Dynamical modelling of haematopoiesis: an integrated view over the system in homeostasis and under perturbation

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.

Predictive nonlinear modeling of malignant myelopoiesis and tyrosine kinase inhibitor therapy

Chronic myeloid leukemia (CML) is a blood cancer characterized by dysregulated production of maturing myeloid cells driven by the product of the Philadelphia chromosome, the BCR-ABL1 tyrosine kinase. Tyrosine kinase inhibitors (TKIs) have proved effective in treating CML, but there is still a cohort of patients who do not respond to TKI therapy even in the absence of mutations in the BCR-ABL1 kinase domain that mediate drug resistance. To discover novel strategies to improve TKI therapy in CML, we developed a nonlinear mathematical model of CML hematopoiesis that incorporates feedback control and lineage branching. Cell-cell interactions were constrained using an automated model selection method together with previous observations and new in vivo data from a chimeric BCR-ABL1 transgenic mouse model of CML. The resulting quantitative model captures the dynamics of normal and CML cells at various stages of the disease and exhibits variable responses to TKI treatment, consistent with those of CML patients. The model predicts that an increase in the proportion of CML stem cells in the bone marrow would decrease the tendency of the disease to respond to TKI therapy, in concordance with clinical data and confirmed experimentally in mice. The model further suggests that, under our assumed similarities between normal and leukemic cells, a key predictor of refractory response to TKI treatment is an increased maximum probability of self-renewal of normal hematopoietic stem cells. We use these insights to develop a clinical prognostic criterion to predict the efficacy of TKI treatment and design strategies to improve treatment response. The model predicts that stimulating the differentiation of leukemic stem cells while applying TKI therapy can significantly improve treatment outcomes.

Understanding Hematopoietic Stem Cell Dynamics—Insights from Mathematical Modelling

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.

Single Cell Transcriptomics to Understand HSC Heterogeneity and Its Evolution upon Aging

Single-cell transcriptomic technologies enable the uncovering and characterization of cellular heterogeneity and pave the way for studies aiming at understanding the origin and consequences of it. The hematopoietic system is in essence a very well adapted model system to benefit from this technological advance because it is characterized by different cellular states. Each cellular state, and its interconnection, may be defined by a specific location in the global transcriptional landscape sustained by a complex regulatory network. This transcriptomic signature is not fixed and evolved over time to give rise to less efficient hematopoietic stem cells (HSC), leading to a well-documented hematopoietic aging. Here, we review the advance of single-cell transcriptomic approaches for the understanding of HSC heterogeneity to grasp HSC deregulations upon aging. We also discuss the new bioinformatics tools developed for the analysis of the resulting large and complex datasets. Finally, since hematopoiesis is driven by fine-tuned and complex networks that must be interconnected to each other, we highlight how mathematical modeling is beneficial for doing such interconnection between multilayered information and to predict how HSC behave while aging.

Multistage hematopoietic stem cell regulation in the mouse: A combined biological and mathematical approach

We have reconciled steady-state and stress hematopoiesis in a single mathematical model based on murine in vivo experiments and with a focus on hematopoietic stem and progenitor cells. A phenylhydrazine stress was first applied to mice. A reduced cell number in each progenitor compartment was evidenced during the next 7 days through a drastic level of differentiation without proliferation, followed by a huge proliferative response in all compartments including long-term hematopoietic stem cells, before a return to normal levels. Data analysis led to the addition to the 6-compartment model, of time-dependent regulation that depended indirectly on the compartment sizes. The resulting model was finely calibrated using a stochastic optimization algorithm and could reproduce biological data in silico when applied to different stress conditions (bleeding, chemotherapy, HSC depletion). In conclusion, our multi-step and time-dependent model of immature hematopoiesis provides new avenues to a better understanding of both normal and pathological hematopoiesis.

