Gene Regulation in Space and Time - or - From Causal Inference to Ellipsoid Packing
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. First, I will present a new method for learning gene regulatory networks. It overcomes the limitations of existing algorithms for learning directed graphs and is based on algebraic, geometric and combinatorial arguments. Second, I will analyze the hypothesis that the differential gene expression is related to the spatial organization of chromosomes. A chromosome arrangement can be viewed as a minimal overlap configuration of ellipsoids of various sizes and shapes inside a convex container, the cell nucleus. I will describe a bilevel optimization formulation to find minimal overlap configurations of ellipsoids. Analyzing the resulting ellipsoid configurations has important implications for the reprogramming of cells during development.
Host: Sara Kalisnik
Caroline Uhler is an assistant professor at MIT. After completing a master’s degree in mathematics and a bachelor’s degree in biology at the University of Zurich, Prof. Uhler received a PhD in statistics from UC Berkeley in 2011. After postdoctoral appointments at the Institute for mathematics and its applications in Minneapolis and at ETH Zurich, Prof. Uhler joined IST Austria in 2012. In 2013 she participated in the semester program on Big Data at the Simons Institute at UC Berkeley.