Linear Relationships between the Ligand Binding Energy and the
Activation Energy of Time-dependent Inhibition of
Steroid 5
-Reductase by
1-4-Azasteroids*
Gaochao
Tian
§ and
Curt D.
Haffner¶
From the Departments of
Molecular Biochemistry and
¶ Medicinal Chemistry, GlaxoSmithKline Research and Development,
Research Triangle Park, North Carolina 27709
Received for publication, January 29, 2001, and in revised form, February 16, 2001
 |
ABSTRACT |
The inhibition of steroid 5
-reductase
(5AR) by
1-4-azasteroids is characterized by a
two-step time-dependent kinetic mechanism where inhibitor
combines with enzyme in a fast equilibrium, defined by the inhibition
constant Ki, to form an initial reversible enzyme-inhibitor complex, which subsequently undergoes a
time-dependent chemical rearrangement, defined by the rate
constant k3, leading to the formation of an
apparently irreversible, tight-binding enzyme-inhibitor complex (Tian,
G., Mook, R. A., Jr., Moss, M. L., and Frye, S. V. (1995) Biochemistry 34, 13453-13459). A detailed kinetic
analysis of this process with a series of
1-4-azasteroids having different C-17
substituents was performed to understand the relationships between the
rate of time-dependent inhibition and the affinity of the
time-dependent inhibitors for the enzyme. A linear
correlation was observed between ln(1/Ki), which is
proportional to the ligand binding energy for the formation of the
enzyme-inhibitor complex, and
ln(1/(k3/Ki)), which is
proportional to the activation energy for the inhibition reaction under
the second order reaction condition, which leads to the formation of
the irreversible, tight-binding enzyme-inhibitor complex. The
coefficient of the correlation was
0.88 ± 0.07 for type 1 5AR
and
1.0 ± 0.2 for type 2 5AR. In comparison, there was no
obvious correlation between ln(1/Ki) and
ln(1/k3), which is proportional to the
activation energy of the second, time-dependent step
of the inhibition reaction. These data are consistent with a
model where ligand binding energies provided at C-17 of
1-4-azasteroids is fully expressed to lower the
activation energy of k3/Ki
with little perturbation of the energy barrier of the second,
time-dependent step.
 |
INTRODUCTION |
5AR1 catalyzes the
NADPH-dependent reductive conversion of testosterone to
dihydrotestosterone. Two isozymes of 5AR, designated types 1 and 2, have been described (1, 2). Although 5AR1 is predominantly expressed in
skin and liver, 5AR2 is mainly expressed in prostate, seminal vesicles,
liver, and epididymis (3). Both 5AR1 and 5AR2 are implicated in benign
prostatic hyperplasia (2), a condition affecting the majority of men
over age of 60 (4). Intense efforts made over the past decade to
develop drugs against the activity of this enzyme has led to the
discovery of potent, time-dependent
1-4-azasteroidal inhibitors of 5AR, including
finasteride and GG745 (see Fig. 1).
Finasteride inhibits both 5AR1 and 5AR2 in a time-dependent
manner (5-7). The kinetic mechanism of this time-dependent
inhibition is characterized by a fast binding step for the formation of
an initial enzyme-inhibitor complex (EI), followed by a
time-dependent event leading to the formation of an
apparently irreversible enzyme-inhibitor complex (EI*). This
time-dependent event involves a chemical transformation at
the
1 double bond (8). The finding of a
NADP-dihydrofinasteride adduct as a product of this
time-dependent inhibition reaction suggests that the
chemical event is a combination of a nucleophilic attack of the hydride
of the enzyme-bound NADPH on the
1 double bond of
finasteride and the subsequent capture of the resulting NADP cation by
the reduced finasteride (7). This NADP-dihydrofinasteride adduct is a
tight-binding inhibitor of both 5AR1 and 5AR2 with a
Ki that is less than 1 pM (7).
