  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.
