 |
INTRODUCTION |
Our pursuit of novel antithrombotic agents has focused on direct
inhibitors of thrombin, a trypsin-like serine proteinase that plays a
key role in thrombosis. One strategy for the design of potent thrombin
inhibitors is to replace the substrate
P11 carboxamido group with an
electrophilic keto or aldehyde group (1). Cyclotheonamide A is a
naturally occurring proteinase inhibitor from a marine sponge
(Theonella) that contains such a potency-enhancing keto
group (2-4). Cyclotheonamide A is a potent (Ki = 1 nM) reversible inhibitor of thrombin (5, 6) and several
other trypsin-like proteinases (5, 7). Various
-ketoamide
derivatives of tripeptide substrates of thrombin have been prepared in
an attempt to identify selective, potent, reversible inhibitors of
thrombin (8, 9). Placement of a t-4-AChxGly2
residue at the P1 position in
-ketoamide thrombin inhibitors provided excellent selectivity for thrombin, relative to tryspin (10-12), probably because the S1 specificity pocket of thrombin is
larger than that of trypsin (13, 14).
In the present study, we show that
-ketoamide inhibitors containing
t-4-AChxGly inactivate thrombin via a two-step reaction, wherein an initially formed weak complex (EI1)
rearranges to a more stable thrombin-inhibitor complex
(EI2) (Scheme I). Inhibitors that inactivate
enzymes via a two-step pathway are usually assumed to form
EI1 rapidly in a preequilibrium reaction where
k
1 is assumed to be much greater than
k2 (15). Sculley et al. (16) recently
discussed the difficulty in distinguishing cases where k
1
k92 from those
where k
1 ~ k2. We now
describe a novel sequential stopped-flow analysis that circumvents this difficulty and allowed us to rigorously evaluate kinetic pathways for
inactivation of thrombin by a family of active site-directed thrombin
inhibitors.
 |
EXPERIMENTAL PROCEDURES |
Methods for the synthesis of the
-ketoamide and desketoamide
derivatives of
H-N-Me-D-Phe-Pro-4-t-AChxGly
have been reported elsewhere (Table I and Refs. 9-12). The inhibitor
concentrations were determined from titration with a known amount of
thrombin as described previously (5). Dansylarginine
N-(3-ethyl-1,5-pentanediyl)amide (DAPA) was obtained from
American Diagnostica. Concentrations of DAPA were determined from
measurements of absorbance at 330 nm using an extinction coefficient of
4.01 cm
1 mM
1 (17). The sources
of other materials were described previously (5, 8). Proteinase assays
were performed at room temperature in 50 mM Tris, pH 7.5, 150 mM NaCl, and 0.1% polyethylene glycol 8000 unless
otherwise indicated.
Determination of Inhibition Constants (Ki)--
The
inhibition constants were determined as described previously (5, 8, 9).
When total inhibitor ([It]) and enzyme
([Et]) concentrations were comparable, the quadratic equation (18-20) for tight-binding inhibitors (Equation 1)
was used to calculate the apparent inhibition constant
(Ki*) from the dependence of substrate hydrolysis on
[It] and [Et], where Vi and
Vo represent the initial rates of substrate
hydrolysis in the presence and absence of inhibitor, respectively.
|
(Eq. 1)
|
When [It]
[Et], the
variation of Vi with [It] is described by
Equation 2.
|
(Eq. 2)
|
In assays where the substrate fully equilibrates with inhibitor
and enzyme (i.e. analysis of progress curves, see below), Equation 3 relates the apparent inhibition constant,
Ki*, to the intrinsic, final inhibition constant
Ki.
|
(Eq. 3)
|
In assays where the inhibitor and enzyme were preequilibrated
(i.e. before addition of substrate), and the rate of
dissociation of inhibitor from enzyme was slow, and didn't occur
during the time of the activity assay, the use of Equation 3 is
inappropriate and the apparent inhibition constant,
Ki*, is equal to Ki. Activity
assays for the determination of Ki were routinely
performed at [S] < Km; hence,
Ki
Ki* and the decision of
when it was appropriate to use Equation 3 were circumvented. The
overall dissociation constant (Ki) is defined by
Equations 4 and 5 for the one- and two-step pathways, respectively
(Scheme I).
|
(Eq. 4)
|
|
(Eq. 5)
|
One- and two-step pathways for inhibition
of thrombin.
Scheme I.
|
|
Determination of Rate Constants for Schemes I and II--
The
rate of inhibitor binding to thrombin was followed by displacement of
the fluorescent probe p-aminobenzamidine from the active
site of thrombin. The decrease in fluorescence (F) was monitored using
an Applied Photophysics stopped-flow spectrometer (DX.17MV) interfaced
with an Archimedes 420/I computer as described previously (5, 8). Rate
constants were derived from analysis of the average of 4-7 replicate
traces with 1000-4000 data points per trace. Typically,
p-aminobenzamidine (100-600 µM) was mixed with 0.25-1 µM thrombin prior to reaction with an equal
volume of inhibitor (2.5-80 µM). When decay of the
fluorescent signal was monophasic, Equation 6 ("single exponential
with floating end point," Applied Photophysics software) was used to
evaluate the kinetic parameter kobs.
|
(Eq. 6)
|
In Equation 6, F is the measured fluorescence at time
t, kobs is the apparent first-order
rate constant for the approach of F to its final value Ff, and
Fo corresponds to the fluorescence at t = 0. The dependence of the pseudo-first-order rate constant
(kobs) for displacement of
p-aminobenzamidine is a linear function of [It].
