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Unformatted text preview: the area diﬀerence expressed in terms of the mean curvature ∆A d (C (S) − C0 (S))dS, (11) Exchange of lipids between the two leaﬂets has been ignored. This process has been measured and is very slow,
occurring on time scales of ∼ 10min to days.
D Area Diﬀerence Elasticity Model This is a generalization of the BC model to slight extensibility. Here, instead of “hard” ﬁxing the area diﬀerence
between the leaﬂets, we allow it a harmonic variation. Although the elastic stretching energy is huge, and leaﬂet areas
change slightly, the relative change is appreciable when compared to the area diﬀerence ∆A = A+ − A− (± denote
the outer and inner leaﬂets). The ADE energy is Hb = Hb [S]dS = κ(S)
(C (S) − C0 (S))2 +
(∆A − ∆A0 )2 .
2 Ad2 (12) Note that k = 0 corresponds to the original spontaneous curvature model, while k → ∞ limit yields the BC model.
Other constraints can be straightforwardly applied by Legendre transforms. For example, if the interior volume of an
impermeable vesicle and its midplane area are ﬁxed, the thermodynamic potential is
Ω[S] = Hb [S] + γA[S] + P V [S],
where S labels each surface conﬁguration. (13) 5
E Membrane Proteins and Hydrophobic Mismatch Thus far, we have not considered local deformations in bilayer thickness. This has been shown to be important
when considering how embedded or adsorbed proteins distribute themselves. Embedded proteins have diﬀerent parts
that like to be in contact with either the lipid tails or the polarizable, hydrogen bonding headgroups. Therefore, a
protein can “pinch” a lipid bilayer much like the buttons on a mattress. In fact this is sometime called the “mattress”
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- Fall '12