2012 Undergraduate Summer Research Program in Mathematical Biosciences

Projects at IUPUI

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Undergraduate Summer Research Program 2012
joint initiative with the NSF-funded Mathematical Biosciences Institute (MBI) in Columbus (OH)

The goal of this MBI NSF-funded program is to introduce students to exciting new areas of mathematical biology, to involve them in collaborative research with their peers and faculty mentors, and to increase their interest in mathematical biology.
The program consists of three parts - each including a mix of educational and social experiences:
Specific research projects offered at IUPUI are:

Dynamical systems, Oscillations, Synchronization and Parkinson's Disease
Faculty Mentor: Leonid Rubchinsky

Parkinson's disease is marked by synchronized oscillatory dynamics of neural activity. It is believed that different kinds of oscillations are a) responsible for major motor symptoms of the disorder and b) known symptomatic therapies actually suppress synchronized oscillatory activity. It is of both fundamental and practical importance to understand the nature and dynamics of these oscillations, as well as to consider new means of their suppression. Moreover, understanding the neurodynamics of the Parkinson's disease will also promote our understanding of the healthy functioning of the brain parts, impacted in the disease. Mathematical and computational approaches are essential in this regard. Applied dynamical systems, time-series analysis, numerical ODE solution and other parts of applied mathematics are used in our group to understand the dynamics of the brain in parkinsonian state. There are several related lines of research, REU students can participate in, ranging from the analysis of synchronization in the data, recorded in Parkinsonian patients during deep brain stimulation surgeries, to the data-constrained modeling of the brain circuits impacted in Parkinson's disease, to the modeling of Parkinsonian tremor genesis, to the exploration of new algorithms for adaptive deep brain stimulation. Students will have a chance to interact with our biomedical collaborators (neurosurgery and neurology).



Mathematical Modeling of Ocular Blood Flow and its Relation to Glaucoma
Faculty Mentors: Giovanna Guidoboni, Julia Arciero

Glaucoma is a disease in which the optic nerve is damaged, leading to progressive, irreversible loss of vision. Glaucoma is the second leading cause of blindness worldwide, and yet the mechanisms underlying its occurrence remain elusive. The proposed research projects focus on open angle glaucoma (OAG) which progresses at a slow rate and the loss of vision may not be noticed by the patient until the disease is significantly advanced. OAG is often associated with increased intraocular pressure (IOP), which is the pressure of the aqueous humor in the eye. Elevated IOP remains the current focus of therapy, but unfortunately many glaucoma patients continue to experience disease progression despite lowered IOP, even to target levels. Clinical observations show that alterations in ocular blood flow play a very important role in the progression of glaucoma. Significant correlations have been found between impaired vascular function and optic nerve damage, but the mechanisms giving rise to these correlations are still unknown. The goal of this project is to investigate the bio-mechanical connections between vascular function and optic nerve damage, in order to gain a better understanding of the risk factors that may be responsible for glaucoma onset and progression. To reach this goal, our group employs a variety of mathematical techniques, including analysis and numerical solution of ODE systems, to describe blood flow in different regions of the eye, including the retina and the optic nerve. Students will have a chance to interact with our collaborators in the department of ophthalmology.



Fusing circadian and synthetic biology: dynamical identification of distinguishing elements in regulatory clocks
Faculty Mentors: Alexey Kuznetsov, Yaroslav Molkov

Regulatory molecular networks are collections of interacting molecules in a cell. One particular kind, oscillatory networks, forms part of many important pathways. Accordingly, diseases linked to abnormalities of the oscillatory regulatory processes range from sleep disorders to cancer. It is a major challenge to identify the structural differences responsible for distinct functional properties of the regulatory networks that generate the oscillations. Mathematical modeling of the circadian clock has reproduced vast experimental data, demonstrated its predictive power, and directed further experimental studies. However, the combination of modeling and experiments has not yet given a consistent picture of what motifs provide the precision and robustness of the circadian clock. Based on our recent modeling work, we proposes a novel approach to identifying the dominant structural details in the circadian clock. This project builds a theoretical basis for examining regulatory oscillators by using synthetic biology. First, we will develop criteria to differentiate oscillatory mechanisms in regulatory oscillators. The major chal-lenge in analyzing the circadian clock and other regulatory networks is their enormous complexity. The project starts with the differentiation of highly simplified models, which also describe artificial regulatory oscillators. The oscillators will be interlocked as in the circadian clock to test their interaction and detect the advantages of the interlocked structure. We will examine the correlation between oscillator design and its robustness. Second, we will characterize the circadian oscillator. The classical circadian oscillator is based on interlocked tran-scription-translation negative feedback loops by the developed criteria. To bridge simple and complex models, molecular details will be added gradually. Tests that detect the alterations most reliably will be proposed for experimental validation. The dynamical properties will be connected to physiological characteristics of the clock, e.g., entrainment by light and temperature compensation.