Protein Molecules: Evolution’s Design for Kinematic Machines

  • Kazem Kazerounian
  • Horea T. Ilieş


The study of geometry in motion can be traced back to the scientists of the ancient world. Since then, kinematics developed into a mature and sophisticated set of tools that can be used to describe and analyze the motion of geometry. Since folding of proteins is fundamentally nothing but coordinated movement of geometry (atoms) under the influence of internal constraints and external stimuli, kinematics can naturally play a key role in the understanding of how proteins fold, which, in itself, is one of the crucial problems in science today. In this chapter we review some of the central kinematic elements used to model proteins and study their folding and flexibility.


Protein Molecule Revolute Joint Morse Function Mobility Analysis Bond Stiffness 
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.



We would like to acknowledge the current and former graduate students involved in the research that made this publication possible: C. Alvarado, P. Bohnenkamp, K. Latif, C. Madden, J. Parker, K. Rodriguez, R. Subramanian, Z. Shahbazi, and P. Tavousi. Kazem Kazerounian was partially supported by the National Science Foundation grants CMMI-0856401, CNS-0923158, and CMMI-1053077. Horea Ilieş was supported in part by the National Science Foundation grants CMMI-0555937, CAREER award CMMI-0644769, CMMI-0856401, CMMI-0927105, and CNS-0923158. The authors would like to gratefully acknowledge this financial support.


