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Current Stem Cell Reports

, Volume 5, Issue 2, pp 57–65 | Cite as

How to Characterize Stem Cells? Contributions from Mathematical Modeling

  • Thomas Stiehl
  • Anna Marciniak-CzochraEmail author
Mathematical Models of Stem Cell Behavior (M Kohandel, Section Editor)
Part of the following topical collections:
  1. Topical Collection on Mathematical Models of Stem Cell Behavior

Abstract

Purpose of Review

Adult stem cells play a key role in tissue regeneration and cancer. To translate findings from stem cell biology into clinics, we require a quantitative characterization of stem cell dynamics in vivo. This review explores how mathematical models can help to characterize stem cell behavior in health and disease.

Recent Findings

Mathematical models significantly contribute to quantification of stem cell traits such as proliferation, self-renewal, and quiescence. They provide insights into the role of systemic and micro-environmental feedback loops during regeneration and cancer. Computer simulations allow linking stem cell properties to tumor composition, clinical course, and drug response. Therefore, models are helpful in personalizing treatments and predicting patient survival.

Summary

Mathematical models coupled with tools of parameter estimation and model selection provide quantitative insights into stem cell properties and their regulation. They help to understand experimentally inaccessible processes occurring in regeneration, aging, and cancer.

Keywords

Cancer stem cell Mathematical model Tumor heterogeneity Clonal evolution Bone marrow transplantation Patient prognosis Differential equations 

Notes

Acknowledgements

This work was funded by research funding from the German Research Foundation DFG (Collaborative Research Center SFB 873, Maintenance and Differentiation of Stem Cells in Development and Disease).

Compliance with Ethical Standards

Conflict of Interest

Thomas Stiehl and Anna Marciniak-Czochra declare that they have no conflict of interest.

Human and Animal Rights and Informed Consent

All reported studies and experiments involving human or animal subjects performed by the authors have been previously published and complied with applicable ethical standards as defined in the Helsinki declaration and its amendments, institutional and national research committee standards, and international/national/institutional guidelines.

References

Papers of particular interest, published recently, have been highlighted as: • Of importance •• Of major importance

