Jennifer Airone, Carnegie Mellon University
(Mentor: Dr. Frederick Lanni)
Computational Simulation of Elastic Deformation In A Collagen Gel
The mechanical activities of cells, and how they affect the surrounding extracellular matrix (ECM) is an interaction that has been intriguing scientists for many years. Next to insitu observation, which is often impossible, the best way to study and understand how a cell behaves under native conditions is to place it in a model ECM similar to that of living tissue. Collagen is one of the main extracellular structural proteins in the body, and therefore is a good medium for this purpose. Images of cell movement in a collagen gel can be put into specially designed software (developed by Steven Vanni in Dr. Lanni’s lab) called the Deformation Quantification Algorithm (DQA). This software computes a field of deformation vectors in the ECM due to the cells’ movement. These deformations can then be analyzed and compared to the cytoskeletal structure of the cell. My work dealt with manipulating Cerruti’s solution to the elastostatic equations for a Hookean solid, in this case a collagen gel. These equations give the deformation field around a point load applied tangent to an elastic material on its surface. Two parameters, the bulk modulus (G) and Poisson’s ratio (ν) characterize the simplest elastic material, and appear as parameters in the Cerruti equations. We have used a modification of the classical solution to simulate the elastostatic behavior of collagen gels in order to better understand the mechanics of cells in native ECM. The bulk modulus for collagen can be measured using various methods, and, in the Cerruti equations, it simply scales the vector field. Poisson’s ratio has a more complicated effect in the equations, and its value is unknown for collagen on a microscopic scale. Images of a microneedle applying a load on a collagen gel were entered into the DQA to obtain a field of deformation vectors. We were then able to use the modified Cerruti equations to compare a list of simulated vectors to the list of vectors from real data. By varying Poisson’s ratio in the equations and seeing how well it matches the real data, an approximate value of Poisson’s ratio for collagen could be found. This could further help scientists understand the properties of collagen and how it reacts with surrounding cells.

Courtney Davis, Trinity University
(Mentor: Dr. Frederick Lanni)
Mathematical Modeling of the Minimum MRI Contrast Agent Concentration Needed in Tissue
The dynamics of cellular events occurring during the onset and progression of autoimmune diseases, such as multiple sclerosis, can be visualized in vivo using magnetic resonance imaging (MRI) techniques. This is achieved using immune cells labeled with intracellular contrast agents, such as superparamagnetic iron oxide (SPIO) particles. Differences in the spinspin relaxation times (T2) between labeled and unlabeled cells give rise to image contrast. However, the MR technique has a limited available signaltonoise ratio and sensitivity. Hence, it is important to know the minimum concentration requirements providing "satisfactory" image contrast when designing experiments using T2 contrast agents. A general set of equations expressing MR signal intensity in relation to T2 agent concentration and other experimentally controlled parameters are known. These equations were manipulated to determine the minimum concentration requirements for two separate T2 agents. The first contrast agent we modeled was Feridex (Berlex Inc.), which is a clinically approved SPIO agent. The second "agent" we examined is the endogenous cellular iron storage protein, ferritin. We generated new equations relating the agent concentration to a minimal number of parameters. Several parameters were determined empirically, such as the background T2 and the contrast agent relaxivity (R); T2 and R were measured from MR images in the living rat brain cortex and in water phantoms doped with Feridex, respectively. The results of this model accurately correspond with contrast levels measured in phantoms containing varying concentrations of contrast agent. The equations derived can be used to predict the agent concentration requirements for MR experiments instead of having to rely on tedious empirical observations as was previously necessary. Such information will be helpful in determining crucial information such as the density of labeled immune cells required for detectable image contrast in the central nervous system and the required efficiency of the cell labeling techniques.

Craig Gallek, Carnegie Mellon University
(Mentors: Dr. David Yaron)
A New Approach to Electronic Structure Theory
The goal of this project was to develop an electron structure calculation method with the accuracy of a highlevel (MCSCF) calculation and the speed of a lowlevel (UHF) calculation. This can best be explained through an example. Let’s say we wanted to run a highlevel calculation on a protein. With current programs, an MCSCF calculation would take years on a protein only a few units long. Our goal was to take advantage of the fact that the individual subsystems of a molecule (the amino acids in this example) look similar from system to system. Our approach was to isolate these subsystems and find a function that models the changes that occur to the subsystems in different environments. First, it is necessary to find a relationship between a highlevel calculation and a lowlevel calculation for each subsystem. Although this calculation is costly, the relationship would only need to be calculated once for each subsystem. Once we understand this relationship, it is possible to calculate highlevel information from a lowlevel calculation.
To accomplish our goal, we adopted the following procedure. First, we isolated the subsystems of our molecule. For each of these subsystems we found a function that would relate a lowlevel calculation to a highlevel calculation for an arbitrary density matrix. Once the corrections functions for each subsystem are obtained, they can then be summed together and added to the lowlevel calculated energy of the system This should then give the accuracy of a highlevel calculation with the speed of a lowlevel calculation.

