A platelet that finds a newly-formed vascular injury must be able to stop, attach firmly to the vessel wall, and recruit other platelets, all under the high-shear environment of blood flow. The receptor αIIbβ3 is vital to the coagulation process that creates thrombi, but at rest it is kept inactive to prevent unwanted blood clots. This project uses a dynamical systems model to examine the intracellular protein kinetics required to activate αIIbβ3 that begin with the binding of ADP to P2Y receptors on the platelet's surface.
Platelets possess a variety of receptors to bind to collagen within injury sites, gel-forming fibrin(ogen), von Willebrand Factor, etc. These bonds apply mechanical forces necessary to stop platelets and keep them stationary when under the shear flow of the blood vessel. This project utilizes numerical solutions to the Navier-Stokes equations and the Immersed Boundary Method to simulate platelets and their mechanical and chemical interactions between themselves and the vessel wall.
The UofU's student chapter of the AWM seeks to foster connections between mathematicians from any and all backgrounds. Learn more about our chapter and get involved by visiting our website here!
In Fall 2021/Spring 2022, I serve as the committee chair of the AWM Speaker Series. Each semester, we invite two mathematicians to talk about research as well as their experiences in Mathematics. View a list of our speakers here.
GSAC is a collection of committees designed to bolster community among graduate students through mentoring, social events, grad student colloquia, professional development, recruitment, etc. Learn more about our committees here.
In Fall 2021/Spring 2022, I serve as co-chair of GSAC, acting as a liason between students and the department.
In Spring 2022, I serve as Recruitment Committee chair, and in Spring 2021, I as a member of the committee. We organize and lead all events related to prospective graduate students visit to Salt Lake City.
This workshop is designed to introduce high school students to the basics of the methods of mathematial modeling. Students learn about modeling frameworks like difference/differential equations and statistical analysis, as well as skills like Python programming and writing. The goal is to give students the tools they need to enter competitions such as the HiMCM and the M3C. Learn more about our program by visiting our website here, or check out our SIAM News article!
Materials from the Fall 2021 workshop can be found here.
Our next workshop, in conjunction with SIAM and M3C, is planned for January 2022. Email us to find out more!
Cells exert forces on their 3-D environments to migrate. The improvements to super-resolution microscopy allows us to examine a cell over time and track motion. This project uses the known mechanical properties of a cell's environment to calculate (via inverse problems) the forces exerted by a cell over time.
Broadly neutrilizing antibodies found in the cervico-vaginal mucus have been shown to have weak affinity to mucin monomers. This project seeks to determine properties of Ab that maximize the trapping and neutrilizing of HIV virions before entering the body.
Kinesin molecular motor proteins transport cargo several times larger than itself by "walking" down microtubules. Single motors are known to detach from the microtubule often, yet the overal transport process is extremely efficient. This project examines the effect of cooperation among molecular motors in transporting cargo from both a stochastic and deterministic standpoint.
Patel KB, Mao S, Lai SK, Forest GM, Newby JM. Limited Processivity of Single Motors Improves Overall Transport Flux of Self-Assembled Motor-Cargo Complexes. Physical Review E. 100:022408. (2019)