  1. 1.
    Ackbarow, T., Chen, X., Keten, S., Buehler, M.J.: Hierarchies, multiple energy barriers, and robustness govern the fracture mechanics of alpha-helical and beta-sheet protein domains. Proc. Natl. Acad. Sci. USA 104(42), 16,410–16,415 (2007) CrossRefGoogle Scholar
  2. 2.
    Alexandrescu, A.T., Snyder, D.R., Abildgaard, F.: NMR of hydrogen bonding in cold-shock protein A and an analysis of the influence of crystallographic resolution on comparisons of hydrogen bond lengths. Protein Sci. 10(9), 1856–1868 (2001) CrossRefGoogle Scholar
  3. 3.
    Arora, J.S.: Introduction to Optimum Design. Elsevier Academic, Amsterdam (2004) Google Scholar
  4. 4.
    Ashby, M., Shercliff, H., Cebon, D.: Materials: Engineering, Science, Processing and Design. Butterworth-Heinemann, Stoneham (2007) Google Scholar
  5. 5.
    Baker, E.N., Hubbard, R.E.: Hydrogen bonding in globular proteins. Prog. Biophys. Mol. Biol. 44(2), 97–179 (1984) CrossRefGoogle Scholar
  6. 6.
    Bohnenkamp, P., Kazerounian, K., Ilieş, H.: Strategies to avoid energy barriers in ab initio protein folding. In: 12th IFToMM (International Federation of the Theory of Mechanisms and Machines) World Congress, Besançon, France (2007) Google Scholar
  7. 7.
    Branden, C., Tooze, J.: Introduction to Protein Structure, 2nd edn. Garland Publishing, New York (1999) Google Scholar
  8. 8.
    Brown, I.: The Chemical Bond in Inorganic Chemistry: The Bond Valence Model. Oxford University Press, London (2006) Google Scholar
  9. 9.
    Buehler, M.J., Keten, S.: Elasticity, strength and resilience: A comparative study on mechanical signatures of α helix, β sheet and tropocollagen domains. Nano Res. 1, 63–71 (2008) CrossRefGoogle Scholar
  10. 10.
    Cornell, W.D., Cieplak, P., Bayly, C.I., Gould, I.R., Merz, K.M., Ferguson, D.M., Spellmeyer, D.C., Fox, T., Caldwell, J.W., Kollman, P.A.: A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc. 117(3), 5179–5197 (1995). doi: 10.2307/40041279 CrossRefGoogle Scholar
  11. 11.
    Daggett, V., Li, A., Fersht, A.: Combined molecular dynamics and ϕ-value analysis of structure-reactivity relationships in the transition state and unfolding pathway of Barnase: structural basis of Hammond and anti-Hammond effects. J. Am. Chem. Soc. 120(49), 12,740–12,754 (1998) CrossRefGoogle Scholar
  12. 12.
    Dahiyat, B., Gordon, D., Mayo, S.: Automated design of the surface positions of protein helices. Protein Sci. 6, 1333–1337 (1997) CrossRefGoogle Scholar
  13. 13.
    Doruker, P., Bahara, I., Baysalb, C., Erman, B.: Collective deformations in proteins determined by a mode analysis molecular dynamics trajectories. Polymer 43, 431–439 (2002) CrossRefGoogle Scholar
  14. 14.
    Duan, Y., Karplus, M.: Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. Science 282, 7404 (1998) CrossRefGoogle Scholar
  15. 15.
    Duan, Y., Wu, C., Chowdhury, S., Lee, M.C., Xiong, G.M., Zhang, W., Yang, R., Cieplak, P., Luo, R., Lee, T., Caldwell, J., Wang, J.M., Kollman, P.: A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations. J. Comput. Chem. 24(16), 1999–2012 (2003) CrossRefGoogle Scholar
  16. 16.
    Favrin, G., Irbäck, A., Mohanty, S.: Oligomerization of amyloid a β 16-22 peptides using hydrogen bonds and hydrophobicity forces. Biophys. J. 87, 3657–3664 (2004) CrossRefGoogle Scholar
  17. 17.
    Fetrow, J., Giammona, A., Kolinski, A., Skolnick, J.: The protein folding problem: a biophysical enigma. Curr. Pharmaceutical Biotechnol. 3(4), 329–347 (2002) CrossRefGoogle Scholar
  18. 18.
    Floudas, C., Klepeis, J., Pardalos, P.: Global optimization approaches in protein folding and peptide docking. DIMACS Ser. Discret. Math. Theor. Comput. Sci. 47, 141–171 (1999) MathSciNetGoogle Scholar
  19. 19.
    Gabovich, A., Li, M.: Mechanical stability of proteins. J. Chem. Phys. 131, 024121 (2009) CrossRefGoogle Scholar
  20. 20.
    Guyon, E., Roux, S., Hansen, A., Bibeau, D., Troadec, J., Crapo, H.: Non-local and non-linear problems in the mechanics of disordered systems: application to granular media and rigidity problems. Rep. Prog. Phys. 53, 3739 (1990) CrossRefGoogle Scholar
  21. 21.
    Hamdia, M., Ferreira, A., Sharmab, G., Mavroidis, C.: Prototyping bio-nanorobots using molecular dynamics simulation and virtual reality. Microelectron. J. 39 (2008) Google Scholar
  22. 22.
    Hardin, C., Pogorelov, T., Luthey-Schulten, Z.: Ab initio protein structure prediction. Curr. Opin. Struct. Biol. 12(2), 176–181 (2002) CrossRefGoogle Scholar
  23. 23.
    Herrmann, T., Güntert, P., Wüthrich, K.: Protein NMR structure determination with automated NOE assignment using the new software CANDID and the torsion angle dynamics algorithm DYANA. J. Mol. Biol. 319(1), 209–227 (2002) CrossRefGoogle Scholar
  24. 24.
    Hoffmann, C., Joan-Arinyo, R.: A brief on constraint solving. Comput-Aided Des. Appl. 2(5), 655–663 (2005) Google Scholar
  25. 25.
    Hwanho, C., Hongsuk, K., Hwangseo, P.: New angle-dependent potential energy function for backbone-backbone hydrogen bond in protein-protein interactions. J. Comput. Chem. 31(5), 897–903 (2010) Google Scholar
  26. 26.
    Irbäck, A., Mitternacht, S., Mohanty, S.: An effective all-atom potential for proteins. PMC Biophys. 2(2) (2009) Google Scholar
  27. 27.
