A mathematical model for reconstitution of granulopoiesis after high dose chemotherapy with autologous stem cell transplantation

High dose chemotherapy supported with hematopoietic progenitor cells gives a characteristic neutropenic period (blood neutrophils <0.510⁹ c/l) ranging from 10 to 16 days. The question of a correlation between the CFU-GM content of the transplanted CD34+ cells and time to neutrophil recovery by patients having been given high-dose chemotherapy (HD-CT) with stem cell support was addressed by means of a mathematical model of granulopoiesis. The model utilizes a convection-reaction partial differential equation (PDE) with feedback from a cytokine compartment on proliferation, maturation, and mobilization of granulocytes from bone marrow to blood. The observed number of CFU-GM cells in the transplanted CD34+ cell autograft was used as input to the model. Using this approach, the observed gross relationship between CFU-GM content in the reinfused blood product and engraftment time could be reproduced. At the same time, the effects of assumed physiological mechanisms, especially some of the effects of G-CSF on proliferation rate, maturation rate, mobilization, and cell death, could be investigated and discussed relative to observed engraftment. The model makes it possible to explain how cytokines interfere with progenitor cell mobilization from bone marrow to blood, and it points out the implications of a regulating mechanism for the granulocyte maturation rate.     

Dynamics of outgrowth in a continuum model of neurite elongation

Neurite outgrowth (dendrites and axons) should be a stable, but easily regulated process to enable a neuron to make its appropriate network connections during development. We explore the dynamics of outgrowth in a mathematical continuum model of neurite elongation. The model describes the construction of the internal microtubule cytoskeleton, which results from the production and transport of tubulin dimers and their assembly into microtubules at the growing neurite tip. Tubulin is assumed to be largely synthesised in the cell body from where it is transported by active mechanisms and by diffusion along the neurite. It is argued that this construction process is a fundamental limiting factor in neurite elongation. In the model, elongation is highly stable when tubulin transport is dominated by either active transport or diffusion, but oscillations in length may occur when both active transport and diffusion contribute. Autoregulation of tubulin production can eliminate these oscillations. In all cases a stable steady-state length is reached, provided there is intrinsic decay of tubulin. Small changes in growth parameters, such as the tubulin production rate, can lead to large changes in length. Thus cytoskeleton construction can be both stable and easily regulated, as seems necessary for neurite outgrowth during nervous system development. Action Editor: Upinder Bhalla     

Synchrony of bone marrow proliferation and maturation as the origin of cyclic haemopoiesis

Abstract. Cyclic haemopoiesis in Grey Collie dogs is characterized by stable oscillations in all haemopoietic lineages. It is proposed that in these animals, in contrast to normal animals, the maturation process of haemopoietic (in particular granuloid) cells from the primitive progenitors to the functional cells is characterized by an abnormally strong synchrony. It is conjectured that the marrow maturation time has a very small variance compared with non-cyclic normal dogs. With a mathematical model of haemopoiesis it is shown that small fluctuations are amplified via regular feedback processes such that stable granuloid oscillations are established. Erythroid oscillations are induced indirectly by granuloid feedback to the stem cell pool. The model calculations further show that the synchrony hypothesis of bone marrow maturation can quantitatively explain the following experimental results: (1) the maintenance of stable cycles of granuloid and erythroid bone marrow and blood cells with a period of approximately 14 d; (2) the disappearance of granuloid and erythroid cycles during the administration of the colony stimulating factor rhG-CSF; (3) the reappearance of oscillations when the administration of CSF is discontinued; (4) the cessation of cycles during endotoxin application; and (5) the persistence of cycles during erythroid manipulations (bleeding anaemia, hypoxia, hypertransfusion). We therefore conclude that cyclic haemopoiesis is not caused by a defect in the regulatory control system but by an unusual maturation process.     

Synchrony of bone marrow proliferation and maturation as the origin of cyclic haemopoiesis.

