References
1. Smith R, Tanford C (1972) The critical micelle concentration of L α -dipalmitoylphosphatidylcholine in water and water/methanol solutions. J Mol Biol 67(1):75–83
2. Israelachvili JN, Mitchell DJ, Ninham BW (1976) Theory of self-assembly of hydrocarbon
amphiphiles into micelles and bilayers. J Chem Soc Faraday Trans 72(2):1525–1568
3. Rawicz W, Olbrich K, McIntosh T, Needham D, Evans E (2000) Effect of chain length and
unsaturation on elasticity of lipid bilayers. Biophys J 79:328–339
4. Canham PB (1970) The minimum energy of bending as a possible explanation of the
biconcave shape of the human red blood cell. J Theoret Biol 26(1):61–81
5. Helfrich W (1973) Elastic properties of lipid bilayers—theory and possible experiments.
Z Naturforsch C 28(11):693–703
6. Evans EA (1974) Bending resistance and chemically induced moments in membrane bilayers. Biophys J 14(12):923–931
7. Helfrich W (1974) The size of bilayer vesicles generated by sonication. Phys Lett A 50
(2):115–116
8. Kreyszig E (1991) Differential geometry. Dover, New York
9. do Carmo M (1976) Differential geometry of curves and surfaces. Prentice Hall, Englewood
Cliffs
10. Lipowsky R, Grotehans S (1993) Hydration versus protrusion forces between lipid bilayers.
Europhys Lett 23:599–604
11. Lipowsky R, Grotehans S (1993) Renormalization of hydration forces by collective protrusion modes. Biophys Chem 49:27–37
12. Goetz R, Gompper G, Lipowsky R (1999) Mobility and elasticity of self-assembled membranes. Phys Rev Lett 82:221–224
13. Brandt EG, Edholm O (2010) Stretched exponential dynamics in lipid bilayer simulations.
J Chem Phys 133:115101
14. Brandt EG, Braun AR, Sachs JN, Nagle JF, Edholm O (2011) Interpretation of fluctuation
spectra in lipid bilayer simulations. Biophys J 100:2104–2111
15. Lindahl E, Edholm O (2000) Mesoscopic undulations and thickness fluctuations in lipid
bilayers from molecular dynamics simulations. Biophys J 79(1):426–433
16. Owicki JC, Springgate MW, McConnell HM (1978) Theoretical study of protein–lipid
interactions in bilayer membranes. Proc Natl Acad Sci USA 75:1616–1619
17. Owicki JC, McConnell HM (1979) Theory of protein–lipid and protein–protein interactions
in bilayer membranes. Proc Natl Acad Sci USA 76:4750–4754
18. Huang HW (1986) Deformation free energy of bilayer membrane and its effect on gramicidin
channel lifetime. Biophys J 50:1061–1070
19. Sperotto MM, Mouritsen OG (1991) Monte Carlo simulation of lipid order parameter profiles
near integral membrane proteins. Biophys J 59:261–270
20. Dan N, Pincus P, Safran SA (1993) Membrane-induced interactions between inclusions.
Langmuir 9:2768–2771
21. Dan N, Berman A, Pincus P, Safran SA (1994) Membrane-induced interactions between
inclusions. J Phys II (France) 4:1713
22. Aranda-Espinoza H, Berman A, Dan N, Pincus P, Safran S (1996) Interaction between
inclusions embedded in membranes. Biophys J 71:648
23. Huang HW (1995) Elasticity of lipid bilayer interacting with amphiphilic helical peptides.
J Phys II (France) 5:1427–1431
24. Nielsen C, Goulian M, Andersen OS (2000) Energetics of inclusion-induced bilayer deformations. Biophys J 74:1966–1983
25. Harroun TA, Heller WT, Weiss TM, Yang L, Huang HW (1999) Theoretical analysis of
hydrophobic matching and membrane-mediated interactions in lipid bilayers containing
gramicidin. Biophys J 76:3176–3185
Computational Studies of Biomembrane Systems: Theoretical Considerations. . .
