About Me

I am working with Professor Alla Borisyuk on modeling the effects of astrocytes on neural dynamics. I received my Ph.D. in Applied Mathematics at UC Davis working with Professors Tim Lewis and Bob Guy. Outside of work, I enjoy playing board games with my wife Becky and playing with my cats Charlie, Cooper, and Funky..

Me (Carter Johnson) holding my cat Cooper


I use mathematical models to understand the biophysical mechanisms underlying different neural phenomena.

A closed-loop schematic for brain-body-behavior-environment interactions. There is a box with a schematic of C. elegans inside, labeled `Body and Nervous System'.  Out of the box flows a red arrow labeled `Behavior' which leads into another red arrow labeled `Environment' which leads back to the box.

In work ongoing from my PhD dissertation, we analyze the neuromechanical mechanisms of coordination in the C. elegans forward locomotion system. We used dynamical systems techniques to dissect out the relative contributions of the neural, muscular, and mechanical components to explain how the locomotive gait adapts to environmental changes.

In a new line of work with Alla Borisyuk at the University of Utah, we investigate how astrocyte dynamics regulate the spiking activity of neural networks. We are building up an astrocyte model that includes relevant ion channels from the literature. The goal of this model is to examine the level of astrocyte calcium activity needed to have a significant impact on extracellular concentrations, and hence, the excitability of nearby neurons.


I am passionate about teaching, especially quantitative methods for biology students. As a grad student at UC Davis, I designed computational lab sections for a new course in Differential Equations for biology students. At the University of Utah, I'm teaching a full year-long sequence of Calculus and Statistics for biology students and developing a large library of lecture videos for the class.



This page has links to conferences, REUs/Summer Programs, and organizations, which you may find helpful.