Reaction Engineering

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Reaction Engineering
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Batch culture exponential phase (balanced growth)
Max growth rate -gt smallest doubling time
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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)

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Monod 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

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Michaelis 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

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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

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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

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Where 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
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Substrate 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

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Substrate 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

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Stoichiometric 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
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Monod 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
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Depletion 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

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Modeling 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

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Growth and Production Kinetic

• Cellular growth rate
• Monod approximation
• Yield factor
• Substrate Utilization
• Product Formation
• (Beginning of Stationary Phase)

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Factors Determining Kinetics

• Rate per microbe, which depends on
• Species
• Substrates
• Environmental factors
• Total numbers of microbes

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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

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Fermentation Technology
-gt Why is it important to know the kinetics of
the reaction in the fermenter?
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Fermentation Technology
-gt What is going on in a fermenter? -gt How to
control the process in a fermenter?
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Stochiometric Coefficients
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Mass Balance
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Rates (Kinetics) and Balances
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Example
-gt Too complex !!!!
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• -gt Blackbox effect

substrates cells ? extracellular products
more cells ( ?S X ? ?P
nX)
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Model 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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Primary metabolic products
Secondary metabolic products
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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
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Biotechnological 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.
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Batch 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
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Growth and Production Kinetic in Batch

• Cellular growth rate
• Monod approximation
• Yield factor
• Substrate Utilization
• Product Formation
• (Beginning of Stationary Phase)

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Biotechnological 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.