Thermodynamic analysis of remote substrate binding energy in 3α-hydroxysteroid dehydrogenase/carbonyl reductase catalysis

Article abstract of DOI:10.1016/j.cbi.2019.02.011

The binding energy of enzyme and substrate is used to lower the activation energy for the catalytic reaction. 3α-HSD/CR uses remote binding interactions to accelerate the reaction of androsterone with NAD⁺. Here, we examine the enthalpic and entropic components of the remote binding energy in the 3α-HSD/CR-catalyzed reaction of NAD⁺ with androsterone versus the substrate analogs, 2-decalol and cyclohexanol, by analyzing the temperature-dependent kinetic parameters through steady-state kinetics. The effects of temperature on k_cat/K_m for 3α-HSD/CR acting on androsterone, 2-decalol, and cyclohexanol show the reactions are entropically favorable but enthalpically unfavorable. Thermodynamic analysis from the temperature-dependent values of K_m and k_cat shows the binding of the E-NAD⁺ complex with either 2-decalol or cyclohexanol to form the ternary complex is endothermic and entropy-driven, and the subsequent conversion to the transition state is both enthalpically and entropically unfavorable. Hence, solvation entropy may play an important role in the binding process through both the desolvation of the solute molecules and the release of bound water molecules from the active site into bulk solvent. As compared to the thermodynamic parameters of 3α-HSD/CR acting on cyclohexanol, the hydrophobic interaction of the B-ring of steroids with the active site of 3α-HSD/CR contributes to catalysis by increasing exclusively the entropy of activation (ΔTΔS^? = 1.8 kcal/mol), while the BCD-ring of androsterone significantly lowers ΔΔH^? by 10.4 kcal/mol with a slight entropic penalty of ?1.9 kcal/mol. Therefore, the remote non-reacting sites of androsterone may induce a conformational change of the substrate binding loop with an entropic cost for better interaction with the transition state to decrease the enthalpy of activation, significantly increasing catalytic efficiency.

Full text of DOI:10.1016/j.cbi.2019.02.011

Accepted Manuscript
Thermodynamic analysis of remote substrate binding energy in 3α-hydroxysteroid
dehydrogenase/carbonyl reductase catalysis
Chi-Ching Hwang, Pei-Ru Chang, Chia-Lin Hsieh, Yun-Hao Chou, Tzu-Pin Wang
PII:
S0009-2797(18)31229-8
https://doi.org/10.1016/j.cbi.2019.02.011
CBI 8544
DOI:
Reference:
To appear in: Chemico-Biological Interactions
Received Date: 25 September 2018
Revised Date: 30 January 2019
Accepted Date: 14 February 2019
Please cite this article as: C.-C. Hwang, P.-R. Chang, C.-L. Hsieh, Y.-H. Chou, T.-P. Wang,
Thermodynamic analysis of remote substrate binding energy in 3α-hydroxysteroid dehydrogenase/
carbonyl reductase catalysis, Chemico-Biological Interactions (2019), doi: https://doi.org/10.1016/
j.cbi.2019.02.011.
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ACCEPTED MANUSCRIPT
Graphical abstract- Thermodynamic analysis of remote substrate binding
interactions in 3α-hydroxysteroid dehydrogenase/carbonyl reductase catalysis

ACCEPTED MANUSCRIPT
Thermodynamic analysis of remote substrate binding energy in 3α-
hydroxysteroid dehydrogenase/carbonyl reductase catalysis
1
,2
1
3
3
Chi-Ching Hwang *, Pei-Ru Chang , Chia-Lin Hsieh , Yun-Hao Chou and Tzu-Pin
4
Wang
1
Department of Biochemistry, School of Medicine, College of Medicine, Kaohsiung
Medical University, Kaohsiung 80708, Taiwan
2
Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung
8
0708, Taiwan
3
Graduate Institute of Medicine, College of Medicine, Kaohsiung Medical University,
Kaohsiung 80708, Taiwan
4
Department of Medicinal and Applied Chemistry, Kaohsiung Medical University,
Kaohsiung 80708, Taiwan
Corresponding author:
Chi-Ching Hwang, Ph.D.
Department of Biochemistry, Kaohsiung Medical University
1
8
8
00 Shih-Chuan 1st RD. Kaohsiung, Taiwan
86-7-3121101 ext 2306 (office)
86-7-3218309 (fax)
cchwang@kmu.edu.tw
Running Title: Enthalpic and entropic contributions from remote binding energy to
enzyme catalysis
1

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Abstract
The binding energy of enzyme and substrate is used to lower the activation energy
for the catalytic reaction. 3α-HSD/CR uses remote binding interactions to accelerate the
+
reaction of androsterone with NAD . Here, we examine the enthalpic and entropic
+
components of the remote binding energy in the 3α-HSD/CR-catalyzed reaction of NAD
with androsterone versus the substrate analogs, 2-decalol and cyclohexanol, by analyzing
the temperature-dependent kinetic parameters through steady-state kinetics. The effects
m
of temperature on kcat/K for 3α-HSD/CR acting on androsterone, 2-decalol, and
cyclohexanol show the reactions are entropically favorable but enthalpically unfavorable.
Thermodynamic analysis from the temperature-dependent values of K and k shows
m
cat
+
the binding of the E-NAD complex with either 2-decalol or cyclohexanol to form the
ternary complex is endothermic and entropy-driven, and the subsequent conversion to the
transition state is both enthalpically and entropically unfavorable. Hence, solvation
entropy may play an important role in the binding process through both the desolvation of
the solute molecules and the release of bound water molecules from the active site into
bulk solvent. As compared to the thermodynamic parameters of 3α-HSD/CR acting on
cyclohexanol, the hydrophobic interaction of the B-ring of steroids with the active site of
3
α-HSD/CR contributes to catalysis by increasing exclusively the entropy of activation
‡
‡
(∆T∆S = 1.8 kcal/mol), while the BCD-ring of androsterone significantly lowers ∆∆H
by 10.4 kcal/mol with a slight entropic penalty of -1.9 kcal/mol. Therefore, the remote
non-reacting sites of androsterone may induce a conformational change of the substrate
binding loop with an entropic cost for better interaction with the transition state to
decrease the enthalpy of activation, significantly increasing catalytic efficiency.
2

