Density distributions, bilayer membrane

For bilayer membrane problems it may be a mistake to treat permeation through the membrane as a single diffusion process. In the first place it is extremely unlikely that the distribution of permeant molecules across the membrane is described by the diffusion equation. Second, the permeation may be related to lateral density fluctuations in the membrane, giving a quite nonuniform lateral distribution of the permeant molecules near the membrane surface at any instant. 

Figure 4 The modified stalk mechanism of membrane fusion and inverted phase formation, (a) planar lamellar (La) phase bilayers (b) the stalk intermediate the stalk is cylindrically-symmetrical about the dashed vertical axis (c) the TMC (trans monolayer contact) or hemifusion structure the TMC can rupture to form a fusion pore, referred to as interlamellar attachment, ILA (d) (e) If ILAs accumulate in large numbers, they can rearrange to form Qn phases, (f) For systems close to the La/H phase boundary, TMCs can also aggregate to form H precursors and assemble Into H domains. The balance between Qn and H phase formation Is dictated by the value of the Gaussian curvature elastic modulus of the bIlayer (reproduced from (25) with permission of the Biophysical Society) The stalk in (b) is structural unit of the rhombohedral phase (b ) electron density distribution for the stalk fragment of the rhombohedral phase, along with a cartoon of a stalk with two lipid monolayers merged to form a hourglass structure (reproduced from (26) with permission of the Biophysical Society).

Fig. 10 Left Mean-field equation of state for the hydrophobic A strand melt, for = —15.15 and u>aaa = 0.564375 (see (15)). The vertical green line marks, at P/kgT = 0, the coexistence density of the melt with its vapor, Pa = 20. The red line marks the tangent to the P/kgT curve at P/ksT = 0,Pa = 20. Its slope is inversely proportional to the melt compressibility. Right The density distribution of the A and B bilayer components is shown across a free edge, membrane patch (see inset) which is thin in the z direction (i.e., vertically to the graph plane). The red and the green symbols correspond to the densities of the hydrophobic and the hydrophilic segments, respectively...

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