Molecular Biology Commons^™

Tools For Biomolecular Modeling And Simulation, Xin Yang

Mathematics Theses and Dissertations

Electrostatic interactions play a pivotal role in understanding biomolecular systems, influencing their structural stability and functional dynamics. The Poisson-Boltzmann (PB) equation, a prevalent implicit solvent model that treats the solvent as a continuum while describes the mobile ions using the Boltzmann distribution, has become a standard tool for detailed investigations into biomolecular electrostatics. There are two primary methodologies: grid-based finite difference or finite element methods and body-fitted boundary element methods. This dissertation focuses on developing fast and accurate PB solvers, leveraging both methodologies, to meet diverse scientific needs and overcome various obstacles in the field.

Modeling Biphasic, Non-Sigmoidal Dose-Response Relationships: Comparison Of Brain- Cousens And Cedergreen Models For A Biochemical Dataset, Venkat D. Abbaraju, Tamaraty L. Robinson, Brian P. Weiser

Rowan-Virtua School of Osteopathic Medicine Faculty Scholarship

Biphasic, non-sigmoidal dose-response relationships are frequently observed in biochemistry and pharmacology, but they are not always analyzed with appropriate statistical methods. Here, we examine curve fitting methods for “hormetic” dose-response relationships where low and high doses of an effector produce opposite responses. We provide the full dataset used for modeling, and we provide the code for analyzing the dataset in SAS using two established mathematical models of hormesis, the Brain-Cousens model and the Cedergreen model. We show how to obtain and interpret curve parameters such as the ED50 that arise from modeling, and we discuss how curve parameters might change …

Computationally Modeling Dynamic Biological Systems, Katherine Jarvis

Electronic Theses and Dissertations

Modeling biological systems furthers our understanding of dynamic relationships and helps us make predictions of the unknown properties of the system. The simple interplay between individual species in a dynamic environment over time can be modeled by equation-based modeling or agent- based modeling (ABM). Equation based modeling describes the change in species quantity using ordinary differential equations (ODE) and is dependent on the quantity of other species in the system as well as a predetermined rates of change. Unfortunately, this method of modeling does not model each individual agent in each species over time so individual dynamics are assumed to …

Genetic Polymorphism Of Bitter Taste Perception In Tempe, Arizona And Its Association With Nutritional Status, Daniel Woodley, Benjamin Cabrera

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Stochastic Modeling Of Neuronal Transport In Various Cellular Geometries, Abhishek Choudhary Mr., Peter Kramer

Biology and Medicine Through Mathematics Conference

No abstract provided.

Hpcnmf: A High-Performance Toolbox For Non-Negative Matrix Factorization, Karthik Devarajan, Guoli Wang

COBRA Preprint Series

Non-negative matrix factorization (NMF) is a widely used machine learning algorithm for dimension reduction of large-scale data. It has found successful applications in a variety of fields such as computational biology, neuroscience, natural language processing, information retrieval, image processing and speech recognition. In bioinformatics, for example, it has been used to extract patterns and profiles from genomic and text-mining data as well as in protein sequence and structure analysis. While the scientific performance of NMF is very promising in dealing with high dimensional data sets and complex data structures, its computational cost is high and sometimes could be critical for …

A Time-And-Space Parallelized Algorithm For The Cable Equation, Chuan Li

Doctoral Dissertations

Electrical propagation in excitable tissue, such as nerve fibers and heart muscle, is described by a nonlinear diffusion-reaction parabolic partial differential equation for the transmembrane voltage $V(x,t)$, known as the cable equation. This equation involves a highly nonlinear source term, representing the total ionic current across the membrane, governed by a Hodgkin-Huxley type ionic model, and requires the solution of a system of ordinary differential equations. Thus, the model consists of a PDE (in 1-, 2- or 3-dimensions) coupled to a system of ODEs, and it is very expensive to solve, especially in 2 and 3 dimensions.

In order to …

Bilinear Programming And Protein Structure Alignment, J. Cain, D. Kamenetsky, N. Lavine

Mathematical Sciences Technical Reports (MSTR)

Proteins are a primary functional component of organic life, and understanding their function is integral to many areas of research in biochemistry. The three-dimensional structure of a protein largely determines this function. Protein structure alignment compares the structure of a protein with known function to that of a protein with unknown function. A protein’s three-dimensional structure can be transformed through a smooth piecewise-linear sigmoid function to a real symmetric contact matrix that represents the functional significance of certain parts of the protein. We address the protein alignment problem as a minimization of the 2-norm difference of two proteins’ contact matrices. …

Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper

Mathematical Sciences Technical Reports (MSTR)

We introduce a new measure for comparing protein structures that is especially applicable to analysis of molecular dynamics simulation results. The new measure generalizes the widely used root-mean-squared-deviation (RMSD) measure from three dimensional to n-dimensional Euclidean space, where n equals the number of atoms in the protein molecule. The new measure shows that despite significant fluctuations in the three dimensional geometry of the estrogen receptor protein, the protein's intrinsic contact geometry is remarkably stable over nanosecond time scales. The new measure also identifies significant structural changes missed by RMSD for a residue that plays a key biological role in …

Fast Protein Structure Alignment, Yosi Shibberu, Allen Holder, Kyla Lutz

Mathematical Sciences Technical Reports (MSTR)

We address the problem of aligning the 3D structures of two proteins. Our pairwise comparisons are based on a new optimization model that is succinctly expressed in terms of linear transformations and highlights the problem’s intrinsic geometry. The optimization problem is approximately solved with a new polynomial time algorithm. The worst case analysis of the algorithm shows that the solution is bounded by a constant depending only on the data of the problem.

