Stabilization of ion channels due to membrane-mediated elastic interaction

Journal of Chemical Physics

Volumn 118, Issue 22, 2003, Pages 10306-10311

  Partenskii, Michael B ^a   Miloshevsky, Gennady V ^a   Jordan, Peter C ^a  

^a BRANDEIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; ELASTIC MODULI; HYDROGEN BONDS; HYDROPHOBICITY; MONOMERS; POLYELECTROLYTES; SYNTHESIS (CHEMICAL); VAN DER WAALS FORCES; X RAY DIFFRACTION ANALYSIS;

DIMYRISTOYLPHOSPHATIDYLCHOLINE; EULER-LAGRANGE EQUATIONS; ION CHANNELS; MEMBRANE-MEDIATED ELASTIC INTERACTION;

POLYPEPTIDES;

EID: 0038608222     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1572460     Document Type: Article

References (57)

1. H. Huang, Biophys. J. 50, 1061 (1986).
2. P. Helfrich and E. Jakobsson, Biophys. J. 57, 1075 (1990).
3. C. Nielsen, M. Goulian, and O. S. Andersen, Biophys. J. 74, 1966 (1998).
4. J. A. Lundbæk and O. Andersen, Biophys. J. 76, 889 (1999).
5. C. Nielsen and O. S. Andersen, Biophys. J. 79, 2583 (2000).
6. N. Dan, A. Berman, P. Pincus, and S. Safran, J. Phys. II 4, 1713 (1994).
7. H. Aranda-Espinoza et al., Biophys. J. 71, 648 (1996).
8. R. Menes and S. Safran, Phys. Rev. E 56, 1891 (1997).
9. R. R. Netz, J. Phys. I 7, 833 (1997).
10. T. Harroun et al., Biophys. J. 76, 937 (1999).
11. T. Harroun et al., Biophys. J. 76, 3176 (1999).
12. P. Jordan, G. Miloshevsky, and M. Partenskii, in Interfacial Catalysis, edited by A. G. Volkov (Marcel Dekker, New York, 2003), pp. 493-534.
13. M. Partenskii and P. Jordan, J. Chem. Phys. 117, 10768 (2002).
14. O. Andersen et al., Nat. Struct. Biol. 72, 609 (1999).
15. H. Kolb and E. Bamberg, Biochim. Biophys. Acta 464, 127 (1977).
16. J. Elliot, D. Needham, J. Digler, and D. Haydon, Biochim. Biophys. Acta 735, 95 (1983).
17. N. Mobashery, C. Nielsen, and O. Andersen, FEBS Lett. 412, 15 (1997).
18. S. Young and M. Poo, J. Biol. Chem. 304, 161 (1983).
19. K. Iwasa, G. Ehrenstein, M. Moran, and M. Jia, Biophys. J. 50, 513 (1986).
20. E. Yeramian, A. Trautmann, and P. Claverie, Biophys. J. 50, 253 (1986).
21. K. Manivannan, S. Ramanan, R. Mathias, and P. Brink, Biophys. J. 61, 216 (1992).
22. A. Keleshian, R. Edeson, G.-J. Liu, and B. W. Madsen, Biophys. J. 78, 1 (2000).
23. M. Krouse and J. Wine, J. Membr. Biol. 82, 223 (2000).
24. A. Duke and D. Bray, Proc. Natl. Acad. Sci. U.S.A. 96, 10104 (1999).
25. S. Marx, K. Ondrias, and A. Marks, Science (Washington, DC, U.S.) 281, 818 (1998).
26. E. Tkachenko and M. Simons, Nature (London) 277, 19946 (2002).
27. A. V. Krylov, E. A. Kotova, A. A. Yaroslavov, and Y. N. Antonenko, Biochim. Biophys. Acta 1509, 373 (2000).
28. T. I. Rokitskaya et al., Biochemistry 39, 13053 (2000).
29. Y. Antonenko, T. Rokitskaya, and E. Kotova, Biophys. J. 82, 556a (2002).
30. Y. Antonenko et al., Biophys. J. 82, 1308 (2002).
31. R. Goforth, A. K. Chi, and O. Andersen, Biophys. J. 82, 557a (2002).
32. R. Goforth et al., J. Gen. Physiol. (to be published).
33. G. V. Miloshevsky, M. Partenskii, and P. Jordan, Biophys. J. 82, 714a (2002).
34. A. Ring, Biochim. Biophys. Acta 1278, 147 (1996).
35. Y. S. Neustadt and M. B. Partenskii, arXiv:physics/0212038 (2002).
36. M. Goulian, R. Bruinsma, and P. Pincus, Europhys. Lett. 22, 145 (1993).
37. N. Dan, P. Pincus, and S. Safran, Langmuir 9, 2768 (1993).
38. J. Kim, K. S. Neu, and G. Oster, Biophys. J. 75, 2274 (1998).
39. P.-G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, 1995).
40. M. Goulian et al., Biophys. J. 74, 328 (1998).
