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Bast L, Buck MC, Hecker JS, Oostendorp RAJ, Götze KS, Marr C. Computational modeling of stem and progenitor cell kinetics identifies plausible hematopoietic lineage hierarchies. iScience 2021; 24:102120. [PMID: 33665548 PMCID: PMC7897991 DOI: 10.1016/j.isci.2021.102120] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Revised: 01/08/2021] [Accepted: 01/22/2021] [Indexed: 12/11/2022] Open
Abstract
Classically, hematopoietic stem cell (HSC) differentiation is assumed to occur via progenitor compartments of decreasing plasticity and increasing maturity in a specific, hierarchical manner. The classical hierarchy has been challenged in the past by alternative differentiation pathways. We abstracted experimental evidence into 10 differentiation hierarchies, each comprising 7 cell type compartments. By fitting ordinary differential equation models with realistic waiting time distributions to time-resolved data of differentiating HSCs from 10 healthy human donors, we identified plausible lineage hierarchies and rejected others. We found that, for most donors, the classical model of hematopoiesis is preferred. Surprisingly, multipotent lymphoid progenitor differentiation into granulocyte-monocyte progenitors is plausible in 90% of samples. An in silico analysis confirmed that, even for strong noise, the classical model can be identified robustly. Our computational approach infers differentiation hierarchies in a personalized fashion and can be used to gain insights into kinetic alterations of diseased hematopoiesis. We assembled 10 lineage hierarchy models of human hematopoiesis Multiparameter immunophenotyping determines HSC differentiation for 10 healthy donors ODE fitting and model selection allows to identify plausible hierarchies A simulation study confirms robustness of model selection for different noise levels
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Affiliation(s)
- Lisa Bast
- Helmholtz Zentrum München-German Research Center for Environmental Health, Institute of Computational Biology, Neuherberg, Germany.,Technical University of Munich, Department of Mathematics, Chair of Mathematical Modeling of Biological Systems, Garching, Germany
| | - Michèle C Buck
- Technical University of Munich, School of Medicine, Klinikum rechts der Isar, Department of Internal Medicine III, Munich, Germany
| | - Judith S Hecker
- Technical University of Munich, School of Medicine, Klinikum rechts der Isar, Department of Internal Medicine III, Munich, Germany
| | - Robert A J Oostendorp
- Technical University of Munich, School of Medicine, Klinikum rechts der Isar, Department of Internal Medicine III, Munich, Germany
| | - Katharina S Götze
- Technical University of Munich, School of Medicine, Klinikum rechts der Isar, Department of Internal Medicine III, Munich, Germany.,German Cancer Consortium (DKTK), Heidelberg, Partner Site Munich, Germany
| | - Carsten Marr
- Helmholtz Zentrum München-German Research Center for Environmental Health, Institute of Computational Biology, Neuherberg, Germany.,Technical University of Munich, Department of Mathematics, Chair of Mathematical Modeling of Biological Systems, Garching, Germany
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Getto P, Gyllenberg M, Nakata Y, Scarabel F. Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods. J Math Biol 2019; 79:281-328. [PMID: 31004216 PMCID: PMC6598990 DOI: 10.1007/s00285-019-01357-0] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2018] [Revised: 03/29/2019] [Indexed: 11/29/2022]
Abstract
We consider a mathematical model describing the maturation process of stem cells up to fully mature cells. The model is formulated as a differential equation with state-dependent delay, where maturity is described as a continuous variable. The maturation rate of cells may be regulated by the amount of mature cells and, moreover, it may depend on cell maturity: we investigate how the stability of equilibria is affected by the choice of the maturation rate. We show that the principle of linearised stability holds for this model, and develop some analytical methods for the investigation of characteristic equations for fixed delays. For a general maturation rate we resort to numerical methods and we extend the pseudospectral discretisation technique to approximate the state-dependent delay equation with a system of ordinary differential equations. This is the first application of the technique to nonlinear state-dependent delay equations, and currently the only method available for studying the stability of equilibria by means of established software packages for bifurcation analysis. The numerical method is validated on some cases when the maturation rate is independent of maturity and the model can be reformulated as a fixed-delay equation via a suitable time transformation. We exploit the analytical and numerical methods to investigate the stability boundary in parameter planes. Our study shows some drastic qualitative changes in the stability boundary under assumptions on the model parameters, which may have important biological implications.