Cyclic haemopoiesis in Grey Collie dogs is characterized by stable oscillations in all haemopoietic lineages. It is proposed that in these animals, in contrast to normal animals, the maturation process of haemopoietic (in particular granuloid) cells from the primitive progenitors to the functional cells is characterized by an abnormally strong synchrony. It is conjectured that the marrow maturation time has a very small variance compared with non-cyclic normal dogs. With a mathematical model of haemopoiesis it is shown that small fluctuations are amplified via regular feedback processes such that stable granuloid oscillations are established. Erythroid oscillations are induced indirectly by granuloid feedback to the stem cell pool. The model calculations further show that the synchrony hypothesis of bone marrow maturation can quantitatively explain the following experimental results: (1) the maintenance of stable cycles of granuloid and erythroid bone marrow and blood cells with a period of approximately 14 d; (2) the disappearance of granuloid and erythroid cycles during the administration of the colony stimulating factor rhG-CSF; (3) the reappearance of oscillations when the administration of CSF is discontinued; (4) the cessation of cycles during endotoxin application; and (5) the persistence of cycles during erythroid manipulations (bleeding anaemia, hypoxia, hypertransfusion). We therefore conclude that cyclic haemopoiesis is not caused by a defect in the regulatory control system but by an unusual maturation process.     

Calcium signaling induced by adhesion mediates protein tyrosine phosphorylation and is independent of pHi

Our goal was to evaluate early signaling events that occur as epithelial cells make initial contact with a substrate and to correlate them with phosphorylation. The corneal epithelium was chosen to study signaling events that occur with adhesion because it represents a simple system in which the tissue adheres to a basal lamina, is avascular, and is bathed by a tear film in which changes in the local environment are hypothesized to alter signaling. To perform these experiments we developed a novel adhesion assay to capture the changes in intracellular Ca(2+) and pH that occur as a cell makes its initial contact with a substrate. The first transient cytosolic Ca(2+) peak was detected only as the cell made contact with the substrate and was demonstrated using fluorimetric assays combined with live cell imaging. We demonstrated that this transient Ca(2+) peak always preceded a cytoplasmic alkalization. When the intracellular environment was modified, the initial response was altered. Pretreatment with 1,2-bis(o-aminophenoxy)ethane-N,N, N'N'-tetraacetic acid (BAPTA), an intracellular chelator, inhibited Ca(2+) mobilization, whereas benzamil altered the duration of the oscillations. Thapsigargin caused an initial Ca(2+) release followed by a long attenuated response. An inositol triphosphate analog induced a large initial response, whereas heparin inhibited Ca(2+) oscillations. Inhibitors of tyrosine phosphorylation did not alter the initial mobilization of cytosolic Ca(2) but clearance of cytosolic Ca(2+) was inhibited. Exposing corneal epithelial cells to BAPTA, benzamil, or thapsigargin also attenuated the phosphorylation of the focal adhesion protein paxillin. However, although heparin inhibited Ca(2+) oscillations, it did not alter phosphorylation of paxillin. These studies demonstrate that the initial contact that a cell makes with a substrate modulates the intracellular environment, and that changes in Ca(2+) mobilization can alter later signaling events such as the phosphorylation of specific adhesion proteins. These findings may have implications for wound repair and development.     

Effects of 5-azacytidine and trichostatin A on dendritic cell maturation

Maturation of dendritic cells (DC) towards functional antigen-presenting cells is a complex process, the regulation of which may also involve epigenetic mechanisms. Thus, it is of interest to investigate how gene expression changes during DC maturation can be influenced with epigenetic agents, such as DNA methyltransferase or histone deacetylase inhibitors. Here, we document the effects of DNA methyltransferase inhibitor 5-azacytidine (5AC) and histone deacetylase inhibitor trichostatin A (TSA) on the murine bone marrow-derived, as well as on the human monocyte-derived DC maturation. The major impact of 5AC and TSA on the DC maturation process consisted in the inhibition of unmethylated CpG oligodeoxynucleotide (CpG ODN) 1826 or LPS-induced activation of pro- and anti-inflammatory cytokine gene expression activation. In the in vitro studies, TSA but not 5AC significantly reduced the capacity of the peptide-pulsed DC to induce total spleen as well as CD8(+) or CD4(+) cell proliferation. IFNγ production by the specific CD4(+) spleen cells co-cultured with TSA- but not with 5AC-treated DC was lower, as compared to the cytokine production after co-cultivation with untreated mature DC. Collectively, these results demonstrate the potential of epigenetic agents, which are under intensive investigation as promising anti-tumour agents, to hamper the immune response induction through their inhibitory effects on DC.     

