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

Cyclical neutropenia (CN) is a rare hematopoietic disorder in which the patient's neutrophil level drops to extremely low levels for a few days approximately every three weeks. CN is effectively treated with granulocyte colony stimulating factor (G-CSF), which is known to interfere with apoptosis in neutrophil precursors and to consequently increase the circulating neutrophil level. However, G-CSF treatment usually fails to eliminate the oscillation. In this study, we establish an age-structured model of hematopoiesis, which reduces to a set of four delay differential equations with specific forms of initial functions. We numerically investigate the possible stable solutions of the model equations with respect to changes in the parameters as well as the initial conditions. The results show that the hematopoietic system possesses multistability for parameters typical of the normal healthy state. From our numerical results, decreasing the proliferation rate of neutrophil precursors or increasing the stem cell death rate are two possible mechanisms to induce cyclical neutropenia, and the periods of the resulting oscillations are independent of the changing parameters. We also discuss the dependence of the model solution on the initial condition at normal parameter values corresponding to a healthy state. Using insight from our results we design a hybrid treatment method that is able to abolish the oscillations in CN.     

Oscillations in cyclical neutropenia: new evidence based on mathematical modeling

We present a dynamical model of the production and regulation of circulating blood neutrophil number. This model is derived from physiologically relevant features of the hematopoietic system, and is analysed using both analytic and numerical methods. Supercritical Hopf bifurcations and saddle-node bifurcations of limit cycles are shown to exist. We make the estimation of kinetic parameters for dogs and then apply the model to cyclical neutropenia (CN) in the grey collie, a rare disorder in which oscillations in all blood cell counts are found. We conclude that the major cause of the oscillations in CN is an increased rate of apoptosis of neutrophil precursors which leads to a destabilization of the hematopoietic stem cell compartment.     

A mathematical model of hematopoiesis--I. Periodic chronic myelogenous leukemia

Periodic chronic myelogenous leukemia (PCML) is an interesting dynamical disease of the hematopoietic system in which oscillating levels of circulating leukocytes, platelets and/or reticulocytes are observed. Typically all of these three differentiated cell types have the same oscillation period, but the relation of the oscillation mean and amplitude to the normal levels is variable. Given the appearance of the abnormal Philadelphia chromosome in all of the nucleated progeny of the hematopoietic stem cells (HSCs), the most parsimonious conclusion is that chronic myelogenous leukemia, and its periodic variant, arise from derangements partially involving the dynamics of the stem cells. Here, we have synthesized several previous mathematical models of HSC dynamics, and models for the regulation of neutrophils, platelets and erythrocytes into a comprehensive model for the regulation of the hematopoietic system. Based on estimates of parameters for a typical normal human, we have systematically explored the changes in some of these parameters necessary to account for the quantitative data on leukocyte, platelet and reticulocyte cycling in 11 patients with PCML. Our results indicate that the critical model parameter changes required to simulate the PCML patient data are an increase in the amplification in the leukocyte line, an increase in the differentiation rate from the stem cell compartment into the leukocyte line, and the rate of apoptosis in the stem cell compartment. Our model system is particularly sensitive to changes in stem cell apoptosis rates, suggesting that changes in the numbers of proliferating stem cells may be important in generating PCML.     

The rate of apoptosis in post mitotic neutrophil precursors of normal and neutropenic humans

Abstract. Using data on the fraction of post-mitotic neutrophil precursors (CD15⁺ cells) displaying positive markers for apoptosis in 12 normal humans, and a simple mathematical model, we have estimated the apoptotic rate to be about 0.28/day in this compartment. This implies that the influx of myelocytes into the post-mitotic compartment exceeds twice the granulocyte turnover rate (GTR), and that about 55% of the cells entering this compartment die before being released into the blood. The normal half life of apoptotic post-mitotic neutrophil precursors is calculated to be 10.4 h. Comparable calculations for patients indicate apoptosis rates in the post-mitotic compartment of about 17 times normal for one myelokathexis patient and rates of about 13 times normal for the one cyclical neutropenic patient and two severe congenital neutropenic patients. The estimated half life for apoptotic post-mitotic neutrophil precursors in the myelokathexis patient was about 0.4 h, 1.4 h in the cyclical neutropenia patient, and about 0.6 h in the severe congenital neutropenic patients.     

Modeling complex neutrophil dynamics in the grey collie

We have developed a mathematical model for the peripheral regulation of neutrophil production mediated by granulocyte colony-stimulating factor. We have used that model to show that the pattern of neutrophil oscillations in nine grey collies is consistent with the hypothesis that cyclical neutropenia is due to an oscillatory stem cell input to the neutrophil regulatory system, and not due to autonomous oscillations in the peripheral neutrophil regulatory system. In the process of interfacing our model with the laboratory data, we have estimated parameters for the peripheral neutrophil control system consistent with higher than normal apoptotic cell loss within the recognizable neutrophil precursors. This is in agreement with other experimental data. Our estimated model parameters also predict that the peripheral neutrophil production system is globally stable in the grey collies we studied. This further supports our hypothesis that the origin of the oscillatory behavior in cyclical neutropenia is in the stem cell population, consistent with other clinical and experimental evidence.     

