Negative Gaussian curvature distribution in physical and biophysical systems-Curved nanocarbons and ion-channel membrane proteins

Journal of Applied Physics

Volumn 112, Issue 11, 2012, Pages

  Gupta, Sanju ^a,b   Saxena, Avadh ^c  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b DREXEL UNIVERSITY   (United States)

^c CENTER FOR NONLINEAR STUDIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BENDING ENERGIES; CATENOIDS; DIFFERENTIAL GEOMETRY; DRUG DELIVERY APPLICATIONS; ELASTIC BENDING ENERGY; GAUSSIAN BENDING; GAUSSIAN CURVATURES; GEOMETRICAL SHAPES; GYROIDS; INORGANIC SOLIDS; ION CHANNEL; LENGTH SCALE; MEAN CURVATURE; MEMBRANE PROTEINS; MINIMAL SURFACES; NANOCARBONS; PERIODIC MINIMAL SURFACES; SCHWARZITES; SELF-ASSEMBLED; STRUCTURAL DIVERSITY; TOPOLOGICAL FEATURES; TOPOLOGICAL VARIATIONS;

BIOLOGICAL MEMBRANES; BLOCK COPOLYMERS; DRUG DELIVERY; GAUSSIAN DISTRIBUTION; IONS; MEDICAL NANOTECHNOLOGY; PROTEINS; TOPOLOGY;

GEOMETRY;

EID: 84871205329     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4768207     Document Type: Article

References (105)

