Cell kinetic status of haematopoietic stem cells

Dynamically adjusted cell fate decisions and resilience to mutant invasion during steady-state hematopoiesis revealed by an experimentally parameterized mathematical model

A major next step in hematopoietic stem cell (HSC) biology is to enhance our quantitative understanding of cellular and evolutionary dynamics involved in undisturbed hematopoiesis. Mathematical models have been and continue to be key in this respect, and are most powerful when parameterized experimentally and containing sufficient biological complexity. In this paper, we use data from label propagation experiments in mice to parameterize a mathematical model of hematopoiesis that includes homeostatic control mechanisms as well as clonal evolution. We find that nonlinear feedback control can drastically change the interpretation of kinetic estimates at homeostasis. This suggests that short-term HSC and multipotent progenitors can dynamically adjust to sustain themselves temporarily in the absence of long-term HSCs, even if they differentiate more often than they self-renew in undisturbed homeostasis. Additionally, the presence of feedback control in the model renders the system resilient against mutant invasion. Invasion barriers, however, can be overcome by a combination of age-related changes in stem cell differentiation and evolutionary niche construction dynamics based on a mutant-associated inflammatory environment. This helps us understand the evolution of e.g., TET2 or DNMT3A mutants, and how to potentially reduce mutant burden.

Computational modeling reveals key factors driving treatment-free remission in chronic myeloid leukemia patients

Patients with chronic myeloid leukemia (CML) who receive tyrosine kinase inhibitors (TKIs) have been known to achieve treatment-free remission (TFR) upon discontinuing treatment. However, the underlying mechanisms of this phenomenon remain incompletely understood. This study aims to elucidate the mechanism of TFR in CML patients, focusing on the feedback interaction between leukemia stem cells and the bone marrow microenvironment. We have developed a mathematical model to explore the interplay between leukemia stem cells and the bone marrow microenvironment, allowing for the simulation of CML progression dynamics. Our proposed model reveals a dichotomous response following TKI discontinuation, with two distinct patient groups emerging: one prone to early molecular relapse and the other capable of achieving long-term TFR after treatment cessation. This finding aligns with clinical observations and underscores the essential role of feedback interaction between leukemic cells and the tumor microenvironment in sustaining TFR. Notably, we have shown that the ratio of leukemia cells in peripheral blood (PBLC) and the tumor microenvironment (TME) index can be a valuable predictive tool for identifying patients likely to achieve TFR after discontinuing treatment. This study provides fresh insights into the mechanism of TFR in CML patients and underscores the significance of microenvironmental control in achieving TFR.

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.

A mathematical model with aberrant growth correction in tissue homeostasis and tumor cell growth

Cancer is usually considered a genetic disease caused by alterations in genes that control cellular behaviors, especially growth and division. Cancer cells differ from normal tissue cells in many ways that allow them to grow out of control and become invasive. However, experiments have shown that aberrant growth in many tissues burdened with varying numbers of mutant cells can be corrected, and wild-type cells are required for the active elimination of mutant cells. These findings reveal the dynamic cellular behaviors that lead to a tissue homeostatic state when faced with mutational and nonmutational insults. The current study was motivated by these observations and established a mathematical model of how a tissue copes with the aberrant behavior of mutant cells. The proposed model depicts the interaction between wild-type and mutant cells through a system of two delay differential equations, which include the random mutation of normal cells and the active extrusion of mutant cells. Based on the proposed model, we performed qualitative analysis to identify the conditions of either normal tissue homeostasis or uncontrolled growth with varying numbers of abnormal mutant cells. Bifurcation analysis suggests the conditions of bistability with either a small or large number of mutant cells, the coexistence of bistable steady states can be clinically beneficial by driving the state of mutant cell predominance to the attraction basin of the state with a low number of mutant cells. This result is further confirmed by the treatment strategy obtained from optimal control theory.

Effect of dedifferentiation on noise propagation in cellular hierarchy

Many fast renewing tissues have a hierarchical structure. Tissue-specific stem cells are at the root of this cellular hierarchy, which give rive to a whole range of specialized cells via cellular differentiation. However, increasing evidence shows that the hierarchical structure can be broken due to cellular dedifferentiation in which cells at differentiated stages can revert to the stem cell stage. Dedifferentiation has significant impacts on many aspects of hierarchical tissues. Here we investigate the effect of dedifferentiation on noise propagation by developing a stochastic model composed of different cell types. The moment equations are derived, via which we systematically investigate how the noise in the cell number is changed by dedifferentiation. Our results suggest that dedifferentiation have different effects on the noises in the numbers of stem cells and nonstem cells. Specifically, the noise in the number of stem cells is significantly reduced by increasing dedifferentiation probability. Due to the dual effect of dedifferentiation on nonstem cells, however, more complex changes could happen to the noise in the number of nonstem cells by increasing dedifferentiation probability. Furthermore, it is found that even though dedifferentiation could turn part of the noise propagation process into a noise-amplifying step, it is very unlikely to turn the entire process into a noise-amplifying cascade.

