Kinetics of Amycolatopsis mediterranei DSM 43304 lipase-mediated ...

for the kinetic model building [10,11]. The description of this mechanism and the associated rate (r) is given
by Eq. (1) [35].
⎪⎧
[ ] [ ]
[ ΙΑΑc] × [ Η ] ⎪⎫
2Ο
ν
fν
r ⎨ Αc
× Η
2Ο
−
⎬
⎪⎩
keq
r =
⎪⎭
(1)
⎛
{ [ ] [ ]
[ ΙΑΑ]
⎞ ν
f
km,
Η Ο
ν
f
k
2
m,
ΙΑΑc
ν
⎜
⎟
f
km,
ΙΑΑ
Αc
+ ν
rkm,
Αc
ΙΑΑ × 1 + + [ ΙΑΑc] + [ Η
2Ο] + ν
f
[ Αc] × [ Η2Ο]
⎝ k'
ΙΑΑ ⎠ keq
keq
ν
f
km,
Η Ο
ν
f
ν
rk
2
m,
Αc
+ [ Αc] × [ ΙΑΑc] + [ ΙΑΑc] × [ Η2Ο] + [ ΙΑΑ] × [ Η
2Ο] }
k k
k
k
eq i,
Αc
eq
i,
Η 2Ο
where v f and v r are the maximal velocities for the forward and the reverse reactions, respectively, k eq is the
equilibrium constant, k m,IAA , k m,Ac , k m,H2O and k m,IAAc are the Michaelis-Menten constants for isoamyl alcohol
(IAA), acetic acid (Ac), water (H 2 O) and isoamyl acetate (IAAc), respectively, k’ IAA is the inhibition constant
for IAA, and k i,Ac and k i,H2O are the dissociation constants for Ac and H 2 O from the specific enzyme-inhibitor
complex, respectively.
Owing to the mathematical complexity of this full-model involving ten adjustable parameters with associated
problems of unidentifiability and indistinguishability of different parameters under normal experimental
situations, a strategy to study the effect of dropping out some parameter(s) in order to produce a simpler
model was implemented [11, 34]. Following the methodology of Paiva et al. [11], the Michaelis-Menten
dissociation constant terms for each of the compounds (k m,x , where ‘x’ represents either [Ac], [IAA], [IAAc]
or [H 2 O]) from the enzyme complex were considered for model reduction; the elimination of these
parameters from the denominator of model rate constant would mean that such parameters assume high
values in respect to the experimental data and there is no evidence of saturation in the concentration range
studied or there is no affinity of the enzyme to the compound in question. In order to study the adequacy of
this hypothesis, the model from Segel [35] was reformulated by eliminating the dissociation constants
yielding simpler models. These models were separately fitted to the experimental data and F-tests were
performed on the associated residual sum of squares with the aim of investigating the statistical likelihood of
such simplifications. The results obtained in this comparison are presented in Table 1.
Table 1. F-test results for model nesting
Source model SSQ parameters
Model
(NP)
df RSS a df
Extra
(σ) b
Mean
square
(s 2 ) c F
ratio d
P
value
Full model vs. Nested-1
Eq- 1 793.49 10 53 – – 14.97 – –
Eq-2 792.97 4 59 -0.52 6 -0.09 -0.01 0.99
a Residual sum of squares is the difference in the SSQ of models, b Extra degrees of freedom is the difference in the
number of model parameters. c Mean square is the residual sum of squares divided by degrees of freedom (df). d F ratio is
the full model (f) mean square divided by the mean square of the nested model (n),
It can be concluded that, at p < 0.05 level of statistical significance, the resulting rate expression can be
described by Eq. (2).
⎪⎧
[ ΙΑΑc] × [ Η ] ⎪⎫
2Ο
{( k
cat f
[ Et
]) × ( k
cat r
[ Et
])} × ⎨[ Αc] × [ ΙΑΑ]
−
⎬
⎪⎩
k
eq ⎪⎭
r =
(2)
( k
f
[ Et
])
( k [ ])[ Αc] × [ ΙΑΑ] cat
cat r
Et
+ [ ΙΑΑc] × [ Η
2Ο]
k
The experimental concentration profiles were modeled using Eq. (2). Experimental points and the simulated
curves obtained with the developed model are shown in Figure 1. The simulated curves follow reasonably
well the experimental points, showing the kinetic model using Eq. (2) is able to describe the entire reaction
progress under conditions of equimolar initial substrate concentrations as well as excess of one of the
substrates (see Figure 1 for prediction and Table 2 for estimated parameters).
eq