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Full-Text Articles in Life Sciences
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.