A General Model for Amino Acid Interaction Networks

In this paper we introduce the notion of protein interaction network. This is a graph whose vertices are the protein-s amino acids and whose edges are the interactions between them. Using a graph theory approach, we identify a number of properties of these networks. We compare them to the general small-world network model and we analyze their hierarchical structure.

Authors:

• Omar Gaci
• Stefan Balev

Keywords:

• interaction network
• protein structure
• small-world network.

References:

[1] R. Albert, H. Jeong, and A.-L. Barab'asi. The diameter of the world
wide web. Nature, 401:130-131, 1999.
[2] A. R. Atilgan, P. Akan, and C. Baysal. Small-world communication
of residues and significance for protein dynamics. Biophys J, 86(1 Pt
1):85-91, January 2004.
[3] H. M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat,
H. Weissig, I. N. Shindyalov, and P. E. Bourne. The protein data bank.
Nucleic Acids Research, 28:235-242, 2000.
[4] C. Branden and J. Tooze. Introduction to protein structure. Garland
Publishing, 1999.
[5] K. V. Brinda and S. Vishveshwara. A network representation of protein
structures: implications for protein stability. Biophys J, 89(6):4159-
4170, December 2005.
[6] A. Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata,
A. Tomkins, and J. Wiener. Graph structure in the Web. Computer
Networks, 33(1-6):309-320, 2000.
[7] N. V. Dokholyan, L. Li, F. Ding, and E. I. Shakhnovich. Topological
determinants of protein folding. Proc Natl Acad Sci U S A, 99(13):8637-
8641, June 2002.
[8] P. Erd˜os and A. R'enyi. On random graphs I. Publicationes Mathematicae.,
6:290-297, 1959.
[9] P. Erd˜os and A. R'enyi. On the evolution of random graphs. Publ. Math.
Inst. Hung. Acad. Sci., 7:17, 1960.
[10] A. Ghosh, K. V. Brinda, and S. Vishveshwara. Dynamics of lysozyme
structure network: probing the process of unfolding. Biophys J,
92(7):2523-2535, April 2007.
[11] H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai, and A.-L. Barab'asi. The
large-scale organization of metabolic networks. Nature, 407(6804):651-
654, October 2000.
[12] U. K. Muppirala and Z. Li. A simple approach for protein structure
discrimination based on the network pattern of conserved hydrophobic
residues. Protein Eng Des Sel, 19(6):265-275, June 2006.
[13] A. G. Murzin, S. E. Brenner, T. Hubbard, and C. Chothia. SCOP: a
structural classification of the protein database for the investigation of
sequence and structures. J. Mol. Biol., 247:536-540, 1995.
[14] C. A. Orengo, A. D. Michie, S. Jones, D. T. Jones, M. B. Swindells, and
J. M. Thornton. CATH - a hierarchic classification of protein domain
structures. Structure., 5:1093-1108, 1997.
[15] R. Solomonoff and A. Rapoport. Connectivity of random nets. Bull.
Math. Biophys., 13:107111, 1951.
[16] S. Wasserman and K. Faust. Social network analysis : methods and
applications , volume 8 of Structural analysis in the social sciences.
Cambridge University Press, Cambridge, 1994.
[17] D. J. Watts. Small Worlds. Princeton University Press, Princeton, New
Jersey, 1999.
[18] D. J. Watts and S. H. Strogatz. Collective dynamics of -small-world-
networks. Nature., 393:440-442, 1998.