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Invited Paper Session Abstracts - Mathematics and the Life Sciences at MBI

Friday, August 5, 1:00 p.m. - 4:10 p.m., Harrison

In this session we demonstrate how the mathematical sciences help address important and interesting questions in neuroscience, virology, cancer immunology, cellular communication, and sleep cycle dynamics.

Abstract: Using mathematics to gain new insights into the biological sciences requires the use of existing techniques and also the development of new mathematics. The interplay between math and life sciences is a key component of the mission of the Mathematical Biosciences Institute (MBI). This session samples research related to several of MBI's recent and upcoming thematic programs: molecular biosciences, cancer and the immune system, network dynamics, mathematical neuro-science, and the analysis of complex data.

In this session, we discuss how the mathematical sciences are utilized to make contributions to biological and biomedical questions. Theory and concepts from algebra, geometry, dynamical systems, numerical analysis, probability theory, and other areas will be presented. The math will be used to uncover symmetries in neural activity, quantify signaling dynamics inside cancerous immune cells, consider the impact of oscillations on coupled cells, investigate circadian rhythms and energy regulation, and increase the understanding of viruses and how to overcome their resistant nature.

Why We Sleep: Math Sheds New Light on Personal Energy Conservation

1:00 p.m. - 1:30 p.m
Janet Best, The Ohio State University

While sleep was long considered an energy conservation strategy, the modest calculated savings led to skepticism that energy conservation is the function of sleep, particularly given sleep's inherent costs in vulnerability. Using a mathematical model, we recalculate the energy savings due to sleep and argue that energy conservation is actually the ultimate function of sleep.

Dynamical Systems and Emergent Properties of Cell Networks

1:40 p.m. - 2:10 p.m.
Richard L. Buckalew, Mathematical Biosciences Institute

The dynamics of individual cells lies at the root of much of biology, yet individual cells almost never exist in isolation. Modes of interaction between cells are usually limited to simple signals, but simple interactions at the individual level can lead to surprisingly complex behavior at the population (or organism) level. Syncytial embryos, wherein many nuclei share their cytoplasm, are fertile ground for demonstrating and investigating such behaviors. Simple interactions lend themselves well to mathematical description, and through mathematical modeling we have gained insight into the fascinating behavior of Drosophila and Xenopus embryos, both of which are syncytial.

Singled Out: Using Single-Cell Data to Identify Signaling Trends in Leukemia

2:20 p.m. - 2:50 p.m.
Reginald L. McGee, Mathematical Biosciences Institute

Mass cytometers can record tens of features for millions of cells in a sample, and in particular, for leukemic cells. Many methods consider how to cluster or identify populations of phenotypically similar cells within cytometry data, but there has yet to be a connection between cell activity and other features and these groups or clusters. We use differential geometric ideas to consider how cell cycle and signaling features vary as a function of the cell populations. This consideration leads to a better understanding of the nonlinear relationships that exist in the cytometry data.

An Insight to Viral Assembly through Normal Model Analysis

3:00 p.m. - 3:30 p.m.
Farrah Sadre-Marandi, Mathematical Biosciences Institute

Normal mode analysis, also known as harmonic analysis, is applicable to many fields. It identifies the natural, resonant movements of a physical object, such as a building, guitar string or molecule. In this talk, I will demonstrate how to apply normal mode analysis to proteins. Specifically, this analysis will be applied to predict how proteins move during HIV viral assembly.

Binocular Rivalry and Symmetry Breaking

3:40 p.m. - 4:10 p.m.
Marty Golubitsky, Mathematical Biosciences Institute

Binocular rivalry discusses how a subject perceives images when different images are shown to the subject's left and right eyes. More generally, rivalry addresses the question of how the brain deals with contradictory information.

This talk will discuss a generalized model for rivalry proposed by Hugh Wilson and show how rigid phase-shift synchrony in periodic solutions of coupled systems of differential equations can help understand the surprising results of several binocular rivalry experiments. This is joint work with Casey Diekman

Year: 
2016