1. For a review, please see, S. Gupta and A. Saxena, J. Raman Spectrosc. 40, 1127 (2009). 10.1002/jrs.2245
2. S. T. Hyde, S. Andersson, Z. Blum, S. Lidin, K. Larsson, T. Landh, and B. W. Ninham, The Language of Shape (Elsevier Science B.V., Amsterdam, The Netherlands, 1997).
3. S. Gupta and A. Saxena, J. Appl. Phys. 109, 074316 (2011) [10.1063/1.3553860
4. S. Gupta and A. Saxena, Virtual J. Nanoscale Sci. Technol. 23 (2011)].
5. G. Shin, M. Y. Bae, H. J. Lee, S. K. Hong, C. H. Yoon, G. Zi, J. A. Rogers, and J. S. Ha, ACS Nano 5, 10009 (2011). 10.1021/nn203790a
6. M. I. Monastyrskii, Topology of Gauge Fields and Condensed Matter (Plenum, New York, 1993).
7. J. M. Sneddon, Biochim. Biophys. Acta 1031, 1 (1990). 10.1016/0304-4157(90)90002-T
8. Geometry in Condensed Matter Physics, edited by, J. F. Sadoc, (World Scientific, Singapore, 1990).
9. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 2 (Wiley-Interscience, 1996) (New edition).
10. J. M. Sneddon and R. H. Templer, in Handbook of Biological Physics, edited by, E. Sackmann, (Elsevier Science, New York, 1995), Vol. 1, p. 97.
11. Z. A. Almsherqi, S. D. Kohlwein, and Y. Deng, J. Cell Biol. 173, 839 (2006). 10.1083/jcb.200603055
12. S. Ihara, S. Itoh, and J. Kitakami, Phys. Rev. B 48, 5643 (1993). 10.1103/PhysRevB.48.5643
13. M. Sano, A. Kamino, J. Okamura, and S. Shinkai, Science 293, 1299 (2001). 10.1126/science.1061050
14. D. H. Oh, J. M. Park, and K. S. Kim, Phys. Rev. B 62, 1600 (2000). 10.1103/PhysRevB.62.1600
15. I. A. Ovid'ko, Rev. Adv. Mater. Sci. 30, 201 (2012) and references therein.
16. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature 438, 197 (2005). 10.1038/nature04233
17. D. Farias, A. M. Shikin, K.-H. Rieder, and Y. S. Dedkov, J. Phys.: Condens. Matter 11, 8453 (1999). 10.1088/0953-8984/11/43/308
18. R. B. King, J. Chem. Inf. Comput. Sci. 38, 180 (1998) [see Eqs. (15) and (17)].
19. H. Terrones and A. L. Mackay, in Growth Patterns in Physical Sciences and Biology, edited by, J. M. Garcia-Ruiz, E. Louis, P. Meakin, and, L. M. Sander, (Plenum, New York, 1993), pp. 315-320.
20. A. Rubio, J. Corkill, and M. L. Cohen, Phys. Rev. B 49, 5081 (1994). 10.1103/PhysRevB.49.5081
21. X. Blasé, A. Rubio, S. G. Louie, and M. L. Cohen, Europhys. Lett. 28, 335 (1994). 10.1209/0295-5075/28/5/007
22. N. G. Chopra, R. J. Luyken, K. Cherrey, V. H. Crespi, M. L. Cohen, S. G. Louie, and A. Zettl, Science 269, 966 (1995). 10.1126/science.269.5226.966
23. L. Loiseau, F. Willaime, N. Demoncy, G. Hug, and H. Pascard, Phys. Rev. Lett. 76, 4737 (1996). 10.1103/PhysRevLett.76.4737
24. Z. Liu, E. L. Zechiedrich, and H. S. Chan, Biophys. J. 90, 2344 (2006). 10.1529/biophysj.105.076778
25. Z.-G. Wang and S. A. Safran, Europhys. Lett. 11, 425 (1990). 10.1209/0295-5075/11/5/007
26. S. Spadoni, L. Colombo, P. Milani, and G. Benedek, Europhys. Lett. 39, 269 (1997). 10.1209/epl/i1997-00346-7
27. T. Lenovsky, X. Gonze, M. Teter, and V. Elser, Nature 355, 333 (1992). 10.1038/355333a0
28. V. Saranathana, C. O. Osuji, S. G. J. Mochrieb, H. Noh, S. Narayanan, A. Sandy, E. R. Dufresne, and R. O. Prum, Proc. Natl. Acad. Sci. 107, 11676 (2010). 10.1073/pnas.0909616107
29. E. L. Thomas, D. M. Anderson, C. Henkee, and D. Hoffman, Nature 334, 598 (1988). 10.1038/334598a0
30. V. Luzatti and P. A. Spegt, Nature (London) 215, 701 (1967). 10.1038/215701a0
31. L. Martín-Moreno, F. J. García-Vidal, and A. M. Somoza, Phys. Rev. Lett. 83, 73 (1999). 10.1103/PhysRevLett.83.73
32. J. Israelachvili, Intermolecular and Surface Forces, 2nd ed. (Academic, London, 1991).
33. J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University Press, Princeton, New Jersey, 1995).
34. Y. Jiang, A. Lee, J. Chen, V. Ruta, M. Cadene, B. T. Chait, and R. MacKinnon, Nature 423, 33 (2003). 10.1038/nature01580
