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Bulletin of Mathematical Biology

, Volume 57, Issue 5, pp 651–677 | Cite as

Density and diffusion limited aggregation in membranes

  • Jes Stollberg
Article
  • 71 Downloads

Abstract

Aggregation of membrane molecules is a crucial phenomenon in developing organisms, a classic example being the aggregation of post-synaptic receptors during synaptogenesis. Our understanding of the molecular events involved is improving, but most models of the aggregation or concentration process do not address binding events on the molecular level. An exception is the study of diffusion limited aggregation, in which the aggregation process is simulated on a molecular level. In this analysis, however, important physical parameters such as molecular size, diffusion constant and initial density are not addressed. Thus no predictions about the rate at which such aggregates will form is possible. In the present work the model of diffusion limited aggregation is extended to incorporate these parameters and make the corresponding predictions.

Keywords

Fractal Dimension Acetylcholine Receptor Radial Growth Initial Density Diffusion Constant 
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.

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References

  1. Anderson, M. J. and M. W. Cohen. Nerve-induced and spontaneous redistribution of acetylcholine receptors on cultured muscle cells.J. Physiol. (Lond). 268, 757–773.Google Scholar
  2. Angelides, K. J., L. W. Elmer, D. Loftus and E. Elson. 1988. Distribution and lateral mobility of voltage-dependent sodium channels in neurons [published erratum appears inJ. Cell Biol. (1989) May;108(5): preceding 2001].J. Cell Biol. 106, 1911–1925.CrossRefGoogle Scholar
  3. Axelrod, D., P. Ravdin, D. E. Koppel, J. Schlessinger, W. W. Webb, E. L. Elson and T. R. Podleski. 1976. Lateral motion of fluorescently labeled acetylcholine receptors in membranes of developing muscle fibers.Proc. Natl. Acad. Sci. U.S.A. 73, 4594–4598.CrossRefGoogle Scholar
  4. Baker, L. P. and H. B. Peng. 1993. Tyrosine phosphorylation and acetylcholine receptor cluster formation in cultured Xenopus muscle cells.J. Cell Biol. 120, 185–195.CrossRefGoogle Scholar
  5. Chao, N. M., S. H. Young and M. M. Poo. 1981. Localization of cell membrane components by surface diffusion into a “trap”.Biophys. J. 36, 139–153.Google Scholar
  6. Dewey, T. G. and M. M. Datta. 1989. Determination of the fractal dimension of membrane protein aggregates using fluorescence energy transfer.Biophys. J. 56, 415–420.Google Scholar
  7. Dubinsky, J. M., D. J. Loftus, G. D. Fischbach and E. L. Elson. 1989. Formation of acetylcholine receptor clusters in chick myotubes: migration or new insertion?J. Cell Biol. 1733–1743.Google Scholar
  8. Edidin, M. 1987. Rotational and lateral diffusion of membrane proteins and lipids: phenomena and function. InCurrent Topics in Membranes and Transport, pp. 91–119. Orlando: Academic Press.Google Scholar
  9. Edwards, C. and H. L. Frisch. 1976. A model for the localization of acetylcholine receptors at the muscle endplate.J. Neurobiol. 7, 377–381.CrossRefGoogle Scholar
  10. Gershon, N. D. 1978. Model for capping of membrane receptors based on boundary surface effects.Proc. Natl. Acad. Sci. U.S.A. 75, 1357–1360.CrossRefGoogle Scholar
  11. Joe, E. and K. J. Angelides. 1993. Clustering and mobility of voltage-dependent sodium channels during myelination.J. Neurosci. 13, 2993–3005.Google Scholar
  12. Kolb, M., R. Botet and R. Jullien. 1983. Scaling of kinetically growing clusters.Phys. Rev. Lett. 51, 1123–1126.CrossRefGoogle Scholar
  13. Kusumi, A., Y. Sako and M. Yamamoto. 1993. Confined lateral diffusion of membrane receptors as studied by single particle tracking (nanovid microscopy). Effects of calcium-induced differentiation in cultured epithelial cells.Biophys. J. 65, 2021–2040.Google Scholar
