The Hausdorff chirality measure and a proposed Hausdorff structure measure

Yewande, Emmanuel O.; Neal, Maureen P.; Low, Robert J.

doi:10.1080/00268970902835611

Cited by 18 publications

(13 citation statements)

References 24 publications

(31 reference statements)

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“…Molecular chirality and chiral molecular self-assembly can be studied by circular dichroism spectroscopy [46][47][48][49], and while convincing qualitative evaluations prove our concept, it is of immense importance to obtain quantitative estimates of the proportions and chirality signs of structures at various hierarchic levels. The problem still lacks a solution, although many studies have been performed in this field [50][51][52][53][54]. In essence, the problem includes two questions that are related to introducing a measure of chirality and that mutually complement each other: how the degree of chirality and the chirality sign can be quantitatively estimated for molecular structures with the same symmetry type, and how the degrees of chirality can be quantitatively compared for structures with different types of symmetry.…”

Section: Discussionmentioning

confidence: 99%

Chiral Dualism as an Instrument of Hierarchical Structure Formation in Molecular Biology

Твердислов

Malyshko

2020

Symmetry

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The origin of chiral asymmetry in biology has attracted the attention of the research community throughout the years. In this paper we discuss the role of chirality and chirality sign alternation (L-D-L-D in proteins and D-L-D-L in DNA) in promoting self-organization in biology, starting at the level of single molecules and continuing to the level of supramolecular assemblies. In addition, we also discuss chiral assemblies in solutions of homochiral organic molecules. Sign-alternating chiral hierarchies created by proteins and nucleic acids are suggested to create the structural basis for the existence of selected mechanical degrees of freedom required for conformational dynamics in enzymes and macromolecular machines. Author Contributions: Conceptualization, V.A.T.; investigation, E.V.M.; writing-original draft preparation, V.A.T. and E.V.M. All authors have read and agreed to the published version of the manuscript.

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Section: Discussionmentioning

confidence: 99%

Chiral Dualism as an Instrument of Hierarchical Structure Formation in Molecular Biology

Твердислов

Malyshko

2020

Symmetry

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“…There is a sufficient number of various methods for developing a criterion for symmetry breaking [77][78][79][80][81]. However, even the most successful of these methods only allow one to determine the degree of similarity of the initial set of points with its mirror image and, therefore, do not allow tracing the "switching" of the chirality sign for opposite stereoisomers.…”

Section: Cytoskeletonmentioning

confidence: 99%

Chiral Dualism as a Unifying Principle in Molecular Biophysics

et al. 2021

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The origin and potential role of chiral asymmetry remain one of the most exciting issues in biology. In this paper we review the chirality of biological macromolecules, starting at the level of single molecules and continuing to the level of supramolecular assemblies. We discuss the physical and chemical consequences of the presence of chirality and their role in the self-organization and formation of structural hierarchies in cells. Homochirality may serve as an essential factor that invokes mechanisms required to control the formation of discrete structural hierarchies in macromolecules and macromolecular assemblies. Symmetry is of fundamental importance not only for all molecular biology as a systemic factor of its organization but also for pharmacology, as well as a systemic factor of drug stereospecificity.

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“…Very recently the scaled chirality index has also been successfully used to predict chirality of proteins which opens a new field for its application [13]. The Hausdorff chirality measure has also been applied to real molecules [14,15] but the application technique is still to be optimised.…”

Section: Introductionmentioning

confidence: 98%

Correlation between the molecular chirality index and the spontaneous polarisation in series of smectic C* liquid crystals

Becke¹,

Haller²,

Osipov³

et al. 2010

Molecular Physics

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A correlation between spontaneous polarisation and the chirality index of the constituent molecules, multiplied by the molecular transverse dipole, has been considered for five series of ferroelectric smectic C* liquid crystals. A good correlation has been found within each series, and it has been shown that the scaled chirality index may be used to estimate the spontaneous polarisation in a series of smectic C* mesogens with small systematic changes of the molecular structure. At the same time one cannot expect any significant correlation between the polarisation and the chirality index for smectic C* materials of sufficiently different structure because the spontaneous polarisation may be significantly effected by some details of the molecule's structure including the orientation of the transverse dipole with respect to the primary short molecular axis.

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The Hausdorff chirality measure and a proposed Hausdorff structure measure

Cited by 18 publications

References 24 publications

Chiral Dualism as an Instrument of Hierarchical Structure Formation in Molecular Biology

Chiral Dualism as an Instrument of Hierarchical Structure Formation in Molecular Biology

Chiral Dualism as a Unifying Principle in Molecular Biophysics

Correlation between the molecular chirality index and the spontaneous polarisation in series of smectic C* liquid crystals

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