a batch solvent system. The hypothesis consists of four steps. The lipase forms a
TAGE complex in the first step, followed by a DAGE complex and fatty acid
in the second step. The DAGE complex is then combined with the other fatty
acid to turn into the other TAGE complex. The last stage, in which the new
TAGE complex dissociates, completes the reaction. The steps can be summarized
as:
TAG 1 +EÐTAG 1 EÐDAG 1 E+FA 1
DAG 1 E+FA 2 ÐTAG 2 EÐTAG 2 +E
Under water content control of the system by spontaneous regulation during the
reaction in each experiment, the rate constants for each step, after a series of stu-
dies, were found to be affected by the water content in the system (Kyotani et
al., 1988b).
It is tempting to develop simple kinetic models for practical applications with
fewer rate constants. This often needs to consider overall performance of the reac-
tion instead of the reaction mechanism. When studied by Xu et al. (1988a), the
apparent incorporation of acyl donors was found to have a relationship with reaction
time in form of the Michaelis – Menten equation (Equation 15).
Inc¼
Incmaxt
Kiþt
ð 15 Þ
The Incmax, equivalent toVmax, was confirmed to be equal to the incorporation under
equilibrium at certain substrate molar ratios, which can be calculated directly from
the substrate molar ratio [Equation (8)]. Basheer et al. (1995a,b) derived equations
for both ester – ester exchange and acidolysis in a solvent system. The concentration
change of each species in the reaction mixture as the function of time was established
for both reactions. The models fitted the experimental data well, and only one con-
stant existed in the models. For the comparison of reaction rates under different
conditions and for the screening of lipases for enzymatic interesterification, the fol-
lowing simple model is much useful:
r¼
1
t
ln
IncmaxInc 0
IncmaxInct
ð 16 Þ
wheretis the reaction time or residence time, Incmax, Inc 0 , and Inctare the maximum
incorporation of acyl donors, acyl incorporation at time 0 andt. The enzyme activity
can be compared by calculating rV/WwhereVis the volume of the substrate liquid in
the reactor andWis the weight of enzyme in the reactor.
198 11 Modification of Oils and Fats by Lipase-Catalyzed Interesterification
