microbial growth kineticsrs

8/2/2019 Microbial Growth KineticsRS

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Microbial Growth Kinetics


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Batch CultureBatch culture is a closed culture systemwhich contains an initial, limited amount ofnutrient.lag phase- After inoculation there is aperiod during which it appears that nogrowth takes place (a time of adaptation)

In a commercial process the length of

the lag phase should be reduced asmuch as possible

Log or exponential growth- the cells grow ata constant, maximum, rateStationary Phase- after a certain time thegrowth rate of the culture decreases until

growth ceases. The cessation of growthmay be due tothe depletion of essential nutrient in themedium (substrate limitation),the accumulation of some autotoxicproduct of organism in the medium (toxinlimitation)or a combination of the both


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Exponential Phase

Integrating

Exponential phase may be described by the =n

x is the concentration of microbial biomass,t is time, in hours is the specific growth rate, in hours -1

xo is the original biomass concentration,xt is the biomass concentration after the time interval, t hours

During the exponential phase nutrients are in excess and the organism is growingat its maximum specific growth rate, max

Mycelial organisms which show apical growth also grow exponentially.Trinci (1974) demonstrated that the total hyphal length of a mycelium and thenumber of tips increased exponentially

The rate of increase in hyphal mass, total lengthand number of tips is dictated by the specific growth rate

H is the hyphal length, A is the number of growing tips

1

2


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Doubling Time

Doubling time can be calculated from

Taking ln, we getln x t /x0 = t

ln 2x 0 /x0 = tln 2 = t

0.693= ttd = 0.693/

td is doubling time


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Stationary Phase

Deceleration Growth Phase Very short phase, during which growthdecelerates due to either:

Depletion of one or more essentialnutrients The accumulation of toxic by-products of

growth (e.g. Ethanol in yeast

fermentations) Period of unbalanced growth: Cellsundergo internal restructuring to increasetheir chances of survival


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The depletion of essential nutrientin the medium (substratelimitation),The accumulation of someautotoxic product of organism inthe medium (toxin limitation)

A combination of the bothZone A to B - an increase in initialsubstrate concentration gives aproportional increase in the biomassproduced at stationary phase

x is the concentration of biomass producedY is the yield factor (g biomass produced g -1 substrate consumed),S R is the initial substrate concentration, ands is the residual substrate concentration

Zone B to C - utilization of thesubstrate is deleteriously affected bythe accumulating toxins or theavailability of another substrate.Zone C to D An increase in the initialsubstrate concentration does not give aproportional increase in biomassThis may be due to either theexhaustion of another substrate or theaccumulation of toxic products.

Stationary Phase


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Yield factor (Y)

Is a measure of the efficiency of conversion ofany one substrate into biomass and

It can be used to predict the substrateconcentration required to produce a certainbiomass concentration.Y is not a constant. It varies according togrowth rate, pH, temperature, the limitingsubstrate and the concentration of thesubstrates in excess.


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Stationary phase

- Cell lysis may occur and viable cell mass may drop.A second growth phase may occur and cells maygrow on lysis products of lysed cells (cryptic growth)

- Endogenous metabolism occurs by catabolizingcellular reserves for new building blocks and energy-producing monomer (maintenance energy).The rate describing the conversion of cell mass intomaintenance energy or the loss of cell mass due tocell lysis:

.metabolismendogenousforconstantratetheisd

d

k

X k dt

dX


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Stationary Phase

Death PhaseThe living organism population decreases with time,

due to a lack of nutrients and toxic metabolic by-products.

The rate of death usually follows:

constanratedeathorder-first theis'

'

d

d

k

N k

dt

dN


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Stationary PhaseDecrease in growth rate ( ) and thecessation of growth, due to depletion ofsubstrate may be described by:Monod equation

= max s/ (K s + s )s is the residual substrate conc.K

s is the substrate utilization const. and is

a measure of the affinity of the organismfor its substrate


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If the organism has a very high affinity for the limitingsubstrate (a low Ks value) the growth rate will not beaffected until the substrate concentration hasdeclined to a very low level. Thus, the decelerationphase for such a culture would be short.However, if the organism has a low affinity for thesubstrate (a high Ks value) the growth rate will bedeleteriously affected at a relatively high substrateconcentration. Thus, the deceleration phase for sucha culture would be relatively long.The biomass concentration at the end of the

exponential phase is at its highest and, thus, thedecline in substrate concentration will be very rapidso that the time period during which the substrateconcentration is close to K s is very short.