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We describe a new 6-compartment time-dependent regulated model of hematopoiesis

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Biological data under steady state and stress and cell dynamics were used

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Modeling is able to recapitulate effects from chemotherapy, bleeding, or HSC depletion

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.

Modeling low-dose radiation-induced acute myeloid leukemia in male CBA/H mice

The effect of low-dose ionizing radiation exposure on leukemia incidence remains poorly understood. Possible dose-response curves for various forms of leukemia are largely based on cohorts of atomic bomb survivors. Animal studies can contribute to an improved understanding of radiation-induced acute myeloid leukemia (rAML) in humans. In male CBA/H mice, incidence of rAML can be described by a two-hit model involving a radiation-induced deletion with Sfpi1 gene copy loss and a point mutation in the remaining Sfpi1 allele. In the present study (historical) mouse data were used and these processes were translated into a mathematical model to study photon-induced low-dose AML incidence in male CBA/H mice following acute exposure. Numerical model solutions for low-dose rAML incidence and diagnosis times could respectively be approximated with a model linear-quadratic in radiation dose and a normal cumulative distribution function. Interestingly, the low-dose incidence was found to be proportional to the modeled number of cells carrying the Sfpi1 deletion present per mouse following exposure. After making only model-derived high-dose rAML estimates available to extrapolate from, the linear-quadratic model could be used to approximate low-dose rAML incidence calculated with our mouse model. The accuracy in estimating low-dose rAML incidence when extrapolating from a linear model using a low-dose effectiveness factor was found to depend on whether a data transformation was used in the curve fitting procedure.

Optimal experimental design for mathematical models of haematopoiesis

The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters.

A somatic evolutionary model of the dynamics of aneuploid cells during hematopoietic reconstitution

Aneuploidy is a feature of many cancers. Recent studies demonstrate that in the hematopoietic stem and progenitor cell (HSPC) compartment aneuploid cells have reduced fitness and are efficiently purged from the bone marrow. However, early phases of hematopoietic reconstitution following bone marrow transplantation provide a window of opportunity whereby aneuploid cells rise in frequency, only to decline to basal levels thereafter. Here we demonstrate by Monte Carlo modeling that two mechanisms could underlie this aneuploidy peak: rapid expansion of the engrafted HSPC population and bone marrow microenvironment degradation caused by pre-transplantation radiation treatment. Both mechanisms reduce the strength of purifying selection acting in early post-transplantation bone marrow. We explore the contribution of other factors such as alterations in cell division rates that affect the strength of purifying selection, the balance of drift and selection imposed by the HSPC population size, and the mutation-selection balance dependent on the rate of aneuploidy generation per cell division. We propose a somatic evolutionary model for the dynamics of cells with aneuploidy or other fitness-reducing mutations during hematopoietic reconstitution following bone marrow transplantation. Similar alterations in the strength of purifying selection during cancer development could help explain the paradox of aneuploidy abundance in tumors despite somatic fitness costs.

Global dynamics of healthy and cancer cells competing in the hematopoietic system

Stem cells in the bone marrow differentiate to ultimately become mature, functioning blood cells through a tightly regulated process (hematopoiesis) including a stem cell niche interaction and feedback through the immune system. Mutations in a hematopoietic stem cell can create a cancer stem cell leading to a less controlled production of malfunctioning cells in the hematopoietic system. This was mathematically modelled by Andersen et al. (2017) including the dynamic variables: healthy and cancer stem cells and mature cells, dead cells and an immune system response. Here, we apply a quasi steady state approximation to this model to construct a two dimensional model with four algebraic equations denoted the simple cancitis model. The two dynamic variables are the clinically available quantities JAK2V617F allele burden and the number of white blood cells. The simple cancitis model represents the original model very well. Complete phase space analysis of the simple cancitis model is performed, including proving the existence and location of globally attracting steady states. Hence, parameter values from compartments of stem cells, mature cells and immune cells are directly linked to disease and treatment prognosis, showing the crucial importance of early intervention. The simple cancitis model allows for a complete analysis of the long term evolution of trajectories. In particular, the value of the self renewal of the hematopoietic stem cells divided by the self renewal of the cancer stem cells is found to be an important diagnostic marker and perturbing this parameter value at intervention allows the model to reproduce clinical data. Treatment at low cancer cell numbers allows returning to healthy blood production while the same intervention at a later disease stage can lead to eradication of healthy blood producing cells. Assuming the total number of white blood cells is constant in the early cancer phase while the allele burden increases, a one dimensional model is suggested and explicitly solved, including parameters from all original compartments. The solution explicitly shows that exogenous inflammation promotes blood cancer when cancer stem cells reproduce more efficiently than hematopoietic stem cells.

