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Use of circular variance to quantify the deviation of a macromolecule from the spherical shape

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Abstract

It is shown that the extent of deviation of a molecular shape from spherical can be characterized by comparing the distribution of the circular variances, a measure originally proposed to quantify angular spread, of the vectors from each atom to the rest of the molecule to the circular variance of a collection of atoms filling the unit sphere. Different measures for quantifying the difference between distribution are proposed and compared.

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References

  1. P.G. Mezey, Shape in Chemistry: An Introduction to Molecular Shape and Topology (VCH Publishers, New York, 1993)

    Google Scholar 

  2. D.S. Kim, J.K. Kim, C.I. Won, C.M. Kim, J.Y. Park, J. Bhak, Sphericity of a protein via the \(\beta \) – complex. J. Mol. Graph. Model. 28, 636–649 (2010)

    Article  CAS  Google Scholar 

  3. J. Hass, P. Koehl, How round is a protein? Exploring protein structured for globularity using conformal mapping. Front. Mol. Biosci. 1, 1–11 (2014)

    Article  Google Scholar 

  4. K.V. Mardia, P.E. Jupp, Directional Statistics (Wiley, Chichester, 2000)

    Google Scholar 

  5. M. Mezei, A new method for mapping macromolecular topography. J. Mol. Graph. Model. 21, 463–472 (2003)

    Article  CAS  Google Scholar 

  6. M. Mezei, Statistical properties of protein–protein interfaces. Algorithms 8, 92–99 (2015)

    Article  Google Scholar 

  7. E. Silla, F. Villar, O. Nilsson, J.L. Pascual-Ahuir, O. Tapia, Molecular volumes and surfaces of biomacromolecules via GEPOL: a fast and efficient algorithm. J. Mol. Graph. 8, 168–172 (1990)

    Article  CAS  Google Scholar 

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Acknowledgments

Computational resources and staff expertise was provided by the Department of Scientific Computing at the Icahn School of Medicine at Mount Sinai. Prof. Patrice Koehl is thanked for providing the CATH533 database of protein domain structures used in testing.

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Authors and Affiliations

  1. Department of Structural and Chemical Biology, Icahn School of Medicine at Mount Sinai, New York, NY, 10029, USA

    Mihaly Mezei

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  1. Mihaly Mezei
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Correspondence to Mihaly Mezei.

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Mezei, M. Use of circular variance to quantify the deviation of a macromolecule from the spherical shape. J Math Chem 53, 2184–2190 (2015). https://doi.org/10.1007/s10910-015-0540-4

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  • DOI: https://doi.org/10.1007/s10910-015-0540-4

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