A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

STOCHASTIC MODELING OF HEMATOPOIETIC STEM CELL DYNAMICS

The study of hematopoietic stem cell (HSCs) maintenance and differentiation to supply the hematopoietic system presents unique challenges, given the complex regulation of the process and the difficulty in observing cellular interactions in the stem cell niche. Quantitative methods and tools have emerged as valuable mechanisms to address this issue; however, the stochasticity of HSCs presents significant challenges for mathematical modeling, especially when bridging the gap between theoretical models and experimental validation. In this work, we have built a flexible and user-friendly stochastic dynamical and spatial model for long-term HSCs (LT-HSCs) and short-term HSCs (ST-HSCs) that captures experimentally observed cellular variability and heterogeneity. Our model implements the behavior of LT-HSCs and ST-HSCs and predicts their homeostatic dynamics. Furthermore, our model can be modified to explore various biological scenarios, such as stress-induced perturbations mediated by apoptosis, and successfully implement these conditions. Finally, the model incorporates spatial dynamics, simulating cell behavior in a 2D environment by combining Brownian motion with spatially graded parameters.

An integrative systems biology approach to overcome venetoclax resistance in acute myeloid leukemia

The over-expression of the Bcl-2 protein is a common feature of many solid cancers and hematological malignancies, and it is typically associated with poor prognosis and resistance to chemotherapy. Bcl-2-specific inhibitors, such as venetoclax, have recently been approved for the treatment of chronic lymphocytic leukemia and small lymphocytic lymphoma, and they are showing promise in clinical trials as a targeted therapy for patients with relapsed or refractory acute myeloid leukemia (AML). However, successful treatment of AML with Bcl-2-specific inhibitors is often followed by the rapid development of drug resistance. An emerging paradigm for overcoming drug resistance in cancer treatment is through the targeting of mitochondrial energetics and metabolism. In AML in particular, it was recently observed that inhibition of mitochondrial translation via administration of the antibiotic tedizolid significantly affects mitochondrial bioenergetics, activating the integrated stress response (ISR) and subsequently sensitizing drug-resistant AML cells to venetoclax. Here we develop an integrative systems biology approach to acquire a deeper understanding of the molecular mechanisms behind this process, and in particular, of the specific role of the ISR in the commitment of cells to apoptosis. Our multi-scale mathematical model couples the ISR to the intrinsic apoptosis pathway in venetoclax-resistant AML cells, includes the metabolic effects of treatment, and integrates RNA, protein level, and cellular viability data. Using the mathematical model, we identify the dominant mechanisms by which ISR activation helps to overcome venetoclax resistance, and we study the temporal sequencing of combination treatment to determine the most efficient and robust combination treatment protocol.

In this work, we develop a multi-scale systems biology approach to study the mechanisms by which the integrated stress response (ISR) activation helps to overcome venetoclax resistance in acute myeloid leukemia (AML). The multi-scale model enables the integration of RNA-level, protein-level, and cellular viability and proliferation data. The model developed in this work can predict several important features of the resistant AML cell lines that are consistent with experimental data. Further, our integrative systems biology approach led to the determination of the optimal combination treatment protocol.

Stability Analysis of Equilibria for a Model of Maintenance Therapy in Acute Lymphoblastic Leukemia

In this paper, we study two mathematical models, involving delay differential equations, which describe the processes of erythropoiesis and leukopoiesis in the case of maintenance therapy for acute lymphoblastic leukemia. All types of possible equilibrium points were determined, and their stability was analyzed. For some of the equilibrium points, conditions for parameters that imply stability were obtained. When this was not feasible, due to the complexity of the characteristic equation, we discuss the stability through numerical simulations. An important part of the stability study for each model is the examination of the critical case of a zero root of the characteristic equation. The mathematical results are accompanied by biological interpretations.

On the Controllability of a System Modeling Cell Dynamics Related to Leukemia

In this paper, two control problems for a symmetric model of cell dynamics related to leukemia are considered. The first one, in connection with classical chemotherapy, is that the evolution of the disease under treatment should follow a prescribed trajectory assuming that the drug works by increasing the cell death rates of both malignant and normal cells. In the case of the second control problem, as for targeted therapies, the drug is assumed to work by decreasing the multiplication rate of leukemic cells only, and the control objective is that the disease state reaches a desired endpoint. The solvability of the two problems as well as their stability are proved by using a general method of analysis. Some numerical simulations are included to illustrate the theoretical results and prove their applicability. The results can possibly be used to design therapeutic scenarios such that an expected clinical evolution can be achieved.

Analysis of the effectiveness of the treatment of solid tumors in two cases of drug administration

A complete stability analysis of the equilibrium solutions of a system modeling tumor chemotherapy is performed in two cases of administration of the treatment, by continuous infusion and by periodic infusion. Several numerical simulations illustrate and complement the theory.