Stability maintenance in reaction-diffusion systems

Summer 2017

Easun Arunachalam : Chemistry, Chemical Engineering

Mentor: Phillip Geissler

Interplay between spatial organization and interconversion of different molecules leads to complex pattern formation in simple chemical systems. Some have suggested implications for biological systems, especially in the context of embryonic development. However, unlike idealized chemical systems, biological systems are characterized by complex and dynamic environments. Nevertheless, biological pattern formation appears to be largely stable. This stands in stark contrast to current theories, which predict extreme sensitivity to fluctuations and initial conditions in systems with feedback delays - delays in the response of a system to a stimulus. A comprehensive theory must account for stability despite such time delays, which are common in biological systems. My goal is to develop a theoretical description of pattern formation in the presence of perturbations. Using theory and computer simulation, I will contribute to a quantitative description of stability maintenance in the face of feedback delays. A mathematical description of such systems is valuable because it provides insights into how to manipulate their behavior. It is especially critical to understanding and preventing birth defects, and for developing advanced manufacturing techniques.

The Rose Hills Fellowship has played a pivotal role in solidifying my interest in biophysics and applied math. My work this summer helped me develop skills to independently formulate questions, construct models, and design tests, which I had never done for theoretical research. This theoretical and computational work has given me a valuable starting point for experimental studies of these systems in the near future. I am hopeful that this work will ultimately contribute to a better understanding of early development and biological pattern formation in general. I am grateful to the Rose Hills Foundation for their generous support of my work this summer. I very much enjoyed the opportunity to work on my own research project and broaden my scientific horizons, and this experience has solidified my desire to pursue a career in basic and applied research.