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

## TL;DR

This paper develops a structured population model to understand clonal selection in acute leukemias, highlighting the role of self-renewal fractions in driving clonal dominance, and providing analytical and numerical insights based on patient data.

## Contribution

It introduces a multi-compartmental, analytically tractable model of leukemia clonal dynamics that incorporates multiple maturation stages and is calibrated with real patient data.

## Key findings

- Clonal selection is primarily driven by self-renewal fractions of leukemic stem cells.
- Proliferation rates of non-stem cells have limited impact on clonal selection.
- The model offers a formal understanding of how clonal dominance emerges in leukemia.

## 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.