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The protein backbone is described as a smooth curved and twisted line in three-dimensional (3D) space and characterized by its curvature κ and torsion τ both expressed as a function of arc length s. It is shown that the function τ(s) is sufficient to analyze the contributions of all amino acids to the conformation of the protein backbone. The characteristic(More)
A new method for the Automated Protein Structure Analysis (APSA) is derived, which simplifies the protein backbone to a smooth curve in 3-dimensional space. For the purpose of obtaining this smooth line each amino acid is represented by its C α atom, which serves as suitable anchor point for a cubic spline fit. The backbone line is characterized by arc(More)
The Automated Protein Structure Analysis (APSA) method, which describes the protein backbone as a smooth line in three-dimensional space and characterizes it by curvature kappa and torsion tau as a function of arc length s, was applied on 77 proteins to determine all secondary structural units via specific kappa(s) and tau(s) patterns. A total of 533(More)
The Automated Protein Structure Analysis (APSA) method is used for the classification of supersecondary structures. Basis for the classification is the encoding of three-dimensional (3D) residue conformations into a 16-letter code (3D-1D projection). It is shown that the letter code of the protein makes it possible to reconstruct its overall shape without(More)
Convergence problems of meta-GGA (generalized gradient approximation) XC (exchange and correlation) functionals containing a self-interaction correction term are traced back to a singularity of the latter that occurs at critical points of the electron density. This is demonstrated for the bond critical point of equilibrium and stretched H2. A simple remedy(More)
A new method is presented to describe deformations of an N-membered planar ring (N-ring) molecule in terms of deformation vectors that can be expressed by a set of 2N-3 deformation amplitudes and phase angles. The deformation coordinates are directly derived from the normal vibrational modes of the N-ring and referenced to a regular polygon (N-gon) of unit(More)
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