Improved algorithms for symmetry analysis: structure preserving permutations

Alon, Gil; Tuvi-Arad, Inbal

doi:10.1007/s10910-017-0788-y

Cited by 23 publications

(52 citation statements)

References 41 publications

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“…The first step towards an efficient method for calculating the CSM was the work of Pinsky et al [15] who developed an efficient method for finding the optimal direction vector, for any given permutation. They also introduced a division of the molecule’s atom into certain equivalence classes, based on the atoms’ type and the connectivity map of the molecule [16]. This division narrows down the realm of possibilities for the atom permutation, but the number of permutations remains too large to enumerate, except for very small molecules.…”

Section: Introductionmentioning

confidence: 99%

“…Starting with a reasonable guess of the direction vector, a sequence of iterative steps is performed where in each step a new atom permutation is calculated from the direction vector, and a new direction vector is calculated from that permutation, until convergence is reached. While the method of calculating the vector from the permutation (similar to the strategy of Pinsky et al [15]) is both efficient and exact, as we recently proved [16], the method of calculating the permutation from the direction vector uses a greedy algorithm to find the permutation, which is relatively fast, yet generally provides only a crude approximation as compared with the exact algorithm. Nevertheless, the method provided the first practical tool for estimating the CSM of proteins, macromolecules and nanomaterials [17].…”

Section: Introductionmentioning

confidence: 99%

“…In a somewhat different direction, we have recently developed an algorithm for an exact calculation of the CSM [16], which is feasible for small to medium sized molecules. This algorithm takes into account all the information from the connectivity map of the molecule, and enumerates only the permutations that preserve the molecule’s bonding structure.…”

Section: Introductionmentioning

confidence: 99%

“…All of the methods described above are insufficient for estimating the symmetry of proteins. For the exact method [15, 16], the number of atoms, and consequently the number of permissible permutations are simply too large for the algorithms to complete the calculation in a reasonable time. The approximate method of Dryzun et al [17] is also ineffective for this case, because of accumulated inaccuracies due to the approximate scheme and the use of the greedy algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Improved algorithms for quantifying the near symmetry of proteins: complete side chains analysis

Tuvi-Arad

Alon

2019

J Cheminform

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Symmetry of proteins, an important source of their elegant structure and unique functions, is not as perfect as it may seem. In the framework of continuous symmetry, in which symmetry is no longer a binary yes/no property, such imperfections can be quantified and used as a global descriptor of the three-dimensional structure. We present an improved algorithm for calculating the continuous symmetry measure for proteins that takes into account their complete set of atoms including all side chains. Our method takes advantage of the protein sequence and the division into peptides in order to improve the accuracy and efficiency of the calculation over previous methods. The Hungarian algorithm is applied to solve the assignment problem and find the permutation that defines the symmetry operation. Analysis of the symmetry of several sets of protein homomers, with various degrees of rotational symmetry is presented. The new methodology lays the foundations for accurate, efficient and reliable large scale symmetry analysis of protein structure and can be used as a collective variable that describes changes of the protein geometry along various processes, both at the backbone level and for the complete protein structure. Electronic supplementary material The online version of this article (10.1186/s13321-019-0360-9) contains supplementary material, which is available to authorized users.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improved algorithms for quantifying the near symmetry of proteins: complete side chains analysis

Tuvi-Arad

Alon

2019

J Cheminform

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“…The main challenge in CSM calculation is finding the closest symmetric structure. An exact algorithm has been recently developed for small-to medium-sized molecules [34], in which all structure-preserving permutations are scanned to find the closest symmetric structure. In the case of proteins, this algorithm is not applicable due to the enormous number of possible permutations, which requires an approximate calculation.…”

Section: Plos Onementioning

confidence: 99%

Side chain flexibility and the symmetry of protein homodimers

Shalit

Tuvi-Arad

2020

PLoS ONE

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A comprehensive analysis of crystallographic data of 565 high-resolution protein homodimers comprised of over 250,000 residues suggests that amino acids form two groups that differ in their tendency to distort or symmetrize the structure of protein homodimers. Residues of the first group tend to distort the protein homodimer and generally have long or polar side chains. These include: Lys, Gln, Glu, Arg, Asn, Met, Ser, Thr and Asp. Residues of the second group contribute to protein symmetry and are generally characterized by short or aromatic side chains. These include: Ile, Pro, His, Val, Cys, Leu, Trp, Tyr, Phe, Ala and Gly. The distributions of the continuous symmetry measures of the proteins and the continuous chirality measures of their building blocks highlight the role of side chain geometry and the interplay between entropy and symmetry in dictating the conformational flexibility of proteins.

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Effects of Temperature on the Shape and Symmetry of Molecules and Solids

Carreras

Bernuz

Marugan

et al. 2018

Chemistry A European J

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Despite its undeniable problems from a philosophical point of view, the concept of molecular structure, with attributes such as shape and symmetry, directly borrowed from the description of macroscopic objects, is nowadays central to most of the chemical sciences. Descriptions such as "the tetrahedral carbon atom" or "octahedral coordination complexes" are widely used as much in elementary textbooks as in the most up-to-date research articles. The definition of molecular shape is, however, not as simple as it might seem at first sight. Molecules don't behave as macroscopic objects do, and the arrangement of atoms within a molecule changes continuously due to the incessant motion of its constituent particles, nuclei, and electrons. How are molecular shape and symmetry affected by this thermal motion? In this Minireview, we introduce the language of continuous symmetry measures as a new tool to quantitatively describe the effects of temperature on molecular shape and symmetry, enriching in this way the set of molecular descriptors that might be used in the establishment of new empirical structure-property relations, of great interest in concomitant areas such as medicinal chemistry or materials science.

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Improved algorithms for symmetry analysis: structure preserving permutations

Cited by 23 publications

References 41 publications

Improved algorithms for quantifying the near symmetry of proteins: complete side chains analysis

Improved algorithms for quantifying the near symmetry of proteins: complete side chains analysis

Side chain flexibility and the symmetry of protein homodimers

Effects of Temperature on the Shape and Symmetry of Molecules and Solids

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