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Full-Text Articles in Molecular Biology
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.