## Maximum Space Time Yield in Well Mixed Suspensions

The system analyzed here is schematically presented in Fig. 1. The maximum space-time yield in a system containing a suspension of one solid substrate is equal to the maximum rate of mass transfer from the solid to the liquid phase. The biocatalyst activity Vmax required to convert this amount of substrate per unit time can be estimated from the following pseudo-steady-state condition, assuming simple Michaelis-Menten kinetics:

Fig. 2. Progress curves for equilibrium- or kinetically controlled biotransformations for dissolved substrates and products. A and B give the optimal end points of these processes. After the reaching the maximum, the yield in kinetically controlled reactions declines as the rate of product (AN) hydrolysis becomes larger than the rate of its formation. The loss of AN can be reduced if the reaction is carried out under conditions where the product precipitates (i.e., in suspensions).

Fig. 2. Progress curves for equilibrium- or kinetically controlled biotransformations for dissolved substrates and products. A and B give the optimal end points of these processes. After the reaching the maximum, the yield in kinetically controlled reactions declines as the rate of product (AN) hydrolysis becomes larger than the rate of its formation. The loss of AN can be reduced if the reaction is carried out under conditions where the product precipitates (i.e., in suspensions).

where kL is the mass transfer coefficient and a is the surface area per unit suspension volume. The maximum rate of mass transfer is obtained when [AB]* >> [AB][. When [AB][>^m, the enzyme activity required to convert the dissolved substrate is Vmax > kLa [AB]*. The estimation of Vmax is done as follows. The solid substrate is considered to exist as spherical particles with radius rAB,0 at the start of the reaction and occupy the volume fraction p of the suspension. Then the rate of dissolution is:

3Sh^ABP

2rAB

where Sh is the Sherwood number (the ratio of the particle diameter to the thickness 5 of the diffusion layer [Sh «10 in well-mixed suspensions (14)] and CABis the diffusion coefficient (approx 5 x 10-6 cm2/s for substrates with the molecular weight in the range 300-500 Daltons). With p = 0.1 and [AB]* = 10 mM, the maximum dissolution rate or the minimum enzyme content required for the conversion is:

750 x 10-6M/s = 45000 U/L for rAB = 100 ^m 8300 x 10-6M/s = 500000 U/L for rAB = 30 ^m

It has been observed with different substrates that the particle size in suspensions is about 100 ^m, reducing to 30 ^m at the very latest stages of the reaction (approx 3% of the remaining substrate) because of the continuous reduction of the particle size during the biotransformation (see Note 1). Thus, the required enzyme activities can be easily obtained with commercially available enzymes in the free and immobilized forms.

To assess the potential of biotransformations in suspension for practical applications, some of the factors that may influence the space-time yield in this system should also be considered:

• The rate of mass transfer and control of pH, if required, and the dependence of these parameters on the suspension content |3, which also reflects the water content of the system.

• The feasibility of using immobilized enzymes, especially when one of the products precipitates out. In this case, a method of separating the insoluble product and immobilized enzyme must be available.

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