Gene Regulation in Space and Time

Although the genetic information in each cell within an organism is identical, gene expression varies widely between different cell types. The quest to understand this phenomenon has led to many interesting mathematics problems.

In this talk given as part of the 2016 Models, Inference & Algorithms series, Caroline Uhler presents a new method for learning gene regulatory networks that overcomes the limitations of existing algorithms for learning directed graphs and is based on algebraic, geometric and combinatorial arguments. Uhler analyzes the hypothesis that the differential gene expression is related to the spatial organization of chromosomes, and describes a bi-level optimization formulation to find minimal overlap configurations of ellipsoids and model chromosome arrangements. Analyzing the resulting ellipsoid configurations has important implications for the reprogramming of cells during development.