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.     

High frequency spikes in long period blood cell oscillations

Several hematological diseases are characterised by oscillations of various blood cell populations. Two of these are a variant of chronic myelogenous leukemia (CML) and cyclical neutropenia (CN). These oscillations typically have long periods ranging from 20 to 60 days, despite the fact that the stem cell cycling time is thought to be of the order of 2–3 days. Clinical data from humans and laboratory data from the grey collie animal model of CN is suggestive of the idea that these long period oscillations may also contain higher frequency spiky oscillations. We show how such oscillations can be understood in the context of slow periodic stem cell oscillations, by analysing a two component differential-delay equation model of stem cell and neutrophil populations.For Karl Hadeler, on his 70th birthday, leader, teacher, colleague and friend.     

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.     

Reduced variance of bone-marrow transit time of granulopoiesis—a possible pathomechanism of human cyclic neutropenia

Abstract. Human cyclic neutropenia (CN) is a haematological disorder characterized by oscillations in the numbers of neutrophilic granulocytes and other blood cells with a stable period of approximately 21 days. In most cases the neutrophils oscillate well below normal values such that these patients are chronically neutropenic. A comprehensive concept of the origin of CN is proposed. It assumes an abnormally small variance of the transit time of bone marrow cells (compared to normal human granulopoiesis) for the origin of the characteristic cycles. Furthermore, a reduced responsiveness of the immature granulopoietic bone marrow cells to the mitotic feedback stimuli is assumed to account for the subnormal neutrophil peaks. Together with feedback control provided in a simulation model of normal human granulopoiesis these two abnormalities can explain experimental and clinical cell kinetic data for bone marrow and blood in CN.     

Eye movement instabilities and nystagmus can be predicted by a nonlinear dynamics model of the saccadic system

The study of eye movements and oculomotor disorders has, for four decades, greatly benefitted from the application of control theoretic concepts. This paper is an example of a complementary approach based on the theory of nonlinear dynamical systems. Recently, a nonlinear dynamics model of the saccadic system was developed, comprising a symmetric piecewise-smooth system of six first-order autonomous ordinary differential equations. A preliminary numerical investigation of the model revealed that in addition to generating normal saccades, it could also simulate inaccurate saccades, and the oscillatory instability known as congenital nystagmus (CN). By varying the parameters of the model, several types of CN oscillations were produced, including jerk, bidirectional jerk and pendular nystagmus. The aim of this study was to investigate the bifurcations and attractors of the model, in order to obtain a classification of the simulated oculomotor behaviours. The application of standard stability analysis techniques, together with numerical work, revealed that the equations have a rich bifurcation structure. In addition to Hopf, homoclinic and saddlenode bifurcations organised by a Takens-Bogdanov point, the equations can undergo nonsmooth pitchfork bifurcations and nonsmooth gluing bifurcations. Evidence was also found for the existence of Hopf-initiated canards. The simulated jerk CN waveforms were found to correspond to a pair of post-canard symmetry-related limit cycles, which exist in regions of parameter space where the equations are a slow-fast system. The slow and fast phases of the simulated oscillations were attributed to the geometry of the corresponding slow manifold. The simulated bidirectional jerk and pendular waveforms were attributed to a symmetry invariant limit cycle produced by the gluing of the asymmetric cycles. In contrast to control models of the oculomotor system, the bifurcation analysis places clear restrictions on which kinds of behaviour are likely to be associated with each other in parameter space, enabling predictions to be made regarding the possible changes in the oscillation type that may be observed upon changing the model parameters. The analysis suggests that CN is one of a range of oculomotor disorders associated with a pathological saccadic braking signal, and that jerk and pendular nystagmus are the most probable oscillatory instabilities. Additionally, the transition from jerk CN to bidirectional jerk and pendular nystagmus observed experimentally when the gaze angle or attention level is changed is attributed to a gluing bifurcation. This suggests the possibility of manipulating the waveforms of subjects with jerk CN experimentally to produce waveforms with an extended foveation period, thereby improving visual resolution.     

