Debra Knisley - Academia.edu (original) (raw)
Papers by Debra Knisley
We describe how a team approach that we developed as a mentoring strategy can be used to recruit,... more 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 re-search 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 incorpo-rating new st...
Copyright © 2011 Rhydon Jackson et al. This is an open access article distributed under the Creat... more Copyright © 2011 Rhydon Jackson et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Machine learning was applied to a challenging and biologically significant protein classification problem: the prediction of avonoid UGT acceptor regioselectivity from primary sequence. Novel indices characterizing graphical models of residues were proposed and found to be widely distributed among existing amino acid indices and to cluster residues appropriately. UGT subsequences biochemically linked to regioselectivity were modeled as sets of index sequences. Several learning techniques incorporating these UGT models were compared with classifications based on standard sequence alignment scores. These techniques included an application of time series distance functions to protein classification. Time series distances defined on the ...
Algebraic and Combinatorial Computational Biology, 2019
Abstract Biological structures and phenomena often operate at multiple scales, and investigating ... more Abstract Biological structures and phenomena often operate at multiple scales, and investigating important biological problems effectively often involves understanding these different scales and how they interact. However, the biological data often look very different depending on the scale of investigation, thereby making different modeling tools more or less effective. In this chapter, we present two case studies that focused on RNA and protein structures, describing how a variety of graph-theoretic tools that have been used to understand the folding, functioning, and evolution of these biomolecular structures at a variety of scales. In addition to introducing readers to specific graph-theoretic tools, the chapter aims to use these case studies as exemplars of modeling at different scales.
For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set ... more For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for arbitrary properties P that are closed under disjoint unions and subgraphs.
JOURNAL OF ADVANCES IN BIOTECHNOLOGY, 2016
Cystic fibrosis is one of the most prevalent inherited diseases. This disease is caused by a muta... more Cystic fibrosis is one of the most prevalent inherited diseases. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. The most prevalent mutation of CFTR is located in one of two nucleotide binding domains, namely, the nucleotide binding domain one (NBD1). However, some mutations in nucleotide binding domain two (NBD2) can equally cause cystic fibrosis. In this work, a graph-theoretic model is built for NBD2. Using this model for NBD2, we examine the consequences of single point mutations on NBD2. We collate the wildtype structure with eight of the most prevalent mutations and observe how the NBD2 is affected by each of these mutations.
Match Communications in Mathematical and in Computer Chemistry, 2008
ABSTRACT The authors demonstrate that graphical invariants from the field of mathematical graph t... more ABSTRACT The authors demonstrate that graphical invariants from the field of mathematical graph theory can be used to numerically identify characteristics of secondary RNA structures sufficiently well and that an artificial neural network can be trained to recognize the differences. These invariants measure the structural characteristics of the molecules when represented as a graph. Using graphical invariants of RNA trees of orders 7, 8, and 9 together with trees of orders 7, 8, and 9 classified as not RNA-like, the authors train an artificial neural network based on multi-layer perceptrons to recognize a tree as an RNA tree or as not RNA-like in structure. The results for the trees of order seven and eight agree with the RNA data base RAG classification in 32 out of 34 cases. Forty four trees of order nine are classified which are not in the data base.
ABSTRACT A graph G is a (t,r)-regular graph if every collection of t independent vertices is coll... more ABSTRACT A graph G is a (t,r)-regular graph if every collection of t independent vertices is collectively adjacent to exactly r vertices. Let p, s, and m be positive integers, where m≥2 and let G be a (2,r)-regular graph. If n is sufficiently large, then G is isomorphic to G=K s +mK p , where 2(p-1)+s=r. A nested (2,r)-regular graph is constructed by replacing selected cliques in a (2,r)-regular graph with a (2,r ' )-regular graph and joining the vertices of the peripheral cliques. We examine the network properties such as the average path length, clustering coefficient, and the spectrum of these nested graphs.
