No Access Submitted: 12 December 2017 Accepted: 10 January 2018 Published Online: 02 February 2018
J. Chem. Phys. 148, 054902 (2018);
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  • Salvatore Assenza
  • Raffaele Mezzenga
We perform a simulation study of the diffusion of small solutes in the confined domains imposed by inverse bicontinuous cubic phases for the primitive, diamond, and gyroid symmetries common to many lipid/water mesophase systems employed in experiments. For large diffusing domains, the long-time diffusion coefficient shows universal features when the size of the confining domain is renormalized by the Gaussian curvature of the triply periodic minimal surface. When bottlenecks are widely present, they become the most relevant factor for transport, regardless of the connectivity of the cubic phase.
The authors are indebted to R. Ghanbari, C. Speziale, and L. Antognini for useful discussions, and to G. Schröeder-Turk both for insightful discussions and for providing the numerical data on the distribution of local radii for the various IBCPs. S.A. acknowledges support from the Swiss National Science Foundation under the Grant No. 200021_162355.
  1. 1. E. M. Landau and J. P. Rosenbusch, “Lipidic cubic phases: A novel concept for the crystallization of membrane proteins,” Proc. Natl. Acad. Sci. U. S. A. 93, 14532–14535 (1996)., Google ScholarCrossref
  2. 2. C. Speziale, L. S. Manni, C. Manatschal, E. M. Landau, and R. Mezzenga, “A macroscopic H+ and Cl ions pump via reconstitution of EcClC membrane proteins in lipidic cubic mesophases,” Proc. Natl. Acad. Sci. U. S. A. 113, 7491–7496 (2016)., Google ScholarCrossref
  3. 3. C. Fong, T. Le, and C. J. Drummond, “Lyotropic liquid crystal engineering–ordered nanostructured small molecule amphiphile self-assembly materials by design,” Chem. Soc. Rev. 41, 1297–1322 (2012)., Google ScholarCrossref
  4. 4. R. Mezzenga, P. Schurtenberger, A. Burbidge, and M. Michel, “Understanding foods as soft materials,” Nat. Mater. 4, 729–740 (2005)., Google ScholarCrossref
  5. 5. X. Mulet, B. J. Boyd, and C. J. Drummond, “Advances in drug delivery and medical imaging using colloidal lyotropic liquid crystalline dispersions,” J. Colloid Interface Sci. 393, 1–20 (2013)., Google ScholarCrossref
  6. 6. Z. A. Almsherqi, S. D. Kohlwein, and Y. Deng, “Cubic membranes: A legend beyond the flatland* of cell membrane organization,” J. Cell Biol. 173, 839–844 (2006)., Google ScholarCrossref
  7. 7. E. L. Snapp, R. S. Hegde, M. Francolini, F. Lombardo, S. Colombo, E. Pedrazzini, N. Borgese, and J. Lippincott-Schwartz, “Formation of stacked er cisternae by low affinity protein interactions,” J. Cell Biol. 163, 257–269 (2003)., Google ScholarCrossref
  8. 8. Y. Deng, M. Marko, K. F. Buttle, A. Leith, M. Mieczkowski, and C. A. Mannella, “Cubic membrane structure in amoeba (chaos carolinensis) mitochondria determined by electron microscopic tomography,” J. Struct. Biol. 127, 231–239 (1999)., Google ScholarCrossref
  9. 9. S. T. Hyde and G. E. Schröder-Turk, “Geometry of interfaces: Topological complexity in biology and materials,” Interface Focus 2, 529 (2012)., Google ScholarCrossref
  10. 10. N. Garti, P. Somasundaran, and R. Mezzenga, Self-Assembled Supramolecular Architectures: Lyotropic Liquid Crystals (John Wiley & Sons, 2012), Vol. 3. Google ScholarCrossref
