Biological Physics: Energy, Information, Life

382 Chapter 10. Enzymes and molecular machines[[Student version, January 17, 2003]]

15

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40

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

1/

v^0

, s m

M

-1

1/c, mM-1

0

0.008

0.016

0.024

0.032

0.04

0.048

0.056

0.064

051015 20

v^0

, m

M

-1 s

c, mM

ab

Figure 10.20:(Experimental data.) (a)Reaction velocity versus substrate concentration for the reaction catalyzed
bypancreatic carboxypeptidase (see the Example on page 381). (b)The same data, plotted in the Lineweaver–Burk
form (see Equation 10.21). [Data from Lumry et al., 1951.]

with a linear sequence of steps) effectively gives rise to a rate law of the form Equation 10.20, as
long as the last step is irreversible.

10.4.2 Modulation of enzyme activity

Enzymes create and destroy molecular species. To keep everything working, the cell must regulate
these activities. One strategy involves regulating the rate at which an enzyme is itself created, by
regulating the gene coding for it (see Section 2.3.3 on page 57). For some applications, however,
this strategy is not fast enough; instead the cell regulates the turnover numbers of the existing
enzyme molecules. For example, an enzyme’s activity may be slowed by the presence of another
molecule that binds to, or otherwise directly interferes with, its substrate binding site (“competitive
inhibition”; see Problem 10.4). Or a control molecule may bind to a second site on the enzyme,
altering activity at the substrate site by an allosteric interaction (“noncompetitive inhibition”; see
Problem 10.5). One particularly elegant arrangement is when a chain of enzymes synthesizes a
product, and the first in the chain is inhibited by the presence of the final product itself, a feedback
loop (see Figure 9.10 on page 331).

10.4.3 Two-headed kinesin as a tightly coupled, perfect ratchet

Section 10.3.4 suggested that the kinetics of a tightly coupled molecular motor would be much the
same as those of an enzyme. In the language of free energy landscapes (Figure 10.9 on page 362), this
means that we expect to find a one-dimensional random walk down a single valley, corresponding
to the successive processing of substrate to product (shown as motion toward negative values of
α), combined with successive spatial steps (shown as motion toward negative values ofβ). If the
concentration of product is kept very low, then the random walk alongαwill have an irreversible
step, and hence so will the overall motion along the valley. We therefore expect that the analysis