Ghasem D. Najafpour. Biochemical Engineering and Biotechnology

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lipase in the EMR. The product inhibition constants (K

) for the two systems are given in

Table 5.3. The 2-ethoxyethanol was found to be a non-competitive inhibitor to the substrate

as determined by the EKP software, with the mechanism shown in Figure 5.19.

In non-competitive inhibition, the substrate (S) and inhibitor (I) have equal potential to

bind to the free enzyme (E). The inhibitor forms a ternary complex with enzyme–substrate

(ES) whereas the substrate will form another ternary complex with enzyme–inhibitor (EI).

Since the non-competitive inhibitor had no effect on the binding of substrate to the enzyme,

the K

value remained consistent (or unchanged). There are two different ways for the for-

mation of ESI ternary complex; this complex would not form the product and therefore

was decreased. Non-competitive inhibitor had no effect on substrate binding or the

enzyme–substrate affinity, therefore the apparent rate constant (K

app

) was unchanged.

A possible reason for product inhibition was because of the nature of 2-ethoxyethanol,

134 BIOCHEMICAL ENGINEERING AND BIOTECHNOLOGY

-20

100

120

-80 -60 -40 -20 0 20 40 60 80

[S] (mmol/L)

[S] / ν

(h)

0 mmol/L

90 mmol/L

160 mmol/L

250 mmol/L

360 mmol/L

470 mmol/L

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

010203040506070

[

]

(

mmol/L

)

(mmol/L.h)

0 mmol/L

90 mmol/L

160 mmol/L

250 mmol/L

360 mmol/L

470 mmol/L

FIG. 5.17. Free lipase in batch system: Product inhibition plots (Left: Hanes-woolf; Right: Curve fit).

-20

100

-80 -60 -40 -20 0 20 40 60 80

[S] (mmol/L)

0 mmol/L

90 mmol/L

160 mmol/L

250 mmol/L

360 mmol/L

470 mmol/L

0.0

0.5

1.0

1.5

2.0

2.5

010203040506070

[S] (mmol/L)

0 mmol/L

90 mmol/L

160 mmol/L

250 mmol/L

350 mmol/L

470 mmol/L

[S] / ν

(h)

(mmol/L.h)

FIG. 5.18. Immobilised lipase in EMR: Product inhibition plots (Left: Hanes-woolf; Right: Curve fit).

Ch005.qxd 10/27/2006 10:44 AM Page 134

which is miscible in both aqueous buffer and organic solvent. K

was larger than K

an order of magnitude, i.e. K

was 337.94 mmol⭈l

⫺1

for the free lipase system and

354.20 mmol⭈l

⫺1

for EMR while K

was 43.07 mmol⭈l

⫺1

for the batch system and

49.52 mmol⭈l

⫺1

for EMR.

5.9.3 Enzyme Kinetics for Rapid Equilibrium System

(quasi-equilibrium)

Enzyme reaction kinetics were modelled on the basis of rapid equilibrium assumption.

Rapid equilibrium condition (also known as quasi-equilibrium) assumes that only the early

components of the reaction are at equilibrium.

8–10

In rapid equilibrium conditions, the enzyme

(E), substrate (S) and enzyme–substrate (ES), the central complex equilibrate rapidly com-

pared with the dissociation rate of ES into E and product (P⬘). The combined inhibition

effects by 2-ethoxyethanol as a non-competitive inhibitor and (S)-ibuprofen ester as an

uncompetitive inhibition resulted in an overall mechanism, shown in Figure 5.20.

5.9.4 Derivation of Enzymatic Rate Equation from

Rapid Equilibrium Assumption

The mechanism involved the overall conversion of [S] to [P]. The reverse reaction is

insignificant because only the initial velocity in one of the forward direction is concerned.

The mass balance equation expressing the distribution of the total enzyme is:

(5.9.4.1)

[[]

E E ES EI ESI ESS

] [][ ][ ] [ ]⫽⫹ ⫹ ⫹ ⫹

GROWTH KINETICS 135

EI S

ESI

P' E

FIG. 5.19. Enzyme mechanism with non-competitive product inhibition.