  14. Mandelbrot, B. B. and C. J. G. Evertsz. 1990. The potential distribution around growing fractal clusters.Nature 348, 143–145.CrossRefGoogle Scholar
  15. Meakin, P. 1983. Formation of fractal clusters and networks by irreversible diffusion-limited aggregation.Phys. Rev. Lett. 51, 1119–1122.CrossRefGoogle Scholar
  16. Meakin, P. 1987. Noise-reduced diffusion-limited aggregation.Phys. Rev. A 36, 332–339.CrossRefGoogle Scholar
  17. Moreira, F., R. R. Freire and C. M. Chaves. 1989. Scaling laws for the noise-reduced diffusion-limited aggregation.Phys. Rev. A 40, 2225–2228.CrossRefGoogle Scholar
  18. Muthukumar, M. 1983. Mean-field theory for diffusion-limited cluster formation.Phys. Rev. Let. 50, 839.CrossRefGoogle Scholar
  19. Northrup, S. H. and H. P. Erickson. 1992. Kinetics of protein-protein association explained by Brownian dynamics computer simulation.Proc. Natl. Acad. Sci. U.S.A. 89, 3338–3342.CrossRefGoogle Scholar
  20. Ossadnik, P. 1991. Multiscaling analysis of large-scale off-lattice DLA.Physica A 176, 454–462.CrossRefGoogle Scholar
  21. Peng, H. B., L. P. Baker and Z. Dai. 1993. A role of tyrosine phosphorylation in the formation of acetylcholine receptor clusters induced by electric fields in cultured Xenopus muscle cells.J. Cell Biol. 120, 197–204.CrossRefGoogle Scholar
  22. Poo, M.-m. 1982. Rapid lateral diffusion of functional ACh receptors in embryonic muscle cell membrane.Nature 295, 332–335.CrossRefGoogle Scholar
  23. Sander, L. M. 1986. Fractal growth processes.Nature 322, 789–793.CrossRefGoogle Scholar
  24. Saxton, M. J. 1992. Lateral diffusion and aggregation. A Monte Carlo study.Biophys. J. 61, 119–128.Google Scholar
  25. Saxton, M. J. 1993. Lateral diffusion in an archipelago. Dependence on tracer size.Biophys. J. 64, 1053–1062.Google Scholar
  26. Stenberg, M. and H. Nygren. 1991. Computer simulation of surface-induced aggregation of ferritin.Biophys. Chem. 41, 131–141.CrossRefGoogle Scholar
  27. Stollberg, J. 1994. A model for diffusion-limited aggregation in membranes.Com. Mol. Cell. Biophys. 8, 188–198.Google Scholar
  28. Stollberg, J. and S. E. Fraser. 1988. Acetylcholine receptors and concanavalin A-binding sites on cultured Xenopus muscle cells: electrophoresis, diffusion and aggregation.J. Cell. Biol. 197. 1397–1408.CrossRefGoogle Scholar
  29. Stollberg, J. and S. E. Fraser. 1990. Local accumulation of acetylcholine receptors is neither necessary nor sufficient to induce cluster formation.J. Neurosci. 10, 247–255.Google Scholar
  30. Stollberg, J. and H. Gordon. 1992. Diffusion-trapping of acetylcholine receptors: a numerical model.Invited Seminar (Keystone Symposia: Synapse formation and function: The neuromuscular junction and the central nervous system).Google Scholar
  31. Tokuyama, M. and K. Kawasaki. 1984. Fractal dimensions for diffusion-limited aggregation.Phys. Lett. 100A, 337–340.Google Scholar
  32. Wallace, B. G. 1991. The mechanism of agrin-induced acetylcholine receptor aggregation.Philos. Trans. R. Soc. Lond. [Biol.] 331, 273–280.Google Scholar
  33. Wallace, B. G. 1994. Staurosporine inhibits agrin-induced acetylcholine receptor phosphorylation and aggregation.J. Cell. Biol. 125, 661–668.CrossRefGoogle Scholar
  34. Wallace, B. G., Z. Qu and R. L. Huganir. 1991. Agrin induces phosphorylation of the nicotinic acetylcholine receptor.Neuron 6, 869–878.CrossRefGoogle Scholar
  35. Weaver, D. L. 1983. Diffusion-mediated localization on membrane surfaces.Biophys. J. 41, 81–86.CrossRefGoogle Scholar
  36. Witten, T. A., Jr. and P. Meakin. 1983. Diffusion-limited aggregation at multiple growth sites.Phys. Rev. B 28, 5632–5642.CrossRefGoogle Scholar
  37. Witten, T. A. and L. M. Sander. 1981. Diffusion-limited aggregation, a kinetic critical phenomenon.Phys. Rev. Lett. 47, 1400–1403.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1995

Authors and Affiliations

  • Jes Stollberg
    • 1
  1. 1.Békésy Laboratory of NeurobiologyUniversity of Hawaii at ManoaHonoluluUSA

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