Biological Physics: Energy, Information, Life

9.6. Allostery[[Student version, January 17, 2003]] 333

0.01

0.1

1

10 -6 10 -5 0.001 0.01 0.1 1 10 100

N

(t

)

time, s

T=160K

140 K

120 K

100 K

80 K

60 K

40 K

10 -4

a

0.2

0.4

0.6

energy, kJ/mole

g(

E

)

b

Figure 9.12: (Experimental data; theoretical model.) Rebinding of carbon monoxide to myoglobin after flash
photodissociation. The myoglobin was suspended in a mixture of water and glycerol to prevent freezing. (a)The
vertical axis gives the fractionN(t)ofmyoglobin molecules that havenotrebound their CO by timet. Dots:
experimental data at various values of the temperatureT. None of these curves is a simple exponential. (b)The
distribution of activation barriers in the sample, inferred from just one of the datasets in (a) (namelyT= 120 K).
The curves drawn in (a) were all computed using this one fit function; thus, the curves at every temperature other
than 120Kare all predictions of the model described in Section 9.6.3′on page 344. [Data from Austin et al., 1974.]

Wemight first try to model CO binding as a simple two-state system, like the ones discussed
earlier in Section 6.6.2 on page 194. Then we’d expect the number of unbound myoglobin molecules
to relax exponentially to its (very small) equilibrium value, following Equation 6.30 on page 196.
This behavior was not observed, however. Instead Austin and coauthors proposed that

• EachindividualMb molecule indeed has a simple exponential rebinding probability,
  reflecting an activation barrierEfor the CO molecule to rebind, but


• The many Mb molecules in a bulk sample were each in slightly differentconformational
  substates.Each substate is functional (it can bind CO), and so can be considered
  to be “native.” But each differs subtly; for example, each has a different activation
  barrier to binding.

This hypothesis makes a testable prediction: It should be possible to deduce the probability of
occupying the various substates from the rebinding data. More precisely, we should be able to find
adistributiong(E)dEof the activation barriers by studying a sample at one particular temperature,
and from this function predict the time course of rebinding at other temperatures. Indeed Austin
and coauthors found that the rather broad distribution shown in Figure 9.12b could account for all
the data in Figure 9.12a. They concluded that a given primary structure (amino acid sequence) does
notfold to a unique lowest-energy state, but rather arrives at a group of closely related tertiary
structures, each differing slightly in activation energy. These structures are the conformational
substates. Pictorial reconstructions of protein structure from X-ray diffraction generally do not
reveal this rich structure: They show only the one (or few) most heavily populated substates
(corresponding to the peak in Figure 9.12b).
T 2 Section 9.6.3′on page 344 gives details of the functions drawn in Figure 9.12.