. ©2015 AACR.

Supplemental Methods. Detailed derivation and calibration of mathematical model.

Supplemental Figure 1. The figure depicts fit of model to individual patients' marrow blast counts.

Supplemental Figure 2. The figure depicts estimated LSC properties for the subgroup of FLT3-ITD (a typical leukemogenetic mutation) positive patients.

Supplemental Figure 3. The figure compares estimated LSC properties in first and second relapse of 4 patients.

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., Graphical abstract, High-throughput screening of 177 AAV capsid variants identifies variants with high tropism for the adult subventricular zone. Single-cell transcriptomics shows that lineages arising from transduced stem cells are comparable to non-transduced ones. Mathematical modeling and flow cytometry indicate transduction of 30%−60% stem cells within the subventricular zone.

Extensive genetic and epigenetic variegation has been demonstrated in many malignancies. Importantly, their interplay has the potential to contribute to disease progression and treatment resistance. To shed light on the complex relationships between these different sources of intra-tumour heterogeneity, we explored their relative contributions to the evolutionary dynamics of Acute Lymphoblastic Leukemia (ALL) in children with Down syndrome, which has particularly poor prognosis. We quantified the tumour propagating potential of genetically distinct sub-clones using serial transplantation assays and SNP-arrays. While most leukaemias were characterized by a single dominant subclone, others were highly heterogeneous. Importantly, we provide clear and direct evidence that genotypes and phenotypes with functional relevance to leukemic progression and treatment resistance can co-segregate within the disease. Hence, individual genetic lesions can be restricted to well-defined cell immunophenotypes, corresponding to different stages of the leukemic differentiation hierarchy and varied proliferation potentials. As a result of this difference in fitness, which can be accurately quantified via competitive transplantation assays, matching diagnostic, post-treatment, and relapse leukemias can be dominated by different genotypes, including pre-leukemic clones persisting throughout the disease progression and treatment. Intriguingly, plasticity also appears to be a temporally defined property that can segregate with genotype. These results suggest that Down Syndrome ALL should be viewed as a complex matrix of cells exhibiting genetic and epigenetic heterogeneity that foster extensive clonal evolution and competition. Therapeutic intervention reshapes this ‘eco-system’ and may provide the right conditions for the preferential expansion of selected compartments and subsequently relapse.

Stem cells (2022). doi:10.1093/stmcls/sxac079, Published by Oxford University Press, Oxford

Blood advances 6(6), 1780-1796 (2022). doi:10.1182/bloodadvances.2021006061, Published by American Society of Hematology, Washington, DC

The myeloproliferative neoplasms are associated with chronic kidney disease but whether clonal haematopoiesis of indeterminate potential (CHIP) is associated with impaired kidney function is unknown. In the Danish General Suburban Population Study (N = 19 958) from 2010 to 2013, 645 individuals were positive for JAK2V617F (N = 613) or CALR (N = 32) mutations. Mutation-positive individuals without haematological malignancy were defined as having CHIP (N = 629). We used multiple and inverse probability weighted (IPW)-adjusted linear regression analysis to estimate adjusted mean (95% confidence interval) differences in estimated glomerular filtration rate (eGFR; ml/min/1.73 m2) by mutation status, variant allele frequency (VAF%), blood cell counts, and neutrophil-to-lymphocyte ratio (NLR). We performed 11-year longitudinal follow-up of eGFR in all individuals. Compared to CHIP-negative individuals, the mean differences in eGFR were −5.6 (−10.3, −0.8, p =.02) for CALR, −11.9 (−21.4, −2.4, p = 0.01) for CALR type 2, and −10.1 (−18.1, −2.2, p =.01) for CALR with VAF ≥ 1%. The IPW-adjusted linear regression analyses showed similar results. NLR was negatively associated with eGFR. Individuals with CALR type 2 had a worse 11-year longitudinal follow-up on eGFR compared to CHIP-negative individuals (p =.004). In conclusion, individuals with CALR mutations, especially CALR type 2, had impaired kidney function compared to CHIP-negative individuals as measured by a lower eGFR at baseline and during 11-year follow-up.

Adult stem cells play a key role in tissue regeneration and cancer. To translate findings from stem cell biology into clinics, we require a quantitative characterization of stem cell dynamics in vivo. This review explores how mathematical models can help to characterize stem cell behavior in health and disease. Mathematical models significantly contribute to quantification of stem cell traits such as proliferation, self-renewal, and quiescence. They provide insights into the role of systemic and micro-environmental feedback loops during regeneration and cancer. Computer simulations allow linking stem cell properties to tumor composition, clinical course, and drug response. Therefore, models are helpful in personalizing treatments and predicting patient survival. Mathematical models coupled with tools of parameter estimation and model selection provide quantitative insights into stem cell properties and their regulation. They help to understand experimentally inaccessible processes occurring in regeneration, aging, and cancer.