35. G. Chang, R. H. Spencer, A. T. Lee, M. T. Barclay, and D. C. Rees, Science 282, 2220 (1998). 10.1126/science.282.5397.2220
36. M. Sotomayor and K. Schulten, Biophys. J. 87, 3050 (2004). 10.1529/biophysj.104.046045
37. V. Vasquez, M. Sotomayor, D. M. Cortes, B. Roux, K. Schulten, and E. Perozo, J. Mol. Biol. 378, 55 (2008). 10.1016/j.jmb.2007.10.086
38. J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, M. Matthias, A. P. Seitsonen, S. Moussa, X. Feng, K. Müllen, and R. Fasel, Nat. Lett. 466, 470 (2010). 10.1038/nature09211
39. D. A. Christian, S. Cai, O. B. Garbuzenko, T. Harada, A. L. Zajac, T. Minko, and D. E. Discher, Flexible Mol. Pharm. 6, 1343 (2009). 10.1021/mp900022m
40. M. Ferrari, Nat. Nanotech. 3, 131 (2008). 10.1038/nnano.2008.46
41. K. R. Yamamoto, Ann. Rev. Genet. 19, 209 (1985). 10.1146/annurev.ge.19. 120185.001233
42. M. Menon and D. Srivastava, Phys. Rev. Lett. 79, 4453 (1997). 10.1103/PhysRevLett.79.4453
43. D. Heymann, L. W. Jenneskens, J. Jehlicka, C. Koper, and E. Vlietstra, Fullerenes, Nanotubes Carbon Nanostruct. 11, 333 (2003). 10.1081/FST-120025855
44. H. Aoki, M. Koshino, D. Takeda, H. Morise, and K. Kuroki, Phys. Rev. B 65, 035102-1 (2001). 10.1103/PhysRevB.65.035102
45. K. Michielsen and D. G. Stavenga, J. R. Soc., Interface 5, 85 (2008). 10.1098/rsif.2007.1065
46. L. L. Bucciarelli, N. Dworsky, and S. Germain, An Essay in the History of the Theory of Elasticity (D. Reidel Publishing Co., Dordrecht, 1980).
47. W. Helfrich, Z. Naturforsch. C 28, 693 (1973).
48. P. B. Canham, J. Theor. Biol. 26, 61 (1970). 10.1016/S0022-5193(70)80032- 7
49. T. Taniguchi, Phys. Rev. Lett. 76, 4444 (1996). 10.1103/PhysRevLett.76. 4444
50. D. S. Dean and R. R. Horgan, Phys. Rev. E 73, 011906 (2006). 10.1103/PhysRevE.73.011906
51. M. M. A. E. Claessens, B. F. van Oort, F. A. M. Leermakers, F. A. Hoekstra, and M. A. C. Stuart, Phys. Rev. E 76, 011903-1 (2007). 10.1103/PhysRevE.76.011903
52. S. Andersson, S.T. Hyde, and H.-G. von Schnering, Z. Kristallog. 168, 1 (1984). 10.1524/zkri.1984.168.1-4.1
53. B. J. Dair, A. Avgeropoulos, N. Hadjichristidis, and E. L. Thomas, J. Mater. Sci. 35, 5207 (2000). 10.1023/A:1004816723095
54. J. Weitkamp, Sol. State Ionics 131, 175 (2000). 10.1016/S0167-2738(00) 00632-9
55. D. Hoffman, F. Wei, and H. Karcher, Bull. Am. Math. Soc. 29, 77 (1993). 10.1090/S0273-0979-1993-00401-4
56. S. Ono and H. Shima, Phys. Rev. B 79, 235407 (2009) and references therein. 10.1103/PhysRevB.79.235407
57. R. C. T. da Costa, Phys. Rev. A 23, 1982 (1981). 10.1103/PhysRevA.23.1982
58. R. Dandoloff, A. Saxena, and B. Jensen, Phys. Rev. B 81, 014102 (2010). 10.1103/PhysRevB.81.014102
59. V. A. Atanasov, R. Dandoloff, and A. Saxena, Phys. Rev. B 79, 033404 (2009). 10.1103/PhysRevB.79.033404
60. S. K. Baek, H. Shima, and B. J. Kim, Phys. Rev. E 79, 060106-1 (2009). 10.1103/PhysRevE.79.060106
61. P. López-Sancho, M. A. H. Vozmediano, T. Stauber, and F. Guinea, Springer Series: Mathematics in Industry (Springer-Verlag, 2007), Vol. 12, p. 483
62. A. V. Rode, E. G. Gamaly, A. G. Christy, J. G. Fitz Gerald, S. T. Hyde, R. G. Elliman, B. Luther-Davies, A. I. Veinger, J. Androulakis, and J. Giapintzakis, Phys. Rev. B 70, 054407 (2004). 10.1103/PhysRevB.70.054407
63. D. Arčon, Z. Jagličič, A. Zorko, A. V. Rode, A. G. Christy, N. R. Madsen, E. G. Gamaly, and B. Luther-Davies, Phys. Rev. B 74, 014438 (2006). 10.1103/PhysRevB.74.014438
64. J. González, F. Guinea, and M. A. H. Vozmediano, Nucl. Phys. B 406, 771 (1993). 10.1016/0550-3213(93)90009-E
65. See for example, P. W. Fowler and E. Steiner, J. Chem. Soc. Faraday Trans. 89, 1915 (1993). 10.1039/ft9938901915
66. N. Park, M. Yoon, S. Berber, J. Ihm, E. Osawa, and D. Tománek, Phys. Rev. Lett. 91, 237204 (2003). 10.1103/PhysRevLett.91.237204
67. P. C. W. Davies, BioSystems 78, 69 (2004). 10.1016/j.biosystems.2004.07. 001