Matthew Kofke, Carnegie Mellon University
(Mentor: Dr. David Yaron)
The Photophysics of Helical Cyanine Dye Aggregates
3,3'Diethylthidicarbocyanine, cyanine dyes are unique molecules in that they form cofacial dimers that insert into the minor groove of duplex DNA. The dimers exhibit selectivity to regions consisting of alternating adenine/thymine base pairs, not alternating guanine/cytosine base pairs. Thus, duplex DNA serves as a nanotemplate for the self assembly of helical cyanine dye aggregates. Theoretical excited state modeling using INDO/CI methods allows us to extract structural information from the experimental spectra. The model indicates that there is a shift of 4A between dyes in the dimer, and that the dimers are closely packed into the minor groove. For an experimental system with two dimers separated by regions of GC base pairs, the experimental spectra did not correlate well to the theoretical spectra. The ability of the theoretical model to rationalize all aspects of the experimental system, save for the instance where GC base pairs separate the dimers, suggests the experimental system with separated dimers adopts a unique geometry.

Gregory Porreca, College of New Jersey
(Mentor: Dr. Robert Murphy)
Classifying images of protein subcellular location from any source: Increasing the robustness of the feature set
Although protein sequence and structure information can be determined and communicated objectively and consistently, equally important localization pattern information cannot. It is subjectively determined, and an insufficient vocabulary limits the level of detail that can be communicated. A system has been previously developed that solves this problem by numerically describing any localization pattern. Using numerical features, a neural network classifier was trained to distinguish between ten different classes of such patterns, comprising all major subcellular locations (mitochondria, endoplasmic reticulum, Golgi, etc.) with an accuracy of 83%. Initially, a study was conducted here to compare the classification ability of a human to that of the system. Although both were able to distinguish between the ten classes with an average accuracy of 83%, the system was better able to differentiate between two Golgi patterns, while the human could identify mitochondrial, endosomal, nucleolar, and tubulin patterns with higher accuracy. Since a human's ability to characterize the pattern in an image is not dramatically affected by the resolution or intensity scale of an image, and since a goal of this work is the development of a method that is both as robust as humans and still objective and consistent, we sought to minimize the influence of these factors on the set of Haralick features used in classification. The normalization strategy developed was to downsample the set of training images to a 5bit (32 value) intensity range and 1.15 micrometer/pixel resolution. As a result, any image that has an intensity range and resolution above these 'least common denominators' can be classified after first being downsampled to these values. This will allow the system to be used for the classification of images from widely disparate sources, including online journal articles. To further improve classification accuracy, Support Vector Machines were evaluated as an alternate classification method. A classifier was trained that gave an overall classification accuracy of 86% using the allversusall method of Ding and Dubchak (Bioinformatics 17:349358, 2001), and was able to distinguish between certain classes much better than the neural network. Determination of the causes for this difference between classification methods should allow for improvements to either the feature set or the classifier, further increasing accuracy.

Ruben Valas, Carnegie Mellon University
(Mentor: Dr. Christopher Langmead)
DataDriven Prediction of Macromolecular Motions
Recent advances in Nuclear Magnetic Resonance (NMR) spectroscopy present new opportunities for investigating the conformational dynamics of proteins in solution. In particular, order parameters for motions relevant to biological function can be obtained via experimental measurement of Residual Dipolar Couplings (RDCs). These order parameters have been used by others to identify mobile regions within proteins. We extend these results and introduce the first technique for characterizing the nature of the motion (hinge, shear, etc.). Motion tensors are extracted from the RDCs and used to train a classifier for macromolecular motions. Using a set of 2,400 dynamic protein models spanning seven different classes of motion, our classifier achieves an accuracy of 91% using 10fold crossvalidation.
