Anna Marciniak-Czochra

Universität Heidelberg, Heidelburg, Baden-Württemberg, Germany

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Publications (67)110.13 Total impact

  • Anna Marciniak-Czochra · Grzegorz Karch · Kanako Suzuki · Jacek Zienkiewicz
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    ABSTRACT: In this paper we provide an example of a class of two reaction-diffusion-ODE equations with homogeneous Neumann boundary conditions, in which Turing-type instability not only destabilizes constant steady states but also induces blow-up of nonnegative spatially heterogeneous solutions. Solutions of this problem preserve nonnegativity and uniform boundedness of the total mass. Moreover, for the corresponding system with two non-zero diffusion coefficients, all nonnegative solutions are global in time. We prove that a removal of diffusion in one of the equations leads to a finite-time blow-up of some nonnegative spatially heterogeneous solutions.
    No preview · Article · Nov 2015
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    Karolina Kropielnicka · Piotr Gwiazda · Anna Marciniak-Czochra
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    DESCRIPTION: The Escalator Boxcar Train method (EBT) is a numerical method for structured population models of McKendrick-von Foerster type. Those models consist of a certain class of hyperbolic partial differential equations and describe time evolution of the distribution density of the structure variable de-scribing a feature of individuals in the population. The method was introduced in late eighties and widely used in theoretical biology, but its convergence was proven only in recent years using the framework of measure-valued solutions. Till now the EBT method was developed only for scalar equation models. In this paper we derive a full numerical EBT scheme for age-structured, two-sex population model (Fredrickson-Hoppensteadt model), which consists of three coupled hyperbolic partial differential equations with nonlocal boundary con-ditions. It is the first step towards extending the EBT method to systems of structured population equations.
    Full-text · Research · Aug 2015
  • Philipp Getto · Anna Marciniak-Czochra
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    ABSTRACT: Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.
    No preview · Article · Jun 2015 · Methods in molecular biology (Clifton, N.J.)
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    Steffen Härting · Anna Marciniak-Czochra · Izumi Takagi
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    ABSTRACT: Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that equilibrium. In this paper we show that coupling reaction-diffusion equations with ordinary differential equations (ODE) may lead to a novel pattern formation phenomenon in which DDI causes destabilization of both constant solutions and Turing patterns. Bistability and hysteresis effects in the null sets of model nonlinearities yield formation of far from the equilibrium patterns with jump discontinuity. We derive conditions for stability of stationary solutions with jump discontinuity in a suitable topology which allows disclosing the discontinuity points and leads to the definition of ({\epsilon}0 , A)-stability. Additionally, we provide conditions on stability of patterns in a quasi-stationary model reduction. The analysis is illustrated on the example of three-component model of receptor-ligand binding. The proposed model provides an example of a mechanism of de novo formation of far from the equilibrium patterns in reaction-diffusion-ODE models involving co-existence of DDI and hysteresis.
    Preview · Article · Jun 2015
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    Thomas Carraro · Christian Goll · Anna Marciniak-Czochra · Andro Mikelić
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    ABSTRACT: It is generally accepted that the effective velocity of a viscous flow over a porous bed satisfies the Beavers-Joseph slip law. To the contrary, in the case of a forced infiltration of a viscous fluid into a porous medium the interface law has been a subject of controversy. In this paper, we prove rigorously that the effective interface conditions are: (i) the continuity of the normal effective velocities; (ii) zero Darcy's pressure and (iii) a given slip velocity. The effective tangential slip velocity is calculated from the boundary layer and depends only on the pore geometry. In the next order of approximation, we derive a pressure slip law. An independent confirmation of the analytical results using direct numerical simulation of the flow at the microscopic level is given, as well.