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Borrow et al (1961) investigated the biosynthesis ofgibberellic acid (secondary metabolite) by Gibberella fujikuroi and divided the growth of the organism intoseveral phases:The balanced phase equivalent to the early tomiddle exponential phase.The storage phase equivalent to the lateexponential phase where the increase in mass is dueto the accumulation of lipid and carbohydrate.The maintenance phase equivalent to thestationary phase.Gibberellic acid was synthesized only towards theend of the storage phase and during the maintenancephase.


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Growth-linked Products Kinetics

Growth-linked may be considered equivalent toprimary metabolites which are synthesized bygrowing cells andNon-growth-linked may be considered equivalent tosecondary metabolites.


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The formation of a growth-linked product may be described bythe equation:

..1p is the concentration of productand q p is the specific rate of product formation (mg product g -1

biomass h -1)Also, product formation is related to biomass production by the

equation: ..2

where Y p/x is the yield of product in terms of biomass (g product g -1 biomass)

Multiply 2 by dx/dt

But dx/dt = x

..3


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When product formation is growth associated the

specific rate of product formation increases withspecific growth rateThus, productivity in batch culture will be greatest atmax and improved product output will be achieved by

increasing both and biomass concentrationNon-growth linked product formation is related tobiomass concentration and, thus, increasedproductivity in batch culture should be associatedwith an increase in biomassHowever, it should be remembered that non-growthrelated secondary metabolites are produced onlyunder certain physiological conditions primarily underlimitation of a particular substrate


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Thus, batch fermentation may be used to producebiomass, primary metabolites and secondary

metabolitesFor biomass production, cultural conditionssupporting the fastest growth rate and maximum cellpopulation would be used

For primary metabolite production conditions toextend the exponential phase accompanied byproduct excretion, andFor secondary metabolite production, conditionsgiving a short exponential phase and an extendedproduction phase, or conditions giving a decreasedgrowth rate in the log phase resulting in earliersecondary metabolite formation.


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Continuous CultureExponential growth in batch culture may be prolonged bythe addition of fresh medium to the vessel.Provided that the medium has been designed such thatgrowth is substrate limited, and not toxin limited,exponential growth will proceed until the additionalsubstrate is exhaustedThis may be repeated until the vessel is fullIf an overflow device were fitted to the fermenter such thatthe added medium displaced an equal volume of culturefrom the vessel then continuous production of cells canbe achievedIf medium is fed continuously to such a culture at asuitable rate, steady state is achieved eventually, that is,formation of new biomass by the culture is balanced bythe loss of cells from the vessel


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Flow of medium into the vessel is related to the volume ofthe vessel by the term dilution rate, D, defined as:

D =F/Vwhere F is the flow rate (dm 3 h -1)V is the volume (dm 3)D is expressed in the units h -1

The net change in cell concentration over a time period maybe expressed as:

dx/dt = growth outputdx/dt = x Dx

Under steady-state conditions the cell concentration remainsconstant, thus dx/dt = 0, hence x = D x

= D


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= D Thus under steady-state conditions the specific growth rateis controlled by the dilution rate

Thus, the dilution rate may be used to control the growthrate of the cultureThe growth of the cells in a continuous culture of this typeis controlled by the availability of the growth limiting

chemical component of the medium and, thus, the systemis described as a chemostat


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The mechanism of controlling effect of

the dilution rate is expressed as: = max s/ (K s + s )

At steady state, = D , therefore

s the steady-state concentration ofsubstrate in the chemostat


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1Above equation predicts that the substrate concentration isdetermined by the dilution rate

