When Alexa Gordon '20 combined mathematics and neuroscience to create a joint major, research through an independent study was a natural next step to tie her current and future academic goals together.

“Performing undergraduate research allowed me to explore computational neuroscience and biostatistics and fine tune my future field of study. It allows you to tailor the work you do for your major(s) to an area of interest and integrate interest and understanding,” says Alexa. “I’m pursuing a Master of Science in Biostatistics at Georgetown University, so the statistical analysis and programming work I have done will be a huge help.  Also, working one-on-one with a professor and other students doing research has been a great way to develop skills in teamwork and leadership.”

“This experience allowed me to develop a close relationship with a professor and work on a topic that is specifically tailored to the interests I plan to pursue after F&M that weren’t part of pre-existing curriculum.”

Alexa's Spring 2020 project with Prof. Christina Weaver, “Modeling Systems of Neuronal Resonance and Understanding Subthreshold Oscillations,” had two general aims:  to analyze resonance data that had been collected from brain cells of monkeys from two different regions of the cortex; and to study mathematical models of neuronal function, including resonance. 

“I was unfamiliar with the concept of resonance which is the ability of neurons to vibrate at specific frequencies in response to stimuli. By reading published papers on this topic, we connected topics from Prof. Weaver’s MAT 439 (Nonlinear Dynamics), such as bifurcations, methods of analyzing linear and nonlinear systems of equations to systems of neurons that exhibited this type of neuronal resonance,” the joint major explains.

Prof. Weaver adds, “The brain generates rhythms in different frequency bands, to connect activity across different brain areas.  So, it is useful for many neurons to have a stronger response to inputs at some frequencies more than others. This preferential response is called resonance.”

“Alexa was a joint major in neuroscience and mathematics, and wanted to do a year-long research experience with me.  I decided to supervise both Alexa and Fanzhou “Vicky” Wei ‘20 in the Fall 2019,” the professor remarks. “It worked well:  they took turns presenting content from a textbook called Theoretical Neuroscience (authors Dayan & Abbott), and describing pieces from a journal article in Frontiers in Computational Neuroscience (Ibañez et al., 2020), co-authored by former F&M Post-doctural Fellow Sara Ibañez, other colleagues and myself.”   During the Fall semester, both students learned some MATLAB programming and computational neuroscience, and worked on different aspects of the Ibañez et al. neuron network models.  “Alexa's experience in biology and neuroscience was a nice asset in our meetings,” comments Prof. Weaver.

“It’s important to be flexible in what the project entails because you must be able to adapt and change the trajectory of the project when additional data is available.”

In Spring 2020, the pair decided to shift the focus away from the network models, to something that would complement MAT439 which Alexa was currently taking.   So, the professor designed Alexa’s Spring project to be something that combined the data and nonlinear models of neurons.  The project is a prime example of how math can be used to model complex biological systems such as the brain, and how neuronal resonance affects cognitive processing.

Alexa had planned to present her work at the Spring Research Fair.  That didn't work out, but she did still create a poster that will hang in Stager Hall.  Here is a link to the poster.  

Says Prof. Weaver, “By the end of the semester, Alexa's project united the resonance data and the course content very nicely.”