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One of the main differences between monolayers and bilayers in the context of bending is that any mismatch in the areas of outer and inner layers in the latter can induce spontaneous bending. This effect can cooperate with or compete against the spontaneous curvature arising from local properties of lipids such as lipid packing as detailed later (see subsection Bilayers in the Results). However our description in this section is common for both cases
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One of the main differences between monolayers and bilayers in the context of bending is that any mismatch in the areas of outer and inner layers in the latter can induce spontaneous bending. This effect can cooperate with or compete against the spontaneous curvature arising from local properties of lipids such as lipid packing as detailed later (see subsection Bilayers in the Results). However our description in this section is common for both cases.
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See ref 3 for a pedagogical estimation of γ. Recall γ is conjugate to area each lipid occupies. This has to be differentiated from the macroscopic counterpart, that is, the one conjugate to the total membrane area, which varies with the number of constituents lipids. (28)
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See ref 3 for a pedagogical estimation of γ. Recall γ is conjugate to area each lipid occupies. This has to be differentiated from the macroscopic counterpart, that is, the one conjugate to the total membrane area, which varies with the number of constituents lipids. (28)
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What is left out is the electrostatic screening due to free divalent salts, typically in the low millimolar range. To justify this, first note that the surface potential of a highly charged surface is almost independent of bulk salt concentrations (see Chapter 12 of ref 4). On the other hand, in the two-state model, free ions can influence counterion association only through the surface potential (see, for instance, eq 10 in ref 20). It is thus clear that free ions will contribute to counterion condensation mainly through their entropy, more precisely the entropic penalty for bringing them onto the membrane surface
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What is left out is the electrostatic screening due to free divalent salts, typically in the low millimolar range. To justify this, first note that the surface potential of a highly charged surface is almost independent of bulk salt concentrations (see Chapter 12 of ref 4). On the other hand, in the two-state model, free ions can influence counterion association only through the surface potential (see, for instance, eq 10 in ref 20). It is thus clear that free ions will contribute to counterion condensation mainly through their entropy, more precisely the entropic penalty for bringing them onto the membrane surface.
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Note that since the thickness is not necessarily the same for the two layers if bent, the interface between the layers is not always identical to the midplane. But the difference is minimal, especially for small C
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Note that since the thickness is not necessarily the same for the two layers if bent, the interface between the layers is not always identical to the midplane. But the difference is minimal, especially for small C.
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39
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77956561940
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This does not mean that two neutral surfaces are needed for describing bilayer bending. A common neutral surface can be constructed as discussed here and in ref 36. In our case, however, the midplane essentially coincides with the bilayer neutral surface, as discussed in subsection Neutral Surface in section Results
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This does not mean that two neutral surfaces are needed for describing bilayer bending. A common neutral surface can be constructed as discussed here and in ref 36. In our case, however, the midplane essentially coincides with the bilayer neutral surface, as discussed in subsection Neutral Surface in section Results.
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