C O M M U N I C A T I O N S
similar instances that the slow step is due to the sluggish dissociation
of a metal-bound water molecule that is necessary before the
inhibitor can make optimal interactions within the active site.3a The
pH dependence and solvent isotope effects for inhibition of
stromelysin by a peptide phosphonamidate suggest that kon is limited
by ligand exchange for a zinc-bound water.8 It is likely that the
small value of k1 for the binding of 1 with NagA is due to a similar
phenomenon.
Scheme 3. Models for Binding of Enzyme Inhibitors
Figure 2. Time dependence for the onset of inhibition by 1 (panel A) with
NagA and 2 (panel B) with DGD. In panel A, the concentrations of 1 are
0.40 µM (O); 0.80 µM (0); 1.6 µM (3); 2.4 µM (4). In panel B, the
concentrations of 2 are 15 nM (O); 25 nM (0); 50 nM (3); 80 nM (4).
The time courses were fit to eq 2 to obtain the first-order rate constants for
the formation of the enzyme-inhibitor complex.
The two phosphonamidate analogues synthesized for this inves-
tigation proved to be extraordinary potent inhibitors of two
deacetylases belonging to the amidohydrolase superfamily. The
inhibition constants for compounds 1 and 2 are 4 × 103- and 5 ×
105-fold smaller than the respective Michaelis constants of their
target enzyme. The Ki values for these compounds are among the
lowest ever measured for the inhibition of deacetylases.9
of NagA was determined by plotting kobs versus the concentration
of 1 as shown in Figure 3A. From the slope of this plot, the apparent
second-order rate constant is 1.3 × 103 M-1 s-1. Correction of the
apparent second-order rate for the concentration of substrate accord-
ing to eq 3 gave a value for k1 of 6.1 × 103 M-1 s-1 (see Scheme 3).
The dissociation constant for the binding of 2 with DGD was
determined by incubating 2.0 nM enzyme with 0.5-60 nM 2 for
75 min at pH 7.6. The residual enzyme activity was then determined
with 3.0 mM N-formyl-D-glutamate as the substrate in 50 mM
HEPES buffer, pH 7.6. The results are shown in Figure 1B and a
fit of the data to eq 1 gives a Ki of 460 ( 70 pM. The time courses
for the onset of inhibition by 2 were determined by measuring the
rate of bond cleavage as a function of time. In these experiments,
1.0 nM DGD was added to a solution of 1.5 mM substrate
containing between 10 and 300 nM of 2 at pH 7.6, and the formation
of formate was determined as a function of time. The time courses
were fit to eq 2 to yield the first-order rate constants for the onset
of inhibition, and the results are presented in Figure 2B. The
apparent first-order rate constants for the onset of inhibition were
plotted versus the concentration of 2, and the results are presented
in Figure 3B.
Vi/Vo ) ([Et] - Ki - [I] + (([I] + Ki - [Et])2 +
(4Ki[Et]))1/2)/(2[Et]) (1)
obst)
P ) Vst + ((Vr - Vs)/kobs)(1 - e(-k
k1 ) appkobs (1 + [S]/[Km])
)
(2)
(3)
k3 ) (kobs - k4) (1 + (app(k2/k1)/[I]))
(4)
Acknowledgment. This work was supported in part by the NIH
(GM 33894 and GM 71790).
Supporting Information Available: The syntheses of compounds
1 and 2 are described. This material is available free of charge via the
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Figure 3. Effect of inhibitor concentration on the onset of inhibition by 1
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