  1. 1.
    Slack JMW. What is a stem cell? Wiley Interdiscip Rev Dev Biol. 2018;15:e323.CrossRefGoogle Scholar
  2. 2.
    Duan JJ, Qiu W, Xu SL, Wang B, Ye XZ, Ping YF, et al. Strategies for isolating and enriching cancer stem cells: well begun is half done. Stem Cells Dev. 2013;22(16):2221–39.CrossRefGoogle Scholar
  3. 3.
    Hawley RG, Ramezani A, Hawley TS. Hematopoietic stem cells. Methods Enzymol. 2006;419:149–79.CrossRefGoogle Scholar
  4. 4.
    Grade S, Götz M. Neuronal replacement therapy: previous achievements and challenges ahead. NPJ Regen Med. 2017;2:29.CrossRefGoogle Scholar
  5. 5.
    Jiang FX, Morahan G. Pancreatic stem cells remain unresolved. Stem Cells Dev. 2014;23(23):2803–12.CrossRefGoogle Scholar
  6. 6.
    Reya T, Morrison SJ, Clarke MF, Weissman IL. Stem cells, cancer, and cancer stem cells. Nature. 2001;414:105–11.CrossRefGoogle Scholar
  7. 7.
    Bonnet D, Dick JE. Human acute myeloid leukemia is organized as a hierarchy that originates from a primitive hematopoietic cell. Nat Med. 1997;3(7):730–7.CrossRefGoogle Scholar
  8. 8.
    Crabtree JS, Miele L. Breast cancer stem cells. Biomedicines. 2018;6(3):E77.  https://doi.org/10.3390/biomedicines6030077.CrossRefPubMedGoogle Scholar
  9. 9.
    Skvortsov S, Skvortsova II, Tang DG, Dubrovska A. Prostate cancer stem cells: current understanding. Stem Cells. 2018;36:1457–74.  https://doi.org/10.1002/stem.2859.CrossRefPubMedGoogle Scholar
  10. 10.
    Aderetti DA, Hira VVV, Molenaar RJ, van Noorden CJF. The hypoxic peri-arteriolar glioma stem cell niche, an integrated concept of five types of niches in human glioblastoma. Biochim Biophys Acta. 2018;1869(2):346–54.Google Scholar
  11. 11.
    Skoda J, Veselska R. Cancer stem cells in sarcomas: getting to the stemness core. Biochim Biophys Acta. 2018;1862(10):2134–9.CrossRefGoogle Scholar
  12. 12.
    Marciniak-Czochra A, Stiehl T, Ho AD, Jäger W, Wagner W. Modeling of asymmetric cell division in hematopoietic stem cells - regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev. 2009;18:377–85.CrossRefGoogle Scholar
  13. 13.
    Stiehl T, Marciniak-Czochra A. Characterization of stem cells using mathematical models of multistage cell lineages. Math Comp Modell. 2011;53:1505–17.CrossRefGoogle Scholar
  14. 14.
    Busse JE, Gwiazda P, Marciniak-Czochra A. Mass concentration in a nonlocal model of clonal selection. J Math Biol. 2016;73:1001–33.CrossRefGoogle Scholar
  15. 15.
    Doumic M, Marciniak-Czochra A, Perthame B, Zubelli J. Structured population model of stem cell differentiation. SIAM J Appl Math. 2011;71:1918–40.CrossRefGoogle Scholar
  16. 16.
    Cho H, Ayers K, de Pills L, Kuo YH, Park J, Radunskaya A, et al. Modelling acute myeloid leukaemia in a continuum of differentiation states. Lett Biomath. 2018;5:S69–98.CrossRefGoogle Scholar
  17. 17.
    •• Ashcroft P, Manz MG, Bonhoeffer S. Clonal dominance and transplantation dynamics in hematopoietic stem cell compartments. PLoS Comput Biol. 2017;13(10):e1005803 Develops models of the murine hematopoietic stem cell niche to quantify migration of HSC between bone marrow and blood. Suggests that clonal hematopoiesis in mice has to be linked to a selective advantage of the expanding clone. CrossRefGoogle Scholar
  18. 18.
    •• Ziebell F, Dehler S, Martin-Villalba A, Marciniak-Czochra A. Revealing age-related changes of adult hippocampal neurogenesis using mathematical models. Development. 2018;145(1):dev153544.  https://doi.org/10.1242/dev.153544 Provides insights into age related changes of neural stem cell proliferation, self-renewal and quiescence. CrossRefPubMedPubMedCentralGoogle Scholar
  19. 19.
