This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Using Fixed Point Theorems to Model the Binding in Protein-Protein Interactions
August 2005 (vol. 17 no. 8)
pp. 1079-1087
The binding in protein-protein interactions exhibits a kind of biochemical stability in cells. The mathematical notion of fixed points also describes stability. A point is a fixed point if it remains unchanged after a transformation by a function. Many points may not be a fixed point, but they may approach a stable status after multiple steps of transformation. In this paper, we define a point as a protein motif pair consisting of two traditional protein motifs. We propose a function and propose a method to discover stable motif pairs of this function from a large protein interaction sequence data set. There are many interesting properties for this function (for example, the convergence). Some of them are useful for gaining much efficiency in the discovery of those stable motif pairs; some are useful for explaining why our proposed fixed point theorems are a good way to model the binding of protein interactions. Our results are also compared to biological results to elaborate the effectiveness of our method.

[1] A.K. Mohamed and A.K. William, An Introduction to Metric Spaces and Fixed Point Theory. John Wiley & Sons, 2001.
[2] S.W. Meng, Z. Zhang, and J. Li, “Twelve c2h2 Zinc Finger Genes on Human Chromosome 19 Can Be Each Translated into the Same Type of Protein after Frameshifts,” Bioinformatics, vol. 20, pp. 1-4, 2004.
[3] A. Bruce, B. Dennis, L. Julian, R. Martin, R. Keith, and W. James, Molecular Biology of the Cell, fourth ed. New York: Garland Science, 2002.
[4] P. Bork and E. Koonin, “Protein Sequence Motifs,” Current Opinion in Structural Biology, vol. 6, no. 3, pp. 366-376, 1996.
[5] A. Dziembowski and B. Seraphin, “Recent Developments in the Analysis of Protein Complexes,” FEBS Letters, vol. 556, nos. 1-3, pp. 1-6, Jan. 2004.
[6] J.D. Bernal, I. Fankuchen, and M.F. Perutz, “An X-Ray Study of Chymotrypsin and Haemoglobin,” Nature, vol. 141, pp. 523-524, 1938.
[7] J. Drenth, Principles of Protein X-Ray Crystallography. Springer Verlag, 1994.
[8] K. Wuthrich, NMR of Proteins and Nucleic Acids. New York: John Wiley and Sons, 1986.
[9] A. Wand and S. Englander, “Protein Complexes Studied by NMR Spectroscopy,” Current Opinion in Biotechnology, vol. 7, no. 4, pp. 403-408, 1996.
[10] A. Brazma, I. Jonassen, I. Eidhammer, and D. Gilbert, “Approaches to the Automatic Discovery of Patterns in Biosequences,” J. Computional Biology, vol. 5, no. 2, pp. 279-305, 1998.
[11] F. Pazos and A. Valencia, “Similarity of Phylogenetic Trees as Indicator of Protein-Protein Interaction,” Protein Eng., vol. 14, pp. 609-614, 2001.
[12] S. Pages, A. Belaich, J. Belaich, E. Morag, R. Lamed, Y. Shoham, and E. Bayer, “Species-Specificity of the Cohesin-Dockerin Interaction between Clostridium Thermocellum and Clostridium Cellulolyticum: Prediction of Specificity Determinants of the Dockerin Domain,” Proteins, vol. 29, no. 4, pp. 517-527, Dec. 1997.
[13] K. Fryxell, “The Coevolution of Gene Family Trees,” Trends in Genetics, vol. 12, no. 9, pp. 364-369, Sept. 1996.
[14] A.B. Sparks et al., “Distinct Ligand Preferences of Src Homology 3 Domains from Src, Yes, Abl, Cortactin, p53bp2, Plcgamma, Crk, and Grb2,” Proc. Nat'l Academy of Sciences, no. 4, pp. 1540-1544, 1996.
[15] B.K. Kay, M.P. Williamson, and M. Sudol, “The Importance of Being Proline: The Interaction of Proline-Rich Motifs in Signaling Proteins with Their Cognate Domains,” FASEB J., vol. 14, no. 2, pp. 231-241, 2000.