BMC bioinformatics, Jan 3, 2006
It has become increasingly apparent that a comprehensive database of RNA motifs is essential in o... more It has become increasingly apparent that a comprehensive database of RNA motifs is essential in order to achieve new goals in genomic and proteomic research. Secondary RNA structures have frequently been represented by various modeling methods as graph-theoretic trees. Using graph theory as a modeling tool allows the vast resources of graphical invariants to be utilized to numerically identify secondary RNA motifs. The domination number of a graph is a graphical invariant that is sensitive to even a slight change in the structure of a tree. The invariants selected in this study are variations of the domination number of a graph. These graphical invariants are partitioned into two classes, and we define two parameters based on each of these classes. These parameters are calculated for all small order trees and a statistical analysis of the resulting data is conducted to determine if the values of these parameters can be utilized to identify which trees of orders seven and eight are R...
ISRN Bioinformatics, 2012
The prediction of secondary RNA folds from primary sequences continues to be an important area of... more 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 alg...
Handbook of Applied Algorithms
Discrete Mathematics, 2002
A set S of vertices in a graph G is called a total irredundant set if, for each vertex v in G; v ... more A set S of vertices in a graph G is called a total irredundant set if, for each vertex v in G; v or one of its neighbors has no neighbor in S − {v}. We investigate the minimum and maximum cardinalities of maximal total irredundant sets.
Cell Biology Education, 2011
We describe how a team approach that we developed as a mentoring strategy can be used to recruit,... more 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 stud...
BMC Bioinformatics, 2010
Background: Determining the secondary structure of RNA from the primary structure is a challengin... more Background: Determining 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. Results: The 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. Conclusions: There 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.
<b>Copyright information:</b>Taken from "A quantitative analysis of secondary RN... more <b>Copyright information:</b>Taken from "A quantitative analysis of secondary RNA structure using domination based parameters on trees"BMC Bioinformatics 2006;7():108-108.Published online 3 Mar 2006PMCID:PMC1420337.Copyright © 2006 Haynes et al; licensee BioMed Central Ltd.
For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set ... more For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for arbitrary properties P that are closed under disjoint unions and subgraphs.
We describe how a team approach that we developed as a mentoring strategy can be used to recruit,... more 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 re-search 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 incorpo-rating new st...
Copyright © 2011 Rhydon Jackson et al. This is an open access article distributed under the Creat... more Copyright © 2011 Rhydon Jackson et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Machine learning was applied to a challenging and biologically significant protein classification problem: the prediction of avonoid UGT acceptor regioselectivity from primary sequence. Novel indices characterizing graphical models of residues were proposed and found to be widely distributed among existing amino acid indices and to cluster residues appropriately. UGT subsequences biochemically linked to regioselectivity were modeled as sets of index sequences. Several learning techniques incorporating these UGT models were compared with classifications based on standard sequence alignment scores. These techniques included an application of time series distance functions to protein classification. Time series distances defined on the ...
Algebraic and Combinatorial Computational Biology, 2019
Abstract Biological structures and phenomena often operate at multiple scales, and investigating ... more Abstract Biological structures and phenomena often operate at multiple scales, and investigating important biological problems effectively often involves understanding these different scales and how they interact. However, the biological data often look very different depending on the scale of investigation, thereby making different modeling tools more or less effective. In this chapter, we present two case studies that focused on RNA and protein structures, describing how a variety of graph-theoretic tools that have been used to understand the folding, functioning, and evolution of these biomolecular structures at a variety of scales. In addition to introducing readers to specific graph-theoretic tools, the chapter aims to use these case studies as exemplars of modeling at different scales.
For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set ... more For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for arbitrary properties P that are closed under disjoint unions and subgraphs.
JOURNAL OF ADVANCES IN BIOTECHNOLOGY, 2016
Cystic fibrosis is one of the most prevalent inherited diseases. This disease is caused by a muta... more Cystic fibrosis is one of the most prevalent inherited diseases. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. The most prevalent mutation of CFTR is located in one of two nucleotide binding domains, namely, the nucleotide binding domain one (NBD1). However, some mutations in nucleotide binding domain two (NBD2) can equally cause cystic fibrosis. In this work, a graph-theoretic model is built for NBD2. Using this model for NBD2, we examine the consequences of single point mutations on NBD2. We collate the wildtype structure with eight of the most prevalent mutations and observe how the NBD2 is affected by each of these mutations.