Equation 7 was used to obtain k1, where
[I]eff = [It]/(1 + [P]/Kp)
and Kp (the equilibrium constant for dissociation of
the enzyme-p-aminobenzamide complex) is equal to 47 µM (5).
|
(Eq. 7)
|
When the decay of fluorescence accompanying probe displacement
was a biphasic process, Equation 8 ("double exponential with floating
end point," Applied Photophysics software) was used to yield the
kinetic parameters kobs1 and
kobs2.
|
(Eq. 8)
|
In Equation 8 kobs1 and
kobs2 are the apparent first-order rate
constants for the approach of F to its final value, and A and B are amplitude terms associated with their
corresponding first-order processes. The dependence on [It]
of the pseudo-first-order rate constants, kobs1
and kobs2, for displacement of
p-aminobenzamidine was a linear and hyperbolic function of [I]eff, respectively, and was fit by Equations 9 and 10
for evaluation of k1, k2,
and Ki, init.
|
(Eq. 9)
|
|
(Eq. 10)
|
Stopped-flow experiments also yielded progress curves for
thrombin-mediated hydrolysis of Z-GPR-afc (400-nm excitation with a
455-nm emission block) in the presence of inhibitor (5, 8). Briefly,
inhibitor was mixed with Z-GPR-afc (22 µM) prior to
reaction with an equal volume of 5-20 nM thrombin.
Substrate depletion was less than 10% during the run. Rates were
measured under pseudo-first-order conditions (i.e.
[inhibitor]
[thrombin], [Z-GPR-afc]
[thrombin], and
[Z-GPR-afc] < Km). The best fit for a single
exponential decay was "single exponential with steady state" (from
the kinetic software package supplied by Applied Photophysics), or
alternatively, the data were transferred to Kaleidagraph (version 3.0.5 Abelbeck Software) and fitted using Equation 11. Kaleidagraph utilizes
the Levenberg-Marquardt algorithm
|
(Eq. 11)
|
for nonlinear least-squares regression. Equation 11 as developed
by Williams and Morrison (18) and by Cha (20) is commonly used in the
analysis of monophasic progress curves. In Equation 11, F is the
measured fluorescence defined as a function of the initial
(Vi, init) and final
(Vs) steady state velocities (change in fluorescence
per unit time due to thrombin-catalyzed substrate hydrolysis) and the
apparent first-order rate constant (kobs) for
the approach of enzymic activity to its final value. To monitor
directly the time-dependent inhibition of thrombin in the
presence of a substrate, the following analysis was employed. At long
times (kobs t
1) where Equation 11 reduces to Equation 12, F is a linear function of time.
Extrapolation of the linear time dependence
|
(Eq. 12)
|
of F at long times to zero time and determination of the
difference (
) between the values of F on the extrapolated linear plot (Equation 12) and those on the plot describing the time dependence of the experimentally determined values of F (Equation 11) should provide an indication of the time-dependent approach of
enzymic activity to its final value as indicated by Equation 13 where
o is the value of
at t = 0.
|
(Eq. 13)
|
When the time-dependent decrease in the parameter
/
o was biphasic, the dependence of F on time was fit by
Equation 14 where C and A are constants.
|
(Eq. 14)
|
As in the case of the monophasic process described above, the
dependence of F on time should become linear at long times (Equation 15). Extrapolation of the linear portion
|
(Eq. 15)
|
of the F versus time plot to zero time and
determination of the differences (
) between the values of F on the
extrapolated plot and the plot defined by the observed time dependence
of F yields a biphasic time dependence for the parameter
/
o as indicated by Equation 16.
|
(Eq. 16)
|
It is important to note that the relative magnitude of the
amplitude factors A and 1
A reflect the
relative amount of hydrolysis products formed in the fast and slow
phases and not the relative amount of enzyme inactivated in the slow
and fast phases.
When the time-dependent approach of enzymic activity to its
final value was monophasic, the dependence of
kobs on [I]eff (where [I]eff = [It]/(1 + [S]/Km)) was fit by Equation 7 to obtain
k1. When the approach of enzymic activity to its
final value was biphasic, the time dependence of fluorescence was fit by Equations 14 or 16 to determine kobs1,
kobs2, and A (the fraction of the
biphasic reaction described by kobs1). The
dependence of kobs1 and
kobs2 on [I]eff was fit by
Equations 9-10 to obtain the parameters k1,
k2, and
Ki, init. The values for k
1 and k
2 could not
always be determined accurately from the fit of the data by Equations
7, 9, and 10. In such cases, other methods were used to determine their
values (see below).
The value of k
2 was determined from the
time-dependent regeneration of free enzyme as measured by
the hydrolysis of a fluorogenic substrate
(Scheme II). Thrombin was preincubated with inhibitor at a concentration much greater than
Ki and for sufficient amount of time to ensure
complete formation of EI2. After preincubation
the enzyme-inhibitor complex was diluted into a solution containing 60 µM D-Phe-Pro-Arg-afc ([S]
Km, Km = 0.3 µM). The
resulting progress curve was fit to Equation 11 to obtain
kobs which is equivalent to
koff. Equation 17 was used to relate
koff to the rate constants for the two-step pathway depicted in Schemes I and II.
|
(Eq. 17)
|
For very potent inhibitors, k
2 was
exceedingly small and the long times required for complete regeneration
of enzyme compromised enzyme stability. In these cases
Vs was determined in a separate experiment from an
identical dilution of enzyme with substrate. The experimentally
determined value of Vs was fixed in Equation 11, and
the initial data from the progress curve (~3-5 half-lives) was
fitted by nonlinear regression to Equation 11 to determine
koff.
Regeneration of active enzyme via the
two-step reaction pathway.
Scheme II.
|
|
Sequential Stopped-flow--
To determine the value of
k
1, a sequential stopped-flow method was used.
Equal volumes of thrombin and inhibitor ([I]t
Ki, init) were aged long enough (first
mix) to ensure complete formation of EI1 but
with minimal formation of EI2 (see Scheme I).
After preincubation (first mix), EI1 was diluted
(second mix) with an equal volume of DAPA
(Scheme III). There is an increase in
fluorescence when DAPA binds to the active site of thrombin (excitation
280 nm, emission block 420 nm (17, 21)). A high concentration of
DAPA (
40 µM) ensured that the pseudo-first-order rate
constant (kDAPA[DAPA]) for the reaction rate of E with DAPA was much greater than
k
1 + k2 and
k1[I]; hence, the reaction of thrombin with
DAPA is not rate-limiting. In Scheme III the pseudo-first-order rate
constant, kobs, for regeneration of E
from EI1 is described by Equation 18.
|
(Eq. 18)
|
The value of kobs was estimated using
Equation 11 to fit the time-dependent increase of
fluorescence associated with DAPA binding to the active site of
thrombin concomitant with inhibitor displacement. Equation 11 was used
to correct for the small but detectable steady state drift due to
photo-bleaching of DAPA. In a typical experiment for the determination
of k
1 + k2 for the
reaction of thrombin with L-370,518, 0.8 µM thrombin was aged with an equal volume of 4 µM L-370,518 (first mix).
