A Geometrical Perspective on the Insulin Evolution

Authors: Yuhei Kunihiro, Sorin V. Sabau, Kazuhiro Shibuya

Abstract:

We study the molecular evolution of insulin from metric geometry point of view. In mathematics, and in particular in geometry, distances and metrics between objects are of fundamental importance. Using a weaker notion than the classical distance, namely the weighted quasi-metrics, one can study the geometry of biological sequences (DNA, mRNA, or proteins) space. We analyze from geometrical point of view a family of 60 insulin homologous sequences ranging on a large variety of living organisms from human to the nematode C. elegans. We show that the distances between sequences provide important information about the evolution and function of insulin.

Keywords: Metric geometry, evolution, insulin.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1089635

References:

[1] E. N. Baker, T. L. Blundell, J. F. Cutfield, S. M. Cutfield, E. J. Dodson, G. G. Dodson, D. M. C. Hodgkin, R. E. Hubbard, N. W. Isacs, C. D. Reynolds, K. Sakabe, N. Sakabe and N. M. Vijayan, The structure 2 Zn pig insulin crystal at 1.5 A resolution, Philos. Trans. R. Soc. London Ser. B 319: 369-456, 1988.
[2] J. Baussand and A. Carbone, Inconsistent distances in substitution matrices can be avoided by properly handling hydrophobic residues, Evol. Bioinform online, 4, 255-261, 2008.
[3] D. Burago, Y. Burago and S. Ivanov, A course in Metric Geometry,GSM, 33, American Mathematical Soceiety. 2001.
[4] J. M. Conlon, Molecular Evolution of Insulin in Non-Mammalian Vertebrates, Amer. Zool., 40: 200-212, 2000.
[5] R. H. M. Ebberink, A. B. Smit and J. Van Minnen, The insulin family: evolution of structure and function in vertebrates and invertebrates, Biol, Bull, 177: 176-182, 1989.
[6] F. M. Gregoire, N. Chomiki, D. Kachinskas and C. H. Warden, Cloning and developmental regulation of a novel member of the insulin-like gene family in Caenorhabditis elegans, Biochemical and Biophysical Research Communications; 249, 385 - 390, 1998.
[7] M. Kimura, The neutral theory of molecular evolution, Cambridge University Press, 1983.
[8] H. Koshiyama, Explanation of the Insulin Paradox From the Evolutionary Point of View, Jpn Clin Med. 2012; 3: 2124, 2012.
[9] C. Kristensen, T. Kjeldsen, F. C. Wiberg, L. Schaffer, M. Hach, S. Havelund, J. Bass, D. F. Steiner and A. S. Andersen, Alanine scanning mutagenesis of insulin, J. Biol. Chem, 272: 12978-12983, 1997.
[10] Y. Kunihiro and S. V. Sabau, Quasi-metrics. Geometry of Sequence Comparison, Proceedings of Asia Symposium on Engineering and Information, 2013, p. 186-196.
[11] H. P. A. Kunzi and V. Vajner, Weighted quasi-metrics, in: Papers on General topology and Applic., Annals New York Acad. Sci. 728, 64-77, 1994.
[12] S. G. Mattews, Partial metric topology, in: Papers on General topology and Applic., Ninth Summer Conf. Slippery Rock, PA, Annals of the New York Acad. Sci. 728, 183-197, 1993.
[13] J. Pevnser, Bioinformatics and Functional Genomics, Second Edition, 2003.
[14] S. V. Sabau, K. Shibuya and H. Shimada, Metric structures associated to Finsler metrics, arXiv: 1305. 5880
[math.DG], 2013.
[15] A. Stojmirovi´c and Y. Yu, Geometric aspects of biological sequence comparison, J. Comput. Biol., 16(4), 579-601, 2009.