Jeff Knisley

A predictive model for secondary RNA structure using graph theory and a neural network

BackgroundDetermining the secondary structure of RNA from the primary structure is a challenging computational problem. A number of algorithms have been developed to predict the secondary structure from the primary structure. It is agreed that there is still room for improvement in each of these approaches. In this work we build a predictive model for secondary RNA structure using a graph-theoretic tree representation of secondary RNA structure. We model the bonding of two RNA secondary structures to form a larger secondary structure with a graph operation we call merge. We consider all combinatorial possibilities using all possible tree inputs, both those that are RNA-like in structure and those that are not. The resulting data from each tree merge operation is represented by a vector. We use these vectors as input values for a neural network and train the network to recognize a tree as RNA-like or not, based on the merge data vector. The network estimates the probability of a tree being RNA-like.ResultsThe network correctly assigned a high probability of RNA-likeness to trees previously identified as RNA-like and a low probability of RNA-likeness to those classified as not RNA-like. We then used the neural network to predict the RNA-likeness of the unclassified trees.ConclusionsThere are a number of secondary RNA structure prediction algorithms available online. These programs are based on finding the secondary structure with the lowest total free energy. In this work, we create a predictive tool for secondary RNA structures using graph-theoretic values as input for a neural network. The use of a graph operation to theoretically describe the bonding of secondary RNA is novel and is an entirely different approach to the prediction of secondary RNA structures. Our method correctly predicted trees to be RNA-like or not RNA-like for all known cases. In addition, our results convey a measure of likelihood that a tree is RNA-like or not RNA-like. Given that the majority of secondary RNA folding algorithms return more than one possible outcome, our method provides a means of determining the best or most likely structures among all of the possible outcomes.

Research Article: Predicting protein-protein interactions using graph invariants and a neural network

The PDZ domain of proteins mediates a protein-protein interaction by recognizing the hydrophobic C-terminal tail of the target protein. One of the challenges put forth by the DREAM (Discussions on Reverse Engineering Assessment and Methods) 2009 Challenge consists of predicting a position weight matrix (PWM) that describes the specificity profile of five PDZ domains to their target peptides. We consider the primary structures of each of the five PDZ domains as a numerical sequence derived from graph-theoretic models of each of the individual amino acids in the protein sequence. Using available PDZ domain databases to obtain known targets, the graph-theoretic based numerical sequences are then used to train a neural network to recognize their targets. Given the challenge sequences, the target probabilities are computed and a corresponding position weight matrix is derived. In this work we present our method. The results of our method placed second in the DREAM 2009 challenge.

Mentoring Interdisciplinary Undergraduate Students via a Team Effort

We describe how a team approach that we developed as a mentoring strategy can be used to recruit, advance, and guide students to be more interested in the interdisciplinary field of mathematical biology, and lead to success in undergraduate research in this field. Students are introduced to research in their first semester via lab rotations. Their participation in the research of four faculty members—two from biology and two from mathematics—gives them a first-hand overview of research in quantitative biology and also some initial experience in research itself. However, one of the primary goals of the lab rotation experience is that of developing teams of students and faculty that combine mathematics and statistics with biology and the life sciences, teams that subsequently mentor undergraduate research in genuine interdisciplinary environments. Thus, the team concept serves not only as a means of establishing interdisciplinary research, but also as a means of incorporating new students into existing research efforts that will then track those students into meaningful research of their own. We report how the team concept is used to support undergraduate research in mathematical biology and what types of team-building strategies have worked for us.

Classifying Multigraph Models of Secondary RNA Structure Using Graph-Theoretic Descriptors

The prediction of secondary RNA folds from primary sequences continues to be an important area of research given the significance of RNA molecules in biological processes such as gene regulation. To facilitate this effort, graph models of secondary structure have been developed to quantify and thereby characterize the topological properties of the secondary folds. In this work we utilize a multigraph representation of a secondary RNA structure to examine the ability of the existing graph-theoretic descriptors to classify all possible topologies as either RNA-like or not RNA-like. We use more than one hundred descriptors and several different machine learning approaches, including nearest neighbor algorithms, one-class classifiers, and several clustering techniques. We predict that many more topologies will be identified as those representing RNA secondary structures than currently predicted in the RAG (RNA-As-Graphs) database. The results also suggest which descriptors and which algorithms are more informative in classifying and exploring secondary RNA structures.

Inferring gene expression from ribosomal promoter sequences, a crowdsourcing approach

The Gene Promoter Expression Prediction challenge consisted of predicting gene expression from promoter sequences in a previously unknown experimentally generated data set. The challenge was presented to the community in the framework of the sixth Dialogue for Reverse Engineering Assessments and Methods (DREAM6), a community effort to evaluate the status of systems biology modeling methodologies. Nucleotide-specific promoter activity was obtained by measuring fluorescence from promoter sequences fused upstream of a gene for yellow fluorescence protein and inserted in the same genomic site of yeast Saccharomyces cerevisiae. Twenty-one teams submitted results predicting the expression levels of 53 different promoters from yeast ribosomal protein genes. Analysis of participant predictions shows that accurate values for low-expressed and mutated promoters were difficult to obtain, although in the latter case, only when the mutation induced a large change in promoter activity compared to the wild-type sequence. As in previous DREAM challenges, we found that aggregation of participant predictions provided robust results, but did not fare better than the three best algorithms. Finally, this study not only provides a benchmark for the assessment of methods predicting activity of a specific set of promoters from their sequence, but it also shows that the top performing algorithm, which used machine-learning approaches, can be improved by the addition of biological features such as transcription factor binding sites.

