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Danciu DP, Hooli J, Martin-Villalba A, Marciniak-Czochra A. Mathematics of neural stem cells: Linking data and processes. Cells Dev 2023; 174:203849. [PMID: 37179018 DOI: 10.1016/j.cdev.2023.203849] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2023] [Revised: 04/29/2023] [Accepted: 05/05/2023] [Indexed: 05/15/2023]
Abstract
Adult stem cells are described as a discrete population of cells that stand at the top of a hierarchy of progressively differentiating cells. Through their unique ability to self-renew and differentiate, they regulate the number of end-differentiated cells that contribute to tissue physiology. The question of how discrete, continuous, or reversible the transitions through these hierarchies are and the precise parameters that determine the ultimate performance of stem cells in adulthood are the subject of intense research. In this review, we explain how mathematical modelling has improved the mechanistic understanding of stem cell dynamics in the adult brain. We also discuss how single-cell sequencing has influenced the understanding of cell states or cell types. Finally, we discuss how the combination of single-cell sequencing technologies and mathematical modelling provides a unique opportunity to answer some burning questions in the field of stem cell biology.
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Affiliation(s)
- Diana-Patricia Danciu
- Heidelberg University, Institute of Mathematics (IMA), Im Neuenheimer Feld 205, 69120 Heidelberg, Germany; Interdisciplinary Center for Scientific Computing (IWR), Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Jooa Hooli
- Heidelberg University, Institute of Mathematics (IMA), Im Neuenheimer Feld 205, 69120 Heidelberg, Germany; Interdisciplinary Center for Scientific Computing (IWR), Im Neuenheimer Feld 205, 69120 Heidelberg, Germany; Heidelberg University, Faculty of Biosciences, Im Neuenheimer Feld 234, 69120 Heidelberg, Germany; German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, 69120 Heidelberg, Germany
| | - Ana Martin-Villalba
- German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, 69120 Heidelberg, Germany
| | - Anna Marciniak-Czochra
- Heidelberg University, Institute of Mathematics (IMA), Im Neuenheimer Feld 205, 69120 Heidelberg, Germany; Interdisciplinary Center for Scientific Computing (IWR), Im Neuenheimer Feld 205, 69120 Heidelberg, Germany.
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2
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Busse JE, Cuadrado S, Marciniak-Czochra A. Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation. J Math Biol 2022; 84:10. [PMID: 34988700 DOI: 10.1007/s00285-021-01708-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Revised: 11/01/2021] [Accepted: 11/19/2021] [Indexed: 11/30/2022]
Abstract
In this paper we consider a system of non-linear integro-differential equations (IDEs) describing evolution of a clonally heterogeneous population of malignant white blood cells (leukemic cells) undergoing mutation and clonal selection. We prove existence and uniqueness of non-trivial steady states and study their asymptotic stability. The results are compared to those of the system without mutation. Existence of equilibria is proved by formulating the steady state problem as an eigenvalue problem and applying a version of the Krein-Rutmann theorem for Banach lattices. The stability at equilibrium is analysed using linearisation and the Weinstein-Aronszajn determinant which allows to conclude local asymptotic stability.
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Affiliation(s)
- Jan-Erik Busse
- Institute of Applied Mathematics, Interdisciplinary Center for Scientific Computing (IWR) and BIOQUANT Center, Heidelberg, Germany
| | - Sílvia Cuadrado
- Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Spain
| | - Anna Marciniak-Czochra
- Institute of Applied Mathematics, Interdisciplinary Center for Scientific Computing (IWR) and BIOQUANT Center, Heidelberg, Germany.