Why Are Periodic Erythrocytic Diseases so Rare in Humans?

Many studies have shown that periodic erythrocytic (red blood cell linked) diseases are extremely rare in humans. To explain this observation, we develop here a simple model of erythropoiesis in mammals and investigate its stability in the parameter space. A bifurcation analysis enables us to sketch stability diagrams in the plane of key parameters. Contrary to some other mammal species such as rabbits, mice or dogs, we show that human-specific parameter values prevent periodic oscillations of red blood cells levels. In other words, human erythropoiesis seems to lie in a region of parameter space where oscillations exclusively concerning red blood cells cannot appear. Further mathematical analysis show that periodic oscillations of red blood cells levels are highly unusual and if exist, might only be due to an abnormally high erythrocytes destruction rate or to an abnormal hematopoietic stem cell commitment into the erythrocytic lineage. We also propose numerical results only for an improved version of our approach in order to give a more realistic but more complex approach of our problem.

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

Reconciling Flux Experiments for Quantitative Modeling of Normal and Malignant Hematopoietic Stem/Progenitor Dynamics

Hematopoiesis serves as a paradigm for how homeostasis is maintained within hierarchically organized cell populations. However, important questions remain as to the contribution of hematopoietic stem cells (HSCs) toward maintaining steady state hematopoiesis. A number of in vivo lineage labeling and propagation studies have given rise to contradictory interpretations, leaving key properties of stem cell function unresolved. Using processed flow cytometry data coupled with a biology-driven modeling approach, we show that in vivo flux experiments that come from different laboratories can all be reconciled into a single unifying model, even though they had previously been interpreted as being contradictory. We infer from comparative analysis that different transgenic models display distinct labeling efficiencies across a heterogeneous HSC pool, which we validate by marker gene expression associated with HSC function. Finally, we show how the unified model of HSC differentiation can be used to simulate clonal expansion in the early stages of leukemogenesis.

Stochastic stem cell models with mutation: A comparison of asymmetric and symmetric divisions

In order to fulfill cell proliferation and differentiation through cellular hierarchy, stem cells can undergo either asymmetric or symmetric divisions. Recent studies pay special attention to the effect of different modes of stem cell division on the lifetime risk of cancer, and report that symmetric division is more beneficial to delay the onset of cancer. The fate uncertainty of symmetric division is considered to be the reason for the cancer-delaying effect. In this paper we compare asymmetric and symmetric divisions of stem cells via studying stochastic stem cell models with mutation. Specially, by using rigorous mathematical analysis we find that both the asymmetric and symmetric models show the same statistical average, but the symmetric model shows higher fluctuation than the asymmetric model. We further show that the difference between the two models would be more remarkable for lower mutation rates. Our work quantifies the uncertainty of cell division and highlights the significance of stochasticity for distinguishing between different modes of stem cell division.

Characterizing Chemotherapy-Induced Neutropenia and Monocytopenia Through Mathematical Modelling

In spite of the recent focus on the development of novel targeted drugs to treat cancer, cytotoxic chemotherapy remains the standard treatment for the vast majority of patients. Unfortunately, chemotherapy is associated with high hematopoietic toxicity that may limit its efficacy. We have previously established potential strategies to mitigate chemotherapy-induced neutropenia (a lack of circulating neutrophils) using a mechanistic model of granulopoiesis to predict the interactions defining the neutrophil response to chemotherapy and to define optimal strategies for concurrent chemotherapy/prophylactic granulocyte colony-stimulating factor (G-CSF). Here, we extend our analyses to include monocyte production by constructing and parameterizing a model of monocytopoiesis. Using data for neutrophil and monocyte concentrations during chemotherapy in a large cohort of childhood acute lymphoblastic leukemia patients, we leveraged our model to determine the relationship between the monocyte and neutrophil nadirs during cyclic chemotherapy. We show that monocytopenia precedes neutropenia by 3 days, and rationalize the use of G-CSF during chemotherapy by establishing that the onset of monocytopenia can be used as a clinical marker for G-CSF dosing post-chemotherapy. This work therefore has important clinical applications as a comprehensive approach to understanding the relationship between monocyte and neutrophils after cyclic chemotherapy with or without G-CSF support.

Periodic hematological disorders: Quintessential examples of dynamical diseases

This paper summarizes the evidence supporting the classification of cyclic neutropenia as a dynamical disease and periodic chronic myelogenous leukemia is also considered. The unsatisfactory state of knowledge concerning the genesis of cyclic thrombocytopenia and periodic autoimmune hemolytic anemia is detailed.

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.

