eMB: Mathematical analyses of multidimensional single cell transcriptional vector fields

University Of Pittsburgh, Pittsburgh PA

Investigators

Abstract

Cells can exist in different types such as liver cells and neurons. It is a fundamental question in biology how a cell can develop into an organism composed of different cell types. Furthermore, one can induce a cell to change from one type (e.g., skin cells) to another type (e.g., neurons or heart muscle cells) for curing various diseases such as Alzheimer’s disease. Current advances of single cell techniques and machine learning algorithms lead to development of data-driven mathematical equations to describe how a large number of genes regulate each other to regulate the cell types. The funded research is to apply mathematical tools originally developed in other fields to analyze these equations. Such mathematical analyses will provide mechanistic insights on understanding how genes coordinately regulate cell types, and guide experimental designs to effectively accelerate or slow down transitions between different cell types, which are of high biomedical significance. The project also fosters collaborations between mathematicians and cell biologists as well as train students and researchers of the next generation in interdisciplinary research. With advances of single cell genomics techniques, an emerging direction is to learn dynamical models from the data. The research aims to address a new challenge to expand the tools for downstream analyses of the dynamical equations and apply tools developed in other contexts to single cell data analyses. In mathematical biology researchers have toolkits to analyze the behaviors of a biological system described by a set of dynamical equations. These tools, such as phase-plane analyses and bifurcation analyses, are typically restricted to either a system with a few degrees of freedom or a few selected parameters. Thus, new tools are needed for analyzing dynamical equations with a large number (e.g., > 20) of degrees of freedom. The investigators will use the recently developed discrete graph representation of a vector field together with discrete Hodge decomposition and other network analysis methods for characterizing multi-dimensional vector field and system dynamics including cyclic transitions on developmental and cell fate transition processes. The investigators will also study nonlinear dynamical systems, including dynamical mode decomposition, Koopman operator analysis, pseudospectral analyses, and spectral submanifold analyses, and analyze the collective dynamical modes of cellular dynamics within and between attractors. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.