My undergraduate degree was in Physics, Mathematics, and Economics, so I have a wide variety of interests. For my PhD, I wanted to go in a physics direction. I ended up on biophysics side of things, so I have had to learn lots of biology!
The first project I worked on was on chromatin dynamics. Our collaborators at Princeton are able to fluorescently tag (ms2 GFP) single gene foci in Drosophila(Fruit Flies), so we have the ability to track a single gene throughout the early stages of development(nuclear cycles 11-14, see Figure 1A for an example of what live imaging can look like in early development). There are a few genes in Drosophila that are incredibly vital to development, and we would like to have a better picture of how these specific genes are moving within the nucleus (which brings up the broader question of how are DNA and its larger macromolecule Chromatin packaged?). From trajectories of individual genes, I have created a Bayesian Classification scheme to select the method of motion (for example Diffusion, Directed Diffusion, or Anomalous Diffusion), and its relevant parameters for the live imaging data from the Gregor Group. With this information on the motion of DNA loci, we can then draw conclusions on the connections between the parameters guiding DNA packing/unpacking, the type of motion undergone, nuclear forces, and transcriptional activity for each nuclear cycle stage, or even within an nuclear cycle or position within the embryo. The paper describing our mathematical method can be found here, and the code I developed is available on GitHub. Applying our method to the Gregor Group Data will be coming in the next few months, once we hire an undergraduate to do the analysis.
With the Munro Group, I am examining pulsatile actomyosin dynamics in the C. elegans zygote. The Munro group has many movies of Actin, Myosin, and RhoA (both in wild type forms and various mutants) that demonstrate pulsatile dynamics, as seen in a still of a movie to the right (actin in green, myosin in red). While the group has already learned many important things about the dynamics of this system (sizes of pulses, time between pulses of different types), there is much mathematical modeling that can be done. We wish to develop tools to analyze movies on the full image scale, instead of zooming into pulses. The main portion of this project is developing a reaction-diffusion-advection partial differential equations model to encapsulate these type of dynamics. We initially are using the Fitzhugh-Nagumo model in one dimension to start our modeling, using noise to generate pulses. From there, will will add in the effects of mechanochemical stresses and tissue mechanics to make the model more physical. From there, we will extend the system into two dimensions. With this system, we will explore parameter space to find out the limits of the behavior of the system. We hope to then use the mathematical tools that we and the larger group have developed to do a type of “mathematical phenotyping”, matching experimental movies to the simulated PDE system results.