How to Characterize Stem Cells? Contributions from Mathematical Modeling

Mathematics of neural stem cells: Linking data and processes

Adult stem cells are described as a discrete population of cells that stand at the top of a hierarchy of progressively differentiating cells. Through their unique ability to self-renew and differentiate, they regulate the number of end-differentiated cells that contribute to tissue physiology. The question of how discrete, continuous, or reversible the transitions through these hierarchies are and the precise parameters that determine the ultimate performance of stem cells in adulthood are the subject of intense research. In this review, we explain how mathematical modelling has improved the mechanistic understanding of stem cell dynamics in the adult brain. We also discuss how single-cell sequencing has influenced the understanding of cell states or cell types. Finally, we discuss how the combination of single-cell sequencing technologies and mathematical modelling provides a unique opportunity to answer some burning questions in the field of stem cell biology.

Understanding Hematopoietic Stem Cell Dynamics—Insights from Mathematical Modelling

Purpose of review

Hematopoietic stem cells (HSCs) drive blood-cell production (hematopoiesis). Out-competition of HSCs by malignant cells occurs in many hematologic malignancies like acute myeloid leukemia (AML). Through mathematical modelling, HSC dynamics and their impact on healthy blood cell formation can be studied, using mathematical analysis and computer simulations. We review important work within this field and discuss mathematical modelling as a tool for attaining biological insight.

Recent findings

Various mechanism-based models of HSC dynamics have been proposed in recent years. Key properties of such models agree with observations and medical knowledge and suggest relations between stem cell properties, e.g., rates of division and the temporal evolution of the HSC population. This has made it possible to study how HSC properties shape clinically relevant processes, including engraftment following an HSC transplantation and the response to different treatment.

Summary

Understanding how properties of HSCs affect hematopoiesis is important for efficient treatment of diseases. Mathematical modelling can contribute significantly to these efforts.

Dynamic behavior and stabilization of brain cell reconstitution after stroke under the proliferation and differentiation processes for stem cells

Stem cells play a critical role in regulatory operations, overseeing tissue regeneration and tissue homeostasis. In this paper, a mathematical model is proposed and analyzed to study the impact of stem cell transplantation on the dynamical behavior of stroke therapy, which is assumed to be based on transplanting dead brain cells following a stroke. We transform the method of using hierarchical cell systems into a method of using different compartment variables by using ordinary differential equations, each of which elucidates a well-defined differentiation stage along with the effect of mature cells in improving the brain function after a stroke. Stem cells, progenitor cells, and the impacts of the stem cells transplanted on brain cells are among the variables considered. The model is studied analytically and solved numerically using the fourth-order Runge-Kutta method. We analyze the structure of equilibria, the ability of neural stem cells to proliferate and differentiate, and the stability properties of equilibria for stem cell transplantation. The model is considered to be stable after transplantation if the stem cells and progenitor cells differentiate into mature nerve cells in the brain. The results of the model analysis and simulation facilitate the identification of various biologically probable parameter sets that can explain the optimal time for stem cell replacement of damaged brain cells. Associating the classified parameter sets with recent experimental and clinical findings contributes to a better understanding of therapeutic mechanisms that promote the reconstitution of brain cells after an ischemic stroke.

Mathematical Modeling Provides Evidence for Niche Competition in Human AML and Serves as a Tool to Improve Risk Stratification

Acute myeloid leukemia (AML) is a stem cell-driven malignant disease. There is evidence that leukemic stem cells (LSC) interact with stem cell niches and outcompete hematopoietic stem cells (HSC). The impact of this interaction on the clinical course of the disease remains poorly understood. We developed and validated a mathematical model of stem cell competition in the human HSC niche. Model simulations predicted how processes in the stem cell niche affect the speed of disease progression. Combining the mathematical model with data of individual patients, we quantified the selective pressure LSCs exert on HSCs and demonstrated the model's prognostic significance. A novel model-based risk-stratification approach allowed extraction of prognostic information from counts of healthy and malignant cells at the time of diagnosis. This model's feasibility was demonstrable based on a cohort of patients with ALDH-rare AML and shows that the model-based risk stratification is an independent predictor of disease-free and overall survival. This proof-of-concept study shows how model-based interpretation of patient data can improve prognostic scoring and contribute to personalized medicine. SIGNIFICANCE: Combining a novel mathematical model of the human hematopoietic stem cell niche with individual patient data enables quantification of properties of leukemic stem cells and improves risk stratification in acute myeloid leukemia.