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Abbreviations: 3α-HSD/CR, 3α-hydroxysteroid dehydrogenase/carbonyl reductase; 2-
decalol, decahydro-2-naphthanol; SDR, short chain dehydrogenase/reductase; ∆G,ꢀ theꢀ
‡
Gibbsꢀfreeꢀenergyꢀchange;ꢀ∆G ,ꢀtheꢀGibbsꢀfreeꢀenergyꢀofꢀactivation; ∆H,ꢀtheꢀenthalpyꢀ
‡
‡
change;ꢀ ∆H ,ꢀ theꢀ enthalpyꢀ changeꢀ ofꢀ activation; ∆S,ꢀ theꢀ entropyꢀ change;ꢀ ∆H ,ꢀ theꢀ
entropyꢀchangeꢀofꢀactivation;
Keywords: Enzyme catalysis, binding energy, steady-state kinetics, Gibbs free energy
change, enthalpy and entropy
3

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1
. Introduction
The mechanism of catalysis with high substrate specificity of enzymes attracts great
interest of biochemists (1-3). Enzymes catalyze the reaction by binding the substrates to
form an enzyme-substrate complex, interacting with the transition-state, and forming and
releasing the product. The binding energy of enzyme and substrate is used for substrate
destabilization and transition state stabilization to lower the activation energy and
facilitate catalysis (4,5). Jencks proposed a Circe effect for enzyme catalysis in which the
binding energy is used for the distortion, electrostatic interactions, desolvation, and
entropy loss for bringing the substrates in the proper position for reaction and for better
binding to the transition state (6).
The binding interactions between enzyme and substrate, both at the site of chemical
transformation and with a non-reacting portion of the substrate, have been shown to
contribute to catalysis (6-8). As compared to the catalysis with a truncated substrate
analog, enzymes can use binding interactions with a non-reacting portion of the substrate
to destabilize the ground state and stabilize the transition state (6), assist in binding and
enhance the effective local concentration (1), provide substantial contributions to specific
transition state stabilization (6,9-11), induce a conformational change, and promote
significant changes in dynamics for residues located remotely from the binding site,
thereby accelerating the chemical reactions (12-17). Remote binding interactions in 3-
oxoacid CoA transferase, ketosteroid isomerase, triose phosphate isomerase, and
orotidine 5-monophosphate decarboxylase have been demonstrated to provide substantial
contributions to stabilize the transition state (9-11,18).
We have demonstrated the contributions of remote binding energy in the 3α-
4

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+
HSD/CR-catalyzed reaction of NAD with androsterone as compared to that for the
truncated analog (Figure 1)(19). The steroid rings are involved in the 3α-HSD/CR
catalysis. The B-ring of steroid improves catalysis (k /K ) without increasing k by
cat
B
cat
equally stabilizing both the transition state and ground state of the ternary complex by 2.2
kcal/mol. The remote BCD- and CD-rings of androsterone improve catalysis on both kcat
B
and kcat/K through differential binding interactions with the active site of 3α-HSD/CR by
contributing 8.5 and 6.4 kcal/mol to the stabilization of the transition state, respectively.
To obtain a clearer understanding of the factors involved in the energetics, the
enthalpy and entropy changes that accompany the formation of an enzyme-substrate
complex in both the ground state and transition state have been studied. Comparing the
value of kcat of the enzymatic reaction with the corresponding non-enzymatic reaction
(knon) shows that enzyme catalysis may arise mainly by reducing the enthalpy of
activation (20,21). However, the actions of cytidine deaminase on 5,6-dihydrocytidine
and GTP hydrolysis by EF-Tu on the ribosome have indicated that the reactions are
entropy-driven (22-25). To better understand enthalpic and entropic contributions to
enzyme catalysis, we compare an enzymatic reaction with a good substrate to the same
reaction with its truncated analog, thereby enabling the determination of the function of
remote binding interactions in catalysis. In this study, we determine the thermodynamic
+
parameters for the reaction of androsterone with NAD catalyzed by 3α-HSD/CR.
Moreover, we compare these parameters to the thermodynamic parameters for the
reaction with truncated analogs, 2-decalol and cyclohexanol. We analyze the kinetic
parameters of 3α-HSD/CR-catalyzed reaction with varied temperatures, giving the
‡
‡
thermodynamics parameters for the changes in enthalpy (∆H ) and entropy (∆S ) in the
5

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transition state and the changes in enthalpy (∆H) and entropy (∆S) in the ground state for
the binding interactions of enzyme and substrate. These energetic values provide valuable
insight into how remote interactions of the active site with substrate contribute to
catalysis.
+
Figure 1. 3α-HSD/CR-catalyzed oxidoreduction of NAD with androsterone and
truncated analogs, cyclohexanol and 2-decalol.
2
. Materials and methods
2
.1. Materials
Androsterone came from Steraloids, while cyclohexanol, racemic 2-decalol,
+
NAD , and equine alcohol dehydrogenase came from Sigma-Aldrich. All reagents were
of the highest purity available.
6