Bifurcations in a white-blood-cell production model

We study the dynamics of a model of white-blood-cell (WBC) production. The model consists of two compartmental differential equations with two discrete delays. We show that from normal to pathological parameter values, the system undergoes supercritical Hopf bifurcations and saddle-node bifurcations of limit cycles. We characterize the steady states of the system and perform a bifurcation analysis. Our results indicate that an increase in apoptosis rate of either hematopoietic stem cells or WBC precursors induces a Hopf bifurcation and an oscillatory regime takes place. These oscillations are seen in some hematological diseases.     

Neutrophil mobilization from the bone marrow during polymicrobial sepsis is dependent on CXCL12 signaling

Neutrophils are essential for successful host eradication of bacterial pathogens and for survival to polymicrobial sepsis. During inflammation, the bone marrow provides a large reserve of neutrophils that are released into the peripheral circulation where they traverse to sites of infection. Although neutrophils are essential for survival, few studies have investigated the mechanisms responsible for neutrophil mobilization from the bone marrow during polymicrobial sepsis. Using a cecal ligation and puncture model of polymicrobial sepsis, we demonstrated that neutrophil mobilization from the bone marrow is not dependent on TLR4, MyD88, TRIF, IFNARα/β, or CXCR2 pathway signaling during sepsis. In contrast, we observed that bone marrow CXCL12 mRNA abundance and specific CXCL12 levels are sharply reduced, whereas splenic CXCR4 mRNA and cell surface expression are increased during sepsis. Blocking CXCL12 activity significantly reduced blood neutrophilia by inhibiting bone marrow release of granulocytes during sepsis. However, CXCL12 inhibition had no impact on the expansion of bone marrow neutrophil precursors and hematopoietic progenitors. Bone marrow neutrophil retention by CXCL12 blockade prevented blood neutrophilia, inhibited peritoneal neutrophil accumulation, allowed significant peritoneal bacterial invasion, and increased polymicrobial sepsis mortality. We concluded that changes in the pattern of CXCL12 signaling during sepsis are essential for neutrophil bone marrow mobilization and host survival but have little impact on bone marrow granulopoiesis.     

Granulocyte colony-stimulating factor and its receptor in normal hematopoietic cell development and myeloid disease

Hematopoiesis, the process of blood cell formation, is orchestrated by cytokines and growth factors that stimulate the expansion of different progenitor cell subsets and regulate their survival and differentiation into mature blood cells. Granulocyte colony-stimulating factor (G-CSF) is the major hematopoietic growth factor involved in the control of neutrophil development. G-CSF is now applied on a routine basis in the clinic for treatment of congenital and acquired neutropenias. G-CSF activates a receptor of the hematopoietin receptor superfamily, the G-CSF receptor (G-CSF-R), which subsequently triggers multiple signaling mechanisms. Here we review how these mechanisms contribute to the specific responses of hematopoietic cells to G-CSF and how perturbations in the function of the G-CSF-R are implicated in various types of myeloid disease.     

Immune network behavior—I. From stationary states to limit cycle oscilations

We develop a model for the idiotypic interaction between two B cell clones. This model takes into account B cell proliferation, B cell maturation, antibody production, the formation and subsequent elimination of antibody-antibody complexes and recirculation of antibodies between the spleen and the blood. Here we investigate, by means of stability and bifurcation analysis, how each of the processes influences the model's behavior. After appropriate nondimensinalization, the model consists of eight ordinary differential equations and a number of parameters. We estimate the parameters from experimental sources. Using a coordinate system that exploits the pairwise symmetry of the interactions between two clones, we analyse two simplified forms of the model and obtain bifurcation diagrams showing how their five equilibrium states are related. We show that the so-called immune states lose stability if B cell and antibody concentrations change on different time scales. Additionally, we derive the structure of stable and unstable manifolds of saddle-tye equilibria, pinpoint their (global) bifurcations and show that these bifurcations play a crucial role in determining the parameter regimes in which the model exhibits oscillatory behavior.     

