ii. AbstractStatistical and mathematical modeling are crucial to describe, interpret, compare and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment. The current prominence of high-resolution and live-cell imaging data provides an unprecedented opportunity to study the spatiotemporal dynamics of these cells within their stem cell niche and learn more about aberrant, but also unperturbed, normal hematopoiesis. However, this requires careful quantitative statistical analysis of the spatial and temporal behavior of cells and the interaction with their microenvironment. Moreover, such quantification is a prerequisite for the construction of hypothesis-driven mathematical models that can provide mechanistic explanations by generating spatiotemporal dynamics that can be directly compared to experimental observations. Here, we provide a brief overview of statistical methods in analyzing spatial distribution of cells, cell motility, cell shapes and cellular genealogies. We also describe cellbased modeling formalisms that allow researchers to simulate emergent behavior in a multicellular system based on a set of hypothesized mechanisms. Together, these methods provide a quantitative workflow for the analytic and synthetic study of the spatiotemporal behavior of hematopoietic stem and progenitor cells.iii.
IntroductionDespite major advances in the identification of molecular and genetic components and biomarkers of the local bone marrow environments ("niches"), in which hematopoietic stem and progenitor cells (HSPC) reside, much remains to be learned about the spatiotemporal dynamics of normal and aberrant hematopoiesis (1-3). There are many remaining open questions concerning e.g. the localization of HSPC relative to various, potentially different stem cell niches, their chemotactic and migratory behavior within the bone marrow, the heterogeneity of cellular morphologies, the role of niche factors on cell fate decisions, etc.Modern microscopy provides image data with increasing spatial and temporal resolution, e.g. high resolution imaging of deep tissue of the bone marrow (4), live cell video microscopy of stem cell cultures (5-7), as well as intravital imaging of HSPC within the bone marrow (8-11). However, in order to interpret such rich image data and use it to test scientific hypothesis, e.g. on the spatiotemporal organization of HSPCs, requires statistical and mathematical modeling. On the one hand, data-driven statistical models provide frameworks to describe and quantify experimentally observed aspects of HSPC behavior, to formulate (null-)hypotheses, and to formally compare and potentially distinguish the observed behavior from a formulated hypothesis, such as random behavior. Hypothesis-driven mathematical models, on the other hand, provide mathematical and computational frameworks to test whether a set of assumptions on the cellular behavior and interactions of cells is, in principle, able to generate the observe...