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.     

Cost-effective G-CSF therapy strategies for cyclical neutropenia: mathematical modelling based hypotheses

Using computer simulations of a mathematical model for the regulation of stem cell and neutrophil production in dogs, we have studied the efficacy of four different treatment protocols for cyclical neutropenia involving granulocyte colony stimulating factor (G-CSF). The first treatment scheme is based on the bifurcation analysis of the mathematical model and proposes a daily, phase-dependent, protocol. The second involves alternate day administration of G-CSF. The third triggers G-CSF administration whenever neutrophil levels fall below a predetermined level, and the fourth one follows a random administration protocol. The computer simulations predict that clinically desirable results can be achieved with the three last methods, using far less G-CSF than would be needed with the standard daily treatment. If the results of this modelling are borne out clinically, they will entail a considerable financial savings for patients.     

G-CSF Control of Neutrophils Dynamics in the Blood

White blood cell neutrophil is a key component in the fast initial immune response against bacterial and fungal infections. Granulocyte colony stimulating factor (G-CSF) which is naturally produced in the body, is known to control the neutrophils production in the bone marrow and the neutrophils delivery into the blood. In oncological practice, G-CSF injections are widely used to treat neutropenia (dangerously low levels of neutrophils in the blood) and to prevent the infectious complications that often follow chemotherapy. However, the accurate dynamics of G-CSF neutrophil interaction has not been fully determined and no general scheme exists for an optimal G-CSF application in neutropenia. Here we develop a two-dimensional ordinary differential equation model for the G-CSF—neutrophil dynamics in the blood. The model is built axiomatically by first formally defining from the biology the expected properties of the model, and then deducing the dynamic behavior of the resulting system. The resulting model is structurally stable, and its dynamical features are independent of the precise form of the various rate functions. Choosing a specific form for these functions, three complementary parameter estimation procedures for one clinical (training) data set are utilized. The fully parameterized model (6 parameters) provides adequate predictions for several additional clinical data sets on time scales of several days. We briefly discuss the utility of this relatively simple and robust model in several clinical conditions. Dedicated to Lee Segel who guided us to apply mathematics for the benefit of mankind—a teacher, a colleague, a friend. L.A. Segel passed away on 31 January 2005.     

Granulopoeisis and leukemogenesis: lessons from congenital neutropenia

Congenital neutropenia are extremely rare diseases, defined by a permanent or cyclic decrease of blood neutrophils. Molecular basis of several congenital neutropenia has been recently determined, involving gene coding for the neutrophil elastase gene (ELA2), GFI1, WAS protein and mitochondrial HAX1 protein. These mutations, dominant (ELA2, GFI1), X-linked (WAS) and autosomal recessive (HAX1), result in instability of the contents of the granules- particularly the neutrophil elastase- or in abnormalities of the cytoskeleton, and possibly, in an increased apoptosis. ELA2 mutations resulting both in profound and permanent neutropenia, and in cyclic--pseudo sinusoidal--neutropenia lead to consider that time pattern is very close in the two apparently distinct phenotypes. This observation suggests that temporal variations of neutrophils could be represented by non linear functions. Congenital neutropenia, specifically ELA2 mutated, are also characterized by a high rate of leukemia (about 15% at 20 years of age). Leukemia risk does not appear to be related to an oncogenic effect of ELA2 mutations, but much likely to the deepness of the neutropenia, and the intensity of G-CSF therapy.     

The effect of recombinant human granulocyte/macrophage-colony-stimulating factor (rHu GM-CSF) and rHu G-CSF administration on neutrophil chemiluminescence assay in patients following cyclic chemotherapy

Secondary infections related to neutropenia and functional defects of phagocytes are common consequences in patients treated for cancer. The hematopoietic colony-stimulating factors (CSF) have been introduced into clinical practice as additional supportive measures that can reduce the incidence of infectious complications in patients with cancer and neutropenia. The aim of this study was to determine the role of␣granuolcyte/macrophage(GM)-CSF and granulocyte(G)-CSF in enhancing in vivo human neutrophil function. A luminol-dependent chemiluminescence assay was developed to evaluate whether the repair in neutropenia accompanies the ability of neutrophils to function. A dose of 5 μg G-CSF kg⁻¹ day⁻¹ [recombinant human (rHu) G-CSF; filgrastim] or 250 μg GM-CSF m⁻² day⁻¹ (rHu GM-CSF; molgramostim) was administered subcutaneously once daily to 12 metastatic cancer patients being treated with different cytotoxic regimens. All injections of CSF were given after the initiation of neutropenia and continued until the occurrence of an absolute neutrophil recovery. rHu GM-CSF and rHu G-CSF, administered once daily at the 250 μg m⁻² day⁻¹ and 5 μg kg⁻¹ day⁻¹ level, were effective in increasing the absolute neutrophil count and neutrophil function, as measured by an automated chemiluminescence system. Received: 26 February 1998 / Accepted: 21 May 1998     

Clinical applications of recombinant human colony-stimulating factors.