After 1 s, the aged solution was mixed (second mix) with an equal
volume of 80 µM DAPA.
Partitioning of
EI1 in sequential stopped-flow.
Scheme III.
|
|
 |
RESULTS |
Inhibition of Thrombin Catalysis--
Treatment of thrombin with
L-371,912 or the corresponding
-ketoamide analog L-370,518 inhibited
thrombin-catalyzed hydrolysis of a fluorogenic substrate (Fig.
1). The equilibrium constants (Ki) for dissociation of the complexes between
thrombin and the desketoamide L-371,912 and the ketoamide L-370,518
were 5 ± 0.5 nM and 90 ± 10 pM,
respectively. The titrations shown in the figure insets established
that these inhibitors form 1:1 complexes with thrombin that are devoid
of catalytic activity.

View larger version (17K):
[in this window]
[in a new window]
|
Fig. 1.
Determination of the equilibrium constants
(Ki) for dissociation of the thrombin·L-371,912
and thrombin·L-370,518 complexes. Reactions were initiated by
addition of 1.25 µM Z-GPR-afc (final concentration) to
equilibrated solutions of 0.1 nM thrombin containing L-371,912 (A) or L-370,518 (B) at the
plotted concentrations. The inhibited substrate hydrolysis
(Vi) was compared with substrate hydrolysis in the
absence of inhibitor (Vo) as described under
"Materials and Methods." The solid lines represent the
best nonlinear least squares fit of Equation 2 to the data.
Inset, stoichiometric titration of thrombin with L-371,912
(A) or L-370,518 (B). The inhibited substrate
hydrolysis (Vi) was compared with substrate
hydrolysis in the absence of inhibitor (Vo) after
addition of 200 µM Spectrozyme-PL to a preincubated
mixture of 1 µM (for L-371 912) or 2 µM
(for L-370,518) thrombin and the plotted concentrations of L-371,912 and L-370,518.
|
|
Kinetic analysis of the binding of the desketoamide L-371,912 and
ketoamide L-370,518 to thrombin suggested that they bind to thrombin
via different kinetic pathways. Fig. 2
shows the monophasic and biphasic time-dependent inhibition
of thrombin obtained upon mixing thrombin with desketoamide or
ketoamide, respectively, and a fluorogenic substrate. The data in Fig.
2 were fit by a monoexponential (desketoamide, Equation 13) and
biexponential (ketoamide, Equation 16) decay equations to yield
pseudo-first-order rate constants for desketoamide L-371,912,
(kobs), and ketoamide L-370,518
(kobs1, kobs2) of 2.9, 1.36, and 0.034 s
1, respectively.

View larger version (13K):
[in this window]
[in a new window]
|
Fig. 2.
Monophasic and biphasic inactivation of
thrombin by L-371,912 and L-370,518 under stopped-flow conditions.
Thrombin (20 nM) was mixed with an equal volume of 23 µM Z-GPR-afc and 1 µM L-371,912 (open
squares) or L-370,518 (open circles). The solid
lines represent the best fit to the data by Equation 13
(L-371,912) or Equation 16 (L-370,518). Using the values of the rate
constants (k1, k 1,
k2, k 2) listed in Table
II, a theoretical time dependence of / 0
(indistinguishable from that defined by the solid lines in
the figure) was obtained for the biphasic reaction by Runge-Kutta
digital integration of the differential equations describing the
two-step reaction pathway in Scheme I. Only 5% of the collected data
points are shown for reasons of clarity.
|
|
Figs. 3 and
4A illustrate the linear
dependence of kobs (desketoamide) and
kobs1 (ketoamide) on the inhibitor
concentration. In contrast the dependence of
kobs2 on the concentration of ketoamide was
hyperbolic (Fig. 4B). Both the monophasic
time-dependent inhibition of thrombin by the desketoamide
L-371,912 and the linear dependence of the corresponding
pseudo-first-order rate constant on the inhibitor concentration suggest
that the desketoamide binds to thrombin via a single one-step process.
A two-step pathway (Scheme I) is required to account for the biphasic
time-dependent inhibition of thrombin by the ketoamide
L-370,518 and the linear and hyperbolic dependence of
kobs1 and kobs2 on
inhibitor concentration. A two-step pathway (Scheme I) involves
formation of an initial complex (EI1) that
subsequently rearranges to a more stable complex
(EI2). The best fit of
kobs (Fig. 3) and kobs1
(Fig. 4A) by Equations 7 and 9 yielded
k1 values of 9.4 ± 0.5 and 3.6 ± 0.3 µM
1 s
1 for the desketoamide
and ketoamide, respectively. The dependence of
kobs2 on the effective inhibitor concentration
can be represented by Equation 10, wherein
Ki, init is equivalent to
k
1/k1 when
k
1
k2. The best
fit of kobs2 for the ketoamide L-370,518 to
Equation 10 (Fig. 4B) yielded k2 and Ki, init values of 0.035 ± 0.003 s
1 and 15 ± 5 nM, respectively. The
transient accumulation and decay of EI1 gives
rise to the biphasic ligand binding kinetics associated with a two-step
pathway. At lower inhibitor concentrations, EI1 accumulation decreases and the biphasic binding process becomes monophasic. This situation made it difficult to determine
kobs2 at inhibitor concentrations < Ki, init and is responsible for the
uncertainty in the value of Ki, init determined from the fit of the data in Fig. 4B to Equation 10.

View larger version (10K):
[in this window]
[in a new window]
|
Fig. 3.