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3
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Stiehl T, Marciniak-Czochra A. Computational Reconstruction of Clonal Hierarchies From Bulk Sequencing Data of Acute Myeloid Leukemia Samples. Front Physiol 2021; 12:596194. [PMID: 34497529 PMCID: PMC8419336 DOI: 10.3389/fphys.2021.596194] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Accepted: 07/26/2021] [Indexed: 11/13/2022] Open
Abstract
Acute myeloid leukemia is an aggressive cancer of the blood forming system. The malignant cell population is composed of multiple clones that evolve over time. Clonal data reflect the mechanisms governing treatment response and relapse. Single cell sequencing provides most direct insights into the clonal composition of the leukemic cells, however it is still not routinely available in clinical practice. In this work we develop a computational algorithm that allows identifying all clonal hierarchies that are compatible with bulk variant allele frequencies measured in a patient sample. The clonal hierarchies represent descendance relations between the different clones and reveal the order in which mutations have been acquired. The proposed computational approach is tested using single cell sequencing data that allow comparing the outcome of the algorithm with the true structure of the clonal hierarchy. We investigate which problems occur during reconstruction of clonal hierarchies from bulk sequencing data. Our results suggest that in many cases only a small number of possible hierarchies fits the bulk data. This implies that bulk sequencing data can be used to obtain insights in clonal evolution.
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Affiliation(s)
- Thomas Stiehl
- Institute for Computational Biomedicine – Disease Modeling, RWTH Aachen University, Aachen, Germany
- Institute of Applied Mathematics, Interdisciplinary Center for Scientific Computing and Bioquant Center, Heidelberg University, Heidelberg, Germany
| | - Anna Marciniak-Czochra
- Institute of Applied Mathematics, Interdisciplinary Center for Scientific Computing and Bioquant Center, Heidelberg University, Heidelberg, Germany
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Chulián S, Martínez-Rubio Á, Marciniak-Czochra A, Stiehl T, Goñi CB, Rodríguez Gutiérrez JF, Ramírez Orellana M, Castillo Robleda A, Pérez-García VM, Rosa M. Dynamical properties of feedback signalling in B lymphopoiesis: A mathematical modelling approach. J Theor Biol 2021; 522:110685. [PMID: 33745905 DOI: 10.1016/j.jtbi.2021.110685] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2020] [Revised: 12/09/2020] [Accepted: 03/15/2021] [Indexed: 12/11/2022]
Abstract
Haematopoiesis is the process of generation of blood cells. Lymphopoiesis generates lymphocytes, the cells in charge of the adaptive immune response. Disruptions of this process are associated with diseases like leukaemia, which is especially incident in children. The characteristics of self-regulation of this process make them suitable for a mathematical study. In this paper we develop mathematical models of lymphopoiesis using currently available data. We do this by drawing inspiration from existing structured models of cell lineage development and integrating them with paediatric bone marrow data, with special focus on regulatory mechanisms. A formal analysis of the models is carried out, giving steady states and their stability conditions. We use this analysis to obtain biologically relevant regions of the parameter space and to understand the dynamical behaviour of B-cell renovation. Finally, we use numerical simulations to obtain further insight into the influence of proliferation and maturation rates on the reconstitution of the cells in the B line. We conclude that a model including feedback regulation of cell proliferation represents a biologically plausible depiction for B-cell reconstitution in bone marrow. Research into haematological disorders could benefit from a precise dynamical description of B lymphopoiesis.
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Affiliation(s)
- Salvador Chulián
- Department of Mathematics, Universidad de Cádiz, Puerto Real, Cádiz, Spain; Biomedical Research and Innovation Institute of Cádiz (INiBICA), Hospital Universitario Puerta del Mar, Cádiz, Spain.