    Full-text · Article · May 2015 · Computer Methods in Applied Mechanics and Engineering
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    Moritz Mercker · Alexandra Köthe · Anna Marciniak-Czochra
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    ABSTRACT: Tissue morphogenesis comprises the self-organized creation of various patterns and shapes. Although detailed underlying mechanisms are still elusive in many cases, an increasing amount of experimental data suggests that chemical morphogen and mechanical processes are strongly coupled. Here, we develop and test a minimal model of the axis-defining step (i.e., symmetry breaking) in aggregates of the Hydra polyp. Based on previous findings, we combine osmotically driven shape oscillations with tissue mechanics and morphogen dynamics. We show that the model incorporating a simple feedback loop between morphogen patterning and tissue stretch reproduces a wide range of experimental data. Finally, we compare different hypothetical morphogen patterning mechanisms (Turing, tissue-curvature, and self-organized criticality). Our results suggest the experimental investigation of bigger (i.e., multiple head) aggregates as a key step for a deeper understanding of mechanochemical symmetry breaking in Hydra. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.
    Full-text · Article · May 2015 · Biophysical Journal
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    Moritz Mercker · Anna Marciniak-Czochra
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    ABSTRACT: Membrane budding is essential for processes such as protein sorting and transport. Recent experimental results with ESCRT proteins reveal a novel budding mechanism, with proteins emerging in bud necks but separated from the entire bud surface. Using an elastic model, we show that ESCRT protein shapes are sufficient to spontaneously create experimentally observed structures, with protein-membrane interactions leading to protein scaffolds in bud-neck regions. Furthermore, the model reproduces experimentally observed budding directions and bud sizes. Finally, our results reveal that membrane-mediated sorting has the capability of creating structures more complicated than previously assumed. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.
    Full-text · Article · Feb 2015 · Biophysical Journal
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    Thomas Stiehl · Natalia Baran · Anthony D Ho · Anna Marciniak-Czochra
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    ABSTRACT: Acute myeloid leukemia is a heterogeneous disease in which a variety of distinct genetic alterations occur. Recent studies to identify the leukemia stem-like cells (LSCs) have also indicated heterogeneity of these cells. Based on mathematical modeling and computer simulations we have provided evidence that proliferation and self-renewal rates of the LSC population have greater impact on the course of disease than proliferation and self-renewal rates of leukemia blast populations, i.e. leukemia progenitor cells. The modeling approach has enabled us to estimate the LSC properties of 31 individuals with relapsed AML and to link them to patient survival. Based on the estimated LSC properties the patients can be divided into two prognostic groups which differ significantly with respect to overall survival after first relapse. The results suggest that high LSC self-renewal and proliferation rates are indicators of poor prognosis. Nevertheless, high LSC self-renewal rate may partially compensate for slow LSC proliferation and vice versa. Thus, model-based interpretation of clinical data allows estimation of prognostic factors that cannot be measured directly. This may have clinical implications for designing treatment strategies. Copyright © 2015, American Association for Cancer Research.
    Full-text · Article · Jan 2015 · Cancer Research
  • Grzegorz Karch · Anna Marciniak-Czochra

    No preview · Article · Jan 2015
  • Anna Marciniak-Czochra

    No preview · Article · Jan 2015 · Lecture Notes in Mathematics -Springer-verlag-
  • Thomas Stiehl · Anthony D Ho · Anna Marciniak-Czochra
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    ABSTRACT: Hematopoiesis is a complex and strongly regulated process. In case of regenerative pressure, efficient recovery of blood cell counts is crucial for survival of an individual. We propose a quantitative mathematical model of white blood cell formation based on the following cell parameters: (1) proliferation rate, (2) self-renewal, and (3) cell death. Simulating this model we assess the change of these parameters under regenerative pressure. The proposed model allows to quantitatively describe the impact of these cell parameters on engraftment time after stem cell transplantation. Results indicate that enhanced self-renewal during the posttransplant period is crucial for efficient regeneration of blood cell counts while constant or reduced self-renewal leads to delayed recovery or graft failure. Increased cell death in the posttransplant period has a similar impact. In contrast, reduced proliferation or pre-homing cell death causes only mild delays in blood cell recovery which can be compensated sufficiently by increasing the dose of transplanted cells.