Dependence of the rate constant
kobs on L-371,912 concentration under
stopped-flow conditions. Thrombin (5-20 nM) was mixed with an equal volume of 23 µM Z-GPR-afc and
L-371,912 (final concentration, 0.25-2 µM). The
solid line represents the best fit of Equation 7 to the
data.
|
|

View larger version (16K):
[in this window]
[in a new window]
|
Fig. 4.
Dependence of the rate constants
kobs1 (A) and
kobs2 (B) on L-370,518
concentration under stopped-flow conditions. Thrombin (2.5-50
nM) was mixed with an equal volume of 23 µM
Z-GPR-afc and L-370,518 (final concentaration, 0.025-1
µM). A, the solid line represents
the best fit of Equation 9 to the data. The solid circles
are the pseudo-first-order rate constants (kobs)
for displacement (as derived from stopped-flow) of 300 µM
p-aminobenzamidine from 0.5 µM thrombin by 2.5 and 5 µM L-370,518. To compare the different experimental
procedures, the concentration of L-370,518 was adjusted to yield
[L-370,518]eff as described under "Experimental
Procedures." B, the solid line represents the
best nonlinear least squares fit of Equation 10 to the data.
|
|
Displacement of a Fluorescent Probe from the Active Site of
Thrombin by Inhibitors--
To characterize further the reaction
pathway for the binding of the desketoamide L-371,912 and ketoamide
L-370,518 to thrombin, the fluorescent probe
p-aminobenzamidine was employed to monitor ligand binding to
thrombin. In the concentration ranges studied, p-aminobenzamidine displacement by L-371,912 or L-370,518
was a monophasic first-order process (Fig.
5, inset). The linear
dependence of the pseudo-first-order rate constant
(kobs) for p-aminobenzamidine displacement (Equation 7) on the concentration of L-371,912 and L-370,518 (Fig. 5) yielded k1 values of 8.2 ± 0.3 and 3.4 ± 0.2 µM
1
s
1 for binding of the desketoamide L-371,912 and
ketoamide L-370,518 to thrombin, respectively. The similarity of these
k1 values to those obtained from the plots
depicted in Fig. 3 and 4A (Table II) indicates that these
second-order rate constants are truly equivalent to
k1.

View larger version (21K):
[in this window]
[in a new window]
|
Fig. 5.
Dependence of the rate constant,
kobs, for displacement of
p-aminobenzamidine from the active site of thrombin on
L-371,912 (squares) or L-370,518 (circles)
concentration under stopped-flow conditions. Solutions containing
thrombin (0.05-1 µM) and p-aminobenzamidine
(100 µM) were mixed with L-371,912 (final concentration, 0.25-20 µM) or L-370,518 (final concentration, 2.5-50
µM) in the stopped-flow. The solid lines
represent the best fit of Equation 7 to the data. Inset,
monophasic loss of fluorescence from displacement of
p-aminobenzamidine (50 µM) from the active
site of thrombin (0.5 µM) by 5 µM L-371,912
(squares) or L-370,518 (circles). The solid
lines represents the best nonlinear least squares fit of Equation 6 to the data and yielded kobs values of 19.2 and 8.5 s 1 for L-371,912 and L-370,518,
respectively.
|
|
The apparent discrepancy between the biphasic inhibition of
thrombin-catalyzed substrate hydrolysis and the monophasic
p-aminobenzamidine displacement observed in the case of
L-370,518 stems from the differences in the two experimental methods.
With the elevated L-370,518 concentrations used for the
p-aminobenzamidine displacement studies (2.5-25
µM), only a small amount of free enzyme is present at the
end of the first phase (Ki, init ~15
nM, see Fig. 4B); hence, the binding of
E to I to form EI1 is the dominant
reaction. The amplitude of the second phase, which is governed by the
conversion of residual E to EI1 and
EI2, is too small to measure by the
p-aminobenzamidine displacement method. On the other hand,
the activity assay can detect the small amount of active enzyme present
at the end of the first phase and measure its subsequent decay during
the second phase.
According to Equation 7, the y intercept of the linear plots
of kobs versus inhibitor
concentration (Figs. 3, 4A, and 5) should be equal to
k
1. However, the proximity of the y
intercept to the origin precluded accurate determination of
k
1. An estimation of the value of
k
1 for dissociation of the
thrombin·L-371,912 complex of 0.047 s
1 was obtained
from the relationship k
1 = Ki × k1 using
Ki = 5 nM and k1 = 9.4 µM
1 s
1. Likewise, an
estimate for k
1 for the thrombin·L-370,518 complex of 0.054 s
1 was obtained from the equation
k
1 = Ki, init × k1 using
Ki, init = 15 nM and
k1 = 3.6 µM
1
s
1. However, the similarity of
k
1 and k2 values (0.054 and 0.035 s
1, respectively) violated the requisite
condition of rapid equilibrium between EI1 with
E and I (i.e. k
1
k2); hence, an alternative approach for
determination of k
1 for the
thrombin·L-370,518 complex was required.
Use of Sequential Stopped-flow Analysis to Characterize Individual
Steps in Inhibitory Pathways--
Fig.
6A depicts the results of a
sequential stopped-flow experiment designed to determine the individual
rate constants of a two-step pathway. Accordingly, thrombin was mixed
with L-370,518 and aged sufficiently to ensure formation of
EI1 and partial conversion of
EI1 to EI2. The aged
mixture was subsequently mixed with DAPA, a fluorogenic ligand that
binds tightly to the active site of uncomplexed thrombin. Fig.
6A shows the increase of fluorescence as E is
regenerated from EI1 and combines with DAPA.
