Semester

Spring

Date of Graduation

2023

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Mathematics

Committee Chair

Adam Halasz

Committee Member

Marjorie Darrah

Committee Member

Jessica Deshler

Committee Member

Harvey Diamond

Committee Member

Casian Pantea

Committee Member

Tudor Stanescu

Abstract

I use mathematical modeling to understand aspects of molecular processes in living cells. Specifically, we look at the first few steps in cell signaling. Signal initiation requires that receptors located on the cell membrane bind together to form dimers. Microscopic imaging of receptors on the cell membrane revealed that receptors tend to accumulate in small areas (clusters). Studies also show that the membrane has a complex landscape consisting of domains and barriers of various origin.

Here we study the way receptor dimerization is influenced by domains on the cell membrane. Our underlying hypothesis is that the physical and chemical properties of certain types of microdomains cause the accumulation of receptors. We know that dimerization increases the tendency of receptors to accumulate in attractive domains. However, it is not clear whether this is enough to explain the dramatic increase in cluster sizes observed during signaling. We aim to understand whether receptors accumulate more or less uniformly in all domains (of the appropriate type) or there are effects that favor non-uniform accumulation, resulting in fewer, larger clusters upon increased and / or non-uniform ligand concentrations.

We study compartment-based models representing multiple domains on the cell membrane, each with a network of chemical reactions derived from VEGF signal initiation. Our central result is a complete analytical solution of the two-compartment model. We establish that the closed version of this system has a unique steady state. Further analysis led us to a four-domain structure, with two low density domains in contact with each other, each surrounding a small, high affinity domain. This system has the potential to concentrate liganded receptors in one of the high affinity domains in response to a mild difference in VEGF concentrations.

Embargo Reason

Publication Pending

Share

COinS