Skip to main content
SpringerLink
Log in

Evolutionary dynamics of cancer: From epigenetic regulation to cell population dynamics—mathematical model framework, applications, and open problems

  • Reviews
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

Predictive modeling of the evolutionary dynamics of cancer is a challenging issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer, including plasticity and heterogeneity in cancer cells. Cancer is a group of diseases involving abnormal cell growth, during which abnormal regulation of stem cell regeneration is essential for the dynamics of cancer development. In general, the dynamics of stem cell regeneration can be simplified as a G0 phase cell cycle model, which leads to a delay differentiation equation. When cell heterogeneity and plasticity are considered, we establish a differential-integral equation based on the random transition of epigenetic states of stem cells during cell division. The proposed model highlights cell heterogeneity and plasticity; connects the heterogeneity with cell-to-cell variance in cellular behaviors (for example, proliferation, apoptosis, and differentiation/senescence); and can be extended to include gene mutation-induced tumor development. Hybrid computational models are developed based on the mathematical model framework and are applied to the processes of inflammation-induced tumorigenesis and tumor relapse after chimeric antigen receptor (CAR)-T cell therapy. Finally, we propose several mathematical problems related to the proposed differential-integral equation. Solutions to these problems are crucial for understanding the evolutionary dynamics of cancer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bernard S, Bélair J, Mackey M C. Oscillations in cyclical neutropenia: New evidence based on mathematical modeling. J Theoret Biol, 2003, 223: 283–298

    MathSciNet  Google Scholar 

  2. Burns F J, Tannock I F. On the existence of a Go-phase in the cell cycle. Cell Tissue Kinet, 1970, 3: 321–334

    Google Scholar 

  3. Chamseddine I M, Rejniak K A. Hybrid modeling frameworks of tumor development and treatment. WIREs Syst Biol Med, 2020, 12: e1461

    Google Scholar 

  4. Chang H H, Hemberg M, Barahona M, et al. Transcriptome-wide noise controls lineage choice in mammalian progenitor cells. Nature, 2008, 453: 544–547

    Google Scholar 

  5. Clevers H. At the crossroads of inflammation and cancer. Cell, 2004, 118: 671–674

    Google Scholar 

  6. de Martel C, Ferlay J, Franceschi S, et al. Global burden of cancers attributable to infections in 2008: A review and synthetic analysis. Lancet Oncol, 2012, 13: 607–615

    Google Scholar 

  7. Dingli D, Traulsen A, Pacheco J M. Stochastic dynamics of hematopoietic tumor stem cells. Cell Cycle, 2007, 6: 461–466

    Google Scholar 

  8. Dykstra B, Kent D, Bowie M, et al. Long-term propagation of distinct hematopoietic differentiation programs in vivo. Stem Cell, 2007, 1: 218–229

    Google Scholar 

  9. Elinav E, Nowarski R, Thaiss C A, et al. Inflammation-induced cancer: Crosstalk between tumours, immune cells and microorganisms. Nat Rev Cancer, 2013, 13: 759–771

    Google Scholar 

  10. Gibson T M, Gersbach C A. Single-molecule analysis of myocyte differentiation reveals bimodal lineage commitment. Integr Biol (Camb), 2015, 7: 663–671

    Google Scholar 

  11. Graf T. Differentiation plasticity of hematopoietic cells. Blood, 2002, 99: 3089–3101

    Google Scholar 

  12. Grivennikov S I, Greten F R, Karin M. Immunity, inflammation, and cancer. Cell, 2010, 140: 883–899

    Google Scholar 

  13. Guo Y C, Nie Q, MacLean A L, et al. Multiscale modeling of inflammation-induced tumorigenesis reveals competing oncogenic and onco-protective roles for inflammation. Cancer Res, 2017, 77: 6429–6441

    Google Scholar 

  14. Hanahan D, Weinberg R A. The hallmarks of cancer. Cell, 2000, 100: 57–70

    Google Scholar 

  15. Hanselmann R G, Welter C. Origin of cancer: An information, energy, and matter disease. Front Cell Dev Biol, 2016, 4: 121

    Google Scholar 

  16. Hayashi K, de Sousa Lopes S M C, Tang F C, et al. Dynamic equilibrium and heterogeneity of mouse pluripotent stem cells with distinct functional and epigenetic states. Stem Cell, 2008, 3: 391–401

    Google Scholar 

  17. Hu G M, Lee C Y, Chen Y-Y, et al. Mathematical model of heterogeneous cancer growth with an autocrine signalling pathway. Cell Prolif, 2012, 45: 445–455

    Google Scholar 

  18. Huang R S, Lei J Z. Dynamics of gene expression with positive feedback to histone modifications at bivalent domains. Internat J Modern Phys B, 2017, 4: 1850075

    MathSciNet  Google Scholar 

  19. Huang R S, Lei J Z. Cell-type switches induced by stochastic histone modification inheritance. Discrete Contin Dyn Syst Ser B, 2019, 22: 1–19

    MathSciNet  MATH  Google Scholar 

  20. Lander A D, Gokoffski K K, Wan F Y M, et al. Cell lineages and the logic of proliferative control. PLoS Biol, 2009, 7: e15

    Google Scholar 

  21. Le Magnen C, Shen M M, Abate-Shen C. Lineage plasticity in cancer progression and treatment. Annu Rev Cancer Biol, 2018, 2: 271–289

    Google Scholar 

  22. Lei J Z. A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration. BioRxiv, 2019, https://doi.org/10.1101/592139

  23. Lei J Z, Levin S A, Nie Q. Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation. Proc Natl Acad Sci USA, 2014, 111: E880–E887