A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration

Stem cell heterogeneity is essential for homeostasis in tissue development. This paper establishes a general mathematical framework to model the dynamics of stem cell regeneration with cell heterogeneity and random transitions of epigenetic states. The framework generalizes the classical G0 cell cycle model and incorporates the epigenetic states of individual cells represented by a continuous multidimensional variable. In the model, the kinetic rates of cell behaviors, including proliferation, differentiation, and apoptosis, are dependent on their epigenetic states, and the random transitions of epigenetic states between cell cycles are represented by an inheritance probability function that describes the conditional probability of cell state changes. Moreover, the model can be extended to include genotypic changes and describe the process of gene mutation-induced tumor development. The proposed mathematical framework provides a generalized formula that helps us to understand various dynamic processes of stem cell regeneration, including tissue development, degeneration, and abnormal growth.

Paracrine mechanisms in early differentiation of human pluripotent stem cells: Insights from a mathematical model

With their capability to self-renew and differentiate into derivatives of all three germ layers, human pluripotent stem cells (hPSCs) offer a unique model to study aspects of human development in vitro. Directed differentiation towards mesendodermal lineages is a complex process, involving transition through a primitive streak (PS)-like stage. We have recently shown PS-like patterning from hPSCs into definitive endoderm, cardiac as well as presomitic mesoderm by only modulating the bulk cell density and the concentration of the GSK3 inhibitor CHIR99021, a potent activator of the WNT pathway. The patterning process is modulated by a complex paracrine network, whose identity and mechanistic consequences are poorly understood. To study the underlying dynamics, we here applied mathematical modeling based on ordinary differential equations. We compared time-course data of early hPSC differentiation to increasingly complex model structures with incremental numbers of paracrine factors. Model simulations suggest at least three paracrine factors being required to recapitulate the experimentally observed differentiation kinetics. Feedback mechanisms from both undifferentiated and differentiated cells turned out to be crucial. Evidence from double knock-down experiments and secreted protein enrichment allowed us to hypothesize on the identity of two of the three predicted factors. From a practical perspective, the mathematical model predicts optimal settings for directing lineage-specific differentiation. This opens new avenues for rational stem cell bioprocessing in more advanced culture systems, e.g. in perfusion-fed bioreactors enabling cell therapies.

A mathematical model of stem cell regeneration with epigenetic state transitions

In this paper, we study a mathematical model of stem cell regeneration with epigenetic state transitions. In the model, the heterogeneity of stem cells is considered through the epigenetic state of each cell, and each epigenetic state defines a subpopulation of stem cells. The dynamics of the subpopulations are modeled by a set of ordinary differential equations in which epigenetic state transition in cell division is given by the transition probability. We present analysis for the existence and linear stability of the equilibrium state. As an example, we apply the model to study the dynamics of state transition in breast cancer stem cells.

A model of hematopoietic bone marrow apoptosis during growth factor deprivation in combination with a cytokine

Background

The process by which blood cells are formed is referred to as hematopoiesis. This process involves a complex sequence of phases that blood cells must complete. During hematopoiesis, a small fraction of cells undergo cell death. Causes of cell death are dependent upon various factors; one such factor being growth factor deprivation.

Methods

In this paper, a mathematical model of hematopoiesis during growth factor deprivation is presented. The model consists of a set of three coupled differential delay equations. Phase plane and linear stability analysis are performed in order to locate and determine stability of fixed points. Numerical simulations of the governing equations are run and provide a visual display of the behavior of the stem cell population undergoing growth factor deprivation. In addition, the effect of cytokine administration is incorporated in the model in an effort to understand how cytokine administration can offset the negative effects of apoptosis caused by growth factor deprivation.

Conclusions

The model produces qualitatively similar results to that observed during serum deprivation. The model captures apoptosis levels of cells at different time points. Additionally, it is shown that cytokine administration stabilizes the stem cell count.

Quantitative translational modeling to facilitate preclinical to clinical efficacy & toxicity translation in oncology

Significant scientific advances in biomedical research have expanded our knowledge of the molecular basis of carcinogenesis, mechanisms of cancer growth, and the importance of the cancer immunity cycle. However, despite scientific advances in the understanding of cancer biology, the success rate of oncology drug development remains the lowest among all therapeutic areas. In this review, some of the key translational drug development objectives in oncology will be outlined. The literature evidence of how mathematical modeling could be used to build a unifying framework to answer these questions will be summarized with recommendations on the strategies for building such a mathematical framework to facilitate the prediction of clinical efficacy and toxicity of investigational antineoplastic agents. Together, the literature evidence suggests that a rigorous and unifying preclinical to clinical translational framework based on mathematical models is extremely valuable for making go/no-go decisions in preclinical development, and for planning early clinical studies.

Congenital neutropenia in the era of genomics: classification, diagnosis, and natural history

This review focuses on the classification, diagnosis and natural history of congenital neutropenia (CN). CN encompasses a number of genetic disorders with chronic neutropenia and, for some, affecting other organ systems, such as the pancreas, central nervous system, heart, bone and skin. To date, 24 distinct genes have been associated with CN. The number of genes involved makes gene screening difficult. This can be solved by next-generation sequencing (NGS) of targeted gene panels. One of the major complications of CN is spontaneous leukaemia, which is preceded by clonal somatic evolution, and can be screened by a targeted NGS panel focused on somatic events.

