Continuous symmetry and chirality measures: approximate algorithms for large molecular structures

Abstract

Quantifying imperfect symmetry of molecules can help explore the sources, roles and extent of structural distortion. Based on the established methodology of continuous symmetry and chirality measures, we develop a set of three-dimensional molecular descriptors to estimate distortion of large structures. These three-dimensional geometrical descriptors quantify the gap between the desirable symmetry (or chirality) and the actual one. They are global parameters of the molecular geometry, intuitively defined, and have the ability to detect even minute structural changes of a given molecule across chemistry, including organic, inorganic, and biochemical systems. Application of these methods to large structures is challenging due to countless permutations that are involved in the symmetry operations and have to be accounted for. Our approach focuses on iteratively finding the approximate direction of the symmetry element in the three-dimensional space, and the relevant permutation. Major algorithmic improvements over previous versions are described, showing increased accuracy, reliability and structure preservation. The new algorithms are tested for three sets of molecular structures including pillar[5]arene complexes with Li+, C100 fullerenes, and large unit cells of metal organic frameworks. These developments complement our recent algorithms for calculating continuous symmetry and chirality measures for small molecules as well as protein homomers, and simplify the usage of the full set of measures for various research goals, in molecular modeling, QSAR and cheminformatics.

CSM Software: Continuous Symmetry and Chirality Measures for Quantitative Structural Analysis

“…This algorithm replaces the Hungarian algorithm 21 with an algorithm that prioritize permutations with minimal distances between the permuted atoms. 22 3. fibonacci n: This flag calls the Hungarian algorithm 21 and apply the Fibonacci sphere algorithm 25 to generate n initial direction vectors which are uniformly distributed on the unit sphere, as described in Alon et al 22 Note that n is an integer. Several additional options are available for protein homomers in pdb format:…”

“…This algorithm replaces the Hungarian algorithm with an algorithm that prioritize permutations with minimal distances between the permuted atoms : This flag calls the Hungarian algorithm and apply the Fibonacci sphere algorithm to generate n initial direction vectors which are uniformly distributed on the unit sphere, as described in Alon et al . Note that is an integer. Several additional options are available for protein homomers in format: : This flag uses the sequence data in the file to determine which atoms are equivalent, based on their chain index, type of residue, serial number in the sequence as well as the chemical element. : This flag invokes an algorithm that searches for the chains’ permutation along with the atoms’ permutation. : This flag allows CSM calculation on selected chains of a protein oligomer. : This flag allows CSM calculation on selected residues of a protein oligomer.…”

“…Additional performance data of the CSM software was published previously. 19,20,22 ■ SUMMARY Symmetry is a fundamental property used to describe numerous types of molecules. Although it is often associated with minimum energy and stability, the common practice is that molecules are only approximately symmetric.…”

“… The code can operate without the flag, and sometimes find a smaller CSM value in these cases, on the expense of breaking the connectivity map of the molecule when forming the nearest symmetric structure. This strategy can be used with small structures for which the total number of permutations can be scanned in a reasonable time frame : As an alternative for permutation scanning, the user can supply a specific permutation as a text file using this flag.…”

“…In this version, we replaced the greedy algorithm originally used by Dryzun et al with the Hungarian algorithm, in order to achieve better accuracy. Recently, several alternative algorithms to calculate the approximate CSM for general large structures were suggested by us . The CSM code described here is an up-to-date python version of the complete set of algorithms, spanning all types of molecules.…”