TABLE 5.3. K

value for batch system and EMR

Product inhibition K

(mmol⭈l

⫺1

)

Batch system Non-competitive 337.94

EMR Non-competitive 354.20

Ch005.qxd 10/27/2006 10:45 AM Page 135

The rate-dependent equation was expressed in the form:

(5.9.4.2)

where v indicates the initial rate of the product-forming species. The rate equation was

divided by [E]

(5.9.4.3)

where [E]

contains a total of five enzyme species of one free and four complexes of

enzyme, substrate and inhibitor. The concentration of each enzyme species was expressed

in terms of free enzyme, E. This was accomplished by rearranging the expressions for the

various equilibria. In this case, there are four equilibria:

(5.9.4.4)

(5.9.4.5)

(5.9.4.6)

(5.9.4.7)

[]

[][][ ]

ESS

⫽

[]

[][][]

ESI

⫽

[]

[][]

⫽

⫽⫽

[][]

[]

[]

kES

E E ES EI ESI ESS

[]

[] [][ ][ ][ ][ ]

⫽

⫽⫹ ⫹ ⫹ ⫹

vkES

⫽ []

136 BIOCHEMICAL ENGINEERING AND BIOTECHNOLOGY

EI S

ESI

ESS*

FIG. 5.20. Kinetics mechanism with uncompetitive substrate inhibition and non-competitive product inhibition.

Ch005.qxd 10/27/2006 10:45 AM Page 136

Each enzyme complex in the rate-dependent equation was substituted by the above equa-

tions in terms of [E]. After cancelling [E] and substituting k

[E]

⫽ V

max

the following rate

equation was obtained.

(5.9.4.8)

The above equation can be transformed into the Michaelis–Menten equation by multiply-

ing the numerator and denominator by K

(5.9.4.9)

In the present work, [I] ⫽ [P] and [S*] ⫽ [S], so the equation becomes:

(5.9.4.10)

The above rate equation is in agreement with that reported by Madhav and Ching [3]. This

rapid equilibrium treatment is a simple approach that allows the transformations of all

complexes in terms of [E], [S], K

and K

, which only deal with equilibrium expressions

for the binding of the substrate to the enzyme. In the absence of inhibition, the enzyme

kinetics are reduced to the simplest Michaelis–Menten model, as shown in Figure 5.21.

The rate equation for the Michaelis–Menten model is given in ordinary textbooks and is as

follows:

(5.9.4.11)

⫽

⫹

max

[]

⫽

⫹⫹⫹

max

[]

([])

[] []

IP IS

max

[]

[] [][ ]

⫽

⫹⫹⫹

()

IP IS

mmm

max

[]

[] [][] [] [][ ]

⫽

⫹⫹ ⫹⫹1

IP IP IS

GROWTH KINETICS 137

E S

P ' E

FIG. 5.21. First-order reaction kinetics mechanism without inhibitions.

Ch005.qxd 10/27/2006 10:45 AM Page 137

5.9.5 Verification of Kinetic Mechanism

The velocity equation for rapid equilibrium system was easily derived by inversing the

numerator and denominator of (5.9.4.10):

(5.9.5.1)

(5.9.5.2)

(5.9.5.3)

Plotting 1/n against [P] will result in a Dixon plot, which is plotted at different fixed [S]

with the slope:

(5.9.5.4)

and the y-intersect:

(5.9.5.5)

The plotting of Dixon plot and its slope re-plot (see 5.9.5.9) is a commonly used graphical

method for verification of kinetics mechanisms in a particular enzymatic reaction.

The

proposed kinetic mechanism for the system is valid if the experimental data fit the rate

equation given by (5.9.4.4). In this attempt, different sets of experimental data for kinetic

resolution of racemic ibuprofen ester by immobilised lipase in EMR were fitted into the

rate equation of (5.7.5.6). The Dixon plot is presented in Figure 5.22.