Single-cell analyses to reveal hematopoietic stem cell fate decisions

Hematopoietic stem cells (HSCs) are the best studied adult stem cells with enormous clinical value. Most of our knowledge about their biology relies on assays at the single HSC level. However, only the recent advances in developing new single cell technologies allowed the elucidation of the complex regulation of HSC fate decision control. This Review will focus on current attempts to investigate individual HSCs at molecular and functional levels. The advantages of these technologies leading to groundbreaking insights into hematopoiesis will be highlighted, and the challenges facing these technologies will be discussed. The importance of combining molecular and functional assays to enlighten regulatory networks of HSC fate decision control, ideally at high temporal resolution, becomes apparent for future studies.

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.

A Mathematical Model of Granulopoiesis Incorporating the Negative Feedback Dynamics and Kinetics of G-CSF/Neutrophil Binding and Internalization

We develop a physiological model of granulopoiesis which includes explicit modelling of the kinetics of the cytokine granulocyte colony-stimulating factor (G-CSF) incorporating both the freely circulating concentration and the concentration of the cytokine bound to mature neutrophils. G-CSF concentrations are used to directly regulate neutrophil production, with the rate of differentiation of stem cells to neutrophil precursors, the effective proliferation rate in mitosis, the maturation time, and the release rate from the mature marrow reservoir into circulation all dependent on the level of G-CSF in the system. The dependence of the maturation time on the cytokine concentration introduces a state-dependent delay into our differential equation model, and we show how this is derived from an age-structured partial differential equation model of the mitosis and maturation and also detail the derivation of the rest of our model. The model and its estimated parameters are shown to successfully predict the neutrophil and G-CSF responses to a variety of treatment scenarios, including the combined administration of chemotherapy and exogenous G-CSF. This concomitant treatment was reproduced without any additional fitting to characterize drug-drug interactions.

Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: Mathematical modelling guides dose optimisation to minimise neutropenia

The choice of chemotherapy regimens is often constrained by the patient's tolerance to the side effects of chemotherapeutic agents. This dose-limiting issue is a major concern in dose regimen design, which is typically focused on maximising drug benefits. Chemotherapy-induced neutropenia is one of the most prevalent toxic effects patients experience and frequently threatens the efficient use of chemotherapy. In response, granulocyte colony-stimulating factor (G-CSF) is co-administered during chemotherapy to stimulate neutrophil production, increase neutrophil counts, and hopefully avoid neutropenia. Its clinical use is, however, largely dictated by trial and error processes. Based on up-to-date knowledge and rational considerations, we develop a physiologically realistic model to mathematically characterise the neutrophil production in the bone marrow which we then integrate with pharmacokinetic and pharmacodynamic (PKPD) models of a chemotherapeutic agent and an exogenous form of G-CSF (recombinant human G-CSF, or rhG-CSF). In this work, model parameters represent the average values for a general patient and are extracted from the literature or estimated from available data. The dose effect predicted by the model is confirmed through previously published data. Using our model, we were able to determine clinically relevant dosing regimens that advantageously reduce the number of rhG-CSF administrations compared to original studies while significantly improving the neutropenia status. More particularly, we determine that it could be beneficial to delay the first administration of rhG-CSF to day seven post-chemotherapy and reduce the number of administrations from ten to three or four for a patient undergoing 14-day periodic chemotherapy.

Understanding, treating and avoiding hematological disease: better medicine through mathematics?

This paper traces the experimental, clinical and mathematical modeling efforts to understand a periodic hematological disease-cyclical neutropenia. It is primarily a highly personal account by two scientists from quite different backgrounds of their interactions over almost 40 years and their attempts to understand this intriguing disease. It's also a story of their efforts to offer effective treatments for the patients who suffer from cyclic neutropenia and other conditions causing neutropenia and infections.

Interactions and tradeoffs between cell recruitment, proliferation, and differentiation affect CNS regeneration

Regeneration of central nervous system (CNS) lesions requires movement of progenitor cells and production of their differentiated progeny. Although damage to the CNS clearly promotes these two processes, the interplay between these complex events and how it affects a response remains elusive. Here, we use spatial stochastic modeling to show that tradeoffs arise between production and recruitment during regeneration. Proper spatial control of cell cycle timing can mitigate these tradeoffs, maximizing recruitment, improving infiltration into the lesion, and reducing wasteful production outside of it. Feedback regulation of cell lineage dynamics alone however leads to spatial defects in cell recruitment, suggesting a novel, to our knowledge, hypothesis for the aggregation of cells to the periphery of a lesion in multiple sclerosis. Interestingly, stronger chemotaxis does not correct this aggregation and instead, substantial random cell motions near the site of the lesion are required to improve CNS regeneration.

Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation

Adult stem cells, which exist throughout the body, multiply by cell division to replenish dying cells or to promote regeneration to repair damaged tissues. To perform these functions during the lifetime of organs or tissues, stem cells need to maintain their populations in a faithful distribution of their epigenetic states, which are susceptible to stochastic fluctuations during each cell division, unexpected injury, and potential genetic mutations that occur during many cell divisions. However, it remains unclear how the three processes of differentiation, proliferation, and apoptosis in regulating stem cells collectively manage these challenging tasks. Here, without considering molecular details, we propose a genetic optimal control model for adult stem cell regeneration that includes the three fundamental processes, along with cell division and adaptation based on differential fitnesses of phenotypes. In the model, stem cells with a distribution of epigenetic states are required to maximize expected performance after each cell division. We show that heterogeneous proliferation that depends on the epigenetic states of stem cells can improve the maintenance of stem cell distributions to create balanced populations. A control strategy during each cell division leads to a feedback mechanism involving heterogeneous proliferation that can accelerate regeneration with less fluctuation in the stem cell population. When mutation is allowed, apoptosis evolves to maximize the performance during homeostasis after multiple cell divisions. The overall results highlight the importance of cross-talk between genetic and epigenetic regulation and the performance objectives during homeostasis in shaping a desirable heterogeneous distribution of stem cells in epigenetic states.

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

A very high number of different types of blood cells must be generated daily through a process called haematopoiesis in order to meet the physiological requirements of the organism. All blood cells originate from a population of relatively few haematopoietic stem cells residing in the bone marrow, which give rise to specific progenitors through different lineages. Steady-state dynamics are governed by cell division and commitment rates as well as by population sizes, while feedback components guarantee the restoration of steady-state conditions. In this study, all parameters governing these processes were estimated in a computational model to describe the haematopoietic hierarchy in adult mice. The model consisted of ordinary differential equations and included negative feedback regulation. A combination of literature data, a novel divide et impera approach for steady-state calculations and stochastic optimization allowed one to reduce possible configurations of the system. The model was able to recapitulate the fundamental steady-state features of haematopoiesis and simulate the re-establishment of steady-state conditions after haemorrhage and bone marrow transplantation. This computational approach to the haematopoietic system is novel and provides insight into the dynamics and the nature of possible solutions, with potential applications in both fundamental and clinical research.

Stochastic modeling of stem-cell dynamics with control

Tissue development and homeostasis are thought to be regulated endogenously by control loops that ensure that the numbers of stem cells and daughter cells are maintained at desired levels, and that the cell dynamics are robust to perturbations. In this paper we consider several classes of stochastic models that describe stem/daughter cell dynamics in a population of constant size, which are generalizations of the Moran process that include negative control loops that affect differentiation probabilities for stem cells. We present analytical solutions for the steady-state expectations and variances of the numbers of stem and daughter cells; these results remain valid for non-constant cell populations. We show that in the absence of differentiation/proliferation control, the number of stem cells is subject to extinction or overflow. In the presence of linear control, a steady state may be maintained but no tunable parameters are available to control the mean and the spread of the cell population sizes. Two types of nonlinear control considered here incorporate tunable parameters that allow specification of the expected number of stem cells and also provide control over the size of the standard deviation. We show that under a hyperbolic control law, there is a trade-off between minimizing standard deviations and maintaining the system robustness against external perturbations. For the Hill-type control, the standard deviation is inversely proportional to the Hill coefficient of the control loop. Biologically this means that ultrasensitive response that is observed in a number of regulatory loops may have evolved in order to reduce fluctuations while maintaining the desired population levels.

Embryonic development of hematopoietic stem cells: implications for clinical use

Hematopoietic stem cell (HSC) transplantation is an important treatment modality for hematological malignancies or to correct congenital immunodeficiency disorders. Several stem cell sources are currently applied clinically, with a recent increased application of umbilical cord blood. The low number of HSCs available, particularly in umbilical cord blood, is a limiting factor, and different lines of research are ongoing to circumvent this issue. In this review, we will describe the research strategies developed to expand adult HSCs in vitro and to generate new HSCs from pluripotent stem cell lines. We will also discuss the importance of studying the embryonic microenvironment since it allows both generation and extensive expansion of HSCs. Understanding the mechanisms that underlie HSC production, self-renewal and differentiation is necessary for the establishment of optimal in vitro HSC cultures, where a limitless and manipulatable resource of HSCs would be available for both clinical and fundamental research.

Neutrophil dynamics after chemotherapy and G-CSF: the role of pharmacokinetics in shaping the response