    • Hamis S, Nithiarasu P, Powathil GG. What does not kill a tumour may make it stronger: in silico insights into chemotherapeutic drug resistance. J Theor Biol. 2018;454:253–67 Develops a cellular automaton model to study the impact of different resistance mechanisms on treatment outcome. CrossRefGoogle Scholar
  20. 20.
    •• Kather JN, Charoentong P, Suarez-Carmona M, Herpel E, Klupp F, Ulrich A, et al. High-throughput screening of combinatorial immunotherapies with patient-specific in silico models of metastatic colorectal cancer. Cancer Res. 2018.  https://doi.org/10.1158/0008-5472.CAN-18-1126 Develops a computational model of solid tumors including cancer cells, fibroblasts and immune cells. Calibration of the model to individual colorectal cancer samples allows to predict patient survival and to simulate treatment schedules.
  21. 21.
    • Stiehl T, Lutz C, Marciniak-Czochra A. Emergence of heterogeneity in acute leukemias. Biol Direct. 2016;11:51 Investigates how cell proliferation and self-renewal change during clonal evolution of AML. CrossRefGoogle Scholar
  22. 22.
    •• Nazari F, Pearson AT, Nör JE, Jackson TL. A mathematical model for IL-6-mediated, stem cell driven tumor growth and targeted treatment. PLoS Comput Biol. 2018;14(1):e1005920 Develops a multiscale model of IL6-mediated cancer cell expansion in head and neck squamous cell cancer and applies it to optimize treatment with antibodies against the IL6 receptor. Suggests that antibodies against the IL6 receptor act stronger on cancer cell death than on cancer cell self-renewal. CrossRefGoogle Scholar
  23. 23.
    Gwiazda P, Jamroz G, Marciniak-Czochra A. Models of discrete and continuous cell differentiation in the framework of transport equation. SIAM J Math Anal. 2012;44:1103–33.CrossRefGoogle Scholar
  24. 24.
    •• Werner B, Beier F, Hummel S, Balabanov S, Lassay L, Orlikowsky T, et al. Reconstructing the in vivo dynamics of hematopoietic stem cells from telomere length distributions. Elife. 2015.  https://doi.org/10.7554/eLife.08687 Provides insights into age related changes of hematopoietic stem cell self-renewal based on telomere length distributions.
  25. 25.
    •• Stiehl T, Ho AD, Marciniak-Czochra A. Mathematical modeling of the impact of cytokine response of acute myeloid leukemia cells on patient prognosis. Sci Rep. 2018;8(1):2809.  https://doi.org/10.1038/s41598-018-21115-4 Studies how cytokine-dependence of leukemic cells impacts on disease dynamics and suggests that autonomous cell growth is linked to a poor prognosis. CrossRefPubMedPubMedCentralGoogle Scholar
  26. 26.
    •• Stiehl T, Baran N, Ho AD, Marciniak-Czochra A. Cell division patterns in acute myeloid leukemia stem-like cells determine clinical course: a model to predict patient survival. Cancer Res. 2015;75:940–9 Provides evidence that clinical dynamics of AML depend on leukemic stem cell proliferation and self-renewal. Estimation of these properties from data allow patient specific risk scoring. CrossRefGoogle Scholar
  27. 27.
    •• Kim E, Kim JY, Smith MA, Haura EB. Anderson ARA. Cell signaling heterogeneity is modulated by both cell-intrinsic and -extrinsic mechanisms: An integrated approach to understanding targeted therapy. PLoS Biol. 2018;16(3):e2002930 Develops a models to study the impact of intercellular signaling heterogeneity on outcome of targeted therapies. The model is used to predict response to kinase inhibitors and model predictions are validated using in vitro data. Possible mechanisms of resistance are investigated. Google Scholar
  28. 28.
    Marciniak-Czochra A, Mikelić A, Stiehl T. Renormalization group second-order approximation for singularly perturbed nonlinear ordinary differential equations. Math Methods Appl Sci. 2018;51(14):5691–710.CrossRefGoogle Scholar
  29. 29.
