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

€

€

rx =dCx

dt

€

€

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