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2
.2. Overexpression and purification of 3α-HSD/CR
3
α-HSD/CR was expressed in Escherichia coli as described (19). In brief, the
BL21 (DE3) cells were cultivated in 1 L LB medium at 37 °C. The recombinant 3α-
HSD/CR was overexpressed by adding 0.5 mM isopropyl β-D-thiogalactopyranoside
(
IPTG) when the culture reached an optical density at 600 nm of 0.6-1. After an
additional 4 h for growth, the cells were harvested and lysed by sonication for 5 min with
0 s on and 10 s off cycles on ice. The cell debris was removed by centrifugation, and the
1
2
+
supernatant was loaded onto a Ni -NTA resin column (GE Healthcare Life Sciences).
The enzyme was eluted via a stepwise increase in the concentration of imidazole from 10
mM to 500 mM to purify the protein. 3α-HSD/CR was purified to homogeneity, as
determined using 12% SDS-PAGE. The protein concentration was determined by
Bradford assay with bovine serum albumin as a standard.
2
.3. Steady-state kinetics
The oxidation of androsterone and its truncated analogs catalyzed by 3α-
HSD/CRs was monitored by the formation of NADH spectrophotometrically at 340 nm
−
1
−1
(
ε = 6220 M cm ), using a Perkin Elmer Lambda 650 UV-vis spectrophotometer
equipped with a temperature-controlled Peltier block multicell changer. Assays were
performed across a suitable range of temperatures of 10-40 °C for 3α-HSD/CR-catalyzed
+
reaction of NAD with androsterone, 2-decalol and cyclohexanol, respectively. The initial
velocity patterns were obtained by varying the concentration of androsterone or the
+
truncated analog at several fixed concentrations of NAD in 0.1 mg/mL bovine serum
albumin (BSA), 0.1 M sodium 3-(cyclohexylamino)-1-propane sulfonate (Caps) buffer at
7

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pH 10.5 at varied temperatures. The assay was performed at pH 10.5 for an optimum
enzyme-catalyzed reaction (26). Due to the difference in activity for the truncated
analogs, different amounts of 3α-HSD/CR were added for assays. Typically, the
concentrations of 3α-HSD/CR for the assays of androsterone, 2-decalol, and
cyclohexanol were 0.085 nM, 85 nM, and 34 nM, respectively. All reactions were
initiated by adding enzyme. The initial velocity patterns were determined twice for 3α-
HSD/CR acting on androsterone at each temperature, and representative data are shown.
Other experiments were done once.
2
.4. Data fitting and calculation of the thermodynamic parameters
Data from the initial rate measurements were fitted using Sigmaplot software with
appropriate rate equations to obtain the kinetic parameters. Data for substrate saturation
curves were fitted using Eq. 1. In Eq. 1, v and V represent the initial and maximum
A
velocities and K the Michaelis constant for substrate A. Data for a sequential or a rapid
equilibrium ordered mechanism were fitted to Eqs. 2 and 3, respectively, where A and B
are the varied substrates, K is the inhibition constant for A, and K is the Michaelis
iA
B
constants for substrate B, respectively. The standard errors associated with these kinetic
parameters of V, K , K , K , V/K , and V/K were calculated from the program. Double
iA
A
B
A
B
reciprocal plots of the families of lines obtained from the initial velocities against
substrate concentrations were constructed for illustration.
Based on the transition state theory for chemical and enzyme-catalyzed reactions
(27-29), the rate constant k for a reaction as a function of the temperature T is given by
8

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‡
Eq. 4, where R is the gas constant, T is the temperature in Kelvin, and ∆G is the Gibbs
free energy of activation, i.e., the difference in free energy between the transition state
and ground state. The factor (k T/h) is a frequency factor for crossing the transition state,
B
B
where k and h are the Boltzmann and Planck constants, respectively. The Gibbs free
energy change, ∆G, is calculated from the binding constant, K , for the substrate using
S
Eq. 5. The relationship between the Gibbs free energy change (∆G) and the changes in
enthalpy (∆H) and entropy (∆S) is shown in Eq. 6. Similarly, the Gibbs free energy of
‡
activation (∆G ) is separated into the enthalpic and entropic terms and shown in Eq. 7.
The kinetic analysis of the enzyme-catalyzed reaction with varied temperature giving the
‡
thermodynamics parameters of the Gibbs free energy of activation (∆G ) is Eq. 4, which
‡
‡
can be derived into Eq. 8. Therefore, the changes in enthalpy (∆H ) and entropy (∆S ) in
transition state are calculated with the Eyring equation (Eq. 9) by plotting ln(k/T) versus
(1/T). The changes in enthalpy (∆H) and entropy (∆S) for the interactions of enzyme and
substrate in the ground state are obtained with the van’t Hoff equation (Eq.10) by plotting
lnK
s
versus (1/T).
The kinetic scheme for the ordered bi bi kinetic mechanism with enzyme, E,
saturated with A to form EA complex and the rate equations for kinetic parameters, kcat,
k /K and K , are illustrated in Scheme 1. EA binds B with rate constant k to form the
cat
B
B
3
EAB complex, which reacts to form the EPQ complex with rate constant k , followed by
5
the release of the products P and Q with rate constants k and k , respectively. k and k
6
7
9
4
are the reverse rate constants, representing the dissociation of B from EAB, and the
conversion of EPQ to EAB, respectively. These kinetic parameters are defined based on
Cleland’s nomenclature (30,31) with the derived microscopic rate constants for the
9

