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Articles 1 - 10 of 10
Full-Text Articles in Life Sciences
Robust Analysis Of Metabolic Pathways, Emily Gruber, Amy Ko, Michael Macgillvray, Miranda Sawyer
Robust Analysis Of Metabolic Pathways, Emily Gruber, Amy Ko, Michael Macgillvray, Miranda Sawyer
Mathematical Sciences Technical Reports (MSTR)
Flux Balance Analysis (FBA) is a widely used computational model for studying the metabolic pathways of cells and the role individual metabolites and reactions play in maintaining cell function. However, the successes of FBA have been limited by faulty biological assumptions and computational imperfections. We introduce Robust Analysis of Metabolic Pathways (RAMP) to provide a more theoretically sound and computationally accurate model of cellular metabolism. RAMP overcomes the faulty assumptions of traditional FBA by allowing deviation from steady-state and accounting for variability across a cellular culture. Computationally, RAMP more successfully predicts the lethality of gene knockouts and reduces degeneracy in …
Fundamentals Of Protein Structure Alignment, Allen Holder, Mark Brandt, Yosi Shibberu
Fundamentals Of Protein Structure Alignment, Allen Holder, Mark Brandt, Yosi Shibberu
Mathematical Sciences Technical Reports (MSTR)
The central dogma of molecular biology asserts a one way transfer of information from a cell’s genetic code to the expression of proteins. Proteins are the functional workhorses of a cell, and studying these molecules is at the foundation of much of computational biology. Our goal here is to present a succinct introduction to the biological, mathematical, and computational aspects of making pairwise comparisons between protein structures. The presentation is intended to be useful for those who are entering this research area. The chapter begins with a brief introduction to the biology of protein comparison, which is followed by a …
Computational Biology, Harvey Greenberg, Allen Holder
Computational Biology, Harvey Greenberg, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
Computational biology is an interdisciplinary field that applies the techniques of computer science, applied mathematics, and statistics to address biological questions. OR is also interdisciplinary and applies the same mathematical and computational sciences, but to decision-making problems. Both focus on developing mathematical models and designing algorithms to solve them. Models in computational biology vary in their biological domain and can range from the interactions of genes and proteins to the relationships among organisms and species.
G-Lattices For An Unrooted Perfect Phylogeny, Monica Grigg
G-Lattices For An Unrooted Perfect Phylogeny, Monica Grigg
Mathematical Sciences Technical Reports (MSTR)
We look at the Pure Parsimony problem and the Perfect Phylogeny Haplotyping problem. From the Pure Parsimony problem we consider structures of genotypes called g-lattices. These structures either provide solutions or give bounds to the pure parsimony problem. In particular, we investigate which of these structures supports an unrooted perfect phylogeny, a condition that adds biological interpretation. By understanding which g-lattices support an unrooted perfect phylogeny, we connect two of the standard biological inference rules used to recreate how genetic diversity propagates across generations.
A Spectral Approach To Protein Structure Alignment, Yosi Shibberu, Allen Holder
A Spectral Approach To Protein Structure Alignment, Yosi Shibberu, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
We present two algorithms that use spectral methods to align protein folds. One of the algorithms is suitable for database searches, the other for difficult alignments. We present computational results for 780 pairwise alignments used to classify 40 proteins as well as results for a separate set of 36 protein alignments used for comparison to four other alignment algorithms. We also provide a mathematically rigorous development of the intrinsic geometry underlying our spectral approach.
Bilinear Programming And Protein Structure Alignment, J. Cain, D. Kamenetsky, N. Lavine
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
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
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.
A Decomposition Of The Pure Parsimony Problem, Allen Holder, Thomas M. Langley
A Decomposition Of The Pure Parsimony Problem, Allen Holder, Thomas M. Langley
Mathematical Sciences Technical Reports (MSTR)
We partially order a collection of genotypes so that we can represent the problem of inferring the least number of haplotypes in terms of substructures we call g-lattices. This representation allows us to prove that if the genotypes partition into chains with certain structure, then the NP-Hard problem can be solved efficiently. Even without the specified structure, the decomposition shows how to separate the underlying integer programming model into smaller models.
Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk
Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk
Mathematical Sciences Technical Reports (MSTR)
Stochastic models in population genetics leading to diffusion equations are considered. When the drift and the square of the diffusion coefficients are polynomials, an infinite system of ordinary differential equations for the moments of the diffusion process can be derived using the Martingale property. An example is provided to show how the classical Fokker-Planck Equation approach may not be appropriate for this derivation. A Gauss-Galerkin method for approximating the laws of the diffusion, originally proposed by Dawson (1980), is examined. In the few special cases for which exact solutions are known, comparison shows that the method is accurate and the …