Modeling erythroblastic islands: Using a hybrid model to assess the function of central macrophage

Pharmacokinetic/pharmacodynamic model of a methionine starvation based anti-cancer drug

A new therapeutic approach against cancer is developed by the firm Erytech. This approach is based on starved cancer cells of an amino acid essential to their growth (the L-methionine). The depletion of plasma methionine level can be induced by an enzyme, the methionine-γ-lyase. The new therapeutic formulation is a suspension of erythrocytes encapsulating the activated enzyme. Our work reproduces a preclinical trial of a new anti-cancer drug with a mathematical model and numerical simulations in order to replace animal experiments and to have a deeper insight on the underlying processes. With a combination of a pharmacokinetic/pharmacodynamic model for the enzyme, substrate, and co-factor with a hybrid model for tumor, we develop a "global model" that can be calibrated to simulate different human cancer cell lines. The hybrid model includes a system of ordinary differential equations for the intracellular concentrations, partial differential equations for the concentrations of nutrients and drugs in the extracellular matrix, and individual based model for cancer cells. This model describes cell motion, division, differentiation, and death determined by the intracellular concentrations. The models are developed on the basis of experiments in mice carried out by Erytech. Parameters of the pharmacokinetics model were determined by fitting a part of experimental data on the concentration of methionine in blood. Remaining experimental protocols effectuated by Erytech were used to validate the model. The validated PK model allowed the investigation of pharmacodynamics of cell populations. Numerical simulations with the global model show cell synchronization and proliferation arrest due to treatment similar to the available experiments. Thus, computer modeling confirms a possible effect of treatment based on the decrease of methionine concentration. The main goal of the study is the development of an integrated pharmacokinetic/pharmacodynamic model for encapsulated methioninase and of a mathematical model of tumor growth/regression in order to determine the kinetics of L-methionine depletion after co-administration of Erymet product and Pyridoxine.

Stochastic intracellular regulation can remove oscillations in a model of tissue growth

The work is devoted to the analysis of cell population dynamics where cells make a choice between differentiation and apoptosis. This choice is based on the values of intracellular proteins whose concentrations are described by a system of ordinary differential equations with bistable dynamics. Intracellular regulation and cell fate are controlled by the extracellular regulation through the number of differentiated cells. It is shown that the total cell number necessarily oscillates if the initial condition in the intracellular regulation is fixed. These oscillations can be suppressed if the initial condition is a random variable with a sufficiently large variation. Thus, the result of the work suggests a possible answer to the question about the role of stochasticity in the intracellular regulation.

Human erythrocytes: cytoskeleton and its origin

In the last few years, erythrocytes have emerged as the main determinant of blood rheology. In mammals, these cells are devoid of nuclei and are, therefore, unable to divide. Consequently, all circulating erythrocytes come from erythropoiesis, a process in the bone marrow in which several modifications are induced in the expression of membrane and cytoskeletal proteins, and different vertical and horizontal interactions are established between them. Cytoskeleton components play an important role in this process, which explains why they and the interaction between them have been the focus of much recent research. Moreover, in mature erythrocytes, the cytoskeleton integrity is also essential, because the cytoskeleton confers remarkable deformability and stability on the erythrocytes, thus enabling them to undergo deformation in microcirculation. Defects in the cytoskeleton produce changes in erythrocyte deformability and stability, affecting cell viability and rheological properties. Such abnormalities are seen in different pathologies of special interest, such as different types of anemia, hypertension, and diabetes, among others. This review highlights the main findings in mammalian erythrocytes and their progenitors regarding the presence, conformation and function of the three main components of the cytoskeleton: actin, intermediate filaments, and tubulin.

Calibration, Selection and Identifiability Analysis of a Mathematical Model of the in vitro Erythropoiesis in Normal and Perturbed Contexts

The in vivo erythropoiesis, which is the generation of mature red blood cells in the bone marrow of whole organisms, has been described by a variety of mathematical models in the past decades. However, the in vitro erythropoiesis, which produces red blood cells in cultures, has received much less attention from the modelling community. In this paper, we propose the first mathematical model of in vitro erythropoiesis. We start by formulating different models and select the best one at fitting experimental data of in vitro erythropoietic differentiation obtained from chicken erythroid progenitor cells. It is based on a set of linear ODE, describing 3 hypothetical populations of cells at different stages of differentiation. We then compute confidence intervals for all of its parameters estimates, and conclude that our model is fully identifiable. Finally, we use this model to compute the effect of a chemical drug called Rapamycin, which affects all states of differentiation in the culture, and relate these effects to specific parameter variations. We provide the first model for the kinetics of in vitro cellular differentiation which is proven to be identifiable. It will serve as a basis for a model which will better account for the variability which is inherent to the experimental protocol used for the model calibration.