68. P. Ball, Nature 474, 272 (2011). 10.1038/474272a
69. A. Boudaoud, P. Patrício, and M. B. Amar, Phys. Rev. Lett. 83, 3836 (1999). 10.1103/PhysRevLett.83.3836
70. D. Vanderbilt and J. Tersoff, Phys. Rev. Lett. 68, 511 (1992). 10.1103/PhysRevLett.68.511
71. R. Ghafouri and R. Bruinsma, Phys. Rev. Lett. 94, 138101 (2005). 10.1103/PhysRevLett.94.138101
72. M. Nakahara, Geometry, Topology and Physics, Graduate Student Series in Physics (Adam Hilger, Bristol, 1990).
73. See http://www-klinowski.ch.cam.ac.uk/pmshome.html for further details on periodic minimal surfaces.
74. S. Torquato and A. Donev, Proc. R. Soc. London, Ser A 460, 1849 (2004). 10.1098/rspa.2003.1269
75. S. Sakurai, H. Irie, H. Umeda, S. Nomura, H. H. Lee, and J. K. Kim, Macromolecules 31, 336 (1998). 10.1021/ma970471e
76. J. Charvolin and J. F. Sadoc, J. Phys. (France) 48, 1559 (1987).
77. W. Gozdz and R. Holyst, Macromol. Theory Simul. 5, 321 (1996). 10.1002/mats.1996.040050212
78. S. Andersson, S. T. Hyde, K. Larsson, and S. Lidin, Chem. Rev. 88, 221 (1988). 10.1021/cr00083a011
79. H. A. Schwarz, Gesammelte Mathematische Abhandlunge (Springer, Berlin, 1890).
80. A. L. Mackay, Nature 314, 604 (1985). 10.1038/314604a0
81. S. J. Townsend, T. J. Lenosky, D. A. Muller, C. S. Nichols, and V. Elser, Phys. Rev. Lett. 69, 921 (1992). 10.1103/PhysRevLett.69.921
82. W. Saenger, Principles of Nucleic Acid Structure (Springer-Verlag, Berlin, 1984).
83. Photonic Band Gaps and Localization, edited by, C. M. Soukoulis, (Plenum, New York, 1993).
84. R. Bar-Ziv and E. Moses, Phys. Rev. Lett. 73, 1392 (1994). 10.1103/PhysRevLett.73.1392
85. Physics of Amphiphilic Layers, edited by, J. Meunier, D. Langevin, and, N. Boccara, (Springer-Verlag, Berlin, 1987).
86. P. Nelson, T. Powers, and U. Seifert, Phys. Rev. Lett. 74, 3384 (1995). 10.1103/PhysRevLett.74.3384
87. K. Michielsen, H. De Raedt, and D. G. Stavenga, J. R. Soc., Interface 7, 765 (2010). 10.1098/rsif.2009.0352
88. S. T. Hyde and G. E. Schröder-Turk, Interface Focus 2, 529 (2012). 10.1098/rsfs.2012.0035
89. H. G. von Schnering and R. Nesper, Z. Phys. B: Condens. Matter 83, 407 (1991). 10.1007/BF01313411
90. M. Wohlgemuth, N. Yfa, J. Hoffman, and E. L. Thomas, Macromolecules 34, 6083 (2001). 10.1021/ma0019499
91. G. P. Sorenson, K. L. Coppage, and M. K. Mahanthappa, J. Am. Chem. Soc. 133, 14928 (2011). 10.1021/ja2063555
92. C. T. Kresge, M. E. Leonowicz, W. J. Roth, J. C. Vartuli, and J. S. Beck, Nature 359, 710 (1992). 10.1038/359710a0
93. S. Horike, S. Shimomura, and S. Kitagawa, Nature Chem. 1, 695 (2009). 10.1038/nchem.444
94. A. L. Mackay and H. Terrones, Nature 352, 762 (1991). 10.1038/352762a0
95. H. Terrones, M. Terrones, and J. L. M.-López, Curr. Sci. 81, 1011 (2001).
96. E. Barborini, P. Piseri, P. Milani, G. Benedek, C. Ducati, and J. Robertson, Appl. Phys. Lett. 81, 3359 (2002). 10.1063/1.1516635
97. D. Donadio, L. Colombo, P. Milani, and G. Benedek, Phys. Rev. Lett. 83, 776 (1999). 10.1103/PhysRevLett.83.776
98. The Mathematics and Topology of Fullerenes, Carbon Materials: Chemistry and Physics, edited by, F. Cataldo, A. Graovac, and, O. Ori, (Springer, New York, 2011), Vol. 4, Chap..
99. H. Terrones and A. L. Mackay, Prog. Cryst. Growth Charact. Mater. 34, 25 (1997). 10.1016/S0960-8974(97)00003-X
100. S. Iijima, T. Ichihashi, and Y. Ando, Nature 356, 776 (1992). 10.1038/356776a0
101. M. O'Keefe, G. B. Adams, and O. F. Sankey, Phys. Rev. Lett. 68, 2324 (1992).
102. H. Aoki, M. Koshino, D. Takeda, H. Morise, and K. Kuroki, Physica E 22, 696 (2004). 10.1016/j.physe.2003.12.102
103. H. Terrones and A. L. Mackay, J. Math. Chem. 15, 183 (1994). 10.1007/BF01277558
104. W. N. Zagotta, Nature 440, 427 (2006) 10.1038/440427a.
105. M. Sotomayor, V. Vasquez, E. Perozo, and K. Schulten, Biophys. J. 92, 886 (2007). 10.1529/biophysj.106.095232