Download - Fermentation kinetics
FermentationFermentation Kinetics of Yeast Growth Kinetics of Yeast Growth
and Productionand Production
IntroductionIntroduction Fermentation can be defined as an energy yielding process where yeast Fermentation can be defined as an energy yielding process where yeast
converts organic molecules (such as sugar) into energy, carbon dioxide converts organic molecules (such as sugar) into energy, carbon dioxide or/and ethanol depending on the respiration pathway.or/and ethanol depending on the respiration pathway.
Yeast can respire in anaerobically and aerobically. Yeast can respire in anaerobically and aerobically. However, yeast gets more energy from aerobic respiration, but in the However, yeast gets more energy from aerobic respiration, but in the
absence of oxygen it can continue to respire anaerobically, though it does absence of oxygen it can continue to respire anaerobically, though it does not get as much energy from the substrate. Yeast produces ethanol when it not get as much energy from the substrate. Yeast produces ethanol when it respires anaerobically and ultimately the ethanol will kill the yeast (find respires anaerobically and ultimately the ethanol will kill the yeast (find out why is yeast continue to produce ethanol even the last is an inhibitor).out why is yeast continue to produce ethanol even the last is an inhibitor).
C6H1206 → 2 CH3CH2OH + 2 CO2 + 2 ATP C6H1206 + 6O2 6CO→ 2 + 6H2O + 16-18 APT
When the feed substrate to the reactor is not When the feed substrate to the reactor is not monosaccharide e.g. sucrose (Cmonosaccharide e.g. sucrose (C1212HH2222OO1111), yeast ), yeast enzyme cause glycosidic bond to break in a process enzyme cause glycosidic bond to break in a process called hydrolysiscalled hydrolysis
Industrial and Commercial ApplicationsIndustrial and Commercial Applications
Food IndustryFood Industry~ Beer~ Beer~ Bread~ Bread~ Cheese~ Cheese~ Wine~ Wine~ Yogurt~ Yogurt
Pharmaceutical IndustryPharmaceutical Industry~ Insulin~ Insulin~ Vaccine Adjuvants~ Vaccine Adjuvants
EnergyEnergy~ Fuel Ethanol~ Fuel Ethanol
ObjectiveObjective
To find the kinetics of the system by usingTo find the kinetics of the system by using Nonlinear Regression (guess for kNonlinear Regression (guess for k s s and and μμmm)) The Sum of the Least Squares and the The Sum of the Least Squares and the
Lineweaver-Burk Plot methods in order to Lineweaver-Burk Plot methods in order to determine the parameters µdetermine the parameters µmm and k and ks s
To determine the yield coefficient and to To determine the yield coefficient and to project min. and max. amount yeast cell mass, project min. and max. amount yeast cell mass, carbon dioxide and ethanol producedcarbon dioxide and ethanol produced
Experimental Set UpExperimental Set Up
ApparatusApparatus
Bioreactor
pH meter
Sampling device
Mixer
Temperature sensor
YSI 2700 Biochemistry Analyzer
pH probe
D-oxygen probe
Experimental: ProcedureExperimental: Procedure
Using Biochemistry Analyzer and Spectrophotometer Using Biochemistry Analyzer and Spectrophotometer to measure and make calibration curves for sugar and to measure and make calibration curves for sugar and yeast cell concentrationsyeast cell concentrations
Reactant initial concentrationReactant initial concentration– dextrose/or sucrose 25 g/L dextrose/or sucrose 25 g/L – yeast 3 g/Lyeast 3 g/L– volume reactant solution 2 Lvolume reactant solution 2 L
Initial conditions & assumptionsInitial conditions & assumptions
Initial ConditionsInitial Conditions– 2 L of solution2 L of solution– 50 g sugar50 g sugar– pH around 5.0pH around 5.0– Temperature around 28-30°CTemperature around 28-30°C AssumptionsAssumptions
the bioreactor content is the bioreactor content is – well mixed and has a constant medium volume at a certain well mixed and has a constant medium volume at a certain
initial conditionsinitial conditions– Temperature is constant Temperature is constant – pH maintained at optimal pH of 3.00pH maintained at optimal pH of 3.00– All reactants or nutrients present in excess except for sugar All reactants or nutrients present in excess except for sugar
substrate.substrate.
TheoryTheory In ideal fermentation process in which the growing cells are In ideal fermentation process in which the growing cells are
consuming the substrate (sugars), and producing more cells consuming the substrate (sugars), and producing more cells according to the following scheme.according to the following scheme.
