Stochastic Approach for Enzyme Reaction in Nano Size via Different Algorithms

Conference paper

Abstract

Stochastic simulations have been done for enzyme kinetics reaction with Michaelis-Menten mechanism in low population number. Gillespie and Poisson algorithms have been used for investigation of population number and fluctuation population around their mean values as a function of time. Our result shows that equilibrium time for population dynamics via Poisson algorithm is smaller than Gillespie algorithm. Variations of average population number versus time for all species have the following order: deterministic approach (mean fields) > Gillespie > Poisson. There is asymptotic limit for fluctuation population as a function of time via Poisson algorithm but there is not such trend for fluctuation population via Gillespie algorithm. There is a maximum for fluctuation population for all species for kinetics reaction with Michaelis-Menten mechanism as a function of time via Gillespie algorithm. The stochastic approach has also been used for horse liver alcohol dehydrogenase which catalyses the NAD \( ^{+} \) (nicotinamide heterocyclic ring) oxidation of ethanol to acetaldehyde and three kinds of third order reactions. Probability distribution function and fluctuation population for reactants are calculated as a function of time. Increasing a variety of species for third order reactions leads to decrease of coefficient variation.

Keywords

Master Equation Stochastic Simulation Product Species Deterministic Approach Fluorescence Correlation Spectroscopy 
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.

Notes

Acknowledgements

We are thankful to the Computational and Theoretical Physical Chemistry Research Center of Razi University and we wish to acknowledge Mr. Mohammad Reza Poopari for useful suggestion and continued support on this work.

