A biological interpretation of transient anomalous subdiffusion. II. Reaction kinetics

Biophysical Journal

Volumn 94, Issue 3, 2008, Pages 760-771

  Saxton, Michael J ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BINDING SITE; BIOLOGY; CALCULATION; CELL MEMBRANE; CHEMICAL REACTION KINETICS; MODEL; MONTE CARLO METHOD; NOISE; PROBABILITY; STATISTICAL DISTRIBUTION; TIME;

EID: 38549161544     PISSN: 00063495     EISSN: None     Source Type: Journal    
DOI: 10.1529/biophysj.107.114074     Document Type: Article

References (66)

1. Saxton, M. J. 2007. A biological interpretation of transient anomalous subdiffusion. I. Qualitative model. Biophys. J. 92:1178-1191.
2. den Hollander, F., and G. H. Weiss. 1994. Aspects of trapping in transport processes. In Contemporary Problems in Statistical Physics. Society for Industrial and Applied Mathematics, Philadelphia, PA. 147-203.
3. Kozak, J. J. 2000. Chemical reactions and reaction efficiency in compartmentalized systems. Adv. Chem. Phys. 115:245-406.
4. Melo, E., and J. Martins. 2006. Kinetics of bimolecular reactions in model bilayers and biological membranes. A critical review. Biophys. Chem. 123:77-94.
5. Barzykin, A. V., K. Seki, and M. Tachiya. 2001. Kinetics of diffusion-assisted reactions in microheterogeneous systems. Adv. Colloid Interface Sci. 89:47-140.
6. ben-Avraham, D., and S. Havlin. 2000. Diffusion and Reactions in Fractals and Disordered Systems. Cambridge University Press, Cambridge, UK.
7. Berry, H. 2002. Monte Carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation. Biophys. J. 83:1891-1901.
8. Dewey, T. G. 1997. Fractals in Molecular Biophysics. Oxford University Press, New York.
9. Savageau, M. A. 1995. Michaelis-Menten mechanism reconsidered: implications of fractal kinetics. J. Theor. Biol. 176:115-124.
10. Saxton, M. J. 1996. Anomalous diffusion due to binding: a Monte Carlo study. Biophys. J. 70:1250-1262.
11. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. 1992. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd Ed. Cambridge University Press, Cambridge.
12. Saxton, M. J. 2007. Modeling 2D and 3D diffusion. In Methods in Membrane Lipids (Methods in Molecular Biology, Vol. 400). A. M. Dopico, editor. Humana Press, Totowa, NJ. 295-321.
13. Bollt, E. M., and D. ben-Avraham. 2005. What is special about diffusion on scale-free nets? New J. Phys. 7:26.
14. Argyrakis, P., and R. Kopelman. 1987. Self-stirred vs. well-stirred reaction kinetics. J. Phys. Chem. 91:2699-2701.
15. Kopelman, R., and Y.-E. Koo. 1991. Reaction kinetics in restricted spaces. Israel J. Chem. 31:147-157.
16. Hughes, B. D. 1995. Random Walks and Random Environments, Vol. 1. Oxford University Press, New York.
17. Harder, H., S. Havlin, and A. Bunde. 1987. Diffusion on fractals with singular waiting-time distribution. Phys. Rev. B. 36:3874-3879.
18. Montroll, E. W. 1969. Random walks on lattices. 3. Calculation of first-passage times with application to exciton trapping on photosynthetic units. J. Math. Phys. 10:753-765.
19. den Hollander, W. T. F., and P. W. Kasteleyn. 1982. Random walks with spontaneous emission on lattices with periodically distributed imperfect traps. Physica A. 112:523-543.
20. Montroll, E. W. 1969. Random walks on lattices containing traps. J. Phys. Soc. Jpn. Suppl. 26:6-10.
