Lipase-catalyzed hydrazinolysis of phenyl benzoate: Kinetic modeling approach

Article abstract of DOI:10.1016/j.procbio.2009.12.005

Immobilized lipase-catalyzed synthesis of benzoic acid hydrazide from hydrazine and phenyl benzoate is reported in this work. A series of immobilized lipases such as Candida antarctica lipase B, Mucor miehei lipase and Thermomyces lanuginosus lipase were screened to establish that C. antarctica lipase B was the best lipase for hydrazinolysis. When phenyl benzoate (0.01 mol) and hydrazine (0.02 mol) in toluene (15 ml) were reacted with C. antarctica lipase B (Novozym 435) at 50 °C, 95% of phenyl benzoate was converted to benzoic acid hydrazide after 2 h. The effects of various parameters such as speed of agitation, concentration of the substrates, temperature, enzyme concentration, and reusability of the enzyme were studied to deduce kinetics and mechanism of the reaction. A mechanism based on an ordered bi-bi dead end complex with hydrazine was found to fit the data. Systematic deactivation studies indicated that the enzyme was deactivated due to the hydrazine and phenol, enzyme deactivation obeys first-order series model. The kinetic parameters deduced from these models were used to simulate the lipase activity. There was a very good agreement between the simulated and experimental values.

Full text of DOI:10.1016/j.procbio.2009.12.005

Process Biochemistry 45 (2010) 586–592
Contents lists available at ScienceDirect
Process Biochemistry
journal homepage: www.elsevier.com/locate/procbio
Lipase-catalyzed hydrazinolysis of phenyl benzoate: Kinetic modeling approach
*
Ganapati D. Yadav , Indrakant V. Borkar
Department of Chemical Engineering, Institute of Chemical Technology, Nathalal Parekh Marg, Matunga, Mumbai 400019, India
A R T I C L E I N F O
A B S T R A C T
Article history:
Immobilized lipase-catalyzed synthesis of benzoic acid hydrazide from hydrazine and phenyl benzoate is
reportedinthiswork. AseriesofimmobilizedlipasessuchasCandidaantarcticalipaseB, Mucormieheilipase
and Thermomyceslanuginosuslipasewere screened toestablishthat C. antarctica lipase B wasthebestlipase
for hydrazinolysis. When phenyl benzoate (0.01 mol) and hydrazine (0.02 mol) in toluene (15 ml) were
reacted withC. antarcticalipaseB(Novozym435)at50 8C, 95%ofphenylbenzoatewasconverted tobenzoic
acid hydrazide after 2 h. The effects of various parameters such as speed of agitation, concentration of the
substrates, temperature, enzyme concentration, and reusability of the enzyme were studied to deduce
kinetics and mechanism of the reaction. A mechanism based on an ordered bi–bi dead end complex with
hydrazine was found to fit the data. Systematic deactivation studies indicated that the enzyme was
deactivated due to the hydrazine and phenol, enzyme deactivation obeys first-order series model. The
kinetic parameters deduced from these models were used to simulate the lipase activity. There was a very
good agreement between the simulated and experimental values.
Received 23 April 2009
Received in revised form 5 October 2009
Accepted 8 December 2009
Keywords:
Enzyme kinetic
Lipase deactivation
Ordered bi–bi mechanism
Hydrazinolysis
Candida antarctica lipase
Non-aqueous enzymology
ß 2010 Published by Elsevier Ltd.
1. Introduction
[17]. Candida antarctica lipase (CAL) was found to exhibit a very
high activity and specificity in the acylation of primary amines
Synthesis of esters by enzyme catalysis has several advantages
over chemical catalysis since enzymatic reactions need lower
energy and provide enhanced selectivity and purity of the product
[1]. Although aqueous enzymology has been widely practised for a
long time, non-aqueous enzymology has been studied for about
two and half decades for synthesis of fine-chemicals, agrochem-
icals, perfumes, flavors, pharmaceuticals and drugs. Non-aqueous
enzymatic catalysis is particularly beneficial when the reactants
are poorly soluble in aqueous media and the rates are extremely
slow. When hydrolysis is likely to be significant in aqueous media,
it can be suppressed by using non-aqueous enzymology [2,3].
