Kinetics Modeling of a Convergent Cascade Catalyzed by Monooxygenase-Alcohol Dehydrogenase Coupled Enzymes

Article abstract of DOI:10.1021/acs.oprd.0c00372

A convergent cascade reaction coupling a cyclohexanone monooxygenase variant and an alcohol dehydrogenase to make ?-caprolactone from cyclohexanone and 1,6-hexanediol was characterized via progress curve analysis with two kinetic models developed iteratively. A chemical side reaction occurring with the utilized Tris buffer and consequent byproduct formations were considered in Model 2, which reduced the root-mean-square error (RMSE) values by half, compared to Model 1 (RMSE values of 13%-40%). The optimized model, Model 2, led us to simulate the cascade reaction including 22 kinetic parameters with a maximum RMSE value in the range of 10%-21%.

Full text of DOI:10.1021/acs.oprd.0c00372

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Kinetics Modeling of a Convergent Cascade Catalyzed by
Monooxygenase−Alcohol Dehydrogenase Coupled Enzymes
Jennifer Engel, Uwe T. Bornscheuer, and Selin Kara*
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ABSTRACT: A convergent cascade reaction coupling a cyclohexanone monooxygenase variant and an alcohol dehydrogenase to
make ε-caprolactone from cyclohexanone and 1,6-hexanediol was characterized via progress curve analysis with two kinetic models
developed iteratively. A chemical side reaction occurring with the utilized Tris buffer and consequent byproduct formations were
considered in Model 2, which reduced the root-mean-square error (RMSE) values by half, compared to Model 1 (RMSE values of
13%−40%). The optimized model, Model 2, led us to simulate the cascade reaction including 22 kinetic parameters with a maximum
RMSE value in the range of 10%−21%.
KEYWORDS: enzyme kinetics modeling, redox reactions, enzymatic cascade, monooxygenase, alcohol dehydrogenase
components over time (namely, progress curve analysis) can
compensate the limitations that the initial rate analyses has. The
progress curve analysis is able to describe important long-term
effects of the reaction, such as enzyme deactivation and product
inhibition.2 Different inhibition types do exist, which should be
considered in the progress curve analysis.6 Nevertheless,
progress curve analysis also has its bottlenecks. Over the course
of time, unknown side reactions may occur that can be difficult
to identify and characterize. In addition, there could be
inaccuracies in the initial concentrations and reaction starting
times. These challenges can also be encountered in an applied
process and, therefore, must be handled. Fortunately, these
issues can be solved by computational methods.2 Instead of
choosing between these two approaches, the initial rates
approach can be used to determine starting values for the
parameters, which are then refined and completed with
progressive curve analysis.4 While the kinetic laws are
formulated as reaction rates, the experimental data from the
progress curve analysis are captured as concentrations. In order
to derive a kinetic model, two methods can be applied: (i) the
integration of the kinetic law or (ii) formulation of ordinary
differential equations (ODEs) of the concentrations.2,3 The
integration of the kinetic law can be very complex already for
simple equations and, thus, are not applicable for more-complex
systems. Consequently, the common way is the formulation of
ODEs to describe the concentrations in relation to the kinetic
laws.2 The kinetic representation of an enzymatic cascade is
shown to be exemplary on a linear cascade reaction with
INTRODUCTION
■
Modeling of Enzymatic Reactions. In order to get the
most efficient enzymatic reaction, in a cascade system or with a
single enzyme, optimization of the reaction parameters (e.g.,
temperature, pH, and substrate concentration) is necessary.
This can be achieved by investigating these parameters in an
experimental way, either via single run experiments or “Design of
Experiments” (DoE). Another option is developing a kinetic
model describing the enzymatic reaction. The purely exper-
imental way would require a vast amount of experiments, while
the computational way can avoid tedious laboratory work and
save resources. Nevertheless, a fewer number of experiments is
still required, since developing an enzyme kinetic model requires
detailed knowledge about the enzyme kinetic parameters.1−3 An
overview of an exemplary way for enzyme kinetic modeling is
shown in Figure 1.
Since the enzyme kinetic parameters are dependent on
running conditions (e.g., pH, buffer and temperature, medium
components, etc.), initially the reaction conditions, with respect
to those have to be selected. Choosing the reaction conditions,
especially in a multienzymatic system, often is a compromise
between the highest activity and the stability of the enzymes
under these conditions.3,5 Afterward, the kinetic parameters can
be estimated from the experimental data. Generally, there are
two different approaches for the determination of kinetic
parameters: (i) initial rates measurements and (ii) progress
curve analysis.1−3 The initial rates approach is the most common
and vastly used method. It is easy to execute in the laboratory
and the computational capacity is relatively low.2 However, it
lacks the ability to capture reaction equilibria, enzyme
deactivation, decomposition of substrates and/or products,
and, thus, long-term effects of the reaction.1,2 Furthermore,
capturing product inhibition requires many experiments and,
given that, might not even be described accurately.1 Therefore,
the initial rates approach can be time-, material-, and cost-
intensive, In contrast, following the concentrations of reaction
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A

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Figure 1. Flow scheme for the kinetic modeling of an enzymatic reaction. [Adapted from Vasic-Racki et al.3 and Al-Haque et al.4]
byproduct formation, assuming that all reaction steps are
irreversible (Scheme 1, eqs 1 and 2).
Whether the individual steps in the reaction are catalyzed by
the same enzyme or by several enzymes is determined using the
general Michaelis−Menten equation and ODEs are not relevant.