Although it is an extremely potent dual inhibitor of 5AR
thermodynamically in vitro, finasteride does not fully
suppress plasma dihydrotestosterone level at doses up to 100 mg. A
theoretical analysis of pharmacodynamic effects of
time-dependent inhibitors indicates that the in
vivo effects of such inhibitors depend upon both the kinetic and
thermodynamic potency of the inhibitor (9) and provides a theoretical
basis for improving the in vivo efficacy of
1-4-azasteroids by improving their kinetic potency in
the inhibition of 5AR (10, 11). Because a smaller Ki
value would translate into a greater
k3/Ki, the second order rate constant for the time-dependent inhibition, it was reasoned
that improving the affinity of
1-4-azasteroids for 5AR
would enhance the kinetic potency of the inhibitors against 5AR (10,
11). Frye and co-workers (12-14) had shown that structural variation
at C-17 of 6-azasteroids, a class of reversible inhibitors of 5AR, with
bulky lipophilic substituents significantly enhances the affinity of
the steroid inhibitors for 5AR. Replacing the
N-t-butyl substituent at C-17 of finasteride with
a much more lipophilic N-(2,5-bis(trifluoromethyl))phenyl group (GG745; see Fig. 1) indeed significantly increased the rate of
inhibition of 5AR, supporting the strategy to improve the rate of
time-dependent inhibition of 5AR by using ligand binding
energies provided at C-17 of
1-4-azasteroids (10,
11).
Although this approach was successful in discovering GG745, whether it
was generally possible to use ligand binding energies to optimize the
kinetic potency of
1-4-azasteroids remained unclear. In
the current study, we synthesized a series of
1-4-azasteroids with different C-17 substituents and
evaluated the effect of the ligand binding energies of these
1-4-azasteroids on the rate of
time-dependent inhibition of both 5AR1 and 5AR2. Linear
relationships were observed between the binding energies of these
compounds and the reduction in the activation energy for the inhibition
reaction under second order reaction conditions. The fact that
coefficients for these linear relationships were close to unity
indicated full realization of the binding energies provided with
1-4-azasteroids at C-17 in reducing the energy barrier
for the time-dependent inhibition, supporting the notion
that systematic optimization of the kinetic potency of
1-4-azasteroids by enhancing ligand binding energies is feasible.
 |
EXPERIMENTAL PROCEDURES |
Materials--
[1,2,6,7-3H]Progesterone (95 Ci/mmol) was purchased from PerkinElmer Life Sciences.
Progesterone, NADPH, dithiothreitol, glucose 6-phosphate, and
glucose-6-phosphate dehydrogenase were purchased from Sigma. All other
reagents purchased were of the highest quality possible. Human
recombinant 5AR1 and 5AR2 were prepared according to the procedure
described previously (6).
Preparation of Azasteroids--
Finasteride was synthesized as
described (15). GG745 was synthesized as described (16). Other
4-azasteroids and 6-azasteroids were synthesized according to published
procedures (17). The cycloalkylamines used to couple at C-17 were
synthesized via a three-step synthetic procedure utilizing the general
method outlined by Kalir and Balderman (18). The
2-t-butyl-5-trifluoromethyl aniline was synthesized via a
five-step procedure starting with 4-bromotrifluoromethylbenzene whereby
the t-butyl group was incorporated utilizing chemistry as
described (19).
5AR Activity Assays--
Buffers, solutions, and reaction
mixtures were prepared according to the procedure described previously
(6) except that in this study, [1,2,6,7-3H]progesterone
was used in the place of [1,2,6,7-3H]testosterone and
kept at 20 nM. All the assays were performed at pH 7.0, µ = 0.3, and 22 °C unless noted otherwise. These reactions were initiated by addition of enzyme and quenched at desired times with
ethanol. The substrate and product were separated by a C-18 reversed
phase column (4.6 × 150 mm) with a mobile phase of 35% water and
65% acetonitrile. The amount of product formed was quantitated by an
in-line radiodetector (
-Ram; Tampa, FL). The reactions catalyzed by
type 1 5AR was first order in progesterone ([S] = 20 nM
compared with Km = 690 nM), and the
activity of enzyme was expressed as the first order rate constant
(
, min
1) for the loss of substrate. For the
reactions with 5AR2, the substrate concentration (20 nM)
was higher than its Km (4.9 nM). Under
this condition, the activity of enzyme was expressed as the initial
rate (
, nM min
1) at 20 nM substrate.
