Reaction-diffusion description of biological transport processes in general dimension

Journal of Chemical Physics

Volumn 104, Issue 5, 1996, Pages 1918-1936

  Nadler, W ^a   Stein, D L ^b  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001428165     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.471810     Document Type: Article

References (88)

1. R. H. Austin, K. W. Beeson, L. Eisenstein, H. Frauenfelder, and I. C. Gunsalus, Biochemistry 14, 5355 (1975).
2. N. Alberding, S. S. Chan, L. Eisenstein, H. Frauenfelder, D. Good, I. C. Gunsalus, T. J. Nordlund, M. F. Perutz, A. H. Reynolds, and L. B. Sorensen, Biochemistry 17, 43 (1978).
3. D. Beece, L. Eisenstein, H. Frauenfelder, D. Good, M. C. Marden, L. Reinisch, A. H. Reynolds, L. B. Sorensen, and K. T. Yue, Biochemistry 19, 5147 (1980).
4. A. Ansari, J. Berendzen, S. F. Bowne, H. Frauenfelder, I. E. T. Iben, T. B. Sauke, E. Shyamsunder, and R. D. Young, Proc. Natl. Acad. Sci. USA 82, 5000 (1985).
5. A. Ansari, E. DiIorio, D. Dlott, H. Frauenfelder, I. E. T. Iben, P. Langer, H. Roder, T. B. Sauke, and E. Shyamsunder, Biochemistry 25, 3139 (1986).
6. A. Ansari, J. Berendzen, D. Braunstein, B. R. Cowen, H. Frauenfelder, M. K. Hong, I. E. T. Iben, J. B. Johnson, P. Ormos, T. B. Sauke, R. Scholl, A. Schulte, P. J. Steinbach, J. Vittitow, and R. D. Young, Biochemistry 26, 337 (1987).
7. H. Frauenfelder, N. A. Alberding, A. Ansari, D. Braunstein, B. R. Cowen, M. K. Hong, E. Icko, B. J. Johnson, S. Luck, M. C. Marden, J. R. Mourant, P. Ormos, L. Reinisch, R. Scholl, A. Schulte, E. Shyamsunder, L. B. Sorensen, P. J. Steinbach, A. Xie, R. D. Young, and K. T. Yue, J. Phys. Chem. 94, 1024 (1990).
8. D. A. Case and M. Karplus, J. Mol. Biol. 132, 343 (1979).
9. N. Agmon and J. J. Hopfield, J. Chem. Phys. 78, 6947 (1983).
10. N. Agmon and J. J. Hopfield, J. Chem. Phys. 79, 2042 (1983).
11. H. Frauenfelder, Naturwissens. Rund. 38, 311 (1985).
12. W. Doster, Ch. Holtzhey, H. Miesmer, F. Post, and R. A. Tahir-Kheli, J. Biol. Phys. 17, 281 (1990).
13. W. Nadler and D. L. Stein, Proc. Natl. Acad. Sci. USA 88, 6750 (1991).
14. -1/2 law in 3d was done independently in J. B. Miers, J. C. Postlewaite, T. Zyung, S. Chen, G. R. Roomig, X. Won, D. D. Dlott, and A. Szabo, J. Chem. Phys. 93, 8771 (1990); however, these authors discuss binding to protohsme in solution, i.e., heme without the protein shell, rather than the ligand migration process.
15. C. D. Levermore, W. Nadler, and D. L. Stein, Phys. Rev. E 51, 2779 (1995).
16. S. D. Druger, M. A. Ratner, and A. Nitzan, Phys. Rev. B 31, 3939 (1985).
17. M. Sahimi, B. D. Hughes, L. E. Scriven, and H. T. Davis, J. Chem. Phys. 78, 6849 (1983).
18. A. K. Harrison and R. Zwanzig, Phys. Rev. A 32, 1072 (1985).
19. R. Hilfer and R. Orbach, Chem. Phys. 128, 275 (1988).
20. A. Perera, B. Gaveau, M. Moreau, and K. A. Penson, Phys. Lett. A 159, 158 (1991).
21. R. Zwanzig, Chem. Phys. Lett. 164, 639 (1989).
22. M. Tachiya, J. Chem. Phys. 70, 238 (1979);
23. Rad. Phys. Chem. 21, 167 (1983).
24. A. Szabo, D. Soup, S. H. Northrup, and J. A. McCammon, J. Chem. Phys. 77, 4484 (1982).
25. B. I. Hunt and J. G. Powles, Proc. Phys. Soc. 88, 513 (1966).
26. W. Feller, Probability and its Applications (Wiley, New York, 1971), Vol. 2.
27. A. Szabo, K. Schulten, and Z. Schulten, J. Chem. Phys. 72, 4350 (1980).
28. K. Schulten, Z. Schulten, and A. Szabo, J. Chem. Phys. 74, 4426 (1981).
29. W. Nadler and K. Schulten, J. Chem. Phys. 82, 151 (1985).
30. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford University, Oxford, 1959).
31. J. Crank, The Mathematics of Diffusion (Oxford University, Oxford, 1975).
32. N. Agmon, J. Chem. Phys. 81, 2811 (1984).
33. M. J. Lighthill, Introduction to Fourier Analysis and Generalized Functions (Cambridge University, Cambridge, 1958).
34. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
35. H. Sano and M. Tachiya, J. Chem. Phys. 71, 1276 (1979).
36. See, for example, G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1966).
37. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, corrected and enlarged edition (Academic, New York, 1980).
38. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes (Cambridge University, Cambridge, 1992).