Quantifying Drug-Induced Bone Marrow Toxicity Using a Novel Haematopoiesis Systems Pharmacology Model

Haematological toxicity associated with cancer therapeutics is monitored by changes in blood cell count, and their primary effect is on proliferative progenitors in the bone marrow. Using observations in rat bone marrow and blood, we characterize a mathematical model that comprises cell proliferation and differentiation of the full haematopoietic phylogeny, with interacting feedback loops between lineages in homeostasis as well as following carboplatin exposure. We accurately predicted the temporal dynamics of several mature cell types related to carboplatin-induced bone marrow toxicity and identified novel insights into haematopoiesis. Our model confirms a significant degree of plasticity within bone marrow cells, with the number and type of both early progenitors and circulating cells affecting cell balance, via feedback mechanisms, through fate decisions of the multipotent progenitors. We also demonstrated cross-species translation of our predictions to patients, applying the same core model structure and considering differences in drug-dependent and physiology-dependent parameters.

Mathematical models for cytarabine-derived myelosuppression in acute myeloid leukaemia

We investigate the personalisation and prediction accuracy of mathematical models for white blood cell (WBC) count dynamics during consolidation treatment using intermediate or high-dose cytarabine (Ara-C) in acute myeloid leukaemia (AML). Ara-C is the clinically most relevant cytotoxic agent for AML treatment. We extend a mathematical model of myelosuppression and a pharmacokinetic model of Ara-C with different hypotheses of Ara-C's pharmacodynamic effects. We cross-validate the 12 model variations using dense WBC count measurements from 23 AML patients. Surprisingly, the prediction accuracy remains satisfactory in each of the models despite different modelling hypotheses. Therefore, we compare average clinical and calculated WBC recovery times for different Ara-C schedules as a successful methodology for model discrimination. As a result, a new hypothesis of a secondary pharmacodynamic effect on the proliferation rate seems plausible. Furthermore, we demonstrate the impact of treatment timing on subsequent nadir values based on personalised predictions as a possibility for influencing/controlling myelosuppression.

Hematopoietic Stem Cell Dynamics Are Regulated by Progenitor Demand: Lessons from a Quantitative Modeling Approach

The prevailing view on murine hematopoiesis and on hematopoietic stem cells (HSCs) in particular derives from experiments that are related to regeneration after irradiation and HSC transplantation. However, over the past years, different experimental techniques have been developed to investigate hematopoiesis under homeostatic conditions, thereby providing access to proliferation and differentiation rates of hematopoietic stem and progenitor cells in the unperturbed situation. Moreover, it has become clear that hematopoiesis undergoes distinct changes during aging with large effects on HSC abundance, lineage contribution, asymmetry of division, and self-renewal potential. However, it is currently not fully resolved how stem and progenitor cells interact to respond to varying demands and how this balance is altered by an aging-induced shift in HSC polarity. Aiming toward a conceptual understanding, we introduce a novel in silico model to investigate the dynamics of HSC response to varying demand. By introducing an internal feedback within a heterogeneous HSC population, the model is suited to consistently describe both hematopoietic homeostasis and regeneration, including the limited regulation of HSCs in the homeostatic situation. The model further explains the age-dependent increase in phenotypic HSCs as a consequence of the cells' inability to preserve divisional asymmetry. Our model suggests a dynamically regulated population of intrinsically asymmetrically dividing HSCs as suitable control mechanism that adheres with many qualitative and quantitative findings on hematopoietic recovery after stress and aging. The modeling approach thereby illustrates how a mathematical formalism can support both the conceptual and the quantitative understanding of regulatory principles in HSC biology.

