Lecture #3 Notes

D area dierence elasticity model this is a

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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) kπ (C (S) − C0 (S))2 + (∆A − ∆A0 )2 . 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” model. u− £¤ £¤ £¤ £¤ £¤ £¤ £¤ ¡£¤¡¡¡£¤¡¡¡£¤¡¡¡£¤¡£¤¡¡£¤¡£¤¡¡¡£¤¡¡¡£¤¡£¤¡¡¡£¤ £¤ £¤ £¤ £¤ £¤ £¤ £¤ ¤ ¤¤ ¤¤ ¤¤ ¤¤ £¡¡£¡£¡¡£¡£¡¡£¡£¡¡¡¡¡¡£¡£¡¡£¡£¡¡¡£¡£¡ ¡£¤¡¡¡£¤¡¡¡£¤¡¡¡£¤¡£¤¡¡£¤¡£¤¡¡¡£¤¡¡¡£¤¡£¤¡¡¡£¤ £¤ ¤ ¤ ¤ ¤ ¤ ¤¤ ¤¤ ¤¤ ¤¤ £¡¡£¡£¡¡£¡£¡¡£¡£¡¡¡¡¡¡£¡£¡¡£¡£¡¡¡£¡£¡ ¡£¤¡¡¡£¤¡¡¡£¤¡¡¡£¤¡£¤¡¡...
View Full Document

Ask a homework question - tutors are online