21. Walsh, C. A., and J. J. Kozak. 1982. Exact algorithm for d-dimensional walks on finite and infinite lattices with trap. II. General formulation and application to diffusion-controlled reactions. Phys. Rev. B. 26:4166-4189.
22. Grassberger, P., and I. Procaccia. 1982. The long-time properties of diffusion in a medium with static traps. J. Chem. Phys. 77:6281-6284.
23. Toussaint, D., and F. Wilczek. 1983. Particle-antiparticle annihilation in diffusive motion. J. Chem. Phys. 78:2642-2647.
24. Rose, C., and M. D. Smith. 2002. Mathematical Statistics with Mathematica. Springer, New York. 117-148.
25. Weiss, G. H., S. Havlin, and A. Bunde. 1985. On the survival probability of a random walk in a finite lattice with a single trap. J. Stat. Phys. 40:191-199.
26. Weiss, G. H. 1994. Aspects and Applications of the Random Walk. North-Holland, Amsterdam. 157-160.
27. Metzler, R., and J. Klafter. 2004. The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A. 37:R161-R208.
28. Rangarajan, G., and M. Z. Ding. 2000. First passage time distribution for anomalous diffusion. Phys. Lett. A. 273:322-330.
29. Chelminiak, P., and M. Kurzyński. 2004. Mean first-passage time for diffusion on fractal lattices with imposed boundary conditions. Physica A. 342:507-515.
30. Hanson, J. D., J. R. Cary, and J. D. Meiss. 1985. Algebraic decay in self-similar Markov chains. J. Stat. Phys. 39:327-345.
31. Rosenstock, H. B. 1969. Luminescent emission from an organic solid with traps. Phys. Rev. 187:1166-1168.
32. Zumofen, G., and A. Blumen. 1982. Energy transfer as a random walk. II. Two-dimensional regular lattices. J. Chem. Phys. 76:3713-3731.
33. Henyey, F. S., and V. Seshadri. 1982. On the number of distinct sites visited in 2D lattices. J. Chem. Phys. 76:5530-5534.
34. Torney, D. C. 1986. Variance of the range of a random walk. J. Stat. Phys. 44:49-66.
35. Zumofen, G., and A. Blumen. 1982. Random-walk studies of excitation trapping in crystals. Chem. Phys. Lett. 88:63-67.
36. Blumen, A., J. Klafter, and G. Zumofen. 1983. Trapping and reaction rates on fractals: a random-walk study. Phys. Rev. B. 28:6112-6115.
37. Zumofen, G., A. Blumen, and J. Klafter. 1984. Scaling behavior for excitation trapping on fractals. J. Phys. A. 17:L479-L485.
38. Balagurov, B. Y., and V. G. Vaks. 1974. Random walks of a particle on lattices with traps. Sov. Phys. JETP. 38:968-971.
39. Kayser, R. F., and J. B. Hubbard. 1983. Diffusion in a medium with a random distribution of static traps. Phys. Rev. Lett. 51:79-82.
40. Redner, S. 2001. A Guide to First-Passage Processes. Cambridge University Press, Cambridge, UK. 254-262.
41. Barkema, G. T., P. Biswas, and H. van Beijeren. 2001. Diffusion with random distribution of static traps. Phys. Rev. Lett. 87:170601.
42. Bunde, A., S. Havlin, J. Klafter, G. Gräff, and A. Shehter. 1997. Anomalous size dependence of relaxational processes. Phys. Rev. Lett. 78:3338-3341.
43. Gallos, L. K., and P. Argyrakis. 2001. Accurate estimation of the survival probability for trapping in two dimensions. Phys. Rev. E. 64:051111.
44. Gallos, L. K., P. Argyrakis, and K. W. Kehr. 2001. Trapping and survival probability in two dimensions. Phys. Rev. E. 63:021104.
45. Johnson, N. L., S. Kotz, and A. W. Kemp. 1992. Univariate Discrete Distributions, 2nd Ed. Wiley, New York.
