A structured population model of clonal selection in acute leukemias with multiple maturation stages

Funding: TS and AM-C were supported by research funding from the German Research Foundation DFG (SFB 873; subproject B08). TL gratefully acknowledges support from the Heidelberg Graduate School (HGS).Recent progress in genetic techniques has shed light on the complex co-evolution of malignant cell clones in leukemias. However, several aspects of clonal selection still remain unclear. In this paper, we present a multi-compartmental continuously structured population model of selection dynamics in acute leukemias, which consists of a system of coupled integro-differential equations. Our model can be analysed in a more efficient way than classical models formulated in terms of ordinary differential equations. Exploiting the analytical tractability of this model, we investigate how clonal selection is shaped by the self-renewal fraction and the proliferation rate of leukemic cells at different maturation stages. We integrate analytical results with numerical solutions of a calibrated version of the model based on real patient data. In summary, our mathematical results formalise the biological notion that clonal selection is driven by the self-renewal fraction of leukemic stem cells and the clones that possess the highest value of this parameter are ultimately selected. Moreover, we demonstrate that the self-renewal fraction and the proliferation rate of non-stem cells do not have a substantial impact on clonal selection. Taken together, our results indicate that interclonal variability in the self-renewal fraction of leukemic stem cells provides the necessary substrate for clonal selection to act upon.PostprintPeer reviewe

Mathematical Modeling of Stem Cell Dynamics in Acute Leukemias

This thesis is devoted to mathematical modeling of acute leukemias, which form a heterogeneous group of severe blood cancers. New models of dynamic behavior of blood forming (hematopoietic) and leukemic cells are developed and studied analytically. Bone marrow aspiration data contributed from the University Hospital of Heidelberg (Prof. Dr. A. D. Ho) and clonal tracking experiments from literature serve as a test scenario for the proposed models. To reflect the compartmental architecture of the hematopoietic and leukemic cell line, the models are represented by systems of nonlinear ordinary differential equations. Different possible modes of interaction between healthy and leukemic cells are proposed such as competition for environmental signals or autonomous leukemic cell growth and competition for marrow space. Extensive analytical studies of system dynamics and the derived criteria for coexistence and out-competition of the different cell types result in biologically meaningful characterizations of the cancer stem cell state by dynamic cell properties. Numerical studies allow to investigate the impact of different cell parameters on the clinical course and patient prognosis. A model-based prognostic marker for survival of relapsing acute myeloid leukemia patients is developed and tested based on clinical data. The obtained results underline the strong impact of leukemia stem cell behavior on the clinical dynamics. Extensions of the models including multiple leukemic clones allow to link experimental observations of clonal evolution to yet not measurable but clinically meaningful cell parameters at different stages of the disease. The models derived in this thesis depend on a quasi-steady state approximation describing the dependence of cytokine concentrations on mature cell density. In the last part of this work it is rigorously shown that solutions depending on the quasi-steady state approximation are close to solutions of a singular perturbation problem including dynamics of the signal molecules as a separate ordinary differential equation that is scaled with a small parameter. L-infinity bounds for the difference of solutions based on the quasi steady state approximation and solutions of the singular perturbation problem are established for the infinite time interval

Emergence of heterogeneity in acute leukemias

Background: Leukemias are malignant proliferative disorders of the blood forming system. Sequencing studies demonstrate that the leukemic cell population consists of multiple clones. The genetic relationship between the different clones, referred to as the clonal hierarchy, shows high interindividual variability. So far, the source of this heterogeneity and its clinical relevance remain unknown. We propose a mathematical model to study the emergence and evolution of clonal heterogeneity in acute leukemias. The model allows linking properties of leukemic clones in terms of self-renewal and proliferation rates to the structure of the clonal hierarchy. Results: Computer simulations imply that the self-renewal potential of the first emerging leukemic clone has a major impact on the total number of leukemic clones and on the structure of their hierarchy. With increasing depth of the clonal hierarchy the self-renewal of leukemic clones increases, whereas the proliferation rates do not change significantly. The emergence of deep clonal hierarchies is a complex process that is facilitated by a cooperativity of different mutations. Conclusion: Comparison of patient data and simulation results suggests that the self-renewal of leukemic clones increases with the emergence of clonal heterogeneity. The structure of the clonal hierarchy may serve as a marker for patient prognosis. Reviewers: This article was reviewed by Marek Kimmel, Tommaso Lorenzi and Tomasz Lipniacki

Discrete and continuum phenotype-structured models for the evolution of cancer cell populations under chemotherapy

Funding: German Research Foundation DFG (SFB 873; subproject B08) (T.S. and A.M.-C); Heidelberg Graduate School (T.L.).We present a stochastic individual-based model for the phenotypic evolution of cancer cell populations under chemotherapy. In particular, we consider the case of combination cancer therapy whereby a chemotherapeutic agent is administered as the primary treatment and an epigenetic drug is used as an adjuvant treatment. The cell population is structured by the expression level of a gene that controls cell proliferation and chemoresistance. In order to obtain an analytical description of evolutionary dynamics, we formally derive a deterministic continuum counterpart of this discrete model, which is given by a nonlocal parabolic equation for the cell population density function. Integrating computational simulations of the individual-based model with analysis of the corresponding continuum model, we perform a complete exploration of the model parameter space. We show that harsher environmental conditions and higher probabilities of spontaneous epimutation can lead to more effective chemotherapy, and we demonstrate the existence of an inverse relationship between the efficacy of the epigenetic drug and the probability of spontaneous epimutation. Taken together, the outcomes of the model provide theoretical ground for the development of anticancer protocols that use lower concentrations of chemotherapeutic agents in combination with epigenetic drugs capable of promoting the re-expression of epigenetically regulated genes.PostprintPeer reviewe

