Linear Scaling Approaches to Quantum Macromolecular Similarity: Evaluating the
Similarity Function
P. Constans. Linear Scaling Approaches to Quantum Macromolecular Similarity:
Evaluating the Similarity Function. Journal of Computational Chemistry,
23, 1305-1313 (2002).
Abstract
The evaluation of the electron density based similarity function scales
quadratically with respect to the size of the molecules for simplified, atomic shell
densities. Due to the exponential decay of the function’s atom-atom terms most
interatomic contributions are numerically negligible on large systems. An improved
algorithm for the evaluation of the Molecular Quantum Similarity function is
presented. This procedure identifies all non-negligible terms without computing
unnecessary interatomic squared distances, thus effectively turning to linear
scaling the similarity evaluation. Presented also is a minimalist dynamic electron
density model. Approximate, single shell densities together with the proposed
algorithm facilitate fast electron density based alignments on macromolecules.
Keywords
Molecular similarity, linear scaling, protein alignment, electron density
superposition.
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