Chemotherapy has profound effects on the hematopoietic system, most notably leading to neutropenia. Granulocyte colony stimulating factor (G-CSF) is often used to deal with this neutropenia, but the response is highly variable. In this paper we examine the role of pharmacokinetics and delivery protocols in shaping the neutrophil responses to chemotherapy and G-CSF. Neutrophil responses to different protocols of chemotherapy administration with varying dosages, infusion times, and schedules are studied through a mathematical model. We find that a single dose of chemotherapy produces a damped oscillation in neutrophil levels, and short-term applications of chemotherapy can induce permanent oscillations in neutrophil level if there is a bistability in the system. In addition, we confirm previous findings [Zhuge et al., J. Theor. Biol., 293(2012), 111-120] that when periodic chemotherapy is given, there is a significant period of delivery that induces resonance in the system and exacerbates the corresponding neutropenia. The width of this resonant period peak increases with the recovery rate after a single chemotherapy, which is given by the real part of the dominant eigenvalue pair at the steady state, and both are determined by a single cooperativity coefficient in the feedback function for the neutrophils. Our numerical studies show that the neutropenia caused by chemotherapy can be overcome if G-CSF is given early after chemotherapy but can actually be worsened if G-CSF is given later, consistent with results reported in Zhuge et al. (2012). The nadir in neutrophil level is found to be more sensitive to the dosage of chemotherapy than that of the G-CSF. Furthermore, dependence of our results with changes in key pharmacokinetic parameters as well as initial functions are studied. Thus, this study illuminates the potential for destructive resonance leading to neutropenia in response to periodic chemotherapy, and explores and explains why the timing of G-CSF is so crucial for successful reversal of chemotherapy induced neutropenia.

DYNAMICS OF THE DELAY HEMATOLOGICAL CELL MODEL

In this paper, complex dynamics of a two-compartment model of production and regulation of the circulating blood neutrophil number are investigated. It is shown that the proliferative disorders may be possible due to factors of the apoptosis rate rsof the haematopoietic stem cell and the cell cycle duration τs. Applying a recent geometrical criterion for the Hopf bifurcation and transient behaviors of delay systems to this model, we separate the stable regime from the unstable regime on the rs- τsplane. Numerically, regimes of patterned periodic oscillations with low periodicity in the number of circulating blood cells appear on the rs- τsplane. It is found that the dominated period-adding bifurcation mechanism leads transitions from period-n to period-(n + 1), eventually changes to the complex attractor with high-periodicity or chaos.

Evolutionary dynamics of chronic myeloid leukemia

Cancer is an evolutionary process that arises due to mutations and expands through the selection of clones with higher reproductive success that will outcompete their peers. Most tumors require many mutations to explain the cancer phenotype, making it difficult to identify the gene(s) that confer the reproductive fitness to the clone. Moreover, the impact of any oncogene is context dependent: it can increase the fitness of particular stages of cell differentiation but not other stages. In addition, the fitness advantage of an oncogene is not irreversible: sometimes it can be reversed with targeted therapy, for example. The understanding of these dynamical processes and their consequences may be greatly simplified when addressed from an evolutionary perspective. Using the dynamics of chronic myeloid leukemia-perhaps the best understood human neoplasm-as an example, we show how three fundamental evolutionary behaviors provide insights into the dynamics of this disease: (1) BCR-ABL does not affect the reproductive success of any cell within the stem cell pool (resulting therefore in neutral drift), (2) BCR-ABL expression gives a fitness (selective) advantage to progenitor cells, and (3) imatinib therapy reduces the fitness of progenitor cells expressing the oncogene (selective disadvantage) and consequently leads to significant reductions in disease burden. These three different evolutionary dynamics scenarios based on the interpretation of mutation and gene expression as potentially leading to a fitness imbalance of cell populations clearly explain the course of the disease, providing as such a better grasp of cancer dynamics and the role of related therapies.

Chronic myeloid leukemia 2011: successes, challenges, and strategies--proceedings of the 5th annual BCR-ABL1 positive and BCR-ABL1 negative myeloproliferative neoplasms workshop

This report is based on the presentations and discussions at the 5th annual BCR-ABL1 positive and BCR-ABL1 negative myeloproliferative neoplasms (MPN) workshop, which took place immediately following the 52nd American Society of Hematology (ASH) meeting in Orlando, Florida on December 7th-8th, 2011. Relevant data which was presented at the ASH meeting as well as all other recent publications were presented and discussed at the workshop. This report covers front-line therapies of BCR-ABL1-positive leukemias, in addition to addressing some topical biological, pre-clinical and clinical issues, such as new insights into genomic instability and resistance to tyrosine kinase inhibitors (TKIs), risk stratification and optimizing molecular monitoring. A report pertaining to the new therapies and other pertinent preclinical and clinical issues in the BCR-ABL1 negative MPNs is published separately.

Mathematical study on kinetics of hematopoietic stem cells--theoretical conditions for successful transplantation

Numerous haematological diseases occur due to dysfunctions during homeostasis processes of blood cell production. Haematopoietic stem cell transplantation (HSCT) is a therapeutic option for the treatment of haematological malignancy and congenital immunodeficiency. Today, HSCT is widely applied as an alternative method to bone marrow transplantation; however, HSCT can be a risky procedure because of potential side effects and complications after transplantations. Although an optimal regimen to achieve successful HSCT while maintaining quality of life is to be developed, even theoretical considerations such as the evaluations of successful engraftments and proposals of clinical management strategies have not been fully discussed yet. In this paper, we construct and investigate mathematical models that describe the kinetics of hematopoietic stem cell self-renewal and granulopoiesis under the influence of growth factors. Moreover, we derive theoretical conditions for successful HSCT, primarily on the basis of the idea that the basic reproduction number R (0) represents a threshold condition for a population to successfully grow in a given steady-state environment. Successful engraftment of transplanted haematopoietic stem cells (HSCs) is subsequently ensured by employing a concept of dynamical systems theory known as 'persistence'. On the basis of the implications from the modelling study, we discuss how the conditions derived for a successful HSCT are used to link to experimental studies.