However, the concentration of the respective enzyme must be
multiplied by the corresponding reaction velocity/rate. Hence,
which enzyme is the catalyst (e.g., the side reaction) must be
known. In addition, factors such as evaporation/hydrolysis of a
substrate/product and enzyme deactivation must be considered.
The enzyme deactivation can be written as a separate ODE,
when deactivation is considered as a decrease in the “active”
enzyme concentration.
a
Equation 1 gives the general Michaelis−Menten equation:
Scheme 1. General Scheme of a Linear Enzymatic Cascade
vmax,m × cn
vm =
KM,n + cn
(1)
where m represents the reaction number (m = 1−3), n is the
respective substrate of reactions 1−3, v denotes the reaction rate
[U/mg], c is the concentration [mM], vmax represents the
maximum reaction rate [U/mg], and KM is the Michaelis−
Menten constant [mM].
a
Equation 2 defines the ODEs for the change of concentrations
Legend: S, substrate, I, intermediate, P, product, BP, byproduct, and
v, reaction rate.
over the course of the reaction:
B
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a
Scheme 2. Reaction Scheme of the Convergent Cascade with Assigned Rates: Model 1
a
Legend: CHO, cyclohexanone, 1,6-HD, 1,6-hexanediol, ECL, ε-caprolactone, LAC, lactol intermediate, CHL, cyclohexanol (not considered in
model development).
dcS
dt
dcI
dt
RESULTS AND DISCUSSION
■
f(t) =
f(t) =
= (−v1 × cE,1) − x
Our recent study on the BVMO-ADH convergent cascade
revealed that a newly designed combinatorial mutant of
cyclohexanone monooxygenase (CHMO) from Acinetobacter
calcoaceticus, namely, CHMO M16 DS, is the most efficient
variant, with respect to total turnover number.8 In all analyses,
ADH from Thermoanaerobacter ethanolicus (TeSADH)9,10 was
applied. The kinetic parameters of the CHMO M16 DS were
already determined via initial rate measurements,8 and it was
observed that the CHMO variant, such as wild type (WT),
suffers from substrate and product inhibition. Herein, it is
worthwhile to mention that the catalytic mechanism of BVMOs
is known.11 Because of these observed inhibition issues, only low
substrate concentrations were incorporated in the study
represented here. Furthermore, crude cell extracts, instead of
purified enzymes, were used to simplify the enzyme production.
The use of crude cell extract furthermore has the advantage that
H2O2 that formed as a possible byproduct11 can be degraded by
catalase present in the E. coli lysate.
Kinetics Modeling of Convergent Cascade: Model 1. In
our previous study on the BVMO-ADH cascade high byproduct
formation of cyclohexanol (CHL) (Scheme 2), which resulted
from the TeSADH-catalyzed reduction of CHO, was observed.8
After adjusting the ADH concentration to lower amounts, no
significant CHL formation was detected (≤0.1 mM). Therefore,
this side reaction was not considered in the kinetics model
analyzed here. The reaction scheme for the convergent cascade
with annotated reaction rates is shown in Scheme 2.
Within the TeSADH reaction, two intermediates are formed:
6-hydroxyhexanal and the respective lactol (oxepan-2-ol), which
is a cyclized form of the hemiacetal. For simplicity, the
intermediates were considered as one compound: lactol
intermediate (LAC). Datasets with progress curves of different
substrate and enzyme composition were then generated (see
Table SI 1 in the Supporting Information).
The CHMO M16 DS kinetic equation was determined
previously with the initial rates analyses.8 For TeSADH,
competitive substrate and product inhibition was considered.
Since CHO is a possible substrate of TeSADH, it was considered
as a competitive inhibitor as well. The kinetics equations used in
the model can be found in eqs SI(1)−SI(5) in the Supporting
Information.
= (+v1 × cE,1) − (v2 × cE,2) − (v3 × cE,3) − y
dcP
dt
dcBP
dt
f(t) =
= (+v2 × cE,2) − z
= +v3 × cE,3
f(t) =
(2)
Here, x, y, and z are additional factors influencing the
concentrations (e.g., evaporation, hydrolysis, degradation,
enzyme deactivation) [mM/min]; and cE,m represents the
concentration of the enzyme catalyzing reaction m [mg/mL].
Once the parameters are estimated and refined, the model
must be validated. Therefore, simulations and experiments are
conducted under the same reaction conditions.3,4 The numerical
solution of the model is then compared with the experimentally
determined concentrations.3,4 It is important that the exper-
imental dataset is not used for the development of the model. In
the end, the experimental and simulation data must match,
which can be assessed with root-mean-square errors (RMSEs),
with adequate accuracy.3 If not, further circles of parameter
refining can be necessary or maybe certain effects on the reaction
were overlooked.3,4 The finalized model can be a useful tool for
process optimization; it can provide knowledge for conducting
the process in an economically feasible way or to scale it up.1−4 It
can also help for designing new processes and identifying
possible bottlenecks, such as inhibition by substrates or products
and how to handle them, e.g., by finding the optimal feed
rate.2,3,7 The development of an enzyme kinetic model can also
be a tool for identifying the catalytic mechanism of an enzyme.
In this study, we developed a kinetic model for the
bienzymatic redox neutral cascade combining a Baeyer−Villiger
monooxygenase (BVMO) and an alcohol dehydrogenase
(ADH) in a convergent cascade fashion in which cyclohexanone
and 1,6-hexanediol are converted to ε-caprolactone. Herein, our
study is dedicated to find an optimal model that describes the
multivariant multienzymatic reaction system with the best
fitness quantified by RMSE analysis.