Differential tissue expression of erythroblast macrophage protein in a MRL/lpr mouse model of lupus

OBJECTIVE

The objective of this study was to observe the expression features of erythroblast macrophage protein (EMP) between the tissues of MRL/lpr mice, a mouse model of systemic lupus erythematosus (SLE), and control mice.

METHODS

We examined the serum ANA in both mice groups through indirect immunofluorescence (IIF). Expression features of EMP in bone marrow, liver, renal, spleen, brain, and lung tissues of the MRL/lpr mice and control mice groups were followed using quantitative real-time polymerase chain reaction (Q-PCR). Meanwhile, the expression of EMP was located through immunohistochemical (IHC) studies and the expressive cell identified through double immunofluorescent labeling.

RESULTS

IIF showed that lupus mice have strong positive fluorescence, but no significant fluorescence was observed in control mice. Q-PCR detection revealed that EMP was expressed in the marrow, liver, renal, spleen, lung, and brain tissues of lupus mice. The highest levels were observed in the bone marrow, but there was no statistical difference between these tissues. EMP mRNA expression in the liver (t = 2.747, p = 0.01) and bone marrow (t = 3.853, p = 0.008) of lupus mice was significantly higher than in the control mice. However, no differences in EMP mRNA expression were observed in the renal, spleen, lung, and brain tissues between the lupus and control mice (p > 0.05). In addition, the IHC results showed that EMP protein is ubiquitously expressed in all of the tissues of the lupus and control mice. The positive expression rate in the bone marrow and liver tissues of the lupus mice was higher than in the control mice, but without an obvious difference in the other tissues. The double IF staining method shows that EMP protein was expressed in macrophages in the tissues of the lupus mice and the control mice.

CONCLUSIONS

Our data showed that EMP is ubiquitously expressed in macrophages at all of the tissues of the lupus and control mice. However, the expression of EMP in bone marrow and liver tissues of lupus mice was higher than in the control mice, which indicates that EMP may be important in the development of SLE.

Mathematical model of T-cell lymphoblastic lymphoma: disease, treatment, cure or relapse of a virtual cohort of patients

T lymphoblastic lymphoma (T-LBL) is a rare type of lymphoma with a good prognosis with a remission rate of 85%. Patients can be completely cured or can relapse during or after a 2-year treatment. Relapses usually occur early after the remission of the acute phase. The median time of relapse is equal to 1 year, after the occurrence of complete remission (range 0.2-5.9 years) (Uyttebroeck et al., 2008). It can be assumed that patients may be treated longer than necessary with undue toxicity.The aim of our model was to investigate whether the duration of the maintenance therapy could be reduced without increasing the risk of relapses and to determine the minimum treatment duration that could be tested in a future clinical trial.We developed a mathematical model of virtual patients with T-LBL in order to obtain a proportion of virtual relapses close to the one observed in the real population of patients from the EuroLB database. Our simulations reproduced a 2-year follow-up required to study the onset of the disease, the treatment of the acute phase and the maintenance treatment phase.

Hybrid approach to model the spatial regulation of T cell responses

BACKGROUND

Moving from the molecular and cellular level to a multi-scale systems understanding of immune responses requires the development of novel approaches to integrate knowledge and data from different biological levels into mechanism-based integrative mathematical models. The aim of our study is to present a methodology for a hybrid modelling of immunological processes in their spatial context.

METHODS

A two-level hybrid mathematical model of immune cell migration and interaction integrating cellular and organ levels of regulation for a 2D spatial consideration of idealized secondary lymphoid organs is developed. It considers the population dynamics of antigen-presenting cells, CD4 + and CD8 + T lymphocytes in naive-, proliferation- and differentiated states. Cell division is assumed to be asymmetric and regulated by the extracellular concentration of interleukin-2 (IL-2) and type I interferon (IFN), together controlling the balance between proliferation and differentiation. The cytokine dynamics is described by reaction-diffusion PDEs whereas the intracellular regulation is modelled with a system of ODEs.