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corresponding kinetic constants based on Scheme 1. The catalytic constant kcat includes
the steps from the chemical reaction, which converts the EAB to EPQ to the releases of
products of P and Q, and reflects the rate-limiting step in overall reaction. The catalytic
efficiency for B, k /K , includes the steps from the binding of B with the EA complex to
cat
B
the first irreversible step, i.e., the release of the first product P. When the rate limiting
step is the chemical reaction, k , the kinetic parameters of k , and k /K are reduced to
5
cat
cat
B
k
5
, and k
3
k
5
/k
4
, respectively, while K
B
is reduced to k
4
/k
3
, the dissociation constant for B
from EAB.
v = VA/(K + A)
(1)
(2)
(3)
(4)
(5)
A
v = VAB/(K K + K B + K A + AB)
iA
B
A
B
v = VAB/(K K + K A + AB)
iA
B
B
‡
k = (k
B
T/h) exp(-∆G /RT)
∆
∆
∆
G = -RT ln(KS)
G = ∆H - T∆S
(6)
(7)
(8)
(9)
(10)
‡
‡
‡
G = ∆H - T∆S
‡
‡
B
k = (k T/h)exp(∆S /R)exp(-∆H /RT)
‡
‡
ln(k/T) = ln(k /h) + ∆S /R - (∆H /R) (1/T)
B
s
lnK = ∆S/R – (∆H/R)(1/T)
1
0

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Scheme 1. The simplified ordered bireactant mechanism with enzyme saturated
with substrate A and the rate equations for kinetic parameters, k , k /K and K .
cat cat
B
B
3
. Results
3
.1. Temperature dependence of the kinetic parameters for the oxidation of androsterone
-HSD/CR
catalyzed by 3
α
+
We studied the reaction of androsterone with NAD catalyzed by 3α-HSD/CR at
temperatures from 10 to 40 °C at pH 10.5. The pH-profile of the 3α-HSD/CR–catalyzed
reactions is insensitive to changing pH at pH > 9 (26), reducing the likelihood of
complications that might arise from differing temperature effects on proton dissociation
constants. The extinction coefficient of NADH is not changed from 10-40 ° C. To ensure
the enzyme activity is not lost during the assay time of 5 min, we incubated the enzyme at
+
4
0 °C and measured the enzyme activity at 25 °C in the presence of 1 mM NAD , 48.7
11

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µM androsterone, 0.1 mg/mL BSA, 100 mM Caps, pH 10.5, and found that the enzyme
maintained activity within error for up to 20 min at 40 °C.
Initial velocity patterns were determined by varying the concentration of
+
androsterone at several fixed concentrations of NAD at each temperature. Double
reciprocal plots intersected to the left of the y-axis at each temperature and are presented
in the supplementary Figure S1. The data were fitted to Eq. 2 to yield the kinetic
parameters of k , K , K and K at each temperature (Supplementary Table S1). These
cat
iA
A
B
kinetic values increase with increasing temperature. The values of kcat and k /K are
cat
B
-1
7
-1 -1
°
3
-1
(
116 ± 9) s and (6.8 ± 1.4) ×10 M s at 10 C, and increase to (2.8 ± 0.3) ×10 s and
8
-1 -1
°
(
A B
4.5 ± 0.7) ×10 M s at 40 C, respectively. The values of KiA, K and K also increase
°
from 0.16 ± 0.10, 0.14 ± 0.03 and 0.0017 ± 0.0004 mM at 10 C to 1.2 ± 0.4, 1.8 ± 0.4
°
and 0.0063 ± 0.0017 mM at 40 C, respectively. The increases in the inhibition constant
+
KiA for NAD with increasing temperature indicate the dissociation of 3α-HSD/CR-
+
NAD complex is an endothermic reaction.
Plots of the ln(k /K T) and ln(k /T) versus 1/T are linear for 3α-HSD/CR
cat
B
cat
catalysis from 10 to 40 °C (Figure 2), and the data were fitted to Eq. 9. The slope
‡
corresponds to the enthalpy of activation (∆H ), giving 11.3 ± 1.9 and 16.0 ± 2.1 kcal/mol,
‡
respectively, and the intercept determines the entropy of activation (T∆S ), giving 5.1 ±
0
.5 and 2.4 ± 0.3 kcal/mol at 298 K, respectively (Table 1).
1
2

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(A)
(B)
Figure 2. Eyring plots of the kinetic data for 3α-HSD/CR catalyzed reaction of
+
NAD with androsterone, 2-decalol and cyclohexanol. Plots of (A) ln(k /T) vs 1/T,
cat
and (B) ln(k /K T) vs 1/T are linear. The lines represent the fits of the data to Eq. 9,
cat
B
‡
‡
where "k" is either ln(k /T) or ln(k /K T), to obtain the values of ∆H and ∆S recorded
cat
cat
B
in Table 1.
Table 1. Thermodynamic activation parameters for the oxidation of androsterone and the
a,b,c
truncated analogs with NAD catalyzed by 3α-HSD/CR
.
Kinetic
parameters
kcat
k/KB
cyclohexanol
2-decalol
androsterone cyclohexanol
2-decalol
androsterone
Substrate
‡
∆G
17.0±0.8
16.9±1.4
13.6±2.1
14.7±1.3
12.6±1.3
(2.1)
21.4±1.2
(0.3)
8.8±0.5
(-1.8)
6.2±2.0
(8.5)
11.3±1.9
(10.4)
5.1±0.5
(1.9)
(
0.1)
10.1±1.0
2.9)
-6.8±1.0
2.8)
‡
∆H
13.0±0.7
-4.0±0.3
‡
16.0±2.1
2.4±0.3
21.7±1.2
7.0±0.4
(
‡
T∆S
(
a
Values of ∆G are calculated from Eq. 7 with the propagated error calculated.
The values in parenthesis are the differences in the thermodynamic activation parameters
b
in the comparison with the value for cyclohexanol.
c
Values given in kcal/mol at 298 K.
1
3

