Chapter 2 Ft New

8/4/2019 Chapter 2 Ft New

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CHAPTER 2

MICROBIAL GROWTH

KINETICS


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MODE OF FERMENTER OPERATION

BATCH FERMENTATION

- A batch fermentation can be considered to be a closedsystem.

- At the time t=0, the sterilized nutrient solution in the

fermenter is inoculated with microorganisms & incubation is

allowed to proceed under optimal physiological conditions.

- In the course of the entire fermentation, nothing is added

except oxygen (in the form of air), an antifoam, acid/base to

control the pH.

- The composition of the culture medium, the biomass &

metabolite concentration change constantly as a result of the

cell metabolism.


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- Batch fermentation may be used to produce biomass,

primary metabolite.

- To get primary metabolite, extend the exponential

growth phase (or condition supporting growth)

- To get secondary metabolite, shorten the exponentialphase, & extended stationary phase/production phase (or

condition giving a decreases growth rate)


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Advantages of Batch:

1.Low contamination risk.

2.The ability to run different succesive phases in the same

vessel.

3.Closed control of the genetic stability of the

microorganism.4.Operability and reliability : less likely to have instrument

failure on short batch runs.

5.Simplicity of use, depending on the m/o used, can be

finished within 24 hrs


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Disadvantages of Batch:

1. The high proportion of unproductive: down time inbatch fermenter operation will reduce the overall

productivity of the process.

2. build up of toxic metabolites can restrict cell growth

and product formation.

3. initial substrates concentrations may have to be

limited due to problems with inhibition and

repression effects, therefore affecting the amount ofproduct that can be obtained from such simple

systems.

4. batch-to-batch variability


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- Control systems for batch fermentation are normally

associated with pH, dissolve oxygen tension & temperature.

- In batch fermentation, if growth is subject to substrateinhibition, fermentation has to be started with low initial

substrate concentration. Resulted in lower max biomass,

hence, lower max product.


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.

Kinetics of Cell Growth in Batch Fermenter

Batch fermentation kinetics showing the three phases of

growth. Curve (a) represent cell mass in the absence of lysis,

(b) cell mass when lysis occurs & is followed by cryptic

growth, & (c) viable cell count when cell lysis occurs.


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- The inoculated culture will pass through a number of

phases such as lag, log or exponential, stationary and

death phase.

- After inoculation there is a period during which no

growth appears to take place; this period is referred to

as the lag phase and maybe considered as a time of

adaptation. In a commercial process the length of the

lag phase should reduced as much as possible and this

may be achieved by using a suitable inoculums followinga period during which the growth rate of the cells grow

at a constant, maximum rate and this period is known as

the log or exponential phase


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The exponential phase maybe described as

dx/dt = x (2.1)

where, x is the concentration of microbial biomass

t is time, in hours is the specific growth rate, in hours


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On integration, equation (2.1) gives

xt = xoet (2.2)

Xo is the original biomass concentration

Xt is the biomass concentration after the time interval, t hours

e is the base of the natural logarithm

on taking the natural logarithm, equation (2.2) becomes:

ln xt = ln xo + t (2.3)

Thus, a plot of the natural logarithm of biomass concentration

against time should yield a straight line, the slope of which should

equal .During the exponential phase the organism is growing at its

maximum specific growth rate, max for the prevailing condition.


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Equation (2.2) predicts that growth will continue indefinitely.

However, growth results in the consumption of nutrients and the

excretion of microbial products; events which influence the growth

of the organism. Thus, after a certain time the growth rate of

culture decreases until growth ceases. The cessation of the growth

may be due to depletion of some essential nutrient in the medium

(substrate limitation), the accumulation of some autotoxic product

of the organism in the medium (toxin limitation) or a combinationof the two.

The nature of the limitation of growth may be explored by growing

the organism in the presence of a range of substrate

concentrations and expressing the results as shown in Fig. 2.2. Zone

A to B an increase in substrate concentration gives a proportional

increase in the total biomass produced stationary phase.


