1.1. Mass balance : depentend on reactor type -> S, P, X Mass balance : depentend on reactor type -> S, P, X 2.2. Growth Kinetics: -> Monod model (substrate depleting Growth Kinetics: -> Monod model (substrate depleting

model)model)

-> Describes what happens in the reactor in steady state steady state (constant conditions)

1. Mass Ballance: In – Out + Reaction = Accumulation

Biomass: FX0 - FX + ∫r dV = dn/dt dn/dt = d(XV)/dt

r = dX/dt = µ X dn/dt=V (dX/dt) + X (dV/dt)

2. Monod Kinetics:

3. Steady state: dX/dt = 0 (NOT for Batch reactor!!!)

SK

S

s

max

Control:1. Concentration of a

limiting nutrient2. Dilution rate

-> both influences X and P

Fin = Fout ≠ 0V = const.

steady state = cell number, nutrient status remain constant

-> Chemostat

0dt

dS

0dt

dX

1. Concentration of a limiting nutrient

Results from a batch culture

Monod Kinetics applies!!!

2. Dilution rate

DV

F D is dilution rate

F is flow rateV is volumeSubstrate depletion kinetics !!

CV

Mass Balance: In – Out + Reaction = Accumulation

Math: FX0 - FX + r V = dX/dt V

Rearrange: F/V •(X0 –X) + r = dX/dt

V = const.Fin = Fout ≠ 0

GrowthOutput

Take limits as X and t 0

dt

dX

Substitute exponential growth equation for “r”Set X0 = 0 (no influent cells)Make steady state (SS) assumption (no net accumulation or depletion): Let F/V = D = dilution rateRearrange:

0dt

dX

F/V •(X0 –X) + r =

XXV

F V

F D =

r Xμd

dt

X

DV

F

Burk)-Lineweaver (111

mm

S

S

K

D

Chemostat technique: reliable, constant environment, operation may be difficult.

SK

SD

S

mg

In Chemostat: µg=D, varying D obtains D~S

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.05 0.1 0.15 0.2 0.25

D (1/hr)

S, X

(g

/L)

0

0.05

0.1

0.15

0.2

0.25

0.3

DX

(g

/L-h

r)

X S

DX

µm = 0.2 hr-1

Cell Growth in Ideal Chemostat

Washed out: If D is set at a value greater than µm (D > µm),the culture cannot reproduce quickly enough to maintain itself.

-> In batch reactor, S and X are high. No transport of S or X and no control on µ.

-> In chemostat, S and X are low. Transport of S or X and control on µ.

-> In fed batch reactor. Substrate transport in, not out. No biomass transport.

Why fed batch?

1. Low S no toxicity / osmotic problem

2. High X high P easier downstream processing

3. Control of µ?

Batch phase

time

S0

S

Start feeding

Feeding phase under substrate limited conditions

S = 1 – 50 mg/l.

S0 5000 – 20000 mg/l

In substrate limited feeding phase, S is very low. Thus, one can use the pseudo steady state condition for substrate mass balance

-> Useful for Antibiotic fermentation

-> to overcome substrate inhibition!!

Mass Balance: In – Out + Reaction = Accumulation r = dX/dt = µ X

Biomass: FX0 - FX + r V = dn/dt dn/dt = d(XV)/dt0

Substrate balance – no outflow (Fcout = 0), sterile feed St = SV and Xt = XV (mass of substrate or cells in reactor at a given time)S0 = substrate in feed stream

tt

SX

tt

Xdt

dX

Y

XFS

dt

dS

/

0

substratein

substrateconsumed

no substrate out (Flow out = 0)

Substratebalance

Cell balance

Cell balance – sterile feed

This can be a steady state reactor if substrate is consumed as fast as it enters (quasi-steady-state).

Then dX/dt = 0 and μ = D, like in a chemostat.Recall, D = F / V

XDdt

dX

Xrfi

)(

D

DKS

m

S

0dt

dS

0dt

dX

•What this means

•the total amount of cells in the reactor increases with time -> with increasing V

•dilution rate and μ decrease with time in fed batch culture

•Since Since μμ = D, the growth rate is controlled by the dilution = D, the growth rate is controlled by the dilution rate.rate.

tSFYXX 0S/Xt0

t

0dt

dX

Minibioreactors

-> Volumes below 100 ml

Characterized by:

-> area of application-> mass transfer-> mixing characteristics

Minibioreactors

Why do we want to scale down ?

- Parallelization (optimization, screening) - automatization- cost reduction

What can you optimize?

- Biocatalyst (organism) design- medium (growth conditions) design- process design

Minibioreactors

- shake-flasks- microtiter plates- test tubes

- stirred bioreactors

- special reactors

Minibioreactors

Shaking flasks:

-> easy to handle-> low price-> volumne 25 ml – 5 L (filled with medium 20% of volumne)-> available with integrated sensors (O2, pH)

-> limitation: O2 limitation (aeration) -> during growth improved by 1. baffled flasks 2. membranes instead of cotton -> during sampling

Minibioreactors

Microtiter plates:

-> large number of parallel + miniature reactors-> automation using robots-> 6, 12, 24, 48, 96, 384, 1536 well plates-> volumne from 25 μl – 5 ml-> integrated O2 sensor available

Increased throughput rates allow applications:

- screening for metabolites, drugs, new biocatalysts (enzymes) - cultivation of clone libraries - expression studies of recombinant clones - media optimization and strain development

Minibioreactors

Microtiter plates:

-> Problems: - O2 limitation (aeration) -> faster shaking -> contamination - cross-contamination - evaporation -> close with membranes - sampling (small volumne -> only micro analytical methods + stop shaking disturbs the respiration)