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3
.2. Temperature dependence of the kinetic parameters for the oxidation of truncated
analogs catalyzed by 3α-HSD/CR
+
The reaction of 2-decalol and cyclohexanol with NAD by 3α-HSD/CR was
studied at temperatures from 10 to 40 °C. Double reciprocal plots of the initial velocity
patterns for 2-decalol and cyclohexanol intersect on the y-axis at each temperature,
indicating a rapid equilibrium ordered kinetic mechanism, as shown in the supplementary
Figures S2 and S3 for 2-decalol and cyclohexanol, respectively. The data were fitted to
Eq. 3 to yield the kinetic parameters of k , K and KB at each temperature
cat
iA
(
Supplementary Tables S2 and S3). Similarly, the kinetic values of kcat and kcat/K
increase with increasing temperature, while the K values decrease with increasing
temperature. The values of kcat for 2-decalol and cyclohexanol are 0.91 ± 0.11 s and
B
B
-1
-1
°
-1
-1
°
(
0.74 ± 0.07) s at 10 C, and increase to 4.3 ± 0.3 s and 7.2 ± 0.4 s at 40 C,
-1 -1
respectively. The values of k /K for 2-decalol and cyclohexanol are 540 ± 60 M s and
cat
B
-
1 -1
°
4
-1
2
-1 -1
1
4
0
5 ± 2 M s at 10 C, and increase to (2.7 ± 0.5) ×10 s and (5.2 ± 0.9) ×10 M s at
°
0 C, respectively. The values of K for 2-decalol and cyclohexanol decrease from 1.7 ±
B
°
°
.4 and 48 ± 9 mM at 10 C to 0.16 ± 0.04 and 14 ± 3 mM at 40 C, respectively.
Plots of ln(k /K T) and ln(k /T) versus 1/T are linear from 10 to 40 °C for 3α-
cat
B
cat
HSD/CR acting on 2-decalol and cyclohexanol (Figure 2). Data were fitted to Eq. 9. The
analysis of 3α-HSD/CR acting on 2-decalol and cyclohexanol shows a much greater
‡
sensitivity of k /K to temperature than the reaction with androsterone, with a ∆H of
cat
B
‡
2
1.4 ± 1.2 and 21.7 ± 1.2 kcal/mol, but less sensitivity of kcat to temperature with a ∆H
‡
of 10.1 ± 1.0 and 13.0 ± 0.7 kcal/mol, respectively. The entropies of activation (T∆S ) for
1
4

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2
-decalol and cyclohexanol at 298 K are 8.8 ± 0.5 and 7.0 ± 0.4 kcal/mol, respectively,
obtained from the values of k /K and -6.8 ± 1.0 and -4.0 ± 0.3 kcal/mol respectively,
cat B,
obtained from the values of k . The thermodynamic activation parameters calculated
cat
from the observed effects of temperature on the enzymatic oxidation of androsterone, and
truncated substrate analogs, 2-decalol and cyclohexanol, are summarized in Table 1.
The changes in enthalpy (∆H) and entropy (∆S) for the interactions of enzyme
and substrate in the ground state are obtained with the van’t Hoff equation (Eq.10) by
+
plotting ln(1/K ) vs (1/T) as shown in Figure 3 and Table 2. The binding of E-NAD with
B
2
1
2
-decalol or cyclohexanol (1/K ) is endothermic with ∆H values of 11.3 ± 2.1 and 8.7 ±
B
.8 kcal/mol, counterbalanced by an extraordinarily favorable entropy (T∆S) of 15.7 ±
.1 and 11.0 ± 1.8 kcal/mol at 298 K, respectively.
Figure 3. van’t Hoff plots of kinetic data for 3α-HSD/CR-catalyzed reaction of
+
NAD with 2-decalol and cyclohexanol. The lines represent the fits of ln(K ) to Eq. 10
s
for 2-decalol and cyclohexanol to obtain ∆H and ∆S given in Table 2. The kinetic
s B
parameter K is equal to 1/K .
1
5