Modeling large fluctuations of thousands of clones during hematopoiesis: The role of stem cell self-renewal and bursty progenitor dynamics in rhesus macaque

In a recent clone-tracking experiment, millions of uniquely tagged hematopoietic stem cells (HSCs) and progenitor cells were autologously transplanted into rhesus macaques and peripheral blood containing thousands of tags were sampled and sequenced over 14 years to quantify the abundance of hundreds to thousands of tags or “clones.” Two major puzzles of the data have been observed: consistent differences and massive temporal fluctuations of clone populations. The large sample-to-sample variability can lead clones to occasionally go “extinct” but “resurrect” themselves in subsequent samples. Although heterogeneity in HSC differentiation rates, potentially due to tagging, and random sampling of the animals’ blood and cellular demographic stochasticity might be invoked to explain these features, we show that random sampling cannot explain the magnitude of the temporal fluctuations. Moreover, we show through simpler neutral mechanistic and statistical models of hematopoiesis of tagged cells that a broad distribution in clone sizes can arise from stochastic HSC self-renewal instead of tag-induced heterogeneity. The very large clone population fluctuations that often lead to extinctions and resurrections can be naturally explained by a generation-limited proliferation constraint on the progenitor cells. This constraint leads to bursty cell population dynamics underlying the large temporal fluctuations. We analyzed experimental clone abundance data using a new statistic that counts clonal disappearances and provided least-squares estimates of two key model parameters in our model, the total HSC differentiation rate and the maximum number of progenitor-cell divisions.

Hematopoiesis of virally tagged cells in rhesus macaques is analyzed in the context of a mechanistic and statistical model. We find that the clone size distribution and the temporal variability in the abundance of each clone (viral tag) in peripheral blood are consistent with (i) stochastic HSC self-renewal during bone marrow repair, (ii) clonal aging that restricts the number of generations of progenitor cells, and (iii) infrequent and small-size samples. By fitting data, we infer two key parameters that control the level of fluctuations of clone sizes in our model: the total HSC differentiation rate and the maximum proliferation capacity of progenitor cells. Our analysis provides insight into the mechanisms of hematopoiesis and a framework to guide future multiclone barcoding/lineage tracking measurements.

Understanding Hematological Toxicities Using Mathematical Modeling

Balancing antitumor efficacy with toxicity is a significant challenge, and drug-induced myelosuppression is a common dose-limiting toxicity of cancer treatments. Mathematical modeling has proven to be a powerful ally in this field, scaling results from animal models to humans, and designing optimized treatment regimens. Here we outline existing mathematical approaches for studying bone marrow toxicity, identify gaps in current understanding, and make future recommendations to advance this vital field of safety research further.

Exploring intermediate cell states through the lens of single cells

As our catalog of cell states expands, appropriate characterization of these states and the transitions between them is crucial. Here we discuss the roles of intermediate cell states (ICSs) in this growing collection. We begin with definitions and discuss evidence for the existence of ICSs and their relevance in various tissues. We then provide a list of possible functions for ICSs with examples. Finally, we describe means by which ICSs and their functional roles can be identified from single-cell data or predicted from models.