Inhibition Assays of 5AR--
Reactions were performed, and the
product was analyzed as described above except that these reactions
contained an inhibitor (I) at a defined concentration. The inhibition
data were analyzed by non-linear least squares fitting of data to the
following equation,
|
(Eq. 1)
|
where
i is the enzyme activity in the presence of
inhibitor, to obtain IC50, the inhibitor concentration,
where 50% of the original enzyme activity was inhibited (6).
Progress Curve Analysis--
Reaction mixtures were prepared as
described above, and an inhibitor was added at a desired concentration.
The volume of a reaction mixture was set to 400 µl. Enzyme, at a
concentration in the range of 0.1 to 2 nM, with [I]/[E]
being kept at greater than 10, was added to initiate the reaction. At
different times, 20-µl aliquots were removed and quenched with 40 µl of ethanol. Substrate (S) remaining or product
(P) formed during the reaction was monitored as described
above. For 5AR1, data of substrate remaining at different times were
fitted to the following equation (6),
|
(Eq. 2)
|
to obtain kobsd, the observed inhibition
rate constant, and
i, the enzyme activity at 0 min. For
5AR2, data of product formed at various time points were analyzed by
using Equation 3 (20).
|
(Eq. 3)
|
To obtain Ki, the inhibition constant for the
formation of the initial EI complex in a two-step inhibition mechanism (see "Results and Discussion"), and k3, the
rate constant for the second, time-dependent step, either
of the following two methods were used. In the first method,
kobsd values at various inhibitor concentrations
were obtained and then reanalyzed against [I] to abstract
Ki and k3 by using Equation 4
(6).
|
(Eq. 4)
|
This method is necessary for determination of the kinetic
mechanism of the time-dependent inhibition and provides
good estimates of Ki and k3.
For certain inhibitors, the reactions were run at a single [I] to
obtain kobsd and
i. These values
were then used to calculate Ki and
k3, respectively, by using Equations 5 and
6.
|
(Eq. 5)
|
|
(Eq. 6)
|
This method is much simpler to perform than the method of
progress curve analysis at a range of inhibitor concentrations and provides a reasonable estimate of Ki and
k3.
 |
RESULTS AND DISCUSSION |
The in vivo potency of irreversible,
time-dependent inhibitors depends on the kinetic potency of
such inhibitors (9). One way to improve the kinetic potency of
time-dependent inhibitors is to provide the inhibitors with
increased ligand binding energies (10). The primary goal of this study
was to investigate the relationship between ligand binding energies and
the rate of time-dependent inhibition of 5AR by
1-4-azasteroids. Understanding such relationships could
be helpful in the design of strategies for optimizing the kinetic
potency of
1-4-azasteroids. Prior to performing such
investigations, it is necessary to understand the mechanism of the
time-dependent inhibition, which sets the framework upon
which the relationships can be investigated.
Kinetic Mechanism of Time-dependent Inhibition by
4-Azasteroids Is Two Steps--
Previously, the kinetics of
time-dependent inhibition of 5AR by finasteride and GG745
were shown to involve two steps (6, 10), shown in Equation 7,
|
(Eq. 7)
|
where inhibitor associates with enzyme to form an initial
EI, which then undergoes a time-dependent
rearrangement to form EI*. To gain further confidence in this two-step
mechanism for the structural class of
1-4-azasteroids,
we evaluated the inhibition kinetics for four additional
1-4-azasteroids (1-4) (Fig.
1) by using the method of progress curve
analysis at a range of inhibitor concentrations. The mechanism of
inhibition by all the four
1-4-azasteroids showed a
two-step kinetic mechanism as judged from the hyperbolic dependence of
kobsd on the inhibitor concentration [I] (data
not shown). The kinetic constants obtained by this method are
compared with the values obtained previously for finasteride and GG745
in Table I.

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Fig. 1.
Structures of
1-4-azasteroids for which the method of
progress curve analysis at a range of inhibitor concentrations was
performed to determine the kinetic mechanism of inhibition.