Congenital neutropenia: diagnosis, molecular bases and patient management

The term congenital neutropenia encompasses a family of neutropenic disorders, both permanent and intermittent, severe (<0.5 G/l) or mild (between 0.5-1.5 G/l), which may also affect other organ systems such as the pancreas, central nervous system, heart, muscle and skin. Neutropenia can lead to life-threatening pyogenic infections, acute gingivostomatitis and chronic parodontal disease, and each successive infection may leave permanent sequelae. The risk of infection is roughly inversely proportional to the circulating polymorphonuclear neutrophil count and is particularly high at counts below 0.2 G/l.When neutropenia is detected, an attempt should be made to establish the etiology, distinguishing between acquired forms (the most frequent, including post viral neutropenia and auto immune neutropenia) and congenital forms that may either be isolated or part of a complex genetic disease.Except for ethnic neutropenia, which is a frequent but mild congenital form, probably with polygenic inheritance, all other forms of congenital neutropenia are extremely rare and have monogenic inheritance, which may be X-linked or autosomal, recessive or dominant.About half the forms of congenital neutropenia with no extra-hematopoietic manifestations and normal adaptive immunity are due to neutrophil elastase (ELANE) mutations. Some patients have severe permanent neutropenia and frequent infections early in life, while others have mild intermittent neutropenia.Congenital neutropenia may also be associated with a wide range of organ dysfunctions, as for example in Shwachman-Diamond syndrome (associated with pancreatic insufficiency) and glycogen storage disease type Ib (associated with a glycogen storage syndrome). So far, the molecular bases of 12 neutropenic disorders have been identified.Treatment of severe chronic neutropenia should focus on prevention of infections. It includes antimicrobial prophylaxis, generally with trimethoprim-sulfamethoxazole, and also granulocyte-colony-stimulating factor (G-CSF). G-CSF has considerably improved these patients' outlook. It is usually well tolerated, but potential adverse effects include thrombocytopenia, glomerulonephritis, vasculitis and osteoporosis. Long-term treatment with G-CSF, especially at high doses, augments the spontaneous risk of leukemia in patients with congenital neutropenia.

Variable renewal rate and growth properties of cell populations in colon crypts

A nonlinear mathematical model is used to investigate the time evolution of the cell populations in colon crypts (stem, semidifferentiated and fully differentiated cells). To mimic pathological alteration of the biochemical pathways leading to abnormal proliferative activity of the population of semidifferentiated cells their renewal rate is assumed to be dependent on the population size. Then, the effects of such perturbation on the population dynamics are investigated theoretically. Using both theoretical methods and numerical simulations it is shown that the increase in the renewal rate of semidifferentiated cells strongly impacts the dynamical behavior of the cell populations.

How I monitor residual disease in chronic myeloid leukemia

Molecular monitoring in chronic myeloid leukemia (CML) is a powerful tool to document treatment responses and predict relapse. Nonetheless, the proliferation of clinical trials and "guidelines" using the molecular endpoints of CML has outpaced practice norms, commercial laboratory application, and reimbursement practices, leaving some anxiety (if not confusion and despair) about molecular monitoring in the day-to-day treatment of CML. This article will try to address these issues by describing how I monitor CML, which, in summary, is with interest and without panic.

Cell-cell interaction networks regulate blood stem and progenitor cell fate

Communication networks between cells and tissues are necessary for homeostasis in multicellular organisms. Intercellular (between cell) communication networks are particularly relevant in stem cell biology, as stem cell fate decisions (self-renewal, proliferation, lineage specification) are tightly regulated based on physiological demand. We have developed a novel mathematical model of blood stem cell development incorporating cell-level kinetic parameters as functions of secreted molecule-mediated intercellular networks. By relation to quantitative cellular assays, our model is capable of predictively simulating many disparate features of both normal and malignant hematopoiesis, relating internal parameters and microenvironmental variables to measurable cell fate outcomes. Through integrated in silico and experimental analyses, we show that blood stem and progenitor cell fate is regulated by cell–cell feedback, and can be controlled non-cell autonomously by dynamically perturbing intercellular signalling. We extend this concept by demonstrating that variability in the secretion rates of the intercellular regulators is sufficient to explain heterogeneity in culture outputs, and that loss of responsiveness to cell–cell feedback signalling is both necessary and sufficient to induce leukemic transformation in silico.