Interleukin 3-dependent hematopoietic progenitor cell lines

Several biological phenotypes of growth factor-dependent cell lines have been described in recent years, including those with T lymphocyte, neutrophil granulocyte, basophil/mast cell, B lymphocyte, and multipotential stem cell properties. The growth factors for each cell lineage are a subject of intense study. Continuous mouse bone marrow cultures infected with RNA type C viruses (retroviruses) produce nonadherent hematopoietic cells over a longer duration than control cultures. Marrow cultures derived from strains with spontaneously induced ecotropic endogenous retrovirus demonstrate a greater longevity than those from strains with no replicating virus. Cultures infected with murine leukemia virus also generate a greater number, compared with controls, of cloned permanent suspension cell lines dependent for growth on a 41,000-dalton glycoprotein (interleukin 3 [IL 3]). Some are multipotential with capacity for differentiation to erythroid, neutrophil, eosinophil, and basophil/mast cell types. Other cloned IL 3-dependent cell lines are committed to a single pathway. Studies with Friend spleen focus-forming virus indicate that the first effect in the marrow culture is mediated through a subset of adherent hematopoietic stem cells. Bone marrow culture-derived IL 3-dependent cell lines provide a model with which to study the role of viral genes in the control of differentiation and self-renewal capacity of hematopoietic stem cells.     

Peripheral blood progenitor cell mobilization and leukapheresis in pigs

BACKGROUND AND PURPOSE: The pig is being investigated as an organ donor for humans. Induction of immunologic tolerance to pig tissues in primates would overcome the major immunologic barriers to xenotransplantation. A proven method of inducing tolerance to allografts is by the induction of mixed hematopoietic chimerism by bone marrow transplantation. We are therefore investigating induction of mixed hematopoietic chimerism in the pig-to-baboon model. METHODS: To obtain large numbers of pig hematopoietic cells, leukapheresis was used to collect blood cell products in miniature swine (n = 5) after progenitor cell mobilization by use of a course of hematopoietic growth factors (cytokines), consisting of porcine interleukin 3, porcine stem cell factor, and human granulocyte colony-stimulating factor. RESULTS: Cytokine therapy and leukapheresis were well tolerated. Cytokine therapy increased the total white blood cell count and allowed large numbers of leukocytes (60 x 10(10)) to be obtained by apheresis, of which approximately 0.1% were granulocyte-erythrocyte-monocyte-megakaryocyte colony-forming units (CFU-GEMMs), which are considered to be representative of hematopoietic progenitors with multi-lineage potential. CONCLUSIONS: The combination of cytokine therapy and leukapheresis enables hematopoietic progenitor cells to be obtained safely from miniature swine.     

A mathematical model of hematopoiesis: II. Cyclical neutropenia

Cyclical neutropenia is a dynamical disease of the hematopoietic system marked by an oscillation in circulating leukocyte (e.g. neutrophil) numbers to near zero levels and then back to normal. This oscillation is also mirrored in the platelets and reticulocytes which oscillate with the same period. Cyclical neutropenia has an animal counterpart in the grey collie. Using the mathematical model of the hematopoietic system of Colijn and Mackey [A mathematical model of hematopoiesis: I. Periodic chronic myelogenous leukemia. Companion paper to the present paper.] we have determined what parameters are necessary to mimic laboratory and clinical data on untreated grey collies and humans, and also what changes in these parameters are necessary to fit data during treatment with granulocyte colony stimulating factor (G-CSF). Compared to the normal steady-state values, we found that the major parameter changes that mimic untreated cyclical neutropenia correspond to a decreased amplification (increased apoptosis) within the proliferating neutrophil precursor compartment, and a decrease in the maximal rate of re-entry into the proliferative phase of the stem cell compartment. For the data obtained during G-CSF treatment, good fits were obtained only when parameters were altered that would imply that G-CSF led to higher amplification (lower rate of apoptosis) in the proliferating neutrophil precursors, and a elevated rate of differentiation into the neutrophil line.     