rsx = rate of substrate consumptionrsx = rate of substrate consumption
rx = rate of cell growthrx = rate of cell growth
s = substrate concentrations = substrate concentration
x = cell concentrationx = cell concentration
P = ethanol concentration (in anaerobic case)P = ethanol concentration (in anaerobic case)
rx
Cells (x)P
Cells (x)
rsx
TheoryTheory
The plot showing the trends for yeast cell growth over time
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rx =dCx
dt
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€
rx =dx
dtx
Bio
mas
s
Theory continue Theory continue Yeast Growth occurs in 4 stagesYeast Growth occurs in 4 stages
Lag phase, yeast mature and acclimate to environment (no growth occurs)Lag phase, yeast mature and acclimate to environment (no growth occurs) The exponential growth section, the rate of reaction follows first order kineticsThe exponential growth section, the rate of reaction follows first order kinetics
During the deceleration phase, a large number of parameters, each with saturation effects, During the deceleration phase, a large number of parameters, each with saturation effects, have an effect on the kinetics of yeast growth (such as substrate and waste concentrations)have an effect on the kinetics of yeast growth (such as substrate and waste concentrations)
The growth rate is ruled by the limiting substrate concentration (sugar)The growth rate is ruled by the limiting substrate concentration (sugar)
The final equation, often referred to as the Monod equation, looks very similar to the The final equation, often referred to as the Monod equation, looks very similar to the Michaelis-Menten equation.Michaelis-Menten equation.
Stationary phase, no growth occurs due to high waste concentration or compleate substrate Stationary phase, no growth occurs due to high waste concentration or compleate substrate consumingconsuming
xrdt
dxx ⋅== µ
xr sx ⋅= )(µ
+
⋅=ss
sms sk
sμμ )(
ks = the Monod constant (g/L)
μm = a maximum specific growth reaction rate (min-1)
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rx =dx
dt= μm x
S
Ks + S
⎡
⎣ ⎢
⎤
⎦ ⎥⋅
O
Ko + O
⎡
⎣ ⎢
⎤
⎦ ⎥⋅
P
K p + P
⎡
⎣ ⎢
⎤
⎦ ⎥...
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rx =dx
dt= μmx
S
K s + S
⎡
⎣ ⎢
⎤
⎦ ⎥
Lineweaver-Burk RearrangementLineweaver-Burk Rearrangement
+
⋅=ss
sms sk
sμμ )(
mm
s
m
s
s s
k
s
sk
µµµµ111
)(
+⋅=+
=
Nonlinear RegressionNonlinear Regression
1.1. Define ModelDefine Model
2.2. Solve for RSolve for Rpredictedpredicted (dx/dt) (dx/dt) (calculate dx/dt from the polynomial equation fitted (calculate dx/dt from the polynomial equation fitted to the curve x(t)to the curve x(t)
3.3. Make initial guess for kMake initial guess for ks s and and μμmm
(µ(µmm is the max. specific growth rate can be achieved is the max. specific growth rate can be achieved when S >> kwhen S >> kss ks is ks is saturation constant or the value of limiting substrate saturation constant or the value of limiting substrate conc. S at which µconc. S at which µss equal to the half of µ equal to the half of µmm
u Minimize Minimize ΣΣ(R-R(R-Rpredictedpredicted))2 2 using solver function in Excel using solver function in Excel by varying kby varying kss and and μμmm
+
==ss
smx sk
sx
dt
dxr μ
Yield Coefficient DeterminationYield Coefficient Determination
Ratio of cell or Ethanol concentration to substrate concentration.Ratio of cell or Ethanol concentration to substrate concentration.Knowing YKnowing Yx/s x/s will give you an idea for how much additional yeast will give you an idea for how much additional yeast cell mass, on average, is produced for a given amount of sugar cell mass, on average, is produced for a given amount of sugar substrate consumed.substrate consumed.As well allowed you to calculate a lower bound on the As well allowed you to calculate a lower bound on the experimental stoichiometric coefficient, experimental stoichiometric coefficient, γγ, and therefore to , and therefore to calculate ranges for ethanol and COcalculate ranges for ethanol and CO22 production. production.
(Yeast Cell) + C6H12O6- (Yeast Cell) + C6H12O6- →→ γ (CO2 + CH3CH2OH) + (Yeast Cells) γ (CO2 + CH3CH2OH) + (Yeast Cells)
ss
xx
ds
dxY
o
o
s
x −−==
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Yp
s
=dP
ds=
P −P0
s0 − s
Error in Lineweaver-Burk Error in Lineweaver-Burk ParametersParameters
Error in kError in kss and and μμmm relative to error in slope and y-intercept of relative to error in slope and y-intercept of
linear fitlinear fit
Random Error in y values:Random Error in y values:
STDEV of slope:STDEV of slope:
STDEV of y-intercept:STDEV of y-intercept:
( )( )2
ˆ 2
−
−= ∑
n
yys ii
xy
( )∑ −=
2xx
ss
i
xy
b
( )∑∑
−=
2
2
xxn
xss
i
i
xya
Lower Bound on Lower Bound on γγ (stoichiometric coefficient)(stoichiometric coefficient)
(Yeast Cell) + C6H12O6 → ϒ (CO2 + CH3CH2OH) + (Yeast Cells)
Where, theoretically, ϒ = 2. Assume all yeast generated is attributable only to sugar Assume all yeast generated is attributable only to sugar
complete consumptioncomplete consumption
Conservation of mass requires that the remaining product be Conservation of mass requires that the remaining product be equimolar amounts COequimolar amounts CO22 and ethanol and ethanol