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Table 2. Thermodynamic parameters for the binding of 3α-HSD/CR-NAD binary
a,b,c
complex with cyclohexanol and 2-decalol to form the respective ternary complexes
.
cyclohexanol
-2.3 ± 2.5
8.7 ± 1.8
2-decalol
∆
G
H
-4.4 ± 3.0 (2.1)
11.3 ± 2.1 (2.6)
15.7 ± 2.1 (4.7)
∆
T∆S
a
11.0 ± 1.8
Values of ∆G are calculated from Eq. 6 with the propagated error calculated.
The values in parenthesis are the differences between cyclohexanol and 2-decalol in
b
their thermodynamic parameters.
c
Values given in kcal/mol at 298 K.
4
. Discussion
4
.1. Principles of enthalpy and entropy contributions in enzyme catalysis
The transition state theory provides a framework for understanding chemical
reactions and enzyme catalyzed reactions (27-29). The rate constant for a reaction as a
‡
function of the temperature T is given by Eq. 4, where ∆G , the Gibbs free energy of
activation, is the difference in free energy between the transition state and ground state.
Gibbs free energy is separated into enthalpic and entropic terms. The enthalpy change
(∆H) reflects the energy change of the system as a result of forming and disrupting many
individual interactions when the substrate binds to the enzyme. Breaking of bonds with
water, buffer, and/or ion molecules causes an unfavorable ∆H, while the formation of
new bonds with amino acids at the active site leads to a favorable ∆H (32). Entropy is a
measure of the disorder or randomness in a system. The entropy change (∆S) can be
attributed to changes in solvation, in translational and rotational freedom, or to changes in
conformation of enzyme and substrate (32,33).
1
6

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Enzymes can destabilize the enzyme-substrate complex by paying for the energy
to bring the reactants together in an appropriate orientation and induce conformational
changes for better interactions in the transition state, and to carry out general acid-base,
metal ion, and electrostatic catalysis to stabilize the transition state through the functional
groups. The chemical step involved in bond making and breaking in the transition state
costs a large enthalpy change, which can be overcome by favorable ionic and hydrogen
bonding interactions with enzymes that are not available in solution (20). Binding of
substrate with enzyme to form the enzyme-substrate binary complex results in the loss of
translational and rotational degrees of freedom as two molecules become one, and the
loss of conformational degrees of freedom from the substrate and from some residues in
the enzyme (16,34). The release of ordered water molecules that surround hydrophobic
and charged substrates can be associated with a gain of entropy (35,36); the release of a
water molecule from an active site can increase the entropy 2-3 kcal/mol (37).
To understand the origins of enzyme catalysis, we have investigated how the
binding interactions of the enzyme and a non-reacting portion of the substrate contribute
to 3α-HSD/CR catalysis (19). Truncation of androsterone to 2-decalol and cyclohexanol
was shown to increase the K value and significantly reduce the k /K value. To get
m
cat
m
insight into the enthalpic and entropic components of these contributions, we determined
m m
the effects of temperature on the kinetic parameters of kcat, kcat/K and K for the wild-
type enzyme acting on androsterone, 2-decalol and cyclohexanol.
4
.2. Enthalpic and entropic contributions for 3α-HSD/CR acting on androsterone
1
7

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We analyzed the kinetic parameters, kcat and k /K , of the 3α-HSD/CR-catalyzed
cat
B
+
the reaction of androsterone with NAD with varied temperature, yielding the
‡
‡
thermodynamic activation parameters of ∆H and T∆S , respectively. However, the
kinetic complexity of the enzyme reaction complicates the interpretations of these values.
+
3
α-HSD/CR shows an ordered bi bi kinetic mechanism with the NAD binding first and
+
the NADH released last. The kinetic mechanism for enzyme saturated with NAD is
+
shown in Scheme 1, where A and Q refer to NAD and NADH, respectively. B can be
androsterone, 2-decalol or cyclohexanol, and P is its corresponding oxidized carbonyl
products. In previous studies, we demonstrated that the rate limiting step for 3α-HSD/CR
+
catalyzed reaction of androsterone with NAD is the release of NADH in the overall
reaction, but it is hydride transfer at low, limiting concentrations of androsterone (38).
The kinetic parameter kcat reflects the release of NADH from the E-NADH binary
complex for the 3α-HSD/CR acting on androsterone (i.e., k in Scheme 1). The kinetic
9
parameter kcat/K
B
reflects the binding of substrate, the hydride transfer and release of
product for 3α-HSD/CR acting on androsterone, steps k to k (However, when k is fast
3
7.
7
and k is slow, the expression reduces to k k /k .) For this substrate, the expression of the
5
3 5
4
kinetic parameter K is a complicated rate equation (Scheme 1) and cannot be simplified
B
to the dissociation constant for androsterone.
‡
Hence the enthalpy change of activation (∆H ) and entropy change of activation
‡
‡
(
Τ∆S ) obtained from k /K indicate the formation of the transition state of EAB from
cat B
the reaction of EA with B. The free energy of activation for the reaction of EA with
androsterone is 6.2 kcal/mol (Table 1). The corresponding unfavorable enthalpy change
of activation is 11.3 kcal/mol. This large positive enthalpy of activation can be attributed
1
8

ACCEPTED MANUSCRIPT
to the formation of the transition state for the hydride transfer from substrate to
+
nicotinamide ring of NAD in the active site. The corresponding positive entropy change
of activation is 5.1 kcal/mol at 298K indicating a favorable entropy contribution.
‡
The observed unfavorable enthalpy change of activation (∆H ) of 16 kcal/mol and
‡
favorable entropy change of activation (Τ∆S ) of 2.4 kcal/mol obtained from the analysis
of kcat are attributed to the dissociation of NADH from the 3α-HSD/CR-NADH binary
complex as a result of the interruptions of the interactions between 3α-HSD/CR and
NADH within the binary complex and the increasing motion in the active site for the
release of NADH, respectively. A similar thermodynamic activation value for the
dissociate rate of NADH from E-NADH binary complex has been reported for beef heart
‡
‡
lactate dehydrogenase with ∆H of 17.5 kcal/mol and Τ∆S of 2.3 kcal/mol at 298K (39).
4
.3. Enthalpic and entropic contributions in catalysis by 3α-HSD/CR acting on the
truncated substrates
B
We then analyzed the kinetic parameters, kcat and kcat/K , of 3α-HSD/CR acting on
2
-decalol and cyclohexanol with varied temperature to obtain the thermodynamic
‡
‡
activation parameters of ∆H and T∆S , respectively. Since the rate limiting step is
hydride transfer for 3α-HSD/CR acting on cyclohexanol and 2-decalol, the K for 2-
B
decalol and cyclohexanol is then presumably similar to the true dissociation constant K
i.e., k /k ). The kinetic parameter kcat reflects the hydride transfer for cyclohexanol and 2-
decalol (i.e., k ), and k /K reflects the steps from the binding of substrate to the hydride
d
(
4
3
5
cat
B
transfer for the 3α-HSD/CR acting on 2-decalol and cyclohexanol (i.e., k k /k ).
3
5
4
1
9

