8.6. Self-assembly in cells[[Student version, January 17, 2003]] 283
- Thenumerical valuesof the fit parameters fit in with the dense web of other facts we
know about the world. ThusN=3 0 shows that the micelles are too small to scatter
visible light, and indeed their solutions are clear, not milky.
Viewed in this light, introducing an ad-hoc dissociation parameter to improve the fit in Figure 8.6
would be merely a cosmetic measure: Certainly a third free parameter would suffice to match a
third visual feature in the data, but so what?^5 In short,
Afitofamodel to data tells us something interesting only insofar as
a. One or a few fit parameters reproduce several independent features of the
data, or
b. The experimental errors on the data points are exceptionally low, and the fit
reproduces the data to within those errors, or
c. The values of the fit parameters determined by the data mesh with some
independently measured facts about the world.(8.34)
Here are some examples: (a) Figure 3.7 on page 77 matched the entire distribution of molecular
velocities with no fit parameters at all; (b) Figure 9.4 on page 310 in Chapter 9 will be seen to fit
an exceptionally clean dataset; (c) The kink in Figure 8.6 accords with our ideas about the origin
of self-assembly.
In case (c), one could fit a third parameterαto the data, try to create an electrostatic theory
of the dissociation, then see if it successfully predicted the value ofα. But the data shown in
Figure 8.6 are too weak to support such a load of interpretation. Elaborate statistical tools exist to
determine what conclusions may be drawn from a data set, but most often the judgement is made
subjectively. Either way, the maxim is that:The more elaborate the model, the more data we need
to support it.
8.6 Self-assembly in cells
8.6.1 Bilayers self-assemble from two-tailed amphiphiles
Section 8.4.2 began with a puzzle: How can amphiphilic molecules satisfy their hydrophobic tails
in a pure water environment? The answer given there (Figure 8.5) was that they could roll into
asphere. But this solution may not always be available. To pack into a sphere, each surfactant
molecule must fit into something like a cone shape: Its hydrophilic head must be wider than its tail.
More precisely, to form micelles, the volumeNvtailoccupied by the tails ofNsurfactants must be
compatible with the surface areaNaheadoccupied by the heads for someN.While some molecules,
like SDS, may be comfortable with this arrangement, it doesn’t work for two-tailed phospholipid
molecules like thephosphatidylcholines(or “PCs” for short; see Figures 2.16 and 8.3). We have not
yetexhausted Nature’s cleverness, however. An alternative packing strategy, the bilayer membrane,
also presents the hydrophobic tails only to each other. Figure 2.24 on page 53 shows a slice through
abilayer made of PC. To understand the figure, imagine the double row of molecules shown as
extending upward and downward on the page, and out of and into the page, to form a double
blanket. Thus the bilayer’s midplane is a two-dimensional surface, separating the half-space to the
left of the figure from the half-space to the right.
(^5) As the physicist Eugene Wigner memorably put it, “If you give me two free parameters, I can describe an
elephant. If you give me three, I can make him wiggle his tail.”