The Ohio State University

OSU - Departments of Statistics and Mathematics

Topic 1:

Mathematical Neuroscience - Janet Best

Histamine is an important wake-promoting neurotransmitter -- that’s why antihistamines can make you drowsy. While most neurotransmitters are released into a small synaptic space between cells and help transmit electrical signals from one neuron to the next, most histamine release is nonsynaptic, instead diffusing and increasing excitability in target cells distributed widely throughout the brain. Histamine also binds to serotonin cells and reduces serotonin release; low serotonin is associated with mood disorders. The extracellular concentration of histamine is homeostatically regulated via several mechanisms.

One important mechanism for neurotransmitter homeostasis is the presence of autoreceptors on the neuron terminal. For instance, histaminergic neuron terminals have histamine receptors (autoreceptors) that can affect ion channels in the terminal membrane. Many of these autoreceptors will be occupied when the extracellular histamine concentration is high, resulting in inhibition of calcium conductances and decreased histamine release in response to an action potential. The goal of this project is to explore the role of autoreceptors in extracellular histamine concentration, beginning with a simplified mathematical model for ion channels and autoreceptor activity. Students will have the opportunity to work with experimental data.


Topic 2:

Statistical Shape Analysis - Sebastian Kurtek

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 3:

Modeling Epidemics with Avoidance - David Sivakoff

We will investigate the effects of avoidance and local quarantine interventions on the spread of disease in simple epidemic models on networks of individuals or populations. In heterogeneous populations, under what circumstances can local interventions hinder or prevent the spread of a disease? When individuals are allowed to exchange contacts or move between populations, the answer is not so clear, as a local intervention may result in global dispersal of the infection. Students will learn about random graphs, interacting particle systems (disease models), and techniques from Markov chains and percolation theory used to prove the existence (and non-existence) of epidemics.