2012 Joint Mathematics Meetings
Signal transduction begins with a signal binding to receptors on the membrane of the cell. This causes a cascaded of protein interactions within the cell, ending in transcription of targeted genes. The Wnt pathway is a well-studied protein system that plays an important role in the proliferation and adhesion of cancerous cells. When signaled, the Wnt pathway results in a buildup of beta-catenin, which leads to transcription of certain genes. An excess of beta-catenin can cause cells to divide unnecessarily resulting in tumors. Other factors in the pathway, such as Axin and APC, help regulate beta-catenin buildup. In order to sift through the various protein interactions to determine the most influential, we analyze the response of a state variable to a change in the parameter, also known as sensitivity functions. Solving for sensitivity functions analytically in large models such as the Wnt pathway is not practical because it requires computing a large number of partial derivatives. In this project, we use automatic differentiation to compute the partial derivatives related to sensitivity functions. We were interested specifically in beta-catenin and Axin because of their important role in the system, but also investigated other factors. Through our sensitivity analysis of the Wnt pathway, we were able to determine the most influential protein interactions.