Skip to main content
Log in

The role of geometry and elastic strains in dynamic states of proteins

  • Published:
Biophysics of structure and mechanism Aims and scope Submit manuscript

Abstract

A theory is developed, where a linear macromolecule with geometrically constrained ends, elastically strained, exchanging energy with the solvent molecules through random collisions may provide a mechanism for the following specific functions in proteins: a) Induction of transient, oriented strains in substrates during transition between conformations, b) External variation of the rigidity and geometry of the active site. More generally, a macromolecule in solution possessing appropriate geometrical and elastic properties constitutes a machine, whose possible operations have common features with biological function such as passive transport, enzymatic catalysis and active transport. The theory suggests a quantitative law by which new information about the dynamical state of the protein molecule can be elucidated from the Arrhenius plot. It predicts a relationship between the rate of catalysis and the local viscosity of the solution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Koshland, D. E. Jr.: Application of a theory of enzyme specificity to protein synthesis. Proc. Nat. Acad. Sci. USA 44, 98–104 (1958)

    Google Scholar 

  2. Jencks, W. P.: Strain and conformation change in enzymatic catalysis. In: Current aspects of biochemical energetics (eds. N. O. Kaplan, E. P. Kennedy), pp. 273–298. New York: Academic Press 1966

    Google Scholar 

  3. Green, D. E.: A framework of principles for the unification of bioenergetics. Ann. N.Y. Acad. Sci. 227, 5–45 (1974)

    Google Scholar 

  4. Careri, G.: The fluctuating enzyme. In: Quantum statistical mechanics in the natural sciences (eds. S. L. Mintz, S. M. Widmayer), pp. 15–25. New York: Plenum Press 1974

    Google Scholar 

  5. Landau, L. D., Lifshitz, E. M.: Mechanics. London: Pergamon 1960

    Google Scholar 

  6. Hetzel, R., Wüthrich, K., Deisenhofer, J., Huber, R.: Dynamics of the aromatic amino acid residues in the globular conformation of the basic pancreatic trypsin inhibitor (BPTI). II. Semi-empirical energy calculations. Biophys. Struct. Mechanism 2, 159–180 (1976)

    Google Scholar 

  7. Nedev, K. N., Volkova, R. I., Khurgin, Y. I., Chernavskii, D. S.: Modelling the structure of the protein globule. Biophysics 19, 1001–1005 (1974)

    Google Scholar 

  8. Kuntz, I. D.: Tertiary structure in carboxypeptidase. J. Amer. Chem. Soc. 94, 8568–8572 (1972)

    Google Scholar 

  9. Klapper, M. H.: On the nature of the protein interior. Biochim. Biophys. Acta 229, 557–566 (1971)

    Google Scholar 

  10. Levitt, M., Chothia, C.: Structural patterns in globular proteins. Nature 261, 552–558 (1976)

    Google Scholar 

  11. Gibson, K. D., Scheraga, H. A.: Minimization of polypeptide energy. V. Theoretical aspects. Physiol. Chem. Phys. 1, 109–126 (1959)

    Google Scholar 

  12. Levitt, M., Warshel, A.: Computer simulation of protein folding. Nature 253, 694–698 (1975)

    Google Scholar 

  13. Brandts, J. F., Oliveira, R., Westort, C.: Thermodynamics of protein denaturation. Effect of pressure on the denaturation of ribonuclease A. Biochemistry 9, 1038–1047 (1970)

    Google Scholar 

  14. Takano, T., Swanson, R., Kallai, O. B., Dickerson, R. E.: Conformational changes upon reduction of cytochrome c. In: Laboratory of quantitative biology 1971. Cold Spr. Harb. Symp. quant. Biol. 36, 397–404

  15. Birktoft, J. J., Blow, D. M.: Structure of crystalline α-chymotrypsin. J. Mol. Biol. 68, 187–240 (1972)

    Google Scholar 

  16. Huber, R., Kukla, D., Bode, W., Schwager, P., Bartels, K., Deisenhofer, J., Steigemann, W.: Structure of the complex formed by bovine trypsin and bovin pancreatic trypsin inhibitor. J. Mol. Biol. 89, 73–101 (1974)

    Google Scholar 

  17. Kubo, R.: The fluctuation-dissipation theorem. In: Progress in physics (ed. S. F. Edwards), pp. 235–284. New York: Benjamin 1969

