The research in our laboratory is poised at the interface of biology, mathematics, dynamical systems, and control theory. We work on the premise that the application of the appropriate mathematical tools to the investigation of cellular networks, when coupled with iterative rounds of experiments, will dramatically accelerate the pace of biological discoveries. Although this vision is increasingly being embraced by biologists and mathematicians alike, its widespread applicability still awaits breakthroughs in computational and experimental technologies.
At the computational level, unleashing the power of cellular network models is hindered by fundamental mathematical challenges for their validation and systematic analysis. Many of these mathematical challenges are specific to biological systems. Simply put, the mathematical methods developed in engineering and physics cannot, in a large number of cases, be directly transplanted to the study of biological systems largely because the investigation of biological systems requires tools for reverse engineering and analysis, while that of technological systems requires tools for forward engineering. It is also due to distinct physical implementations that differentiate natural and technological systems, ultimately generating different classes of interaction dynamics. As a result, a foundational mathematical infrastructure is necessary to accommodate the particular needs of biological modeling and establish Systems Biology as a solidly-rooted and distinct scientific discipline rather than a superficial application of engineering and physics. At the same time, the best designed models even when analyzed using the most efficient computational algorithms, can only generate limited predictive capabilities if built and validated using unreliable data. Consequently, innovative technologies need to be developed in parallel to generate crisp data that fuel the development and validation of the models, and then enable the quantitative testing of their predictions.
Our research group consists of an exciting mixture of mathematicians, engineers, and biologists who are developing knowledge in three main, but intersecting, directions. Specifically, we are pursuing the development of 1) foundational mathematical toolkits for the computational investigation of various classes of biological networks, 2) technologies that improve the resolution and quality of data necessary for these computational studies, and 3) predictive mathematical models for important cellular behaviors.