C
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Table 1. Kinetic Parameters in Model 1
v
max [U/mg]
KM,Sub [mM]
KM,Sub [mM]
K
i,Sub [mM]
Ki,Prod [mM]
K
i,pot,Sub [mM]
v
max [U/mg]
KM,Sub [mM]
KM,Sub [mM]
CHMO M16 DS Reaction
vmax1
KM1,CHO
KM1,NADPH
Ki1,CHO
Ki1,ECL
8.4
0.002
0.002
30
75
TeSADH Reaction Step 1
+
vmax2a
KM2,1,6‑HD
KM2,NADP
Ki2,1,6‑HD
Ki2,LAC
Ki2,CHO
vmax2aR
KM2a,LAC
KM2a,NADPH
4.25
0.1
0.1
100
2
50
0.5
1
0.1
TeSADH Reaction Step 2
vmax2b
KM2b,LAC
Ki2b,LAC
Ki2b,1,6‑HD
6
2
2
100
Evaporation, Autohydrolysis, Deactivation, Degradation Constants [min−1
]
Deactivation Constant [min−1 mM−1
]
a
b
b
+
Kd,CHO
kd,ECL
kd,NADPH
kd,NADP
kdT,M16DS
kdS,M16DS
kdS,TeSADH
0.0006
0.0002
0.0005
0.0005
0.0003
0.0007
0.0002
a
b
kdTDeactivation constant, enzyme deactivation by substrate. kdSDeactivation constant, enzyme deactivation by substrate.
Figure 2. Simulation Model 1 with data overlay. Experimental data are represented by symbols: dark blue circles, CHO; light blue squares, 1,6-HD;
gray diamonds, ECL. Lines are simulated progress curves from Model 1 (black lines denote LAC; other colors correspond to the symbols for each
compound). Reaction conditions: 100 mM Tris-HCl pH 8, 20 mM CHO, 10 mM 1,6-HD, 0.5 mM NADP+, 2 mg/mL (0.033 mM) CHMO M16 DS,
0.005 mg/mL (0.00013 mM) TeSADH. Enzyme preparation as crude cell extract, amounts refer to target enzyme. Dataset A6 was used for this plot.
The initial kinetic parameters were based on literature
data10,12 or logical assumption. The CHMO M16 DS
parameters were taken from the previous study.8 The kinetics
of TeSADH for 1,6-HD was estimated by Bornadel et al.12 The
evaporation, autohydrolysis, and thermal deactivation constants
were determined experimentally (see Table SI 2 in the
Supporting Information). The latter, although being analyzed
under long-term storage conditions, could be applied in
progressive curve analyses. The parameters were then varied
within certain boundaries (see Tables SI 3 and SI 4 in the
Supporting Information), and the resulting simulations were
evaluated visually. To solve the differential equations, MATLAB
with an ode45 solver was used. The differential equations were
solved solely based on the kinetic parameters given, without
considering the experimental data. However, the experimental
data was used for the visual evaluation. The resulting kinetic
parameters that gave the best fit with dataset A6 (Figure 2) are
shown in Table 1.
Supporting Information), compared to the template data set
(A6). Something that became obvious during the model
development process was, that the simulation of the ECL
concentration would only fit the experimental data, when not all
consumed 1,6-HD is converted to ECL. The change in the
concentration of LAC could only be shown as simulated
concentrations. With the used analytical method, determination
of the LAC intermediate (representing the hemiacetal or cyclic
form) was not possible.
In experiment A1 (see Figure SI 1) an abrupt decrease of
CHO within 30 min was observed. This behavior could not be
elucidated completely, yet. In addition to the visual evaluation,
the root mean square error (RMSE) value was calculated (Table
2). Changing the BVMO concentration, compared to the
template dataset, resulted in a slight increase of the RMSE from
Table 2. Evaluation of Model 1 under Different Reaction
Conditions via Root Mean Square Error (RMSE)
The simulated progress curves with the overlaid experimental
data are shown in the following figures. Figure 2 shows the
simulation and data used to develop the model (dataset A6,
Table SI 1). This dataset will be referred to as template data for
Model 1 in the following. Afterward, the reaction conditions
were changed to use half of the CHMO M16 DS concentration
(Figure SI 1, dataset A1, in the Supporting Information) and
double TeSADH concentration (Figure SI 2, dataset A7, in the
a
CHMO
TeSADH
[mg/mL]
RMSE
[mM]
RMSE
[%]
dataset
[mg/mL]
A6
A1
A7
A4
2.0
1.0
2.0
1.0
0.005
0.005
0.01
0.2
3.79
4.20
5.52
13
14
18
40
12.03
a
Percentage based on a total substrate concentration of 30 mM.
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a
Scheme 3. Reaction Scheme of the Convergent Cascade Including Side Reaction of TeSADH with the Buffer Component Tris
a
Legend: CHO, cyclohexanone; 1,6-HD, 1,6-hexanediol; ECL, ε-caprolactone; LAC, lactol; BP1, byproduct 1; and BP2, byproduct 2. Reversible
reaction that were considered irreversible in the model are shown with gray arrows. Side reaction scheme with Tris buffer adapted from Dithugoe et
al.13
3.8 mM to 4.2 mM (from 13% to 14%). Nevertheless, the
simulation does not fit well to the CHO and ECL concentrations
determined experimentally. But the 1,6-HD reaction course is
represented very well by the model. When the ADH
concentration was doubled, the RMSE increased to 5.5 mM
(18%), and the deviation of the simulation from the
experimental data was visually detectable for all compounds
(see Figure SI 2). When the ADH concentration was increased
even more, the RMSE increased from 3.8 mM to 12.0 mM (from
13% to 40%) and it becomes also visually obvious that the model
is not accurate under these conditions (see Figure SI 3 in the
Supporting Information).
