Searching for partially reactive sites: Analytical results for spherical targets

Journal of Chemical Physics

Volumn 132, Issue 3, 2010, Pages

  Grebenkov, Denis S ^a  

^a LABORATOIRE DE PHYSIQUE DE LA MATIÈRE CONDENSÉE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL RESULTS; BIOCHEMICAL REACTIONS; DENSITY OF PARTICLES; DIFFUSING PARTICLES; EXPLICIT FORMULA; FINITE REACTION RATES; HIGH-DENSITY LIMIT; PROBABILITY DENSITIES; REACTIVE SITE; SEARCH TIME; SUBDIFFUSION; THREE DIMENSIONS; TIME REGIME;

REACTION RATES;

PROBABILITY DENSITY FUNCTION;

ARTICLE; CHEMICAL MODEL; DIFFUSION; ENZYME ACTIVE SITE;

CATALYTIC DOMAIN; DIFFUSION; MODELS, CHEMICAL;

EID: 77249118101     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3294882     Document Type: Article

References (61)

1. A. Szabo, K. Schulten, and Z. Schulten, J. Chem. Phys. 0021-9606 72, 4350 (1980). 10.1063/1.439715
2. G. H. Weiss, J. Stat. Phys. 0022-4715 42, 3 (1986). 10.1007/BF01010838
3. H. Sano and M. Tachiya, J. Chem. Phys. 0021-9606 71, 1276 (1979). 10.1063/1.438427
4. M. Tachiya, Radiat. Phys. Chem. 0969-806X 21, 167 (1983).
5. A. V. Barzykin and M. Tachiya, J. Chem. Phys. 0021-9606 99, 9591 (1993). 10.1063/1.465491
6. M. Coppey, O. B́nichou, R. Voituriez, and M. Moreau, Biophys. J. 0006-3495 87, 1640 (2004). 10.1529/biophysj.104.045773 (Pubitemid 39167021)
7. S. B. Yuste, G. Oshanin, K. Lindenberg, O. B́nichou, and J. Klafter, Phys. Rev. E 1063-651X 78, 021105 (2008). 10.1103/PhysRevE.78.021105
8. K. B́nichou and V. Sheinman, Phys. Rev. Lett. 0031-9007 103, 138102 (2009). 10.1103/PhysRevLett.103.138102
9. M. Tolić-Nørrelykke and O. Thon, Phys. Rev. Lett. 0031-9007 93, 078102 (2004). 10.1103/PhysRevLett.93.078102
10. M. Weiss, M. Elsner, F. Kartberg, and T. Nilsson, Biophys. J. 0006-3495 87, 3518 (2004). 10.1529/biophysj.104.044263 (Pubitemid 40468604)
11. I. Golding and E. C. Cox, Phys. Rev. Lett. 0031-9007 96, 098102 (2006). 10.1103/PhysRevLett.96.098102 (Pubitemid 43385256)
12. J. -P. Bouchaud and A. Georges, Phys. Rep. 0370-1573 195, 127 (1990). 10.1016/0370-1573(90)90099-N
13. R. Metzler and J. Klafter, Phys. Rep. 0370-1573 339, 1 (2000). 10.1016/S0370-1573(00)00070-3
14. G. M. Zaslavsky, Phys. Rep. 0370-1573 371, 461 (2002). 10.1016/S0370-1573(02)00331-9
15. S. Havlin and D. Ben-Avraham, Adv. Phys. 0001-8732 51, 187 (2002). 10.1080/00018730110116353 (Pubitemid 34590201)
16. R. Kimmich, Chem. Phys. 0301-0104 284, 253 (2002). 10.1016/S0301-0104(02) 00552-9
17. R. Metzler and J. Klafter, J. Phys. A 0305-4470 37, R161 (2004). 10.1088/0305-4470/37/31/R01 (Pubitemid 39063557)
18. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, England, 2001).
19. B. D. Hughes, Random Walks and Random Environments (Clarendon, Oxford, 1995).
20. D. Holcman, A. Marchewka, and Z. Schuss, Phys. Rev. E 1063-651X 72, 031910 (2005). 10.1103/PhysRevE.72.031910 (Pubitemid 41778116)
21. P. E. Levitz, D. S. Grebenkov, M. Zinsmeister, K. Kolwankar, and B. Sapoval, Phys. Rev. Lett. 0031-9007 96, 180601 (2006). 10.1103/PhysRevLett.96. 180601
22. S. Condamin, O. B́nichou, and M. Moreau, Phys. Rev. Lett. 0031-9007 95, 260601 (2005). 10.1103/PhysRevLett.95.260601 (Pubitemid 43061522)
23. S. Condamin, O. B́nichou, and M. Moreau, Phys. Rev. E 1063-651X 72, 016127 (2005). 10.1103/PhysRevE.72.016127 (Pubitemid 41521113)
24. S. Condamin, O. B́nichou, V. Tejedor, R. Voituriez, and J. Klafter, Nature (London) 0028-0836 450, 77 (2007). 10.1038/nature06201 (Pubitemid 350070561)
25. D. S. Grebenkov, Phys. Rev. E 1063-651X 76, 041139 (2007). 10.1103/PhysRevE.76.041139 (Pubitemid 350037155)
26. R. C. Lua and A. Y. Grosberg, Phys. Rev. E 1063-651X 72, 061918 (2005). 10.1103/PhysRevE.72.061918 (Pubitemid 43273036)
27. S. B. Yuste and K. Lindenberg, Phys. Rev. E 1063-651X 76, 051114 (2007). 10.1103/PhysRevE.76.051114 (Pubitemid 350126063)
28. S. Condamin, O. B́nichou, and J. Klafter, Phys. Rev. Lett. 0031-9007 98, 250602 (2007). 10.1103/PhysRevLett.98.250602 (Pubitemid 47139905)
