320 Chapter 9. Cooperative transitions in macromolecules[[Student version, January 17, 2003]]
Suppose we pass a beam of polarized light rays through a suspension of perfectly spherical
particles in water. The light will in general scatter: It loses some of its perfect uniformity in
direction and polarization, emerging with a slightly lowerdegreeof polarization. This loss of purity
can tell us something about the density of suspended particles. What we will not find, however,
is any net rotation in thedirectionof polarization of the light. We can understand this important
fact via a symmetry argument. Suppose that our suspension rotated the angle of polarized light by
an angleθ.Imagine a second solution, in which every atom of the first has been reflected through
amirror. Every particle of the second solution is just as stable as in the first, since the laws of
atomic physics are invariant under reflection. And the second solution will rotate the polarization
of incident light by exactly the opposite angle from that of the first, that is, by−θ.But a spherical
object isunchangedupon reflection, and hence so is a random distribution (a suspension) of such
objects. So we must also have that both solutions have thesamevalue ofθ,orinother words that
θ=−θ=0.
Now consider a suspension of identical, but not necessarily spherical, molecules. If each molecule
is equivalent to its mirror image (as is true of water, for example), then the argument just given
again implies thatθ=0—and that’s what we observe in water. But most biological molecules are
notequivalent to their mirror images (see Figure 1.5 on page 22). To drive the point home, it’s
helpful to get a corkscrew and find its handedness, following the caption to Figure 2.19 on page 47.
Next, look at the same corkscrew (or Figure 2.19) in a mirror and discover that its mirror image
has the opposite handedness.^7 The two shapes are genuinely inequivalent: You cannot make the
mirror image coincide with the original by turning the corkscrew end-over-end, nor by any other
kind of rotation. Structures lacking mirror symmetry are calledchiral.
Solutions of chiral molecules really do rotate the polarization of incident light. Most interesting
for our present purposes, asinglechemical species may have different conformations with differing
degreesof chirality (reflection asymmetry). Thus, while the individual amino acids of a protein may
individually be chiral, the protein’s ability to rotate polarized light at certain wavelengths changes
dramatically when the individual monomers organize into the superstructure of the alpha helix. In
fact,
The observed optical rotation of a solution of polypeptide is a linear function
of the fraction of amino acid monomers in the alpha-helical form.(9.22)
Observingθthus lets us measure the degree of a polypeptide’s conversion from random-coil to
alpha-helix conformation. This technique is used in the food industry, whereθis used to monitor
the degree to which starches have been cooked.
Figure 9.6 shows some classic experimental data obtained in 1959 by P. Doty and K. Iso, together
with the results of the analysis developed in Section 9.5.3. These experiments monitored the optical
rotation of an artificial polypeptide in solution while raising its temperature. At a critical value of
T,the rotation abruptly changed from the value typical for isolated monomers to some other value,
signaling the self-assembly of alpha helices.
T 2 Section 9.5.1′on page 344 defines the specific optical rotation, a more refined measurement of
asolution’s rotatory power.
(^7) But don’t look at yourhandin the mirror while doing this! After all, the mirror image of your right hand looks
like your left hand.