Effect of recombinant murine tumor necrosis factor on hemopoietic reconstitution in sublethally irradiated mice

Intravenous bolus administration of a single 2-micrograms dose of murine rTNF-alpha to BALB/c mice 20 h before sublethal total-body irradiation (7.5 Gy) conferred significant protection against radiation-induced leukopenia. Murine rTNF-alpha administration not only reduced the decline of neutrophil and total blood cell counts after radiation, but also accelerated the subsequent normalization of peripheral blood cell counts. This was accompanied by accelerated regeneration of primitive hematopoietic progenitors, as determined by the in vivo spleen CFU assay, and the in vitro assay of the more mature hematopoietic cell compartment. This demonstrates that pretreatment with murine rTNF-alpha enhances hematopoietic reconstitution after sublethal irradiation, and indicates a possible therapeutic potential for this agent in the treatment of radiation-induced myelo-suppression.     

The aged hematopoietic system promotes hippocampal‐dependent cognitive decline

The aged systemic milieu promotes cellular and cognitive impairments in the hippocampus. Here, we report that aging of the hematopoietic system directly contributes to the pro‐aging effects of old blood on cognition. Using a heterochronic hematopoietic stem cell (HSC) transplantation model (in which the blood of young mice is reconstituted with old HSCs), we find that exposure to an old hematopoietic system inhibits hippocampal neurogenesis, decreases synaptic marker expression, and impairs cognition. We identify a number of factors elevated in the blood of young mice reconstituted with old HSCs, of which cyclophilin A (CyPA) acts as a pro‐aging factor. Increased systemic levels of CyPA impair cognition in young mice, while inhibition of CyPA in aged mice improves cognition. Together, these data identify age‐related changes in the hematopoietic system as drivers of hippocampal aging.     

Modeling the Dynamics of Cdc42 Oscillation in Fission Yeast

Regulation of polarized cell growth is essential for many cellular processes, including spatial coordination of cell morphology changes during growth and division. We present a mathematical model of the core mechanism responsible for the regulation of polarized growth dynamics by the small GTPase Cdc42. The model is based on the competition of growth zones of Cdc42 localized at the cell tips for a common substrate (inactive Cdc42) that diffuses in the cytosol. We consider several potential ways of implementing negative feedback between Cd42 and its GEF in this model that would be consistent with the observed oscillations of Cdc42 in fission yeast. We analyze the bifurcations in this model as the cell length increases, and total amount of Cdc42 and GEF increase. Symmetric antiphase oscillations at two tips emerge via saddle-homoclinic bifurcations or Hopf bifurcations. We find that a stable oscillation and a stable steady state can coexist, which is consistent with the experimental finding that only 50% of bipolar cells oscillate. The mean amplitude and period can be tuned by parameters involved in the negative feedback. We link modifications in the parameters of the model to observed mutant phenotypes. Our model suggests that negative feedback is more likely to be acting through inhibition of GEF association rather than upregulation of GEF dissociation.     

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.     

Small-bubble transport and splitting dynamics in a symmetric bifurcation

Simulations of small bubbles traveling through symmetric bifurcations are conducted to garner information pertinent to gas embolotherapy, a potential cancer treatment. Gas embolotherapy procedures use intra-arterial bubbles to occlude tumor blood supply. As bubbles pass through bifurcations in the blood stream nonhomogeneous splitting and undesirable bioeffects may occur. To aid development of gas embolotherapy techniques, a volume of fluid method is used to model the splitting process of gas bubbles passing through artery and arteriole bifurcations. The model reproduces the variety of splitting behaviors observed experimentally, including the bubble reversal phenomenon. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Small bubbles, having initial length less than twice the vessel diameter, were found unlikely to split in the presence of gravitational asymmetry. Maximum shear stresses were found to decrease exponentially with increasing Reynolds number. Vortex-induced shearing near the bifurcation is identified as a possible mechanism for endothelial cell damage.     