RESULTS

The mathematical model has been developed, calibrated and numerically implemented to study various scenarios in the regulation of T cell immune responses to infection, in particular the change in the diffusion coefficient of type I IFN as compared to IL-2. We have shown that a hybrid modelling approach provides an efficient tool to describe and analyze the interplay between spatio-temporal processes in the emergence of abnormal immune response dynamics.

DISCUSSION

Virus persistence in humans is often associated with an exhaustion of T lymphocytes. Many factors can contribute to the development of exhaustion. One of them is associated with a shift from a normal clonal expansion pathway to an altered one characterized by an early terminal differentiation of T cells. We propose that an altered T cell differentiation and proliferation sequence can naturally result from a spatial separation of the signaling events delivered via TCR, IL-2 and type I IFN receptors. Indeed, the spatial overlap of the concentration fields of extracellular IL-2 and IFN in lymph nodes changes dynamically due to different migration patterns of APCs and CD4 + T cells secreting them.

CONCLUSIONS

The proposed hybrid mathematical model of the immune response represents a novel analytical tool to examine challenging issues in the spatio-temporal regulation of cell growth and differentiation, in particular the effect of timing and location of activation signals.

Human Cord Blood and Bone Marrow CD34+ Cells Generate Macrophages That Support Erythroid Islands

Recently, we developed a small molecule responsive hyperactive Mpl-based Cell Growth Switch (CGS) that drives erythropoiesis associated with macrophages in the absence of exogenous cytokines. Here, we compare the physical, cellular and molecular interaction between the macrophages and erythroid cells in CGS expanded CD34+ cells harvested from cord blood, marrow or G-CSF-mobilized peripheral blood. Results indicated that macrophage based erythroid islands could be generated from cord blood and marrow CD34+ cells but not from G-CSF-mobilized CD34+ cells. Additional studies suggest that the deficiency resides with the G-CSF-mobilized CD34+ derived monocytes. Gene expression and proteomics studies of the in vitro generated erythroid islands detected the expression of erythroblast macrophage protein (EMP), intercellular adhesion molecule 4 (ICAM-4), CD163 and DNASE2. 78% of the erythroblasts in contact with macrophages reached the pre reticulocyte orthochromatic stage of differentiation within 14 days of culture. The addition of conditioned medium from cultures of CD146+ marrow fibroblasts resulted in a 700-fold increase in total cell number and a 90-fold increase in erythroid cell number. This novel CD34+ cell derived erythroid island may serve as a platform to explore the molecular basis of red cell maturation and production under normal, stress and pathological conditions.

Travelling Waves of Cell Differentiation

The paper is devoted to modelling of cell differentiation in an initially homogeneous cell population. The mechanism which provides coexistence of two cell lineages in the initially homogeneous cell population is suggested. If cell differentiation is initiated locally in space in the population of undifferentiated cells, it can propagate as a travelling wave converting undifferentiated cells into differentiated ones. We suggest a model of this process which takes into account intracellular regulation, extracellular regulation and different cell types. They include undifferentiated cells and two types of differentiated cells. When a cell differentiates, its choice between two types of differentiated cells is determined by the concentrations of intracellular proteins. Differentiated cells can either stimulate differentiation into their own cell lineage or into another cell lineage. In the case of the positive feedback, only one lineage of differentiated cells will finally appear. In the case of negative feedback, both of them can coexist. In this case a periodic spatial pattern emerges behind the wave.

Stochastic modeling of stress erythropoiesis using a two-type age-dependent branching process with immigration

The erythroid lineage is a particularly sensitive target of radiation injury. We model the dynamics of immature (BFU-E) and mature (CFU-E) erythroid progenitors, which have markedly different kinetics of recovery, following sublethal total body irradiation using a two-type reducible age-dependent branching process with immigration. Properties of the expectation and variance of the frequencies of both types of progenitors are presented. Their explicit expressions are derived when the process is Markovian, and their asymptotic behavior is identified in the age-dependent (non-Markovian) case. Analysis of experimental data on the kinetics of BFU-E and CFU-E reveals that the probability of self-renewal increases transiently for both cell types following sublethal irradiation. In addition, the probability of self-renewal increased more for CFU-E than for BFU-E. The strategy adopted by the erythroid lineage ensures replenishment of the BFU-E compartment while optimizing the rate of CFU-E recovery. Finally, our analysis also indicates that radiation exposure causes a delay in BFU-E recovery consistent with injury to the hematopoietic stem/progenitor cell compartment that give rise to BFU-E. Erythroid progenitor self-renewal is thus an integral component of the recovery of the erythron in response to stress.