A linear method for the curve fitting of multiexponentials

Two single-pass methods for fitting multiexponentials to experimental data are described. These methods rely on the construction of a matrix whose characteristic polynomial is used to determine the rates of decay. In the first method, which we call the multiple-delay method, the matrix is constructed using time delays of the experimental data. This method is fast and highly accurate even if the experimental signal contains exponential components with similar rates of decay. In the second method, which we call the successive-integral method, the matrix is constructed using integrals of the experimental data. This procedure yields good results for noisy signals and is a generalization of the method of Martin et al. ((1993) J. Neurosci. Methods, 51: 135-146). In addition, a particular instability of the multiexponential curve fitting problem is identified and a method for overcoming this instability is given.

Complex Vectors and Image Identification

Lyndell M. Kerley earned an MA from Appalachian State University and a Ph.D. in mathematics from the University of Tennesse in 1977 under the direction of Dr. William R. Wade. He has been on the mathematics faculty at East Tennessee State University since 1967. During the summer of 1990 he partici? pated in an NSF institute, Fourier Analysis, at Southern Illinois University. His research interests are in Fourier analysis, numeri? cal analysis, and computer graphics.

Graph-Theoretic Models of Mutations in the Nucleotide Binding Domain 1 of the Cystic Fibrosis Transmembrane Conductance Regulator

Cystic fibrosis is one of the most common inherited diseases and is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). This protein serves as a chloride channel and regulates the viscosity of mucus lining the ducts of a number of organs. Although much has been learned about the consequences of mutations on the energy landscape and the resulting disrupted folding pathway of CFTR, a level of understanding needed to correct the misfolding has not been achieved. The most common mutations of CFTR are located in one of two nucleotide binding domains, namely, the nucleotide binding domain 1 (NBD1). We model NBD1 using a nested graph model. The vertices in the lowest layer each represent an atom in the structure of an amino acid residue, while the vertices in the mid layer each represent the residue. The vertices in the top layer each represent a subdomain of the nucleotide binding domain. We use this model to quantify the effects of a single point mutation on the protein domain. We compare the wildtype structure with eight of the most common mutations. The graph-theoretic model provides insight into how a single point mutation can have such profound structural consequences.

Developing Student Collaborations across Disciplines, Distances, and Institutions

Because quantitative biology requires skills and concepts from a disparate collection of different disciplines, the scientists of the near future will increasingly need to rely on collaborations to produce results. Correspondingly, students in disciplines impacted by quantitative biology will need to be taught how to create and engage in such collaborations. In response to this important curricular need, East Tennessee State University and Georgia Technological University/Emory University cooperated in an unprecedented curricular experiment in which theoretically oriented students at East Tennessee State designed biophysical models that were implemented and tested experimentally by biomedical engineers at the Wallace H. Coulter Department of Biomedical Engineering at Georgia Technological University and Emory University. Implementing the collaborations between two institutions allowed an assessment of the student collaborations from before the groups of students had met for the first time until after they had finished their projects, thus providing insight about the formation and conduct of such collaborations that could not have been obtained otherwise.

Seeing the results of a mutation with a vertex weighted hierarchical graph

BackgroundWe represent the protein structure of scTIM with a graph-theoretic model. We construct a hierarchical graph with three layers - a top level, a midlevel and a bottom level. The top level graph is a representation of the protein in which its vertices each represent a substructure of the protein. In turn, each substructure of the protein is represented by a graph whose vertices are amino acids. Finally, each amino acid is represented as a graph where the vertices are atoms. We use this representation to model the effects of a mutation on the protein.MethodsThere are 19 vertices (substructures) in the top level graph and thus there are 19 distinct graphs at the midlevel. The vertices of each of the 19 graphs at the midlevel represent amino acids. Each amino acid is represented by a graph where the vertices are atoms in the residue structure. All edges are determined by proximity in the proteins 3D structure. The vertices in the bottom level are labelled by the corresponding molecular mass of the atom that it represents. We use graph-theoretic measures that incorporate vertex weights to assign graph based attributes to the amino acid graphs. The attributes of the corresponding amino acids are used as vertex weights for the substructure graphs at the midlevel. Graph-theoretic measures based on vertex weighted graphs are subsequently calculated for each of the midlevel graphs. Finally, the vertices of the top level graph are weighted with attributes of the corresponding substructure graph in the midlevel.ResultsWe can visualize which mutations are more influential than others by using properties such as vertex size to correspond with an increase or decrease in a graph-theoretic measure. Global graph-theoretic measures such as the number of triangles or the number of spanning trees can change as the result. Hence this method provides a way to visualize these global changes resulting from a small, seemingly inconsequential local change.ConclusionsThis modelling method provides a novel approach to the visualization of protein structures and the consequences of amino acid deletions, insertions or substitutions and provides a new way to gain insight on the consequences of diseases caused by genetic mutations.