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arXiv · 1907.02842

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

Tommaso Lorenzi·Anna Marciniak-Czochra·Thomas Stiehl
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Abstract

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.

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Tommaso Lorenzi, Anna Marciniak-Czochra, Thomas Stiehl. 2019-07-05. A structured population model of clonal selection in acute leukemias with multiple maturation stages. https://arxiv.org/abs/1907.02842

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