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The Book in Retrospect and Prospect

  • Péter Érdi
  • Gábor Lente
Chapter
  • 1.5k Downloads
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

The chapter summarizes the main concepts of the book related also to further possible developments.

Keywords

Stochastic Model Master Equation Deterministic Model Stochastic Resonance Mass Action Kinetic 
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.

References

  1. 1.
    Arányi P, Tóth J (1977) A full stochastic description of the Michaelis-Menten reaction for small systems. Acta Biochimica et Biophysica Academiae Scientificarum Hungariae 12:375–388Google Scholar
  2. 2.
    Arnold L (1980) On the consistency of the mathematical models of chemical reactions. In: Dynamics of synergetic systems. Springer series in synergetics. Springer, Berlin/New York, pp 107–118Google Scholar
  3. 3.
    Blackmond DG (2010) The origin of biological homochirality. Cold Spring Harb Perspect Biol 2(5):a002147CrossRefGoogle Scholar
  4. 4.
    Bowsher CG (2010) Stochastic kinetic models: dynamic independence, modularity and graphs. Ann Stat 38:2242–2281CrossRefGoogle Scholar
  5. 5.
    Bowsher CG (2010) Information processing by biochemical networks: a dynamic approach. J R Soc Interface 8:186–200CrossRefGoogle Scholar
  6. 6.
    Cobb L (1978) Stochastic catastrophe models and multimodal distributions. Behav Sci 23:360–374CrossRefGoogle Scholar
  7. 7.
    Delbrück M (1940) Statistical fluctuation in autocatalytic reactions. J Chem Phys 8:120–124CrossRefGoogle Scholar
  8. 8.
    Érdi P, Tóth J, Hárs V (1981) Some kinds of exotic phenomena in chemical systems. In: Farkas M (ed) Qualitative theory of differential equations (Szeged). Colloquia Mathematica Societatis János Bolyai, vol 30. North-Holland/János Bolyai Mathematical Society, Budapest, pp 205–229Google Scholar
  9. 9.
    Gardiner CW, Chaturvedi S (1977) The poisson representation. I. A new technique for chemical master equations. J Stat Phys 17:429–468Google Scholar
  10. 10.
    Grima R, Thomas P, Straube AV (2011) How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations? J Chem Phys 135:084103CrossRefGoogle Scholar
  11. 11.
    Grima R, Walter NG, Schnell S (2014) Single-molecule enzymology à la Michaelis-Menten. FEBS J. doi:10.1111/febs.12663Google Scholar
  12. 12.
    Hersbach DR (1987) Molecular dynamics of elementary chemical reactions. Angew Chem 26:1121–1143Google Scholar
  13. 13.
    Hilfinger A, Chen M, Paulsson J (2012) Using temporal correlations and full distributions to separate intrinsic and extrinsic fluctuations in biological systems. Phys Rev Lett 109(24):248104CrossRefGoogle Scholar
  14. 14.
    Hill T (1964) Thermodynamics of small systems – two volumes bound as one. Dover, New YorkGoogle Scholar
  15. 15.
    Karplus M, McCammon JA (2002) Molecular dynamics simulations of biomolecules. Nat Struct Biol 9:646–52CrossRefGoogle Scholar
  16. 16.
    Kramers HA (1940) Brownian motion in a field of force and the diffusion model of chemical 605 reactions. Physica 7:284–304CrossRefGoogle Scholar
  17. 17.
    Kurtz TG (1972) The relationship between stochastic and deterministic models for chemical reactions. J Chem Phys 57:2976–2978CrossRefGoogle Scholar
  18. 18.
    Laurenzi IJ (2000) An analytical solution of the stochastic master equation for reversible bimolecular reaction kinetics. J Chem Phys 113:3315CrossRefGoogle Scholar
  19. 19.
    Lente G (2005) Stochastic kinetic models of chiral autocatalysis: a general tool for the quantitative interpretation of total asymmetric synthesis. J Phys Chem A 109:11058–11063CrossRefGoogle Scholar
  20. 20.
    Leontovich MA (1935) Basic equations of kinetic gas theory from the viewpoint of the theory 618 of random processes. J Exp Theor Phys 5:211–231Google Scholar
  21. 21.
    Lestas I, Paulsson J, Ross NE, Vinnicombe G (2008) Noise in gene regulatory networks. IEEE Trans Autom Control 53:189–200CrossRefGoogle Scholar
  22. 22.
    McDonnell MD, Abbott D (2009) What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology. PLoS Comput Biol 5:e1000348CrossRefGoogle Scholar
  23. 23.
    Morneau BM, Kubala JM, Barratt C, Schwartz PM (2014) Analysis of a chemical model system leading to chiral symmetry breaking: implications for the evolution of homochirality. J Math Chem 52:268–282CrossRefGoogle Scholar
  24. 24.
    Nagypál I, Epstein IR (1986) Fluctuations and stirring rate effects in the chlorite-thiosulfate reaction. J Phys Chem 90:6285–6292CrossRefGoogle Scholar
  25. 25.
    Nagypál I, Epstein IR (1988) Stochastic behavior and stirring rate effects in the chlorite-iodide Reaction. J Chem Phys 89:6925–6928CrossRefGoogle Scholar
  26. 26.
    Rényi A (1953) Kémiai reakciók tárgyalása a sztochasztikus folyamatok elmélete segítségével (in Hungarian). (Treating chemical reactions using the theory of stochastic process.) MTA Alk Mat Int Közl 2:83–101Google Scholar
  27. 27.
    Rüdiger S (2014) Stochastic models of intracellular calcium signals. Phys Rep 534:39–87CrossRefGoogle Scholar
  28. 28.
    Siegelmann HT (1995) Computation beyond the Turing limit. Science 268:545–548CrossRefGoogle Scholar
  29. 29.
    Sipos T, Tóth J, Érdi P (1974) Stochastic simulation of complex chemical reactions by digital computer. I. The model. React Kinet Catal Let 1:113–117CrossRefGoogle Scholar
  30. 30.
    Srivastava R, Rawlings JB (2014) Parameter estimation in stochastic chemical kinetic models using derivative free optimization and bootstrapping. Comput Chem Eng 63:152–158CrossRefGoogle Scholar
  31. 31.
    Turner TE, Schnell S, Burrage K (2004) Stochastic approaches for modelling in vivo reactions. Comput Biol Chem 28:165–178CrossRefGoogle Scholar
  32. 32.
    Zhang X, Hu N, Cheng Z, Hu L (2012) Enhanced detection of rolling element bearing fault based on stochastic resonance. Chin J Mech Eng 25:1287–1297CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Péter Érdi
    • 1
    • 2
  • Gábor Lente
    • 3
  1. 1.Center for Complex Systems StudiesKalamazoo CollegeKalamazooUSA
  2. 2.Wigner Research Centre for PhysicsHungarian Academy of SciencesBudapestHungary
  3. 3.Department of Inorganic and Analytical ChemistryUniversity of DebrecenDebrecenHungary

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