374 Chapter 10. Enzymes and molecular machines[[Student version, January 17, 2003]]
language of this chapter, let us imagine a substrate molecule S as an elastic body, with one particular
chemical bond of interest shown in the figure as a spring. The substrate wanders at random until
it encounters an enzyme molecule E. The enzyme molecule has been designed with a binding site
whose shape is almost, but not quite, complementary to that of S. The site is assumed to be lined
with groups that could make energetically favorable contacts with S (hydrogen bonds, electrostatic
attractions, and so on), if only the shapes matched precisely.
Under these circumstances E and S may be able to lower their total free energy by deforming
their shapes, in order to make close contact and profit from the many weak physical attractions
at the binding site.^8 In Haldane’s words, E. Fischer’s famous lock-and-key metaphor should be
amended to allow that “the key does not fit the lock quite perfectly, but rather exercises a certain
strain on it.” We will call the bound complex ES. But the resulting deformation on the particular
bond of interest may push it closer to its breaking point, or in other words reduce its activation
barrier to breaking. Then ES will isomerize to a bound state of enzyme plus product, or EP, much
more rapidly than S would spontaneously isomerize to P. If the product is also not a perfect fit
to the enzyme’s binding site, it can then readily detach, leaving the enzyme in its original state.
Each step in the process is reversible; the enzyme also catalyzes the reverse reaction P→S(see
Figure 10.15).
Let us see how the events in the little story above actually amount to a reduction in activation
energy. Figure 10.17a sketches an imagined free energy landscape for a single molecule S to isomerize
(convert) spontaneously to P (top curve). The geometric change needed to make S fit the binding
site of E is assumed to carry S along its reaction coordinate, with the tightest fit at the transition
state S‡. The enzyme may also change its conformation to one different from its usual (lowest
free energy) state (lower curve). These changes increase the self-energies of E and S, but they are
partially offset by a sharpdecrease in the interaction (or binding) energy of the complex ES (middle
curve). Adding the three curves gives a total free energy landscape with a reduced activation barrier
to the formation of the transition state ES‡(Figure 10.17b).
The picture outlined in the preceding paragraph should not be taken too literally. For example,
there’s really no unambiguous way to divide the free energy into the three separate contributions
shown in Figure 10.17a. Nevertheless, the conclusion is valid:
Enzymes work by reducing the activation energy for a desired reaction. To
bring about this reduction, the enzyme is constructed to bind most tightly to
the substrate’s transition state.(10.12)
In effect, the enzyme-substrate complexborrowssome of the free energy needed to form the tran-
sition state from the many weak interactions between the substrate and the enzyme’s binding site.
This borrowed energy must be paid back when the product unbinds, in order to return the enzyme
to its original state. Thus
An enzyme cannot alter the net∆Gof the reaction. (10.13)An enzyme speeds upboththe forward and backward reactions; the direction actually chosen is still
determined by ∆G,aquantity external to the enzyme, as always (see Idea 8.14 on page 267).
Up to this point we have been imagining a system containing just one molecule of substrate.
With a simple modification, however, we can now switch to thinking of our enzyme as acyclic
(^8) Other kinds of deformations are possible besides shape changes, for example charge rearrangements. This chapter
uses mechanical ideas like shape change as metaphors for all sorts of deformations.