RANCANGAN ALAT BIOPROSES

TPE4211

PERTEMUAN 3

No Pokok Bahasan Sub Pokok Bahasan Waktu (Jam)

1 3 4 5

1. Pengantar Overview Bioreaktor 2 x 50

2. Tahap Inokulasi Dasar mikroorgmisme kurva pertumbuhan

2 x 50

3. Dasar pemodelan reaktor Modelling, matematis monod 2 x 50

4. Konfigurasi Bioreaktor Stirred Tank Bubble colomn

2 x 50

5. Konfigurasi Bioreaktor Airlift Reactor Stirred and Air Driven Reactor

2 x 50

6. Konfigurasi Bioreaktor Packed Bed Trickle Bed

2 x 50

7. Konstruksi Bioreaktor Aseptic Operation Fermenter inoculation and

sampling Materials of construction Sparger design Evaporation control

2 x 50

MATERI KULIAH

Cellular kinetics and associated reactor design:

Modelling Cell Growth

Approaches to modelling cell growth

Unstructured segregated models

Substrate inhibited models

Product inhibited models

Cell Growth Kinetics

where μmax and KS are known as the Monod kinetic parameters.

The most commonly used model for μ is given by the Monod model:

Monod Model is an over simplification of the complicated mechanism of cell growth.

However, it adequately describes the kinetics when the concentrations of inhibitors to cell growth are low.

μ = KS + CS

μm CS

Cell Growth Kinetics Let’s now take a look at the cell growth kinetics, limitations of Monod model, and alternative models.

Unstructured Models (cell population is treated

as single component)

Segregated Models (cells are treated

heterogeneous)

Nonsegregated

Models (cells are treated as

homogeneous)

Structured Models (cell population is treated

as a multi-component

system)

Approaches to modelling cell growth:

Unstructured Nonsegregated

Models (cell population is treated as single component, and cells

are treated as homogeneous)

Structured Segregated Models

(cell population is treated as a multi-component system,

and cells are treated heterogeneous)

Approaches to modeling cell growth:

Simple and applicable to many situations.

Most realistic, but are computationally

complex.

Unstructured, nonsegregated models: Monod model:

μ = KS + CS

μ : specific (cell) growth rate

μm : maximum specific growth rate at saturating substrate concentrations

CS : substrate concentration

KS : saturation constant (CS = KS when μ = μm / 2)

Most commonly used model for cell growth

μm CS

0

0,2

0,4

0,6

0,8

1

0 5 10 15Cs (g/L)

Unstructured, nonsegregated models: Monod model:

μ = μm CS

KS + CS

μ (p

er h

)

μm = 0.9 per h Ks = 0.7 g/L

Most commonly used model for cell growth

Assumptions behind Monod model:

- One limiting substrate

- Semi-empirical relationship

- Single enzyme system with M-M kinetics being responsible for the uptake of substrate

- Amount of enzyme is sufficiently low to be growth limiting

- Cell growth is slow

- Cell population density is low

Other unstructured, nonsegregated models (assuming one limiting substrate):

Blackman equation: μ = μm if CS ≥ 2KS

μ = μm CS

2 KS if CS < 2KS

Tessier equation: μ = μm [1 - exp(-KCS)]

Moser equation: μ = μm CS

n

KS + CSn

Contois equation: μ = μm CS

KSX CX + CS

Blackman equation:

0

0,2

0,4

0,6

0,8

1

0 2 4 6 8 10Cs (g/L)

μ (

pe

r h

)

μm = 0.9 per h Ks = 0.7 g/L

μ = μm

μ = μm CS

2 KS

if CS ≥ 2 KS

if CS < 2 KS

This often fits the data better than the Monod model, but the discontinuity can be a problem.

Tessier equation:

0

0,2

0,4

0,6

0,8

1

0 2 4 6 8 10Cs (g/L)

μ (

per

h)

μm = 0.9 per h K = 0.7 g/L

μ = μm [1 - exp(-KCS)]

Moser equation:

0

0,2

0,4

0,6

0,8

1

0 2 4 6 8 10Cs (g/L)

Monod

n = 0.25

n = 0.5

n = 0.75

μ (

per

h)

μ = μm CS

n

KS + CSn

μm = 0.9 per h Ks = 0.7 g/L

When n = 1, Moser equation describes Monod model.