    No preview · Article · Dec 2014 · Advances in Experimental Medicine and Biology
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    Anna Marciniak-Czochra · Andro Mikelic
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    ABSTRACT: In this paper we investigate the limit behavior of the solution to quasi-static Biot's equations in thin poroelastic plates as the thickness tends to zero. We choose Terzaghi's time corresponding to the plate thickness and obtain the strong convergence of the three-dimensional solid displacement, fluid pressure and total poroelastic stress to the solution of the new class of plate equations. In the new equations the in-plane stretching is described by the 2D Navier's linear elasticity equations, with elastic moduli depending on Gassmann's and Biot's coefficients. The bending equation is coupled with the pressure equation and it contains the bending moment due to the variation in pore pressure across the plate thickness. The pressure equation is parabolic only in the vertical direction. As additional terms it contains the time derivative of the in-plane Laplacean of the vertical deflection of the plate and of the the elastic in-plane compression term.
    Preview · Article · Nov 2014 · Archive for Rational Mechanics and Analysis
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    Piotr Gwiazda · Jędrzej Jabłoński · Anna Marciniak-Czochra · Agnieszka Ulikowska
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    ABSTRACT: Recently developed theoretical framework for analysis of structured population dynamics in the spaces of nonnegative Radon measures with a suitable metric provides a rigorous tool to study numerical schemes based on particle methods. The approach is based on the idea of tracing growth and transport of measures which approximate the solution of original partial differential equation. In this paper we present analytical and numerical study of two versions of Escalator Boxcar Train (EBT) algorithm which has been widely applied in theoretical biology, and compare it to the recently developed split-up algorithm. The novelty of this paper is in showing well-posedness and convergence rates of the schemes using the concept of semiflows on metric spaces. Theoretical results are validated by numerical simulations of test cases, in which distances between simulated and exact solutions are computed using flat metric.
    Full-text · Article · Nov 2014 · Numerical Methods for Partial Differential Equations
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    Full-text · Article · May 2014
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    ABSTRACT: Myelodysplastic syndromes (MDS) are triggered by an aberrant hematopoietic stem cell (HSC). It is, however, unclear how this clone interferes with physiologic blood formation. In this study, we followed the hypothesis that the MDS clone impinges on feedback signals for self-renewal and differentiation and thereby suppresses normal hematopoiesis. Based on the theory that the MDS clone affects feedback signals for self-renewal and differentiation and hence suppresses normal hematopoiesis, we have developed a mathematical model to simulate different modifications in MDS-initiating cells and systemic feedback signals during disease development. These simulations revealed that the disease initiating cells must have higher self-renewal rates than normal HSCs to outcompete normal hematopoiesis. We assumed that self-renewal is the default pathway of stem and progenitor cells which is down-regulated by an increasing number of primitive cells in the bone marrow niche - including the premature MDS cells. Furthermore, the proliferative signal is up-regulated by cytopenia. Overall, our model is compatible with clinically observed MDS development, even though a single mutation scenario is unlikely for real disease progression which is usually associated with complex clonal hierarchy. For experimental validation of systemic feedback signals, we analyzed the impact of MDS patient derived serum on hematopoietic progenitor cells in vitro: in fact, MDS serum slightly increased proliferation, whereas maintenance of primitive phenotype was reduced. However, MDS serum did not significantly affect colony forming unit (CFU) frequencies indicating that regulation of self-renewal may involve local signals from the niche. Taken together, we suggest that initial mutations in MDS particularly favor aberrant high self-renewal rates. Accumulation of primitive MDS cells in the bone marrow then interferes with feedback signals for normal hematopoiesis - which then results in cytopenia.