Whole-body iron transport and metabolism: Mechanistic, multi-scale model to improve treatment of anemia in chronic kidney disease

Iron plays vital roles in the human body including enzymatic processes, oxygen-transport via hemoglobin and immune response. Iron metabolism is characterized by ~95% recycling and minor replenishment through diet. Anemia of chronic kidney disease (CKD) is characterized by a lack of synthesis of erythropoietin leading to reduced red blood cell (RBC) formation and aberrant iron recycling. Treatment of CKD anemia aims to normalize RBC count and serum hemoglobin. Clinically, the various fluxes of iron transport and accumulation are not measured so that changes during disease (e.g., CKD) and treatment are unknown. Unwanted iron accumulation in patients is known to lead to adverse effects. Current whole-body models lack the mechanistic details of iron transport related to RBC maturation, transferrin (Tf and TfR) dynamics and assume passive iron efflux from macrophages. Hence, they are not predictive of whole-body iron dynamics and cannot be used to design individualized patient treatment. For prediction, we developed a mechanistic, multi-scale computational model of whole-body iron metabolism incorporating four compartments containing major pools of iron and RBC generation process. The model accounts for multiple forms of iron in vivo, mechanisms involved in iron uptake and release and their regulation. Furthermore, the model is interfaced with drug pharmacokinetics to allow simulation of treatment dynamics. We calibrated our model with experimental and clinical data from peer-reviewed literature to reliably simulate CKD anemia and the effects of current treatment involving combination of epoietin-alpha and iron dextran. This in silico whole-body model of iron metabolism predicts that a year of treatment can potentially lead to 90% downregulation of ferroportin (FPN) levels, 15-fold increase in iron stores with only a 20% increase in iron flux from the reticulo-endothelial system (RES). Model simulations quantified unmeasured iron fluxes, previously unknown effects of treatment on FPN-level and iron stores in the RES. This mechanistic whole-body model can be the basis for future studies that incorporate iron metabolism together with related clinical experiments. Such an approach could pave the way for development of effective personalized treatment of CKD anemia.

An Integrative multi-lineage model of variation in leukopoiesis and acute myelogenous leukemia

Background

Acute myelogenous leukemia (AML) progresses uniquely in each patient. However, patients are typically treated with the same types of chemotherapy, despite biological differences that lead to differential responses to treatment.

Results

Here we present a multi-lineage multi-compartment model of the hematopoietic system that captures patient-to-patient variation in both the concentration and rates of change of hematopoietic cell populations. By constraining the model against clinical hematopoietic cell recovery data derived from patients who have received induction chemotherapy, we identified trends for parameters that must be met by the model; for example, the mitosis rates and the probability of self-renewal of progenitor cells are inversely related. Within the data-consistent models, we found 22,796 parameter sets that meet chemotherapy response criteria. Simulations of these parameter sets display diverse dynamics in the cell populations. To identify large trends in these model outputs, we clustered the simulated cell population dynamics using k-means clustering and identified thirteen ‘representative patient’ dynamics. In each of these patient clusters, we simulated AML and found that clusters with the greatest mitotic capacity experience clinical cancer outcomes more likely to lead to shorter survival times. Conversely, other parameters, including lower death rates or mobilization rates, did not correlate with survival times.

Conclusions

Using the multi-lineage model of hematopoiesis, we have identified several key features that determine leukocyte homeostasis, including self-renewal probabilities and mitosis rates, but not mobilization rates. Other influential parameters that regulate AML model behavior are responses to cytokines/growth factors produced in peripheral blood that target the probability of self-renewal of neutrophil progenitors. Finally, our model predicts that the mitosis rate of cancer is the most predictive parameter for survival time, followed closely by parameters that affect the self-renewal of cancer stem cells; most current therapies target mitosis rate, but based on our results, we propose that additional therapeutic targeting of self-renewal of cancer stem cells will lead to even higher survival rates.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0469-2) contains supplementary material, which is available to authorized users.