| | - Álvaro Martínez-Rubio
- Department of Mathematics, Universidad de Cádiz, Puerto Real, Cádiz, Spain; Biomedical Research and Innovation Institute of Cádiz (INiBICA), Hospital Universitario Puerta del Mar, Cádiz, Spain
| | - Anna Marciniak-Czochra
- Institute of Applied Mathematics, BioQuant and Interdisciplinary Center of Scientific Computing (IWR), Heidelberg University, Heidelberg, Germany
| | - Thomas Stiehl
- Institute of Applied Mathematics, BioQuant and Interdisciplinary Center of Scientific Computing (IWR), Heidelberg University, Heidelberg, Germany
| | | | | | - Manuel Ramírez Orellana
- Department of Paediatric Haematology and Oncology, Hospital Infantil Universitario Niño Jesús, Instituto Investigación Sanitaria La Princesa, Madrid, Spain
| | - Ana Castillo Robleda
- Department of Paediatric Haematology and Oncology, Hospital Infantil Universitario Niño Jesús, Instituto Investigación Sanitaria La Princesa, Madrid, Spain
| | - Víctor M Pérez-García
- Department of Mathematics, Mathematical Oncology Laboratory (MOLAB), Universidad de Castilla-La Mancha, Ciudad Real, Spain; Instituto de Matemática Aplicada a la Ciencia y la Ingeniería (IMACI), Universidad de Castilla-La Mancha, Ciudad Real, Spain; ETSI Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain
| | - María Rosa
- Department of Mathematics, Universidad de Cádiz, Puerto Real, Cádiz, Spain; Biomedical Research and Innovation Institute of Cádiz (INiBICA), Hospital Universitario Puerta del Mar, Cádiz, Spain
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BAILEY LORAD, KOMAROVA NATALIAL. CELLULAR FEEDBACK NETWORKS AND THEIR RESILIENCE AGAINST MUTATIONS. J BIOL SYST 2021. [DOI: 10.1142/s0218339021400039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Many tissues undergo a steady turnover, where cell divisions are on average balanced with cell deaths. Cell fate decisions such as stem cell (SC) differentiations, proliferations, or differentiated cell (DC) deaths, may be controlled by cell populations through cell-to-cell signaling. Here, we examine a class of mathematical models of turnover in SC lineages to understand engineering design principles of control (feedback) loops, that may operate in such systems. By using ordinary differential equations that describe the co-dynamics of SCs and DCs, we study the effect of different types of mutations that interfere with feedback present within cellular networks. For instance, we find that mutants that do not participate in feedback are less dangerous in the sense that they will not rise from low numbers, whereas mutants that do not respond to feedback signals could rise and replace the wild-type population. Additionally, we asked if different feedback networks can have different degrees of resilience against such mutations. We found that all minimal networks, that is networks consisting of exactly one feedback loop that is sufficient for homeostatic stability of the wild-type population, are equally vulnerable. Mutants with a weakened/eliminated feedback parameter might expand from lower numbers and either enter unlimited growth or reach an equilibrium with an increased number of SCs and DCs. Therefore, from an evolutionary viewpoint, it appears advantageous to combine feedback loops, creating redundant feedback networks. Interestingly, from an engineering prospective, not all such redundant systems are equally resilient. For some of them, any mutation that weakens/eliminates one of the loops will lead to a population growth of SCs. For others, the population of SCs can actually shrink as a result of “cutting” one of the loops, thus slowing down further unwanted transformations.
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Stiehl T. Using mathematical models to improve risk-scoring in acute myeloid leukemia. CHAOS (WOODBURY, N.Y.) 2020; 30:123150. [PMID: 33380018 DOI: 10.1063/5.0023830] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Accepted: 11/30/2020] [Indexed: 06/12/2023]
Abstract
Acute myeloid leukemia (AML) is an aggressive cancer of the blood forming (hematopoietic) system. Due to the high patient variability of disease dynamics, risk-scoring is an important part of its clinical management. AML is characterized by impaired blood cell formation and the accumulation of so-called leukemic blasts in the bone marrow of patients. Recently, it has been proposed to use counts of blood-producing (hematopoietic) stem cells (HSCs) as a biomarker for patient prognosis. In this work, we use a non-linear mathematical model to provide mechanistic evidence for the suitability of HSC counts as a prognostic marker. Using model analysis and computer simulations, we compare different risk-scores involving HSC quantification. We propose and validate a simple approach to improve risk prediction based on HSC and blast counts measured at the time of diagnosis.
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Affiliation(s)
- Thomas Stiehl
- Institute of Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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