When the first reaction mixture is aged long enough for complete
conversion of EI1 to EI2,
no reaction with DAPA is observed within the 100-s observation time
(Fig. 6A, trace F). Trace A shows the
fluorescence/time profile for DAPA-treated thrombin which was
subsequently mixed with L-370,518. The absence of a
time-dependent change of fluorescence indicated that the
rapidly formed thrombin·DAPA complex is not displaceable by L-370,518
over the time and concentration range used in the experiment. The
approach of fluorescence to the final value in traces B-E
(which represents, in rank alphabetical order, increasing incubation
times of L-370,518 and thrombin) was a pseudo-first-order process that
when fit by Equation 11 yielded rate constants of 0.086, 0.085, 0.086, and 0.075 s
1, respectively. The mean rate constant, 0.084 s
1, should be equivalent to k
1 + k2 (Equation 18), provided that the
pseudo-first-order rate constant for reaction of thrombin with DAPA is
greater than k
1 + k2
and that trapping of free thrombin with DAPA is operationally
irreversible. These conditions appear to be satisfied since (i) the
rate constants for displacement of L-370,518 from thrombin by DAPA is
independent of the DAPA concentration (data not shown); (ii) the
pseudo-first-order rate constant for reaction of DAPA with thrombin is
>1000 s
1 which exceeds k1[I]
and k
1 + k2 when DAPA
concentrations are
40 µM (data not shown). Since
k
1 + k2 = 0.084 s
1, a value 0.049 s
1 is obtained for
k
1 using the previously determined
k2 value of 0.035 s
1.

View larger version (32K):
[in this window]
[in a new window]
|
Fig. 6.
Time-dependent increase of DAPA
fluorescence using sequential stopped-flow. Thrombin (0.4 µM) was preincubated (first mix) with L-370,518 (2 µM) for 48 ms (trace B), 140 ms (trace C), 1 s (trace D), 19 s (trace E),
and 192 s (trace F) (panel A) or with
L-371,912 (2 µM) for 18 ms (trace B), 48 ms
(trace C), 1 s (trace D), 19 s
(trace E), and 192 s (trace F) (panel B), before final dilution (second mix) with 80 µM
DAPA. Thrombin was also preincubated with DAPA for 3 s before
dilution with L-370,518 (panel A, trace A) or L-371,912
(panel B, trace A). Only 3% of the collected data points
are shown for reasons of clarity.
|
|
At short aging times of thrombin with L-370,518, a burst of
fluorescence was evident after the addition of DAPA (Fig. 6A, traces B and C) which is attributed to the fact that
conversion of E + I to EI1 was
incomplete at short aging times and the uncomplexed E
reacted with DAPA during the dead time of the instrument. A log plot of
the fraction of uncomplexed E (fEU)
versus aging time with L-370,518 (Fig.
7A) should give a reliable
estimate of k1. The value of
fEU at the end of various aging times was obtained
from the amplitude of the initial fluorescence change produced upon
quenching with DAPA and the use of the following relationship (Equation 19).
|
(Eq. 19)
|
where Fti is the initial fluorescence after aging time
t, FA is the initial fluorescence with no aging with
L-370,518 (trace A, Fig. 6A), and FF is
the fluorescence after complete aging with L-370,518 (trace
F, Fig. 6A). The pseudo-first-order rate constant
derived from the slope in Fig. 7A, 6.7 s
1, was
used to calculate a second-order rate constant, 3.4 µM
1 s
1, from the equation
k1 = 6.7 s
1/[L-370,518] using
the experimental concentration of L-370,518 (2 µM). As
expected, this k1 value is equivalent to that
obtained from studies of substrate hydrolysis and probe
displacement.

View larger version (18K):
[in this window]
[in a new window]
|
Fig. 7.
Semi-log plot of the fraction of thrombin
uncomplexed (A) and recoverable (B)
versus aging time with L-370,518 under sequential stopped-flow conditions. The solid lines are the best
fit to the data by a single exponential decay.
|
|
Even at the shortest preincubation times, thrombin was not fully
recoverable from EI1 as shown by the failure of
trace B (aging time 48 ms) in Fig. 6A to approach
the final fluorescence value of trace A. This observation is
consistent with a two-step pathway (Scheme I) where
k2 is comparable to k
1.
At longer preincubation times (Fig. 6A, traces D and
E) all of E has reacted with L-370,518 to form
EI1 or EI2; hence, the
fraction of enzyme recoverable from EI1 is a
function of both the ratio
k
1/(k2
+k
1) and the time of preincubation. The
fraction of enzyme recoverable from EI1
(fER) at the end of various aging times could be
obtained from the amplitude of the final fluorescence (corrected for
time-dependent bleaching) produced upon quenching with DAPA and the use of the following relationship (Equation 20).
|
(Eq. 20)
|
where Ftf is the final fluorescence after aging time
t and FA and Fti are described above. Fig. 7B depicts a log plot of the fER
versus aging time and yields a pseudo-first-order rate
constant of 0.046 s
1 with an intercept at ~0.5. A
plausible interpretation of the results shown in Fig. 7B is
that 0.046 s
1 is the pseudo-first-order rate constant for
formation of EI2 from
EI1, and 0.5 is the fraction
(k
1/(k
1 + k2)) of free enzyme regenerated from
EI1. It can be deduced from the experimentally
determined values of 0.5 for
k
1/(k
1 + k2) and 0.084 s
1 for
k
1 + k2 that
k
1 and k2 are equal to
0.042 s
1. This k
1 value is
similar to 0.049 s
1 which was derived from the approach
of fluorescence to its final value (Fig. 6A). Likewise this
k2 value is similar to 0.035 s
1
which was derived from the limiting value of a plot of
kobs2 versus inhibitor concentration
(Fig. 4B).
