Computational Studies for Cell Signaling and Cancer Stem Cells

Scaffold, a class of proteins, plays many important roles in signal transduction. Through studying various models of scaffold, I will show novel regulations induced by scaffold binding in a multi-site phosphorylation system and with scaffold's spatial localization. To efficiently compute the models, we introduce a new class of fast numerical algorithm incorporated with adaptive mesh refinement and WENO scheme for solving the stiff systems with spatial dynamics. Finally, I shall also introduce mathematical modeling for the dynamical interaction between cancer stem cells (CSCs) and non-stem cancer cells, and our findings reveal that two negative feedback loops are critical in controlling the balance between the population of CSCs and that of non-stem cancer cells. Furthermore, the model with negative feedback suggests that over-expression of the oncogene HER2 leads to an increase of CSCs by regulating the division mode or proliferation rate of CSCs.