Minibioreactors

Test tubes:

-> useful for developing inoculums-> screening-> volumne 2 -25 ml (20% filled with medium)-> simple and low costs-> O2 transfer rate low-> usually no online monitoring (pH and O2)-> interruption of shaking during sampling

Minibioreactors

Stirred Systems:

-> homogeneous environment

-> sampling, online monitoring,

control possible without disturbance of culture

-> increased mixing (stirring) + mass transfer (gassing rate)

Minibioreactors

Stirred Systems – Stirred Minibioreactor

-> T, pH, dissolved O2 can be controlled-> Volumne from 50 ml – 300 ml

-> small medium requirenments -> low costs (isotope labeling) -> good for research -> good for continous cultivation

-> Limitation: - system expensive due to minimization (control elements) - not good for high-throughput applications

Minibioreactors

Stirred Systems – Spinner flask

-> designed to grow animal cells-> high price instrument-> shaft containing a magnet for stirring -> shearing forces can be too big-> side arms for inoculation, sampling, medium inlet, outlet, ph probe, air (O2) inlet, air outlet-> continous reading of pH and O2 possible

Minibioreactors

Special Devices – Cuvette based microreactor

-> optical sensors (measuring online: pH, OD, O2)-> disposable-> volumne 4 ml-> air inlet/outlet-> magnet bead -> stirring-> similar performance as a 1 L batch reactor

Minibioreactors

Special Devices – Miniature bioreactor with integrated membrane for MS measurement:

-> custom made -> expensive-> a few ml-> online analysis of H2, CH4, O2, N2, CO2, and many other products, substrate,...-> used to follow respiratory dynamics of culture (isotope labeling)-> stirred vessel with control of T, O2, pH-> MS measurements within a few seconds to minutes -> continous detection-> fast kinetic measurements, metabolic studies

Minibioreactors

Special Devices – Microbioreactor:

-> Vessel 5 mm diameter round chamber-> Really small working volumne -> 5 μl -> integrated optical sensors for OD, O2, pH-> made out of polydimethylsiloxane (PDMS) -> transparent (optical measurements), permeable for gases (aeration)

-> E. coli sucessfully grown-> batch and continous cultures possible-> similar profile as 500 ml batch reactors-> limitation: sampling (small volumne -> analytical methods !!!)

MinibioreactorsNanoLiterBioReactor (NLBR):

-> used for growing up to several 100 mammalien cells-> culture volumne around 20 μl-> online control of O2, pH, T-> culture chamber with inlet/outlet ports (microfluidic systems)

-> manufactured by soft-lithography techniques-> made out of polydimethylsiloxane (PDMS) -> transparent (optical measurements), permeable for gases (aeration)-> direct monitoring of culture condition -> PDMS is transparent -> flourescence microscope

-> limitation: batch culture very difficult-> too small volumne -> suffers from nutrient limitation-> But in principle system allows -> batch, fed-batch, continous

MinibioreactorsNanoLiterBioReactor (NLBR):

Circular with central post (CP-NBR)Chamber: 825 μm in diameterVolumne: 20 μl

Perfusion Grid (PG-NBR)Similar VolumneIncorporated sieveWith openings 3-8 μm-> small traps for cells

Multi trap (MT-NBR)larger VolumneIncorporated sieveOpening similar -> multi trap system

-> Seeding was necessary (Introduction of cells into chamber) -> 30 μm filtration necessary -> to prevent clogging in the chamber (aggregated cells)-> Flow rate of medium: 5-50 nl/min

MinibioreactorsNanoLiterBioReactor (NLBR):

MinibioreactorsNanoLiterBioReactor (NLBR):

Minibioreactors

Why do we want micro-and nano reactors?

Applications in:

- Molecular biology

- Biochemistry

- Cell biology

- Medical devices

- Biosensors

-> with the aim to look at single cells !!!

MinibioreactorsMicro/Nanofluidic Device for Single cell based assay:

-> used a microfluidic chip to capture passively a single cell and have nanoliter injection of a drug

MinibioreactorsMicro/Nanofluidic Device for Single cell based assay:

-> used a microfluidic chip to capture passively a single cell and have nanoliter injection of a drug

Microchannel height: 20 μm (animal cells are smaller than 15 μm in diameter)-> If channel larger than 5 μm in diameter -> hydrophilic-> if channel smalles than 5 μm in diameter -> hydrophobic

Gray area is hydrophobic -> air exchange possible -> no liquide (medium) can leak out

Class ExerciseProblem 6.17

E. coli is cultivated in continuous culture under aerobic conditions with glucose limitation. When the system is operated at D= 0.2 hr-1, determine the effluent glucose and biomass concentrations assuming Monod kinetics (S0 = 5 g/l, m= 0.25 hr-1 , KS = 100 mg/L, Y x/s = 0.4 g/g)

Class Exercise – 9.4Penicillin is produced in a fed-batch culture with the

intermittent addition of glucose solution to the culture medium. The initial culture volume at quasi-steady state is V0= 500 L, and the glucose containing nutrient solution is added with a flow rate of F = 50 L/h. X0 = 20 g/L, S0 = 300 g/L, m = 0.2 h-1, Ks = 0.5 g/L and Y x/s= 0.3 g/g

Determine culture volume at t = 10 hDetermine concentration of glucose at t = 10 hDetermine the concentration and total amount of cells at t

= 10 hIf qp = 0.05 g product.g cells h and P0 = 0.1 g/L,

determine the product concentration at t = 10 h