271
1. Smith R, Tanford C (1972) The critical micelle concentration of L α -dipalmitoylphosphatidylcholine in water and water/methanol solutions. J Mol Biol 67(1):75–83
2. Israelachvili JN, Mitchell DJ, Ninham BW (1976) Theory of self-assembly of hydrocarbon
amphiphiles into micelles and bilayers. J Chem Soc Faraday Trans 72(2):1525–1568
3. Rawicz W, Olbrich K, McIntosh T, Needham D, Evans E (2000) Effect of chain length and
unsaturation on elasticity of lipid bilayers. Biophys J 79:328–339
4. Canham PB (1970) The minimum energy of bending as a possible explanation of the
biconcave shape of the human red blood cell. J Theoret Biol 26(1):61–81
5. Helfrich W (1973) Elastic properties of lipid bilayers—theory and possible experiments.
Z Naturforsch C 28(11):693–703
6. Evans EA (1974) Bending resistance and chemically induced moments in membrane bilayers. Biophys J 14(12):923–931
7. Helfrich W (1974) The size of bilayer vesicles generated by sonication. Phys Lett A 50
(2):115–116
8. Kreyszig E (1991) Differential geometry. Dover, New York
9. do Carmo M (1976) Differential geometry of curves and surfaces. Prentice Hall, Englewood
Cliffs
10. Lipowsky R, Grotehans S (1993) Hydration versus protrusion forces between lipid bilayers.
Europhys Lett 23:599–604
11. Lipowsky R, Grotehans S (1993) Renormalization of hydration forces by collective protrusion modes. Biophys Chem 49:27–37
12. Goetz R, Gompper G, Lipowsky R (1999) Mobility and elasticity of self-assembled membranes. Phys Rev Lett 82:221–224
13. Brandt EG, Edholm O (2010) Stretched exponential dynamics in lipid bilayer simulations.
J Chem Phys 133:115101
14. Brandt EG, Braun AR, Sachs JN, Nagle JF, Edholm O (2011) Interpretation of fluctuation
spectra in lipid bilayer simulations. Biophys J 100:2104–2111
15. Lindahl E, Edholm O (2000) Mesoscopic undulations and thickness fluctuations in lipid
bilayers from molecular dynamics simulations. Biophys J 79(1):426–433
16. Owicki JC, Springgate MW, McConnell HM (1978) Theoretical study of protein–lipid
interactions in bilayer membranes. Proc Natl Acad Sci USA 75:1616–1619
17. Owicki JC, McConnell HM (1979) Theory of protein–lipid and protein–protein interactions
in bilayer membranes. Proc Natl Acad Sci USA 76:4750–4754
18. Huang HW (1986) Deformation free energy of bilayer membrane and its effect on gramicidin
channel lifetime. Biophys J 50:1061–1070
19. Sperotto MM, Mouritsen OG (1991) Monte Carlo simulation of lipid order parameter profiles
near integral membrane proteins. Biophys J 59:261–270
20. Dan N, Pincus P, Safran SA (1993) Membrane-induced interactions between inclusions.
Langmuir 9:2768–2771
21. Dan N, Berman A, Pincus P, Safran SA (1994) Membrane-induced interactions between
inclusions. J Phys II (France) 4:1713
22. Aranda-Espinoza H, Berman A, Dan N, Pincus P, Safran S (1996) Interaction between
inclusions embedded in membranes. Biophys J 71:648
23. Huang HW (1995) Elasticity of lipid bilayer interacting with amphiphilic helical peptides.
J Phys II (France) 5:1427–1431
24. Nielsen C, Goulian M, Andersen OS (2000) Energetics of inclusion-induced bilayer deformations. Biophys J 74:1966–1983
25. Harroun TA, Heller WT, Weiss TM, Yang L, Huang HW (1999) Theoretical analysis of
hydrophobic matching and membrane-mediated interactions in lipid bilayers containing
gramicidin. Biophys J 76:3176–3185
Computational Studies of Biomembrane Systems: Theoretical Considerations. . .
271