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Figure 2.2: The effect of initialsubstrate concentration on

the biomass conc. at

the onset of stationary

phase in batch culture (page 12)

Figure 2.1: Growth of a typicalmicrobial culture in batch

conditions


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The situation may be described by the equation:

x = Y (SR s) (2.4)

where,

x is the concentration of biomass produced

Y is the yield factorSR is the original substrate concentration

s is the residual substrate concentration


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Over the zone A to B, s equals zero at the points of cessation of

growth. Thus, the equation (2.4) may be used to predict the

biomass which may be produced form a certain amount ofsubstrate. Over the zone C to D, the culture is toxin limited as an

increase in initial substrate concentration does not give a

proportional increase in biomass. Over the zone B to C the

utilization of substrate is deleteriously affected by the

accumulating toxins. The decrease of growth rate and the

cessation of growth, due to the depletion of substrate may be

described by the relationship between and residual growth-

limiting substrate, represented equation (2.5) and Fig. 2.3

= max S (2.5)

Ks + S


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Where,

s is the residual substrate concentration

Ks is substrate utilization constant, numerically equal to substrateconcentration when is half max and is a measured of the affinity

of the organism for its substrate.

The zone A to B in Fig. 2.3 is equivalent to the exponential phase in

batch culture where substrate concentration is in excess and

growth is at max. The zone C to A in Fig. 2.3 is equivalent to the

deceleration phase of batch culture where the growth of the

organisms has resulted in the depletion of substrate to a growth-

limiting concentration which will not support max. If the organismhas a very high affinity for the limiting substrate (a low Ks, value)

the growth rate will not be affected until the substrate

concentration has declined to a very low level.


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Thus, the deceleration phase for such a culture would be short.

However, if the organism has a low affinity for the substrate (a high

Ks, value) the growth rate will be deleteriously affected at a

relatively high substrate concentration. Thus, the decelerationphase for such a culture would be relatively long.

Figure 2.3: The effect of residual

limiting substrate conc. on the

specific growth rate of ahypothetical bacterium.


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The stationary phase in batch culture is the point where the

growth rate has declined to zero. At this phase, it is a

misnomer in terms of physiology of organism. As thepopulation is still metabolically active during this phase and

produces products called secondary metabolites, which are

not produced during the exponential phase. (Maximum

population phase)

BuLocket.al. coined the terms trophopahse to refer to the

exponential phase, and idiophase to refer to the stationary

phase where secondary metabolites are produced. The

idiophase was depicted as the period subsequent to theexponential phase in which secondary metabolites were

synthesized.


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Rearrange the Monod eq.

1/ = 1/S ks/ max + 1/ max

Get Lineweaver-burk eq.


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Pirt has discussed the kinetics of product formation by microbial

cultures in terms ofgrowth-linked products and non-growth-linked

products.

Growth-linked may be considered equivalent to primary

metabolites which are synthesized by growing cells.

non-growth-linked may be considered equivalent to secondary

metabolites.

The formation of a growth-linked product may be described by the

equation:

dp / dt = qp x (2.6)

p is the concentration of product

qp is the specific rate of product formation


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Also, the product formation is related to biomass production by

equation

dp / dx = Yp/x (2.7)

Yp/x is the yield of product in terms of substrate consumed.

Mutiply (2.7) by dx/dt, and

dx/dt . dp/dx = Yp/x . dx/dt

dp / dt= Yp/x .dx/dt (2.8)

but, dx / dt = x

Therefore:

dp / dt = Yp/x . x (2.9)


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Combining equations (2.6) and (2.9):

qp = Yp/x (2.10)

When the product formation is growth associated the specific rate

of product formation increase with the specific growth rate.

When product formation is non-growth associated the specificrate of product formation may remain constant over a wide range

of growth rates or it may vary in a complex manner.

Thus, batch fermentation maybe used to produce biomass, primaryand secondary metabolites. For biomass production, cultural

conditions supporting the maximum cell population.


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For primary metabolites production, conditions to extend

the exponential phase accompanied by product excretion

and for secondary metabolite production, conditions

giving a short exponential phase and extend stationary orproduction phase or condition giving a decreased growth

rate in the log phase resulting in earlier secondary

metabolite formation.


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CONTINUOUS FERMENTATION

- An extension to the concept of fed-batch operation is to

feeding ad infinitum but to allow some broth to escape from system

so as to maintain a constant volume in the fermenter.

- both feed & outlet are constant an equal.

- Continuous culture is a system in which a well mixed culture

is continuously supplied with fresh nutrients & the volume

of the culture is kept constant by continuous removal of the

culture liquid at the same flow rate as the feeding rate of

fresh nutrient.


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- Hence, its offer a continuation of growth for a long period of

time.

- Provided that the medium has been designed such that growthis substrate limited, & not toxin limited, exponential growth

will proceed until the additional substrate is exhausted.

