I was first introduced to the world of mathematical biology during the summer after my Sophomore year of undergrad, when I had the fortune to work with Professor Todd Quinto on a project in electron tomography. Over those ten weeks I learned microlocal and Fourier analysis, and eventually used my newfound knowledge to improve upon an existing reconstruction algorithm. By the end of the summer, I was able to reconstruct the detailed structure of microscopic particles, such as viruses and polymerases, from data that more closely resembled white noise than it did signal. Having previously been intent on a career in medicine, this experience identified a new potential trajectory and I was dead set on pursuing it further.
I then decided to join Professor Yu-Shan Lin’s group in computational biochemistry. In the Lin group, I experienced a very different scientific approach. By simulating proteins like IgG using a small but powerful set of rules, we were able to understand emergent dynamics as well as likely stable states. I loved that these predictions allowed us to see the otherwise unseeable and find molecular behaviors that could be confirmed through experiment.
My research under Professor Jared Tanner in Oxford centered on the development of invariant representations of data, particularly textures in images. To do this, we studied the scattering transform method, which takes the form of a convolution network in which each of the layers is composed of wavelet filters. The resulting machine learning method is analytically rigorous and can be shown to provide a data representation that is invariant to translational, rotational, and scaling effects.
My current research interests are an amalgamation of behavioral genetics, neurobiology, nonlinear dynamics, and machine learning, all motivated by the following questions: How does the genetic code of an organism lead to intrinsic behaviors? Which sorts of behaviors are intrinsic, and which are learned? To answer these questions, I collaborate with researchers in Northwestern’s Department of Neurobiology to study elementary behavioral phenomena in the model organism Drosophila melanogaster. In the fruit fly, we have what Seymour Benzer, one of the fathers of modern behavioral genetics, famously called an “atom of behavior” (although he later admitted that may have been an oversimplification). In a body less than 4 mm in length and with a brain the size of a poppy seed, a fruit fly is capable of remarkably complex behavior, including walking, jumping, flying, grooming, and courting. Amazingly, many of these behaviors can be traced back to the presence of individual genes or cell types. In my PhD research, I seek to describe the how these intrinsic organismal characteristics yield behaviors that are essential for fitness.
One of my projects focuses on perhaps the most famous example of behavioral genetics in recent memory, the circadian clock. This amazingly conserved biological motif is understood to have at its core a simple transcription-translation feedback loop, in which transcription of a subset of core clock genes leads to delayed negative inhibition of further transcription. The result is an oscillation of expression with a period of approximately 24 hours that is entrained by environmental forcing. The dominant entraining factor is generally thought to be light, although other factors like temperature and feeding schedule have been proven capable of entraining the circadian clock of both flies and mammals.
I employ bioinformatics to identify genes with oscillatory expression and to develop data-driven coupled ODE models to simulate potential interaction dynamics between genes. By connecting elementary processes of transcription and translation, we can interrogate the oscillators and switches that are essential to proper biological function, and we can use these models to make predictions about the impact of environmental perturbations to chronobiological state. Our predictions serve as testable hypotheses that we seek to validate in the lab.
A second project focuses on more intricate behaviors, namely how mechanosensory and thermosensory inputs are processed and converted to movement. In Drosophila, much of the core circuitry for this simple input processing has been studied, and we are using this information to develop realistic computational models that can be readily checked by experiment. Starting from videos of flies in a temperature controlled arena, we can recognize the building blocks of fly movement, as well as how these behaviors are combined and ordered. Using this data, we have the necessary information to develop a model that describes the decision making and movement dynamics of the fly. The results of these simulations can be compared with neuronal imaging experiments in behaving flies, allowing us to recognize the neural circuits implementing these intrinsic behaviors. By combining our models with experiments, we hope to uncover the fundamentals of fly sensory processing and the underlying computation used to generate behavioral output.