46. Douglas, J. B. 1980. Analysis with Standard Contagious Distributions. International Co-operative Publishing House, Fairland, MD.
47. Almeida, P. F. F., and W. L. C. Vaz. 1995. Lateral diffusion in membranes. In Structure and Dynamics of Membranes, Vol. 1. R. Lipowsky and E. Sackmann, editors. Elsevier Science, Amsterdam. 305-357.
48. Saxton, M. J. 1993. Lateral diffusion in an archipelago: dependence on tracer size. Biophys. J. 64:1053-1062.
49. Ziff, R. M., S. N. Majumdar, and A. Comtet. 2007. General flux to a trap in one and three dimensions. J. Phys. Cond. Matter. 19:065102.
50. Berg, H. C., and E. M. Purcell. 1977. Physics of chemoreception. Biophys. J. 20:193-219.
51. Ghaemmaghami, S., W.-K. Huh, K. Bower, R. W. Howson, A. Belle, N. Dephoure, E. K. O'Shea, and J. S. Weissman. 2003. Global analysis of protein expression in yeast. Nature. 425:737-741.
52. Piehler, J. 2005. New methodologies for measuring protein interactions in vivo and in vitro. Curr. Opin. Struct. Biol. 15:4-14.
53. Kinney, J. B., G. Tkačik, and C. G. Callan. 2007. Precise physical models of protein-DNA interaction from high-throughput data. Proc. Natl. Acad. Sci. USA. 104:501-506.
54. Maerkl, S. J., and S. R. Quake. 2007. A systems approach to measuring the binding energy landscapes of transcription factors. Science. 315:233-237.
55. Mukherjee, S., M. F. Berger, G. Jona, X. S. Wang, D. Muzzey, M. Snyder, R. A. Young, and M. L. Bulyk. 2004. Rapid analysis of the DNA-binding specificities of transcription factors with DNA microarrays. Nat. Genet. 36:1331-1339.
56. Kerppola, T. K. 2006. Visualization of molecular interactions by fluorescence complementation. Nature Revs. Mol. Cell. Biol. 7:449-456.
57. Miller, J. P., R. S. Lo, A. Ben-Hur, C. Desmarais, I. Stagljar, W. S. Noble, and S. Fields. 2005. Large-scale identification of yeast integral membrane protein interactions. Proc. Natl. Acad. Sci. USA. 102:12123-12128.
58. Biggin, M. D. 2001. To bind or not to bind. Nat. Genet. 28:303-304.
59. Bar-Even, A., J. Paulsson, N. Maheshri, M. Carmi, E. O'Shea, Y. Pilpel, and N. Barkai. 2006. Noise in protein expression scales with natural protein abundance. Nat. Genet. 38:636-643.
60. Cai, L., N. Friedman, and X. S. Xie. 2006. Stochastic protein expression in individual cells at the single molecule level. Nature. 440:358-362.
61. Golding, I., J. Paulsson, S. M. Zawilski, and E. C. Cox. 2005. Real-time kinetics of gene activity in individual bacteria. Cell. 123:1025-1036.
62. Kaern, M., T. C. Elston, W. J. Blake, and J. J. Collins. 2005. Stochasticity in gene expression: from theories to phenotypes. Nature Rev. Genet. 6:451-464.
63. Raj, A., C. S. Peskin, D. Tranchina, D. Y. Vargas, and S. Tyagi. 2006. Stochastic mRNA synthesis in mammalian cells. PLoS Biol. 4:1707-1719.
64. Rosenfeld, N., J. W. Young, U. Alon, P. S. Swain, and M. B. Elowitz. 2005. Gene regulation at the single-cell level. Science. 307:1962-1965.
65. van Zon, J. S., and P. R. ten Wolde. 2005. Green's-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space. J. Chem. Phys. 123:234910.
66. van Zon, J. S., M. J. Morelli, S. Tǎnase-Nicola, and P. R. ten Wolde. 2006. Diffusion of transcription factors can drastically enhance the noise in gene expression. Biophys. J. 91:4350-4367.