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Friday, April 1, 2011





To determine the feed rate(F), Growth rate(µ) and biomass(x) production rate of the culture Phospho bacterium 

            A fed batch culture is one in which one or more nutrients are fed into the fermentor during the fermentation period. In this way nutrients can be added at the same rate as they are used up, so excess of nutrients and any inhibition resulting from this can be avoided. A classical example is penicillin fermentation where the different nutritional requirements at different phases can be catered for feeding in particular nutrients at the time they are required.

Two basic approaches to the fed batch fermentation can be used:
1.      Fixed volume fed batch
2.      Variable volume fed batch

            As the name implies, 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 is dependent on the requirements, limitations and objectives of the operator.

The feed can be provided according to one of the following options:
1.      The same medium used in the batch mode is added.
2.      A solution of the limiting substrate at the same concentration as that in the initial medium is added.
Variable volume fed batch can still be classified as:
1.      Repeated fed batch process or cyclic fed batch culture.
2.      Single fed batch process.

            In this method once the fermentation reached a certain stage after which is not effective anymore, a quantity of culture is removed from the vessel and replaced by fresh nutrient medium. The decrease in volume results in an increase in the specific growth rate, followed by a gradual decrease as the quasi steady state is established.

In this case, supplementary growth medium is added during the fermentation, but no culture is removed until the end of the batch. This system presents a disadvantage over the fixed volume fed batch and the repeated fed batch process: much of the fermentor volume is not utilized until the end of the batch and consequently, the duration of the batch are limited by the fermentor volume.


1.      Production of high cell densities due to the extension of working of working time.
2.      Controlled conditions in the provision of substrates during the fermentation, particularly regarding the concentration of specific substrates as for example the carbon source.
3.      Control over the production of byproducts or catabolite repression effects due to limited provision of substrates solely required for product formation.
4.      Allows the replacement of water loss by evaporation.
5.      Increase of antibiotic marked plasmid stability by providing the correspondent antibiotic during the time span of the fermentation.

1.      It requires previous analysis of the microorganism, its requirements and the understanding of its physiology with the productivity.
2.      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 and that nutrients other than those incorporated into the feed medium become limiting. Also if many cycles are run, the accumulation of non-producing or low producing variants may result.
There are two types of pumps which are suitable for the aseptic pumping of small volumes of culture media:
1.      Peristaltic pump
2.      Diaphragm dosing pump

            A main body that comprises of both the derive motor and electrics and the rotating unit of rollers typically constitutes the peristaltic pump. This unit if rollers occludes the tube which, as it recovers to its original size passes to the next roller until it is expelled, as the moves around. The flow rate can be varied by either the speed setting or by changing the diameter of the tube being used.

            The diaphragm-dosing pump consists of a main body and a detectable heat sterilizable head. The fluid is sucked into the pump head. The suction inlet tube then closes and the pressure discharge tube opens and forces the fluid out. The suction and pressure forces in the pump head are generated by the reciprocating action of both diaphragm plunger and the return spring.

            In a variable volume fed batch fermentation, an additional element should be considered, the feed. Consequently, the volume of the medium in the fermentor varies because there is an inflow and no outflow. Again, the growth of the fermentation of the microorganism is limited by the concentration of one substrate.
For the mathematical developments that will be presented, the assumptions are:
1.      Specific growth rate is uniquely dependent on the concentration of the limiting substrate.
2.      The concentration of the limiting substrate in feed is constant.
3.      The feed is sterile.
4.      The yields are constant during the fermentation time.