- The unique feature of continuous culture is that microbialgrowth in continuous culture take place under steady-state

condition (growth occur at a constant rate & in a constant

environment)

- Factor such as culture pH, specific growth rate, nutrient & cell

concentration, conc. of metabolites & dissolve oxygen tension,

which change during the growth cycle in a batch culture, are

maintained constant in continuous culture.


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- useful in genetic, physiological & ecological studies with

microorganism.

- In genetic (cont. culture useful in studying the mutationprocess).

- In ecological (Cont. culture as useful model for microbial

growth in nature conditions of low nutrient conc, & havefound special use in studying growth of microorganism.

Application of continuous culture:

1. Application in brewing

2. Application in biomass production

3. Application in strain isolation & selection


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The advantages of continuous fermentation over

conventional batch fermentation

1. Higher productivity (longer periods of productivity with lessdowntime)

2. Ability to relieve repression under specific nutrient

limitation

3. The effects of environmental or physical factors are more easily

analysed in a continuous system, where any changes in the

constant steady state are observed and can be attributed solely to

the change in those factors

4. Evolution in these cultures can be readily studied


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Disadvantages of Continuous Culture

The US FDA does not accept continuous culture in the

production of therapeutic products as a Current GoodManufacturing Practice (cGMP). This is because they require

the manufacturer to segregate such products into batches for

tracebility purposes, precluding continuous culture as a

means of production not all products optimally in continuous processes, e.g. some

fermented foods and beverages require cellular products

released from different phases of batch culture growth for

flavor development. Non growth-associated products such asantibiotics, monoclonal antibodies and toxins are also not

produced well in continuous culture. This is because there are

risks of plasmid loss in genetically modified cultures over a

number of generations.


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contamination can be a major problem in continuous

cultivation, and can result in the wash out of the desired

organism and therefore a loss of product.

culture mutation can easily occur in continuous processes


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Types of Continuous Culture

1) Turbidostat

in a turbidostat, the feed medium contains all of the required

nutrients in excess growth is therefore not substrate limited as it is in the

chemostat, and the microorganism can grow at its maximumspecific growth rate (max)

the system can be controlled at a desired cell density bymonitoring the turbidity, and therefore the biomass,continuously.

this can be achieved by measuring optical density using aspectrophotometer

if the moniter detects a deviation from the cell density set-point value, a signal is relayed to the controller, and so therate at which the feed medium is added to the bioreactor canbe adjusted


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when the turbidity increases above a set point, the feed rate

is increased in order to dilute the culture and bring the

turbidity back to its set point

if the density of the reactor population falls, the feed rate is

decreased, allowing the population to grow until the turbidity

set point is reached, thus avoiding washout of the organism

the turbidiostat is commonly used for the selection of

antibiotic resistant mutans and the degradation of toxic

wastes, where nutrient limitation is not desirable

it is also routinely used to avoid the washout effects that are

more common in chemostat systems, and to produce cells of

approximately uniform morphology and composition over

prolonged periods


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Disadvantages :

fouling of the optical surfaces of the probe used to measure

turbidity caused by unwanted cell growth

gas bubbles trapped in the circulating medium result in

inaccurate optical density measurements and therefore the

system is often difficult to control


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Experimental set-up of turbidiostat culture


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2. Chemostat

Very popular mode of operating a continuous biological

reactor.

Complex control system are not required to maintain a

steady-state.

In this technique, the feed medium contains excess of all butone of the nutrients required for growth of the culture. The

supply of the nutrient that is not in excess therefore

determines growth rate of the microorganism.

In a well-mixed fermenter, a steady-state results when thespecific growth rate of the microorganism balances exactly

the dilution rate.


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when running a chemostat culture, it is imperative that the

condition of steady-state is calculated and monitored; this

means that it is necessary to calculate dilution rate, specific

growth rate, yield of product on substrate, etc.

The chemostat culture also able to vary growth-controllingfactors such as temperature, pH and dissolve oxygen

independently of the specific growth rate

This make continuous culture is a very powerful tool for the

study of microbial physiology, beside its usage infermentation process for production of commercial products.


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Experimental set-up of chemostat culture.


