Clonal selection and therapy resistance in acute leukaemias: mathematical modelling explains different proliferation patterns at diagnosis and relapse

Abstract

Recent experimental evidence suggests that acute myeloid leukaemias may originate from multiple clones of malignant cells. Nevertheless, it is not known how the observed clones may differ with respect to cell properties, such as proliferation and self-renewal. There are scarcely any data on how these cell properties change due to chemotherapy and relapse. We propose a new mathematical model to investigate the impact of cell properties on the multi-clonal composition of leukaemias. Model results imply that enhanced self-renewal may be a key mechanism in the clonal selection process. Simulations suggest that fast proliferating and highly self-renewing cells dominate at primary diagnosis, while relapse following therapy-induced remission is triggered mostly by highly self-renewing but slowly proliferating cells. Comparison of simulation results to patient data demonstrates that the proposed model is consistent with clinically observed dynamics based on a clonal selection process.

A mathematical model of subpopulation kinetics for the deconvolution of leukaemia heterogeneity

“…Clonal heterogeneity of AML and competitive outgrowth of more 'fit' clones in a 'Darwinian' model render the successful treatment of this disease particularly challenging [34]. It is currently unclear which factors within a subclone or in the microenvironment make certain clones out-compete others and how this dynamic can be altered by chemotherapy schedule [9,34,35]. Recently, it has been proposed that tumour-specific cell-autonomous and non-cell-autonomous factors (e.g.…”

Cell Division Patterns in Acute Myeloid Leukemia Stem-like Cells Determine Clinical Course: A Model to Predict Patient Survival

“…Furthermore, we postulate that clearance rates of blasts are constant over time. This might be accurate, provided that there exists still unoccupied bone marrow space (41).…”

“…Especially during the early phase of the disease, when leukemic cell numbers are still small, consumption of resources by healthy cells is not negligible, because it is higher than consumption of resources by leukemic cells. A model including a different mechanism of competition between leukemic and hematopoietic cells has been proposed in (41) and shows similar dynamic properties. Figure 1 gives a schematic representation of the model.…”

“…We further presume that the level of the feedback signal decreases if mature cell counts or leukemic blast counts increase. This form of feedback can be interpreted as competition between healthy and leukemic cells for environmental factors or bone marrow niche space (38,41). The competition of healthy and leukemic cells for environmental factors makes it necessary to model both lineages.…”

Blood Cell Dynamics: Half of a Century of Modelling

“…Most of the published works of the beginning of this decade are in the continuity of the end of the 2000's: cyclical neutropenia treatment by G-CSF [181], [182], [71], [94], [301], CML study [139], [158], [224], [106], [48], [178], [257], AML study [275], [274], [47], granulopoiesis [262], [263], HSC study [234], [207], [277], [33], [276], [281], [218], [5], [18], [136], [74] (with two nice reviews dealing with treatments of hematological diseases [96]), [294], very few on erythropoiesis [90], [261], [68] megakaryopoiesis [269], cell fate analysis [219]. There were mathematical development of structured populations [70], [111], [67], [114] with delay equations [20], [88], [21], [15], [59], [4], …”