Fig. 6B shows a sequential stopped-flow study of the
interaction of the desketoamide L-371,912 with thrombin. DAPA was added to thrombin·L-371,912 that was premixed for increasing lengths of
time (B-F, respectively). The traces of
fluorescence versus time (after DAPA addition) were fit by
Equation 11 to yield pseudo-first-order rate constants of 0.058, 0.053, 0.053, 0.053, and 0.054 s
1 for B-F,
respectively. The mean value of k
1, 0.054 s
1, determined from the sequential stopped-flow
experiment, is similar to the k
1 value, 0.047 s
1, determined from the relationship
k
1 = k1 × Ki. Complete fluorescence recovery via a monophasic
process that was independent of aging time with L-371,912 was
additional evidence against the existence of a second complex
(EI2). Formation of significant
EI2 during the aging reaction (>15 ms) would be
expected to affect the recovery and/or rate of formation of uncomplexed E (from EI1 and
EI2) that is trapped with DAPA. As for
L-370,518, a burst of fluorescence was observed with short aging times
(Fig. 6B, traces B and C) suggesting incomplete
conversion of E + I to EI. A plot of the log
fEU (data not shown) versus aging time
with the desketoamide L-371,912 yielded a pseudo-first-order rate
constant of 18 s
1. A second-order rate constant of 9 µM
1 s
1 was calculated from
the equation k1 = 18 s
1/[L-371,912] using the experimental concentration of
L-371,912 (2 µM). The k1 value
determined from sequential stopped-flow agreed with the
k1 values derived from the slopes in Figs. 3 and
5 (9.4 and 7.8 µM
1 s
1,
respectively). Assuming k1 = 9.4 µM
1 s
1 and
k
1 = 0.054 s
1, the kinetically
determined equilibrium constant using Equation 4 is 5.7 nM
which is similar to the equilibrium constant derived from inhibition of
the steady state velocity for thrombin-catalyzed hydrolysis of a
fluorogenic substrate (Fig. 1A).
Direct Determination of the Rate Constant for Dissociation of a
Thrombin Inhibitor Complex--
The value of
k
2 for dissociation of the
thrombin·L-370,518 complex (Scheme II) was determined by
preincubation of E and I (1:1.2 molar ratio) and subsequent
dilution into substrate solution (at [S]
Km). The progress curve showing the regeneration of
enzyme activity was fit to Equation 11 and yielded a pseudo-first-order
rate constant (koff) of 2 × 10
4 s
1 (data not shown). Since
k
1 is comparable to k2,
k
2 was calculated to be 3.6 × 10
4 s
1 using Equation 17 and the previously
determined values for koff (2 × 10
4 s
1), k2 (0.035 s
1), and k
1 (0.049 s
1). A Ki value was calculated as 136 pM, using Equation 5 and the experimentally determined
values for k1 (3.5 µM
1 s
1),
k
1 (0.049 s
1),
k2 (0.035 s
1), and
k
2 (3.4 × 10
4
s
1). This estimate for Ki is
reasonably close to 90 pM which was determined from the
inhibitory effect of the ketoamide L-370,518 on the steady state
velocity for thrombin-catalyzed hydrolysis of a fluorogenic
substrate (Fig. 1B).
Structural Determinants of Thrombin Inhibitor
Interactions--
Substitution of a hydrogen atom for the N-terminal
methylamino group in desketoamide L-371,912 and the ketoamide L-370,518 yielded the desketoamide L-372,011 and ketoamide L-372,051,
respectively (Table I). Like L-370,518
and L-371,912, L-372,011 was isolated as a single isomeric species.
However, L-372,051 was composed of an equal RS mixture at
the
-carbon of 4-AChxGly; only one of the isomers was active as
determined by thrombin titration (results not shown). The values of
Ki, Ki, init, and
k1 reported for the ketoamide L-372,051 were
adjusted for the concentration of the active isomer. L-372,011 and
L-372,051 formed inhibitory complexes with thrombin with
Ki values of 330 ± 30 nM and
4 ± 0.6 nM, respectively (Table
II). The time-dependent inactivation of thrombin by the desketoamide L-372,011 (as derived from
either substrate hydrolysis or p-aminobenzamidine
displacement) was monophasic (data not shown). The linear dependence of
the pseudo-first-order rate constant on L-372,011 concentration was fit
by Equation 7, and the slope of the line yielded a
k1 value of 7 ± 0.5 µM
1 s
1 (data not shown). The
k
1 value for the interaction between L-372,011
and thrombin was 2.4 s
1 as determined by sequential
stopped-flow (data not shown). The monophasic
time-dependent inhibition of thrombin, the linear
dependence of the pseudo-first-order rate constant on the L-372,011
concentration, and the complete monophasic recovery of fluorescence in
sequential stopped-flow studies are all consistent with L-372,011
inactivating thrombin via a one-step process. The ratio of
k
1 (2.4 s
1) and
k1 (7 µM
1
s
1) yielded a Ki value of 343 nM (Equation 4) for the thrombin·L-372,011 inhibitory
complex. This Ki value based on kinetic rate constants agrees nicely with that determined (330 nM) from
steady state measurements of L-372,011-mediated inhibition of
thrombin-catalyzed substrate hydrolysis.
View this table:
[in this window]
[in a new window]
|
Table II
Kinetic constants for the binding of inhibitors to thrombin
Kinetic constants were determined at pH 7.5 buffer containing 0.05 M Tris, 0.15 M NaCl, 0.1% PEG-8000 at
25 °C.
|
|
The time-dependent inactivation of thrombin by the
ketoamide L-372,051 in the presence of substrate was a biphasic process that was fitted by Equation 16. The first
(kobs1) and second phase (kobs2) exhibited a linear (Fig.
8A) and hyperbolic (Fig.
8B) dependence on the concentration of L-372,051,
respectively. From a plot of kobs2
versus L-372,051 concentration (Fig. 8B),
values of 0.054 ± 0.002 s
1 and 285 ± 44 nM were determined for k2 and
Ki, init, respectively (Equation 10). A
plot of kobs1 versus L-372,051
concentration (Fig. 8A) was analyzed using Equation 9 and
yielded a k1 value of 4.7 ± 0.5 µM
1 s
1.

View larger version (19K):
[in this window]
[in a new window]
|
Fig. 8.
