Star Group
Awildo Gutierrez, Eli (Star) Leake, Caelyn Rivas-Sobie
Research Director: Dr. Anne Shiu
Research Mentor: Jordy Lopez Garcia
The Effect of Operations on the Deficiency of Chemical Reaction Networks
Our Research
The Effect of Operations on the Deficiency of Chemical Reaction Networks
Abstract
Chemical Reaction Networks are a mathematical model with biological motivations from studying phosphorylation networks. Phosphorylation networks describe the process of adding phosphate groups to a molecule via enzymes. We abstract this by using a model consisting of compounds involving species and chemical reactions between them. Banaji introduced six operations on networks, called enlargements, that preserve important properties of networks such as multistationarity and periodic orbits of their steady states; these enlargements involve adding new species, new dependent and independent reactions, and new compounds. We investigate the effects of these operations on deficiency, a nonnegative integer that describes important aspects of the network, including its graphical structure. Using linear algebra and graph theory, we completely characterize the effect of these operations on deficiency, and further conclude that deficiency never decreases after the application of any enlargement.
About Us
Awildo Gutierrez
Awildo Gutierrez is an undergraduate senior math major at Hamilton College. He plans to earn a PhD in pure math and is currently interested in combinatorics research.
Eli (Star) Leake
Eli (Star) Leake and is an undergraduate senior math major with a pure concentration at DePaul University. He has interest in doing research in something combinatorics/discrete math related in graduate school.
Caelyn Rivas-Sobie
Caelyn Rivas-Sobie is an undergraduate senior applied mathematics major at Arizona State University - West. She plans on getting a PhD in mathematics or applied mathematics. She is interested in dynamical systems and mathematical biology.