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Affiliation(s)
- Philipp Getto
- Center for Dynamics, Technische Universität Dresden, 01062 Dresden, Germany
| | - Mats Gyllenberg
- Department of Mathematics and Statistics, University of Helsinki, 00014 Helsinki, Finland
| | - Yukihiko Nakata
- Department of Mathematical Sciences, Shimane University, Matsue, 690-8504 Japan
| | - Francesca Scarabel
- Department of Mathematics and Statistics, University of Helsinki, 00014 Helsinki, Finland
- Present Address: LIAM, Department of Mathematics and Statistics, York University, 4700 Keele St, Toronto, ON M3J 1P3 Canada
- CDLab, Department of Mathematics, Computer Science and Physics, University of Udine, Udine, Italy
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Xu S, Kim S, Chen ISY, Chou T. Modeling large fluctuations of thousands of clones during hematopoiesis: The role of stem cell self-renewal and bursty progenitor dynamics in rhesus macaque. PLoS Comput Biol 2018; 14:e1006489. [PMID: 30335762 PMCID: PMC6218102 DOI: 10.1371/journal.pcbi.1006489] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2017] [Revised: 11/05/2018] [Accepted: 09/05/2018] [Indexed: 01/13/2023] Open
Abstract
In a recent clone-tracking experiment, millions of uniquely tagged hematopoietic stem cells (HSCs) and progenitor cells were autologously transplanted into rhesus macaques and peripheral blood containing thousands of tags were sampled and sequenced over 14 years to quantify the abundance of hundreds to thousands of tags or “clones.” Two major puzzles of the data have been observed: consistent differences and massive temporal fluctuations of clone populations. The large sample-to-sample variability can lead clones to occasionally go “extinct” but “resurrect” themselves in subsequent samples. Although heterogeneity in HSC differentiation rates, potentially due to tagging, and random sampling of the animals’ blood and cellular demographic stochasticity might be invoked to explain these features, we show that random sampling cannot explain the magnitude of the temporal fluctuations. Moreover, we show through simpler neutral mechanistic and statistical models of hematopoiesis of tagged cells that a broad distribution in clone sizes can arise from stochastic HSC self-renewal instead of tag-induced heterogeneity. The very large clone population fluctuations that often lead to extinctions and resurrections can be naturally explained by a generation-limited proliferation constraint on the progenitor cells. This constraint leads to bursty cell population dynamics underlying the large temporal fluctuations. We analyzed experimental clone abundance data using a new statistic that counts clonal disappearances and provided least-squares estimates of two key model parameters in our model, the total HSC differentiation rate and the maximum number of progenitor-cell divisions. Hematopoiesis of virally tagged cells in rhesus macaques is analyzed in the context of a mechanistic and statistical model. We find that the clone size distribution and the temporal variability in the abundance of each clone (viral tag) in peripheral blood are consistent with (i) stochastic HSC self-renewal during bone marrow repair, (ii) clonal aging that restricts the number of generations of progenitor cells, and (iii) infrequent and small-size samples. By fitting data, we infer two key parameters that control the level of fluctuations of clone sizes in our model: the total HSC differentiation rate and the maximum proliferation capacity of progenitor cells. Our analysis provides insight into the mechanisms of hematopoiesis and a framework to guide future multiclone barcoding/lineage tracking measurements.
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Affiliation(s)
- Song Xu
- Center for Biomedical Informatics Research, Department of Medicine, Stanford University, Stanford, California, United States of America
| | - Sanggu Kim
- Department of Veterinary Biosciences, The Ohio State University, Columbus, Ohio, United States of America
| | - Irvin S. Y. Chen
- UCLA AIDS Institute and Department of Microbiology, Immunology, and Molecular Genetics, University of California, Los Angeles, Los Angeles, California, United States of America
| | - Tom Chou
- Center for Biomedical Informatics Research, Department of Medicine, Stanford University, Stanford, California, United States of America
- Department of Mathematics, University of California, Los Angeles, Los Angeles, California, United States of America
- * E-mail:
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Affiliation(s)
- Alexander A. Spector
- Department
of Biomedical Engineering and ‡Translational Tissue Engineering
Center, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205, United States
- Institute for Nanobiotechnology (INBT) and ∥Department of Material Sciences & Engineering, Johns Hopkins University Whiting School of Engineering, Baltimore 21218, Maryland, United States
| | - Warren L. Grayson
- Department
of Biomedical Engineering and ‡Translational Tissue Engineering
Center, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205, United States
- Institute for Nanobiotechnology (INBT) and ∥Department of Material Sciences & Engineering, Johns Hopkins University Whiting School of Engineering, Baltimore 21218, Maryland, United States
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Optimal architecture of differentiation cascades with asymmetric and symmetric stem cell division. J Theor Biol 2016; 407:106-117. [DOI: 10.1016/j.jtbi.2016.07.029] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2015] [Revised: 07/02/2016] [Accepted: 07/20/2016] [Indexed: 11/23/2022]
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Li G, Liu X, Du Q, Gao M, An J. Three dimensional de novo micro bone marrow and its versatile application in drug screening and regenerative medicine. Exp Biol Med (Maywood) 2015; 240:1029-38. [PMID: 26283705 DOI: 10.1177/1535370215594583] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
The finding that bone marrow hosts several types of multipotent stem cell has prompted extensive research aimed at regenerating organs and building models to elucidate the mechanisms of diseases. Conventional research depends on the use of two-dimensional (2D) bone marrow systems, which imposes several obstacles. The development of 3D bone marrow systems with appropriate molecules and materials however, is now showing promising results. In this review, we discuss the advantages of 3D bone marrow systems over 2D systems and then point out various factors that can enhance the 3D systems. The intensive research on 3D bone marrow systems has revealed multiple important clinical applications including disease modeling, drug screening, regenerative medicine, etc. We also discuss some possible future directions in the 3D bone marrow research field.
