Fermentation kinetics

1. FermentationFermentation
Kinetics of Yeast GrowthKinetics of Yeast Growth
and Productionand Production

2. IntroductionIntroduction
 Fermentation can be defined as an energy yielding process where yeastFermentation can be defined as an energy yielding process where yeast
converts organic molecules (such as sugar) into energy, carbon dioxideconverts 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 theHowever, yeast gets more energy from aerobic respiration, but in the
absence of oxygen it can continue to respire anaerobically, though it doesabsence of oxygen it can continue to respire anaerobically, though it does
not get as much energy from the substrate. Yeast produces ethanol when itnot get as much energy from the substrate. Yeast produces ethanol when it
respires anaerobically and ultimately the ethanol will kill the yeast (findrespires 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

3.  When the feed substrate to the reactor is notWhen 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 processenzyme cause glycosidic bond to break in a process
called hydrolysiscalled hydrolysis

4.  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

5. 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 kss andand μμmm))
 The Sum of the Least Squares and theThe Sum of the Least Squares and the
Lineweaver-Burk Plot methods in order toLineweaver-Burk Plot methods in order to
determine the parameters µdetermine the parameters µmm and kand kss
 To determine the yield coefficient and toTo 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

6. Experimental Set UpExperimental Set Up
 ApparatusApparatus
Bioreactor
pH meter
Sampling
device
Mixer
Temperature
sensor
YSI 2700
Biochemistry
Analyzer
pH probe
D-oxygen
probe

7. Experimental: ProcedureExperimental: Procedure
 Using Biochemistry Analyzer and SpectrophotometerUsing Biochemistry Analyzer and Spectrophotometer
to measure and make calibration curves for sugar andto measure and make calibration curves for sugar and
yeast cell concentrationsyeast cell concentrations
 Reactant initial concentrationReactant initial concentration
– dextrose/or sucrose 25 g/Ldextrose/or sucrose 25 g/L
– yeast 3 g/Lyeast 3 g/L
– volume reactant solution 2 Lvolume reactant solution 2 L

8. 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 isthe bioreactor content is
– well mixed and has a constant medium volume at a certainwell mixed and has a constant medium volume at a certain
initial conditionsinitial conditions
– Temperature is constantTemperature 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 sugarAll reactants or nutrients present in excess except for sugar
substrate.substrate.

9. TheoryTheory
 In ideal fermentation process in which the growing cells areIn ideal fermentation process in which the growing cells are
consuming the substrate (sugars), and producing more cellsconsuming 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

10. TheoryTheory
The plot showing the trends for yeast cell growth over time
rx =
dCx
dt
rx =
dx
dt
xBiomass

11. Theory continueTheory 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 theThe 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 substrateStationary phase, no growth occurs due to high waste concentration or compleate substrate
consumingconsuming
xr
dt
dx
x ⋅== µ
xr sx ⋅= )(µ






+
⋅=
ss
s
ms
sk
s
μμ )(
ks = the Monod constant (g/L)
μm = a maximum specific growth reaction rate (min-1
)
rx =
dx
dt
= μm x
S
Ks + S
⎡
⎣
⎢
⎤
⎦
⎥⋅
O
Ko + O
⎡
⎣
⎢
⎤
⎦
⎥⋅
P
Kp + P
⎡
⎣
⎢
⎤
⎦
⎥...
rx =
dx
dt
= μmx
S
Ks + S
⎡
⎣
⎢
⎤
⎦
⎥

12. Lineweaver-Burk RearrangementLineweaver-Burk Rearrangement






+
⋅=
ss
s
ms
sk
s
μμ )(
mm
s
m
s
s s
k
s
sk
µµµµ
111
)(
+⋅=
+
=

13. 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 kss andand μμmm
(µ(µmm is the max. specific growth rate can be achievedis the max. specific growth rate can be achieved
when S >> kwhen S >> kss ks isks is
saturation constant or the value of limiting substratesaturation constant or the value of limiting substrate
conc. S at which µconc. S at which µss equal to the half of µequal to the half of µmm
u MinimizeMinimize ΣΣ(R-R(R-Rpredictedpredicted))22
using solver function in Excelusing solver function in Excel
by varying kby varying kss andand μμmm






+
==
ss
s
mx
sk
s
x
dt
dx
r μ

14. 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/sx/s will give you an idea for how much additional yeastwill give you an idea for how much additional yeast
cell mass, on average, is produced for a given amount of sugarcell 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 theAs 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
dx
Y
o
o
s
x
−
−
== Yp
s
=
dP
ds
=
P − P0
s0 − s

15. Error in Lineweaver-BurkError in Lineweaver-Burk
ParametersParameters
 Error in kError in kss andand μμmm relative to error in slope and y-intercept ofrelative 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
yy
s ii
x
y
( )∑ −
=
2
xx
s
s
i
x
y
b
( )∑
∑
−
= 2
2
xxn
x
ss
i
i
x
ya

16. Lower Bound onLower 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 sugarAssume all yeast generated is attributable only to sugar
complete consumptioncomplete consumption
 Conservation of mass requires that the remaining product beConservation of mass requires that the remaining product be
equimolar amounts COequimolar amounts CO22 and ethanoland ethanol