Finasteride,
17 -N-t-butylcarbamoyl-4-aza-5 -androstan-1-en-3-one;
GG745,
17 -N-(2,5-bis(trifluoromethyl))phenylcarbamoyl-4-aza-5 -androst-1-en-3-one;
1,
17 -N-1-(3,4-methylenedioxyphenyl)cyclohexylcarbamoyl-4-aza-5 -androst-1-en-3-one;
2, 17 -N-1-(4-methoxyphenyl)cyclohexyl
carbamoyl-4-aza-5 -androst-1-en-3-one; 3,
17 -N-1-(4-t-butylphenyl)cyclohexylcarbamoyl-4-aza-5 -androst-1-en-3-one;
4,
17 -N-1-(4-chlorophenyl)cyclopentylcarbamoyl-4-aza-5 -androst-1-en-3-one.
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Table I
Summary of kinetic parameters of the time-dependent
inhibition of 5AR by 1-4-azasteroids obtained using the
method of progress curve analysis at a range of inhibitor
concentrations
|
|
Methods to Improve the Rate of Time-dependent
Inhibition--
Having gained further confidence in the two-step
kinetic mechanism of time-dependent inhibition of 5AR by
1-4-azasteroids, we then turned our efforts to
developing strategies to improve the kinetic potency of
1-4-azasteroids. Analogous to enzyme catalysis,
time-dependent inhibition reactions may be "catalyzed"
by the use of binding energies derived from inhibitor-target
interaction (10). According to the theory developed for understanding
the evolution of maximal catalytic effectiveness of enzymes (21, 22),
the binding energies an enzyme can provide during reaction may be used
to lower the significant reaction energy barriers via three different
mechanisms, "uniform binding", "differential binding," and
"catalysis of an elementary step." Uniform binding is a mechanism
by which the enzyme lowers an energy barrier of the catalyzed reaction
by binding the transition and ground states equally well. Differential
binding is the ability of enzyme to differentiate between internal
states, which although important for enzyme evolution is irrelevant for enhancing the rate of time-dependent inhibition, because
there is only one relevant internal state, that of EI, in a two-step mechanism. The catalysis of an elementary step is the reduction of the
activation energy for an individual step along the reaction coordinate
and requires the enzyme to differentiate between the transition state
and the ground state involving that individual step. Comparing enzyme
catalysis and time-dependent inhibition, the effects of
uniform binding and catalysis of an elementary step in the evolution of
enzyme catalytic effectiveness are equivalent to a
"Ki effect" (Fig.
2B) and a
"k3 effect" (Fig. 2C), respectively, in the enhancement of the rate of
time-dependent inhibition. Obviously, the rate of
inhibition can be improved by either lowering the energy barrier for
the time-dependent event, a k3
effect, or by enhancing the ligand binding to the ground state, a
Ki effect. Although the Ki
effect would produce a linear relationship between the ligand binding
energy and the energy barrier for the inhibition, the
k3 effect may not. Chemically, options to
produce a k3 effect by activating the
1 double bond are limited, and this double bond
activation could also diminish selectivity. Given the understanding
that 5AR tolerates bulky groups at C-17 and the structure-activity
relationship previously revealed between such groups and the affinity
of 6-azasteroids for the enzyme (12-14), it appeared feasible to
improve the rate of time-dependent inhibition of 5AR by
exploiting the Ki effect of the C-17
substitution.

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Fig. 2.
Energy profiles for a typical two-step
time-dependent inhibition. The rectangular
bars represent energies for inhibitor binding or activation
energies for conversion of the internal states, EI (A). The
energy barrier of k3/Ki may
be reduced by a Ki effect (B),
analogous to uniform binding for optimizing enzyme catalysis by the
nature (see "Results and Discussion") that reduces the transition
state and the state of the EI complex equally as indicated by the
arrows. The energy barrier of
k3/Ki may also be reduced by
a k3 effect (C), which, analogous to
the catalysis of an elementary step in optimization of enzyme catalysis
by the nature (see "Results and Discussion"), only reduces the
transition state.
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|
Linear Relationships between the Binding Energy of
1-4-Azasteroids for 5AR and the Activation Energy of
Time-dependent Inhibition--
As indicated above, if
ligand binding energies have purely a Ki effect in
the time-dependent inhibition, one would see a linear
correlation between the ligand binding energy and the activation energy
for the time-dependent reaction. A series of
1-4-azasteroids with a diversified set of C-17
substituents were chosen to evaluate the effect of ligand binding
energies on the rate of time-dependent inhibition of 5AR.