  11. 11. J. Briggs, H. Chung, and M. Caffrey, “The temperature-composition phase diagram and mesophase structure characterization of the monoolein/water system,” J. Phys. II 6, 723–751 (1996)., Google ScholarCrossref
  12. 12. R. Templer, J. Seddon, N. Warrender, A. Syrykh, Z. Huang, R. Winter, and J. Erbes, “Inverse bicontinuous cubic phases in 2:1 fatty acid/phosphatidylcholine mixtures. The effects of chain length, hydration, and temperature,” J. Phys. Chem. B 102, 7251–7261 (1998)., Google ScholarCrossref
  13. 13. D. C. Turner, Z.-G. Wang, S. M. Gruner, D. A. Mannock, and R. N. McElhaney, “Structural study of the inverted cubic phases of di-dodecyl alkyl-β-d-glucopyranosyl-rac-glycerol,” J. Phys. II 2, 2039–2063 (1992)., Google ScholarCrossref
  14. 14. J. Barauskas, M. Johnsson, and F. Tiberg, “Self-assembled lipid superstructures: Beyond vesicles and liposomes,” Nano Lett. 5, 1615–1619 (2005)., Google ScholarCrossref
  15. 15. R. Negrini and R. Mezzenga, “Diffusion, molecular separation, and drug delivery from lipid mesophases with tunable water channels,” Langmuir 28, 16455–16462 (2012)., Google ScholarCrossref
  16. 16. R. Mezzenga, C. Meyer, C. Servais, A. I. Romoscanu, L. Sagalowicz, and R. C. Hayward, “Shear rheology of lyotropic liquid crystals: A case study,” Langmuir 21, 3322–3333 (2005)., Google ScholarCrossref
  17. 17. A. I. Tyler, H. M. Barriga, E. S. Parsons, N. L. McCarthy, O. Ces, R. V. Law, J. M. Seddon, and N. J. Brooks, “Electrostatic swelling of bicontinuous cubic lipid phases,” Soft Matter 11, 3279–3286 (2015)., Google ScholarCrossref
  18. 18. R. Negrini and R. Mezzenga, “ph-responsive lyotropic liquid crystals for controlled drug delivery,” Langmuir 27, 5296–5303 (2011)., Google ScholarCrossref
  19. 19. I. Martiel, N. Baumann, J. J. Vallooran, J. Bergfreund, L. Sagalowicz, and R. Mezzenga, “Oil and drug control the release rate from lyotropic liquid crystals,” J. Controlled Release 204, 78–84 (2015)., Google ScholarCrossref
  20. 20. A. Zabara and R. Mezzenga, “Controlling molecular transport and sustained drug release in lipid-based liquid crystalline mesophases,” J. Controlled Release 188, 31–43 (2014)., Google ScholarCrossref
  21. 21. R. Negrini, W.-K. Fong, B. J. Boyd, and R. Mezzenga, “ph-responsive lyotropic liquid crystals and their potential therapeutic role in cancer treatment,” Chem. Commun. 51, 6671–6674 (2015)., Google ScholarCrossref
  22. 22. E. Nazaruk, P. Miszta, S. Filipek, E. Gorecka, E. M. Landau, and R. Bilewicz, “Lyotropic cubic phases for drug delivery: Diffusion and sustained release from the mesophase evaluated by electrochemical methods,” Langmuir 31, 12753–12761 (2015)., Google ScholarCrossref
  23. 23. J. Clogston, G. Craciun, D. Hart, and M. Caffrey, “Controlling release from the lipidic cubic phase by selective alkylation,” J. Controlled Release 102, 441–461 (2005)., Google ScholarCrossref
  24. 24. J. Clogston and M. Caffrey, “Controlling release from the lipidic cubic phase. Amino acids, peptides, proteins and nucleic acids,” J. Controlled Release 107, 97–111 (2005)., Google ScholarCrossref
  25. 25. K. W. Lee, T.-H. Nguyen, T. Hanley, and B. J. Boyd, “Nanostructure of liquid crystalline matrix determines in vitro sustained release and in vivo oral absorption kinetics for hydrophilic model drugs,” Int. J. Pharm. 365, 190–199 (2009)., Google ScholarCrossref
  26. 26. S. Phan, W.-K. Fong, N. Kirby, T. Hanley, and B. J. Boyd, “Evaluating the link between self-assembled mesophase structure and drug release,” Int. J. Pharm. 421, 176–182 (2011)., Google ScholarCrossref