Kinetics Modeling of Convergent Cascade: Model 2.
Since Model 1 could not describe the cascade accurately, the
strategy for the model development was changed. For once,
other datasets (Table SI 5 in the Supporting Information) were
generated and incorporated in the model development. These
sets also contained controls where one of the substrates was not
added to the reaction and no external addition of cofactor was
provided. Furthermore, the BVMO concentration in the
reactions was increased to verify whether or not the assumption
that the BVMO is a limiting factor in the cascade is correct.
As previously mentioned, for the convergent cascade
reactions, the enzymes were provided as crude cell extracts.
Therefore, the enzyme preparation already contained NADPH
and NADP+, to some extent. The experiments without an
additional cofactor showed that the cascade indeed performed
similar to the cascade with an additional cofactor (Figure SI 4 in
the Supporting Information). After 24 h approximately the same
product concentration of 10 mM was achieved. However, the
product concentration with cofactor addition would have been
higher, if the reaction was stopped sooner. Maximum product
concentration of 13 mM (corresponding to 43% theoretical
yield) was achieved in 8 h in the reaction with the external
cofactor, whereas it was about 10 mM without the external
cofactor.
Next, reactions without one of the substrates were conducted,
respectively. Surprisingly, in the reactions without 1,6-HD
addition, 10 mM of CHO were converted, yielding 4 mM of
ECL (Figure SI 5 in the Supporting Information). Also, the 1,6-
HD was converted in the reactions without CHO; however, no
ECL formation was observed (Figure SI 5). In order to get a
better understanding whether the cascade would be productive
in a fed-batch approach, additional CHO was provided after 8 h
(480 min) of reaction (Figure SI 6 in the Supporting
Information). In the end, the product yield increased from
10 mM (43%, batch) to 23 mM (52%, fed-batch) compared to
the normal batch reaction.
In the meantime, Dithugoe et al.10 reported that TeSADH is
performing a side reaction with Tris buffer. Since it was observed
in Model 1 that apparently not all 1,6-HD was converted to
ECL, this side reaction was incorporated into the convergent
cascade model. The reaction scheme with the annotated
reaction rates, considered in Model 2, is shown in Scheme 3.
As observed in Model 1, the two intermediates of the convergent
cascade reaction of TeSADH are considered as one compound:
LAC. The same is true for the Schiff base and the cyclic
byproduct 1 (BP1) generated in the chemical side reaction.
Byproduct 2 (BP2) generated by TeSADH from BP1 is
considered as the sole product, neglecting the further cyclization
to the acetal product. Some of the reaction steps, such as the
oxidation step from BP1 to BP2 in the side reaction, are
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reversible; however, in the kinetics model, they were considered
to be irreversible.
constant for CHMO M16 DS were not varied during the
modeling steps.
The resulting equations (eqs SI(6)−SI(9) in the Supporting
Information) for the rates of the new reactions are listed in the
Supporting Information. The differential equations were
adjusted accordingly. The reaction rate for v2 remained the
same as described in eq SI(2). The CHMO reaction rate was
adjusted to represent the sequentially ordered mechanism with
incorporated uncompetitive substrate and noncompetitive
product inhibition.
As mentioned previously, for the development of Model 1, the
kinetic parameters were varied manually and the changes in the
fitness of the simulated versus measured data could be
immediately observed and quantified via RMSEs. Because of
the 29 parameters involved, handling of this approach is not
straightforward for progress simulation. The parameter variation
was hence automated and the resulting simulation was evaluated
using RMSE values. Furthermore, more than one dataset was
used to develop Model 2. It was observed that different enzyme
batches led to differences in the performance of the convergent
cascade. Therefore, incorporating data from different batches
should make the model development more robust against
discrepancies resulting only from different enzyme batches. The
different iterative steps of the model development strategy are
listed in Table 3, giving the dataset used for the modeling and
After step 8, it was observed that the simulations of CHO and
ECL concentrations were underestimated, whereas for 1,6-HD,
it was performing well. In step 5, however, ECL and 1,6-HD
concentrations were highly overestimated, whereas CHO
concentration was slightly overestimated. Consequently, the
extremes of both boundaries were combined and another step of
modeling was performed. For this step, dataset B1 was used
instead of dataset A6, although datasets B1 and A6 have the same
reaction conditions. It was discovered that, generally, the
performance within dataset A was lower than that observed in
datasets B and C; therefore, the decision was made to continue
refining the parameters with dataset B.
For all the model steps, the evaporation/autohydrolysis/
thermal deactivation constants were the experimentally
determined ones. In the end, the evaporation constant for
CHO was increased slightly, because, in the preliminary
experiments, the kd parameter was slightly underestimating the
actual autohydrolysis in the preliminary experiment. For the
same reason, the kd parameter for ECL autohydrolysis was
slightly adjusted. The final parameters of the model are listed in
Table 4.
The simulated progress curves with the experimental data
overlay are shown in Figure 3 and Figures SI 7−SI 9. In none of
these datasets, LAC accumulated according to the simulation
and, thus, it is not shown in the progress curve plots. Instead,
BP2 accumulated in the cascade reactions according to our
simulations, whereby, with the analytical method used, no
byproduct formation could be detected.