    • Stiehl T, Baran N, Ho AD, Marciniak-Czochra A. Clonal selection and therapy resistance in acute leukaemias: mathematical modelling explains different proliferation patterns at diagnosis and relapse. J R Soc Interface. 2014;11:20140079 Develops models of clonal evolution in acute leukemias and provides evidence that high-self-renewal confers a selective advantage. CrossRefGoogle Scholar
  30. 30.
    Nikolov S, Santos G, Wolkenhauer O, Vera J. Model-based phenotypic signatures governing the dynamics of the stem and semi-differentiated cell populations in dysplastic colonic crypts. Bull Math Biol. 2018;80(2):360–84.CrossRefGoogle Scholar
  31. 31.
    Stiehl T, Ho AD, Marciniak-Czochra A. Assessing hematopoietic (stem-) cell behavior during regenerative pressure. Adv Exp Med Biol. 2014;844:347–67.CrossRefGoogle Scholar
  32. 32.
    •• Wang W, Stiehl T, Raffel S, Hoang VT, Hoffmann I, Poisa-Beiro L, et al. Reduced hematopoietic stem cell frequency predicts outcome in acute myeloid leukemia. Haematologica. 2017;102(9):1567–77 Develops a model of the human stem cell niche in AML. Provides evidence that competition in the stem cell niche impacts on the clinical course and that a high probability of HSC dislogement by LSC results in low HSC counts at diagnosis and a poor prognosis. Google Scholar
  33. 33.
    • Forouzannia F, Enderling H, Kohandel M. Mathematical modeling of the effects of tumor heterogeneity on the efficiency of radiation treatment schedule. Bull Math Biol. 2018;80(2):283–93 Studies the impact of tumor heterogeneity on the effect of different schemes of radio-therapy. Suggestst that protocols should balance between tumor volume reduction and enrichment of resistant cells. CrossRefGoogle Scholar
  34. 34.
    Stiehl T, Marciniak-Czochra A. Stem cell self-renewal in regeneration and cancer: insights from mathematical modeling. Curr Opin Syst Biol. 2017;5:112–20.CrossRefGoogle Scholar
  35. 35.
    •• Busch K, Klapproth K, Barile M, Flossdorf M, Holland-Letz T, Schlenner SM, et al. Fundamental properties of unperturbed haematopoiesis from stem cells in vivo. Nature. 2015;518:542–6 Uses labeling techniques to quantitate murine hematopoiesis in homeostasis and stress. CrossRefGoogle Scholar
  36. 36.
    •• Simons BD. Deep sequencing as a probe of normal stem cell fate and preneoplasia in human epidermis. PNAS. 2016;113:128–33 Uses somatic mutations as genetic labels to obtain insight into human stem cell dynamics. CrossRefGoogle Scholar
  37. 37.
    •• Lan X, Jörg DJ, Cavalli FMG, Richards LM, Nguyen LV, Vanner RJ, et al. Fate mapping of human glioblastoma reveals an invariant stem cell hierarchy. Nature. 2017;549:227–32 Provides evidence that clonal dynamics in glioma is mostly based on neutral competition. CrossRefGoogle Scholar
  38. 38.
    Ling S, Hu Z, Yang Z, Yang F, Li Y, Lin P, et al. Extremely high genetic diversity in a single tumor points to prevalence of non-Darwinian cell evolution. PNAS. 2015;112:E6496–505.CrossRefGoogle Scholar
  39. 39.
    Ernst PA, Kimmel M, Kurpas M, Zhou Q. Thick distribution tails in models of cancer secondary tumors. arXiv:1801.00982v1. 2018.
  40. 40.
    Hanahan D, Weinberg RA. Hallmarks of cancer: the next generation. Cell. 2011;144:646–74.CrossRefGoogle Scholar
  41. 41.
    Dufour A, Gontran E, Deroulers C, Varlet P, Pallud J, Grammaticos B, et al. Modeling the dynamics of oligodendrocyte precursor cells and the genesis of gliomas. PLoS Comput Biol. 2018;14(3):e1005977.CrossRefGoogle Scholar
  42. 42.
    Stiehl T, Marciniak-Czochra A. Mathematical modeling of leukemogenesis and cancer stem cell dynamics. Math Model Nat Phenomena. 2012;7:166–202.CrossRefGoogle Scholar
  43. 43.
    Gentry SN, Jackson TL. A mathematical model of cancer stem cell driven tumor initiation: implications of niche size and loss of homeostatic regulatory mechanisms. PLoS One. 2013;8:e71128.CrossRefGoogle Scholar
  44. 44.
