Ion exchange phase transitions in water-filled channels with charged walls

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 5, 2006, Pages

  Zhang, J ^a   Kamenev, A ^a   Shklovskii, B I ^a,b  

^a University of Minnesota   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHARGED PARTICLES; ELECTROSTATICS; ION EXCHANGE; PERMITTIVITY; PHASE TRANSITIONS; SEMICONDUCTOR DOPING;

CHARGED WALLS; DIVALENT CA IONS; WATER-FILLED CHANNELS;

CHANNEL FLOW;

EID: 33646768656     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.051205     Document Type: Article

References (36)

1. B. Hille, Ion Channels of Excitable Membranes (Sinauer Associates, Sunderland, MA, 2001).
2. R. MacKinnon, Angew. Chem., Int. Ed. ACIEF5 1433-7851 43, 4265 (2004).
3. D. A. Doyle, Science SCIEAS 0036-8075 10.1126/science.280.5360.69 280, 69 (1998).
4. B. Roux, T. Allen, S. Berneche, and W. Im, Q. Rev. Biophys. QURBAW 0033-5835 10.1017/S0033583504003968 37, 15 (2004).
5. B. Nadler, U. Hollerbach, and R. S. Eisenberg, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.021905 68, 021905 (2003);
6. B. Nadler, Z. Schuss, U. Hollerbach, and R. S. Eisenberg, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.051912 70, 051912 (2004).
7. T. W. Allen, P. S. Andersen, and B. Roux, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.2635314100 101, 117 (2004).
8. S.-H. Chung and B. Corry, Eur. Phys. J. E EPJSFH 1292-8941 1, 417 (2005).
9. A. M. Berezhkovskii, M. A. Pustovoit, and S. M. Bezrukov, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1458935 116, 6216 (2002);
10. A. M. Berezhkovskii, M. A. Pustovoit, and S. M. Bezrukov, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1475758 116, 9952 (2002);
11. A. M. Berezhkovskii, M. A. Pustovoit, and S. M. Bezrukov, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1590957 119, 3943 (2003).
12. D. G. Levitt, Biophys. J. BIOJAU 0006-3495 22, 209 (1978).
13. P. C. Jordan, Biophys. Chem. BICIAZ 0301-4622 10.1016/0301-4622(81)80002- 6 13, 203 (1981).
14. A. Parsegian, Nature (London) NATUAS 0028-0836 221, 844 (1969).
15. P. C. Jordan, Biophys. J. BIOJAU 0006-3495 39, 157 (1982).
16. A. Kamenev, J. Zhang, A. I. Larkin, and B. I. Shklovskii, Physica A PHYADX 0378-4371 10.1016/j.physa.2005.05.097 359, 129 (2006).
17. J. Zhang, A. Kamenev, and B. I. Shklovskii, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.148101 95, 148101 (2005).
18. D. P. Chen and R. S. Eisenberg, Biophys. J. BIOJAU 0006-3495 64, 1405 (1993);
19. R. S. Eisenberg, J. Membr. Biol. JMBBBO 0022-2631 150, 1 (1996).
20. Gisela D. Cymes, Ying Ni, and Claudio Grosman, Nature (London) NATUAS 0028-0836 438, 975 (2005).
21. H. J. Appel, E. Bamberg, H. Alpes, and P. Lauger, J. Membr. Biol. JMBBBO 0022-2631 10.1007/BF01869403 31, 171 (1977).
22. A. Meller, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/15/17/202 15, R581 (2003).
23. J. D. Lear, J. P. Schneider, P. K. Kienker, and W. F. DeGrado, J. Am. Chem. Soc. JACSAT 0002-7863 119, 3212 (1997);
24. G. R. Dieckmann, Biophys. J. BIOJAU 0006-3495 76, 618 (1999).
25. J. Li, D. Stein, C. McMullan, D. Branton, M. J. Aziz, and J. A. Golovchenko, Nature (London) NATUAS 0028-0836 10.1038/35084037 412, 166 (2001);
26. D. Stein, M. Kruithof, and C. Dekker, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.035901 93, 035901 (2004);
27. A. Aksimentiev, J. B. Heng, G. Timp, and K. Schulten, Biophys. J. BIOJAU 0006-3495 10.1529/biophysj.104.042960 87, 2086 (2004);
28. Z. Siwy, I. D. Kosinska, A. Fulinski, and C. R. Martin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.048102 94, 048102 (2005).
29. The factor α22 under the logarithm is the result of having two ions at every dopant, and factor of 6 is obtained by integrating up the allowed volumes of the two ions for all possible ion configurations around the dopant.
30. W. Almers and E. W. McCleskey, J. Physiol. (London) JPHYA7 0022-3751 353, 585 (1984).
31. S. F. Edwards and A. Lenard, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1724281 3, 778 (1962).
32. A. Lenard, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1703757 2, 682 (1961).
33. To prove it, consider the imaginary part of the Hamiltonian 25, -2q â̂́Ì́ θ - â̂' m αm sin (mθ), as a perturbation. Notice that this operator changes the parity of functions it acts on. The wave functions of the unperturbed real Hermitian Hamiltonian are real and have a definite parity. It is clear then that only even-order (and thus purely real) perturbative corrections to the spectrum can be nonzero. Moreover, since â̂́Ì́ θ, is anti-Hermitian, while sin (mθ), is Hermitian, only even powers of q, contribute to this perturbation theory. As a result, the spectrum of the operator 25 Ïμ q (j), is a real symmetric function of q.
34. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed. (Pergamon Press, Oxford, 1980), Pt., Sec..
35. W. R. Smythe, Static and Dynamic Electricity, 3rd ed. (McGraw-Hill, New York, 1968);
36. A. A. Kornyshev and M. A. Vorotyntsev, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/12/22/033 12, 4939 (1979).