• We are sorry, but NCBI web applications do not support your browser and may not function properly. More information
Logo of biophysjLink to Publisher's site
Biophys J. Oct 2002; 83(4): 1891–1901.
PMCID: PMC1302281

Monte carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation.

Abstract

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion on these low-dimensional media, the kinetics are of the fractal type. Consequently, the conventional equations for enzyme kinetics fail to describe the reaction. In particular, we show that the quasi-stationary-state assumption can hardly be retained in these conditions. Moreover, the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial substrate concentration increase. The simulations indicate that these two influences are mainly additive. Finally, the simulations show pronounced S-P segregation over the lattice at obstacle densities compatible with in vivo conditions. This phenomenon could be a source of spatial self organization in biological membranes.

Full Text

The Full Text of this article is available as a PDF (277K).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.
  • Anacker LW, Kopelman R. Steady-state chemical kinetics on fractals: Segregation of reactants. Phys Rev Lett. 1987 Jan 26;58(4):289–291. [PubMed]
  • Argyrakis P, Kopelman R. Nearest-neighbor distance distributions and self-ordering in diffusion-controlled reactions. II. A+B simulations. Phys Rev A. 1990 Feb 15;41(4):2121–2126. [PubMed]
  • Argyrakis P, Kopelman R. Diffusion-controlled binary reactions in low dimensions: Refined simulations. Phys Rev A. 1992 Apr 15;45(8):5814–5819. [PubMed]
  • Kang K, Redner S. Fluctuation-dominated kinetics in diffusion-controlled reactions. Phys Rev A. 1985 Jul;32(1):435–447. [PubMed]
  • Kopelman R. Fractal reaction kinetics. Science. 1988 Sep 23;241(4873):1620–1626. [PubMed]
  • Lin A, Kopelman R, Argyrakis P. Nonclassical kinetics in three dimensions: Simulations of elementary A+B and A+A reactions. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 Feb;53(2):1502–1509. [PubMed]
  • Lindenberg K, West BJ, Kopelman R. Steady-state segregation in diffusion-limited reactions. Phys Rev Lett. 1988 May 2;60(18):1777–1780. [PubMed]
  • Luby-Phelps K, Castle PE, Taylor DL, Lanni F. Hindered diffusion of inert tracer particles in the cytoplasm of mouse 3T3 cells. Proc Natl Acad Sci U S A. 1987 Jul;84(14):4910–4913. [PMC free article] [PubMed]
  • Minton AP. Macromolecular crowding and molecular recognition. J Mol Recognit. 1993 Dec;6(4):211–214. [PubMed]
  • Minton AP. Molecular crowding: analysis of effects of high concentrations of inert cosolutes on biochemical equilibria and rates in terms of volume exclusion. Methods Enzymol. 1998;295:127–149. [PubMed]
  • Saxton MJ. Lateral diffusion in an archipelago. Distance dependence of the diffusion coefficient. Biophys J. 1989 Sep;56(3):615–622. [PMC free article] [PubMed]
  • Saxton MJ. Anomalous diffusion due to obstacles: a Monte Carlo study. Biophys J. 1994 Feb;66(2 Pt 1):394–401. [PMC free article] [PubMed]
  • Savageau MA. Michaelis-Menten mechanism reconsidered: implications of fractal kinetics. J Theor Biol. 1995 Sep 7;176(1):115–124. [PubMed]
  • Scalettar BA, Abney JR, Hackenbrock CR. Dynamics, structure, and function are coupled in the mitochondrial matrix. Proc Natl Acad Sci U S A. 1991 Sep 15;88(18):8057–8061. [PMC free article] [PubMed]
  • Schwille P, Korlach J, Webb WW. Fluorescence correlation spectroscopy with single-molecule sensitivity on cell and model membranes. Cytometry. 1999 Jul 1;36(3):176–182. [PubMed]
  • Shea LD, Omann GM, Linderman JJ. Calculation of diffusion-limited kinetics for the reactions in collision coupling and receptor cross-linking. Biophys J. 1997 Dec;73(6):2949–2959. [PMC free article] [PubMed]
  • Shnerb NM, Louzoun Y, Bettelheim E, Solomon S. The importance of being discrete: life always wins on the surface. Proc Natl Acad Sci U S A. 2000 Sep 12;97(19):10322–10324. [PMC free article] [PubMed]
  • Wachsmuth M, Waldeck W, Langowski J. Anomalous diffusion of fluorescent probes inside living cell nuclei investigated by spatially-resolved fluorescence correlation spectroscopy. J Mol Biol. 2000 May 12;298(4):677–689. [PubMed]
  • Xie XS, Lu HP. Single-molecule enzymology. J Biol Chem. 1999 Jun 4;274(23):15967–15970. [PubMed]
  • Young WR, Roberts AJ, Stuhne G. Reproductive pair correlations and the clustering of organisms. Nature. 2001 Jul 19;412(6844):328–331. [PubMed]
  • Zumofen G, Klafter J, Shlesinger MF. Breakdown of Ovchinnikov-Zeldovich Segregation in the A+B-->0 Reaction under Lévy Mixing. Phys Rev Lett. 1996 Sep 23;77(13):2830–2833. [PubMed]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

Formats:

Related citations in PubMed

See reviews...See all...

Cited by other articles in PMC

See all...

Links

  • PubMed
    PubMed
    PubMed citations for these articles

Recent Activity

Your browsing activity is empty.

Activity recording is turned off.

Turn recording back on

See more...