Statistical and Mathematical Modeling of Spatiotemporal Dynamics of Stem Cells

Mapping Spatiotemporal Heterogeneity in Tumor Profiles by Integrating High-Throughput Imaging and Omics Analysis

Intratumoral heterogeneity associates with more aggressive disease progression and worse patient outcomes. Understanding the reasons enabling the emergence of such heterogeneity remains incomplete, which restricts our ability to manage it from a therapeutic perspective. Technological advancements such as high-throughput molecular imaging, single-cell omics, and spatial transcriptomics allow recording of patterns of spatiotemporal heterogeneity in a longitudinal manner, thus offering insights into the multiscale dynamics of its evolution. Here, we review the latest technological trends and biological insights from molecular diagnostics as well as spatial transcriptomics, both of which have witnessed burgeoning growth in the recent past in terms of mapping heterogeneity within tumor cell types as well as the stromal constitution. We also discuss ongoing challenges, indicating possible ways to integrate insights across these methods to have a systems-level spatiotemporal map of heterogeneity in each tumor and a more systematic investigation of the implications of heterogeneity for patient outcomes.

Spatial molecular profiling: platforms, applications and analysis tools

Molecular profiling technologies, such as genome sequencing and proteomics, have transformed biomedical research, but most such technologies require tissue dissociation, which leads to loss of tissue morphology and spatial information. Recent developments in spatial molecular profiling technologies have enabled the comprehensive molecular characterization of cells while keeping their spatial and morphological contexts intact. Molecular profiling data generate deep characterizations of the genetic, transcriptional and proteomic events of cells, while tissue images capture the spatial locations, organizations and interactions of the cells together with their morphology features. These data, together with cell and tissue imaging data, provide unprecedented opportunities to study tissue heterogeneity and cell spatial organization. This review aims to provide an overview of these recent developments in spatial molecular profiling technologies and the corresponding computational methods developed for analyzing such data.

The recent advances in the mathematical modelling of human pluripotent stem cells

Human pluripotent stem cells hold great promise for developments in regenerative medicine and drug design. The mathematical modelling of stem cells and their properties is necessary to understand and quantify key behaviours and develop non-invasive prognostic modelling tools to assist in the optimisation of laboratory experiments. Here, the recent advances in the mathematical modelling of hPSCs are discussed, including cell kinematics, cell proliferation and colony formation, and pluripotency and differentiation.

Quantitative Spatial Analysis of Metabolic Heterogeneity Across in vivo and in vitro Tumor Models

Metabolic preferences of tumor cells vary within a single tumor, contributing to tumor heterogeneity, drug resistance, and patient relapse. However, the relationship between tumor treatment response and metabolically distinct tumor cell populations is not well-understood. Here, a quantitative approach was developed to characterize spatial patterns of metabolic heterogeneity in tumor cell populations within in vivo xenografts and 3D in vitro cultures (i.e., organoids) of head and neck cancer. Label-free images of cell metabolism were acquired using two-photon fluorescence lifetime microscopy of the metabolic co-enzymes NAD(P)H and FAD. Previous studies have shown that NAD(P)H mean fluorescence lifetimes can identify metabolically distinct cells with varying drug response. Thus, density-based clustering of the NAD(P)H mean fluorescence lifetime was used to identify metabolic sub-populations of cells, then assessed in control, cetuximab-, cisplatin-, and combination-treated xenografts 13 days post-treatment and organoids 24 h post-treatment. Proximity analysis of these metabolically distinct cells was designed to quantify differences in spatial patterns between treatment groups and between xenografts and organoids. Multivariate spatial autocorrelation and principal components analyses of all autofluorescence intensity and lifetime variables were developed to further improve separation between cell sub-populations. Spatial principal components analysis and Z-score calculations of autofluorescence and spatial distribution variables also visualized differences between models. This analysis captures spatial distributions of tumor cell sub-populations influenced by treatment conditions and model-specific environments. Overall, this novel spatial analysis could provide new insights into tumor growth, treatment resistance, and more effective drug treatments across a range of microscopic imaging modalities (e.g., immunofluorescence, imaging mass spectrometry).