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Invited Paper Session Abstracts - Mathematical Diversity in Mathematical Biology

Friday, August 2, 1:30 p.m. - 5:20 p.m., Duke Energy Convention Center, Room 205

In this session, Project NExT'rs from the 2018 cohort will showcase the diversity of mathematics used in better understanding biological systems. This session is designed specifically for an under-graduate audience.

Mathematical biology is grab-bag description for using mathematical techniques to understand biological phenomena. The mathematics applied to study biology is not restricted to a particular sub-discipline of mathematics, but rather is as diverse as the biological systems studied themselves. It requires a blend of existing and contemporary mathematics and fosters wide spread collaboration between not only mathematicians, but also biologists and biomedical scientists. This session will showcase a diverse range of mathematical techniques being applied to a variety of biology systems, from molecular biology and physiology to organismal biology across all length scales of life. Mathematics has been called `biology's next microscope, only better' and to complement that `biology is mathematics' next physics, only better' (J.E. Cohen 2004). This session is designed to be accessible for undergraduate students; we will introduce and discuss how mathematics can contribute to new understanding of biological and biomedical phenomena. Theory and concepts from dynamical systems, optimal control, partial differential equations, numerical analysis, geometry, combinatorics, probability theory, and other areas will be discussed in conjunction with searching for biological insight for problems stemming from cancer biology, epidemiology, psychology, ecology, phylogenetics, organismal biology, personalized medicine, and biomechanics.

Nicholas A. Battista, The College of New Jersey
Rebecca Everett, Haverford College

Comparing Intervention Strategies for Reducing Clostridium difficile Transmission: An Agent-Based Modeling Study

1:30 p.m. - 1:50 p.m.
Brittany Stephenson, Lewis University


In recent years, healthcare facilities have experienced an increasing substantial burden from the toxin-producing bacteria Clostridium difficile, which can cause severe intestinal disease. This bacteria can survive for extended periods of time on hospital surfaces. In this talk, I will discuss the development of an agent-based model that simulates the transmission of C. difficile in a healthcare setting and considers contributions of the pathogen from environmental surfaces. This model explicitly incorporates healthcare workers (HCWs) as vectors of transmission, tracks individual patient antibiotic histories, incorporates varying risk levels of antibiotics with respect to CDI, and tracks contamination levels of ward rooms by C. difficile. I will also discuss how we used the model to evaluate the efficacy of a variety of control interventions and combinations of interventions on reducing C. difficile nosocomial colonizations and infections. The control tech- niques include two forms of antimicrobial stewardship, increased environmental decontamination through room cleaning, improved HCW compliance, and a preliminary assessment of vaccination.


Enhanced Coupling of Cilia Through Cell Rocking

2:00 p.m. - 2:20 p.m.
Forest Mannan, Colorado School of Mines


Motile cilia are long, hair-like organelles that extend from cellular surfaces and induce fluid flows by undergoing an oscillatory bending motion. Cilia often exhibit coordinated beating and many researchers have shown that this synchronization is mediated through hydrodynamic interactions. It has been suggested that the rocking of a free swimming cell body might play an additional role in synchronization. Using the Method of Regularized Stokeslets and modeling the ciliary structure as a system of springs, it is demonstrated that cell rocking can have a significant impact on the coupling of cilia.


Parameter Informatics for Nonlinear Models

2:30 p.m. - 2:50 p.m.
Reginald McGee, College of the Holy Cross


In 2017, Dawes et al. created a nonlinear model for signal transduction in epithelial cell development in roundworms. Via a parameter space sampling procedure over 6000 parameter sets were found to satisfy a wild-type pattern defined by the expressions of a ligand and phosphotase in the signaling network. Moreover, in silico perturbations to the signaling pathway replicated species- specific responses of protein knockout experiments and separated the parameter sets into groups corresponding to the model organism C. elegans and the less studied roundworm C. briggsae. We motivate the advantages of a perspective where each parameter sets is viewed as an observation in a high-dimensional dataset and present an approach for clustering the data by the associated model dynamics. We discuss how the aforementioned perspective could be used to avoid global bifurcation analysis and contrast parameter sets that have been dynamically clustered together, but replicate behaviors of distinct species.