Towards Quantitative Systems Pharmacology Models of Chemotherapy-Induced Neutropenia

Neutropenia is a serious toxic complication of chemotherapeutic treatment. For years, mathematical models have been developed to better predict hematological outcomes during chemotherapy in both the traditional pharmaceutical sciences and mathematical biology disciplines. An increasing number of quantitative systems pharmacology (QSP) models that combine systems approaches, physiology, and pharmacokinetics/pharmacodynamics have been successfully developed. Here, I detail the shift towards QSP efforts, emphasizing the importance of incorporating systems-level physiological considerations in pharmacometrics.

Changing mutational and adaptive landscapes and the genesis of cancer

By the time the process of oncogenesis has produced an advanced cancer, tumor cells have undergone extensive evolution. The cellular phenotypes resulting from this evolution have been well studied, and include accelerated growth rates, apoptosis resistance, immortality, invasiveness, and immune evasion. Yet with all of our current knowledge of tumor biology, the details of early oncogenesis have been difficult to observe and understand. Where different oncogenic mutations may work together to enhance the survival of a tumor cell, in isolation they are often pro-apoptotic, pro-differentiative or pro-senescent, and therefore often, somewhat paradoxically, disadvantageous to a cell. It is also becoming clear that somatic mutations, including those in known oncogenic drivers, are common in tissues starting at a young age. These observations raise the question: how do we largely avoid cancer for most of our lives? Here we propose that evolutionary forces can help explain this paradox. As humans and other organisms age or experience external insults such as radiation or smoking, the structure and function of tissues progressively degrade, resulting in altered stem cell niche microenvironments. As tissue integrity declines, it becomes less capable of supporting and maintaining resident stem cells. These stem cells then find themselves in a microenvironment to which they are poorly adapted, providing a competitive advantage to those cells that can restore their functionality and fitness through mutations or epigenetic changes. The resulting oncogenic clonal expansions then increase the odds of further cancer progression. Understanding how the causes of cancer, such as aging or smoking, affect tissue microenvironments to control the impact of mutations on somatic cell fitness can help reconcile the discrepancy between marked mutation accumulation starting early in life and the somatic evolution that leads to cancer at advanced ages or following carcinogenic insults. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer?, edited by Dr. Robert A. Gatenby.

T Cell Development by the Numbers

T cells are continually generated in the thymus in a highly dynamic process comprising discrete steps of lineage commitment, T cell receptor (TCR) gene rearrangement, and selection. These steps are linked to distinct rates of proliferation, survival, and cell death, but a quantitative picture of T cell development is only beginning to emerge. Here we summarize recent technical advances, including genetic fate mapping, barcoding, and molecular timers, that have allowed the implementation of computational models to quantify developmental dynamics in the thymus. Coupling new techniques with mathematical models has recently resulted in the emergence of new paradigms in early hematopoiesis and might similarly open new perspectives on T cell development.

Long-term genotoxic effects in the hematopoietic system of prenatally X-irradiated mice

PURPOSE

To investigate the genotoxic effects of prenatal X-irradiation in mice and the possible presence of late genomic instability.

MATERIALS AND METHODS

Pregnant mice were exposed to 0, 1 or 2 Gy at embryonic day 11.5. Blood smears were obtained from pups at birth and on post-natal day 11, 21, 42 and 140. Hematological data (diameter of erythrocytes, percentage of reticulocytes and Granulocyte-to-Lymphocyte ratio [GLR]) and genotoxicity (micronucleated erythrocytes, micronucleated reticulocytes, CREST-positive and negative micronuclei) were assessed.

RESULTS

Prenatal irradiation caused perinatal reticulocytosis (which ended on postnatal day 11) and a dose-dependent increase of GLR (indicative of myeloid skewing) on postnatal days 42 and 140. Two temporally distinct genotoxic effects were observed: an early, acute damage (still detectable at birth and soon after) and a late, long-term damage.

CONCLUSIONS

Increases in micronuclei frequencies and GLR observed from day 42 on are both ascribable to DNA damage. Time of appearance of this late effect may be linked to the shift of hematopoiesis from spleen to bone marrow and to cell-extrinsic factor such as the microenvironment. This study confirms that ionizing radiation can induce long-term genotoxic effects in the hematopoietic system and shows that prenatal irradiation determines genomic instability in blood-forming tissues of adult mice.