41. M. Partenskii, G. V. Miloshevsky, and P. Jordan, Biophys. J. 82, 713a (2002).
42. For a single ion channel this results in a "linear spring model" describing membrane deformation due to insertion as in C. Nielsen, M. Goulian, O. S. Andersen, Biophys. J. 74, 1966 (1998).
43. In contrast, a nonlinear elastic approach has been used in R. Menes and S. Satran, Phys. Rev. E 56, 1891 (1997), where the focus was on the significant membrane thinning due to pinning sites. It should be stressed that linearity means that Euler-Lagrange equations [such as Eq. (3)] are of the form L(u)=0, where L is a linear differential operator, a requirement that imposes no restrictions on the order of the differential equations, typically biharmonic for the problems of interest here.
44. We omitted the normal coefficient of 1/2 in Eq. (11), a convention corresponding to the definition of the effective spring constant for an individual insertion [Eq. (21) of C. Nielsen, M. Goulian, and O. S. Andersen, Biophys. J. 74, 1966 (1988)]; it has no physical influence. Equation (11) also holds if the contact slopes is not constrained to 0 but adjust spontaneously to minimize the energy. It is also applicable if interaction with the insertion locally stiffens the membrane, an alternative model that accounts for membrane influences on individual channel lifetime. This nonuniform treatment has not yet been extended to account for membrane-mediated interactions. Therefore, we use a conventional model, with the "constrained" boundary condition.
45. J. T. Durkin, L. L. Providence, R. E. I. Koeppe, and O. S. Andersen, Biophys. J. 62, 145 (1992).
46. G. Miloshevsky, M. Partensky, and P. Jordan, Biophys. J. 84, 2520a (2003).
47. A. S. Arseniev et al., Russian Bioorg. Khim. 18, 182 (1992).
48. W. A. Tucker, S. Sham, L. E. Townsley, and J. F. Hinton, Biochemistry 40, 11676 (2001).
49. R. R. Ketchem, K. C. Lee, S. Huo, and T. A. Cross, J. Biomol. NMR 8, 1 (1996).
50. P. Cavatorta et al., Biochim. Biophys. Acta 689, 113 (1982).
51. J. Mou, D. Czajkowsky, and Z. Shao, Biochemistry 35, 3222 (1996).
52. At small d, an elastic treatment of membrane regions between inclusions is clearly suspect. However, in the regions surrounding the cluster, it is about as realistic as for isolated insertions. While the inter-inclusion area becomes negligible as d→0, the surroundings approach some fixed limit, roughly a semielliptic cylinder embedding two insertions in contact. This leads to some error compensation in the elastic description at small separations because in the area integrals defining the energy, Eq. (2), the ambiguous (inner) contributions almost vanish. This is probably why the elastic approach was effectively used at nearly all interinclusion separations. The elimination of these inner regions indicates that a major source of the elastic force stabilizing two insertions in direct contact is the reduction in the total membrane area effectively perturbed by the inclusions; the "circumference" of two inclusions in contact is less than twice that of a single one.
53. J. T. Durkin, L. L. Providence, R. E. I. Koeppe, and O. S. Andersen, J. Mol. Biol. 231, 1102 (1992).
54. H. Eyring, J. Walter, and G. E. Kimball, Quantum Chemistry (Wiley, New York, 1944), pp. 299-331.
55. I. Tolokh, G. W. N. White, S. Goldman, and C. G. Gray, Mol. Phys. 35, 2351 (2002).
56. A. Krylov et al., J. Membr. Biol. 189, 119 (2002).
57. G. Miloshevsky and P. Jordan, Biophys. J. 84, 247a (2003).