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Point scattering: A new geometric invariant with applications from (Nano)clusters to biomolecules
Author(s) -
Estrada Ernesto
Publication year - 2007
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.20541
Subject(s) - scattering , biomolecule , invariant (physics) , physics , spheres , cluster (spacecraft) , quantum mechanics , materials science , nanotechnology , computer science , astronomy , programming language
Abstract A new geometric invariant is defined from “first principles” for a point ensemble, which can represent clusters, molecules, crystals, and biomolecules. The scattering of a point ensemble is defined in terms of the Euclidean distance matrix and a vector measuring the weighted departure of the points from the cluster centre. Using the Rayleigh–Ritz theorem this function is maximized obtaining the point scattering of the ensemble. The point scattering shows several properties which are useful for studying clusters, molecules, crystals, and biomolecules. We examined different natural clusters of hard spheres such as colloidal particles and fullerenes, as well as protein–peptide complexes and the effect of temperature on protein structure. In all cases point scattering differentiates point ensembles with different structures, which are not distinguished by other geometric invariants, such as the second moment of mass distribution, surface areas, and volumes. Point scattering also shows better correlation with thermodynamic parameters of binding and describes the interior cavities of hollowed ensembles better than the other geometric measures. © 2007 Wiley Periodicals, Inc. J Comput Chem 28: 767–777, 2007