The role of spatial organization of cells in erythropoiesis

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.

Erythroblastic islands foster granulopoiesis in parallel to terminal erythropoiesis

The erythroblastic island (EBI), composed of a central macrophage surrounded by maturing erythroblasts, is the erythroid precursor niche. Despite numerous studies, its precise composition is still unclear. Using multispectral imaging flow cytometry, in vitro island reconstitution, and single-cell RNA sequencing of adult mouse bone marrow (BM) EBI-component cells enriched by gradient sedimentation, we present evidence that the CD11b+ cells present in the EBIs are neutrophil precursors specifically associated with BM EBI macrophages, indicating that erythro-(myelo)-blastic islands are a site for terminal granulopoiesis and erythropoiesis. We further demonstrate that the balance between these dominant and terminal differentiation programs is dynamically regulated within this BM niche by pathophysiological states that favor granulopoiesis during anemia of inflammation and favor erythropoiesis after erythropoietin stimulation. Finally, by molecular profiling, we reveal the heterogeneity of EBI macrophages by cellular indexing of transcriptome and epitope sequencing of mouse BM EBIs at baseline and after erythropoietin stimulation in vivo and provide a searchable online viewer of these data characterizing the macrophage subsets serving as hematopoietic niches. Taken together, our findings demonstrate that EBIs serve a dual role as niches for terminal erythropoiesis and granulopoiesis and the central macrophages adapt to optimize production of red blood cells or neutrophils.

Improving cancer treatments via dynamical biophysical models

Despite significant advances in oncological research, cancer nowadays remains one of the main causes of mortality and morbidity worldwide. New treatment techniques, as a rule, have limited efficacy, target only a narrow range of oncological diseases, and have limited availability to the general public due their high cost. An important goal in oncology is thus the modification of the types of antitumor therapy and their combinations, that are already introduced into clinical practice, with the goal of increasing the overall treatment efficacy. One option to achieve this goal is optimization of the schedules of drugs administration or performing other medical actions. Several factors complicate such tasks: the adverse effects of treatments on healthy cell populations, which must be kept tolerable; the emergence of drug resistance due to the intrinsic plasticity of heterogeneous cancer cell populations; the interplay between different types of therapies administered simultaneously. Mathematical modeling, in which a tumor and its microenvironment are considered as a single complex system, can address this complexity and can indicate potentially effective protocols, that would require experimental verification. In this review, we consider classical methods, current trends and future prospects in the field of mathematical modeling of tumor growth and treatment. In particular, methods of treatment optimization are discussed with several examples of specific problems related to different types of treatment.

Active hematopoiesis triggers exosomal release of PRDX2 that promotes osteoclast formation

Hematopoietic disorders, particularly hemolytic anemias, commonly lead to bone loss. We have previously reported that actively proliferating cancer cells stimulate osteoclastogenesis from late precursors in a RANKL-independent manner. We theorized that cancer cells exploit the physiological role of bone resorption to support expanding hematopoietic bone marrow and examined if hematopoietic cells can trigger osteoclastogenesis. Using phlebotomy-induced acute anemia in mice, we found strong correlation between augmented erythropoiesis and increased osteoclastogenesis. Conditioned medium (CM) from K562 erythroleukemia cells and primary mouse erythroblasts stimulated osteoclastogenesis when added to RANKL-primed precursors from mouse bone marrow or RAW264.7 cells. Using immunoblotting and mass spectrometry, PRDX2 was identified as a factor produced by erythroid cells in vitro and in vivo. PRDX2 was detected in K562-derived exosomes, and inhibiting exosomal release significantly decreased the osteoclastogenic capacity of K562 CM. Recombinant PRDX2 induced osteoclast formation from RANKL-primed primary or RAW 264.7 precursors to levels comparable to achieved with continuous RANKL treatment. Thus, increased bone marrow erythropoiesis secondary to anemia leads to upregulation of PRDX2, which is released in the exosomes and acts to induce osteoclast formation. Increased bone resorption by the osteoclasts expands bone marrow cavity, which likely plays a supporting role to increase blood cell production.

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.

On the Effect of Age-Dependent Mortality on the Stability of a System of Delay-Differential Equations Modeling Erythropoiesis

We present an age-structured model for erythropoiesis in which the mortality of mature cells is described empirically by a physiologically realistic probability distribution of survival times. Under some assumptions, the model can be transformed into a system of delay differential equations with both constant and distributed delays. The stability of the equilibrium of this system and possible Hopf bifurcations are described for a number of probability distributions. Physiological motivation and interpretation of our results are provided.

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.

Mathematical Modeling Reveals That the Administration of EGF Can Promote the Elimination of Lymph Node Metastases by PD-1/PD-L1 Blockade

In the advanced stages of cancers like melanoma, some of the malignant cells leave the primary tumor and infiltrate the neighboring lymph nodes (LNs). The interaction between secondary cancer and the immune response in the lymph node represents a complex process that needs to be fully understood in order to develop more effective immunotherapeutic strategies. In this process, antigen-presenting cells (APCs) approach the tumor and initiate the adaptive immune response for the corresponding antigen. They stimulate the naive CD4+ and CD8+ T lymphocytes which subsequently generate a population of helper and effector cells. On one hand, immune cells can eliminate tumor cells using cell-cell contact and by secreting apoptosis inducing cytokines. They are also able to induce their dormancy. On the other hand, the tumor cells are able to escape the immune surveillance using their immunosuppressive abilities. To study the interplay between tumor progression and the immune response, we develop two new models describing the interaction between cancer and immune cells in the lymph node. The first model consists of partial differential equations (PDEs) describing the populations of the different types of cells. The second one is a hybrid discrete-continuous model integrating the mechanical and biochemical mechanisms that define the tumor-immune interplay in the lymph node. We use the continuous model to determine the conditions of the regimes of tumor-immune interaction in the lymph node. While we use the hybrid model to elucidate the mechanisms that contribute to the development of each regime at the cellular and tissue levels. We study the dynamics of tumor growth in the absence of immune cells. Then, we consider the immune response and we quantify the effects of immunosuppression and local EGF concentration on the fate of the tumor. Numerical simulations of the two models show the existence of three possible outcomes of the tumor-immune interactions in the lymph node that coincide with the main phases of the immunoediting process: tumor elimination, equilibrium, and tumor evasion. Both models predict that the administration of EGF can promote the elimination of the secondary tumor by PD-1/PD-L1 blockade.

