Geometry of single-cell multiplex data reflects biophysical processes in cells

Abstract

Recent advances in experimental techniques allow for measuring multiple (10 - 10^5) biomolecular parameters in single cells from culture and tissue. The information-rich data obtained by these single-cell multiplex techniques are a valuable resource for studying the multiple scales within an organism, from the complex biomolecular signaling networks within a cell to the intricate tissue organizations formed by cell populations. The interpretation and analysis for data of such high dimensionality is challenging; incorporating knowledge of biophysical mechanisms, such as reaction kinetics or inter-cellular interactions, with data analysis is yet another challenge. Single-cell multiplex data ought to provide unique information about the relations and mutual constraints between biophysical mechanisms across scales, if the aforementioned challenges can be overcome. In this thesis, I analyze covariances between single-cell biomolecular abundances, and their correlation functions over the spatial scales of cell populations, as a basic means to characterize the high-dimensional geometry of single-cell multiplex data distributions. I then illustrate a connection between observed data geometry and manifold geometry that arises from the mass action kinetics commonly used to model biochemical reactions. Specifically, I derive a relation between the covariance of biomolecular abundances and the reaction network topology of a general class of mass-action kinetics models. I also empirically observe that the spatial correlations of biomolecular abundances between interacting homogeneous epithelial cells obey simple constraints. I then survey the auto- and cross-correlations of different cell-types in colorectal cancer tissues, and statistically relate the intricate histo-morphology of tumors to the protein expression of single cells. This reaffirms that there are strong, predictive links between biomolecular abundances and the developmental organization of tissues.