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Continuous culture

Medium is fed continuously to such a culture at a suitable rate, a

steady state is achieved, that is, formation of new biomass by theculture is balanced by the loss of cells form the vessel. The flow of

medium into the vessel is related to the volume of vessel by the

term dilution rate, D defined as

D = F (2.11)

V

F is flow rate, is expressed in Lh-1

V is volume, is expressed in LD is expressed in the unit h-1


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The net change in cell concentration over a time period may be

expressed as

dx /dt = growth output

or dx / dt = x Dx (2.12)

under steady state conditions the cell concentration remains constant

, thus dx /dt = 0 and

x = Dx (2.13)

and = D (2.14)

Thus, under steady state condition, the specific growth rate is

controlled by the dilution rate.


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Substituting = (maxs ) / (Ks + s) into equation (2.12)

Then dx / dt = x ( maxs - D ) (2.15)Ks + s

The net change in the residual growth limiting substrate

concentration may be described by the equation:

ds / dt = Input of substrate output of substrate consumption by

cells


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or

ds / dt = DSR Ds max x/y ( s ) (2.16)

Ks + s

At steady state both ds /dt and dx/dt equal zero. Thus, equation

(2.16) and (2.15) may be equated and solve to give:

x = Y (SR s) (2.17)

s = Ks D

maxs D (2.18)

where x is the steady state cell concentration

s is the steady state residual substrate concentration


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The kinetic characteristic of an organism are described by the

numerical value such as

Y (affects the steady state biomass concentration),

max (affects the maximum dilution rate that may be employed),

Ks (affects the residual substrate concentration).

Fig. 2.4 shown the continuous culture behavior of a hypotheticalbacterium with a low Ks value for the limiting substrate, compared

with the initial limiting substrate concentration. With increasing

dilution rate, the residual substrate concentration increase only

slightly until D approaches max

whens

increases significantly.


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The dilution rate at which x equal zero (that is , the cells have been

washed out of the system) is termed the critical dilution rate (Dcrit)

and given by the equation:

Dcrit = maxSRKs + SR (2.19)


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Thus, Dcrit is affected by the constant max and Ks and the variable,

SR

.The larger the SR

the closer is Dcrit

to

max.

Fig. 2.5 illustrates the continuous culture behavior of a hypothetical

bacterium with high Ks for the limiting substrate compared with

initial limiting substrate concentration. With increasing dilution

rate, the residual substrate concentration increase significantly tosupport the increased growth rate. Thus, there is a gradual increase

in s and decrease in x as D approaches Dcrit.


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Figure 2.4: pg 18 Figure 2.5: pg 18


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FED-BATCH FERMENTATION

- Fed-batch culture is defined as a technique in microbial

processes where one or more nutrients are supplied to thefermenter during cultivation but no removal of the culture

until the end of the process.

- The basic characteristic of fed-batch culture is that the

concentrations of nutrients fed into the culture liquid can be

controlled by changing the feed rate.

- In established fed-batch operation, two initial decisions must

be made:1. Nutrients to be fed

2. The mode of feeding


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- Knowledge ofmicrobial physiology, biochemistry & genetics

are required in the identification of the most effective nutrients

while, biochemical engineering knowledge play important

role in deciding the feeding mode.

- Fed-batch culture can be classified according to the feeding

mode such as constant feeding or exponential feeding.

- The main purpose of fed-batch culture operation is to control

the substrate concentration within the liquid culture & hence,

some of the biochemical parameters can be controlled as well.


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Application of Fed-batch Culture

1. Fermentation subject to substrate inhibition

2. Bakers yeast fermentation3. High cell concentration

4. Growth-associated product formation

5. Toxic effects of medium components

Two basic approaches to the fed-batch fermentation

1. Fixed Volume Fed-batch

2. Variable Volume Fed-batch

Fixed Volume Fed batch


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Fixed Volume Fed-batch

- The limiting substrate is fed without diluting the culture.

- The culture volume can also be maintained constant by

feeding the growth limiting substrate in undiluted form.

E.g. concentrated liquid/gas (e.g.oxygen). Alternatively,

the substrate can be added by dialysis or in photosynthetic

culture, radiation can be the growth limiting factor withoutaffecting the culture volume.

- A certain type of extended fed-batch- the cyclic fed-batch

culture for fixed volume system- refers to a periodicwithdrawal of a portion of the culture & use of the residual

culture as the starting point for a further fed-batch process.


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- Once the fermentation reaches a certain stage (e.g. whenaerobic condition cannot be maintained anymore) the culture

is removed & the biomass is diluted to the original volume

with sterile water/ medium containing the feed substrate.

- The dilution decrease the biomass conc. & result in an

increase in the specific growth rate.

- Subsequently, as feeding continues, the growth rate will

decline gradually as biomass increases & approaches the

max sustainable in the vessel once more, at which point the

culture may be diluted again.

