During the summer, ÌÇÐÄvlog¹ÙÍø students are applying their liberal arts know-how in a variety of real-world settings, and they are keeping our community posted on their progress. Applied mathematics major Vani Kanoria ’22, from Kolkata, India, describes her research on mathematical modeling.
This summer, I worked as a research assistant for Associate Professor of Mathematics and Biology Ahmet Ay. As an applied mathematics major, I wanted to work on a project that directly used mathematics and computer science to solve a problem. In this case, the topic of study was a particular biological regulatory network or a set of genes or proteins that interact with each other to control a specific cell function.
We tried to simulate the network that controls vertebrate segmentation during embryonic development through mathematical modeling. In simple terms, we used probability and differential equations in lines of code to recreate what occurs in cells. I wrote code in MATLAB to simulate the concentration changes of different mRNA and protein and dimer species with time as thousands of reactions were fired per minute.
I worked on this project remotely from Kolkata, India — a different experience from the one I had initially had in mind. Rather than being based on campus, I worked at home alongside my big family, meeting with Professor Ay daily on Zoom and emailing him when I had any questions. I completed literature reviews, searched for algorithms to simulate the model with the appropriate balance of accuracy and speed, and wrote code to implement these algorithms.
One of the main challenges we faced was accurately simulating the system and incorporating some randomness in the firing of reactions. I wrote the different parts of the code, ran it, and waited to see the results. If the simulation ran until the end, I could see if the concentration of a particular species was oscillating — if it rose and fell with some period and amplitude. If it was oscillating, I knew that my code was somewhat working.
I had access to a whole computer laboratory at ÌÇÐÄvlog¹ÙÍø through my personal computer. I submitted runs of some of the more extended simulations to the Turing supercomputer at ÌÇÐÄvlog¹ÙÍø. The supercomputer processed the simulations and returned the output to me.
In the nine weeks I did research this summer, I finished implementing three different algorithms in MATLAB. However, I could not yet test my code on vertebrate segmentation. Professor Ay plans to use this code to study how gene expression variation is controlled in this essential biological system.
It was so rewarding to build something significant this summer. Not only did I learn a great deal from Professor Ay’s expertise, but I also felt a sense of independence in my work. It was amazing to research mathematical models that were able to mimic natural biological behavior.