  27. 27. A. Zabara, R. Negrini, O. Onaca-Fischer, and R. Mezzenga, “Perforated bicontinuous cubic phases with ph-responsive topological channel interconnectivity,” Small 9, 3602–3609 (2013)., Google ScholarCrossref
  28. 28. T. G. Meikle, S. Yao, A. Zabara, C. E. Conn, C. J. Drummond, and F. Separovic, “Predicting the release profile of small molecules from within the ordered nanostructured lipidic bicontinuous cubic phase using translational diffusion coefficients determined by pfg-nmr,” Nanoscale 9, 2471–2478 (2017)., Google ScholarCrossref
  29. 29. R. Ghanbari, S. Assenza, A. Saha, and R. Mezzenga, “Diffusion of polymers through periodic networks of lipid-based nanochannels,” Langmuir 33, 3491–3498 (2017)., Google ScholarCrossref
  30. 30. M. H. Jacobs, Diffusion Processes (Springer Science & Business Media, 1967). Google ScholarCrossref
  31. 31. B. Jönsson, H. Wennerström, P. Nilsson, and P. Linse, “Self-diffusion of small molecules in colloidal systems,” Colloid Polym. Sci. 264, 77–88 (1986)., Google ScholarCrossref
  32. 32. D. M. Anderson and H. Wennerstroem, “Self-diffusion in bicontinuous cubic phases, L3 phases, and microemulsions,” J. Phys. Chem. 94, 8683–8694 (1990)., Google ScholarCrossref
  33. 33. G. Allaire, “Homogenization and two-scale convergence,” SIAM J. Math. Anal. 23, 1482–1518 (1992)., Google ScholarCrossref
  34. 34. R. Zwanzig, “Diffusion past an entropy barrier,” J. Phys. Chem. 96, 3926–3930 (1992)., Google ScholarCrossref
  35. 35. D. Reguera and J. Rubi, “Kinetic equations for diffusion in the presence of entropic barriers,” Phys. Rev. E 64, 061106 (2001)., Google ScholarCrossref
  36. 36. J. Kalnin, E. Kotomin, and J. Maier, “Calculations of the effective diffusion coefficient for inhomogeneous media,” J. Phys. Chem. Solids 63, 449–456 (2002)., Google ScholarCrossref
  37. 37. A. M. Berezhkovskii, V. Y. Zitserman, and S. Y. Shvartsman, “Effective diffusivity in periodic porous materials,” J. Chem. Phys. 119, 6991–6993 (2003)., Google ScholarScitation, ISI
  38. 38. N. S. Gov, “Diffusion in curved fluid membranes,” Phys. Rev. E 73, 041918 (2006)., Google ScholarCrossref
  39. 39. Z. Schuss, A. Singer, and D. Holcman, “The narrow escape problem for diffusion in cellular microdomains,” Proc. Natl. Acad. Sci. 104, 16098–16103 (2007)., Google ScholarCrossref
  40. 40. M. Wang and N. Pan, “Predictions of effective physical properties of complex multiphase materials,” Mater. Sci. Eng.: R: Rep. 63, 1–30 (2008)., Google ScholarCrossref
  41. 41. P. S. Burada, P. Hänggi, F. Marchesoni, G. Schmid, and P. Talkner, “Diffusion in confined geometries,” ChemPhysChem 10, 45–54 (2009)., Google ScholarCrossref
  42. 42. N. Ogawa, “Curvature-dependent diffusion flow on a surface with thickness,” Phys. Rev. E 81, 061113 (2010)., Google ScholarCrossref
  43. 43. S. Martens, G. Schmid, L. Schimansky-Geier, and P. Hänggi, “Entropic particle transport: Higher-order corrections to the Fick-Jacobs diffusion equation,” Phys. Rev. E 83, 051135 (2011)., Google ScholarCrossref
  44. 44. C. V. Valdes, “Effective diffusion in the region between two surfaces,” Phys. Rev. E 94, 022121 (2016)., Google ScholarCrossref
  45. 45. R. Hołyst, D. Plewczyński, A. Aksimentiev, and K. Burdzy, “Diffusion on curved, periodic surfaces,” Phys. Rev. E 60, 302 (1999)., Google ScholarCrossref
