2015 Summer Undergraduate REU Program

The Ohio State University

OSU - Department of Mathematics

OSU - Department of Statistics

Topic 1:

Statistical shape analysis – Sebastian Kurtek

Project Description:

Statistical shape analysis of protein structure is an important problem in bioinformatics, providing insight into protein function as well as evolutionary relationships among proteins. Most previous research has focused on studying the primary or secondary structure of proteins, with recent results showing that optimal curve registration provides improved comparisons of secondary structures. In this project, we will analyze tertiary structure by studying protein surfaces using a recent framework for statistical shape analysis of 3D objects proposed by Kurtek et al. (2012). This framework provides a comprehensive set of tools for comparison and statistical modeling of closed surfaces. The main advantage over previous methods is that this method is invariant to re-parameterization of surfaces and allows optimal registration of features across surface shapes. Participating students will begin by exploring variability in different protein classes using statistical methods such as principal component analysis, and then perform a larger classification experiment based on protein shapes in the SCOP database. Students working on this project will learn important techniques in statistics such as principal component analysis, differential geometry, and shape analysis, with specific application to bioinformatics.

Topic 2:

Modeling afferents of central pattern generators – Janet Best

Project Description:

Central pattern generators (CPGs) are neuronal circuits that produce rhythmic patterned output without requiring sensory or other inputs to provide timing information. In many species, spinal CPGs have been found to produce rhythmic motor patterns such as walking, running, and scratching (Frigon, 2012). Spinal CPGs in humans have not been definitively established, though evidence is provided by individuals with spinal injuries and by periodic limb movements occurring during sleep (Bara-Jimenez et al., 2000, Duysens and Van de Crommert, 1998). In this project, we will modify an existing CPG model (Spardy et al., 2011) to develop a mathematical model for a human spinal CPG proposed to generate a stereotyped motion known as the triple flexion reflex (Duysens et al., 2002). We will model the effects of afferents to the CPG such as sensory inputs, sensory feedback, and descending inhibition. We will investigate how these inputs modulate the period of the CPG, and see whether we can account for the range of frequencies reported under different experimental conditions. Students will mathematically model the electrophysiology of neurons and synaptic coupling in humans, and will learn about stable and unstable periodic solutions of differential equations and how properties of solutions can change with parameters.