As seen in Model 1, a change in the amount of BVMO caused
smaller deviations in the fitness of simulated versus experimental
data, compared to a change in ADH amount. In Model 2, there
exists no template dataset, since several datasets were used to
refine the parameters. For the datasets with 0.005 mg/mL
TeSADH, the RMSE was 3−4 mM (10%−13%), whereas, for
the higher ADH concentration, the RMSE increased to 6 mM
and 21% (see Table 5).
In the preliminary experiments, it was shown that full
conversion of 20 mM within 30 min could be achieved with
equimolar amounts of NADPH (Figure SI 10 in the Supporting
Information). This means that CHMO M16 DS is able to
perform the reaction to its full completion, despite CHO
inhibition under these conditions. Another indication from
these experiments is that there is no or no severe NADPH
inhibition using the cofactor at stoichiometric amounts. Thus,
with a maximum of 0.5 mM available cofactor during the cascade
reaction, cofactor inhibition was negligible. Furthermore, the
preliminary experiments showed that the autohydrolysis of ECL
could not be neglected. The same was true for evaporation of
CHO and degradation of NADPH/NADP+. It has been shown
in several cases that consideration of the deactivation of the
enzyme can provide a better fit of the model.14−16 However, not
only thermal deactivation should be considered, which can be
approximated by the long-term storage stability. The inactiva-
tion by reaction components could also have an influence.14
Combined thermal and CHO-mediated deactivation was hence
considered for CHMO M16 DS. However, for TeSADH, only
CHO-mediated deactivation was applied. Since TeSADH is a
thermostable enzyme (temperature optimum of 90 °C17),
thermal deactivation did not seem very likely at a reaction
temperature of 30 °C.
Table 3. Strategy Followed for the Development of Model 2
modeling of
particularity of the dataset
dataset
C1
1
2
TeSADH reaction
experiment contained BVMO, ADH,
1,6-HD and cofactor but no CHO
convergent cascade
convergent cascade
convergent cascade
refine for Ki values
initial rates values for CHMO,
A6
TeSADH boundaries from Step 1
3
4
lower CHMO concentration
higher CHO and 1,6-HD
concentrations
C4
A5
5
6
convergent cascade
transfer to normal conditions
increased 1,6-HD concentration
A6
B3
convergent cascade
refine ADH
reaction
7
convergent cascade
refine ADH
increased 1,6-HD concentration
transfer to normal conditions
transfer to dataset with same
conditions, boundaries from Step 5
and Step 8
B4
reaction
8
9
convergent cascade
convergent cascade
A6
B1
which parameters should especially be refined in the step. After
each step, new boundaries for the parameter variation were
defined, based on the best parameters from the model
evaluation. Depending on the step, 5−20 parameter sets were
taken into consideration for finding new boundaries. The
differential equations were solved by MATLAB via an ODE
solver; within this approach, the ode15s solver was used instead
of ode45. As with the additional equations and parameters, the
problem became too stiff to be solved by ode45.
In order to combine different kinetic parameter values with
each other, vectors for the parameters were created. Each
parameter vector was a randomly uniform distribution of values
between the defined boundaries. Therefore, the values for the
13−22 parameters were combined randomly with each other.
The autohydrolysis constants for ECL and the cofactors, the
evaporation constant for CHO, and the thermal deactivation
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Table 4. Kinetics Parameters in Model 2
vmax [U/mg]
K
M,Sub [mM]
KM,Sub [mM]
K
i,Sub [mM]
Ki,prod [mM]
Ki,pot.Sub [mM]
v
max [U/mg]
KM,Sub [mM]
KM,Sub [mM]
CHMO M16 DS Reaction
vmax1
KM1,CHO
KM1,NADPH
Ki1,CHO
Ki1,ECL
8.39
0.0002
0.002
25.76
35.50
TeSADH Reaction Step 1
+
vmax2a
KM2,1,6‑HD
KM2,NADP
Ki2,1,6‑HD
Ki2,LAC
Ki2,CHO
vmax2aR
KM2a,LAC
KM2a,NADPH
7.72
0.54
0.015
90.07
16.73
44.92
1.19
3.10
0.26
TeSADH Reaction Step 2
vmax2b
KM2b,LAC
Ki2b,LAC
Ki2b,1,6‑HD
4.43
2.90
21.96
67.06
Chemical Reaction and TeSADH Byproduct Formation
+
k
TRIS [L mmol−1 min−1
6.72
]
vmax3b
KM3,BP1
KM3,NADP
8.31
3.92
0.23
Evaporation, Autohydrolysis, Deactivation, Degradation Constants [min−1
]
Deactivation Constant [min−1 mM−1
]
a
b
b
+
kd,CHO
kd,ECL
kd,NADPH
kd,NADP
kdT,M16DS
kdS,M16DS
kdS,TeSADH
0.0002
0.0003
0.0005
0.0003
0.0001
0.0006
0.0003
a
b
kdTDeactivation constant, enzyme deactivation by substrate. kdSDeactivation constant, enzyme deactivation by substrate.
substrate inhibition can certainly be competitive for ADHs,
which has indeed been described in the literature.18,19
Comparison of Models 1 and 2. In both models, the
determined TeSADH kinetic parameters differ from those in the
literature.8 Compared to the documented kinetics data, in the
models developed here, the vmax for the cascade reaction was
40−80 times higher, based on v2a (see Schemes 2 and 3). In
addition, the KM value for 1,6-HD was 4−20 times lower. The
main difference was that the kinetic data from the literature was
determined via photometric measurements of initial rates. This
is challenging for the TeSADH reaction, since it is a two-step
oxidation reaction, i.e., enzymatic dehydrogenation/oxidation of
a hydroxy group to an aldehyde (v2a) and enzymatic
dehydrogenation/oxidation of a hydroxy group to a cyclic
ester/lactone (v2b). These two steps cannot be distinguished in a
photometric assay. Furthermore, in the initial rate measure-
ments, only the TeSADH reaction was present. The first step of
the reaction is reversible; therefore, the determined parameters
could be influenced by the reverse/back reaction. Whereas in the
process curve analyses, also the BVMO reaction was present,
shifting the reaction to the target product side.