In effect, this occurs by the growth of the cells depletingthe substrate to a concentration that supports the growthrate equal to the dilution rateIf substrate is depleted below the level that supports the

growth rate dictated by the dilution rate, the followingsequence of events takes place The growth rate of the cells will be less than the dilution rate and

they will be washed out of the vessel at a rate greater than they arebeing produced, resulting in a decrease in biomass concentration

The substrate concentration in the vessel will rise because fewercells are left in the vessel to consume it

The increased substrate concentration in the vessel will result inthe cells growing at a rate greater than the dilution rate andbiomass concentration will increase

The steady state will be re-established


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Turbidostat the concentration of cells in the culture is keptconstant by controlling the flow of medium such that theturbidity of the culture is kept within certain, narrow limits.This may be achieved by monitoring the biomass with aphotoelectric cell and feeding the signal to a pump supplyingmedium to the culture such that the pump is switched on if the

biomass exceeds the set point and is switched off if thebiomass falls below the set point.Systems other than turbidity may be used to monitor thebiomass concentration, such as CO 2 concentration or pH(biostat).The chemostat is the more commonly used system because ithas the advantage over the biostat of not requiring complexcontrol systems to maintain a steady state.


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The kinetic characteristics of an organism(and, therefore, its behaviour in a chemostat)

are described by the numerical values of theconstants Y, max and Ks The value of Y affects the steady-statebiomass concentrationThe value of max affects the maximumdilution rate that may be employed and thevalue of

Ks affects the residual substrate concentration(and, hence, the biomass concentration) andalso the maximum dilution rate that may beused


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FED BATCH CULTURE


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FEDBATCH CULTUREYoshida et al (1973) introduced the term fed-batch cultureto describe batch cultures which are fed continuously, or

sequentially, with medium, without the removal of culturefluidA fed-batch culture is established initially in batch mode andis then fed according to one of the following feed strategies

i. The same medium used to establish the batch culture isadded, resulting in an increase in volume,

ii. A solution of the limiting substrate at the same concentrationas that in the initial medium is added, resulting in anincrease in volume,

iii.A concentrated solution of the limiting substrate is added ata rate less than in (i) and (ii), resulting in an increase involume

iv. A very concentrated solution of the limiting substrate is

added at a rate less than in i), (ii) and (iii), resulting in aninsignificant increase in volume

Variablevolume

Fixedvolume

bl l f d b h l


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Variable volume fed-batch culturea batch culture in which growth is limited by theconcentration of one substrate; the biomass at any point in

time will be described by the equation

x t is the biomass concentration after time, t hours,and x o is the inoculum concentration

The final biomass concentration produced when s = 0, isx max and, provided that x o is small compared with x max :

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

that the dilution rate is less than max , virtually all thesubstrate will be consumed as fast as it enters the culture,thus:

F is the flow rate of the medium feed, and X is the total biomass in the culture,described by X = xV , where V is the volume of the culture medium in the vessel

at time t, Y is yield factor


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Input of substrate is equalled by consumption ofsubstrate by the cellsThus, ds/dt 0. Although the total biomass in theculture (X) increases with time, cell concentration (x)remains virtually constant, that is (dx/dt )0 andtherefore D This situation is termed a quasi steady stateAs time progresses the dilution rate will decrease asthe volume increases and D will be given theexpression:

V0 is initial volume


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Variable volume Fixed volumeThe major difference between the steady state of a chemostatand the quasi steady state of a fed-batch culture is that isconstant in the chemostat but decreases in the fed-batch

In the genuine steady state of a chemostat, dilution rate and

growth rate are constant whereas in a fed-batch quasi steadystate they change over the time of the fermentationProduct concentration in the chemostat will reach a steadystate, but in a fed-batch system the profile of the productconcentration over the time of the fermentation will be

dependent on the relationship between q p and (hence D)


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Application of fed-batch cultureThe fedbatch system also gives some control overthe organisms growth rate,Both variable and fixed volume systems result in low

limiting substrate concentrations, but the quasisteady-state of the variable volume system has theadvantage of maintaining the concentrations of boththe biomass and the non-limiting nutrients constantAdvantage of cyclic fed-batch culture is that theproductive phase of a process may be extendedunder controlled conditions

microbial growth kineticsrs

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