  46. 46. D. Plewczyński and R. Hołyst, “Reorientational angle distribution and diffusion coefficient for nodal and cylindrical surfaces,” J. Chem. Phys. 113, 9920–9929 (2000)., Google ScholarScitation
  47. 47. E. Sanz and D. Marenduzzo, “Dynamic Monte Carlo versus Brownian dynamics: A comparison for self-diffusion and crystallization in colloidal fluids,” J. Chem. Phys. 132, 194102 (2010)., Google ScholarScitation, ISI
  48. 48. H. Von Schnering and R. Nesper, “Nodal surfaces of fourier series: Fundamental invariants of structured matter,” Z. Phys. B: Condens. Matter 83, 407–412 (1991)., Google ScholarCrossref
  49. 49. I. L. Novak, P. Kraikivski, and B. M. Slepchenko, “Diffusion in cytoplasm: Effects of excluded volume due to internal membranes and cytoskeletal structures,” Biophys. J. 97, 758–767 (2009)., Google ScholarCrossref
  50. 50. E. L. Thomas, D. M. Anderson, C. S. Henkee, and D. Hoffman, “Periodic area-minimizing surfaces in block copolymers,” Nature 334, 598–601 (1988)., Google ScholarCrossref
  51. 51. R. M. Kaufmann, S. Khlebnikov, and B. Wehefritz-Kaufmann, “The geometry of the double gyroid wire network: Quantum and classical,” J. Noncommutative Geom. 6, 623–664 (2012)., Google ScholarCrossref
  52. 52. B. Halperin, S. Feng, and P. N. Sen, “Differences between lattice and continuum percolation transport exponents,” Phys. Rev. Lett. 54, 2391 (1985)., Google ScholarCrossref
  53. 53. G. Schröder-Turk, S. Ramsden, A. Christy, and S. Hyde, “Medial surfaces of hyperbolic structures,” Eur. Phys. J. B 35, 551–564 (2003)., Google ScholarCrossref
  54. 54. A. Aharony and D. Stauffer, Introduction to Percolation Theory (Taylor & Francis, 2003). Google Scholar
  55. 55. R. Mezzenga, J. Ruokolainen, G. H. Fredrickson, E. J. Kramer, D. Moses, A. J. Heeger, and O. Ikkala, “Templating organic semiconductors via self-assembly of polymer colloids,” Science 299, 1872–1874 (2003)., Google ScholarCrossref
  56. 56. L. M. Antognini, S. Assenza, C. Speziale, and R. Mezzenga, “Quantifying the transport properties of lipid mesophases by theoretical modelling of diffusion experiments,” J. Chem. Phys. 145, 084903 (2016)., Google ScholarScitation
  57. 57. D. S. ViswanathTushar, T. K. Ghosh, D. H. L. Prasad, N. V. Dutt, and K. Y. Rani, Viscosity of Liquids. Theory, Estimation, Experiment, and Data (Springer, 2007). Google Scholar
  58. 58. W. M. Haynes, D. R. Lide, and T. J. Bruno, CRC Handbook of Chemistry and Physics, 95th ed. (CRC Press, 2014). Google ScholarCrossref
  59. 59. J. Kim, W. Lu, W. Qiu, L. Wang, M. Caffrey, and D. Zhong, “Ultrafast hydration dynamics in the lipidic cubic phase: Discrete water structures in nanochannels,” J. Phys. Chem. B 110, 21994–22000 (2006)., Google ScholarCrossref
  60. 60. L. Longsworth, “Diffusion measurements, at 25, of aqueous solutions of amino acids, peptides and sugars,” J. Am. Chem. Soc. 75, 5705–5709 (1953)., Google ScholarCrossref
  61. 61. C. A. Lambert, L. H. Radzilowski, and E. L. Thomas, “Triply periodic level surfaces as models for cubic tricontinuous block copolymer morphologies,” Philos. Trans. R. Soc., A 354, 2009–2023 (1996)., Google ScholarCrossref
  62. 62. G. E. Schröder-Turk, A. Fogden, and S. T. Hyde, “Bicontinuous geometries and molecular self-assembly: Comparison of local curvature and global packing variations in genus-three cubic, tetragonal and rhombohedral surfaces,” Eur. Phys. J. B 54, 509–524 (2006)., Google ScholarCrossref
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