Lipases have been employed for the synthesis of organic
chemicals, mainly in aqueous media and in some cases non-
aqueous media, because they are inexpensive, stable, and easy to
recycle [4]. Lipases possess wide substrate specificity, have an
ability to recognize chirality, and do not require labile cofactors
[5,6]. They have been used to catalyze a number of reactions in
non-aqueous media such as esterification, transesterification,
amidation, hydrolysis, hydrazinolysis and epoxidation [5,7–16].
The versatility of lipase catalysis in the synthesis of other groups of
chemicals needs to be explored. Lipases are known to catalyze the
synthesis of amides from non-activated esters. n-Octyl alkyl-
amides, for instance, have been synthesized in anhydrous hexane
with ethyl butyrate [18]. Fatty acid amides have been synthesized
by using Mucor miehei lipase [19]. The fatty acid analogues of
capsaicin have been synthesized by using different lipases and
amongst them Pseudomonas cepacia lipase was the best [20]. In
view of their high reactivity, hydrazides are important starting
materials and intermediates in the synthesis of certain amides,
aldehydes and heterocyclic compounds that are otherwise difficult
to prepare. Hydrazides have also been used in analytical chemistry
to identify carboxylic acids and to detect carbonyl compounds that
form acyl hydrazones. The reactions between hydrazines and
carboxylic acids or their esters are in principle similar to those of
carboxylic acids and esters with amines [21].
The current work focuses on enzymatic hydrazinolysis of
phenyl benzoate using immobilized lipases and deals with enzyme
deactivation and kinetic modeling. There are no literature reports
on the hydrazinolysis of phenyl benzoate by enzymes. The product
benzoic acid hydrazide is commercially useful and the reaction can
be also used as a model for hydrazonolysis of aromatic esters in
non-aqueous media. Special emphasis is laid on the analysis of the
stability and activity of the lipase under different substrate and
product concentrations.
2. Experimental
2.1. Enzymes
All enzymes were procured as gift samples from reputed firms: Novozym 435
(Novo Nordisk, Denmark), Lipozyme IM 20 (Novo Nordisk, Denmark) and Lipozyme
TL IM (Novo Nordisk, Denmark). Novozym 435 is C. antarctica lipase immobilized on
a macroporous polyacrylic resin (activity 10 PLU/g). Lipozyme IM 20 is M. miehei
* Corresponding author. Tel.: +91 22 2414 0865; fax: +91 22 2414 5614.
E-mail addresses: gdyadav@yahoo.com, gd.yadav@ictmumbai.edu.in,
director@ictmumbai.edu.in (G.D. Yadav).
1359-5113/$ – see front matter ß 2010 Published by Elsevier Ltd.
doi:10.1016/j.procbio.2009.12.005

G.D. Yadav, I.V. Borkar / Process Biochemistry 45 (2010) 586–592
587
Scheme 1. Hydrazinolysis of phenyl benzoate.
immobilized on an anionic resin (activity 6 BAUN/g). Lipozyme TL IM is
435 was used as the catalyst. The micro-environment around
the active site pocket of Novozym 435 favors proper interaction
of substrate in non-aqueous media. Since hydrazine hydrate was
used, an equivalent amount of water was present in the reaction
mass. Besides, the supported enzyme contains water in its pore
space and thus a thin layer of water is present on the particle
external surface. The flapping lid of M. miehei and T. lanuginosus
projects into the binding pocket thereby creating steric
hindrance in binding of phenyl benzoate at the active site
which is called ‘‘interfacial inactivation’’ [23]. Since Novozym
435 is highly active in anhydrous media and does not contain a
flapping lid, there is less steric hindrance as compared to other
lipases.
Thermomyces lanuginosus immobilized on silica (activity 75 IUN/g).
2.2. Chemicals
All chemicals including hydrazine hydrate, phenyl benzoate, dodecane, toluene
and other analytical reagents were procured from M/s S.D. Fine Chemicals Pvt. Ltd,
Mumbai, India.
2.3. Experimental setup
The experimental setup consisted of a 3 cm internal diameter fully baffled
mechanically agitated glass reactor of 50 ml capacity, equipped with four baffles
and a six-bladed turbine impeller. The entire reactor assembly was immersed in a
thermostatic water bath and temperature was maintained at a desired value with
an accuracy of ꢀ1 8C. A typical reaction mixture consisted of 0.01 mol phenyl
benzoate and 0.02 mol hydrazine hydrate diluted to 15 ml with toluene as solvent.