Progenitor cell self-renewal and cyclic neutropenia

OBJECTIVES

Cyclic neutropenia (CN) is a rare genetic disorder where patients experience regular cycling of numbers of neutrophils and various other haematopoietic lineages. The nadir in neutrophil count is the main source of problems due to risk of life-threatening infections. Patients with CN benefit from granulocyte colony stimulating factor therapy, although cycling persists. Mutations in neutrophil elastase gene (ELA2) have been found in more than half of patients with CN. However, neither connection between phenotypic expression of ELA2 and CN nor the mechanism of cycling is known.

MATERIALS AND METHODS

Recently, a multicompartment model of haematopoiesis that couples stem cell replication with marrow output has been proposed. In the following, we couple this model of haematopoiesis with a linear feedback mechanism via G-CSF.

RESULTS

We propose that the phenotypic effect of ELA2 mutations leads to reduction in self-renewal of granulocytic progenitors. The body responds by overall relative increase of G-CSF and increasing progenitor cell self-renewal, leading to cell count cycling.

CONCLUSION

The model is compatible with available experimental data and makes testable predictions.

Mathematical model for G-CSF administration after chemotherapy

Granulocyte-colony stimulating factor (G-CSF) is used clinically for treating chemotherapy-induced neutropenia (low neutrophil levels). Here we present a delay differential equation model for the regulation of neutrophil production that accounts for the effects of G-CSF. Using a combination of analysis and numerical simulations, we use this model to study the effects of delaying G-CSF treatment following chemotherapy for two recombinant forms of G-CSF (filgrastim and pegfilgrastim). We also examine the consequences of varying the duration of filgrastim treatment. We found that varying the starting day or the duration of G-CSF treatment can lead to different qualitative responses in the neutrophil count. These changes can be explained by the coexistence of two stable solutions in the mathematical model.

Selection against pathogenic mtDNA mutations in a stem cell population leads to the loss of the 3243A-->G mutation in blood

The mutation 3243A-->G is the most common heteroplasmic pathogenic mitochondrial DNA (mtDNA) mutation in humans, but it is not understood why the proportion of this mutation decreases in blood during life. Changing levels of mtDNA heteroplasmy are fundamentally related to the pathophysiology of the mitochondrial disease and correlate with clinical progression. To understand this process, we simulated the segregation of mtDNA in hematopoietic stem cells and leukocyte precursors. Our observations show that the percentage of mutant mtDNA in blood decreases exponentially over time. This is consistent with the existence of a selective process acting at the stem cell level and explains why the level of mutant mtDNA in blood is almost invariably lower than in nondividing (postmitotic) tissues such as skeletal muscle. By using this approach, we derived a formula from human data to correct for the change in heteroplasmy over time. A comparison of age-corrected blood heteroplasmy levels with skeletal muscle, an embryologically distinct postmitotic tissue, provides independent confirmation of the model. These findings indicate that selection against pathogenic mtDNA mutations occurs in a stem cell population.

Hemopoietic stem cells with higher hemopoietic potential reside at the bone marrow endosteum

It is now evident that hemopoietic stem cells (HSC) are located in close proximity to bone lining cells within the endosteum. Accordingly, it is unlikely that the traditional method for harvesting bone marrow (BM) from mice by simply flushing long bones would result in optimal recovery of HSC. With this in mind, we have developed improved methodologies based on sequential grinding and enzymatic digestion of murine bone tissue to harvest higher numbers of BM cells and HSC from the endosteal and central marrow regions. This methodology resulted in up to a sixfold greater recovery of primitive hemopoietic cells (lineage(-)Sca(+)Kit(+) [LSK] cells) and HSC as shown by transplant studies. HSC from different anatomical regions of the marrow exhibited important functional differences. Compared with their central marrow counterparts, HSC isolated from the endosteal region (a) had 1.8-fold greater proliferative potential, (b) exhibited almost twofold greater ability to home to the BM following tail vein injection and to lodge in the endosteal region, and (c) demonstrated significantly greater long-term hemopoietic reconstitution potential as shown using limiting dilution competitive transplant assays.

Hematopoietic stem-cell behavior in nonhuman primates

Little is known about the behavior of hematopoietic stem cells (HSCs) in primates because direct observations and competitive-repopulation assays are not feasible. Therefore, we used 2 different and independent experimental strategies, the tracking of transgene expression after retroviral-mediated gene transfer (N = 11 baboons; N = 7 rhesus macaques) and quantitation of the average telomere length of granulocytes (N = 132 baboons; N = 14 macaques), together with stochastic methods, to study HSC kinetics in vivo. The average replication rate for baboon HSCs is once per 36 weeks according to gene-marking analyses and once per 23 weeks according to telomere-shortening analyses. Comparable results were derived from the macaque data. These rates are substantially slower than the average replication rates previously reported for HSCs in mice (once per 2.5 weeks) and cats (once per 8.3 weeks). Because baboons and macaques live for 25 to 45 years, much longer than mice ( approximately 2 years) and cats (12-18 years), we can compute that HSCs undergo a relatively constant number ( approximately 80-200) of lifetime replications. Thus, our data suggest that the self-renewal capacity of mammalian stem cells in vivo is defined and evolutionarily conserved.