Variable Volume Fed-batch


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- A variable volume fed-batch is one in which the volume

changes with the fermentation time due to the substrate

feed

- The way this volume changes it is dependent on the

requirements, limitations & objective of the operator.

- The feed can be provided according to one of the following

option:

a. the same medium used in the batch mode is added

b. a solution of the limiting substrate at the same conc. as that

in the initial medium is added; &c. a very concentrated solution of the limiting substrate is

added at a rate less than (a) & (b).


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- This type of fed-batch can still be further classified asrepeated fed-batch process or cyclic fed-batch culture, &

single fed-batch process.

- The former means that once the fermentation reached a

certain stage after which is not effective anymore, a quantity

of culture is removed from the vessel & replaced by fresh

nutrient medium.

- The decrease in volume results in a increase in the specific

growth rate, followed by a gradual decrease as the quasi-

steady state is established


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Advantages of Fed-batch

1. Production of high cell densities due to extension of

working time (particularly important in the production ofgrowth-associated product)

2. Controlled conditions in the provision of substrate during

the fermentation particularly regarding the concentrationof specific substrate as for example the carbon source.

3. Control over the production of by-products or catabolite

repression effects due to limited provision of substrate

solely required for product formation.


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4.The mode of operation can overcome & control deviationsin the organisms growth pattern as found in batch

fermentation.

5. Allow replacement of water loss by evaporation.

6. Alternative mode of operation for fermentation leading with

toxic substrates (cells can only metabolized a certain quantity

at a time) or low solubility compounds.

7. Increased of antibiotic-marked plasmid stability by providing

the correspondent antibiotic during the time span of the

fermentation8. No additional special piece of equipment is required as

compared with batch fermentation.

Disadvantages of Fed batch


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Disadvantages of Fed-batch

1. It requires previous analysis of the microorganism (its

requirements & understanding of its physiology with theproductivity)

2. It requires a substantial amount of operator skill for the set-

up, definition & development of the process.

3. In a cyclic fed-batch culture, care should be taken in the

design of the process to ensure that toxins do not accumulate

to inhibitory levels & that nutrients other than those

incorporated into the feed medium become limiting. Also, ifmany cycles are run, the accumulation of non-producing or

low-producing variants may results.


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4. The quantities of the components to control must be above

the detection limits of the available measuring equipment.


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Fed-batch Culture

Yoshida et. al. introduced the term fed-batch culture to describe

batch cultures which are fed continuously, or sequentially, withmedium and without removal of culture fluid. Thus, volume of

culture increases with time. Consider a batch culture in which

growth is limited by the concentration of one substrate; the

biomass at any point in the time will be described by the equation

Xt= Xo + Y (SR s) (2.22)

Xt is the biomass concentration after time, t hours

Xo is the inoculum concentration

The final biomass concentration produced when s 0 may be


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The final biomass concentration produced when s = 0 may be

described as xmax and, provided that xmax is small compared with x

xmax = YSR (2.23)

If at the time when x = xmax, a medium feed is started, such that

dilution rate is lees thanmax, virtually all the substrate will be

consumed as fast as it enters the culture, thus,

FSR= X

Y (2.24)

F is the flow rate of the medium feed

X is the total biomass in the culture, described by X=xV, where V is

the volume of the vessel at time, t.


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From equation (2.24) it may be concluded that input of substrate

is equalled by consumption of substrate by the cells. Thus, (ds/dt)

= 0. Although the total biomass in the culture (X) increases with

the time, cell concentration (x) remains virtually constant, that is

(dx/dt) = 0 and therefore = D.

This situation is termed a quasi-steady state. As time progresses,

the dilution rate will decrease as the volume increase and D willgiven by the expression:

D = F

Vo

+ Ft (2.25)

Where Vo is the original volume.


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Thus, according to the Monod kinetics, the residual substrate

should decrease as D decrease resulting in an increase in the cell

concentration. However, over most of range of which willoperation in fed-batch culture, SR willbe much larger than K, so

that for all practical purpose, the change in residual substrate

concentration would be extremely small and may be consider as

zero. Thus, provided D is less than max and Ks is much smaller thanSR, a quasi-steady state may be achieved.

The quasi-steady state is illustrated in Fig. 2.10. The major

difference between the steady-state of chemostat and the quasi-

steady state of fed-batch culture is that is constant in thechemostat but decrease in the fed-batch.


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Figure 2.10

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