Figure 3. Simulation Model 2 with data overlay. Experimental data is
denoted as symbols: dark blue circles, CHO; light blue squares, 1,6-
HD; and gray diamonds, ECL. Lines represent simulated progress
curves from model 2. Black lines represent BP1 and BP2 (dotted); other
colors correspond to the symbols for each compound. Reaction
conditions: 100 mM Tris-HCl (pH 8), 20 mM CHO, 10 mM 1,6-HD,
0.5 mM NADP+, 2 mg/mL (0.033 mM) CHMO M16 DS, 0.005 mg/
mL (0.00013 mM) TeSADH. Enzyme preparation as crude cell extract;
amounts refer to the target enzyme. Dataset B1 was used in this plot.
Already in the early stages of the model development for the
convergent cascade, it became obvious that not all consumed
substrates (CHO, 1,6-HD) were converted to the target product
ECL.
Table 5. Evaluation of Model 2 at Different Reaction
Conditions via RMSE
a
CHMO
[mg/mL]
TeSADH
[mg/mL]
RMSE
[mM]
RMSE
[%]
dataset
In Model 1, it was assumed that 1,6-HD was only converted to
the hemiacetal, inhibiting the second reaction. This seemed to
be a well-fitting model, at least for one dataset. However, the
transfer of this assumption to the other reaction conditions
showed that the model was not describing the cascade correctly.
It became especially eminent when the ADH concentration was
increased in the simulations. The model predicted substrate
conversion and product formation rates that were higher than
those observed in the experiments. Therefore, we suspected that
the ADH catalysis was a limiting step of the cascade under these
circumstances. However, this could not be observed in the
experiments. Nor was the CHMO M16 DS observed to be a
limiting factor. When the concentration of the BVMO was
increased from 2 mg/mL to 3 mg/mL, only a slight increase in
ECL formation was detected (see Figure SI 11 in the Supporting
Information). No difference in the CHO reaction course was
observed, but a slight change in the 1,6-HD reaction course was
detected. This could have been caused by the slightly higher
B1
C4
C5
B2
2.0
1.5
3.1
1.0
0.005
0.005
0.005
0.2
2.99
4.04
3.68
6.30
10
13
12
21
a
Percentage based on a total substrate concentration of 30 mM.
As mentioned previously, the byproduct CHL was obtained
from the side reaction of TeSADH with CHO (Scheme 2).
Nevertheless, this reaction and the resulting CHL could not be
detected after reduction of the ADH amount in the cascade
reactions. For TeSADH, competitive inhibition was considered,
whereby all considered compounds were possible substrates of
TeSADH. Usually, substrate inhibition is considered as
uncompetitive, i.e., the inhibitor binds only to the enzyme−
substrate complex. However, since all the compounds are in
direct concurrence, it was more likely that competitive inhibition
is applicable, i.e., the inhibitor binds to the free enzyme. That
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starting concentration of 1,6-HD in datasets C5 and C6, leading
to the higher ECL production. An increase of ADH with 1 mg/
mL BVMO also resulted in a slight change in the reaction course
(see Figure SI 12 in the Supporting Information). But also, this
can be attributed to the slightly higher 1,6-HD concentration in
the respective experiment. In the preliminary experiments, it was
already determined that the CHMO M16 DS should be able to
convert 20 mM CHO within 30 min. Nonetheless, in the
cascade reaction, full conversion was achieved earliest within 8 h
(480 min). Reasons for that could be that the ADH-mediated
cofactor regeneration was not efficient enough and/or other
components of the cascade were inhibiting the BVMO.
determined,7 which was only under storage conditions. It was
already expected that, during the process, the stability would be
lower. Most of the deactivation may occur due to H2O2
formation in the catalytic cycle of the BVMO via a short
cut.11,22−24 In other control experiments, it was observed that
the reaction of the BVMO with CHO produced only small
amounts of H2O2. However, exact determination was not
possible, because the Ampliflu Red assay25 reacted with CHO
and, hence, only high amounts of hydrogen peroxide would have
been detectable. Nonetheless, the CHO-supply control experi-
ment (Figure SI 6) also showed that, with a continuous substrate
feed, higher yields of ECL could be obtained. Here, note that,
because of higher ECL yield, the inhibition of CHMO M16 DS,
as well as the autohydrolysis of the target product ECL, must be
handled carefully. This can be done either by removal of the
product through absorption26,27 or by in situ ring-opening
polymerization (ROP).28 The latter has not been efficiently
implemented in an enzymatic cascade for ECL synthesis. So far,
only oligo-ECL instead of polycaprolactone (PCL) was formed
directly in the cascade.28 Because of the equilibrium reaction,
there is also a risk that the oligo-ECL could hydrolyze again.29,30
Here, it must be emphasized that the TeSADH reaction is
unfortunately still a “black box”. To eliminate the unnecessary
side reactions, both enzymes should be purified for a general
model development. Between datasets A and B/C, a high
difference in the performance of the cascade was observed,
which could have resulted from (i) the activities of the enzymes,
especially from the BVMO was different between enzyme
batches; and (ii) the quantification of the enzyme amounts was
based on SDS-PAGE analysis, which was not accurate enough.
