JBiSE  Vol.2 No.8 , December 2009
Folding rate prediction using complex network analysis for proteins with two- and three-state folding kinetics
Abstract: It is a challenging task to investigate the different in- fluence of long-range and short-range interactions on two-state and three-state folding kinetics of protein. The networks of the 30 two-state proteins and 15 three-state proteins were constructed by complex networks analysis at three length scales: Protein Contact Networks, Long-range Interaction Networks and Short-range Interaction Networks. To uncover the relationship between structural properties and folding kinetics of the proteins, the correlations of protein network parameters with protein folding rate and topology parameters contact order were analyzed. The results show that Protein Contact Networks and Short-range Interaction Networks (for both two-state and three-state proteins) exhibit the “small-world” property and Long-range Interaction networks indicate “scale-free” behavior. Our results further indicate that all Protein Contact Networks and Short- range Interaction networks are assortative type. While some of Long-range Interaction Networks are of assortative type, the others are of disassortative type. For two-state proteins, the clustering coefficients of Short-range Interaction Networks show prominent correlation with folding rate and contact order. The assortativity coefficients of Short-range Interaction Networks also show remarkable correlation with folding rate and contact order. Similar correlations exist in Protein Contact Networks of three-state proteins. For two-state proteins, the correlation between contact order and folding rate is determined by the numbers of local contacts. Short- range interactions play a key role in determining the connecting trend among amino acids and they impact the folding rate of two-state proteins directly. For three-state proteins, the folding rate is determined by short-range and long-range interactions among residues together.
Cite this paper: nullLi, H. and Wang, J. (2009) Folding rate prediction using complex network analysis for proteins with two- and three-state folding kinetics. Journal of Biomedical Science and Engineering, 2, 644-650. doi: 10.4236/jbise.2009.28094.

[1]   M. Vendruscolo, N. V. Dokholyan, E. Paci and M. Karplus. (2002) Small-world view of the amino acids that play a key role in protein folding, Physical Review E, 65, 061910.

[2]   N. V. Dokholyan, L. Li and F. Ding. (2002) Topological determinants of protein folding, Proc. Natl. Acad. Sci. (USA), 99, 8637–8641.

[3]   A. R. Atilgan, P. Akan and C. Baysal. (2004) Small- world communication of residues and significance for protein dynamics, Biophys. J., 86, 85–91.

[4]   G. Amitai, A. Shemesh and E. Sitbon. (2004) Network analysis of protein structures identifies functional residues, J. Mol. Biol., 344, 1135–1146.

[5]   D. J. Jacobs, A. J. Rader and L. A. Kuhn. (2001) Protein flexibility predictions using graph theory, Proteins: Stru- cture, Function, and Genetics, 44, 150–165.

[6]   X. Jiao, S. Chang, C. H. Li, W. Z. Chen and C. X. Wan. (2007) Construction and application of the weighted amino acid network based on energy, Phys. Rev. E., 75, 051903.

[7]   L. H. Greene and V. A. Higman. (2003) Uncovering network systems within protein structures, J. Mol. Biol., 334, 781–791.

[8]   M. Aftabuddin and S. Kundu. (2006) Weighted and unweighted network of amino acids within protein, Physica A., 396, 895–904.

[9]   S. Kundu. (2005) Amino acids network within protein, Physica A., 346, 104–109.

[10]   K. V. Brinda and S. Vishveshwara. (2005) A network re- presentation of protein structures:implications for protein stability, Biophys J., 89, 4159–4170.

[11]   G. Bagler and S. Sinha. (2007) Assortative mixing in protein contact networks and protein folding kinetics, Bioinformatics, 23(14), 1760–1767.

[12]   O. V. Galzitskaya, S. O. Garbuzynskiy, D. N. Ivankov and A. V. Finketics. (2003) Chain length is the main determinant of the folding rate for proteins with three-state folding kinetics, Proteins: Structure, Function, and Genetics, 51, 162–166.

[13]   S. E. Jackson. (1998) How do small single-domain proteins fold? Fold Des., 3, 81–91.

[14]   A. R. Fersht. (1999) Kinetics of protein folding, In: Hadler GL. Editor: Structure and mechanism in protein science, W.H.Freeman & Co., New York, 40–572.

[15]   A. R. Fersht. (2000) Transition-state structure as a unifying basis in protein-folding mechanisms: Contact order, chain topology, stability, and the extended nucleus mechanism, Proc Natl Acad Sci USA, 97, 1525– 1529.

[16]   W. A. Eaton, V. Munoz, S. J. Hagen, G. S. Jas, L. J. Lapidus, E. R. Henry and J. Hofrichter. (2000) Fast kinetics and mechanisms in protein folding, Annu Rev Biophys Biomol Struct, 29, 327–359.

[17]   M. E. J. Newman. (2002) Assortative mixing in networks, Phys. Rev. Lett., 89, 208701–208704.

[18]   D. J. Watts and S. H. Strogatz. (1998) Collective dynamics of “small-world” networks, Nature, 393, 440–442.

[19]   M. E. J. Newman. (2003) The structure and function of complex networks, SIAM Rev., 45(2), 167–256.

[20]   A. R. Fersht. (1995) Optimization of rates of protein folding: The nucleation-condensation mechanism and its implications, Proc Natl Acad Sci USA, 92(24), 10869– 10873.

[21]   M. Aftabuddin and S. Kundu. (2007) Hydrophobic, hydrophilic and charged amino acids’ networks within protein, Biophysical Journal, 93(1), 225–231.

[22]   M. Brede and S. Sinha. (2005) Assortative mixing by degree makes a network more unstable, eprint arXiv: cond-mat/0507710.

[23]   L. Mirny and E. Shalhnovich. (2001) Protein folding theory: From lattice to all-atom models, Annu Rev Biophys Biomol Struct, 30, 361–396.