*Dr. Banerjee received her PhD from Rutgers University in Chemical Engineering. Prior to joining Pitt, she was a postdoctoral fellow in Harvard Medical School. Recipient of 2009 Ralph Powe Junior Faculty Enhancement Award. Reviewer of several journals including Journal of Biotechnology, Tissue Engineering. Member of American Institute of Chemical Engineers, American Physical Society, Biomedical Engineering Society.*

## Mathematical Modeling of Reaction Networks: Hydrocarbon Combustion to Stem Cell Differentiation

##### Friday, July 17, 2:30 – 3:30 pm

##### 1175 Benedum Hall

Detailed simulation of reactive flow systems using complex kinetic mechanisms is a computationally demanding task. In practice, the computational challenge is overcome by replacing the detailed kinetic mechanism by a reduced order model, thereby compromising the model predictive capacity.We have developed a methodology to retain sufficient model resolution while ensuring computational feasibility through an adaptive chemistry approach. The idea behind this approach is to design library of reduced order models specific to local conditions, and adapt the models while integrating the differential equations. Such adaptive chemistry models were derived using an Integer Nonlinear Programming formulation. Details of this approach pertaining to methane combustion will be presented in the seminar.

Analogous reaction network modeling approaches can be extended to a host of biological systems. For example, embryonic stem cell differentiation is a result of complex dynamic interactions between transcription factors, which can be modeled as a set of nonlinear coupled differential equations. Research in stem cell is still in a nascent stage with limited information regarding the network and kinetics of the involved transcription factors. Our focus in this system is to develop mathematical techniques to reconstruct the underlying transcription factor network and kinetics from the knowledge of the system output, given by the dynamic transcription factor profiles. Details of the bi-level mixed integer programming formulation we are developing to identify such networks will be presented.