202 Chapter 6. Entropy, temperature, and free energy[[Student version, January 17, 2003]]
extended unfolded form and less time in the short folded form. Thus, it is possible to control the
thermodynamics and kinetics of the folding reaction in real time, simply by changing the external
force. The only remaining question had to do with the statistics of the hopping reaction. Was
RNA hopping a simple process characterized by a constant probability of hopping per unit time at
agiven force? It appears so: Histograms of the dwell times can be fit to simple exponentials (see
Figure 6.10d and Equation 6.31).
Your Turn 6i
Using the data given in Figure 6.10 and its caption, check how well Equation 6.35 is obeyed by
comparing the folding and opening rates at two different forces. That is, find a combination
of the rates that does not involve ∆F 0 (which we don’t know a priori). Then substitute the
experimental numbers, and see how well your prediction is obeyed.The first time one encounters some kind of complicated process, it’s natural (and frequently
the only thing you can do) to try to strip away as much detail as possible. Then again, such
simplification certainly has risks—what is one missing, and are the approximations really that
good? Yet in this case, the simple two-state model seems to fit the observations very well, and (so
far) we have not detected any behaviors in our RNA hairpin system that would force us to replace
this model with something more elaborate.
Formore details See Liphardt et al., 2001, and the associated on-line supplemental material
(http://www.sciencemag.org/cgi/content/full/292/5517/733/DC1).
Carlos Bustamante is the Howard Hughes Medical Institute Professor of Biochemistry and Molecular Biol-
ogyatthe University of California, Berkeley.... JanLiphardt is currently a Divisional Fellow at Lawrence
Berkeley National Lab. He is interested in how small systems respond to local application of mechanical
forces, and in nonequilibrium statistical mechanics. Ignacio Tinoco, Jr. is Professor of Chemistry at the
University of California, Berkeley. He was chairman of the Department of Energy committee that recom-
mended in 1987 a major initiative to sequence the human genome.
The big picture
Returning to the Focus Question, we found that a system’s useful energy (the portion that can be
harnessed to do mechanical or other useful work) is generally less than its total energy content. A
machine’s efficiency involves how much of this useful energy actually turns into work (with the rest
turning into waste heat). We found a precise measure of useful energy, called “free energy.”
This chapter has been quite abstract, but that’s just the obverse of being very generally applica-
ble. Now it’s time to get at the fascinating details of how the abstract principles get implemented—
to see some concrete realizations in living cells of these ideas. Thus, Chapter 8 will look at self-
assembly, Chapter 9 will develop the mechanics of macromolecules, and Chapter 10 will fuse the
twotoget insight into the operation of molecular motors. All of these biophysical developments
will rest upon the ideas introduced in this chapter.
Key formulas
- Entropy: The disorder of a string ofNrandom, uncorrelated letters drawn from an alphabet