My research is mainly focused on mathematical modeling of biological systems with a focus on regulatory biochemical networks. Although many intracellular regulatory networks have been extensively studied using advanced experimental techniques, it has turned out to be quite difficult to make predictions about how individual components are assembled and dynamically regulated, and how the behavior of metabolism as a whole are related with the properties of the individual parts. Mathematical modeling and computer simulations are widely accepted as promising tools to investigate and address such questions. I am interested in development of quantitative mathematical models that are directly comparable with experimental data to address such questions. Below you'll find my recent research highlights, you need to go to "Research" link to see the details of each section.
(A) Signal transduction in the mating response pathway of yeast S. cerevisiae Signal transduction pathways enable cells to receive, process and respond to biochemical stimuli. These pathways are generally highly nonlinear and often contain multiple feedback and feedforward loops and share common functional components. The questions I seek to address with mathematical models and computer simulations are: (1) What are the functions of feedback and feedforward loops, (2) How signal intensity is controlled in the pathway, (3) How pathway specificity is achieved. I have been collaborating with Profs. Timothy Elston and Henrik Dohlman at UNC on this project.
(B) Exploring transcriptional/translational time delays on dynamics of lactose operon in E.coli The lac operon is a classic example of an inducible genetic network in E.coli. It consists of a small promoter region and three larger structural genes. It is known that this system is capable of showing bistable behaviour. I am interested in how bistability arises in this system and how time delays due to the transcriptional and translation process the dynamics of this system. On this project, I have been collaborating with Prof. Michael C. Mackey from McGill University.
(C) Computer algebra approach to bistability in biological/ and chemical systems Although the capacity to achieve more than one internal steady state for a set of parameters is common in biological/chemical systems, experimentalist often believes the systems under investigation always have single stable steady state. Among the various patterns of behavior emerging from regulation associated with nonlinear kinetics, bistability is extremely interesting.