Understanding the impact of feedback regulations on blood cell production and leukemia dynamics using model analysis and simulation of clinically relevant scenarios

Acute myeloid leukemia (AML) is a paradigmatic example of a stem cell-driven cancer. AML belongs to the most aggressive malignancies and has a poor prognosis. A hallmark of AML is the expansion of malignant cells in the bone marrow and the out-competition of healthy blood-forming (hematopoietic) cells. In the present study, we develop a nonlinear ordinary differential equation model to study the impact of feedback configurations and kinetic cell properties such as symmetric self-renewal probability, symmetric differentiation probability, asymmetric division probability, proliferation rate, or death rate on leukemic cell population dynamics. The model accounts for two healthy cell types (mature and immature) and for two leukemic cell types (cells that can divide and cells that have lost the ability to divide). The model considered here is a generalization of previous models and contains them as a special case. We consider multiple feedback configurations that differ in their impact on symmetric self-renewal, symmetric differentiation, and asymmetric division probabilities. Linearized stability analysis is performed to derive necessary and sufficient conditions for the expansion or extinction of leukemic cells. In our analysis, we distinguish three types of steady states, namely purely leukemic steady states (presence of leukemic and absence of healthy cells), healthy steady states (presence of healthy cells and absence of leukemic cells), and composite steady states where healthy and leukemic cells coexist. Steady-state analysis reveals that under biologically plausible assumptions the healthy and the purely leukemic steady states are unique. If composite steady states exist, they are non-unique and form a one-dimensional manifold. The purely leukemic steady state is locally asymptotically stable if and only if the steady state of healthy cells is unstable. The analytical results are illustrated by numerical simulations. Our models suggest that a slight increase of the symmetric self-renewal probability or a slight decrease of the symmetric differentiation probability in leukemic compared to healthy cells results in a destabilization of the homeostatic equilibrium and expansion of malignant cells. This finding is in line with the differentiation arrest observed in leukemic cells. Changes of these parameters in the opposite direction can re-establish the healthy population. Our model furthermore suggests that the configuration of the feedback loops impacts on healthy cell regeneration, the growth rate of malignant cells, the malignant cell burden in late stage leukemias and the decline of healthy cells in leukemic patients.