The method of progress curve analysis at a single concentration of
inhibitor (see "Experimental Procedures") was used to obtain the
constants k3, Ki, and
k3/Ki. The values obtained
for the inhibition of 5AR1 and 5AR2 are listed in Tables
II and
III, respectively. The value of
ln(1/Ki), which is proportional to the ligand binding energy, was then plotted against
ln(1/(k3/Ki)), which is
proportional to the activation energy of the second order rate
constant, k3/Ki. A linear
relationship between ln(1/Ki) and
ln(1/(k3/Ki)) was evident for
the inhibition of both 5AR1 and 5AR2 as shown in Figs.
3A and
4A, respectively. The
coefficient of the linear correlation was
0.88 ± 0.07 for type
1 5AR and
1.0 ± 0.2 for type 2 5AR. The fact that these
coefficients are close to unity suggests a pure Ki
effect of the ligand binding energies on the activation energy for the
time-dependent inhibition reaction. Also consistent with
this, the ligand binding energies had little effect on the activation
energy of 1/k3 as judged by the lack of
correlation between ln(1/Ki) and ln(1/k3) (Figs. 3B and
4B).
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Table II
Summary of kinetic parameters of the time-dependent inhibition of 5AR1
by 1-4-azasteroids obtained using the method of progress
curve analysis at a single inhibitor concentration
The values of Ki and k3 were
calculated using Equations 5 and 6, respectively, with
kobsd and i values obtained by fitting
data to Equation 2. The relative errors associated with
kobsd and I ranged from 10 to
35%.
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Table III
Summary of kinetic parameters of the time-dependent inhibition of 5AR2
by 1-4-azasteroids obtained using the method of progress
curve analysis at a single inhibitor concentration
The values of Ki and k3 were
calculated using Equations 5 and 6, respectively, with
kobsd and i values obtained by fitting
data to Equation 3. The relative errors associated with
kobsd and I ranged from 10 to
35%.
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Fig. 3.
Effect of ligand binding energies
(ln(1/Ki)) of
1-4-azasteroids on the activation
barrier of k3/Ki
(ln(1/(k3/Ki)))
(A) and k3
(ln(1/(k3))) (B) for
5AR1. The ligand binding energy (ln(1/Ki)) is
linearly correlated to the activation energy of
k3/Ki
(ln(1/(k3/Ki)))
(A), with a coefficient of 0.88 ± 0.07. There is no
apparent correlation between the ligand binding energy
(ln(1/Ki)) and the activation energy of
k3/Ki
(ln(1/(k3/Ki)))
(B).
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Fig. 4.
Effect of ligand binding energies
(ln(1/Ki)) of
1-4-azasteroids on the activation
barrier of k3/Ki
(ln(1/(k3/Ki)))
(A) and k3
(ln(1/(k3))) (B) for
5AR2. The ligand binding energy (ln(1/Ki)) is
linearly correlated to the activation energy of
k3/Ki
(ln(1/(k3/Ki)))
(A), with a coefficient of 1.0 ± 0.2. There is no
apparent correlation between the ligand binding energy
(ln(1/Ki)) and the activation energy of
k3/Ki
(ln(1/(k3/Ki)))
(B).
|
|
Linear Correlation between the Affinity of
1-4-Azasteroids and the Affinity of 6-Azasteroids for
5AR--
The linear relationship demonstrated above for ligand binding
energies and the activation energy for the time-dependent
inhibition of 5AR by
1-4-azasteroids suggests that the
kinetic potency of
1-4-azasteroids can be optimized
systematically by evaluating the binding affinities of these compounds
for 5AR. Given the time-dependent nature of
1-4-azasteroids in the inhibition of 5AR and that
the binding affinities of these compounds cannot be evaluated precisely
by regular, non-time-dependent inhibition kinetics,
time-dependent kinetics are needed for determining the
binding affinities of
1-4-azasteroids for 5AR. However,
the time-consuming nature of performing kinetic studies of
time-dependent inhibition precludes fast evaluation of the
initial binding of
1-4-azasteroids to 5AR. Because a
large number of 6-azasteroids, which are non-time-dependent
inhibitors of 5AR, had been synthesized, one way to circumvent this
technical inconvenience is to conduct regular inhibition assays of
6-azasteroids and then predict the ligand binding energies that the
C-17 substituents could provide with
1-4-azasteroids.
