The Role of Fragmentation on the Formation of Homomeric Protein Complexes

  • Ksenia Guseva
Part of the Springer Theses book series (Springer Theses)


It is known that many protein complexes are made of smaller identical subunits. The mechanism of assembly of those subunits to form a complete complex is still not well understood. In this work we use a Smoluchowski coagulation equation as a mean-field approximation, and study the efficiency of the process of formation of membrane protein complexes by considering both irreversible aggregation and fragmentation. Our objective is to analyze the possible ways biological organisms adapted to avoid wastage, and achieve a fast formation of the required number of complexes.


Open Chain Fragmentation Rate Mechanosensitive Channel Membrane Protein Complex Complete Complex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Ali, M.H., Imperiali, B.: Protein oligomerization: how and why. Bioorg. Med. Chem. 13(17), 5013–5020 (2005)CrossRefGoogle Scholar
  2. 2.
    Blatz, P.J., Tobolsky, A.V.: Note on the kinetics of systems manifesting simultaneous polymerization-depolymerization phenomena. J. Phys. Chem. 49(2), 77–80 (1945)CrossRefGoogle Scholar
  3. 3.
    Blundell, T.L., Srinivasan, N.: Symmetry, stability, and dynamics of multidomain and multicomponent protein systems. Proc. Natl. Acad. Sci. U. S. A. 93(25), 14243–14248 (1996)ADSCrossRefGoogle Scholar
  4. 4.
    Bowie, J.U.: Membrane protein folding: how important are hydrogen bonds? Curr. Opin. Struct. Biol. (2010, in press, corrected proof)Google Scholar
  5. 5.
    Lo Conte, L., Chothia, C., Janin, J.: The atomic structure of protein-protein recognition sites. J. Mol. Biol. 285(5), 2177–2198 (1999)CrossRefGoogle Scholar
  6. 6.
    Davies, S.C.: Self-similar behaviour in the coagulation equations. J. Eng. Math. 36, 57–88 (1999)ADSzbMATHCrossRefGoogle Scholar
  7. 7.
    Dayhoff, J.E., Shoemaker, B.A., Bryant, S.H., Panchenko, A.R.: Evolution of protein binding modes in homooligomers. J. Mol. Biol. 395(4), 860–870 (2010)CrossRefGoogle Scholar
  8. 8.
    Hwang, H., Pierce, B., Mintseris, J., Janin, J., Weng, Z.: Protein-protein docking benchmark version 3.0. Proteins 73(3), 705–709 (2008)CrossRefGoogle Scholar
  9. 9.
    Janin, J., Bahadur, R.P., Chakrabarti, P.: Protein-protein interaction and quaternary structure. Q. Rev. Biophys. 41(2), 133–180 (2008)CrossRefGoogle Scholar
  10. 10.
    Krapivsky, P.L., Redner, S., Ben-Naim, E.: A Kinetic View of Statistical Physics. Cambridge University Press, Cambridge (2010)zbMATHGoogle Scholar
  11. 11.
    Levy, E.D., Pereira-Leal, J.B.: Evolution and dynamics of protein interactions and networks. Curr. Opin. Struct. Biol. 18(3), 349–357 (2008)CrossRefGoogle Scholar
  12. 12.
    Levy, E.D., Erba, E.B., Robinson, C.V.: Assembly reflects evolution of protein complexes. Nature 453(7199), 1262–1265 (2008)ADSCrossRefGoogle Scholar
  13. 13.
    Leyvraz, F.: Scaling theory and exactly solved models in the kinetics of irreversible aggregation. Phys. Rep. 383(2–3), 95–212 (2003)ADSCrossRefGoogle Scholar
  14. 14.
    Leyvraz, F., Tschudi, H.R.: Singularities in the kinetics of coagulation processes. J. Phys. A. Math. Gen. 14(12), 3389–3405 (1981)MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. 15.
    Lukatsky, D.B., Zeldovich, K.B., Shakhnovich, E.I.: Statistically enhanced self-attraction of random patterns. Phys. Rev. Lett. 97(17), 178101 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    Lushnikov, A.A.: Exact kinetics of the sol-gel transition. Phys. Rev. E 71(4), 046129 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    Lushnikov, A.A.: Critical behavior of the particle mass spectra in a family of gelling systems. Phys. Rev. E 76(1), 011120 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    McLeod, J.B.: On an infinite set of non-linear differential equations. Q. J. Math. 13(1), 119 (1962)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Pereira-Leal, J.B., Levy, E.D., Kamp, C., Teichmann, S.A.: Evolution of protein complexes by duplication of homomeric interactions. Genome Biol. 8(4), R51 (2007)CrossRefGoogle Scholar
  20. 20.
    Ramadurai, S., Holt, V.K.A., van den Bogaart, G., Killian, J.A., Poolman, B.: Lateral diffusion of membrane proteins. J. Am. Chem. Soc. 131(35), 12650–12656 (2009)CrossRefGoogle Scholar
  21. 21.
    Redner, S.: A Guide to First-Passage Processes. Cambridge University Press, Cambridge (2001)zbMATHGoogle Scholar
  22. 22.
    Saffman, P.G., Delbrück, M.: Brownian motion in biological membranes. Proc. Natl. Acad. Sci. U. S. A. 72(8), 3111–3113 (1975)ADSCrossRefGoogle Scholar
  23. 23.
    von Smoluchowski, M.: Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Z. Phys. Chem. 92, 124–168 (1917)Google Scholar
  24. 24.
    Tilley, S.J., Saibil, H.R.: The mechanism of pore formation by bacterial toxins. Curr. Opin. Struct. Biol. 16(2), 230–236 (2006)CrossRefGoogle Scholar
  25. 25.
    Villar, G., Wilber, A.W., Williamson, A.J., Thiara, P., Doye, J.P.K., Louis, A.A., Jochum, M.N., Louis, A.C.F., Levy, E.D.: Self-assembly and evolution of homomeric protein complexes. Phys. Rev. Lett. 101(11), 118106 (2009)ADSCrossRefGoogle Scholar
  26. 26.
    Vinothkumar, K.R., Henderson, R.: Structures of membrane proteins. Q. Rev. Biophys. 43(1), 65–158 (2010)CrossRefGoogle Scholar
  27. 27.
    Wattis, J.A.D.: An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach. Phys. D Nonlinear Phenom. 222(1–2), 1–20 (2006)MathSciNetADSzbMATHCrossRefGoogle Scholar
  28. 28.
    Whitesides, G.M., Boncheva, M.: Beyond molecules: self-assembly of mesoscopic and macroscopic components. Proc. Natl. Acad. Sci. U. S. A. 99(8), 4769–4774 (2002)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Physics, Institute of Complex Systems and Mathematical BiologyUniversity of AberdeenAberdeenUK

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