Geometric Build-Up Solutions For Protein Determination Via Distance Geometry, Robert Tucker Davis

Masters Theses & Specialist Projects

Proteins carry out an almost innumerable amount of biological processes that are absolutely necessary to life and as a result proteins and their structures are very often the objects of study in research. As such, this thesis will begin with a description of protein function and structure, followed by brief discussions of the two major experimental structure determination methods. Another problem that often arises in molecular modeling is referred to as the Molecular Distance Geometry Problem (MDGP). This problem seeks to find coordinates for the atoms of a protein or molecule when given only a set of pair-wise distances between …

Microproteomics: Analysis Of Protein Diversity In Small Samples, Howard B. Gutstein, Jeffrey S. Morris, Suresh P. Annangudi, Jonathan V. Sweedler

Jeffrey S. Morris

Proteomics, the large-scale study of protein expression in organisms, offers the potential to evaluate global changes in protein expression and their post-translational modifications that take place in response to normal or pathological stimuli. One challenge has been the requirement for substantial amounts of tissue in order to perform comprehensive proteomic characterization. In heterogeneous tissues, such as brain, this has limited the application of proteomic methodologies. Efforts to adapt standard methods of tissue sampling, protein extraction, arraying, and identification are reviewed, with an emphasis on those appropriate to smaller samples ranging in size from several microliters down to single cells. The …

Statistical Issues In Proteomic Research, Jeffrey S. Morris

Jeffrey S. Morris

No abstract provided.

Laser Capture Sampling And Analytical Issues In Proteomics, Howard Gutstein, Jeffrey S. Morris

Jeffrey S. Morris

Proteomics holds the promise of evaluating global changes in protein expression and post-translational modificaiton in response to environmental stimuli. However, difficulties in achieving cellular anatomic resolution and extracting specific types of proteins from cells have limited the efficacy of these techniques. Laser capture microdissection has provided a solution to the problem of anatomical resolution in tissues. New extraction methodologies have expanded the range of proteins identified in subsequent analyses. This review will examine the application of laser capture microdissection to proteomic tissue sampling, and subsequent extraction of these samples for differential expression analysis. Statistical and other quantitative issues important for …

Prepms: Tof Ms Data Graphical Preprocessing Tool, Yuliya V. Karpievitch, Elizabeth G. Hill, Adam J. Smolka, Jeffrey S. Morris, Kevin R. Coombes, Keith A. Baggerly, Jonas S. Almeida

Jeffrey S. Morris

We introduce a simple-to-use graphical tool that enables researchers to easily prepare time-of-flight mass spectrometry data for analysis. For ease of use, the graphical executable provides default parameter settings experimentally determined to work well in most situations. These values can be changed by the user if desired. PrepMS is a stand-alone application made freely available (open source), and is under the General Public License (GPL). Its graphical user interface, default parameter settings, and display plots allow PrepMS to be used effectively for data preprocessing, peak detection, and visual data quality assessment.

Analysis Of Mass Spectrometry Data Using Bayesian Wavelet-Based Functional Mixed Models, Jeffrey S. Morris, Philip J. Brown, Keith A. Baggerly, Kevin R. Coombes

Jeffrey S. Morris

In this chapter, we demonstrate how to analyze MALDI-TOF/SELDITOF mass spectrometry data using the wavelet-based functional mixed model introduced by Morris and Carroll (2006), which generalizes the linear mixed models to the case of functional data. This approach models each spectrum as a function, and is very general, accommodating a broad class of experimental designs and allowing one to model nonparametric functional effects for various factors, which can be conditions of interest (e.g. cancer/normal) or experimental factors (blocking factors). Inference on these functional effects allows us to identify protein peaks related to various outcomes of interest, including dichotomous outcomes, categorical …

Computational Protein Biomarker Prediction: A Case Study For Prostate Cancer, Michael Wagner, Dayanand N. Naik, Alex Pothen, Srinivas Kasukurti, Raghu Ram Devineni, Bao-Ling Adam, O. John Semmes, George L. Wright Jr.

Mathematics & Statistics Faculty Publications

Background: Recent technological advances in mass spectrometry pose challenges in computational mathematics and statistics to process the mass spectral data into predictive models with clinical and biological significance. We discuss several classification-based approaches to finding protein biomarker candidates using protein profiles obtained via mass spectrometry, and we assess their statistical significance. Our overall goal is to implicate peaks that have a high likelihood of being biologically linked to a given disease state, and thus to narrow the search for biomarker candidates.

Results: Thorough cross-validation studies and randomization tests are performed on a prostate cancer dataset with over 300 patients, obtained …