318 Chapter 9. Cooperative transitions in macromolecules[[Student version, January 17, 2003]]
water is just slightly below 0◦C.There will certainly be occasional thermal fluctuations converting
smallpockets of the ice to water. But the probability of such a fluctuation is suppressed, both
bythe free energy difference between bulk ice and water and by the surface-tension energy, which
grows with the area of the small pockets of water. In one dimension, in contrast, the boundary of
adomain of the energetically disfavored state is always justtwo points,nomatter how large that
domain may be. It turns out that this minor-seeming difference is enough to assure that in one
dimension a nonzero fraction of the sample will always be in the energetically disfavored state—the
transition is never quite complete, just as in our polymer〈z/Ltot〉is never quite equal to 1.
9.5 Thermal, chemical, and mechanical switching
Section 9.4 introduced a conceptual framework—cooperativity—for understanding sharp transitions
in macromolecules induced by externally applied forces. We saw how cooperativity sharpens the
transition from random-coil to straight DNA. We found a simple interpretation of the effect in
terms of a big increase in the effective segment length as we turn on cooperativity, from to e^2 γ
(see Equation 9.21).
Some important conformational transitions in macromolecules really are induced by mechanical
forces. For example, the hair cells in your inner ear respond to pressure waves by a mechanically
actuated ion channel. Understanding how such transitions can be sharp, despite the thermally
fluctuating environment, was a major goal of this chapter. But other macromolecules function
byundergoing major conformational transitions in response tochemical or thermalchanges. This
section will show how these transitions, too, can become sharp by virtue of their cooperativity.
9.5.1 The helix–coil transition can be observed using polarized light
Aprotein is a polymer; its monomers are the amino acids. Unlike DNA, whose large charge density
gives it a uniform self-repulsion, the amino-acid monomers of a protein have a rich variety of
attractive and repulsive interactions. These interactions can stabilize definite protein structures.
Forexample, certain sequences of amino acids can form a right-handed helical structure, the
“alpha helix.” In this structure, the free-energy gain of forming hydrogen bonds between monomers
outweighs the entropic tendency of a chain to assume a random walk conformation. Specifically,
H-bonds can form between the oxygen atom in the carbonyl group of monomerkand the hydrogen
atom in the amide group on monomerk+4,but only if the chain assumes the helical shape shown
in Figure 2.19 on page 47.^6
Thus the question of whether a given polypeptide will assume a random coil or an alpha-helix
(ordered) conformation comes down to a competition between conformational entropy and H-bond
formation. Which side wins this competition will depend on the polypeptide’s composition, and on
its thermal and chemical environment. The crossover between helix and coil as the environment
changes can be surprisingly sharp, with nearly total conversion of a sample from one form to
the other upon a temperature change of just a few degrees (see Figure 9.6). (To see why this is
considered “sharp,” recall that a change of a few degrees implies afractionalchange of the thermal
energy of a few degrees divided by 295K.)
(^6) Other ordered, H-bonded structures exist, for example the “beta sheet”; this section will study only polypeptides
whose main competing conformations are the alpha helix and random coil.