Data Structures and Algorithms for k-th Nearest Neighbours Conformational Entropy Estimation

Entropy of multivariate distributions may be estimated based on the distances of nearest neighbours from each sample from a statistical ensemble. This technique has been applied on biomolecular systems for estimating both conformational and translational/rotational entropy. The degrees of freedom wh...

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Published in:	Biophysica Vol. 2; no. 4; pp. 340 - 352
Main Authors:	Borelli, Roberto, Dovier, Agostino, Fogolari, Federico
Format:	Journal Article
Language:	English
Published:	Merced MDPI AG 01.12.2022
Subjects:	Algorithms conformational entropy Entropy K-D tree Methods nearest neighbours Simulation Variables VP-tree
ISSN:	2673-4125, 2673-4125
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Abstract	Entropy of multivariate distributions may be estimated based on the distances of nearest neighbours from each sample from a statistical ensemble. This technique has been applied on biomolecular systems for estimating both conformational and translational/rotational entropy. The degrees of freedom which mostly define conformational entropy are torsion angles with their periodicity. In this work, tree structures and algorithms to quickly generate lists of nearest neighbours for periodic and non-periodic data are reviewed and applied to biomolecular conformations as described by torsion angles. The effect of dimensionality, number of samples, and number of neighbours on the computational time is assessed. The main conclusion is that using proper data structures and algorithms can greatly reduce the complexity of nearest neighbours lists generation, which is the bottleneck step in nearest neighbours entropy estimation.
AbstractList	Entropy of multivariate distributions may be estimated based on the distances of nearest neighbours from each sample from a statistical ensemble. This technique has been applied on biomolecular systems for estimating both conformational and translational/rotational entropy. The degrees of freedom which mostly define conformational entropy are torsion angles with their periodicity. In this work, tree structures and algorithms to quickly generate lists of nearest neighbours for periodic and non-periodic data are reviewed and applied to biomolecular conformations as described by torsion angles. The effect of dimensionality, number of samples, and number of neighbours on the computational time is assessed. The main conclusion is that using proper data structures and algorithms can greatly reduce the complexity of nearest neighbours lists generation, which is the bottleneck step in nearest neighbours entropy estimation.
Author	Fogolari, Federico Borelli, Roberto Dovier, Agostino
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SubjectTerms	Algorithms conformational entropy Entropy K-D tree Methods nearest neighbours Simulation Variables VP-tree
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