PSU Mark

REU program: TEAMS (Training in Experiment, Analysis, Modeling, and Simulation) in Mathematics for the Applied Sciences

Sample Project: Study of Gramicidin Pore Dynamics.

Ion channels are transmembrane proteins that regulate the ion distribution in biological environments through ionic permeability in cell membranes. They are present in all biological processes due to their role in signaling and sensing pathways, and in connecting the interior and exterior of cells in a selective fashion. Several biosensors have been developed to detect molecular species by exploiting the selectivity mechanisms of these ion channels. Those incorporating gramicidin ion channels into a lipid bilayer membrane to detect the presence of phospholipases, a ubiquitous class of membrane-active enzymes, are important in cellular signaling, proliferation, and membrane trafficking.

Gramicidin A (gA) is a small channel-forming peptide that is secreted from the bacterium {\it Bacillus brevis}. This peptide self-incorporates into lipid membranes. The properties and kinetics of gA channels such as their conductance, lifetime, and opening/closing frequency depend strongly on their membrane environment as well as the recording buffer that surrounds the channel. Once characterized, gA channels can act as nano-sensors and reveal information about their surrounding environment.

Mathematical Models of Traffic Flow

We investigate the kinetics and properties of gA channels under specific experimental conditions to better understand how this peptide responds to its environmental changes. A typical application of gA pores is to sense the activities of phospholipase D (PLD) and phospholipase C (PLC) on lipid bilayers by measuring the conductance changes of the gA pores. Two students in our summer 2013 program, E.M. Shouse and J. Miller, successfully incorporated gA pores into lipid bilayers and measured the step changes in the conductance in Majd's lab (see figure). We propose to engage students similarly in the lab, on the measurement of gA dynamics in different biological environments, such as those in the presence of drugs and other enzymes.

We have developed models and corresponding numerical codes to study the changes of current and conductance in a single Gramicidin pore under the conditions in those known experiments. The model includes the following Poisson-Nernst-Planck (PNP) system:

n_{t} =\nabla\cdot(D_n\nabla n-\frac{D_ne}{K_BT} \nabla\phi n), \quad p_t =\nabla\cdot(D_p\nabla p+\frac{D_pe}{K_BT} \nabla\phi p), (1)
-\nabla\cdot(\epsilon_0\epsilon_r\nabla\phi)=(p-n)ze,. (2)
with specific initial and boundary conditions. Our preliminary computations have qualitatively captured the key phenomena from those experiments. The students will conduct extensive numerical simulations of the above model, along with suitable variations. The numerical results will then be compared with lab measurements. The project will provide students with valuable opportunities to verify and validate such mathematical models with a real application.