Title: Reaction Engineering
1Reaction Engineering
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3Batch culture exponential phase (balanced growth)
Max growth rate -gt smallest doubling time
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5Michaelis 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)
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7Monod Growth Kinetics
- Relates specific growth rate, m, to substrate
concentration - Empirical---no theoretical basisit just fits!
- Have to determine mmax and Ks in the lab
- Each m is determined for a different starting S
8Michaelis Menten vs. Monod
- Michaelis Menten
- 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
9Michaelis 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
10Determining 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
11Where Monod Growth Kinetics Applies
It applies where µ ? 0 -gt exponential growth (µ
µmax ) transition into stationary
- KS is the half-saturation coefficient mg/L
Monod kinetics -gt Substrate depletion
kinetics
12Substrate Depletion Kinetics
- Since
- And
-
Monod applies!! - Then
- And
Y Yield coefficients
Where k
- k is the maximum substrate utilization rate
sec-1 - KS is the half-saturation coefficient mg/L
13Substrate Depletion Kinetics
- Substrate consumption rates have often been
described using Monod kinetics - -gt 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
14Stoichiometric Coefficients for Growth
Yield coefficients, Y, are defined based on the
amount of consumption of another material.
Because ?S changes with growth condition, YX/S is
not a constant
15Monod Growth Kinetics
mixed order
S gtgt KS
S ltlt KS
1
3
2
mmax
m, 1/hr
S, mg/L
Expontential growth µ µmax
Stationary phase µ 0
16Depletion Kinetics
- 1. Zero-order region, S gtgt KS, the equation can
be approximated by µ µmax - -gt exponential growth
- 2. Center region, Monod mixed order kinetics
must be used -gt transition from exponential
growth to stationary growth caused by S
limitation - 3. First-order region, S ltlt KS, the equation can
be approximated as - µ µmaxS/Ks
- -gt transition from exponential growth to
stationary growth caused by S limitation - Just before stationary phase starts (stationary
phase µ 0) -
mixed order
S gtgt KS
S ltlt 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
17Modeling Substrate Depletion
- Three common assumptions
- Monod kinetics applies (mid range
concentrations) - -gt Substrate depletion kinetics
- First-order decay (low concentration of S,
applicable to many natural systems) - Zero-order decay (substrate saturated) µ µmax
- -gt exponential growth
18Growth and Production Kinetic
- Cellular growth rate
- Monod approximation
- Yield factor
- Substrate Utilization
- Product Formation
- (Beginning of Stationary Phase)
19Factors Determining Kinetics
- Rate per microbe, which depends on
- Species
- Substrates
- Environmental factors
- Total numbers of microbes
20Quantification 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
21Fermentation Technology
-gt Why is it important to know the kinetics of
the reaction in the fermenter?
22Fermentation Technology
-gt What is going on in a fermenter? -gt How to
control the process in a fermenter?
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28Stochiometric Coefficients
29Mass Balance
30Rates (Kinetics) and Balances
31Example
-gt Too complex !!!!
32substrates cells ? extracellular products
more cells ( ?S X ? ?P
nX)
33Model to describe what is going on in a
Bio-reactor
Monods model -gt S depletion
- Mass balance depentend on reactor type -gt S, P,
X - Growth Kinetics -gt Monod model (substrate
depleting model) - -gt Describes what happens in the reactor in
steady state (constant conditions)
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35Primary metabolic products
Secondary metabolic products
36Microbial 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
37Biotechnological processes of growing
microorganisms in a bioreactor
Mass Balance Fin Fout 0
Fin ? 0 Fout 0 Fin Fout ?
0 V
const. V increases
V const.
38Batch Reactor
?Closed ?Well-mixed ?Constant volume -gt substrate
growth limiting factor
Mass Balance
Verbal In Out Reaction Accumulation
Math 0 0 rV ?t ?X V
Rearrange r V ?X/?t
V -gt Substrate concentration controls growth
rate
Growth
Growth
39Growth and Production Kinetic in Batch
- Cellular growth rate
- Monod approximation
- Yield factor
- Substrate Utilization
- Product Formation
- (Beginning of Stationary Phase)
40Biotechnological processes of growing
microorganisms in a bioreactor
Mass Balance Fin Fout 0
Fin ? 0 Fout 0 Fin Fout ?
0 V
const. V increases
V const.