References

  1. 1.
    Jilbert AR, Miller DS, Scougall CA, Turnbull H, Burrell C (1996) Kinetics of duck hepatitis B virus infection following low dose virus inoculation: one virus DNA genome is infectious in neonatal ducks. Virology 226:338–345CrossRefGoogle Scholar
  2. 2.
    Srivastava R, You L, Summersy J, Yin J (2002) Stochastic vs. deterministic modeling of intracellular viral kinetics. J Theor Biol 218:309–321CrossRefGoogle Scholar
  3. 3.
    Blake WJ, Kærn M, Cantor CR, Collins JJ (2003) Noise in eukaryotic gene expression. Nature 422:633–637CrossRefGoogle Scholar
  4. 4.
    Elowitz MB, Levine J, Siggia ED, Swain PS (2002) Stochastic gene expression in a single cell. Science 297:1183–1186CrossRefGoogle Scholar
  5. 5.
    Gillespie T (2000) The chemical Langevin equation. J Chem Phys 113:297–306CrossRefGoogle Scholar
  6. 6.
    Peeters P, Nicolis G (1992) Intrinsic fluctuations in chaotic dynamics. Phys A 188:426–435CrossRefGoogle Scholar
  7. 7.
    Geysermans P, Nicolis G (1993) Thermodynamic fluctuations and chemical chaos in a well-stirred reactor: a master equation analysis. J Chem Phys 99:8964–8969CrossRefGoogle Scholar
  8. 8.
    Matias MA, Güémez J (1995) On the effects of molecular fluctuations on models of chemical chaos. J Chem Phys 102:1597–1606CrossRefGoogle Scholar
  9. 9.
    Wang H, Li Q (1998) Master equation analysis of deterministic chemical chaos. J Chem Phys 108:7555–7559CrossRefGoogle Scholar
  10. 10.
    McQuarrie DA (1963) Kinetics of small systems I. J Chem Phys 38:433–436CrossRefGoogle Scholar
  11. 11.
    McQuarrie DA, Jachimowski CJ, Russell ME (1964) Kinetics of small systems II. J Chem Phys 40:2914–2921CrossRefGoogle Scholar
  12. 12.
    Zheng Q, Ross J (1991) Comparison of deterministic and stochastic kinetics for nonlinear systems. J Chem Phys 94:3644–3648CrossRefGoogle Scholar
  13. 13.
    Erdi P, Toth J (1989) Mathematical models of chemical reactions: theory and applications of deterministic and stochastic models. Princeton University Press, PrincetonGoogle Scholar
  14. 14.
    Mavelli F, Piotto S (2006) Stochastic simulations of homogeneous chemically reacting systems. J Mol Struc Theochem 771:55–64CrossRefGoogle Scholar
  15. 15.
    Gomes JANF (1984) Classical dynamics stochastic theories of chemical reactions. J Mol Struc Theochem 107:139–155CrossRefGoogle Scholar
  16. 16.
    Qian J, Elson EL (2002) Single-molecule enzymology: stochastic Michaelis–Menten kinetics. Biophys Chem 101:565–576CrossRefGoogle Scholar
  17. 17.
    Armbruster D, Nagy JD, van de Rijt EAF, Rooda JE (2009) Dynamic simulations of single-molecule enzyme networks. J Phys Chem B 113:5537–5544CrossRefGoogle Scholar
  18. 18.
    Kou SC, Cherayil BJ, Min W, English BP, Xie XS (2005) Single-molecule Michaelis-Menten equations. J Phys Chem B 109:19068–19081CrossRefGoogle Scholar
  19. 19.
    Mathews CK, van Holde KE, Ahern KG (1999) Biochemistry, 3rd edn. Prentice Hall Publ. Co., San FransiscoGoogle Scholar
  20. 20.
    McQuarrie DA (1967) Stochastic approach to chemical kinetics. Methuen, LondonGoogle Scholar
  21. 21.
    Darvey IG, Ninham BW, Staff PJ (1996) Stochastic models for second‐order chemical reaction kinetics. The equilibrium state. J Chem Phys 45:2145–2155CrossRefGoogle Scholar
  22. 22.
    Van Kampen NG (1992) Stochastic processes in physics and chemistry. Elsevier, AmsterdamGoogle Scholar
  23. 23.
    Steinfeld JI, Francisco JS, Hase WL (1998) Chemical kinetics and dynamics. Upper Saddle River, Prentice Hall Publ. Co., San FransiscoGoogle Scholar
  24. 24.
    Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22:403–434CrossRefGoogle Scholar
  25. 25.
    Gillespie DT (1992) A rigorous derivation of the chemical master equation. Phys A 188:404–425CrossRefGoogle Scholar
  26. 26.
    Gillespie DT (2007) Stochastic simulation of chemical kinetics. Annu Rev Phys Chem 58:35–55CrossRefGoogle Scholar
  27. 27.
    Gillespie DT (2001) Approximate accelerated stochastic simulation of chemically reacting systems. J Chem Phys 115:1716–1733CrossRefGoogle Scholar
  28. 28.
    Rao V, Arkin P (2002) Stochastic chemical kinetics and the quasi-steady-state assumption: application to the Gillespie algorithm. J Chem Phys 118:4999–5010CrossRefGoogle Scholar
  29. 29.
    Gibson MA, Bruck J (2000) Efficient exact stochastic simulation of chemical systems with many species and many channels. J Phys Chem A 104:1876–1889CrossRefGoogle Scholar
  30. 30.
    Li W, Zhao Y, Wang Z-Q, Ju C-G, Feng Y-L, Zhang J-L (2010) Theoretical study and rate constants calculations of hydrogen abstraction reactions CF3CHCl2 + F and CF3CHClF + F. J Mol Struc Theochem 959:101–105CrossRefGoogle Scholar
  31. 31.
    Lu RH, Li QS, Zhang SW, Kang LJ (2004) Direct DFT dynamics study of the addition reaction CF2 = CHF + H → Product. J Mol Struc Theochem 685:147–154CrossRefGoogle Scholar
  32. 31.
    Resat H, Wiley HS, Dixon DA (2001) Probability-weighted dynamic Monte Carlo method for reaction kinetics simulations. J Phys Chem B 105:11026–11034CrossRefGoogle Scholar
  33. 32.
    Rigler R (1995) Fluorescence correlations, single molecule detection and large number screening. Applications in biotechnology. J Biotechnol 41:177–186CrossRefGoogle Scholar
  34. 33.
    Turner TE, Schnell S, Burrage K (2004) Stochastic approaches for modeling in vivo reactions. Comput Biol Chem 28:165–178CrossRefGoogle Scholar
  35. 34.
    Bugg T (1997) An introduction to enzyme and coenzyme chemistry. Blackwell Science, LondonGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Physical ChemistryRazi UniversityKermanshahIran

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