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.

Bone marrow infiltration by multiple myeloma causes anemia by reversible disruption of erythropoiesis

Multiple myeloma (MM) infiltrates bone marrow and causes anemia by disrupting erythropoiesis, but the effects of marrow infiltration on anemia are difficult to quantify. Marrow biopsies of newly diagnosed MM patients were analyzed before and after four 28-day cycles of non-erythrotoxic remission induction chemotherapy. Complete blood cell counts and serum paraprotein concentrations were measured at diagnosis and before each chemotherapy cycle. At diagnosis, marrow area infiltrated by myeloma correlated negatively with hemoglobin, erythrocytes, and marrow erythroid cells. After successful chemotherapy, patients with less than 30% myeloma infiltration at diagnosis had no change in these parameters, whereas patients with more than 30% myeloma infiltration at diagnosis increased all three parameters. Clinical data were used to develop mathematical models of the effects of myeloma infiltration on the marrow niches of terminal erythropoiesis, the erythroblastic islands (EBIs). A hybrid discrete-continuous model of erythropoiesis based on EBI structure/function was extended to sections of marrow containing multiple EBIs. In the model, myeloma cells can kill erythroid cells by physically destroying EBIs and by producing proapoptotic cytokines. Following chemotherapy, changes in serum paraproteins as measures of myeloma cells and changes in erythrocyte numbers as measures of marrow erythroid cells allowed modeling of myeloma cell death and erythroid cell recovery, respectively. Simulations of marrow infiltration by myeloma and treatment with non-erythrotoxic chemotherapy demonstrate that myeloma-mediated destruction and subsequent reestablishment of EBIs and expansion of erythroid cell populations in EBIs following chemotherapy provide explanations for anemia development and its therapy-mediated recovery in MM patients.

Multi-class and multi-scale models of complex biological phenomena

Computational modeling has significantly impacted our ability to analyze vast (and exponentially increasing) quantities of experimental data for a variety of applications, such as drug discovery and disease forecasting. Single-scale, single-class models persist as the most common group of models, but biological complexity often demands more sophisticated approaches. This review surveys modeling approaches that are multi-class (incorporating multiple model types) and/or multi-scale (accounting for multiple spatial or temporal scales) and describes how these models, and combinations thereof, should be used within the context of the problem statement. We end by highlighting agent-based models as an intuitive, modular, and flexible framework within which multi-scale and multi-class models can be implemented.

Scanning Electron Microscopy Reveals Two Distinct Classes of Erythroblastic Island Isolated from Adult Mammalian Bone Marrow

Erythroblastic islands are multicellular clusters in which a central macrophage supports the development and maturation of red blood cell (erythroid) progenitors. These clusters play crucial roles in the pathogenesis observed in animal models of hematological disorders. The precise structure and function of erythroblastic islands is poorly understood. Here, we have combined scanning electron microscopy and immuno-gold labeling of surface proteins to develop a better understanding of the ultrastructure of these multicellular clusters. The erythroid-specific surface antigen Ter-119 and the transferrin receptor CD71 exhibited distinct patterns of protein sorting during erythroid cell maturation as detected by immuno-gold labeling. During electron microscopy analysis we observed two distinct classes of erythroblastic islands. The islands varied in size and morphology, and the number and type of erythroid cells interacting with the central macrophage. Assessment of femoral marrow isolated from a cavid rodent species (guinea pig, Cavis porcellus) and a marsupial carnivore species (fat-tailed dunnarts, Sminthopsis crassicaudata) showed that while the morphology of the central macrophage varied, two different types of erythroblastic islands were consistently identifiable. Our findings suggest that these two classes of erythroblastic islands are conserved in mammalian evolution and may play distinct roles in red blood cell production.

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.

Anaemia in kidney disease: harnessing hypoxia responses for therapy

Improved understanding of the oxygen-dependent regulation of erythropoiesis has provided new insights into the pathogenesis of anaemia associated with renal failure and has led to the development of novel therapeutic agents for its treatment. Hypoxia-inducible factor (HIF)-2 is a key regulator of erythropoiesis and iron metabolism. HIF-2 is activated by hypoxic conditions and controls the production of erythropoietin by renal peritubular interstitial fibroblast-like cells and hepatocytes. In anaemia associated with renal disease, erythropoiesis is suppressed due to inadequate erythropoietin production in the kidney, inflammation and iron deficiency; however, pharmacologic agents that activate the HIF axis could provide a physiologic approach to the treatment of renal anaemia by mimicking hypoxia responses that coordinate erythropoiesis with iron metabolism. This Review discusses the functional inter-relationships between erythropoietin, iron and inflammatory mediators under physiologic conditions and in relation to the pathogenesis of renal anaemia, as well as recent insights into the molecular and cellular basis of erythropoietin production in the kidney. It furthermore provides a detailed overview of current clinical experience with pharmacologic activators of HIF signalling as a novel comprehensive and physiologic approach to the treatment of anaemia.