The reaction mass was agitated at 50 8C for 15 min at a speed of 600 rpm and then
35 mg1 of immobilized enzyme was added to initiate the reaction. Liquid samples
were withdrawn periodically from the reaction mixture, filtered and analyzed by GC.
3.2. Mass transfer analysis
The effect of speed of agitation was studied over the range of
200–800 rpm (Fig. 2). Initial reaction rates were nearly
independent of speed at beyond 600 rpm. Thus the optimum
speed was chosen as 600 rpm for further studies. Above 800 rpm
initial rate of reaction was almost constant which indicates that
rate of mass transfer is greater than rate of reaction. Although
Fig. 2 clearly indicates that there were no external mass transfer
limitations beyond 600 rpm, it was necessary to prove it
theoretically also. Evaluation of the contributions of external
solid–liquid mass transfer and intra-particle diffusion resis-
tances was done by theoretical calculations. The liquid phase
diffusivity of hydrazine (B) in toulene (DSL;B) at 50 8C was
2.4. Analysis
The concentrations of the reactants and products were determined by GC
(Chemito Model 8610) equipped with a flame ionization detector. A 4 m ꢁ 3.8 mm
stainless steel column packed with SE-30 was used for analysis. Synthetic mixtures
were prepared of pure samples and calibration was done to quantify the collected
data for conversions and rates of reactions. Benzoic acid hydrazide was confirmed
by GC–MS.
2.5. Determination of initial rates
To determine the initial rates of enzymatic reaction, the concentrations of phenyl
benzoate were varied from 0.66 to 2.64 M for known concentrations of hydrazine
(between 0.66 and 2.64 M) at 50 8C. The total volume was made to 15 ml with
toluene, after which 35 mg Novozym 435 was added to initiate the reaction and the
reaction was continued until 30% conversion. In brief, concentration versus time
plots were made for different substrate concentrations. The derivative of
concentration versus time profile at t = 0 gives the initial rate.
3. Results and discussions
The reaction is represented by Scheme 1.
3.1. Screening of different lipases
The activity of three commercially available lipases such as
Novozym 435, Lipozyme TL IM and Lipozyme RM IM was
evaluated in the synthesis of benzoic acid hydrazide from
phenyl benzoate using the same conditions (Fig. 1). Novozym
435 was the best enzyme. Lipozyme IM showed very less
activity as compared to Novozym 435. Pseudomonas lipase has
been reported to be a very good catalyst for the hydrazinolysis of
aliphatic esters [22], but it was ineffective for aromatic esters.
There seems to be a substrate poisoning in the case of aromatic
esters. In the case of C. antarctica lipase B (Novozym 435) the
conversion was about 95% in 2 h as compared to 32% with M.
miehei lipase (Lipozyme IM) and 25% with T. lanuginosus
(Lipozyme TL). Therefore, in all further experiments Novozym
Fig. 1. Screening of different lipases; reaction conditions: phenyl benzoate—
0.01 mol, hydrazine—0.02 mol, solvent toluene—up to 15 ml, speed of agitation—
600 rpm, lipase—16.22 units/ml, temperature—50 8C.
35=1000 gꢁ7000 units=g
1
Novozym 435 loading ¼
¼ 16:33 units=mL.
15 ml

588
G.D. Yadav, I.V. Borkar / Process Biochemistry 45 (2010) 586–592
Fig. 2. Effect of speed of agitation; reaction conditions: phenyl benzoate—0.01 mol,
hydrazine—0.02 mol, solvent toluene—up to 15 ml, temperature—50 8C. Novozym
435—16.22 units/ml.
Fig. 3. Effect of catalysis loading; reaction conditions: phenyl benzoate—0.01 mol,
hydrazine—0.02 mol, solvent toluene—up to 15 ml, speed of agitation—600 rpm,
temperature—50 8C.
calculated by using Shiebel equation [24] as 2.43 ꢁ 10ꢂ9 m2 sꢂ1
.
The value of solid–liquid mass transfer coefficient kSL was
calculated by assuming
a limiting value of the Sherwood
number, Sh = kSLdp/DS = 2, for non-agitated systems. It should
be noted that the actual Sherwood number, which is a function
of Reynolds number and Schmidt number, would be much
higher in well-agitated systems. However, for the sake of
comparison and for orders-of-magnitude calculation, it is safe to
take the lowest Sherwood number as 2 which is for quiescent
liquids. Thus, kSL;B was calculated as 8.97 ꢁ 10ꢂ6 m sꢂ1 for a
particle size (dp) of Novozym 435 of 0.06 cm. Similarly DSL;A was
calculated as 1.54 ꢁ 10ꢂ9 m2 sꢂ1 for phenyl benzoate (A).