    Google Scholar 

  18. Wang, M. C., Uhlenbeck, G. E.: On the theory of the Brownian motion II. Rev. Mod. Phys. 17, 323–342 (1945)

    Google Scholar 

  19. Kramers, H. A.: Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284–304 (1940)

    Google Scholar 

  20. Wigner, E.: The transition state method. Trans. Farad. Soc. 34, 29–41 (1938)

    Google Scholar 

  21. Weber, G.: Ligand binding and internal equilibria in proteins. Biochemistry 11, 864–878 (1972)

    Google Scholar 

  22. Lumry, R.: Some recent ideas about the nature of the interactions between proteins and liquid water. J. Food Sci. 38, 744–755 (1973)

    Google Scholar 

  23. McLachlan, A. D., Perutz, M. F., Pulsinelli, P. D.: Subunits interactions in haemoglobin. In: Protein protein interactions (eds. R. J. Jaenicke, E. Helmreich), pp. 91–110. Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  24. Boyer, P. D.: Conformational coupling in biological energy transductions. In: Dynamics of energy-transducing membranes (eds. Ernster, Estabrook, Slater), pp. 289–301. Amsterdam: Elsevier 1974

    Google Scholar 

  25. Lumry, R.: Some recent developments in the search for mechanisms of enzymic catalysis. In: Enzymology in medicine (eds. P. Blume, E. Freier), pp. 4–58. New York: Academic Press 1974

    Google Scholar 

  26. Chandrasekhar, S.: Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15, 1–89 (1943)

    Google Scholar 

  27. Chance, B.: The Function of cytochrome c. Ann. N.Y. Acad. Sci. 227, 613–625 (1974)

    Google Scholar 

  28. Dickerson, R. E., Takano, T., Eisenberg, D., Kallai, O. B., Samson, L., Cooper, A., Margoliash, E.: Ferricytochrome c: I. General features of the horse and bonito proteins at 2.8 å resolution. J. Biol. Chem. 246, 1511–1533 (1971)

    Google Scholar 

  29. Phillips, D. C.: The three-dimensional structure of an enzyme molecule. Sci. Amer. 215, (5) 78–90 (1966)

    Google Scholar 

  30. Blake, C. C. F., Johnson, L. N., Mair, G. A., North, A. C. T., Phillips, D. C., Sarma, V. R.: Crystalographic studies of the activity of hen egg-white lysozyme. Proc. Roy. Soc. (Lond.), Ser. B 378–388 (1967); Ibid. Perutz, F. R. S.: Concluding remarks, p. 448

  31. Levitt, M.: On the nature of the binding of hexa-N-acetylglucosamine substrate to lysozyme. In: Peptides, polypeptides and proteins (eds. E. R. Blout, F. A. Bovey, M. Goodman, N. Lotan), pp. 99–125. New York: Wiley 1974

    Google Scholar 

  32. Warshel, A., Levitt, M.: Theoretical studies of enzyme reactions. J. Mol. Biol. 103, 227–249 (1976)

    Google Scholar 

  33. Klotz, I. M., Langerman, N. R., Darnall, D. W.: Quaternary structure of proteins. Ann. Rev. Biochem. 39, 25–62 (1970)

    Google Scholar 

  34. Frenkel, J.: Kinetic theory of liquids, Chap. IV. New York: Dover 1955

    Google Scholar 

  35. Bullock, A. T., Cameron, G. G., Smith, P. M.: Electron spin resonance studies of spin-labelled polymers. J. Chem. Soc. Farad. Trans. II 70, 1202–1221 (1974)

    Google Scholar 

  36. Ke, B., Chaney, T. H., Reed, D. W.: The electrostatic interaction between the reaction-center bacteriochlorophyll derived from Rhodopseudmonas spheroides and mammalian cytochrome c and its effect on light-activated electron transport. In: Quantum statistical mechanics in the natural sciences (eds. S. L. Mintz, S. M. Widmayer), pp. 37–61. New York: Plenum Press 1974

    Google Scholar 

  37. Eigen, M.: Diffusion control in biochemical reactions. Biochim. Biophys. Acta

  38. Brown, K. G., Erfurth, S. C., Small, E. W., Peticolas, W. L.: Conformationally dependent low-frequency motions of proteins by laser Raman spectroscopy. Proc. Nat. Acad. Sci. USA 69, 1467–1469 (1972)

    Google Scholar 

  39. Wüthrich, K.: Personal communication

  40. Landau, L. D., Lifshitz, E. M.: Fluid mechanics. Chap. 2. London: Pergamon 1963

    Google Scholar 

  41. Helfand, E.: Theory of the kinetics of conformational transitions in polymers. J. Chem. Phys. 51, 4651–4661 (1971)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Katzir-Katchalsky Fellow

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gavish, B. The role of geometry and elastic strains in dynamic states of proteins. Biophys. Struct. Mechanism 4, 37–52 (1978). https://doi.org/10.1007/BF00538839

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00538839

Key words

Navigation