A Geometrical Perspective on the Insulin Evolution
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65935", author = "Yuhei Kunihiro and Sorin V. Sabau and Kazuhiro Shibuya", title = "A Geometrical Perspective on the Insulin Evolution", 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.", volume = "7", number = "12", pages = "1731-10", }