For solid (catalyst)–liquid reactions, the contribution of
external mass transfer resistance was calculated in comparison
with the reaction within the particle as is given by Yadav and
Krishnan [25]. By using these values, external mass resistance (RD)
and internal reaction resistance (Rr) for hydrazine were evaluated
as Rr = 355.5 and RD = 38.67, indicating Rr > RD. Since Rr > RD there
was no external mass transfer limitation. It was also checked by
applying the criteria for external mass transfer, given by Bailey and
The sensitivity of initial rate of reaction to enzyme concentra-
tion is shown by the following power-law model equation:
kE2
vi ¼ kE1½Eꢄ
(1)
From the above equation we have
lnðviÞ ¼ kE2lnð½EꢄÞ þ lnðkE1
Þ
(2)
From Eq. (2) kinetic constants were calculated by plotting lnðvi
Þ
versus [E] (not shown) to get the following.
0:4038
vi ¼ 0:0045 ꢁ ½Eꢄ
(3)
The above model was valid with the range of 0.66–3.33 mg/ml of
enzyme loading. The above power-law model shows an
empirical correlation between enzyme activity (the initial rate)
and its concentration. It is expected that the rates should be
linear in enzyme concentration, if there is no onset of inhibition
or the enzyme does not get activated immediately and requires
some time for activation if not incubated with the substrates.
The proposed mechanism, which is discussed in subsequent
section, shows a complex network. Therefore effect of incuba-
tion and inhibition was studied independently and is explained
systematically.
Ollis [26]. [(hB = 0.68, hA = 0.047, fB = 1.143, fA = 18, BiB, = 392,
BiA = 175), (hf2/Bi)B = 0.0022 ꢃ 1, (hf2/Bi)A = 0.087 ꢃ 1]. These
calculations also indicated that the external mass transfer
resistance was absent. Due to uniform particle size of catalyst,
we were not able to study the effect of particle of different sizes. It
was not advisable to crush the particles to study particle size
effects, which would denature the enzyme. The Wiesz–Prater
criterion or modulus (CWP) was also used (CWP = 0.082 ꢃ 1) [27].
CWP was less than one suggesting that there was no intra-particle
diffusion resistance. These theoretical calculations bolster the
experimental observations that the reaction was intrinsically
kinetically controlled.
3.4. Effect of temperature
The hydrazinolysis activity of Novozym 435 was monitored in
the range of 30–60 8C (Fig. 4). A maximum conversion of 95% was
obtained at 60 8C. A preliminary estimate of the activation energy
was done from the observed initial rates at different temperatures
under otherwise similar conditions. The initial rates can also be
used if all other variables except temperature are maintained
constant. It is equivalent to plotting pseudo-rate constants, which
are functions of temperature. Fig. 5 shows the Arrhenius plot
obtained by plotting the ln(initial rate) values against the
reciprocal reaction temperature. The activation energy was found
to be 6.07 kcal/mol. Several authors have reported activation
energy for enzymatic reaction from 0.9 to 9 kcal/mol. Thus, the
activation energy value obtained for enzymatic synthesis of
phenyl benzoate is comparable to that reported for enzymatic
reaction [26].
3.3. The effect of carrier concentration
The effect of enzyme carrier concentration was studied from
0.666 to 3.33 mg/ml (Fig. 3). The experiments were conducted at a
fixed amount of substrate by varying enzyme concentration. As the
concentration of the Novozym 435 increased, the amount of
benzoic acid hydrazide formed also increased. The maximum
conversion of phenyl benzoate was observed after 2 h. For different
concentrations of the enzyme, the initial rate and final conversions
were calculated. The initial rate of reaction increased with
increasing enzyme concentration and the overall conversion also
increased correspondingly from 60% to 95%.

G.D. Yadav, I.V. Borkar / Process Biochemistry 45 (2010) 586–592
589
Fig. 6. Effect of mole ratio of hydrazine; reaction conditions: phenyl benzoate—
0.01 mol, solvent toluene—up to 15 ml, speed of agitation—600 rpm, temperature—
50 8C, catalyst—35 mg.