    Ivana, A., Srboljub, M.M., Karplus, M.: The elastic properties of the structurally characterized myosin ii s2 subdomain: A molecular dynamics and normal mode analysis. Biophys. J. 94, 3779–3789 (2008) CrossRefGoogle Scholar
  28. 28.
    Jacobs, D.J., Rader, A.J., Kuhn, L.A., Thorpe, M.F.: Protein flexibility predictions using graph theory. Proteins Struct. Funct. Genet. 44(2), 150–165 (2001). doi: 10.1002/prot.1081 CrossRefGoogle Scholar
  29. 29.
    Jeffery, A.G., Justin, S.D., James, P.L., Randall, T.C.: Implementation of a Morse potential to model hydroxyl behavior in phyllosilicates. J. Chem. Phys. 130, 134,713 (2009) Google Scholar
  30. 30.
    Kazerounian, K., Latif, K., Alvarado, C.: Protofold: a successive kinetostatic compliance method for protein conformation prediction. J. Mech. Des. 127(4), 712–717 (2005) CrossRefGoogle Scholar
  31. 31.
    Kazerounian, K., Latif, K., Rodriguez, K., Alvarado, C.: Nano-kinematics for analysis of protein molecules. J. Mech. Des. 127(4), 699–711 (2005) CrossRefGoogle Scholar
  32. 32.
    Kellermayer, M.S., Smith, S.B., Bustamante, C., Granzier, H.L.: Complete unfolding of the titin molecule under external force. J. Struct. Biol. 122, 197–205 (1998) CrossRefGoogle Scholar
  33. 33.
    Keskin, O.: Proteins with similar architecture exhibit similar large-scale dynamic behavior. Biophys. J. 78, 2093–2106 (2000) CrossRefGoogle Scholar
  34. 34.
    Kortemme, T., Morozov, A.V., Baker, D.: An orientation-dependent hydrogen bonding potential improves prediction of specificity and structure for proteins and protein-protein complexes. J. Mol. Biol. 326(4), 1239–1259 (2003) CrossRefGoogle Scholar
  35. 35.
    Mark, A.L., Suzanne, P.J., Hiroshi, T., Tomasz, M., Toshinori, K., Nakamara, C., Jun, M.: Stretching the α-helix: A direct measure of the hydrogen bond energy of a single peptide molecule. Chem. Phys. Lett. 315, 61–68 (1999) CrossRefGoogle Scholar
  36. 36.
    McDonald, I.K., Thornton, J.M.: Satisfying hydrogen-bonding potential in proteins. J. Mol. Biol. 238(5), 777–793 (1994) CrossRefGoogle Scholar
  37. 37.
    Mitchel, B.S.: An Introduction to Materials Engineering and Science. Wiley, New York (2003) CrossRefGoogle Scholar
  38. 38.
    Nichols, W.L., Rose, G.D., Ten Eyck, L.F., Zimm, B.H.: Rigid domains in proteins: an algorithmic approach to their identification. Proteins 23(1), 38–48 (1995) CrossRefGoogle Scholar
  39. 39.
    Rief, M., Gautel, M., Oesterhelt, F., Fernandez, J.M., Gaub, H.E.: Reversible unfolding of individual titin immunoglobulin domains by afm. Science 276, 1109 (1997) CrossRefGoogle Scholar
  40. 40.
    Shahbazi, Z.: Role of hydrogen bonds in kinematics mobility and elasticity analysis of protein molecules. Ph.D. Thesis, University of Connecticut (2012) Google Scholar
  41. 41.
    Shahbazi, Z., Ilieş, H., Kazerounian, K.: Hydrogen bonds and kinematic mobility of protein molecules. J. Mech. Robot. 2, 021009 (2010) CrossRefGoogle Scholar
  42. 42.
    Shahbazi, Z., Ilieş, H., Kazerounian, K.: Kinematic motion constraints of the protein molecule chains. ASME Conf. Proc. 2011(54839), 535–542 (2011). doi: 10.1115/DETC2011-48519 Google Scholar
  43. 43.
    Shahbazi, Z., Ilieş, H., Kazerounian, K.: A mechanical model of hydrogen bond. Tech. Rep, University of Connecticut (2012) Google Scholar
  44. 44.
    Shahbazi, Z., Pimentel, T.A., Ilies, H., Kazerounian, K., Burkhard, P.: A kinematic observation and conjecture for stable construct of a peptide nanoparticle. In: Advances in Robot Kinematics, Issue on Motion in Man and Machine. Springer, Berlin (2010) Google Scholar
  45. 45.
    Su, H., Parker, J., Kazerounian, K., Ilies, H.: A comparison of kinetostatic and multibody dynamics models for simulating protein structures. In: Mechanisms and Robotics Conference, ASME IDETC, Las Vegas, September 2007 (2007) Google Scholar
  46. 46.
    Subramanian, R., Kazerounian, K.: Improved molecular model of a peptide unit for proteins. In: ASME 2006 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Philadelphia, Pennsylvania, USA, vol. DETC 2006-99315 (2006) Google Scholar
  47. 47.
    Subramanian, R., Kazerounian, K.: Kinematic mobility analysis of peptide based nano-linkages. Mech. Mach. Theory 42(8), 903–918 (2007) MATHCrossRefGoogle Scholar
  48. 48.
    Subramanian, R., Kazerounian, K.: Residue level inverse kinematics of peptide chains in the presence of observation inaccuracies and bond length changes. J. Mech. Des. 129(3), 312–319 (2007) CrossRefGoogle Scholar
  49. 49.
    Tskhovrebova, L., Trinick, K., Sleep, J., Simmons, M.: Elasticity and unfolding of single molecules of the giant muscle protein titin. Nature 387, 308 (1997) CrossRefGoogle Scholar
  50. 50.
    Wirggers, W., Schulten, K.: Protein domain movements: detection of rigid domains and visualization of hinges in comparisons of atomic coordinates. Proteins 29(1), 1–14 (1997) Google Scholar
  51. 51.
    Xu, D., Tsai, C.J., Nussinov, R.: Hydrogen bonds and salt bridges across protein-protein interfaces. Protein Eng. 10(9), 999–1012 (1997) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringThe University of ConnecticutStorrsUSA
  2. 2.Departments of Computer Science and Mechanical EngineeringThe University of ConnecticutStorrsUSA

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