Multistability in an age-structured model of hematopoiesis: Cyclical neutropenia

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.

New insights into the pathomechanism of cyclic neutropenia

Cyclic neutropenia (CyN) is a hematologic disorder in which peripheral blood absolute neutrophil counts (ANCs) show cycles of approximately 21-day intervals. The majority of CyN patients harbor ELANE mutations, but the mechanism of ANC cycling is unclear. We performed analysis of bone marrow (BM) subpopulations in CyN patients at the peak and the nadir of the ANC cycle and detected high proportions of BM hematopoietic stem cells (HSCs) and hematopoietic stem and progenitor cells (HSPCs) at the nadir of the ANC cycle, as compared with the peak. BM HSPCs produced fewer granulocyte colony-forming unit colonies at the ANC peak. To investigate the mechanism of cycling, we found that mRNA expression levels of ELANE and unfolded protein response (UPR)-related genes (ATF6, BiP (HSPA5), CHOP (DDIT3), and PERK (EIF2AK3)) were elevated, but antiapoptotic genes (Bcl-2 (BCL2) and bcl-xL (BCL2L1)) were reduced in CD34⁺ cells tested at the ANC nadir. Moreover, HSPCs revealed increased levels of reactive oxygen species and gH2AX at the ANC nadir. We suggest that in CyN patients, some HSPCs escape the UPR-induced endoplasmic reticulum (ER) stress and proliferate in response to granulocyte colony-stimulating factor (G-CSF) to a certain threshold at which UPR again affects the majority of HSPCs. There is a cyclic balance between ER stress-induced apoptosis of HSPCs and compensatory G-CSF-stimulated HSPC proliferation followed by granulocytic differentiation.

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.

Severe congenital neutropenias

Severe congenital neutropenias are a heterogeneous group of rare haematological diseases characterized by impaired maturation of neutrophil granulocytes. Patients with severe congenital neutropenia are prone to recurrent, often life-threatening infections beginning in their first months of life. The most frequent pathogenic defects are autosomal dominant mutations in ELANE, which encodes neutrophil elastase, and autosomal recessive mutations in HAX1, whose product contributes to the activation of the granulocyte colony-stimulating factor (G-CSF) signalling pathway. The pathophysiological mechanisms of these conditions are the object of extensive research and are not fully understood. Furthermore, severe congenital neutropenias may predispose to myelodysplastic syndromes or acute myeloid leukaemia. Molecular events in the malignant progression include acquired mutations in CSF3R (encoding G-CSF receptor) and subsequently in other leukaemia-associated genes (such as RUNX1) in a majority of patients. Diagnosis is based on clinical manifestations, blood neutrophil count, bone marrow examination and genetic and immunological analyses. Daily subcutaneous G-CSF administration is the treatment of choice and leads to a substantial increase in blood neutrophil count, reduction of infections and drastic improvement of quality of life. Haematopoietic stem cell transplantation is the alternative treatment. Regular clinical assessments (including yearly bone marrow examinations) to monitor treatment course and detect chromosomal abnormalities (for example, monosomy 7 and trisomy 21) as well as somatic pre-leukaemic mutations are recommended.

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.

A Review of Mathematical Models for Leukemia and Lymphoma

Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy.

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.

Robustness of differentiation cascades with symmetric stem cell division

Stem cells (SCs) perform the task of maintaining tissue homeostasis by both self-renewal and differentiation. While it has been argued that SCs divide asymmetrically, there is also evidence that SCs undergo symmetric division. Symmetric SC division has been speculated to be key for expanding cell numbers in development and regeneration after injury. However, it might lead to uncontrolled growth and malignancies such as cancer. In order to explore the role of symmetric SC division, we propose a mathematical model of the effect of symmetric SC division on the robustness of a population regulated by a serial differentiation cascade and we show that this may lead to extinction of such population. We examine how the extinction likelihood depends on defining characteristics of the population such as the number of intermediate cell compartments. We show that longer differentiation cascades are more prone to extinction than systems with less intermediate compartments. Furthermore, we have analysed the possibility of mixed symmetric and asymmetric cell division against invasions by mutant invaders in order to find optimal architecture. Our results show that more robust populations are those with unfrequent symmetric behaviour.

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.

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.