This approach requires that the C-17 substituent of
non-time-dependent steroids binds 5AR in the same way as
does the C-17 substituent of
1-4-azasteroids. To
evaluate this, the ligand binding energies of a series of
1-4-azasteroids and 6-azasteroids that bear the same set
of C-17 substituents were compared. The Ki values
for the
1-4-azasteroids (Table
IV) were obtained using the method of
progress curve analysis at a single concentration of inhibitor, and
IC50 values (Table IV) of the 6-azasteroids were obtained
using regular inhibition assays. The plots of
ln(1/Ki) versus ln(1/IC50) (Fig. 5) indeed indicate a reasonable
linear correlation between the binding affinities of the
1-4-azasteroids and
6-azasteroids,2 supporting
the approach of using 6-azasteroids to quickly evaluate the ligand
binding energies of various C-17 substituents that can be used to
improve the kinetic potency of
1-4-azasteroids. By using
this approach, a great number of potent
1-4-azasteroids
have been discovered (data not shown), which in turn greatly
facilitated the effort to discover drugs that are effective at
inhibiting 5AR.
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Table IV
Summary of IC50 and Ki values, respectively, of
6-azasteroids and 4-azasteroids with the same C-17 substituents
The Ki values were calculated using Equation 5 with
kobsd and I values (relative errors in
the range of 10 to 35%) obtained using the method of progress curve
analysis at a single inhibitor concentration, and the IC50
values were obtained using the regular inhibition method at pH 7.0, 22 °C (see "Experimental
Procedures").
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Fig. 5.
Correlation of ligand binding energies
(ln(1/Ki)) of
1-4-azasteroids and ligand binding
energies (ln(1/IC50)) of 6-azasteroids for 5AR1
(A) and 5AR2 (B).
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|
Conclusions--
A series of
1-4-azasteroids having
different C-17 substituents were evaluated for their
time-dependent inhibition of 5
-reductase to understand
the relationships between the rate of time-dependent inhibition and the affinity of the time-dependent
inhibitors for the enzyme. The results indicated a linear correlation
between the ligand binding energy for the formation of the EI complex and the activation energy for the overall inhibition reaction under the
second order reaction condition. There was no obvious correlation
between the ligand binding energy and the activation energy for the
second, time-dependent step of the inhibition reaction. These data are consistent with a model where ligand binding energies provided at C-17 of
1-4-azasteroids is fully expressed
to lower the activation energy of the overall
time-dependent inactivation reaction with little perturbation of the energy barrier of the second,
time-dependent step. Subsequently, a strategy and
procedures to improve rates of time-dependent inhibition by
providing inhibitor with ligand binding energies were presented that
may be generally useful for developing potent
time-dependent inhibitors of pharmaceutical values.
 |
ACKNOWLEDGEMENTS |
We thank Dr. Stephen V. Frye for insights
over the entire course of this study and useful discussions during the
writing of this manuscript. J. Darren Stuart is acknowledged for
preparing recombinant human 5AR1 and 5AR2 proteins used in this study.
 |
FOOTNOTES |
*
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement" in
accordance with 18 U.S.C. Section
1734 solely to indicate this fact.
§
To whom correspondence should be addressed. Tel.: 302-886-8138;
Fax: 302-886-4983; E-mail: gaochao.tian@astrazeneca.com.: Dept. of
Lead Discovery, Astrazeneca, Wilmington, DE 19850.
Published, JBC Papers in Press, March 8, 2001, DOI 10.1074/jbc.M100793200
2
The greater scattering in the values determined
for the type 2 5AR may be partly attributed to the
time-dependent nature of some 6-azasteroids in the
inhibition of type 2 5AR (23).
 |
ABBREVIATIONS |
The abbreviations used are:
5AR, 5
-reductase;
EI, enzyme-inhibitor complex;
EI*, apparently
irreversible enzyme-inhibitor complex..
 |
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Copyright © 2001 by The American Society for Biochemistry and Molecular Biology, Inc.
Copyright © 2001 by the American Society for Biochemistry and Molecular Biology.