Role of Resource Allocation and Transport in Emergence of Cross-feeding in Microbial Consortia

3:00 p.m. - 3:20 p.m.
Diana Schepens, Whitworth University


Microbial communities that implement mutual cross-feeding are commonly observed in nature and with synthetic constructs in laboratory experiments. A mathematical model of competition in a chemostat is developed to investigate the role that resource allocation and transport of metabolites play in cooperation. The model contains four cell types that differ by whether they produce two, one, or none of two essential metabolites. Producing cell types may export these resources into the environment, and those that do not produce both metabolites must import the missing resource. The contribution to the emergence of a collaborative consortium of single resource producers from the transport rate of these metabolites and the type of transport used by the cell (active vs. passive) is studied. Multiple instances of bi-stability and tri-stability are observed, and the effect of the initial concentration of a non-cooperative cheater cell type on the final outcome of the competition is examined. When the cost of producing metabolites is introduced into the model, significant changes to the outcome of the competition are observed, including coexistence of multiple cell types.


k-Foldability of RNA

3:30 p.m. - 3:50 p.m.
Garner Cochran, Berry College


I will speak about a model which generalizes the folding of the RNA molecule in biology, first introduced by Black, Drellich, and Tymoczko (2017+). RNA is represented by a word from the alphabet of nucleotides A, U, C, and G in which Watson-Crick bonds form between nucleotides A and U and between C and G. Sometimes RNA sequences will fold such that some base pairs are left unmatched. We wish to consider only the case where all the base pairs completely match up. I will answer the question of when a sequence will fold completely and will answer some questions about the different ways that a sequence can fold onto itself. I will conclude with some open problems in the area.


Mixing and Pumping by Pairs of Helices in a Viscous Fluid

4:00 p.m. - 4:20 p.m.
Amy Buchmann, University of San Diego


It is difficult to mix and pump fluid in microfluidics devices because the traditional methods of mixing and pumping at large length scales dont work at small length scales. Experimental work has suggested that rotating helical flagella may be used to effectively mix and pump fluid in microfluidics devices. To further explore this idea and to characterize the flow features around rotating helices, we study the hydrodynamic interactions between two rigid helices rotating at a constant velocity. Helices are coupled to a viscous fluid using a numerical method based upon a centerline distribution of regularized Stokeslets, and we analyze the effects of spacing and phase shift on mixing and pumping.


Modeling the Impacts of Disturbances: What Can We Learn about Population Responses and Possible Management Strategies?

4:30 p.m. - 4:50 p.m.
Amy Veprauskas, University of Louisiana at Lafayette


As species are increasingly being exposed to disturbances, it is important to be able to better understand and predict how disturbances may impact populations. Here we explore how a population may be affected by a single disturbance or by reoccurring disturbances. Alongside general analysis, we provide an application to a sperm whale model to better understand how disturbances, such as oil spills, may impact this species. We first apply sensitivity analysis to study the recovery process for a population following a single disturbance. We then use a two- state Markov chain to describe disturbances occurring stochastically. We derive an approximation for the stochastic growth rate that allows us to consider how properties of the disturbance, such as duration and magnitude, may impact a populations survival. We find commonalities in both situations that suggest how to focus management strategies.


Don’t Be Jelly: Modeling Effective Jet Propulsion

5:00 p.m. - 5:20 p.m.
Nicholas A. Battista, The College of New Jersey


Jellyfish (Medusozoa) have been deemed the most energy-efficient animals in the world. They are soft body marine organisms composed of gelatinous bell, tentacles containing nematocists for prey capture, and either 4 or 8 oral arms. Their nervous system typically consists of a distributed net of cells. There are between four and sixteen distributed nets of cells around the rim of the bell, which coordinate muscular contraction to propel the jellyfish forward. Their simple morphology and nervous systems make them attractive to robotocists, but we do not understand the limits of jellyfish jet propulsion and maneuverability. Numerous scientists have developed sophisticated computational models of jellyfish that produce forward propulsion, even having compared swimming performance over a large mechanospace of bell flexibility, muscular contraction strength, and contraction frequencies. However previous studies have not addressed swimming performance in the presence of ambient oscillatory flows, like those in natural oceanic environments, nor have they considered the effects of complex morphologies, e.g., tentacles, or using non-buoyant materials for building a biomimetic robotic jellyfish. And so our work dives headfirst into that.