Generalized Moment Description of Brownian Dynamics in Biological Systems

  • K. Schulten
  • A. Brünger
  • W. Nadler
  • Z. Schulten
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 22)


Many biological processes are controlled by the time that the participating bio-molecules need to diffuse around and encounter each other. Nature has devised, therefore, a variety of ways to shorten this time by guiding biomolecules into lower dimensional spaces, e.g., into the plane of membranes. Still the time spent on Brownian motion before the actual molecular reactions is exceedingly long compared to the time scale of the single diffusive displacements. Brownian transport processes also play a role in elementary biological reactions lasting as short as 10−12s since even on this time scale the motion of molecules and molecular fragments in the dense biological media at physiological temperatures is of a Brownian nature. One may envisage that in such situations the fastest Brownian relaxation processes govern the reaction dynamics. This is not the case as is shown by a typical biochemical reaction proceeding along a reaction coordinate with a potential barrier. Diffusive barrier crossing is a very slow process and occurs only in the long time tail of Brownian relaxation. In recent years it has become apparent that proteins, the main carriers of biological function, exhibit an intrinsic dynamic disorder. The disorder originates from a local Brownian motion of the constituent atoms1. Fluctuations of the protein conformations which contribute to the protein function again occur very slowly compared to the time scale of local Brownian motion. All the processes described which last as long as 1 min and as short as 10−12s require a description which accounts properly for the long time behavior of the intrinsic stochastic dynamics.


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  1. 1.
    H. Frauenfelder, G.A. Petsko, and D. Tsernoglu, Nature 280, 558–563 (1979).ADSCrossRefGoogle Scholar
  2. 2.
    N.G. van Kampen, “Stochastic Processes in Physics and Chemistry”, (North Holland Publ. Comp., Amsterdam, 1981 ).Google Scholar
  3. 3.
    C.W. Gardiner, “Handbook of Stochastic Methods” ( Springer, Berlin, 1983 ).zbMATHGoogle Scholar
  4. 4.
    A. Szabo, K. Schulten, and Z. Schulten, J. Chem. Phys. 72 4350–4357 (1980).Google Scholar
  5. 5.
    R. Peters, A. Brünger and K. Schulten, Proc. Natl. Acad. Sci. USA 78, 962–966 (1981).ADSCrossRefGoogle Scholar
  6. 6.
    See for example F. Parak, E.N. Frolov, R.L. Mößbauer and V.l. Goldansldi, J. Mol. Biol. 145, 825–833 (1981).Google Scholar
  7. 7.
    This can be readily derived from Eq.(5) in K.S. Singwi and A. Sjölander, Phys. Rev. 120, 1093 (1960).Google Scholar
  8. 8.
    See for example B. Noble, “Applied Linear Algebra” ( Prentice Hall, Englewood Cliffs, N.J., 1969 ).Google Scholar
  9. 9.
    O. Goscinski and E. Brändas, Int. J. Quant. Chem. 5, 131–156 (1971).CrossRefGoogle Scholar
  10. 10.
    W.B. Jons, W.J. Thron and H. Waadeland, Trans. Am. Math. Soc., 261, 503–529 (1980); A. Ag. Németh and Gy. Paris, J. Math. Phys. 22, 1192–1195 (1981).Google Scholar
  11. 11.
    See for example S. Grossmann, Phys. Rev. A. 17, 1123–1132 (1978) and references therein.Google Scholar
  12. 12.
    K. Schulten, Z. Schulten and A. Szabo, J. Chem. Phys. 74, 4426–4432 (1981).MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    W. Nadler and K. Schulten, Phys. Rev. Lett. 51, 1712–1715 (1983).ADSCrossRefGoogle Scholar
  14. 14.
    W. Nadler and K. Schulten (to be submitted).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • K. Schulten
    • 1
  • A. Brünger
    • 1
  • W. Nadler
    • 1
  • Z. Schulten
    • 1
  1. 1.Physik DepartmentTechnische Universität MünchenGarchingFed. Rep. of Germany

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