    Full-text · Article · Apr 2014 · PLoS Computational Biology
  • Joanna Kawka · Dominik Sturm · Sabrina Pleier · Stefan Pfister · Anna Marciniak-Czochra
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    ABSTRACT: Deregulation of signaling pathways and subsequent abnormal interactions of downstream genes very often results in carcinogenesis. In this paper, we propose a two-compartment model describing intricate dynamics of the target genes of the Wnt signaling pathway in medulloblastoma. The system of nine nonlinear ordinary differential equations accounts for the formation and dissociation of complexes as well as for the transcription, translation and transport between the cytoplasm and nucleus. We focus on the interplay between MYC and SGK1 (serum and glucocorticoid-inducible kinase 1), which are the products of Wnt/β-catenin signaling pathway, and GSK3β (glycogen synthase kinase). Numerical simulations of the model solutions yield a better understanding of the process and indicate the importance of the SGK1 gene in the development of medulloblastoma, which has been confirmed in our recent experiments. The model is calibrated based on the gene expression microarray data for two types of medulloblastoma, characterized by monosomy and trisomy of chromosome 6q to highlight the difference between diagnoses.
    No preview · Article · Mar 2014 · Journal of Theoretical Biology
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    Full-text · Article · Mar 2014 · Genome Medicine
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    Thomas Stiehl · Natalia Baran · Anthony D Ho · Anna Marciniak-Czochra
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    ABSTRACT: Recent experimental evidence suggests that acute myeloid leukaemias may originate from multiple clones of malignant cells. Nevertheless, it is not known how the observed clones may differ with respect to cell properties, such as proliferation and self-renewal. There are scarcely any data on how these cell properties change due to chemotherapy and relapse. We propose a new mathematical model to investigate the impact of cell properties on the multi-clonal composition of leukaemias. Model results imply that enhanced self-renewal may be a key mechanism in the clonal selection process. Simulations suggest that fast proliferating and highly self-renewing cells dominate at primary diagnosis, while relapse following therapy-induced remission is triggered mostly by highly self-renewing but slowly proliferating cells. Comparison of simulation results to patient data demonstrates that the proposed model is consistent with clinically observed dynamics based on a clonal selection process.
    Full-text · Article · Feb 2014 · Journal of The Royal Society Interface
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    Frederik Ziebell · Ana Martin-Villalba · Anna Marciniak-Czochra
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    ABSTRACT: In the adult hippocampus, neurogenesis-the process of generating mature granule cells from adult neural stem cells-occurs throughout the entire lifetime. In order to investigate the involved regulatory mechanisms, knockout (KO) experiments, which modify the dynamic behaviour of this process, were conducted in the past. Evaluating these KOs is a non-trivial task owing to the complicated nature of the hippocampal neurogenic niche. In this study, we model neurogenesis as a multicompartmental system of ordinary differential equations based on experimental data. To analyse the results of KO experiments, we investigate how changes of cell properties, reflected by model parameters, influence the dynamics of cell counts and of the experimentally observed counts of cells labelled by the cell division marker bromodeoxyuridine (BrdU). We find that changing cell proliferation rates or the fraction of self-renewal, reflecting the balance between symmetric and asymmetric cell divisions, may result in multiple time phases in the response of the system, such as an initial increase in cell counts followed by a decrease. Furthermore, these phases may be qualitatively different in cells at different differentiation stages and even between mitotically labelled cells and all cells existing in the system.
    Full-text · Article · Feb 2014 · Journal of The Royal Society Interface
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    Piotr Gwiazda · Anna Marciniak-Czochra · Jan-Erik Stecher
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    ABSTRACT: Self-renewal is a constitutive property of stem cells. Testing the cancer stem cell hypothesis requires investigation of the impact of self-renewal on cancer expansion. To understand better this impact, we propose a mathematical model describing dynamics of a continuum of cell clones structured by the self-renewal potential. The model is an extension of the finite multi-compartment models of interactions between normal and cancer cells in acute leukemias. It takes a form of a system of integro-differential equations with a nonlinear and nonlocal coupling, which describes regulatory feedback loops in cell proliferation and differentiation process. We show that such coupling leads to mass concentration in points corresponding to maximum of the self-renewal potential and the model solutions tend asymptotically to a linear combination of Dirac measures. Furthermore, using a Lyapunov function constructed for a finite dimensional counterpart of the model, we prove that the total mass of the solution converges to a globally stable equilibrium. Additionally, we show stability of the model in space of positive Radon measures equipped with flat metric. The analytical results are illustrated by numerical simulations.
    Preview · Article · Jan 2014