ACCEPTED MANUSCRIPT
The free energies of activation for the reaction of EA with 2-decalol and
cyclohexanol are 12.6 and 14.7 kcal/mol, respectively (Table 1). These reactions have
favorable, positive entropy changes of activation of 8.8 and 7.0 kcal/mol at 298K, and the
corresponding unfavorable enthalpy changes of activation are 21.4 and 21.7 kcal/mol.
The enthalpies of activation are similar for 3α-HSD/CR acting on 2-decalol and
cyclohexanol, but are significantly smaller for androsterone.
‡
The formation of EAB from EAB for 2-decalol and cyclohexanol are both
enthalpically and entropically unfavorable, with the same free energy of activation of 17
kcal/mol. However, the enthalpic and entropic components contribute differently to
‡
‡
enzyme catalysis, so that 2-decalol oxidation has values of both ∆∆H and ∆Τ∆S that are
lower by about 3 kcal/mol relative to cyclohexanol. Hence, the B-ring of the steroid
participates in favorable binding interactions in the transition state in the active site of
enzyme that are compensated for by the same entropic cost.
+
The binding of 2-decalol and cyclohexanol with the E-NAD complex is entropy-
driven with T∆S of 15.7 and 11.0 kcal/mol, but strongly endothermic with ∆H of 11.3
and 8.7 kcal/mol, respectively (Table 2). Binding of substrate with a positive entropy
change has been indicated for nonpolar compounds. A hydrophobic molecule causes
local water molecules to rearrange around the nonpolar molecule, thereby increasing the
local order and decreasing the entropy of the system. Since the configurational entropy of
+
2
-decalol and cyclohexanol can be expected to decrease on binding to the E-NAD
complex, these results indicate the importance of hydrophobic effects in the binding
process, that is, water molecules surrounding 2-decalol and cyclohexanol can increase
+
their entropy by binding to the active site of the E-NAD complex, and ordered water
2
0

ACCEPTED MANUSCRIPT
molecules in the active site also increase their entropy as they transfer to the bulk solvent
on ligand binding. Meanwhile, breaking hydrogen-bonding interactions within the
ordered water molecules causes the observed unfavorable ∆H.
4
.4. Enthalpic and entropic contributions from remote portion of substrate in the 3
α-
HSD/CR-catalyzed reaction
The thermodynamic activation parameters calculated from the observed effects of
temperature on the kinetic parameters, k , k /K , and 1/K for the 3α-HSD/CR
cat
cat
B
B
+
catalyzed reaction of NAD with androsterone, and its truncated analogs, 2-decalol and
cyclohexanol, are summarized in Tables 1 and 2. Energy diagrams are shown in Figure 4
for assessing the remote binding energy and its enthalpic and entropic contributions to
3
α-HSD/CR catalysis by comparing androsterone with its truncated analogs, 2-decalol
and cyclohexanol. The energy state for EAB is not reported for androsterone because K
B
does not provide a dissociation constant for B. We have shown both uniform binding
interactions and differential binding interactions from the non-reacting portion of
androsterone with the active site in 3α-HSD/CR catalysis (19). In this study, we show
that the B-ring of steroid contributes equally to the stabilization of both the transition
state and ground state of the ternary complex by 2.1 kcal/mol, whereas the remote BCD-
ring and CD-ring of androsterone improves catalysis through differential binding
interactions with the active site of 3α-HSD/CR by contributing 8.5 and 6.4 kcal/mol to
the stabilization of the transition state, respectively (Figure 4A). We dissect the free
2
1

ACCEPTED MANUSCRIPT
energy change into their enthalpic and entropic components. The enthalpy (∆H) and
entropy (-T∆S) changes that occur from the binding of EA with androsterone, 2-decalol,
‡
and cyclohexanol to form EAB , respectively, are illustrated in Figure 4B.
As compared to cyclohexanol, the k /K value for 3α-HSD/CR acting on 2-decalol
cat
B
increases 37-fold by decreasing the free energy of activation of 2.1 kcal/mol at 25 °C.
The forces involved in the hydrophobic interactions of the B-ring of steroid with the
active site of 3α-HSD/CR are mainly due to an increase in the entropy of activation
without a change in enthalpy of activation in forming the transition state in the EAB
ternary complex. Meanwhile, enthalpy–entropy compensation from the hydrophobic
interactions of the B-ring of steroid with the active site of 3α-HSD/CR in proceeding
from the ternary complex to the transition state is observed, leading to equal free energy
contributions on the stabilization of the ground state and transition state of the ternary
complex EAB; thereby the kcat value is the same for 3α-HSD/CR acting on cyclohexanol
and 2-decalol. Comparing the entropy of activation for reaching the transition state from
the EAB ternary complex with 2-decalol and cyclohexanol, deletion of a ring of 2-decalol
‡
to form cyclohexanol becomes more favorable (∆T∆S of 2.8 kcal/mol at 298K),
consistent with the possibility that the increase in the substrate’s range of motion within
the active site may interfere with catalysis. In contrast, an additional B-ring provides
‡
better interaction in the transition state with the active site (∆∆H of 2.9 kcal/mol).
Therefore, the increased binding interactions by the B-ring in a binding process result in
‡
‡
more negative ꢀH at the expense of increased order, leading to a more negative TꢀS .
As compared to cyclohexanol and 2-decalol, the k /K value for 3α-HSD/CR
cat
B
6
5
acting on androsterone increases 1.8×10 - and 4.9×10 -fold by decreasing the free energy
2
2