Dual roles for Rac2 in neutrophil motility and active retention in zebrafish hematopoietic tissue

Neutrophil homeostasis is essential for host defense. Here we identify dual roles for Rac2 during neutrophil homeostasis using a zebrafish model of primary immune deficiency induced by the human inhibitory Rac2D57N mutation in neutrophils. Noninvasive live imaging of Rac2 morphants or Rac2D57N zebrafish larvae demonstrates an essential role for Rac2 in regulating 3D motility and the polarization of F-actin dynamics and PI(3)K signaling in?vivo. Tracking of photolabeled Rac2-deficient neutrophils from hematopoietic tissue also shows increased mobilization into the circulation, indicating that neutrophil mobilization does not require traditionally defined cell motility. Moreover, excessive neutrophil retention in hematopoietic tissue resulting from a constitutively active CXCR4 mutation in zebrafish warts, hypogammaglobulinemia, infections, and myelokathexis (WHIM) syndrome is partially rescued by the inhibitory Rac2 mutation. These findings reveal that Rac2 signaling is necessary for both neutrophil 3D motility and CXCR4-mediated neutrophil retention in hematopoietic tissue, thereby limiting neutrophil mobilization, a critical first step in the innate immune response.     

小鼠骨髓造血干细胞、外周血组成随年龄的变化趋势及其相关性分析

造血干细胞是具有自我更新能力并能分化为血液中各种血细胞组分的多能干细胞。近来研究显示,不同造血干细胞表面标志物标记的造血干细胞具有分化为不同血细胞的趋势,但是这种分化的内在关系仍不清楚。对小鼠CD34~-/Sca-1~+骨髓造血干细胞、外周血组成随小鼠年龄增长的变化情况进行了分析,结果显示:随着年龄的增长,骨髓中的CD34~-/Sca-1~+骨髓造血干细胞比率显著增加;而外周血各组分则随年龄变化呈现不同的趋势。对不同年龄段小鼠的骨髓造血干细胞及其他组分与外周血组分的同步分析发现,外周血中血小板密度变化趋势与CD34~-/Sca-1~+骨髓造血干细胞变化情况相关系数为0.804 8;外周血中淋巴细胞密度变化趋势与CD34~+/Sca-1~-骨髓细胞的变化情况相关系数为0.947 97;外周血中白细胞密度变化趋势与CD34~+/Sca-1~+骨髓细胞变化情况相关系数为0.763 1(大于0.9为极度相关,0.7到0.9为高度相关)。     

Early fetal hematopoietic development from in vitro differentiated embryonic stem cells.

In this report we describe the efficient hematopoietic differentiation of embryonic stem (ES) cells in vitro. When cultured in semisolid medium two of five ES cell lines efficiently generated embryoid bodies (EBs) containing blood islands in which hematopoietic cells from all six myeloid lineages could be detected. Among a variety of growth factors tested, only erythropoietin significantly increased blood island formation. We directly demonstrate the presence of hematopoietic progenitors in the EBs by employing an in vitro precursor assay. Colony-forming cells (CFC) of all myeloid lineages as well as bi- and multipotent (CFC-MIX) progenitors were readily identified, and a detailed time-course analysis of their appearance was performed. Despite a high frequency of CFC-MIX in vitro, we did not observe any spleen colony-forming cells (CFU-S) in vivo. We conclude that hematopoietic differentiation of ES cells under these conditions reflects formation of the complete range of blood cells found in the yolk sac of the early fetus. Therefore this system provides a unique model in which to study the earliest events of hematopoietic development in vitro.