Match Communications in Mathematical and in Computer Chemistry, 2008
ABSTRACT The authors demonstrate that graphical invariants from the field of mathematical graph t... more ABSTRACT The authors demonstrate that graphical invariants from the field of mathematical graph theory can be used to numerically identify characteristics of secondary RNA structures sufficiently well and that an artificial neural network can be trained to recognize the differences. These invariants measure the structural characteristics of the molecules when represented as a graph. Using graphical invariants of RNA trees of orders 7, 8, and 9 together with trees of orders 7, 8, and 9 classified as not RNA-like, the authors train an artificial neural network based on multi-layer perceptrons to recognize a tree as an RNA tree or as not RNA-like in structure. The results for the trees of order seven and eight agree with the RNA data base RAG classification in 32 out of 34 cases. Forty four trees of order nine are classified which are not in the data base.
ABSTRACT A graph G is a (t,r)-regular graph if every collection of t independent vertices is coll... more ABSTRACT A graph G is a (t,r)-regular graph if every collection of t independent vertices is collectively adjacent to exactly r vertices. Let p, s, and m be positive integers, where m≥2 and let G be a (2,r)-regular graph. If n is sufficiently large, then G is isomorphic to G=K s +mK p , where 2(p-1)+s=r. A nested (2,r)-regular graph is constructed by replacing selected cliques in a (2,r)-regular graph with a (2,r ' )-regular graph and joining the vertices of the peripheral cliques. We examine the network properties such as the average path length, clustering coefficient, and the spectrum of these nested graphs.
BMC bioinformatics, Jan 3, 2006
It has become increasingly apparent that a comprehensive database of RNA motifs is essential in o... more It has become increasingly apparent that a comprehensive database of RNA motifs is essential in order to achieve new goals in genomic and proteomic research. Secondary RNA structures have frequently been represented by various modeling methods as graph-theoretic trees. Using graph theory as a modeling tool allows the vast resources of graphical invariants to be utilized to numerically identify secondary RNA motifs. The domination number of a graph is a graphical invariant that is sensitive to even a slight change in the structure of a tree. The invariants selected in this study are variations of the domination number of a graph. These graphical invariants are partitioned into two classes, and we define two parameters based on each of these classes. These parameters are calculated for all small order trees and a statistical analysis of the resulting data is conducted to determine if the values of these parameters can be utilized to identify which trees of orders seven and eight are R...
ISRN Bioinformatics, 2012
The prediction of secondary RNA folds from primary sequences continues to be an important area of... more 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 alg...
Handbook of Applied Algorithms
Discrete Mathematics, 2002
A set S of vertices in a graph G is called a total irredundant set if, for each vertex v in G; v ... more A set S of vertices in a graph G is called a total irredundant set if, for each vertex v in G; v or one of its neighbors has no neighbor in S − {v}. We investigate the minimum and maximum cardinalities of maximal total irredundant sets.
Cell Biology Education, 2011
We describe how a team approach that we developed as a mentoring strategy can be used to recruit,... more 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 stud...
BMC Bioinformatics, 2010
Background: Determining the secondary structure of RNA from the primary structure is a challengin... more Background: Determining 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. Results: The 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. Conclusions: There 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.
<b>Copyright information:</b>Taken from "A quantitative analysis of secondary RN... more <b>Copyright information:</b>Taken from "A quantitative analysis of secondary RNA structure using domination based parameters on trees"BMC Bioinformatics 2006;7():108-108.Published online 3 Mar 2006PMCID:PMC1420337.Copyright © 2006 Haynes et al; licensee BioMed Central Ltd.
For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set ... more For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for arbitrary properties P that are closed under disjoint unions and subgraphs.