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., Comment: Submitted to Journal of Theoretical Biology

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, AAV9_A2 and AAV1_P5, both of which transduce active and quiescent NSCs. Further optimization of AAV1_P5 by judicious selection of promoter and dose of injected viral genomes enabled labeling of 30-60% of the NSC compartment, which was validated by FACS analyses and single cell RNA sequencing. Importantly, transduced NSC readily produced neurons. The present study identifies AAV variants with a high regional tropism towards the v-SVZ with high efficiency in targeting adult NSCs, thereby paving the way for preclinical testing of regenerative gene therapy.

SUMMARYNeural stem cell numbers fall rapidly in the hippocampus of juvenile mice but stabilise during adulthood, ensuring lifelong hippocampal neurogenesis. We show that this reduction in stem cell depletion rate is the result of multiple coordinated changes in stem cell behaviour. In particular, while active neural stem cells divide only once or twice before differentiating rapidly in juveniles, they increasingly return to a resting state of shallow quiescence and progress through additional self-renewing divisions in adulthood. Single-cell transcriptomic, mathematical modelling 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 progressive changes in stem cell behaviour result from reduced expression of the pro-activation protein ASCL1 due to increased post-translational degradation. These mechanisms help reconcile current contradictory models of hippocampal NSC dynamics and may contribute to the different rates of decline of hippocampal neurogenesis in mammalian species including humans.

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.

Background: Fibrosing chronic graft-versus-host disease (cGVHD) is a debilitating complication after allogeneic stem cell transplantation (allo-SCT), and its pathophysiology is poorly understood. Kynurenine and its metabolites were shown to associate with both, interferon-gamma (IFNg) activation and fibrosis. This study investigates the interplay between members of the IFNγ pathway and Kynurenin-derived metabolites in cGVHD. Methods: Using a liquid chromatography tandem mass spectrometry approach on sera obtained on day+100 (n=430) and/or at onset of cGVHD symptoms (n=196) of our prospectively collected biobank after alloSCT, we measured concentrations of Kyn pathway metabolites (kynurenin (Kyn), anthranilic acid (AA), kynurenic acid (KA), 3-hydroxykynurenine (3-HK), and 3-hydroxy-anthranilic acid (3-HAA). We also measured C-X-C chemokine ligand 9 (CXCL9), interleukin (IL-)18, tryptophane (Trp) and indoleamine-2,3-dioxygenase (IDO) by ELISA. Results: We observed increased CXCL9 and IDO levels, and increased activity of the Kynurenine pathway in both non-severe and severe cGVHD. Interestingly, severe fibrosing cGVHD differed from any other form of cGVHD in a significant pathway shift toward AA and KA. This resulted in a reduced 3-HAA/AA ratio. A score consisting of low 3-HAA/AA ratio and high KA serum levels at onset of mild cGVHD symptoms predicted risk specifically of severe fibrosing cGVHD. This altered pathway in severe fibrosing cGVHD correlated with reduced activity of the Vitamin-B2-dependent kynurenine monooxygenase, low vitamin B6, and increased interleukin-18. Our results are consistent with a triple-hit model for fibrosing cGVHD including low activity of kynurenine monooxygenase (KMO, Vitamin B2 and B6 dependent) in the context of high IL18 serum levels and CXCL9-induced IDO activation (Figure 1). Conclusion: Chronic GVHD associates with an IFNg signature and increased activity of the Kynurenin pathway. KA and 3-HAA/AA defined the first molecular distinction between fibrosing and non-fibrosing cGVHD. The mechanism may involve Vitamin B2/B6 deficiency, and high CXCL9 and IL18. The Kyn metabolite signature is a candidate biomarker for severe fibrosing cGHVD and provides a rationale for translational trials on prophylactic Vitamin B2/B6 supplementation for cGVHD prevention. Figure 1: Triple hit model of fibrosing cGVHD (Hypothesis): Severe fibrosing cGVHD associates with a strong CXCL9-induced activation of IDO. The result of this activation is influenced by a reduced activity of kynurenine monooxygenase (KMO), either due to genetic polymorphisms or lack of Vitamin B2, and further aggravated by lack of Vitamin B6. The resulting metabolic deviation increases AA concentrations and reduces the 3-HAA/AA ratio. Finally, high IL-18 associates with increased serum KA. These three hits result in a metabolic situation with high KA and a low ratio 3-HAA/AA that predicts risk of fibrosing cGVHD. Figure 1 Figure 1. Disclosures Mueller-Tidow: Janssen Cilag: Consultancy, Research Funding; Pfizer: Consultancy, Research Funding; Bioline: Consultancy, Research Funding.