Fig. 4. Effect of temperature; reaction conditions: phenyl benzoate—0.01 mol,
hydrazine—0.02 mol, solvent toluene—up to 15 ml, speed of agitation—600 rpm,
catalyst—35 mg.
3.6. Reusability of enzyme
After each reuse, the enzyme was washed with toluene and
solvent was evaporated prior to reuse. The activity of lipase was
decreased by almost 13% after first reuse and then it was
gradually decreased during further reuses. Lipases are known to
be deactivated by various physical parameters and chemicals
[12]. The reduction in activity after each reuse indicates that the
enzyme is strongly inhibited by substrate and product (Fig. 7).
However, it is possible that hydrazine, toluene, phenyl benzoate
might also have caused denaturation. Extensive study of lipase
deactivation in toluene was previously studied by us in whom it
was found that there was no deactivation of lipase by toluene
[12]. The detailed analysis regarding deactivation due to various
factors is discussed in kinetic modeling part.
Fig. 5. Arrhenius plot.
3.5. Effect of mole ratio of hydrazine
The effect of mole ratio of phenyl benzoate to hydrazine was
studied by using Novozym 435. In one set of experiments, different
moles of hydrazine were used in the range of 0.01–0.04 mol,
whereas the amount of phenyl benzoate was kept constant at
0.01 mol. In all these experiments, the total volume of the liquid
phase was the same. The initial rate is plotted against mole ratio in
Fig. 6. The initial rate was practically the same for a mole ratio of
1:4 and 1:3. This would suggest that all sites are occupied by
hydrazine at 1:3 and thus additional concentration of hydrazine
does not increase the rate since no sites are available or hydrazine
concentration beyond a certain value has an inhibitory effect. It
will be discussed separately.
Fig. 7. Reusability of lipase; reaction conditions: phenyl benzoate—0.01 mol,
hydrazine—0.02 mol, solvent toluene—up to 15 ml, speed of agitation—600 rpm,
temperature—50 8C, catalyst—35 mg.

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G.D. Yadav, I.V. Borkar / Process Biochemistry 45 (2010) 586–592
Table 1
4. Kinetic modeling
Kinetic parameters for hydrazinolysis of phenyl benzoate with
hydrazine.
4.1. Kinetic modeling for hydrazinolysis
Kinetic constants
Value by Polymath 5.1
vm (M minꢂ1
KmA (M)
KmB (M)
Ki (M)
a
)
2.340
2.837
1.263
4.084
0.121
0.0623
Reactions were carried out under standard conditions in
toluene, as described earlier. The double reciprocal plot of
reciprocal of rate versus reciprocal of concentration of phenyl
benzoate is illustrated in Fig. 8. It was observed that the initial
reaction rate had increased as the concentration of phenyl
benzoate (A) was increased. When hydrazine (B) concentration
was increased, the effect of substrate inhibition by hydrazine was
notable which caused the reaction rate to fall. It suggests that both
slope and intercepts are affected in a non-competitive inhibition
[26]. The plot also shows that as the concentration of hydrazine is
b
The values represent an average of duplicates with standard
error <10%.
where
v
is the rate of reaction (M minꢂ1), vm is the maximum
increased, the slope increases and intercepts on 1=
v
axis decrease.
rate of reaction (M minꢂ1), [A0] is the initial concentration of
phenyl benzoate (M), [B0] is the initial concentration of
hydrazine (M), KmA is the Michaelis constant for phenyl
benzoate (M), KmB is the Michaelis constant of hydrazine (M),
The inhibition is due to the formation of a dead end complex. A
typical reaction sequence is shown below. According to it, the
lipase (E) may react with hydrazine [B] to yield a dead end complex
(BE) or it may bind to A site to give AE. BE can bind with B to form
another dead end complex BEB. Similarly AE can bind with B to
form complex EAB which gives rise to either the product P and Q or
a complex EB and A. Thus, EB can react with B again to give the dead
end complex BEB [28,29]. The reaction sequence may thus be
depicted as follows:
Ki is the inhibition constant of hydrazine (M),
dimensionless constants.
a and b are the
The data from initial rate measurement were used for the
optimization of parameters by least square error estimation
using the software Polymath 5.1. The values of the kinetic
parameters obtained from non-linear regression analysis are
given in Table 1. From this detail kinetic modeling it was
observed that affinity of hydrazine is greater as compared to
phenyl benzoate. The high values of concentration used are also
reflected in the Michaelis constants. These are certainly intrinsic
parameters since the mass transfer effects were all eliminated.