Dependence of the rate constants
kobs1 (A) and
kobs2 (B) on L-372,051
concentration under stopped-flow conditions. Open circles
depict experiments where thrombin (10-100 nM) was mixed with an equal volume of 24 µM Z-GPR-afc and L-372,051
(1-30 µM). Closed symbols depict experiments
where p-aminobenzamidine (100-300 µM) was
displaced from thrombin (0.1-1 µM) by L-372,051 (1-80 µM). Closed circles depict the rate constants
kobs1 and kobs2 derived
from a biphasic fit (Equation 8) of the p-aminobenzamidine displacement by L-372,051 at low concentrations of inhibitor, whereas
closed squares depict the rate constant
kobs derived from a monophasic fit (Equation 6)
of p-aminobenzamidine displacement by L-372,051 at high
concentrations of inhibitor. A, the solid line
represents the best fit of Equation 9 to the data. Inset, concentration expansion of A. B, the solid
line represents the best nonlinear least squares fit of Equation 10 to the data.
|
|
The binding of the ketoamide L-372,051 to thrombin was also studied by
p-aminobenzamidine displacement. In contrast to the behavior
of the ketoamide L-370,518, displacement of
p-aminobenzamidine from thrombin at low concentrations of
L-372,051 was a biphasic process (data not shown). As expected the
pseudo-first-order rate constants (kobs1 and
kobs2) derived from
p-aminobenzamidine displacement were similar to those
obtained from substrate hydrolysis (see Fig. 8). Monophasic and
biphasic displacement of p-aminobenzamidine from thrombin
obtained with the ketoamides L-370,518 and L-372,051, respectively, is
due to their different Ki, init values.
With L-370,518 concentrations used for the
p-aminobenzamidine displacement experiment, residual free
thrombin after transient formation of EI1
(Ki, init ~15 nM) during
the first phase was undetectable; in contrast, a substantial fraction of free thrombin was present at the end of the first phase with L-372,051 (Ki, init = 285 nM). When concentrations ([It] > 10 µM) of L-372,051 were much greater than
Ki, init the second phase disappeared.
The loss of the second phase at high L-372,051 concentrations is
consistent with a two-step pathway (Scheme I). If the
EI1 complex involving L-372,051 is in rapid equilibrium with E and I, an estimate for the
k
1 value, 1.34 s
1, can be
deduced from the relationship k
1 = Ki, init × k1
and the experimentally determined values of
Ki, init (285 nM) and
k1 (4.7 µM
1
s
1). Comparison of the k
1 value
with the value of k2 (0.054 s
1)
obtained from Fig. 8B indicates that the assumption of a
rapid equilibrium of EI1 with E and I
(k
1
k2) is
justified.
Fig. 9 shows the results of a sequential
stopped-flow experiment wherein thrombin is reacted with L-372,051 for
increasing lengths of time (traces B-H,
respectively) and then reacted with DAPA. When the first reaction
mixture is aged long enough to allow complete conversion of
EI1 to EI2, no reaction
with DAPA is observed (Fig. 9, trace H). The approach of
fluorescence to its final value in traces B-G was a
pseudo-first-order process (Equation 11) with a mean rate constant of
1.34 ± 0.11 s
1. Since k
1
k2, this rate constant should be
equivalent to k
1 (see Equation 18). As
expected for a two-step process (when k
1
k2), the k
1 value (1.34 s
1) determined from the sequential stopped-flow
experiment is equal to the value (1.34 s
1) calculated
from the relationship k
1 = Ki, init × k1.
At short aging times (trace B, 42 ms), there was no
significant burst of fluorescence suggesting that conversion of
E + I to EI1 was complete. This
finding was anticipated since the L-372,051 concentration, 20 µM, was 10-fold higher than that used in the sequential
stopped-flow experiment for L-370,518. Hence, the second-order rate
constant (k1) for association of L-372,051 with
thrombin could not be determined in this experiment. At aging times
<500 ms, all of the enzyme was recoverable from
EI1. This observation is consistent with a
two-step pathway, wherein k
1
k2 (i.e. EI1 dissociates
to E and I more rapidly than it converts to
EI2) and EI1 was not
converted to EI2 (within the 500 ms time interval). At longer preincubation times (Fig. 9, traces
C-H), EI1 was converted to
EI2; hence, the fraction of enzyme recoverable from EI1 is a function of both
k
1/(k2 + k
1) and the preincubation time. The
fER at the end of various aging times was obtained
as described for L-370,518. A log plot of fER
versus aging time yielded a pseudo-first-order rate constant
of 0.058 s
1 with an intercept at 1.0 (data not shown).
One interpretation of the results is that 0.058 s
1 is the
pseudo-first-order rate constant for formation of
EI2 from EI1 and 1.0 represents the fraction of enzyme recoverable (k
1/(k
1 + k2)) which is consistent with a two-step reaction scheme with k
1
k2. The k2 value from
sequential stopped-flow, 0.058 s
1, is comparable to the
k2 value, 0.054 s
1, from the
limiting rate in a plot of kobs2
versus L-372,051 concentration (Fig.
8B).

View larger version (28K):
[in this window]
[in a new window]
|
Fig. 9.
Time-dependent increase of DAPA
fluorescence using sequential stopped-flow. Thrombin (0.4 µM) was preincubated (first mix) with L-372,051 (20 µM) for 42 ms (B), 1 s (C),
4.8 s (D), 9.6 s (E), 14 s
(F), 29 s (G), and 200 s (H)
before final dilution (second mix) with 80 µM DAPA.
Thrombin is also preincubated with DAPA for 3 s before dilution
with L-372,051 (A).
|
|
The value of k
2 for the reaction of the
ketoamide L-372,051 with thrombin was determined as described
previously for L-370,518 (data not shown). The progress curve depicting
the regeneration of enzyme activity was fit by Equation 11 to yield a
pseudo-first-order rate constant (koff) of
8 × 10
4 s
1 (data not shown). Since
k
1
k2, Equation 17 indicates that the koff value (8 × 10
4 s
1) is essentially equivalent to
k
2. Using Equation 5 and the experimentally
determined values of k1 (4.72 µM
1 s
1),
k
1 (1.34 s
1),
k2 (0.054 s
1), and
k
2 (8 × 10
4
s
1), a value of 4.2 nM was calculated for
Ki. The calculated value of Ki
(4.2 nM) agreed with the value determined (4 nM) from steady state measurements of the inhibition of
thrombin-catalyzed substrate hydrolysis by L-372,051.