    MathSciNet  MATH  Google Scholar 

  24. Lei J Z, Mackey M C. Multistability in an age-structured model of hematopoiesis: Cyclical neutropenia. J Theoret Biol, 2011, 270: 143–153

    MathSciNet  MATH  Google Scholar 

  25. Mackey M C. Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. Blood, 1978, 51: 941–956

    Google Scholar 

  26. Mackey M C. Cell kinetic status of haematopoietic stem cells. Cell Prolif, 2001, 34: 71–83

    Google Scholar 

  27. Malta T M, Sokolov A, Gentles A J, et al. Machine learning identifies stemness features associated with oncogenic dedifferentiation. Cell, 2018, 173: 338–354

    Google Scholar 

  28. Mangel M, Bonsall M B. Phenotypic evolutionary models in stem cell biology: Replacement, quiescence, and variability. PLoS One, 2008, 3: e1591

    Google Scholar 

  29. Mangel M, Bonsall M B. Stem cell biology is population biology: Differentiation of hematopoietic multipotent progenitors to common lymphoid and myeloid progenitors. Theor Biol Med Model, 2013, 10: 5

    Google Scholar 

  30. Parkin D M. The global health burden of infection-associated cancers in the year 2002. Int J Cancer, 2006, 118: 3030–3044

    Google Scholar 

  31. Probst A V, Dunleavy E, Almouzni G. Epigenetic inheritance during the cell cycle. Nat Rev Mol Cell Biol, 2009, 10: 192–206

    Google Scholar 

  32. Puram S V, Tirosh I, Parikh A S, et al. Single-cell transcriptomic analysis of primary and metastatic tumor ecosystems in head and neck cancer. Cell, 2017, 171: 1611–1624

    Google Scholar 

  33. Rockne R C, Hawkins-Daarud A, Swanson K R, et al. The 2019 mathematical oncology roadmap. Phys Biol, 2019, 16: 041005

    Google Scholar 

  34. Rodriguez-Brenes I A, Komarova N L, Wodarz D. Evolutionary dynamics of feedback escape and the development of stem-cell-driven cancers. Proc Natl Acad Sci USA, 2011, 108: 18983–18988

    Google Scholar 

  35. Schepeler T, Page M E, Jensen K B. Heterogeneity and plasticity of epidermal stem cells. Development, 2014, 141: 2559–2567

    Google Scholar 

  36. Serra-Cardona A, Zhang Z G. Replication-coupled nucleosome assembly in the passage of epigenetic information and cell identity. Trends Biochem Sci, 2018, 43: 136–148

    Google Scholar 

  37. Singer Z S, Yong J, Tischler J, et al. Dynamic heterogeneity and DNA methylation in embryonic stem cells. Mol Cell, 2014, 55: 319–331

    Google Scholar 

  38. Situ Q J, Lei J Z. A mathematical model of stem cell regeneration with epigenetic state transitions. Mol Biol Evol, 2017, 14: 1379–1397

    MathSciNet  MATH  Google Scholar 

  39. Song Y, Yang S Y, Lei J Z. ParaCells: A GPU architecture for cell-centered models in computational biology. IEEE/ACM Trans Comput Biol Bioinf, 2018, 16: 994–1006

    Google Scholar 

  40. Su Y P, Wei W, Robert L, et al. Single-cell analysis resolves the cell state transition and signaling dynamics associated with melanoma drug-induced resistance. Proc Natl Acad Sci USA, 2017, 114: 13679–13684

    Google Scholar 

  41. Takaoka K, Hamada H. Origin of cellular asymmetries in the pre-implantation mouse embryo: A hypothesis. Philos Trans R Soc Lond B Biol Sci, 2014, 369: 20130536

    Google Scholar 

  42. Tarabichi M, Antoniou A, Saiselet M, et al. Systems biology of cancer: Entropy, disorder, and selection-driven evolution to independence, invasion and “swarm intelligence”. Cancer Metastasis Rev, 2013, 32: 403–421

    Google Scholar 

  43. Traulsen A, Lenaerts T, Pacheco J M, et al. On the dynamics of neutral mutations in a mathematical model for a homogeneous stem cell population. J R Soc Interface, 2012, 10: 20120810

    Google Scholar 

  44. Wu H, Zhang Y. Reversing DNA methylation: Mechanisms, genomics, and biological functions. Cell, 2014, 156: 45–68

    Google Scholar 

  45. Zernicka-Goetz M, Morris S A, Bruce A W. Making a firm decision: Multifaceted regulation of cell fate in the early mouse embryo. Nat Rev Genet, 2009, 10: 467–477

    Google Scholar 

  46. Zhou D, Wu D M, Li Z, et al. Population dynamics of cancer cells with cell state conversions. Quant Biol, 2013, 1: 201–208

    Google Scholar 

Download references

Acknowledgements

This research was supported by National Natural Science Foundation of China (Grant Nos. 91730101 and 11831015).

Author information

Author notes

  1. Jinzhi Lei

    Present address: Current address: School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China

Authors and Affiliations

  1. Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, 100084, China

    Jinzhi Lei

Authors
  1. Jinzhi Lei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinzhi Lei.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lei, J. Evolutionary dynamics of cancer: From epigenetic regulation to cell population dynamics—mathematical model framework, applications, and open problems. Sci. China Math. 63, 411–424 (2020). https://doi.org/10.1007/s11425-019-1629-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-019-1629-7

Keywords

MSC(2010)

Search

Navigation