Dixon Plot:

(5.9.5.6)

The slope and intersect of the illustrated plot were determined and compared with values

calculated from (5.9.5.7) and (5.9.5.8):

(5.9.5.7)

Slope

max

app

⫽⫹

[]

111

⫽⫹⫹⫹⫹

max

app

max

app

[]

IIS

max

[]

⫹⫹

max

[]

⫹

111

vV K

⫽⫹⫹⫹⫹

max max

[]

IP IS

⫽⫹⫹⫹

max max

[]

[] []

IP IS

mmax

[]

[] []

⫽

⫹

⫹⫹

IP IS

138 BIOCHEMICAL ENGINEERING AND BIOTECHNOLOGY

Ch005.qxd 10/27/2006 10:45 AM Page 138

(5.9.5.8)

The experimental values fit the velocity equation with insignificant deviation in the slope

and intersect values at maximum error of ⫾5.94 % (see Table 5.4). The corresponding

slope re-plot given by (5.9.5.9) was plotted in Figure 5.23.

(5.9.5.9)

(5.9.5.10)

Slope

app

max

app

⫽

Slope re-plot

app

max

app

IP max

app

⫽⫹

[]

Intersect

max

app

⫽⫹⫹

[]

GROWTH KINETICS 139

-350 -250 -150 -50 50 150 250 350 450 550

Concentration of 2-ethoxyethanol, [

]

1/v

[S]=5 mmol/L

[S]=10 mmol/L

[S]=20 mmol/L

[S]=30 mmol/L

[S]=35 mmol/L

[S]=50 mmol/L

FIG. 5.22. Dixon plot: 1/v versus [P] at different initial substrate concentrations.

TABLE 5.4. Comparison between graphical value (Figure 5.21) and calculated value

[S] (mmol·1

⫺1

) Slope Intersect

From Calculated Error From Calculated Error

Figure 5.21 from (5.135) (%) Figure 5.21 from (5.136) (%)

5 0.0070 0.00720 2.7 2.6509 2.567 3.23

10 0.0039 0.00400 2.5 1.5292 1.4828 3.10

20 0.0024 0.00244 1.64 0.9360 0.9870 5.17

30 0.0020 0.00190 5.26 0.8140 0.8630 5.68

35 0.0018 0.00176 2.27 0.7911 0.8406 5.94

50 0.0015 0.00150 0.00 0.7852 0.8276 5.19

Ch005.qxd 10/27/2006 10:45 AM Page 139

(5.9.5.11)

The values determined from Figure 5.23 agree well with the values calculated from the

equations (Table 5.5), with an error of ⫾3.81% for the slope and ⫾4.65% for the intersect,

respectively. The obtained experimental data were consistent with the proposed enzymatic

reaction and the reaction mechanisms with uncompetitive substrate inhibition and the non-

competitive product inhibition model.

REFERENCES

1. Battistel, E., Bianchi, D., Cesti, P. and Pina, C., Biotechnol. Bioengng 38, 659 (1991).

2. Giorno, L., Molinari, R. Natoli, M. and Drioli, E., J. Membr. Sci. 125, 177 (1997).

3. Madhav, M.V. and Ching, C.B., J. Chem. Technol. Biotechnol. 76, 941 (2001).

Intersect

max

app

⫽

140 BIOCHEMICAL ENGINEERING AND BIOTECHNOLOGY

= 0.0303

+ 0.0009

-0.001

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25

1/[

]

Slope of the Dixon plot

FIG

. 5.23. Slope re-plot: the slope of the Dixon plot was plotted against 1/[S].

TABLE 5.5. Slope re-plot (slope of Dixon plot versus 1/[S])

Slope Intersect

Slope re-plot Calculated from Error Slope re-plot Calculated from Error

(Figure 5.22) (5.138) (%) (Figure 5.22) (5.139) (%)

0.0303 0.0315 3.81 0.0009 0.00086 4.65

Ch005.qxd 10/27/2006 10:45 AM Page 140

4. Xiu, G.-H., Jiang, L. and Li, P., Biotechnol. Bioengng 74, 29 (2001).

5. Chaplin, M.F. and Bucke, C., In “Enzyme Technology”. Cambridge University Press, London, 1990.

6. Matson, S.L. and López, J.L., In “Frontiers in Bioprocessing”. CRC Press, Florida, 1990.

7. Xiu, G.-H. and Jiang, L., Ind. Eng. Chem. Res. 39, 4054 (2000).

8. Segel, I.H., “Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme

Systems”. John Wiley & Sons, New York, 1975.

