Investigation of Catalytic Properties of Immobilized Enzymes and Cells by Flow Microcalorimetry - Advances in Biochemical Engineering Biotechnology - page 84

observed biocatalytic reaction rate is influenced by exchange of mass between
the interior of the particle and its surroundings.A reaction rate profile is built
up inside the particle, and the overall reaction rate is different from the kinetic
rate.Therefore,the effectiveness factor is not longer unity and its value must be
introduced into the mathematical model. The effectiveness factor is calculated
by solving the particle mass balance equations (7) and (8).
The first investigation of the influence of particle mass transfer on the reac-
tion kinetics in a flow microcalorimeter, dealing with properties of urease
immobilized on controlled pore glass, was published in 1985 [25]. More recent-
ly,the evaluation of microcalorimetric data in the case of particle-diffusion limi-
tation was improved and simplified by introducing the principle of the differen-
tial bed [28,29].
In certain cases, restriction of the experimental conditions to low substrate
concentrations (c S

K m ) is an acceptable condition for the investigation of bio-
catalyst properties. In this case, the enzyme kinetics can be simplified to the
form of a pseudo-first order kinetics expressed by the relation
V m

v(c S ,c P , P ) = c S = k 1 c S (31)

5

K m
where k 1 is the pseudo-first order rate constant. Then, Eq. (7) can be solved
analytically and, for example, in the case of spherical geometry the follow-
ing explicit expression can be obtained for the effectiveness factor calcula-
tion [36]:

3 1 1

63 2 2

h = - (32)

3 3

F tanh FF

where F is the Thiele modulus

k 1

=R d 34 . F (33)

D S

This approach was used in the study of the properties of D -amino acid oxidase
isolated or fixed in cells of Tr i gonops i s var i abi l i s and entrapped in calcium
pectate or polyacrylamide gel [28]. The approach of a differential reactor (low
enzyme activity in the packed bed) was applied. The experimental thermo-
metric data,

T r ,were transformed to reaction rates,v obs ,according to Eq. (21),
whereas parameter

D

was determined by the calibration shown in Fig. 5. The
data were described by the equation

a

(1- e )

v obs = h v kin = h 63 k 1 c Sb (34)

e

that was obtained by combining Eqs. (6), (14) and (31). The kinetic parameter,
k 1 , was evaluated by comparing the experimental and calculated data. The
results of the treatment of the data,listed in Table2,illustrate the influence of cell