Self-renewal is the process by which stem cells give rise to stem cells. Recent insights from experimental and theoretical models suggest that self-renewal not only influences the stem cell population but has a crucial impact on dynamics of non-stem cells. Efficient production of mature cells in tissue regeneration requires up-regulation of stem cell self-renewal. Increased self-renewal confers a competitive advantage on cancer cell clones by leading to aggressive expansion of both stem and non-stem cancer cells. Recent models suggest that self-renewal is the key parameter to understand clonal competition, selection and emergence of resistance in cancer cell populations.

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.

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., Author summary Plants continuously generate new organs such as leaves, roots and flowers. This process is driven by stem cells which are located in specialized regions, so-called meristems. Dividing stem cells give rise to offspring that, during a process referred to as cell fate transition, become more specialized and give rise to organs. Plant architecture and crop yield crucially depend on the regulation of meristem dynamics. To better understand this regulation, we develop a computational model of the shoot meristem. The model describes the meristem as a two-dimensional disk that can grow and shrink over time, depending on the concentrations of the signalling factors in its interior. This allows studying how the non-linear interaction of multiple transcription factors is linked to cell division and fate-transition. We test the model by simulating perturbations of meristem signals and comparing them to experimental data. The model allows simulating different hypotheses about signal effects. Based on the model we study the specific role of the transcription factor HECATE and provide new insights in its action on cell dynamics and in its interrelation with other known transcription factors in the meristem.

Human blood cell production is maintained by hematopoietic stem cells (HSC) which give rise to all types of mature blood cells. Experimental observation of HSC in their physiologic bone-marrow microenvironment, the so-called stem cell niche, is challenging. Therefore, the details of HSC dynamics and the cellular interactions in the stem cell niche remain elusive. Mutations that lead to a competitive advantage are the cause of clinical challenges when treating HSC-derived malignancies such as acute myeloid leukemia or the myeloproliferative neoplasms (MPNs). To investigate the significance of the interaction between the HSC and the stem cell niche in these malignancies, we propose and analyse a mechanism-based mathematical model of HSC dynamics within the bone-marrow microenvironment. The model is based on the central hypothesis that HSC self-renewal depends on the niche. In the model, the interaction of HSC with specific niches located in the bone marrow are key to the indefinite HSC renewal necessary for long-term maintenance of blood cell production. We formulate a general model of n distinct clones that differ with respect to cell properties. We identify an attractive trapping region and compute and classify all steady states. A concept of HSC fitness naturally arises from the model analysis. HSC fitness is found to determine the asymptotic behaviour of the model, as the HSC clone with the highest fitness is related to the unique locally stable steady state. Based on biological assumptions about HSC, we propose two reduced models of different complexity. A thorough mathematical analysis reveals that both reduced models have the same asymptotic behaviour as the full model. We compare the simpler of the two models, a logistic equation of the disease burden, to clinical data of MPN-patients. The reduced model is found to agree well with data and suggests a simple interpretation and possible prediction of patient prognosis. The proposed mathematical model and the reduced forms have the potential to provide insights into the regulation of HSC dynamics and blood cell formation, and ultimately for future advances in treatment of hematologic malignancies.

Acute myeloid leukemia (AML) is an aggressive cancer of the blood forming (hematopoietic) system. Due to the high patient variability of disease dynamics, risk-scoring is an important part of its clinical management. AML is characterized by impaired blood cell formation and the accumulation of so-called leukemic blasts in the bone marrow of patients. Recently, it has been proposed to use counts of blood-producing (hematopoietic) stem cells (HSCs) as a biomarker for patient prognosis. In this work, we use a non-linear mathematical model to provide mechanistic evidence for the suitability of HSC counts as a prognostic marker. Using model analysis and computer simulations, we compare different risk-scores involving HSC quantification. We propose and validate a simple approach to improve risk prediction based on HSC and blast counts measured at the time of diagnosis.

Funding: TS and AM-C were supported by research funding from the German Research Foundation DFG (SFB 873; subproject B08). TL gratefully acknowledges support from the Heidelberg Graduate School (HGS). 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. Postprint

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., 34 pages, 5 figures, 2 tables; new references added, new figure added, typos corrected