Stem-cell dynamics and lineage topology from in vivo fate mapping in the hematopoietic system

In recent years, sophisticated fate-mapping tools have been developed to study the behavior of stem cells in the intact organism. These experimental approaches are beginning to yield a quantitative picture of how cell numbers are regulated during steady state and in response to challenges. Focusing on hematopoiesis and immune responses, we discuss how novel mathematical approaches driven by these fate-mapping data have provided insights into the dynamics and topology of cellular differentiation pathways in vivo. The combination of experiment and theory has allowed to quantify the degree of self-renewal in stem and progenitor cells, shown how native hematopoiesis differs fundamentally from post-transplantation hematopoiesis, and uncovered that the diversification of T lymphocytes during immune responses resembles tissue renewal driven by stem cells.

The overshoot and phenotypic equilibrium in characterizing cancer dynamics of reversible phenotypic plasticity

The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which extends the cellular hierarchy proposed by the classical cancer stem cell (CSC) theory. Since it is still questionable if the phenotypic plasticity is a crucial improvement to the hierarchical model or just a minor extension to it, it is worthwhile to explore the dynamic behavior characterizing the reversible phenotypic plasticity. In this study we compare the hierarchical model and the reversible model in predicting the cell-state dynamics observed in biological experiments. Our results show that the hierarchical model shows significant disadvantages over the reversible model in describing both long-term stability (phenotypic equilibrium) and short-term transient dynamics (overshoot) in cancer cell populations. In a very specific case in which the total growth of population due to each cell type is identical, the hierarchical model predicts neither phenotypic equilibrium nor overshoot, whereas the reversible model succeeds in predicting both of them. Even though the performance of the hierarchical model can be improved by relaxing the specific assumption, its prediction to the phenotypic equilibrium strongly depends on a precondition that may be unrealistic in biological experiments. Moreover, it still does not show as rich dynamics as the reversible model in capturing the overshoots of both CSCs and non-CSCs. By comparison, it is more likely for the reversible model to correctly predict the stability of the phenotypic mixture and various types of overshoot behavior.

Mathematical modeling reveals differential effects of erythropoietin on proliferation and lineage commitment of human hematopoietic progenitors in early erythroid culture

Erythropoietin is essential for the production of mature erythroid cells, promoting both proliferation and survival. Whether erythropoietin and other cytokines can influence lineage commitment of hematopoietic stem and progenitor cells is of significant interest. To study lineage restriction of the common myeloid progenitor to the megakaryocyte/erythroid progenitor of peripheral blood CD34(+) cells, we have shown that the cell surface protein CD36 identifies the earliest lineage restricted megakaryocyte/erythroid progenitor. Using this marker and carboxyfluorescein succinimidyl ester to track cell divisions in vitro, we have developed a mathematical model that accurately predicts population dynamics of erythroid culture. Parameters derived from the modeling of cultures without added erythropoietin indicate that the rate of lineage restriction is not affected by erythropoietin. By contrast, megakaryocyte/erythroid progenitor proliferation is sensitive to erythropoietin from the time that CD36 first appears at the cell surface. These results shed new light on the role of erythropoietin in erythropoiesis and provide a powerful tool for further study of hematopoietic progenitor lineage restriction and erythropoiesis.

