284 Chapter 8. Chemical forces and self-assembly[[Student version, January 17, 2003]]
Figure 8.7: (Photomicrograph.) Bilayer structures formed by nonanoic acid, one of several bilayer-forming fatty
acids identified in meteorites. The vesicles have been stained with rhodamine, a fluorescent dye. [Digital image
kindly supplied by D. Deamer.]
Your Turn 8i
a. Suppose thatNamphiphiles pack into a spherical micelle of radiusR. Find two relations
betweenahead,vtail,R,andN.Combine these into a single relation betweenahead,vtail,andR.
b. Suppose instead that amphiphiles pack into a planar bilayer of thickness 2d.Find a relation
betweenahead,vtail,andd.
c. In each of the two situations above suppose that the hydrocarbon tails of the amphiphiles
cannot stretch beyond a certain length .Find the resulting geometric constraints onaheadand
vtail.
d. Why are one-tail amphiphiles likely to form micelles, while two-tail amphiphiles are likely to
form bilayers?Two-chain amphiphiles occurring naturally in cells generally belong to a chemical class called
“phospholipids.” We can already understand several reasons why Nature has chosen the phospho-
lipid bilayer membrane as the most ubiquitous architectural component of cells:
- The self-assembly of two-chain phospholipids (like PC) into bilayers is even more avid than
that of one-chain surfactants (like SDS) into micelles. The reason is simply that the hy-
drophobic cost of exposingtwochains to water is twice as great as for one chain. This free
energy costenters the equilibrium constant and hence the CMC, a measure of the chemi-
cal drive to self-assembly, via its exponential. There’s a big difference between e−/kBTrand
e−^2 /kBTr,sothe CMC for phospholipid formation is tiny. Membranes resist dissolving even
in environments with extremely low phospholipid concentration. - Similarly, phospholipid membranes automatically form closed bags, since any edge to the
planar structure in Figure 2.24 would expose the hydrocarbon chains to the surrounding
water. Such bags, orbilayer vesicles,can be almost unlimited in extent. In particular it is
straightforward to make “giant” vesicles of radius 10μm,the size of eukaryotic cells. This
is many thousands of times larger than the thickness of the membrane; giant vesicles are
self-assembled structures composed of tens of millions of individual phospholipid molecules.