Coupled somatic cell kinetics and germ cell growth: multiscale model-based insight on ovarian follicular development

International audienceThe development of ovarian follicles is a unique instance of a morphogenesis process still occurring during adult life and resulting from the interactions between somatic and germ cells. In mammals, the initiation of follicular development from the pool of resting follicles is characterized by an increase in the oocyte size concomitant with the surrounding somatic cells proliferating to build an avascular tissue called granulosa. We present a stochastic individual-based model describing the first stages of follicular development, where the cell population is structured with respect to age (progression within the cell cycle) and space (radial distance from the oocyte). The model accounts for the molecular dialogue existing between the oocyte and granulosa cells. Three dynamically interacting scales are considered in the model: (i) a microscopic, local scale corresponding to an individual cell embedded in its immediate environment, (ii) a mesoscopic, semi-local scale corresponding to anatomical or functional areas of follicles and (iii) a macroscopic, global scale corresponding to the morphology of the follicle. Numerical simulations are performed to reproduce the 3D morphogenesis of follicles and follow simultaneously the detailed spatial distribution of individual granulosa cells, their organization as concentric layers or functional cell clones and the increase in the follicle size. Detailed quantitative simulation results are provided in the ovine species, in which well characterized genetic mutations lead to a variety of phenotypic follicle morphogenesis. The model can help to explain pathological situations of imbalance between oocyte growth and follicular cell proliferation 1. Introduction. A highly efficient reproductive capacity is a major advantage for species preservation, faced with the natural selection process, and for individuals within species. In mammalian females, ovarian function is the subject of intensive investigations with the aim to improve the reproductive capacity of domestic and wild animal species and to treat ovarian failures leading to infertility in humans. The issues are crucial for both clinical and zootechnical applications. In humans, the prevalence of the polycystic ovarian syndrome, which is a main cause of infertility, has been estimated at up to 10% among reproductive-age women [19]. Improvement of reproductive biotechnologies, including in vitro fertilization, intra-cytoplasmic sperm injection, frozen embryo replacements and egg donation, is a key issue for a better management of reproduction. Improving the knowledge upon ovarian function and its control will help to improve the success of assisted reproductive technologies, hence to prevent ovarian failure or hyperstimulation syndrome in women and to manag

Hindlimb suspension in Wistar rats: Sex-based differences in muscle response

Ground-based animal models have been used extensively to understand the effects of microgravity on various physiological systems. Among them, hindlimb suspension (HLS), developed in 1979 in rats, remains the gold-standard and allows researchers to study the consequences of total unloading of the hind limbs while inducing a cephalic fluid shift. While this model has already brought valuable insights to space biology, few studies have directly compared functional decrements in the muscles of males and females during HLS. We exposed 28 adult Wistar rats (14 males and 14 females) to 14 days of HLS or normal loading (NL) to better assess how sex impacts disuse-induced muscle deconditioning. Females better maintained muscle function during HLS than males, as shown by a more moderate reduction in grip strength at 7 days (males: −37.5 ± 3.1%, females: −22.4 ± 6.5%, compared to baseline), that remains stable during the second week of unloading (males: −53.3 ± 5.7%, females: −22.4 ± 5.5%, compared to day 0) while the males exhibit a steady decrease over time (effect of sex × loading p = 0.0002, effect of sex × time × loading p = 0.0099). This was further supported by analyzing the force production in response to a tetanic stimulus. Further functional analyses using force production were also shown to correspond to sex differences in relative loss of muscle mass and CSA. Moreover, our functional data were supported by histomorphometric analyzes, and we highlighted differences in relative muscle loss and CSA. Specifically, female rats seem to experience a lesser muscle deconditioning during disuse than males thus emphasizing the need for more studies that will assess male and female animals concomitantly to develop tailored, effective countermeasures for all astronauts

Повышение эффективности противопожарной защиты магазина «Fix Price»

Целью работы является усовершенствование системы противопожарной защиты магазина "Fix Price". В выпускной квалификационной работе проведен обзор литературных источников по вопросам состояния проблем обеспечения пожарной безопасности на предприятиях торговли, дан анализ автоматических систем пожаротушения, обоснован выбор автоматической установки пожаротушения тонкораспылённой водой для объекта исследования, произведены расчёты индивидуального пожарного риска.The aim of the work is to improve the fire protection system of the "Fix Price" store. In the final qualifying work, a review of literature sources on the state of problems of fire safety in commercial enterprises is conducted, an analysis of automatic fire extinguishing systems is given, the choice of an automatic fire extinguishing system with thin-sprayed water for the object of research is justified, and calculations of individual fire risk are made