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Explore the complex mathematical challenges in modeling hematopoietic stem cell (HSC) dynamics and clonal progression in this 42-minute conference talk from IPAM's Mathematics of Cancer workshop. Delve into the fundamental question of whether HSCs exist in binary "active" or "quiescent" states or operate along a continuous spectrum of functional activity, examining how individual HSCs may gradually shift their proliferative activity and differentiation potential in response to external cues. Learn about the mathematical frameworks needed to model state-dependent division, differentiation and death rates, and discover how to relate continuum models to experimentally accessible markers such as flow-cytometry and sequencing data. Investigate the clinical challenges of detecting and monitoring rare clones that emerge early in life and drive gradual clonal expansion over decades, potentially contributing to leukemia and other hematological diseases. Understand the formal frameworks required to distinguish pre-leukemic clonal expansion from physiological fluctuations, quantify uncertainty in clonal developments, and identify relevant competition parameters from realistic datasets. Examine the computational and theoretical challenges in parameter estimation, identifiability, and efficiency for advanced mechanistic models of HSC organization and leukemia progression, essential for risk stratification in clonal hematopoiesis and development of targeted therapeutic interventions.