[16] R. Agrawal and R. Srikant, “Fast Algorithms for Mining Association Rules,” Proc. 20th Int'l Conf. Very Large Databases, pp. 487-499, Sept. 1994.
[17] F. Glaser, D. Steinberg, I. Vakser, and N. Ben-Tal, “Residue Frequencies and Pairing Preferences at Protein-Protein Interfaces,” Proteins, vol. 43, no. 2, pp. 89-102, 2001.
[18] D. Burdick, M. Calimlim, and J. Gehrke, “Mafia: A Maximal Frequent Itemset Algorithm for Transactional Databases,” Proc. Int'l Conf. Data Eng., pp. 443-452, 2001.
[19] G. Grahne and J. Zhu, “Efficiently Using Prefix-Trees in Mining Frequent Itemsets,” Proc. Workshop Frequent Itemset Mining Implementations (FIMI'03), Nov. 2003.
[20] S. Sheu, D.J. Lancia, K. Clodfelter, M. Landon, and S. Vajda, “Precise: A Database of Predicted and Consensus Interaction Sites in Enzymes,” Nucleic Acids Research, vol. 33, no. 1, pp. D206-D211, Jan. 2005.
[21] B. Doray and S. Kornfeld, “Gamma Subunit of the Ap-1 Adaptor Complex Binds Clathrin: Implications for Cooperative Binding in Coated Vesicle Assembly,” Molecular Biology of the Cell, vol. 12, no. 7, pp. 1925-1935, 2001.
[22] H. Li and J. Li, “Discovery of Stable and Significant Binding Motif Pairs from PDB Complexes and Protein Interaction Datasets,” Bioinformatics, vol. 21, no. 3, pp. 314-324, 2005.
[23] H. Li, J. Li, S.H. Tan, and S.K. Ng, “Discovery of Binding Motif Pairs from Protein Complex Structural Data and Protein Interaction Sequence Data,” Proc. Ninth Pacific Symp. Biocomputing (PSB), pp. 312-323, 2004.
[24] C. von Mering et al., “Comparative Assessment of Large-Scale Data Sets of Protein-Protein Interactions,” Nature, vol. 417, no. 6887, pp. 399-403, 2002.
[25] Y. Jiang, A. Lee, J. Chen, V. Ruta, M. Cadene, B.T. Chait, and R. Mackinnon, “X-ray Structure of a Voltage-Dependent k+ Channel,” Nature, vol. 423, no. 6935, pp. 33-41, 2003.
[26] P. Pellicena and W. Miller, “Processive Phosphorylation of p130cas by SRC Depends on SH3-polyproline Interactions,” J. Biological Chemistry, vol. 276, no. 30, pp. 28190-28196, 2001.
[27] R. Russell, J. Breed, and G. Barton, “Conservation Analysis and Structure Prediction of the SH2 Family of Phosphotyrosine Binding Domains,” FEBS Letters, vol. 304, no. 1, pp. 15-20, 1992.
[28] E. Azarya-Sprinzak, D. Naor, H.J. Wolfson, and R. Nussinov, “Interchanges of Spatially Neighbouring Residues in Structurally Conserved Environments,” Protein Eng., vol. 10, no. 10, pp. 1109-1122, 1997.
[29] K. Vancompernolle, J. Vandekerckhove, M.R. Bubb, and E.D. Korn, “The Interfaces of Actin and Acanthamoeba Actobindin. Identification of a New Actin-Binding Motif,” J. Biological Chemistry, vol. 266, no. 23, pp. 5427-5431, 1991.

Index Terms:
Index Terms- Bioinformatics (genome or protein) database, mining methods and algorithms, generating functions, stability and instability, biology and genetics.
Citation:
Jinyan Li, Haiquan Li, "Using Fixed Point Theorems to Model the Binding in Protein-Protein Interactions," IEEE Transactions on Knowledge and Data Engineering, vol. 17, no. 8, pp. 1079-1087, Aug. 2005, doi:10.1109/TKDE.2005.134
Usage of this product signifies your acceptance of the Terms of Use.