328 Chapter 9. Cooperative transitions in macromolecules[[Student version, January 17, 2003]]
Uext=−fz(Equation 9.7). This term altered the equilibrium between forward- and backward-
pointing monomers from equally probable (at low force) to mainly forward (at high force). Sec-
tion 6.7 on page 199 gave another example, where mechanical force altered the balance between the
folded and unfolded states of a single RNA molecule.
Here are three more examples of Idea 9.27.
Overstretching DNA DNA in its ordinary state adopts a conformation called the “B” form
(Figure 2.17), in which the two chains of bases each stack on each other like the steps of a spiral
staircase. The sugar-phosphate backbones of the two chains then wind around the center line. That
is, the two backbones are far from being straight. The distance traveled along the molecule’s axis
when we take one step up the staircase is thus considerably shorter than it would be if the backbones
were straight. Idea 9.27 then suggests that pulling on the two ends could alter the equilibrium
between B-DNA and some other, “stretched,” form, in which the backbones are straightened.
Figure 9.3 shows thisoverstretching transitionas region “D” of the graph. At a critical value of
the applied force, DNA abandons the linear-elasticity behavior studied in Section 9.4.2 and begins
to spend most of its time in a new state, about 60% longer than before. A typical value forfcritin
lambda phage DNA is 65pN.The sharpness of this transition implies that it is highly cooperative.
Unzipping DNA It is even possible to tear the two strands of DNA apart without breaking
them. F. Heslot and coauthors accomplished this in 1997 by attaching the two strands at one end
of a DNA duplex to a mechanical stretching apparatus. They and later workers found the average
force needed to “unzip” the strands to be about 10–15pN.
Unfolding titin Proteins, too, undergo massive structural changes in response to mechanical
force. For example, titin is a structural protein found in muscle cells. In its native state, titin
consists of a chain of globular domains. Under increasing tension, the domains pop open one at
atime, somewhat like the RNA hairpin in Section 6.7 on page 199, leading to a sawtooth-shaped
force-extension relation. Upon release of the applied force, titin resumes its original structure, ready
to be stretched again.
9.6 Allostery
So far, this chapter has focused on showing how nearest-neighbor cooperativity can create sharp
transitions between conformations of rather simple polymers. It is a very big step to go from
these model systems to proteins, with complicated, nonlocal interactions between residues that are
distant along the chain backbone. Indeed we will not attempt any more detailed calculations. Let
us instead look at some biological consequences of the principle that cooperative effects of many
weak interactions can yield definite conformations with sharp transitions.
9.6.1 Hemoglobin binds four oxygen molecules cooperatively
Returning to this chapter’s Focus Question, first consider a protein critical to your own life,
hemoglobin.Hemoglobin’s job is to bind oxygen molecules on contact with air, then release them
at the appropriate moment, in some distant body tissue. As a first hypothesis, one might imagine
that