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Invited Paper Session Abstracts - Recent Advances in Mathematical and Computational Biology, Highlighting Contributions from Undergraduate Researchers

MAA Invited Paper Session

Recent Advances in Mathematical and Computational Biology, Highlighting Contributions from Undergraduate Researchers

Please note: all sessions are listed in Eastern Daylight Time (EDT = UTC-4:00)

Friday, August 4, 3:00 p.m. - 5:50 p.m., Room 118/119

Some of biology’s most complex questions are best answered through mathematical modeling, using tools which range from stochastic and statistical models to deterministic differential equations models. The utility of mathematical models within biology is also vast, answering questions within subfields such as ecology, neuroscience, immunology, physiology, and more. Furthermore, mathematical biology contributes to mathematics as the complex models formed to represent biological phenomena drive the creation of new mathematical tools for model analysis.

With this symposium we hope to highlight mathematical descriptions from a large range of biological disciplines. Including a variety of biological disciplines underscores the versatility of mathematical modeling as the cutting edge tool throughout biology and makes known the commonality of analytical tools and methods across fields of application. Additionally, we hope to highlight the contributions of undergraduate researchers within mathematical biology research through this symposium. Because mathematical biology is placed within an application, the research may be accessible to undergraduate students, and oftentimes undergraduate researchers can be involved easily in these projects. By highlighting the specific role of undergraduate researchers within larger research projects, we aim to clearly depict ways to involve undergraduate researchers in future research projects.

Anna Nelson, Duke University
Kelly Buch, Austin Peay State University

From Flashing Fireflies to Bursting Neurons: Finding Sync with Undergraduate Collaborators

3:00 p.m. - 3:20 p.m.
Matthew Mizuhara, The College of New Jersey

Biological and physical oscillators, ranging from fireflies, to neurons, to power-grid networks, often exhibit large, collective dynamics arising from mere pairwise interactions. Analysis of the emergence of synchronization or other pattern formation is challenging due to the non-linear and high dimensional nature of their mathematical models. In this talk we discuss recent advances using a variety of analytical and numerical approaches. We will particularly highlight how undergraduate collaborators have been integral to these projects.

A Bit of Biology for the Mathematicians, a Bit of Math for the Biologists, Some Programming for Everyone

3:30 p.m. - 3:50 p.m.
Sean Laverty, University of Central Oklahoma

I will present an overview of 2-3 long-term student mathematical biology research projects. In one project, a motivated biology major gained experience and skill with data-wrangling, data visualization, and application of an intricate mathematical and statistical modeling technique: capture-mark-recapture analysis. This project, part of a larger collaborative effort within the College, set a motivated student on a path to data-intensive research at a biomedical research foundation and opened the door to his pursuit of a post-graduate degree in Bio-Statistics. In another project, I highlight the appreciation gained by mathematics students learning about application and interpretation of mathematical modeling to biological systems. Finally, I will discuss how several undergraduate students from multiple disciplines and institutions have contributed to a long-term project on modeling blood clot degradation.

Pulsing Corals and Swimming Jellyfish: Including Undergraduates in Biological Fluid-Structure Interaction Research

4:00 p.m. - 4:20 p.m.
Matea Santiago, University of Arizona

Fluid-structure interaction simulations of biological organisms offer a steep learning curve to undergraduate researchers. Many undergraduates, particularly mathematics majors, have not had a fluids course or substantial coding experience. I will highlight two projects I am working on with undergraduate researchers, simulating the motion of pulsing soft corals and blue blubber jellyfish. Both pulsing soft corals and blue blubber jellyfish generate motion by activating their muscles, resulting in fluid flow. These projects can be particularly challenging for undergraduate research. 1) The governing equations are a system of non-linear partial differential equations called the incompressible Navier-Stokes equations. Solving them on a three-dimensional domain requires high computational cost, requiring HPC tools. 2) These organisms are elastic and deforming, requiring specialized numerical methods to reconcile an evolving boundary condition and the fluid-structure interface. The immersed boundary finite-element method, developed by Boyce Griffith, is an extension of the classical immersed boundary method. It allows for a fully three-dimensional structure, making it desirable for many biologically complex organisms. Using existing open-source software, undergraduates can run simulations, assist with parameter tuning, and develop intuition and insight into problems.

A Global Sensitivity Analysis Framework for Rumen Fermentation Modeling Identifies Key Modifiers of Enteric Methane Production

4:30 p.m. - 4:50 p.m.
Kathryn Link, Pfizer Inc.

Ruminant animals rely on microbes to convert complex plant material into metabolizable compounds. During the enteric fermentation process a group of archaea produce methane (CH4), which is then eructated and released into the atmosphere by the ruminant. The emitted CH4 has a global warming potential 28-fold higher than carbon dioxide, leading to significant efforts to reduce enteric CH4 production. The red seaweed Asparagopsis taxiformis has been identified as a promising feed additive that reduced enteric CH4 by over 80% when added to regular cattle diet. This significant response has been partially attributed to a compound known as bromoform and its ability to inhibit the key enzyme of archaeal methanogenesis, however, the entire mode-of-action is still not fully understood. Quantitative methods incorporating mechanistic mathematical models describing microbial interactions and responses to feed additives are urgently needed for development of more sustainable strategies for the reduction of methane from ruminant animals. In this work, we developed a modeling framework in which we extended an existing rumen fermentation model and calibrated it with functional microbial groups and gas emission data. We then identified the optimal distribution of functional microbial groups, including microbes of unknown functions, that then explained the observed reduction of enteric methane in the presence of A. taxiformis. Lastly, we utilized both local and global sensitivity analysis approaches to identify rumen parameters as key drivers in enteric methane production and potential targets for advanced methane mitigation strategies.

Undergraduate Research Aimed at Solving Clostridioides difficile: Mathematical Models of Transmission and Control in Healthcare Settings

5:00 p.m. - 5:20 p.m.
Cara Sulyok, Lewis University

Clostridioides difficile (C. difficile) is the leading cause of infectious diarrhea and the most frequently identified healthcare-acquired infection in United States hospitals. C. difficile is typically contracted after antibiotic use, when healthy gut microbiota that prevent colonization is compromised. Colonized patients, both symptomatic and asymptomatic, shed C. difficile endospores that can survive for long periods on surfaces outside the host and are resistant to many commonly-used disinfectants. Transmission pathways can include contact with endospores on fomites, objects likely to carry infection.

This talk will focus on various mathematical models aimed at quantifying the transmission of C. difficile in healthcare settings ranging from systems of ordinary differential equations to agent-based models – all developed by undergraduate student researchers! We will discuss the progress and results from these student projects. Results can be applied by healthcare professionals by focusing on precautionary measures that reduce patient colonization with C. difficile.

An Ounce of Prevention Is Worth a Pound of Cure?

5:30 p.m. - 5:50 p.m.
Ben Morin, Vassar College

The spread of drug use throughout a community can be represented through epidemiological models typically found in studies on infectious disease dynamics. These mathematical models are based on the idea that similar to infectious diseases, drug use spreads through interactions between individuals. Previous models of drug use don’t take into consideration the preferences an individual may have in their interactions. We propose a compartmental model for heroin use that accounts for preferred mixing as well as the element of choice in seeking or avoiding individuals based on their drug use habits. In this talk, I will introduce the compartmental model framework, derive the preferential mixing function, and highlight a few interesting effects while discussing the process undertaken by undergraduate scholars. This work was completed during a 6-week REU by 3 undergraduate students from various majors under the direction of Benjamin Morin at Vassar College.