Considering the overall mass balance
(Input) = (output) + (accumulation)
F = 0 + dV/dt
F = dV/dt                                                                                                        (1)
V – the time volume of the fermentor
T – time
F – the feed rate (volume/time)
Considering now the balance to the biomass
                                     (Accumulation) = (in) + (produced) – (lost by cell death)
                        d(Vx)/dt = F. Xo + rx.V – rd.V                                                                         (2)
                        x – biomass concentration (mass of biomass/volume)
                        Xo - biomass concentration in the feed (mass of biomass in feed/volume)
                        rx- biomass production rate (mass of biomass/volume. time)
                        rd – biomass death rate (mass of biomass /volume. time)
As the feed is considered to be sterile, Xo amounts to zero.
Therefore eqn (2) becomes
          d (Vx)/dt = rx.V – rd.V
            V.dx/dt + xdV/dt = rx.V – rd.V
             V.dx/dt + xF =  rx.V – rd.V                                                                        (using eqn 1)
            rx.V = µ.x.V    and      rd.V = kd.x.V
µ =specific growth rate (time-1)
k d = specific death rate (time-1)
            V.dx/dt + xF =  µ.x.V- kd.x.V
 Rearranging the equation
            dx/dt = x (µ.V- kd.V - F)/ V
Specific growth rate is smaller so it can be neglected.
Consider now the balance to limit substrate
  (accumulation) = (in) + (consumed)
d(V.s)/dt = – rs.V
s is the substrate concentration in the fermentor (mass of substrate / volume)
so is the substrate concentration in the feed (mass of substrate in feed/ volume)
rs is the consumption rate of substrate (mass of substrate/volume. time)
Vds/dt + s.dV/dt = – rs. V
It should be noted that the consumption rate of substrate includes the specific consumption used for biomass production, product formation and maintenance of the cell. Including now the concept of yield
                         rs. V = µ. x. V/Yx/s
Yx/s is the ratio between the mass of cells produced per mass of substrate consumed.
Substituting rs. V = µ. x. V/Yx/s
 Vds/dt + s. F = – µ. x. V/Yx/s
Rearranging the equation,
            ds/dt = F.(so – s)/ V - µ.x./Yx/s
The table below summarizes the equations that have just been developed:
Mass balance for the main components for a fed batch reaction:
Mass balance equation
F = dV/dt
dx/dt = x (µ.V- kd.V - F)/ V
ds/dt = F.(so – s)/ V - µ.x./Yx/s
dp/dt = Qp.x – P.F/V

V is the volume of the fermentor
T is the time
F is the feed rate (Volume/time)
X is the biomass concentration (mass of biomass / volume)
µ is the specific growth rate. (time–1)
kd is the specific death rate (time-1)
s is the substrate concentration in the fermentor (mass of substrate / volume)
so is the substrate concentration in the feed (mass of substrate /volume)
Yx/s is the yield factor (mass of biomass / mass of substrate)
Γ is product concentration (mass of product / volume)
Qp is the specific production rate of product (mass of product /mass of biomass. time)

BIOREACTOR (Ex-situ type)
The studies that will be reported here were conducted on 5lit (working volume 2.5lit) reactor. This reactor is equipped with flat four-blade Rushton turbine. Height 265mm, diameter of tank 146mm, diameter of impeller 58mm, inter impeller distance 93mm, distance between last impeller and tank 212mm. The tank has two baffles with a width and height of 16 and 25mm.
The organism used was Phosphobacterium.

COMPOSITION                   g/lt
Beef extract                            3
Peptone                                   5
NaCl                                        5
Distilled water                                    1000ml
            A single loop of Phosphobacterium culture was scrapped using a sterile inoculation loop and then aseptically transferred into a 15ml nutrient medium. This starter culture was grown overnight. This was mixed with 300ml of media (having same composition as the reactor media i.e. nutrient medium) and then inoculated into 2.5lt reactor media to start fed batch fermentation.

Time of sterilization    9:00am
Temperature                121ºC
Pressure                       1bar
Hold time                    20min
Inoculum                     300ml
Time of feed               2:00pm           

            The experimentation was conducted in a 5L fermentor equipped with temperature, pH, airflow, DO, pressure and agitation controllers. The experiment was conducted at 30 ºC. DO was measured by a DO probe. The culture media of the above composition was used.
When the substrate is completely consumed by the biomass, ds/dt = 0
Hence the substrate balance equation reduces to
FoS/V =µ.x.Yx/s
F = µ. x. V/S0 Yx/s

           Hence the feed rate (F),  growth rate (µ)and biomass concentration(x) are determined for the culture of Phospho bacterium.

Through the fed batch method following graphs were determined for

OD Vs X :
From this standard graph corresponding biomass concentration are determined with respect to OD values.

Feed rate Vs Time:
We obtain a graph of increasing order to the corresponding values of feed and time, which concludes the increase in the growth rate of the organism.
 Growth rate Vs Time:
                      From this graph we obtain a linear increase in growth corresponding to the time till the substrate is completely utilized, then the growth rate decreases.

OD Vs time:
                     There exists a linear increase in OD with respect to time.

ln OD Vs time:
                     There exists a linear decrease in OD with respect to time.


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