Computational study of signaling specificity and epigenetic regulation

Cells usually respond specifically to different environmental stimuli for survival. The signal transduction pathways involved in sensing these stimuli often share the same or homologous proteins. Despite potential cross-wiring, cells show specificity of response. A loss of signaling specificity may cause development diseases such as cancers. We developed a mathematical model of ODE system to capture the dynamic formation of the key complexes and their interactions with pathway-specific promoters in Saccharomyces cerevisiae. We found two mechanisms explaining the behaviors of cells and results in the signaling specificity. And our two hypotheses driven by models were tested through experiments. Another interesting topic is cell fate switching driven by epigenetics in Candida albicans, which is one of the most important and common agents of serious fungal infection in humans. It can switch (but not necessarily) due to the environmental cues between two different phases: white phase and opaque phase. To study the detailed mechanisms of the negative feedback and its effect on switching, we developed new models and identified several topologies of the networks consisting the negative and positive feedbacks that could capture the critical temporal features in the experimental data. There is more numerical analysis about stiff reaction-diffusion-advection equations, derived from challenging biological questions. For reaction-diffusion-advection equations, the stiffness from the reaction and diffusion terms often requires very restricted time step size, while the nonlinear advection term may lead to a sharp gradient in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. For reaction-diffusion systems with both stiff reaction and diffusion terms, implicit integration factor (IIF) method and its higher dimensional analog compact IIF (cIIF) (methods developed by our group) serve as an efficient class of time-stepping methods. For nonlinear hyperbolic equations, weighted essentially non-oscillatory (WENO) methods are a class of schemes with a uniformly high order of accuracy in smooth regions of the solution. We couple IIF/cIIF with WENO methods using the operator splitting approach to solve reaction-diffusion-advection equations. Both the theoretical analysis and direct numerical comparisons with other approaches consistently reveal excellent efficiency and stability properties.