Computational model for effects of ligand/receptor binding properties on interleukin-2 trafficking dynamics and T cell proliferation response

Multisubunit cytokine receptors such as the heterotrimeric receptor for interleukin-2 (IL-2) are ubiquitous in hematopoeitic cell types of importance in biotechnology and are crucial regulators of cell proliferation and differentiation behavior. Dynamics of cytokine/receptor endocytic trafficking can significantly impact cell responses through effects of receptor down-regulation and ligand depletion, and in turn are governed by ligand/receptor binding properties. We describe here a computational model for trafficking dynamics of the IL-2 receptor (IL-2R) system, which is able to predict T cell proliferation responses to IL-2. This model comprises kinetic equations describing binding, internalization, and postendocytic sorting of IL-2 and IL-2R, including an experimentally derived dependence of cell proliferation rate on these properties. Computational results from this model predict that IL-2 depletion can be reduced by decreasing its binding affinity for the IL-2R betagamma subunit relative to the alpha subunit at endosomal pH, as a result of enhanced ligand sorting to recycling vis-à-vis degradation, and that an IL-2 analogue with such altered binding properties should exhibit increased potency for stimulating the T cell proliferation response. These results are in agreement with our recent experimental findings for the IL-2 analogue termed 2D1 [Fallon, E. M. et al. J. Biol. Chem. 2000, 275, 6790-6797]. Thus, this type of model may enable prediction of beneficial cytokine/receptor binding properties to aid development of molecular design criteria for improvements in applications such as in vivo cytokine therapies and in vitro hematopoietic cell bioreactors.     

Apoptosis-independent functions of killer caspases

Caspases are well known for their role in the execution of the apoptotic program by cleaving specific target proteins, leading to the dismantling of the cell, as well as for mediating cytokine maturation. Recent work has highlighted novel non-apoptotic activities of apoptotic caspases. These reports indicate that caspases are much more versatile enzymes than we originally expected. In addition to regulating cell survival and cytokine maturation, caspases may be involved in regulating cell differentiation, cell proliferation, spreading and receptor internalization.     

Calcium oscillations induced by lindane in peritoneal macrophages of mice: control by the maturation stage of the macrophage

Mouse resident peritoneal macrophages loaded with Fluo-3 were examined for changes in cytosolic calcium concentration ([Ca2+]i) after stimulation with gamma-hexachlorocyclohexane (Lindane or gamma-HCCH). These studies, realized on macrophage populations, or single cells, by digital imaging microscopy, sought to determine the role of calcium influx on cyclical changes according to maturation stages of macrophages. Single cell analysis of [Ca2+]i changes in macrophages, after gamma-HCCH exposure in 600 microM extracellular calcium, demonstrated that: 1) these [Ca2+]i variations were asynchronous oscillations with the same frequency (1.7 min-1), and 2) these [Ca2+]i variations in macrophages were not at the same [Ca2+]i level. This heterogeneity could be correlated to a cell size partition of the macrophage population (10.1 +/- 0.44 and 11.45 +/- 0.43 microns). In the presence of 100 microM calcium, gamma-HCCH induced a calcium influx into the two subpopulations, but the calcium oscillations appeared only in small macrophages. In the largest ones, [Ca2+]i slowly decreased back down to the basal level. The cell size variation could be correlated to a phenotypic heterogeneity, linked to the differenciation stage of the cell. Peroxydase activity showed that small macrophages were in fact exudate macrophages and the largest ones were resident macrophages. Inhibition of the oscillatory patterns by a decrease in the extracellular calcium concentration ([Ca2+]ext) or by lanthanum chloride (LaCl3) addition is indicative of the important role of calcium influx in the triggering of oscillations. The calcium influx was transient and induced inositol phosphate (InsP3) production in macrophages. The maintainance of these calcium oscillations depended on calcium mobilization from intracellular calcium stores by InsP3, since neomycin and 8-(diethylamino) octyl 3,4,5-trimethoxybenzoate (TMB-8) abolished the oscillations. gamma-HCCH induced a transient calcium entry which triggered phospholipase C activation and the associated [Ca2+]i oscillations. However, we showed that differences in cell responses were observed in relationship with the differentiation stage of the mouse peritoneal macrophages, and with the extracellular calcium concentration.     