Contois equation:

Saturation constant (KSX CX ) is proportional to cell concentration μ =

μm CS

KSX CX + CS

Extended Monod model:

0

0,2

0,4

0,6

0,8

1

0 2 4 6 8 10Cs (g/L)

μ (

per

h)

μm = 0.9 per h Ks = 0.7 g/L CS,min = 0.5 g/L

μ = μm (CS – CS,min)

KS + CS – CS,min

Extended Monod model includes a CS,min term, which denotes the minimal substrate concentration needed for cell growth.

Monod model for two limiting substrates:

μ = CS1

KS1 + CS1 μm

CS2

KS2 + CS2

Monod model modified for rapidly-growing, dense cultures:

Monod model is not suitable for rapidly-growing, dense cultures.

The following models are best suited for such situations:

μ = μm CS

KS0 CS0 + CS

μ = μm CS

KS1 + KS0 CS0 + CS

where CS0 is the initial substrate concentration and KS0 is dimensionless.

0

0,2

0,4

0,6

0,8

1

0 2 4 6 8 10Cs (g/L)

μ (

per

h)

Monod model does not model substrate inhibition. Substrate inhibition means increasing substrate concentration beyond certain value reduces the cell growth rate.

Monod model modified for substrate inhibition:

μ = μm CS KS + CS + CS

2/KI

where KI is the substrate inhibition constant.

Monod model modified for cell growth with noncompetitive substrate inhibition:

μ = μm (1 + KS/CS)(1 + CS/KI )

If KI >> KS then

= μm CS KS + CS + CS2/KI + KS CS/KI

where KI is the substrate inhibition constant.

Monod model modified for cell growth with competitive substrate inhibition:

μ = μm CS KS(1 + CS/KI) + CS

Monod model modified for cell growth with product inhibition: Monod model does not model product inhibition (where increasing product concentration beyond certain value reduces the cell growth rate)

where Cp is the product concentration and Kp is a product inhibition constant.

For competitive product inhibition:

For non-competitive product inhibition:

μ = μm (1 + KS/CS)(1 + Cp/Kp )

μ = μm CS KS(1 + Cp/Kp) + CS

Monod model modified for cell growth with product inhibition:

where Cpm is the product concentration at which growth stops.

Ethanol fermentation from glucose by yeasts is an example of non-competitive product inhibition. Ethanol is an inhibitor at concentrations above nearly 5% (v/v). Rate expressions specifically for ethanol inhibition are the following:

μ = μm CS

(KS + CS) (1 + Cp/Cpm)

μ = μm CS

(KS + CS) exp(-Cp/Kp)

Monod model modified for cell growth with toxic compound inhibition:

where CI is the product concentration and KI is a constant to be determined.

For competitive toxic compound inhibition:

For non-competitive toxic compound inhibition:

μ = μm (1 + KS/CS)(1 + CI/KI )

μ = μm CS KS(1 + CI/KI) + CS

Monod model extended to include cell death kinetics:

where kd is the specific death rate (per time).

μ = μm CS

KS + CS - kd

Beyond this slide, modifications will be made.

Other unstructured, nonsegregated models (assuming one limiting substrate):

Luedeking-Piret model:

rP = rX + β CX

Used for lactic acid formation by Lactobacillus debruickii where production of lactic acid was found to occur semi-independently of cell growth.

Modelling μ under specific conditions:

There are models used under specific conditions. We will learn them as the situation arises.

Limitations of unstructured non-segregated models: • No attempt to utilize or recognize knowledge about cellular metabolism and regulation

• Show no lag phase

• Give no insight to the variables that influence growth

• Assume a black box

• Assume dynamic response of a cell is dominated by an internal process with a time delay on the order of the response time

• Most processes are assumed to be too fast or too slow to influence the observed response.

Filamentous Organisms:

• Types of Organisms

– mold

– bacteria or yeast entrapped in a spherical gel particle

– formation of microbial pettlets in suspension

• Model - no mass transfer limitations

where R is the radius of the cell floc or pellet or mold colony

constkdt

dR

Filamentous Organisms:

Then the growth of the biomass (M) can be written as

3/2

22 44

Mdt

dM

or

Rkdt

dRR

dt

dMp

3/1)36( pkwhere

Filamentous Organisms:

• Integrating the equation:

• M0 is usually very small then

• Model is supported by experimental data.

33

3/1

033

ttMM

3tM

Chemically Structured Models :

• Improvement over nonstructured, nonsegregated models

• Need less fudge factors, inhibitors, substrate inhibition, high concentration different rates etc.

• Model the kinetic interactions amoung cellular subcomponents

• Try to use Intrinsic variables - concentration per unit cell mass- Not extrinsic variables - concentration per reactor volume

• More predictive

• Incorporate our knowledge of cell biology

THANK YOU...