39. W. Nadler and K. Schulten, J. Chem. Phys. 84, 4015 (1986).
40. E. Pines, D. Huppert, and N. Agmon, J. Chem. Phys. 88, 5620 (1988).
41. M. Tachiya (private communication).
42. A. Brünger, R. Peters, and K. Schulten, J. Chem. Phys. 82, 2147 (1985).
43. H.-U. Bauer, K. Schulten, and W. Nadler, Phys. Rev. B 38, 445 (1988).
44. This follows from Koenig's theorem, a very general result on the zeros of Padé approximants; see A. S. Housholder, The Numerical Treatment of a Single Nonlinear Equation (McGraw-Hill, New York, 1970).
45. C. W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1983).
46. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1984).
47. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992).
48. H. Frauenfelder, G. A. Petsko, and D. Tsemoglu, Nature 280, 558 (1979).
49. H. Frauenfelder, in Structure and Dynamics: Nucleic Acids and Proteins, edited by E. Clementi and R. H. Sarma (Adenine, New York, 1983), p. 369-376.
50. H. Frauenfelder, in Structure and Motion: Membranes, Nucleic Acids and Proteins, edited by E. Clementi and R. H. Sarma (Adenine, New York, 1985), p. 205-217.
51. B. Hille, Ionic Channels and Excitable Membranes (Sinauer, Sunderland MA, 1984).
52. B. Hille, in The Harvey Lectures, Series 82, (Alan R. Liss Inc. 1988), p. 47-69.
53. D. L. Stein, Spin Glasses and Biology (World Scientific, Singapore, 1992).
54. C. M. Newman and D. L. Stein, Ann. Inst. Henri Poincaré 31, 249 (1995).
55. D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor and Francis, London, 1992).
56. H. Frauenfelder, S. G. Sugar, and P. Wolynes, Science 254, 1598 (1991).
57. S. A. Kauffman, Origins of Order (Oxford University, Oxford, 1993).
58. R. G. Palmer, Adv. Phys. 31, 669 (1982);
59. Heidelberg Colloquium on Spin Glasses, edited by J. L. van Hemmen and I. Morgenstern (Springer, Berlin, 1983), pp. 234-251.
60. D. L. Stein and C. M. Newman, Phys. Rev. E 51, 5228 (1995).
61. P. A. Ferrari, S. Goldstein, and J. L. Lebowitz, in Statistical Physics and Dynamical Systems, Rigorous Results, edited by J. Fritz, A. Jaffe, and D. Szász (Birkhäuser, Boston, 1985), pp. 405-441.
62. R. Zwanzig, Proc. Natl. Acad. Sci. USA 85, 2029 (1988).
63. W. Nadler and K. Schulten, Proc. Natl. Acad. Sci. USA 81, 5719 (1984).
64. P. Läuger, Biophys. J. 53, 877 (1988).
65. Single-Channel Recording, edited by B. Sakman and E. Neher (Plenum, New York, 1983).
66. L. S. Liebovitch and J. M. Sullivan, Biophys. J. 25, 979 (1987).
67. R. McGee Jr., M. S. P. Sansom, and P. N. R. Usherwood, J. Memb. Biol. 102, 21 (1988).
68. G. L. Millhauser, E. E. Salpeter, and R. E. Oswald, Proc. Natl. Acad. Sci. USA 85, 1503 (1988).
69. G. L. Millhauser, E. E. Salpeter, and R. E. Oswald, Biophys. J. 54, 1165 (1988).
70. r are connected to the experimental time resolution.
71. G. L. Millhauser, Biophys. J. 57, 857 (1990).
72. R. E. Oswald, G. L. Millhauser, and A. Carter, Biophys. J. 57, 857 (1991).
73. C. A. Condat, Phys. Rev. A 39, 2112 (1989).
74. C. A. Condat and J. Jäckle, Biophys. J. 55, 915 (1989).
75. W. Doster, W. Schirmacher, and M. Settles, Biophys. J. 57, 681 (1990).
76. L. S. Liebovitch, L. Y. Selector, and R. P. Kline, Biophys. J. 63, 1579 (1992).
77. S. J. Korn, and R. Horn, Biophys. J. 54, 871 (1988).
78. O. B. McManus, D. S. Weiss, C. E. Spivak, A. L. Blatz, and K. L. Magleby, Biophys. J. 54, 859 (1988).
79. J. D. Becker, J. Honerkamp, J. Hirsch, U. Fröbe, and R. Greger, Eur. J. Physiol. (Pflügers Arch.) 426, 328 (1994).
80. D. Colquhoun and F. J. Sigworth, in Ref. 63, p. 191-263.
81. L. S. Liebovitch, Biophys. J. 55, 373 (1989).
82. R. Horn and S. J. Korn, Biophys. J. 55, 379 (1989).
83. O. B. McManus, C. E. Spivak, A. L. Blatz, D. S. Weiss, and K. L. Magleby, Biophys. J. 54, 383 (1989).
84. C. M. Armstrong and F. Bezanilla, J. Gen. Physiol. 70, 567 (1977).
85. T. Hoshi, W. N. Zagotta, and R. W. Aldrich, Science 250, 533 (1990).
86. W. N. Zagotta, T. Hoshi, and R. W. Aldrich, Science 250, 568 (1990).
87. M. K. Hong, E. Shyamsunder, and R. H. Austin, Phys. Rev. Lett. 66, 2673 (1991).
88. W. D. Tian, J. T. Sage, V. Srajer, and P. M. Champion, Phys. Rev. Lett. 68, 408 (1992).