Deconstructing the role of myosin contractility in force fluctuations within focal adhesions

Force fluctuations exhibited in focal adhesions that connect a cell to its extracellular environment point to the complex role of the underlying machinery that controls cell migration. To elucidate the explicit role of myosin motors in the temporal traction force oscillations, we vary the contractility of these motors in a dynamical model based on the molecular clutch hypothesis. As the contractility is lowered, effected both by changing the motor velocity and the rate of attachment/detachment, we show analytically in an experimentally relevant parameter space, that the system goes from decaying oscillations to stable limit cycle oscillations through a supercritical Hopf bifurcation. As a function of the motor activity and the number of clutches, the system exhibits a rich array of dynamical states. We corroborate our analytical results with stochastic simulations of the motor-clutch system. We obtain limit cycle oscillations in the parameter regime as predicted by our model. The frequency range of oscillations in the average clutch and motor deformation compares well with experimental results.     

Mathematical modeling of human granulopoiesis: the possible importance of regulated apoptosis

Steady state human granulopoiesis was modeled by a convection-reaction differential equation of the Rubinow type for the bone marrow granulocyte precursors and an ordinary differential equation for the blood granulocytes. Measured values reported from several laboratories were used as sources for the model proliferation, maturation, and mobilization rates. Due to the large variability in the measured input data, four alternative models were constructed initially, each one with a specific combination of proliferation rate and maturation rate. They were all able to produce output values for the bone marrow neutrophil count and turnover rate close to accepted data, but neither of them could reproduce good values for the differential fractions of the neutrophil precursor stages. The model output was especially sensitive to changes in transit time in the mitotic relative to the postmitotic precursor compartments. When the net proliferation rate was modeled to optimize the bone marrow differential fractions according to published data, the total bone marrow neutrophil count would not fit with published data. However, a composite model optimizing differential fractions, bone marrow neutrophil count, and turnover rate yielded plausible output values and a reduced proliferation rate in the myelocyte stage. This result opens for a possibly substantial apoptosis rate at the myelocyte stage in accordance with results from earlier investigators. However, the result was based on a special choice of precursor transit times, taken from the literature. More precise data concerning granulocyte precursor cycle times, transit times, and differential fractions would radically improve the model's ability to clarify the role of apoptosis during granulocyte production and storage.     

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.     

Cathelicidin antimicrobial peptides block dendritic cell TLR4 activation and allergic contact sensitization

Cathelicidins are antimicrobial peptides of the innate immune system that establish an antimicrobial barrier at epithelial interfaces and have been proposed to have a proinflammatory function. We studied the role of cathelicidin in allergic contact dermatitis, a model requiring dendritic cells of the innate immune response and T cells of the adaptive immune response. Deletion of the murine cathelicidin gene Cnlp enhanced an allergic contact response, whereas local administration of cathelicidin before sensitization inhibited the allergic response. Cathelicidins inhibited TLR4 but not TLR2 mediated induction of dendritic cell maturation and cytokine release, and this inhibition was associated with an alteration of cell membrane function and structure. Further analysis in vivo connected these observations because inhibition of sensitization by exogenous cathelicidin was dependent on the presence of functional TLR4. These observations provide evidence that cathelicidin antimicrobial peptides mediate an anti-inflammatory response in part by their activity at the membrane.     

Structured population on two patches: modeling dispersal and delay

We derive from the age-structured model a system of delay differential equations to describe the interaction of spatial dispersal (over two patches) and time delay (arising from the maturation period). Our model analysis shows that varying the immature death rate can alter the behavior of the homogeneous equilibria, leading to transient oscillations around an intermediate equilibrium and complicated dynamics (in the form of the coexistence of possibly stable synchronized periodic oscillations and unstable phase-locked oscillations) near the largest equilibrium.     