Erythroblastic islands in the bone marrow of patients with immune-related pancytopenia

BACKGROUND

Immune-related pancytopenia (IRP) is characterized by pancytopenia caused by autoantibody-mediated bone marrow destruction or suppression. The bone marrows of IRP patients have remarkably increased erythroblastic islands (EIs).

METHODOLOGY AND PRINCIPAL FINDINGS

We determined the immunoglobulin G (IgG) autoantibodies in some parts of EIs of IRP patients using immunofluorescence to investigate the biological function of EIs with IgG in the pathophysiology of IRP. The dominant class of autoantibodies detected in mononuclear cells was IgG (CD34 IgG, CD15 IgG, and GlycoA IgG), specifically IgG on GlycoA-positive cells (GlycoA IgG). Results show that extravascular hemolysis occurred in IRP through IgG autoantibodies in the EIs. These data included a high percentage of reticulocytes in the peripheral blood, hypererythrocytosis in the bone marrow, and high serum bilirubin. Furthermore, we examined the macrophages in the bone marrow of IRP patients. The results show that the number of activated macrophages relatively increased, and the phagocytic activity of macrophages significantly increased.

CONCLUSIONS AND SIGNIFICANCE

Increased EIs with IgG were the sites of erythroblast phagocytosis by the activated macrophages, rather than erythropoietic niches. The IgG autoantibodies in the EIs possibly functioned as adhesion molecules for a ring of erythroblasts around the macrophages, thereby forming morphologic EIs.

The role of spatial organization of cells in erythropoiesis

Erythropoiesis, the process of red blood cell production, occurs mainly in the bone marrow. The functional unit of mammalian erythropoiesis, the erythroblastic island, consists of a central macrophage surrounded by adherent erythroid progenitor cells (CFU-E/Pro-EBs) and their differentiating progeny, the erythroblasts. Central macrophages display on their surface or secrete various growth or inhibitory factors that influence the fate of the surrounding erythroid cells. CFU-E/Pro-EBs have three possible fates: (a) expansion of their numbers without differentiation, (b) differentiation into reticulocytes that are released into the blood, (c) death by apoptosis. CFU-E/Pro-EB fate is under the control of a complex molecular network, that is highly dependent upon environmental conditions in the erythroblastic island. In order to assess the functional role of space coupled with the complex network behavior in erythroblastic islands, we developed hybrid discrete-continuous models of erythropoiesis. A model was developed in which cells are considered as individual physical objects, intracellular regulatory networks are modeled with ordinary differential equations and extracellular concentrations by partial differential equations. We used the model to investigate the impact of an important difference between humans and mice in which mature late-stage erythroblasts produce the most Fas-ligand in humans, whereas early-stage erythroblasts produce the most Fas-ligand in mice. Although the global behaviors of the erythroblastic islands in both species were similar, differences were found, including a relatively slower response time to acute anemia in humans. Also, our modeling approach was very consistent with in vitro culture data, where the central macrophage in reconstituted erythroblastic islands has a strong impact on the dynamics of red blood cell production. The specific spatial organization of erythroblastic islands is key to the normal, stable functioning of mammalian erythropoiesis, both in vitro and in vivo. Our model of a simplified molecular network controlling cell decision provides a realistic functional unit of mammalian erythropoiesis that integrates multiple microenvironmental influences within the erythroblastic island with those of circulating regulators of erythropoiesis, such as EPO and glucocorticosteroids, that are produced at remote sites.

Hybrid model of erythropoiesis

A hybrid model of cell dynamics is presented. It is illustrated by model examples and applied to study erythropoiesis (red blood cell production). In this approach, cells are considered as discrete objects while intra-cellular proteins and extra-cellular biochemical substances are described with continuous models. Spatial organization of erythropoiesis occurring in specific structures of the bone marrow, called erythroblastic island, is investigated.