Alternatively, instead of using concentrations, units of the
enzymes for their activities can be implemented in the cascade.
After knowing that the side chemical reaction due to the Tris
buffer is not negligible, an alternative buffer system (e.g.,
phosphate buffer) could be used. Phosphate buffer was not
chosen initially because the stability of the nicotinamide
cofactors is negatively influenced by it.31 In addition, glycine
NaOH buffer gave lower CHMO stabilities, compared to the
Tris buffer (data not shown) seen in our preliminary studies.
Overall, our study showed that Model 2 seemed to have a
better description of the cascade reaction than Model 1. The
RMSE for the simulation of dataset B1 was 10% better than that
observed for Model 1 (dataset A6, 13%; see Tables 2 and 5).
Increasing the ADH concentration, compared to these
conditions, caused, in both cases, a higher RMSE value.
However, in Model 2, the RMSE with 21% was 2-fold lower
than that observed for Model 1 (40%; see Tables 2 (dataset B2)
and 5 (dataset A4)). For refinement of the ADH kinetic
parameters, more datasets would be necessary.
In Model 1, the deviation between simulation and
experimental data was lowest when only the BVMO
concentration was changed. This is a hint that it was mainly
the ADH reaction that was not captured entirely by the model.
When the model was transferred to dataset A1, which had half
the BVMO concentration as the template dataset, the RMSE
decreased only slightly. In the development of Model 2, the
strategy was changed. Not only was one dataset used to model
the reaction: several were used. As already implemented for
Model 1, the model was developed without direct modeling
against the experimental data. This was inspired by the
technique developed by Finnigan et al.7 Since the cascade was
very complex with a vast amount of unknown parameters, the
datasets were used to refine the model by finding boundaries
(see Tables SI 3 and SI 4) with the best fit to the experimental
data. In addition, another approach was considered: modeling
first only the individual reactions to find starting parameters for
the model.4 Afterward, different datasets were used to refine the
model parameters. Furthermore, the BVMO reaction equation
was switched from normal Michaelis−Menten with uncompe-
titive substrate and noncompetitive product inhibition to an
equation that describes the sequentially ordered mechanism of
the reaction. A sequentially ordered mechanism should give a
better description of the BVMO kinetics and has been used in
models previously, using 2-propanol as a cosubstrate for cofactor
regeneration.20 During the initial rate measurements for CHMO
M16 DS, it was determined that the inhibition is already eminent
at a concentration of 20 mM CHO. Thus, it is not negligible in
the model developed here. At the end, the inhibition terms were
introduced in the respective parts of the equation that are
associated with the inhibitor complexes.21
During the iterative steps of model refinement, a dataset with
50 mM CHO was applied. However, it was observed that, with
the higher CHO concentration, the model was not giving a good
fit. This had been also observed when applying the final Model 1
and Model 2 to higher CHO concentrations. This was most
likely due to the aforementioned oxygen limitation in the case of
higher CHO concentrations. Since oxygen as a third substrate of
the BVMO reaction was not incorporated in the model, it is not
applicable to higher CHO concentrations. Consequently, the
inhibition terms could perhaps not be captured entirely, since
high concentrations were not modeled successfully. For BVMO,
these were determined with initial rate measurements; however,
the final model had a lower Ki value for ECL than that
determined with the initial rates.
CONCLUSIONS
■
In the work presented herein, CHMO M16 DS was
implemented in the convergent cascade coupled with TeSADH
for the synthesis of ECL. Preliminary experiments showed that
the BVMO was able to convert 20 mM CHO within 30 min,
when equimolar NADPH was supplied. Hence, 20 mM CHO
was chosen as the substrate concentration for further experi-
ments. Moreover, it was verified that, at 30 °C, significant
autohydrolysis of ECL occurred, which must be considered and
addressed in the future development of the cascade. Possible
solutions could be absorption of ECL on a resin or in-situ
polymerization to PCL.24−26 The latter has been shown in
organic media to a great extent, yet polymerization in aqueous
Other control experiments with an additional supply of CHO,
after 8 h of reaction time, showed that the BVMO is still active
after that time (see Figure SI 6 in the Supporting Information).
However, the reaction rate was lower, most likely because of
deactivation of the CHMO. During the characterization of the
CHMO M16 DS, a half-life time of 116 h at 30 °C was
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media has still its faults.26,27,30 On the other hand, in an
alternative case, the ECL was hydrolyzed intentionally, to lower
the inhibition of the CHMO in the cascade.32 The generated 6-
hydroxyhexanoate can still be polymerized to PCL via a lipase in
organic media.32
DEXTM 120 capillary column (30 m × 0.25 mm, df 0.25 μm,
Supelco Sigma-Aldrich) was used. The temperature profile is
shown in Table SI 6 in the Supporting Information.
Simulations. The kinetic models were developed with the
aid of MATLAB scripts (The MathWorks, Inc., Natick, MA).
Differential equations were solved via ode45 (Model 1) or
ode15s (Model 2). In the development of Model 2, the
boundaries for each iterative step were found within the
parameter combinations, with the best RMSE being 5−10.