These values are valid for the concentration range used. A plot of
experimental rates versus simulated rates shows that the
proposed model fits the experimental data very well (Fig. 9).
There was some departure at low values of rates. The reason for
the departure at lower value of rate is due to less influence of the
inhibition at lower concentrations of the reactants, particularly
hydrazine and phenol. Novozym 435 is strongly inhibited by
hydrazine. Values of dimensional less parameter indicate that
the rate of enzyme–acetate–hydrazine ternary complex forma-
tion is greater than that of hydrazine–enzyme–hydrazine
ternary complex.
(4)
where, A is phenyl benzoate; B is hydrazine; EA is enzyme phenyl
benzoate complex; BE is dead end enzyme hydrazine complex; BEB
is dead end enzyme hydrazine complex; EB is effective enzyme
hydrazine complex; EA is effective enzyme phenyl benzoate
complex; EAB is effective enzyme phenyl benzoate hydrazine
complex; P is phenol and Q is benzoic acid hydrazide.
The final equation for the above reaction sequence is [29]:
4.2. Kinetic modeling for deactivation of lipase
vm½Aꢄ
ꢀ
ꢁ
ꢀ
ꢁ
v
¼
(5)
½Bꢄ
KmB
½Bꢄ
KmB
Ki
aKmB
½Bꢄ
a
KmA 1 þ
þ
þ
þ ½Aꢄ 1 þ
bKi
A number of parameters were studied to understand the
deactivation of Novozym 435 [12]. Novozym 435 lipase was
Fig. 8. Linewear–Burk plot for different hydrazine concentrations.
Fig. 9. Parity plot for enzymatic kinetic model.

G.D. Yadav, I.V. Borkar / Process Biochemistry 45 (2010) 586–592
591
Table 2
stirred with the solvent along with hydrazine and phenol
Different kinetic parameters for deactivation of lipase.
individually for 120 min at 30 8C and the reaction was initiated
by adding appropriate reactant, and found that the enzyme get
deactivated by hydrazine and phenol. Enzyme activity was
tested for different time intervals such as 10, 30, 60, 90 and
120 min. The activity of enzyme after 10 min incubation was
almost same as fresh enzyme (without incubation). For the
above reason we have not integrated kinetic model with
deactivation model. The same sets of experiments were carried
out to analysis whether the deactivation was due to the other
remaining reactants and products. It was found that in the
presence of phenyl benzoate and benzoic acid hydrazide, lipase
showed no loss in activity.
Kinetic constants Value by Polymath 5.1
kd1 (minꢂ1
kd2 (minꢂ1
)
)
0.0028
1.8079
The multiphasic nature of the protein molecule during the
deactivation process strengthens the suggestion that complex
internal events take place during its conformational transition. In
this way, a series-type deactivation model involving two first-
order steps with one active precursor and a final enzyme state with
possible non-zero activity was considered for analyzing lipase
deactivation. The overall equation for the deactivation of Novozym
435 by hydrazine and phenol is generally represented by the
following equations:
kd1
E þ Bꢂ!E0B
(6)
kd2
E0B þ Pꢂ!E0BP
(7)
(8)
kd1
kd2
E0ꢂ!E0Bꢂ!E0BP
Fig. 10. Validation of deactivation model.
where E0, E, E0B and EB0 P are enzyme states at different stages such
initial, at time t, deactivation due to hydrazine and phenol,
respectively; kd1 and kd2 are first-order deactivation rate constants
(minꢂ1).
Rearranging
E0BP ¼ E0 ꢂ E ꢂ E0B
(17)
From Eq. (6)
From Eqs. (9) and (14) we get
ꢂ
ꢃ
dE
kd2
kd1
E0BP ¼ E0 1 þ
eꢂk
þ
eꢂk
(18)
(19)
d1t
d2t
¼ ꢂkd1E
(9)
dt
kd1 ꢂ kd2
kd2 ꢂ kd1
dE0B
dt
total concentration enzyme
¼ kd1E ꢂ kd2E0B
¼ ꢂkd2E0B
(10)
(11)
¼ concentration of deactivated enzyme
þ concentration of active enzyme
E0 ¼ E0BP þ EBP
dE0BP
dt
Therefore
By integrating Eq. (9)
EBP ¼ E0 ꢂ E0BP
(20)
(21)
E
d1t
¼ eꢂk
(12)
From Eqs. (18) and (20)
E0
ꢂ
ꢃ
kd2
kd1
d1t
d2t
eꢂk
EBP ¼ E0
eꢂk
þ
Rearranging Eq. (10)
kd2 ꢂ kd1
kd1 ꢂ kd2
dE0B
þ kd1E0B ¼ kd2
E
(13)
(14)
(15)
This is the final equation active enzyme concentration. It should be
noted that EBP is the concentration of active enzyme. Quantifica-
tion of active enzyme is based on initial rate measurement. Activity
based on initial rate of fresh enzyme without any deactivation is
considered as (E0). Thus, EBP is the concentration of active enzyme
after deactivation ðE0 ꢂ E0BPÞ. Here EB0 P is the total enzyme
deactivated by hydrazine and phenol.