    • Stiehl T, Ho AD, Marciniak-Czochra A. The impact of CD34+ cell dose on engraftment after SCTs: personalized estimates based on mathematical modeling. Bone Marrow Transplant. 2014;49:30–7. Provides evidence that some patients might profit from higher doses of transplanted cells. CrossRefGoogle Scholar
  45. 45.
    Theocharides A, Rongvaux A, Fritsch K, Flavell R, Manz M. Humanized hemato-lymphoid system mice. Haematologica. 2016;101:5–19.CrossRefGoogle Scholar
  46. 46.
    Matatall KA, Jeong M, Chen S, Sun D, Chen F, Mo Q, et al. Chronic infection depletes hematopoietic stem cells through stress-induced terminal differentiation. Cell Rep. 2016;17(10):2584–95.CrossRefGoogle Scholar
  47. 47.
    Andersen M, Sajid Z, Pedersen RK, Gudmand-Hoeyer J, Ellervik C, Skov V, et al. Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development. PLoS One. 2017;12(8):e0183620.CrossRefGoogle Scholar
  48. 48.
    Walenda T, Stiehl T, Braun H, Fröbel J, Ho AD, Schroeder T, et al. Feedback signals in myelodysplastic syndromes: increased self-renewal of the malignant clone suppresses normal hematopoiesis. PLoS Comput Biol. 2014;10:e1003599.CrossRefGoogle Scholar
  49. 49.
    Goldman A, Majumder B, Dhawan A, Ravi S, Goldman D, Kohandel M, et al. Temporally sequenced anticancer drugs overcome adaptive resistance by targeting a vulnerable chemotherapy-induced phenotypic transition. Nat Commun. 2015;6:6139.CrossRefGoogle Scholar
  50. 50.
    Zapperi S, La Porta CA. Do cancer cells undergo phenotypic switching? The case for imperfect cancer stem cell markers. Sci Rep. 2012;2:441.CrossRefGoogle Scholar
  51. 51.
    Zhou D, Mao S, Cheng J, Chen K, Cao X, Hu J. A Bayesian statistical analysis of stochastic phenotypic plasticity model of cancer cells. J Theor Biol. 2018;454:70–9.CrossRefGoogle Scholar
  52. 52.
    • Kozłowska E, Färkkilä A, Vallius T, Carpén O, Kemppainen J, Grénman S, et al. Mathematical modeling predicts response to chemotherapy and drug combinations in ovarian cancer. Cancer Res. 2018;78(14):4036–44 Develops a stochastic modeling approach to predict resistance development and outcome of different drug combinations in ovarian cancer. CrossRefGoogle Scholar
  53. 53.
    Bayer P, Brown JS, Staňková K. A two-phenotype model of immune evasion by cancer cells. J Theor Biol. 2018;455:191–204.CrossRefGoogle Scholar
  54. 54.
    Mahasa KJ, Ouifki R, Eladdadi A, Pillis L. Mathematical model of tumor-immune surveillance. J Theor Biol. 2016;404:312–30.CrossRefGoogle Scholar
  55. 55.
    Djema W, Bonnet C, Mazenc F, Clairambault J, Fridman E, Hirsch P, et al. Control in dormancy or eradication of cancer stem cells: mathematical modeling and stability issues. J Theor Biol. 2018;449:103–23.CrossRefGoogle Scholar
  56. 56.
    • Tonekaboni SAM, Dhawan A, Kohandel M. Mathematical modelling of plasticity and phenotype switching in cancer cell populations. Math Biosci. 2017;283:30–7 Provides evidence that, depending on the context, dedifferentiation of cancer cells can be advanategeous or disadvantageous for survival of the cancer cell population. CrossRefGoogle Scholar
  57. 57.
    Medina MÁ. Mathematical modeling of cancer metabolism. Crit Rev Oncol Hematol. 2018;124:37–40.CrossRefGoogle Scholar
  58. 58.
    Wooten DJ, Quaranta V. Mathematical models of cell phenotype regulation and reprogramming: make cancer cells sensitive again! Biochim Biophys Acta. 2017;1867(2):167–75.Google Scholar
  59. 59.
    Wang J. Landscape and flux theory of non-equilibrium dynamical systems with application to biology. Adv Phys. 2015;64(1):1–137.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Applied Mathematics, Interdisciplinary Center of Scientific Computing and BioQuant CenterHeidelberg UniversityHeidelbergGermany

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