Depending on the step, 100−100 000 simulations were
performed with different parameter values and combinations.
The preliminary optimization study8 had shown that a
reduction in the amount of TeSADH was possible and necessary
to reduce the side reaction resulting in CHL. As a consequence,
the byproduct formation of CHL was reduced to ≤0.1 mM and
was not considered further in the development of the kinetic
models for the convergent cascade.
Model 1 of the cascade considered only the convergent
cascade reaction without side reactions. It was noticed that the
cosubstrate 1,6-HD was not fully converted to ECL, but it was
anticipated that inhibition of the second step of the TeSADH
reaction was the cause.
ASSOCIATED CONTENT
* Supporting Information
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/acs.oprd.0c00372.
■
sı
Recently, Opperman and co-workers described that the
intermediate of the TeSADH reaction, 6-hydroxyhexanal, was
All control experiments, tables for the datasets, and the
corresponding reaction conditions, as well as equations
used in the simulations (PDF)
undergoing a chemical reaction with the Tris buffer.13
A
subsequently formed byproduct BP1 was then further converted
by TeSADH to another byproduct BP2.13 Therefore, in Model
2, this side reaction was implemented. The conversion of BP1 to
BP2 by TeSADH also provided the cofactor regeneration that
the second step in the TeSADH reaction would have provided.
Generally, the use of purified enzymes would lead to precise
control of the cascade system, but one must remember that it
would be too expensive, especially for a bulk chemical.33 Using
whole cells would reduce the costs of enzyme production and
could potentially increase the stability of the BVMO. Nonethe-
less, as already shown by Kohl et al.,34 balancing the ratio of the
BVMO and the ADH in the cells is very important. Since this has
already been managed for the linear cascade, resulting in a more
efficient cascade,34,35 we have no doubt that this will also be
possible for the convergent cascade.
AUTHOR INFORMATION
Corresponding Author
■
Selin Kara − Department of Engineering, Biocatalysis and
Bioprocessing Group, Aarhus University, 8000 Aarhus,
Denmark; orcid.org/0000-0001-6754-2814;
Email: selin.kara@eng.au.dk
Authors
Jennifer Engel − Department of Engineering, Biocatalysis and
Bioprocessing Group, Aarhus University, 8000 Aarhus,
Denmark
Uwe T. Bornscheuer − Department of Biotechnology and
Enzyme Catalysis, Institute of Biochemistry, Greifswald
University, 17489 Greifswald, Germany; orcid.org/0000-
0003-0685-2696
EXPERIMENTAL SECTION
■
Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.oprd.0c00372
Materials and Methods. All chemicals were purchased
from VWR International (Denmark) and Carl Roth and used as
received.
Notes
Quantification of Enzymes. The estimation of CHMO
M16 DS and TeSADH was as described in the work of Engel et
al.,8 but the gels were scanned and analyzed in a Gel DocTM EZ
Imager (BioRad). The software used was Image Lab (BioRad),
instead of ImageJ.
Cascade Reactions. The convergent cascade reaction were
performed in 100 mM Tris-HCl (pH 8), in a volume of 1 mL in
35-mL glass vessels. 0−100 mM CHO, 0−50 mM 1,6-HD,
0.5 mM NADP+, 1−3.1 mg/mL (0.016−0.05 mM) CHMO
M16 DS and 0.005−0.2 mg/mL (0.00013−0.005 mM)
TeSADH were used in the reactions. The enzymes were
supplied as crude cell extracts, and the concentrations refer to
the amount of the respective target enzyme in the extract. The
mixtures were incubated in a shaking incubator with 120 rpm
and 30 °C for up to 24 h.
GC-Analytics. From the cascade reactions, 25 μL samples
were taken in different time intervals and extracted with 250 μL
of ethyl acetate containing 5 mM dodecane as an internal
standard. After centrifugation, 200 μL of the ethyl acetate phase
was transferred to a new tube and dried with MgSO4. The
sample was centrifuged to separate the drying agent and the
organic phase and was analyzed afterward via gas chromatog-
raphy (GC). For analysis, a Nexis GC-2030 system coupled with
a flame ionization detector (Shimadzu) and equipped with a β-
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
Authors J.E. and S.K. acknowledge the financial support from
German Research Foundation (Deutsche Forschungsgemein-
schaft, Grant No. KA 4399/1-1). The authors thank Assoc. Prof.
Dr. Diederik J. Opperman (University of the Free State, South
Africa) for the plasmid harboring CHMO M16 DS, as well as
Kim Møller Johansen and Michelle Leganger Juul Sørensen for
their technical support. Furthermore, author J.E. would like to
thank Jannis Reich, for his kind help with MATLAB, and
Frederic Perz, for fruitful discussions.
ABBREVIATIONS
■
CHMO, cyclohexanone monooxygenase; ADH, alcohol de-
hydrogenase; CHO, cyclohexanone; 1, 6-HD, 1,6-hexanediol;
BP, byproduct; LAC, lactol intermediate; ECL, ε-caprolactone;
PCL, polycaprolactone; v, reaction rate [mM/min]; ODE,
ordinary differential equations; vmax, maximum reaction rate [U/
mg]; KM, Michaelis−Menten constant [mM]; Ki, inhibition
constant [mM]; dc/dt, rate of component concentration change
[mM/min]; ccompound, compound concentration [mM]; cenzyme
enzyme concentration, based on density [mg/mL]; ce′nzyme
,
,
I
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enzyme deactivation rate constant [mM−1 min−1]
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