Comparison of mathematical frameworks for modeling erythropoiesis in the context of malaria infection

Malaria is an infectious disease present all around the globe and responsible for half a million deaths per year. A within-host model of this infection requires a framework capable of properly approximating not only the blood stage of the infection but also the erythropoietic process that is in charge of overcoming the malaria induced anemia. Within this context, we compare ordinary differential equations (ODEs) with and without age classes, delayed differential equations (DDEs), and discrete recursive equations (DREs) with age classes. Results show that ODEs without age classes are fair approximations that do not provide a crisp temporal representation of the processes involved, and inclusion of age classes only mitigates the problem to some degree. DDEs perform well with respect to generating the essentially fixed delay between cell production and cell removal due to age, but the inclusion of any other processes, such as sudden blood loss, becomes cumbersome. The framework that was found to perform best in representing the dynamics of red blood cells during malaria infection is a DRE with age classes. In this model structure, the amount of time a cell remains alive is easily controlled, and the addition of age dependent or independent processes is straightforward. All events that populations of cells face during their lifespan, like growth or adaptation in differentiation or maturation rate, are properly represented in this framework.

Stem cell regulation: Implications when differentiated cells regulate symmetric stem cell division

We use a mathematical model to show that if symmetric stem cell division is regulated by differentiated cells, then changes in the population dynamics of the differentiated cells can lead to changes in the population dynamics of the stem cells. More precisely, the relative fitness of the stem cells can be affected by modifying the death rate of the differentiated cells. This result is interesting because stem cells are less sensitive than differentiated cells to environmental factors, such as medical therapy. Our result implies that stem cells can be manipulated indirectly by medical treatments that target the differentiated cells.

Engineering control into medicine

The human body is a tightly controlled engineering miracle. However, medical training generally does not cover "control" (in the engineering sense) in physiology, pathophysiology, and therapeutics. A better understanding of how evolved controls maintain normal homeostasis is critical for understanding the failure mode of controlled systems, that is, disease. We believe that teaching and research must incorporate an understanding of the control systems in physiology and take advantage of the quantitative tools used by engineering to understand complex systems. Control systems are ubiquitous in physiology, although often unrecognized. Here we provide selected examples of the role of control in physiology (heart rate variability, immunity), pathophysiology (inflammation in sepsis), and therapeutic devices (diabetes and the artificial pancreas). We also present a high-level background to the concept of robustly controlled systems and examples of clinical insights using the controls framework.

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.

Merging concepts - coupling an agent-based model of hematopoietic stem cells with an ODE model of granulopoiesis

Background

Hematopoiesis is a complex process involving different cell types and feedback mechanisms mediated by cytokines. This complexity stimulated various models with different scopes and applications. A combination of complementary models promises to provide their mutual confirmation and to explain a broader range of scenarios. Here we propose a combination of an ordinary differential equation (ODE) model of human granulopoiesis and an agent-based model (ABM) of hematopoietic stem cell (HSC) organization. The first describes the dynamics of bone marrow cell stages and circulating cells under various perturbations such as G-CSF treatment or chemotherapy. In contrast to the ODE model describing cell numbers, our ABM focuses on the organization of individual cells in the stem population.

Results

We combined the two models by replacing the HSC compartment of the ODE model by a difference equation formulation of the ABM. In this hybrid model, regulatory mechanisms and parameters of the original models were kept unchanged except for a few specific improvements: (i) Effect of chemotherapy was restricted to proliferating HSC and (ii) HSC regulation in the ODE model was replaced by the intrinsic regulation of the ABM. Model simulations of bleeding, chronic irradiation and stem cell transplantation revealed that the dynamics of hybrid and ODE model differ markedly in scenarios with stem cell damage. Despite these differences in response to stem cell damage, both models explain clinical data of leukocyte dynamics under four chemotherapy regimens.

Conclusions

ABM and ODE model proved to be compatible and were combined without altering the structure of both models. The new hybrid model introduces model improvements by considering the proliferative state of stem cells and enabling a cell cycle-dependent effect of chemotherapy. We demonstrated that it is able to explain and predict granulopoietic dynamics for a large variety of scenarios such as irradiation, bone marrow transplantation, chemotherapy and growth factor applications. Therefore, it promises to serve as a valuable tool for studies in a broader range of clinical applications, in particular where stem cell activation and proliferation are involved.