Fast Simulation of Random Walks on the Endoplasmic Reticulum by Reduction to the Gambler's Ruin Problem

Abstract

The endoplasmic reticulum (ER) plays a critical role in many eukaryotic cell functions, including protein synthesis and development. In this thesis, we will use increasingly coarse grained models of random walks on graphs to efficiently simulate the movement of structures, such as mitochondria, along the ER. We will use a data set obtained from ER dynamics videos created by Jonathan Friedman, and research conducted by Joel Stavans. The 2D topology of the ER is similar to that of a foam network, primarily because both can be viewed as stable structures which provide a framework upon which biological processes can be observed. Specifically, we will pay close attention to the dwell time of mitochondria along the ER. By observing and drawing conclusions about these dwell times, we may reveal insight about these important cell processes.