9. Long, W.S., Ph.D thesis. Universiti Sains Malaysia, Penang, Malaysia, 2004.

10. Long, W.S., Azlina Harun, K. and Bhatia, S., Chem. Eng. Sci. 60, 4957 (2005).

11. Voet, D. and Voet, J.G., “Fundamentals of Biochemistry”, 3rd edn. John Wiley, New York, 2004.

GROWTH KINETICS 141

Ch005.qxd 10/27/2006 10:45 AM Page 141

142

CHAPTER 6

Bioreactor Design

6.1 INTRODUCTION

To design a bioreactor, some objectives have to be defined. The decisions made in the

design of the bioreactor might have a significant impact on overall process performance.

Knowledge of reaction kinetics is essential for understanding how a biological reactor

works. Other areas of bioprocess engineering such as mass and energy balances, mixing,

mass transfer and heat transfer are also required.

The bioreactor is the heart of any biochemical process in which enzymes, microbial, mam-

malian or plant cell systems are used for manufacture of a wide range of useful biological

products. The performance of any bioreactor depends on many functions, such as those listed

below:

• Biomass concentration • Nutrient supply

• Sterile conditions • Product removal

• Effective agitations • Product inhibition

• Heat removal • Aeration

• Correct shear conditions • Metabolisms/microbial activities

There are three groups of bioreactor currently in use for industrial production:

1. Non-stirred, non-aerated system: about 70% of bioreactors are in this category.

2. Non-stirred, aerated system: about 10% of bioreactors.

3. Stirred and aerated systems: about 20% of the bioreactors in industrial operation.

Non-stirred, aerated vessels are used in the process for traditional products such as wine, beer

and cheese production. Most of the newly found bioprocesses require microbial growth in

an aerated and agitated system. The percentage distribution of aerated and stirred vessels

for bioreactor applications is shown in Table 6.1. The performances of various bioreactor

systems are compared in Table 6.2. Since these processes are kinetically controlled, trans-

port phenomena are of minor importance.

Non-stirred, non-aerated vessels are used for traditional products such as wine, beer and

cheese. Most of the new products require growth of microorganisms in aerated, agitated

vessels.

Ch006.qxd 10/27/2006 10:44 AM Page 142

BIOREACTOR DESIGN 143

6.2 BACKGROUND TO BIOREACTORS

The main function of a properly designed bioreactor is to provide a controlled environment

to achieve optimal growth and/or product formation in the particular cell system employed.

Frequently the term “fermenter” is used in the literature to mean “bioreactor”.

1–3

The

performance of any bioreactor depends on many functions including:

• Biomass concentration must remain high enough to show high yield.

• Sterile conditions must be maintained for pure culture system.

• Effective agitation is required for uniform distribution of substrate and microbes in the

working volume of the bioreactor.

• Heat transfer is needed to operate the bioreactor at constant temperature, as the desired

optimal microbial growth temperature.

• Creation of the correct shear conditions. High shear rate may be harmful to the organism

and disrupt the cell wall; low shear may also be undesirable because of unwanted floccula-

tion and aggregation of the cells, or even growth of bacteria on the reactor wall and stirrer.

6.3 TYPE OF BIOREACTOR

Aerobic bioreactors are classified into four categories, depending on how the gas is

distributed.

TABLE 6.1. Percentage of distribution aerated and stirred

vessel in bioreactor application

Non-stirred, non-aerated 76%

Non-stirred, aerated 11%

Stirred, aerated 13%

Total 100%

TABLE 6.2. Performances of bioreactors

Concentration Productive bioreactors Wastewater treatment

10–50 Aerobic Anaerobic

(kg/m

)550

Moulds Bacteria/yeast Mixed Culture

Viscosity High Low Low Low

Oxygen consumption High High Low Absent

Mass transfer Low High Low Absent

Heat production 3–15 3–15 0.03–0.14 Negligible

metabolic (kW/m

)

Power consumption, hp 3–15 fewer than 5 0.02–05 Negligible

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