Replacement of the P1' N-methylcarboxamide in L-370,518 with
azetidylcarboxamide yielded ketoamide L-372,228 (Table I). Using methods previously described for L-370,518 and L-372,051, the equilibrium and rate constants for the inactivation of thrombin by
L-372,228 were determined (Table II). The equilibrium constant for the
inhibition of thrombin-catalyzed hydrolysis of a fluorogenic substrate
by the azetidyl-substituted ketoamide L-372,228 was 40 ± 5 pM. The kinetically determined equilibrium constant for the
thrombin·L-372,228 complex using Equation 5 and the experimentally determined values of k1 (0.52 µM
1 s
1),
k
1 (0.42 s
1),
k2 (0.56 s
1), and
k
2(3.5 × 10
5
s
1) was 50 pM which was similar to the value
of 40 pM derived from steady state measurements of the
inhibition of thrombin-catalyzed substrate hydrolysis by L-372,228.
 |
DISCUSSION |
The sequential stopped-flow procedures used in this study enabled
us for the first time to determine directly the individual rate
constants k1, k
1, and
k2 for a two-step inhibitory pathway without
invoking any assumptions regarding the relative rates of the first and
second steps. Prior evaluation of individual rate constants of two-step
inhibitory reactions where k
1 was comparable
to k2 (e.g. Ref. 22), have relied
upon the effects of viscogens on reaction rates with the assumption
that the viscosity enhancing agents only alters diffusion-controlled
processes and does not compromise the conformation of the reactants.
Our sequential stopped-flow method avoided the use of perturbants and
allowed us to directly and precisely evaluate the individual rate
constants for two-step inhibitory pathways.
We have presented evidence that the desketoamides, L-371,912 and
L-372,011, inhibit thrombin via a one-step pathway; in contrast, their
respective
-ketoamide analogs, L-370,518 and L-372,051, inhibit
thrombin via a two-step pathway. It is unlikely that the two-step
binding pathway seen with the ketoamides reflects a cis to
trans conformational transition around the proline amide
bond of the inhibitor, since this proline amide bond is in a
trans conformation in both the desketoamide L-371,912 and
the corresponding ketoamide L-370,518 complexes of thrombin (12). The
value of the equilibrium constant (K
1 = 14 nM) for dissociation of the EI1
complex between thrombin and L-370,518 was similar to the value of the
equilibrium constant (Ki = 5 nM) for
dissociation of the thrombin·L-371,912 complex. Additionally, similar
values were observed for the equilibrium constant
(K
1 = 285 nM) for dissociation of
the initial complex between thrombin and L-372,051 and the dissociation
constant for the thrombin·L-372,011 complex (Ki = 330 nM). This correspondence is consistent with the view
that L-370,518 and L-372,051 form initial complexes with thrombin
wherein the
-ketoamide moiety interacts minimally with thrombin, and
the interactions between thrombin and the remainder of the inhibitors
are similar to those of the corresponding desketoamide analogs. If this
view is correct, the second step in the inhibitory pathway observed
with the
-ketoamide inhibitors would reflect formation of the
hemiketal adduct, together with any reorientation of the inhibitor
dictated by the geometrical constraints imposed by hemiketal
formation.
Substitution of an
-ketoamide group for the hydrogen atom in
L-371,912 (Ki = 5 nM) to yield L-370,518
(Ki = 90 pM) resulted in only a 56-fold
gain in inhibitory potency (10-12), whereas the same substitution in
L-372,112 (Table II) (Ki = 1.2 µM) to
afford L-370,310 (Ki = 2.8 nM) resulted
in a 429-fold gain in inhibitory potency (8, 9). Interestingly, the
cyclohexyl group of L-370,518 in the thrombin inhibitor complex is
rotated 90° from its position in the thrombin·L-371,912 complex
(12). This fact suggests that formation of the hemiketal adduct of
L-370,518 with thrombin may force the cyclohexylamino group to assume a
conformation in the S1 pocket that is energetically less favorable than
that in the thrombin·L-371,912 complex, wherein the cyclohexylamino
group has a greater degree of freedom to optimize its interaction in
the S1 pocket. In contrast, formation of the corresponding hemiketal
adduct of L-370,310 with thrombin may not result in less favorable
binding interactions between the less bulky
-amino alkyl chain and
the S1 pocket in thrombin. These factors may well account for the fact
that a lower potency ratio is observed for the L-370,518/L-371,912
ketoamide/desketoamide pair than is observed for the corresponding
L-370,310/L-372,112 ketoamide/desketoamide pair.
The observation that L-372,228 forms a weaker initial complex with
thrombin than does L-370,518 suggests that the more bulky P1' group in
L-372,228 contributes repulsive interactions with thrombin in the
initial inhibitory complex. Surprisingly, these unfavorable
interactions appear to be restricted to the EI1
complex as evidenced by the 16-fold increase in the value of
k2 and the 10-fold decrease of
k
2 for the binding of L-372,228 to thrombin
relative to the corresponding kinetic constants for L-370,518. This
change from an endergonic contribution of the P1' group of L-372,228 in
the EI1 complex to an exergonic contribution in
the EI2 complex is consistent with reorientation
of thrombin and/or inhibitor upon formation of the hemiketal adduct
involving the active site serine residue of thrombin.
The enhanced inhibitory potency of L-370,518 relative to that of
L-372,051 reflects the importance of the hydrogen bond between the P3
amino group of L-370,518 and
Gly-2163 of thrombin as shown
by x-ray crystallographic analysis (12). Moreover, the increased
stability of the initial complex formed with L-370,518 relative to that
of the initial complex formed with L-372,051 suggests that the P3 amino
hydrogen bond is formed in the initial complex. Comparisons of rate
constants for formation and dissociation of the
EI1 complexes formed with L-370,518 and L-372,051 indicate that the predominant effect of this hydrogen bond is
to decrease the rate constant for dissociation of the initial complex
by about 27-fold (Table II).
In summary we have demonstrated that certain
-ketoamide inhibitors
of thrombin inactivate thrombin via a two-step pathway, wherein
formation of the covalent bond between the inhibitor and the active
site serine residue probably occurs in the second step. Additionally,
individual rate constants for the two-step inhibitory pathway were
evaluated directly using a novel sequential stopped-flow analysis which
should be applicable to the kinetic characterization of other
enzyme-inhibitor pathways.