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13.2 The Temperature Effect on the NHase–Amidase Bi-Enzymatic Cascade System  285

               Table 13.1  Equations used to calculate reaction-rate in batch and continuous stirred UF-
               membrane bioreactors.

               Substrate  Batch reactor            Continuous stirred UF-membrane reactor

                                                          ∗
                                                                   ∗
                                       d[acid]
               Amide    v AMase  =  d[P] AMase  =  U AMase dt  v AMase  =  Q [P] AMase  =  Q [acid]
                               U AMase dt
                                                                  U AMase
                                                          U AMase
                                                          ∗
               Nitrile  v    =  d[P] NHase  =  d[amide] formed  v  =  Q [P] NHase
                         NHase  U NHase dt  U NHase dt  NHase  U NHase
                                                           ∗
                             =  d[amide+acid] detected  =  Q [amide] formed
                                  U NHase dt                U NHase
                                                           ∗
                                                        =  Q [amide+acid] detected
                                                              U NHase
                                                                           −1
                                                                   ◦
               Where P, U,and Q are the product concentration (mM), the units of enzyme at 20 C(μmol min ),
                               −1
               and the flow-rate (ml min ) respectively.
               NHase–AMase cascade system that naturally acts as a sequential system can be
               adequately decoupled by feeding the bioreactor with the appropriate substrate. The
               NHase activity was evaluated at various temperatures in the presence of acrylonitrile
               [20], propionitrile [18], benzonitrile [21], and 3-cyanopyridine [22] as substrates,
               while the AMase activity was separately investigated with the corresponding
               amides [23]. The kinetics of both enzymes examined in an appropriate substrate
               concentration range were reported to follow the Michaelis–Menten equation, as
               reviewed previously [24].
                Two reactor configurations (batch and CSMR) were used throughout these
               studies, and the specific reaction rates were calculated from the product formed
               (Table 13.1).
                The operational conditions, that is, the concentration of substrate and enzyme,
               the temperature range, and the reactor configuration are summarized in Table 13.2.
               The activation energy of the reaction, E , was typically obtained for a batch reactor
                                             a
               and compared with that calculated for a CSMR. The data obtained in the CSMR
               at steadystate enabled us, by using a semi-log plot of reaction rate versus time, to
               identify a first-order mechanism of enzyme deactivation and to determine both
               its first-order deactivation constant, k , and the reaction rate at time zero, r ,for
                                            d
                                                                          0
               each substrate and temperature. It was thus possible to compare the effect of the
               operational parameters on the activity and stability of these two enzymes. From the
               Arrhenius plot of these r ,the E -values were determined for each substrate, and
                                  0     a
               were found to match the values obtained in the batch reactors.
                                                                       ∗
                Finally, the different activation energies of the enzyme inactivation, E ,during
                                                                       a
               nitrile or amide reactions are also reported, and when unavailable, the inactivation
               constants, k are given instead.
                        d
                The E of the NHase appears to be dependent on the substrate used. Indeed, for
                     a
               acrylonitrile and propionitrile, the E falls into the lower range of the values cited in
                                          a
               the literature, while for the aromatic substrates, benzonitrile and 3-cyanopyridine,
               the E is higher, thus suggesting a partial effect of mass transport for the aliphatic
                   a
               substrates. It must be also noted that the activation energies of the AMase catalyzed
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