1. Reaction Engineering

3. Batch culture: exponential phase (balanced growth)
Exponential phase = log-phase
„midexponential“: bacteria often used for functional studies
Maximum growth rates μmax
Max growth rate -> smallest doubling time

5. Michaelis Menten Kinetics
Used when microbe population is constant = non-growing (or short time spans)
Derivable from first principles (enzyme-substrate binding rates and equilibria expressions)
Parameter determination methods used for Monod calculations (i.e. Lineweaver Burke)

7. Monod Growth Kinetics
Relates specific growth rate, m, to substrate concentration
Empirical---no theoretical basis—it just “fits”!
Have to determine mmax and Ks in the lab
Each m is determined for a different starting S

8. Michaelis Menten vs. Monod
Kinetic expression derived (theoretical)
Constant enzyme pool
Free enzymes
Non-growing microbes
v vs. S where v is velocity
Km is half saturation constant
Monod
Empirical expression
Growth
Enzyme concentration increases with time
Relates microbial growth rate constant to S
μ vs S
Ks is half saturation constant

9. Michaelis Menten vs. Monod
Parameters (vmax or μmax; Ks or Km) are determined by linearization (e.g. Lineweaver Burke model) or nonlinear curve fitting.
Relationship between dependent variable and S determined experimentally, in the lab
Range of S
Set conditions (T, chemistry, enzyme or microbe)
Measure the v or μ for each S
Plot v or μ vs. S; analyze data for parameter estimation

10. Determining Monod parameters
Double reciprocal plot (Lineweaver Burke)
Commonly used
Caution that data spread are often insufficient
Other linearization (Eadie Hofstee)
Less used, better data spread
Non-linear curve fitting
More computationally intensive
Progress-curve analysis (for substrate depletion)
Less lab work (1 curve), more uncertainty

11. Where Monod Growth Kinetics Applies
It applies where μ ǂ 0 -> exponential growth (μ = μmax ) + transition into stationary
KS is the half-saturation coefficient [mg/L]
Monod kinetics
-> “Substrate depletion kinetics”

12. Substrate Depletion Kinetics
Since
And
Monod applies!!
Then
Y Yield coefficients
Where k =
k is the maximum substrate utilization rate [sec-1]
KS is the half-saturation coefficient [mg/L]

13. Substrate Depletion Kinetics
Substrate consumption rates have often been described using ‘Monod kinetics’
-> Substrate controls
growth Kinetics
S is the substrate concentration [mg/L]
X is the biomass concentration [mg/ L]
k is the maximum substrate utilization rate [sec-1]
KS is the half-saturation coefficient [mg/L]

14. Stoichiometric Coefficients for Growth
Yield coefficients, Y, are defined based on the amount of consumption of
another material.
Because ΔS changes with growth condition, YX/S is not a constant

15. Monod Growth Kinetics mixed order mmax S >> KS S << KS 1 32
mmax
m, 1/hr
S, mg/L
Expontential growth μ = μmax
Stationary phase
μ = 0

16. Depletion Kinetics mixed order mmax S >> KS S << KS 1 3 2
1. Zero-order region, S >> KS, the equation can be approximated by μ = μmax
-> exponential growth
2. Center region, Monod “mixed order” kinetics must be used -> transition from exponential growth to stationary growth caused by [S] limitation
3. First-order region, S << KS, the equation can be approximated as
μ = μmaxS/Ks
-> transition from exponential growth to stationary growth caused by [S] limitation
Just before stationary phase starts (stationary phase μ = 0)
mixed order
S >> KS
S << KS 1 3 2
mmax
m, 1/hr
S, mg/L
k is the maximum substrate utilization rate [sec-1]
KS is the half-saturation coefficient [mg/L]

17. Modeling Substrate Depletion
Three common assumptions
Monod kinetics applies (mid range concentrations)
-> “Substrate depletion kinetics”
First-order decay (low concentration of S, applicable to many natural systems)
Zero-order decay (substrate saturated) μ =μmax
-> exponential growth

18. Growth and Production Kinetic
Cellular growth rate
Monod approximation
Yield factor
Substrate Utilization
Product Formation
(Beginning of Stationary Phase)

19. Factors Determining Kinetics
Rate per microbe, which depends on
Species
Substrates
Environmental factors
Total numbers of microbes

20. Quantification of Microbes in the Environment
Culture-based (limited: 2000 species vs. 13,000 species of bacteria in soil by DNA-based methods
Counting colony forming units (CFUs)
Activity assays: need cell or biomass count to normalize
Culture-independent
Direct Counts
General fluorescent stain, like acridine orange or SYBR gold
Counting cells in FISH assay
Biomass assays
Quantification of an element like C or N
Chloroform fumigation / incubation or direct extraction
Total protein or DNA

21. Fermentation Technology
-> Why is it important to know the kinetics of the reaction in the fermenter?

22. Fermentation Technology
-> What is going on in a fermenter?
-> How to control the process in a fermenter?

28. Stochiometric Coefficients

29. Mass Balance

30. Example
-> Too complex !!!!

31. -> Blackbox effect
substrates + cells → extracellular products + more cells
( ∑S X → ∑P nX)

32. Model to describe what is going on in a Bio-reactor
Monod’s model -> S depletion
Mass balance : depentend on reactor type -> S, P, X
Growth Kinetics: -> Monod model (substrate depleting model)
-> Describes what happens in the reactor in steady state (constant conditions)

34. Primary metabolic products
Secondary metabolic products

35. Microbial Products 1. Growth associated products
: products appear simultaneoulsy with cells in culture
qp is the specific rate of product formation (mg product per g biomas per hours
2. Non-growth associated products
: products appear during stationary phase of batch growth
3. Mixed-growth associated products
: products appear during slow growth and stationary phase

36. Biotechnological processes of growing microorganisms in a bioreactor
Mass Balance: Fin = Fout = Fin ≠ 0; Fout = Fin = Fout ≠ 0
V= const V increases V = const.

37. Model to describe what is going on in a Bio-reactor
Mass balance : depentend on reactor type -> S, P, X
Growth Kinetics: -> Monod model (substrate depleting model)
-> Describes what happens in the reactor in steady state (constant conditions)
1. Mass Ballance: In – Out + Reaction = Accumulation
Biomass: FX0 - FX + r V = dn/dt dn/dt = d(XV)/dt
r = dX/dt = µ X
2. Monod Kinetics:
3. Steady state: dX/dt = 0 (NOT for Batch reactor!!!)

38. Batch Reactor Closed Well-mixed Constant volumeCV
Closed
Well-mixed
Constant volume
-> substrate growth limiting factor
Mass Balance:
Acc = dn/dt
n = mole
Verbal: In – Out + Reaction = Accumulation
dn/dt = d(XV)/dt = dX/dt V
Math: r V dX/dt V
Rearrange: r V = dX/dt V
-> Substrate concentration controls growth rate
Growth
Growth

39. Growth and Production Kinetic in Batch
Cellular growth rate
Monod approximation
Yield factor
Substrate Utilization
Product Formation
(Beginning of Stationary Phase)

40. Biotechnological processes of growing microorganisms in a bioreactor
Mass Balance: Fin = Fout = Fin ≠ 0; Fout = Fin = Fout ≠ 0
V= const V increases V = const.