In this article, we describe a novel methodology to extract semantic characteristics from protein structures using linear algebra in order to compose structural signature vectors which may be used efficiently to compare and classify protein structures into fold families. These signatures are built from the pattern of hydrophobic intrachain interactions using Singular Value Decomposition (SVD) and Latent Semantic Indexing (LSI) techniques. Considering proteins as documents and contacts as terms, we have built a retrieval system which is able to find conserved contacts in samples of myoglobin fold family and to retrieve these proteins among proteins of varied folds with precision of up to 80%. The classifier is a web tool available at our laboratory website. Users can search for similar chains from a specific PDB, view and compare their contact maps and browse their structures using a JMol plug-in.
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http://dx.doi.org/10.1590/S1415-47572009000300032 | DOI Listing |
PLoS One
January 2025
Facultad de Ciencias Naturales e Ingenieria, Universidad de Bogota Jorge Tadeo Lozano, Bogota, Colombia.
The Lie group method is a powerful technique for obtaining analytical solutions for various nonlinear differential equations. This study aimed to explore the behavior of nonlinear elastic wave equations and their underlying physical properties using Lie group invariants. We derived eight-dimensional symmetry algebra for the (3+1)-dimensional nonlinear elastic wave equation, which was used to obtain the optimal system.
View Article and Find Full Text PDFForm Methods Syst Des
April 2022
Institute for Algebra, Johannes Kepler University, Linz, Austria.
Unlabelled: Automated reasoning techniques based on computer algebra have seen renewed interest in recent years and are for example heavily used in formal verification of arithmetic circuits. However, the verification process might contain errors. Generating and checking proof certificates is important to increase the trust in automated reasoning tools.
View Article and Find Full Text PDFNanomaterials (Basel)
December 2024
Theoretical Physical Chemistry, UR MOLSYS, University of Liege, B4000 Liège, Belgium.
Dynamical symmetries, time-dependent operators that almost commute with the Hamiltonian, extend the role of ordinary symmetries. Motivated by progress in quantum technologies, we illustrate a practical algebraic approach to computing such time-dependent operators. Explicitly we expand them as a linear combination of time-independent operators with time-dependent coefficients.
View Article and Find Full Text PDFActa Crystallogr A Found Adv
January 2025
Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA.
Group-theoretical and linear-algebraic methods and tools have recently been developed that aim to exhaustively identify the small-angle rotational rigid-unit modes (RUMs) of a given framework material. But in their current form, they fail to detect RUMs that require a compensating lattice strain which grows linearly with the amplitude of the rigid-unit rotations. Here, we present a systematic approach to including linear strain compensation within the linear-algebraic RUM-search method, so that any geometrically possible small-angle RUM can be detected.
View Article and Find Full Text PDFSci Rep
December 2024
Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia.
In light of the ponderomotive force, this article focuses on establishing the exact wave structures of the ion sound system. It is the result of non-linear force and affects a charged particle oscillating in an inhomogeneous electromagnetic field. By using the Riemann-Liouville operator, -operator, and Atangana-Baleanu fractional analysis, the examined equation-which consists of the normalized electric field of the Langmuir oscillation and normalized density perturbation-is thoroughly examined.
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