The differentiation and maturation of hematopoietic progenitor cells are regulated by certain growth factors. Several of these glycoproteins have been characterized, and their amino acid sequences have been delineated. Modern DNA technology provides sufficient quantities of these hormones for testing in clinical trials. Erythropoietin (EPO) has been shown to increase the hemoglobin level and hematocrit in patients with end-stage renal disease. Granulocyte colony-stimulating factor (G-CSF) and granulocyte-macrophage CSF (GM-CSF) can increase the numbers of neutrophils and monocytes, in a dose-dependent fashion. The function of granulocytes and monocytes is also enhanced. Clinical studies of the toxicity and activity of G-CSF and GM-CSF have been conducted in patients with acquired immune deficiency syndrome, aplastic anemia, myelodysplastic syndromes, and neutropenia due to cancer and chemotherapy. In almost all patients the neutrophil count increased within 24 hours after the start of treatment. Side effects of G-CSF and GM-CSF are infrequent and usually mild. Combinations of CSFs may be even more effective.     

Short-term exposure of umbilical cord blood CD34+ cells to granulocyte–macrophage colony-stimulating factor early in culture improves ex vivo expansion of neutrophils

Background aimsDespite the availability of modern antibiotics/antimycotics and cytokine support, neutropenic infection accounts for the majority of chemotherapy-associated deaths. While transfusion support with donor neutrophils is possible, cost and complicated logistics make such an option unrealistic on a routine basis. A manufactured neutrophil product could enable routine prophylactic administration of neutrophils, preventing the onset of neutropenia and substantially reducing the risk of infection. We examined the use of pre-culture strategies and various cytokine/modulator combinations to improve neutrophil expansion from umbilical cord blood (UCB) hematopoietic stem and progenitor cells (HPC).MethodsEnriched UCB HPC were cultured using either two-phase pre-culture strategies or a single phase using various cytokine/modulator combinations. Outcome was assessed with respect to numerical expansion, cell morphology, granulation and respiratory burst activity.ResultsPre-culture in the absence of strong differentiation signals (e.g. granulocyte colony-stimulating factor; G-CSF) failed to provide any improvement to final neutrophil yields. Similarly, removal of differentiating cells during pre-culture failed to improve neutrophil yields to an appreciable extent. Of the cytokine/modulator combinations, the addition of granulocyte–macrophage (GM)-colony-stimulating factor (CSF) alone gave the greatest increase. In order to avoid production of monocytes, it was necessary to remove GM-CSF on day 5. Using this strategy, neutrophil expansion improved 2.7-fold.ConclusionsAlthough all cytokines and culture strategies employed have been reported previously to enhance HPC expansion, we found that the addition of GM-CSF alone was sufficient to improve total cell yields maximally. The need to remove GM-CSF on day 5 to avoid monocyte differentiation highlights the context and time-dependent complexity of exogenous signaling in hematopoietic cell differentiation and growth.     

Homeostatic regulation of blood neutrophil counts

Blood neutrophil counts are determined by the differentiation and proliferation of precursor cells, the release of mature neutrophils from the bone marrow, margination, trafficking and transmigration through the endothelial lining, neutrophil apoptosis, and uptake by phagocytes. This brief review summarizes the regulation of blood neutrophil counts, which is in part controlled by G-CSF, IL-17, and IL-23. Neutrophils are retained in the bone marrow through interaction of CXCL12 with its receptor CXCR4. The relevance of this mechanism is illustrated by rare diseases in which disrupting the desensitization of CXCR4 results in failure to release mature neutrophils from bone marrow. Although blood neutrophil numbers in inbred mouse strains and individual human subjects are tightly controlled, their large variation among outbred populations suggests genetic factors. One example is benign ethnic neutropenia, which is found in some African Americans. Reduced and elevated neutrophil counts, even within the normal range, are associated with excess all-cause mortality.     

