A structured population model of clonal selection in acute leukemias with multiple maturation stages

J Math Biol. 2019 Oct;79(5):1587-1621. doi: 10.1007/s00285-019-01404-w. Epub 2019 Jul 26.


Recent progress in genetic techniques has shed light on the complex co-evolution of malignant cell clones in leukemias. However, several aspects of clonal selection still remain unclear. In this paper, we present a multi-compartmental continuously structured population model of selection dynamics in acute leukemias, which consists of a system of coupled integro-differential equations. Our model can be analysed in a more efficient way than classical models formulated in terms of ordinary differential equations. Exploiting the analytical tractability of this model, we investigate how clonal selection is shaped by the self-renewal fraction and the proliferation rate of leukemic cells at different maturation stages. We integrate analytical results with numerical solutions of a calibrated version of the model based on real patient data. In summary, our mathematical results formalise the biological notion that clonal selection is driven by the self-renewal fraction of leukemic stem cells and the clones that possess the highest value of this parameter are ultimately selected. Moreover, we demonstrate that the self-renewal fraction and the proliferation rate of non-stem cells do not have a substantial impact on clonal selection. Taken together, our results indicate that interclonal variability in the self-renewal fraction of leukemic stem cells provides the necessary substrate for clonal selection to act upon.

Keywords: Acute leukemia; Asymptotic analysis; Clonal selection; Continuously structured population models; Integro-differential equations.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Acute Disease
  • Cell Differentiation
  • Cell Proliferation
  • Cell Self Renewal
  • Clonal Evolution* / genetics
  • Clone Cells / pathology
  • Computer Simulation
  • Humans
  • Leukemia / genetics
  • Leukemia / pathology*
  • Mathematical Concepts
  • Models, Biological*
  • Neoplastic Stem Cells / pathology