29. S. Condamin, V. Tejedor, R. Voituriez, O. B́nichou, and J. Klafter, Proc. Natl. Acad. Sci. U.S.A. 0027-8424 105, 5675 (2008). 10.1073/pnas. 0712158105 (Pubitemid 351758430)
30. F. C. Collins and G. E. Kimball, J. Colloid Sci. 0095-8522 4, 425 (1949). 10.1016/0095-8522(49)90023-9
31. B. Sapoval, Phys. Rev. Lett. 0031-9007 73, 3314 (1994). 10.1103/PhysRevLett.73.3314
32. D. S. Grebenkov, in Focus on Probability Theory, edited by, L. R. Velle, (Nova Science Publishers, New York, 2006), pp. 135-169.
33. A. Singer, Z. Schuss, A. Osipov, and D. Holcman, SIAM J. Appl. Math. 0036-1399 68, 844 (2008). 10.1137/060663258
34. D. S. Grebenkov, M. Filoche, and B. Sapoval, Phys. Rev. E 1063-651X 73, 021103 (2006). 10.1103/PhysRevE.73.021103 (Pubitemid 43287759)
35. M. Filoche and B. Sapoval, Eur. Phys. J. B 1434-6028 9, 755 (1999). 10.1007/s100510050820
36. D. S. Grebenkov, M. Filoche, and B. Sapoval, Eur. Phys. J. B 1434-6028 36, 221 (2003). 10.1140/epjb/e2003-00339-4 (Pubitemid 41200936)
37. M. Felici, M. Filoche, C. Straus, T. Similowski, and B. Sapoval, Respir. Physiol. Neurbiol. 1569-9048 145, 279 (2005). 10.1016/j.resp.2004.10.012
38. D. S. Grebenkov, Fractals 0218-348X 14, 231 (2006). 10.1142/ S0218348X06003209 (Pubitemid 44533723)
39. D. S. Grebenkov, Rev. Mod. Phys. 0034-6861 79, 1077 (2007). 10.1103/RevModPhys.79.1077 (Pubitemid 47357951)
40. J. M. Schurr, Biophys. J. 0006-3495 10, 717 (1970). 10.1016/S0006- 3495(70)86331-7
41. G. Seisenberger, M. U. Ried, T. Endres, H. Büning, M. Hallek, and C. Bräuchle, Science 0036-8075 294, 1929 (2001). 10.1126/science.1064103 (Pubitemid 33101590)
42. T. Chou and M. R. D'Orsogna, J. Chem. Phys. 0021-9606 127, 105101 (2007). 10.1063/1.2764053 (Pubitemid 47416112)
43. G. Wilemski and M. Fixman, J. Chem. Phys. 0021-9606 58, 4009 (1973). 10.1063/1.1679757
44. D. Holcman and Z. Schuss, J. Chem. Phys. 0021-9606 122, 114710 (2005). 10.1063/1.1849155 (Pubitemid 40661781)
45. K. R. Brownstein and C. E. Tarr, Phys. Rev. A 1050-2947 19, 2446 (1979). 10.1103/PhysRevA.19.2446
46. E. Barkai, R. Metzler, and J. Klafter, Phys. Rev. E 1063-651X 61, 132 (2000). 10.1103/PhysRevE.61.132
47. E. Barkai, Phys. Rev. E 1063-651X 63, 046118 (2001). 10.1103/PhysRevE.63. 046118
48. M. M. Meerschaert and H. -P. Scheffler, J. Appl. Probab. 0021-9002 41, 623 (2004). 10.1239/jap/1091543414 (Pubitemid 39620503)
49. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications (Gordon and Breach, Amsterdam, 1993).
50. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Mathematics Studies Series, Vol. 204 (Elsevier, Amsterdam, 2006). 10.1016/S0304-0208(06)80001-0
51. K. Seki, M. Wojcik, and M. Tachiya, J. Chem. Phys. 0021-9606 119, 2165 (2003). 10.1063/1.1587126
52. J. D. Eaves and D. R. Reichman, J. Phys. Chem. B 1089-5647 112, 4283 (2008). 10.1021/jp0749017
53. J. Sung and R. J. Silbey, Phys. Rev. Lett. 0031-9007 91, 160601 (2003). 10.1103/PhysRevLett.91.160601
54. M. A. Lomholt, I. M. Zaid, and R. Metzler, Phys. Rev. Lett. 0031-9007 98, 200603 (2007). 10.1103/PhysRevLett.98.200603 (Pubitemid 47139586)
55. A. N. Borodin and P. Salminen, Handbook of Brownian Motion: Facts and Formulae (Birkhauser Verlag, Berlin, 1996).
56. M. E. Muller, Ann. Math. Stat. 0003-4851 27, 569 (1956). 10.1214/aoms/1177728169
57. L. H. Zheng and Y. C. Chiew, J. Chem. Phys. 0021-9606 90, 322 (1989). 10.1063/1.456532
58. S. B. Lee, I. C. Kim, C. A. Miller, and S. Torquato, Phys. Rev. B 0163-1829 39, 11833 (1989). 10.1103/PhysRevB.39.11833
59. D. S. Grebenkov, Phys. Rev. Lett. 0031-9007 95, 200602 (2005). 10.1103/PhysRevLett.95.200602 (Pubitemid 41777109)
60. D. S. Grebenkov, A. A. Lebedev, M. Filoche, and B. Sapoval, Phys. Rev. E 1063-651X 71, 056121 (2005). 10.1103/PhysRevE.71.056121 (Pubitemid 41481009)
61. D. S. Grebenkov, " Subdiffusion in a bounded domain with a partially absorbing/reflecting boundary.," Phys. Rev. E 1063-651X (in print).