Oral ezatiostat HCl (Telintra®, TLK199) and Idiopathic Chronic Neutropenia (ICN): a case report of complete response of a patient with G-CSF resistant ICN following treatment with ezatiostat, a glutathione S-transferase P1-1 (GSTP1-1) inhibitor

Idiopathic chronic neutropenia (ICN) describes a heterogeneous group of hematologic diseases characterized by low circulating neutrophil levels often associated with recurrent fevers, chronic mucosal inflammation, and severe systemic infections. The severity and risk of complications, including serious infections, are inversely proportional to the absolute neutrophil count (ANC), with the greatest problems occurring in patients with an ANC of less than 0.5 × 10⁹/L. This case report describes a 64-year-old female with longstanding rheumatoid arthritis who subsequently developed ICN with frequent episodes of sepsis requiring hospitalization and prolonged courses of antibiotics over a 4-year period. She was treated with granulocyte colony stimulating factors (G-CSF) but had a delayed, highly variable, and volatile response. She was enrolled in a clinical trial evaluating the oral investigational agent ezatiostat. Ezatiostat, a glutathione S-transferase P1-1 inhibitor, activates Jun kinase, promoting the growth and maturation of hematopoietic progenitor stem cells. She responded by the end of the first month of treatment with stabilization of her ANC (despite tapering and then stopping G-CSF), clearing of fever, and healing of areas of infection. This ANC response to ezatiostat treatment has now been sustained for over 8 months and continues. These results suggest potential roles for ezatiostat in the treatment of patients with ICN who are not responsive to G-CSF, as an oral therapy alternative, or as an adjunct to G-CSF, and further studies are warranted.     

24p3 in differentiation of myeloid cells

24p3 is a secreted lipocalin that has been variously related to apoptosis, proliferation, and the neutrophil lineage of blood cells. We have investigated the expression of 24p3 mRNA and protein in myeloid cell lines induced to differentiate by insulin-like growth factor 1 (IGF-1) and the granulocytic-colony simulating factor (G-CSF). Both these growth factors, which cause myeloid cells to differentiate into granulocytes, induced a marked increase in the expression of both 24p3 protein and mRNA. The mRNA especially appeared early after the cells were induced with either IGF-1 or G-CSF, at a time when the cells were still proliferating and are morphologically undifferentiated. 24p3 can be considered an early marker of granulocytic differentiation.     

Current insights into neutrophil homeostasis

Neutrophil granulocytes represent the first immunologic barrier against invading pathogens, and neutropenia predisposes to infection. However, neutrophils may also cause significant collateral inflammatory damage. Therefore, neutrophil numbers are tightly regulated by an incompletely understood homeostatic feedback loop adjusting the marrow's supply to peripheral needs. Granulocyte colony-stimulating factor (G-CSF) is accepted to be the major determinant of neutrophil production, and G-CSF levels have, soon after its discovery, been described to be inversely correlated with neutrophil counts. A neutrophil sensor, or "neutrostat," has, therefore, been postulated. The prevailing feedback hypothesis was established in adhesion molecule-deficient mice; it includes macrophages and Th17 cells, which determine G-CSF levels in response to the number of peripherally transmigrated, apoptosing neutrophils. Recent work has deepened our understanding of homeostatic regulation of neutrophil granulopoiesis, but there are still inconsistent findings and unresolved questions when it comes to a plausible hypothesis, similar to the feedback control models of red cell or platelet homeostasis.     

Neutropenia dynamics in a case of T‐LGL lymphoproliferation illustrate rapid turnover of granulocyte progenitors

Objectives: To elucidate the natural history of T‐cell large granular lymphocyte (T‐LGL) lymphoproliferation, we followed changes in associated fluctuating neutropenia for 3 years in an untreated patient presenting with the disease. Materials and methods: We report a nonlinear mathematical analysis of irregular neutrophil fluctuation, using iterative data maps, to detect long‐term regulation of the neutrophil population. Results: This geometric analysis indicated that variations of this sequence of neutrophil counts followed bounded deterministic dynamics around a fixed low level equilibrium, a situation similar to that previously observed for cultured mouse early bone marrow progenitor cells. Conclusion: These findings illustrate how the deleterious effect of T‐LGL on neutrophils is balanced, over periods of years, by pulses of compensatory neutrophil production, potentially accounting for the commonly observed prolonged indolent course of the disease.     

G-CSF: From granulopoietic stimulant to bone marrow stem cell mobilizing agent

G-CSF was among the first cytokines to be identified and rapidly transitioned into clinical medicine. Initially used to promote the production of neutrophils in patients with chemotherapy-induced neutropenia it helped to revolutionize the delivery of cancer therapy. Its ability to mobilize hematopoietic stem cells from the bone marrow into the blood was subsequently exploited, changing the face of hematopoietic stem cell transplantation. Today the knowledge gained in unraveling the mechanisms of stem cell mobilization by G-CSF is being explored as a means to increase chemosensitivity in hematological malignancies. This review provides a brief history of G-CSF and then focuses on recent advances in our understanding of G-CSF-induced stem cell mobilization and the potential clinical application of this knowledge in chemo-sensitization.