# Ching-Shan Chou

# Computational Biology of Cell Polarization

Cell polarity is fundamental to cell physiology. It underlies the development and various functions of a cell, and it can also lead to cell morphological changes, which are crucial for the vectored processes such as cell motility. The process of cell polarization and morphogenesis typically relies upon a complex signaling network, on which enormous efforts have been made to identify regulatory molecules and the feedbacks.

In my research, I study the establishment and mantenance of cell polarity with a model system, budding yeast, *Saccharomyces cerevisiae*. While the cell cycles of budding yeast cells involve both mating and budding, I study cell polarity in both processes.

**Yeast Cell Mating
**

Two haploid budding yeast cells, alpha cell and *a* cell, can mate each other through sensing pheromone molecules secreted from their mating partners. The mating is very accurate and robust. We are interested in understanding this process and investigate the follwoing questions: How do cells repond accurately to different gradients and average levels of pherone? How do cells filter external and internal noise to accurately sense the location of its mating partner? How do cells coordinate the intricate intracellular network and their morphogenesis during mating?

We use mathematical modeling, computation, along with experiments, to understand this system. We also investigate this system while cells are changing their shapes. My biologist collaborators are Tau-Mu Yi (UCSB), Travis Moore (Harvard).

**Budding Patterns in Yeast Cells**

Budding yeast can reproduce asexually by making a new bud, which later separates from the mother cell and becomes a daughter cell. The selection of the bud site depends on a spatial cue inherited from the previous budding event. In this project, we are interested in understanding bud site selection and how the polarity is established and maintained. Specifically, we investigate why the unique bud is formed robustly. Our work considers the normal cell physiology, where the inherited spatial cues are present, and this differs from other works on 'symmetry breaking', in which spatial cues are not included. We use computational models to understand the polarity machinery, and the mathematical part is closely integrated with experiments. My biologist collaborator is Hay-Oak Park (OSU).

# Numerical Algorithms for Hyperbolic Problems

My numerical projects focus on computation of hyperboic problems. The methods that I am working on are finite difference methods and discontinuous Galerkin methods.

**Energy Preserving Discontinuous Galerkin Methods for Wave Equations**

Wave equations have wide applications in physics and engineering. One of the most important properties of the equations is the conservation of energy. It was shown that an energy preserving numerical methods needs to be used in order to maintain the shape and phase of the solution. In this project, we use the local discontinuous Galerkin method, with an carefully designed numerical fluxes for accuracy and stability. The aim is to design a general method for wave propagation in heterogeneous media and on an unstructure mesh.

**Fast Sweeping Methods for Steady State Hyperbolic Problems**

Computing hyperbolic equations is challenging. It is well-known that the computational time for explicit methods are constrained by CFL number. When steady state problems are considered, we attempt to find a fast solver to relax the CFL constraint. In this project, we design fast sweeping methods, which was originally designed for Hamilton-Jacobi equations. Fast sweeping methods rely on the choice of conservative numerical fluxes and alternating iteration directions. Our goal in this project is to design a fast solver by choosing appropriate numerical fluxes and combine that with techniques such as multigrid method.

**My research is supported by National Science Foundation grant DMS-1020625 and DMS-1253481.**