Targeting IL-10 in Auto-immune Diseases

IL-10 is a multifunctional cytokine secreted by a variety of cells. It not only inhibits activation of monocyte/macrophage system and synthesis of monocyte cytokine and inflammatory cytokine but also promotes the proliferation and maturation of non-monocyte-dependent T cell, stimulating proliferation of antigen-specific B cell. Increasing evidence indicates that IL-10 plays an important role in both the onset and development of auto-immune diseases, such as systemic lupus erythematosus (SLE), rheumatoid arthritis (RA), Sjogren’s syndrome (SS), multiple sclerosis (MS), Crohn’s disease (CD), and psoriasis. However, the exact mechanisms of IL-10 in auto-immune diseases remain unclear. In the present review, we will summarize the biological effects of IL-10, as well as its role and therapeutic potential in auto-immune diseases.     

Autonomous oscillations in Saccharomyces cerevisiae during batch cultures on trehalose

We report that autonomous oscillations, which usually happen in aerobic glucose-limited continuous cultures of yeast at low dilution rate, were also observed in trehalose discontinuous cultures of Saccharomyces cerevisiae. This unexpected oscillatory behaviour was therefore examined using fast Fourier transformation of online gas measurements. This robust mathematical analysis underlined the existence of two types of oscillation. The first was found to be linked to the cell cycle because (a) the periodicity corresponded to a fraction of the generation time and (b) the oscillations were accompanied by a transient increase in the budding index, mobilization of storage carbohydrates, and fermentative activity. Moreover, these oscillations occurred in a range of specific growth rates between 0.04 and 0.15 h(-1). All these criteria were consistent with the cell-cycle-related metabolic oscillations observed in the same range of growth rates in glucose-limited continuous cultures. The second type were short-period respiratory oscillations, independent of the specific growth rate. Both types of oscillation were found to take place consecutively and/or simultaneously during batch culture on trehalose. In addition, mobilization of intracellular trehalose emerged as a key parameter for the sustainability of these autonomous oscillations as they were no longer observed in a mutant defective in neutral trehalase activity. We propose that batch culture on trehalose may be an excellent device for further investigation of the molecular mechanisms that underlie autonomous oscillations in yeast.     

Oscillations in the lateral pressure of lipid monolayers induced by nonlinear chemical dynamics of the second messengers MARCKS and protein kinase C

The binding of the MARCKS peptide to the lipid monolayer containing PIP₂ increases the lateral pressure of the monolayer. The unbinding dynamics modulated by protein kinase C leads to oscillations in lateral pressure of lipid monolayers. These periodic dynamics can be attributed to changes in the crystalline lipid domain size. We have developed a mathematical model to explain these observations based on the changes in the physical structure of the monolayer by the translocation of MARCKS peptide. The model indicates that changes in lipid domain size drives these oscillations. The model is extended to an open system that sustains chemical oscillations.     

Modeling the interrelations between the calcium oscillations and ER membrane potential oscillations

A refined electrochemical model accounting for intracellular calcium oscillations and their interrelations with oscillations of the potential difference across the membrane of the endoplasmic reticulum (ER) or other intracellular calcium stores is established. The ATP dependent uptake of Ca2+ from the cytosol into the ER, the Ca2+ release from the ER through channels following a calcium-induced calcium release mechanism, and a potential-dependent Ca2+ leak flux out of the ER are included in the model and described by plausible rate laws. The binding of calcium to specific proteins such as calmodulin is taken into account. The quasi-electroneutrality condition allows us to express the transmembrane potential in terms of the concentrations of cytosolic calcium and free binding sites on proteins, which are the two independent variables of the model. We include monovalent ions in the model, because they make up a considerable portion in the balance of electroneutrality. As the permeability of the endoplasmic membrane for these ions is much higher than that for calcium ions, we assume the former to be in Nernst equilibrium. A stability analysis of the steady-state solutions (which are unique or multiple depending on parameter values) is carried out and the Hopf bifurcation leading from stable steady states to self-sustained oscillations is analysed with the help of appropriate mathematical techniques. The oscillations obtained by numerical integration exhibit the typical spike-like shape found in experiments and reasonable values of frequency and amplitude. The model describes the process of switching between stationary and pulsatile regimes as well as changes in oscillation frequency upon parameter changes. It turns out that calcium oscillations can arise without a permanent influx of calcium into the cell, when a calcium-buffering system such as calmodulin is included.