ACCEPTED MANUSCRIPT
of activation by 8.5 and 6.4 kcal/mol at 25 °C, respectively. The remote BCD-ring and
CD-ring of androsterone contribute to the enthalpic stabilization of transition state by
1
0.4 and 10.1 kcal/mol, with entropic costs of 1.9 and 3.7 kcal/mol in an overall
energetically more favorable enzymatic reaction, respectively. The crystal structures of
+
apo- and NAD -bound 3α-HSD/CR have been determined and exhibit an incomplete and
unresolved substrate binding loop (40). The flexible substrate binding loop of 3α-
HSD/CR is involved in binding the nucleotide cofactor and androsterone to participate in
catalysis (38,41). A significant induced conformational change from a disordered
substrate binding loop to a closed helix-turn-helix is demonstrated in the binding of
NADH with Pseudomonas sp. 3α-HSD (42). Therefore, the BCD-ring and CD-ring of
androsterone may be involved in the conformational change of the substrate binding loop
for better binding in the transition state than in the ground state of the EAB complex,
resulting in the entropy cost and enthalpy gain. Loop closure upon substrate binding is
important for enzyme catalysis. The lyase activity of isochorismate-pyruvate lyase is
enthalpically driven with a very large entropic penalty of -24.3 cal/(mol K) for the
ordering of the loop and substrate for the conversion of the ES complex to the transition
state (33). The binding energy from the remote interaction of phosphite dianion with a
flexible phosphate gripper loop is used by triosephosphate isomerase, glycerol 3-
phosphate dehydrogenase, and orotidine 5’-monophosphate decarboxylase to facilitate
catalysis (43,44). The increase in phosphate gripper loop size in orotidine 5’-
monophosphate decarboxylases can contribute to greater enthalpic transition state
stabilization through more extensive loop-substrate interactions with a larger entropic
penalty for immobilization of the larger loop (45).
2
3

ACCEPTED MANUSCRIPT
In summary, we used the truncated analogues to explore the function of a non-
reacting portion of androsterone in 3α-HSD/CR catalysis by analyzing the enthalpy and
entropy changes during the reaction. The truncation in the analogues of cyclohexanol and
2
B
-decalol significantly decreases catalytic efficiency (kcat/K ) for the 3α-HSD/CR-
catalyzed reaction as compared to that for androsterone. Both the conformational change
of the substrate binding loop of 3α-HSD/CR and the hydrophobic effect of the steroid
ring contribute to enzyme catalysis. Thermodynamic analysis shows that the binding of
+
the E-NAD complex with either 2-decalol or cyclohexanol to form the ternary
complexes is endothermic and entropy-driven, indicating that desolvation plays an
important role in the binding process and that the hydrophobic interactions of the B-ring
of the steroids with the active site of 3α-HSD/CR can contribute to catalysis by mainly
increasing the entropy of activation. Although the enthalpy of activation is unfavorable in
forming the transition state for the 3α-HSD/CR-catalyzed reaction, the remote BCD-ring
of androsterone may induce a conformational change of the substrate binding loop of 3α-
HSD/CR for better interactions in the transition state by lowering the enthalpy of
activation by 10 kcal/mol. However, the B-ring of the steroid probably cannot induce the
conformational change of this loop and makes no further contribution to the enthalpic
stabilization of the transition state. These results are consistent with the induced fit model
(46) proposed by Koshland in that the changes in the enzyme structure caused by the
substrate will bring the catalytic groups into the proper alignment for enzyme action,
whereas poor-substrates will not. Our results show why 3α-HSD/CR catalyzes a very fast
reaction with the optimal substrate androsterone and a very slow reaction with the poor
substrates 2-decalol and cyclohexanol.
2
4

ACCEPTED MANUSCRIPT
(A)
(B)
Figure 4. Energy diagram for the 3α-HSD/CR-catalyzed reaction. (A) Gibbs free
energy diagram, and (B) enthalpy and entropy diagram. The energy profile for 3α-
HSD/CR acting on androsterone (black trace) is compared to that with 2-decalol (red
trace) and cyclohexanol (green trace). The x-axis corresponds to the reaction coordinate
for the 3α-HSD/CR-catalyzed reaction. Entropy units are given as -T∆S for the direct
comparison as an increase in -T∆S is unfavorable and a decrease in -T∆S is favorable.
The listed values are from the Tables 1 and 2, and the values of ∆G and -T∆S are
presented at 298K.
Conflict of Interest
The authors declare that there are no conflicts of interest.
Acknowledgements
2
5

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This work was supported by a grant from Kaohsiung Medical University Research
Foundation (KMU-M107001; KMU-M108008), Taiwan.
2
6

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