Kinetic parameters were refined by using Polymath 5.1. Enzyme
was incubated in hydrazine and phenol for different time intervals.
For each incubation time the activity was evaluated. Knowing the
experimental initial rates with respect to incubation time, all the
rate constants were calculated by applying non-linear regression
to rate equation using Polymath 5.1. The best-fit values obtained
are tabulated in Table 2.
dt
which is first-order linear differential equation of the form
dy
þ Py ¼ Q
dx
By integrating above Eq. (13) we get
EB0
kd1
E0 kd2 ꢂ kd1
d1t
d2t
¼
ðeꢂk ꢂ eꢂk
Þ
initial enzyme concentration
¼ free enzyme concentration
þ deactivated enzyme concentration due to hydrazine
þ deactivated enzyme concentration due to phenolE0
¼ E þ E0BP þ E0B
These values were then used to generate simulated initial rate
values. Simulated values of lipase activity so obtained were
compared with experimental values (Fig. 10). From these rate
(16)

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G.D. Yadav, I.V. Borkar / Process Biochemistry 45 (2010) 586–592
constants it is clearly seen that the rate of deactivation with respect
to phenol is greater than that of hydrazine hydrate.
Rr
v
vi
vmax
X
internal reaction resistance
rate of reaction (M minꢂ1
initial rate of reaction (M minꢂ1
)
)
5. Conclusions
maximum velocity in enzymatic step (M minꢂ1
)
fractional conversion
Synthesis of benzoic acid hydrazide was conducted by employ-
ing different lipases, amongst which Novozym 435 was found to be
the most active catalyst. The effects of various parameters on the
conversion and rates of reaction were studied with Novozym 435
as the catalyst and toluene as the solvent. Initial rate and progress
curve data were used to arrive at a suitable model and various
parameters were estimated. The apparent fit of the kinetic data to
the assumed ordered bi–bi dead end complex with hydrazine
provides support for the mechanism. This model was used to
simulate the rate data, which were in excellent agreement with
experimental values. The deactivation study demonstrated that
the enzyme was deactivated by hydrazine and phenol. The rate
constants clearly indicate that the rate of deactivation of enzyme
with respect to phenol is greater than that of hydrazine hydrate.
The kinetic parameters deduced from deactivation model were
used to simulate the initial rate, which are in good agreement with
the experimental values.
Greek letters
h
f
a
b
effectiveness factor
Thiele modulus
dimensionless constant
dimensionless constant
References
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A
phenyl
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ABE
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benzoate
AE
B
enzyme–phenyl benzoate complex
hydrazine
Bi
Biot number
DSL;A
DSL;B
dp
liquid phase diffusivity of phenyl benzoate (cm2 sꢂ1
)
liquid phase diffusivity of hydrazine (cm2 sꢂ1
diameter of enzyme particle (cm)
free enzyme
)
E
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E0
initial concentration of enzyme,
enzyme–benzoic acid hydrazide complex
concentration of active enzyme
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total enzyme deactivated by hydrazine and phenol
inhibition constant
deactivation constant due to hydrazine (minꢂ1
deactivation constant due to phenol (minꢂ1
kd1
kd2
)
)
kE1,kE2 constants in Eq. (1)
Ki
inhibition constant
KmA
KmB
kSL;A
Michaelis constant for phenyl benzoate (M)
Michaelis constant for hydrazine (M)
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liquid side mass transfer coefficient for phenyl benzoate
(cm sꢂ1
)
kSL;B
P
liquid side mass transfer coefficient for hydrazine (cm sꢂ1
)
phenol
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Q
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R
RD
external mass transfer resistance