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Affiliation(s)
- Guanqun Li
- Department of Pharmacology, State University of New York, Upstate Medical University, Syracuse, NY 13202, USA
| | - Xujun Liu
- Department of Pharmacology, State University of New York, Upstate Medical University, Syracuse, NY 13202, USA
| | - Qian Du
- Department of Neuroscience and Physiology, State University of New York, Upstate Medical University, Syracuse, NY 13202, USA
| | - Mei Gao
- Department of Pharmacology, State University of New York, Upstate Medical University, Syracuse, NY 13202, USA SUNY Upstate Cancer Research Institute, State University of New York, Upstate Medical University, Syracuse, NY 13202, USA
| | - Jing An
- Department of Pharmacology, State University of New York, Upstate Medical University, Syracuse, NY 13202, USA SUNY Upstate Cancer Research Institute, State University of New York, Upstate Medical University, Syracuse, NY 13202, USA
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Sánchez-Taltavull D, Alarcón T. Robustness of differentiation cascades with symmetric stem cell division. J R Soc Interface 2014; 11:20140264. [PMID: 24718457 DOI: 10.1098/rsif.2014.0264] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
Stem cells (SCs) perform the task of maintaining tissue homeostasis by both self-renewal and differentiation. While it has been argued that SCs divide asymmetrically, there is also evidence that SCs undergo symmetric division. Symmetric SC division has been speculated to be key for expanding cell numbers in development and regeneration after injury. However, it might lead to uncontrolled growth and malignancies such as cancer. In order to explore the role of symmetric SC division, we propose a mathematical model of the effect of symmetric SC division on the robustness of a population regulated by a serial differentiation cascade and we show that this may lead to extinction of such population. We examine how the extinction likelihood depends on defining characteristics of the population such as the number of intermediate cell compartments. We show that longer differentiation cascades are more prone to extinction than systems with less intermediate compartments. Furthermore, we have analysed the possibility of mixed symmetric and asymmetric cell division against invasions by mutant invaders in order to find optimal architecture. Our results show that more robust populations are those with unfrequent symmetric behaviour.
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Affiliation(s)
- Daniel Sánchez-Taltavull
- Centre de Recerca Matemàtica, , Edifici C, Campus de Bellaterra, 08193 Bellaterra (Barcelona), Spain
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Adimy M, Angulo O, Marquet C, Sebaa L. A mathematical model of multistage hematopoietic cell lineages. ACTA ACUST UNITED AC 2014. [DOI: 10.3934/dcdsb.2014.19.1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Serna S, Nirody JA, Rácz MZ. Analysis of unstable behavior in a mathematical model for erythropoiesis. J Math Biol 2013; 66:595-625. [DOI: 10.1007/s00285-012-0524-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2011] [Revised: 03/07/2012] [Indexed: 10/28/2022]
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Silva A, Anderson ARA, Gatenby R. A multiscale model of the bone marrow and hematopoiesis. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2011; 8:643-58. [PMID: 21631151 PMCID: PMC3754791 DOI: 10.3934/mbe.2011.8.643] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
The bone marrow is necessary for renewal of all hematopoietic cells and critical for maintenance of a wide range of physiologic functions. Multiple human diseases result from bone marrow dysfunction. It is also the site in which liquid tumors, including leukemia and multiple myeloma, develop as well as a frequent site of metastases. Understanding the complex cellular and microenvironmental interactions that govern normal bone marrow function as well as diseases and cancers of the bone marrow would be a valuable medical advance. Our goal is the development of a spatially-explicit in silico model of the bone marrow to understand both its normal function and the evolutionary dynamics that govern the emergence of bone marrow malignancy. Here we introduce a multiscale computational model of the bone marrow that incorporates three distinct spatial scales, cell, hematopoietic subunit, whole marrow. Our results, using parameter estimates from literature, recapitulates normal bone marrow function and suggest an explanation for the fractal-like structure of trabeculae and sinuses in the marrow, which would be an optimization of the hematopoietic function in order to maximize the number of mature blood cells produced daily within the volumetric restrictions of the marrow.
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Affiliation(s)
- Ariosto Silva
- H Lee Moffitt Cancer Center, Tampa, FL 33612, United States.
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