Fermentation Lecture

8/19/2019 Fermentation Lecture

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FermentationFermentation

Kinetics of Yeast GrowthKinetics of Yeast Growthand Productionand Production


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IntroductionIntroduction

Fermentation can be defined as an energy yielding process where yeastFermentation can be defined as an energy yielding process where yeastconverts organic molecules (such as sugar) into energy, carbon dioxideconverts organic molecules (such as sugar) into energy, carbon dioxideor/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 doesnot get as much energy from the substrate. Yeast produces ethanol when itnot get as much energy from the substrate. Yeast produces ethanol when itrespires anaerobically and ultimately the ethanol will ill the yeast (findrespires anaerobically and ultimately the ethanol will ill the yeast (findout 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 CH→ 3CH2OH + 2 CO2 + 2 ATP

C6H1206 + 6O2 6CO→ 2 + 6H2O + 16-18 APT


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When the feed substrate to the reactor is notWhen the feed substrate to the reactor is notmonosaccharide e! sucrose "Cmonosaccharide e! sucrose "C1212HH2222OO1111#$ %east#$ %east

en&%me cause !'%cosidic bond to brea( in a )rocessen&%me cause !'%cosidic bond to brea( in a )rocessca''ed h%dro'%sisca''ed h%dro'%sis


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ObjectiveObjective

+o find the inetics of the system by using+o find the inetics of the system by using

onlinear -egression (guess for onlinear -egression (guess for ss andand mm))

+he um of the 0east 1uares and the+he um of the 0east 1uares and the0ineweaver2#ur &lot methods in order to0ineweaver2#ur &lot methods in order todetermine the parameters 3determine the parameters 3mm and and ss

+o determine the yield coefficient and to+o determine the yield coefficient and to

proect min. and max. amount yeast cell mass, proect min. and max. amount yeast cell mass,carbon dioxide and ethanol producedcarbon dioxide and ethanol produced


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Experimental! ProcedureExperimental! Procedure

:sing #iochemistry naly8er and pectrophotometer:sing #iochemistry naly8er and pectrophotometer

to measure and mae calibration curves for sugar andto measure and mae calibration curves for sugar and

yeast cell concentrationsyeast cell concentrations

-eactant initial concentration-eactant initial concentration ; dextrose/or sucrose 5< g/0dextrose/or sucrose 5< g/0

; yeast = g/0yeast = g/0

; volume reactant solution 5 0volume reactant solution 5 0


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!nitial conditions > assumptions!nitial conditions > assumptions

!nitial $onditions!nitial $onditions ; 5 0 of solution5 0 of solution

;


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+heory+heory

!n ideal fermentation process in which the growing cells are!n 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 A rate of substrate consumptionrsx A rate of substrate consumption

rx A rate of cell growthrx A rate of cell growth

s A substrate concentrations A substrate concentration

x A cell concentrationx A cell concentration

& A ethanol concentration (in anaerobic case)& A ethanol concentration (in anaerobic case)

rxCells (x)

P

Cells (x)

rsx


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+heory+heory

The plot showing the trends for yeast cell growth over time

r x =

dC x

dt

r x =

dx

dt

x B i o m a s s


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"heor# continue"heor# continueYeast Growth occurs in $ sta%esYeast Growth occurs in $ sta%es

0ag phase, yeast mature and acclimate to environment (no growth occurs)0ag phase, yeast mature and acclimate to environment (no growth occurs)

+he exponential growth section, the rate of reaction follows first order inetics+he exponential growth section, the rate of reaction follows first order inetics

9uring the deceleration phase, a large number of parameters, each with saturation effects,9uring the deceleration phase, a large number of parameters, each with saturation effects,

have an effect on the inetics of yeast growth (such as substrate and waste concentrations)have an effect on the inetics of yeast growth (such as substrate and waste concentrations)

+he growth rate is ruled by the limiting substrate concentration (sugar)+he growth rate is ruled by the limiting substrate concentration (sugar)

+he final e1uation, often referred to as the 4onod e1uation, loos very similar to the+he final e1uation, often referred to as the 4onod e1uation, loos very similar to the

4ichaelis24enten e1uation.4ichaelis24enten e1uation.

tationary phase, no growth occurs due to high waste concentration or compleate substratetationary phase, no growth occurs due to high waste concentration or compleate substrate

consumingconsuming

x r dt

dx x ×== µ

x r s x ×= )( µ

+×=

ss

sms

sk

s µ µ )(

(s * the onod constant "!,#

.m * a ma/imum s)ecific !roth reaction rate "min-1#

r x = dx dt

= µ m x SK s+ S

× O

K o +O

× P

K p + P

...

r x = dx

dt = µ m x

S

K s+ S


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&ineweaver'(ur) *earran%ement&ineweaver'(ur) *earran%ement

+×= sssmssk

s µ µ )(

mm

s

m

s

s s

k

s

sk

µ µ µ µ

BBB

)(+×=

+=


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+onlinear *e%ression+onlinear *e%ression

B.B. 9efine 4odel9efine 4odel

5.5. olve for - olve for - predicted predicted (dx/dt)(dx/dt)

(calculate dx/dt from the polynomial e1uation fitted(calculate dx/dt from the polynomial e1uation fittedto the curve x(t)to the curve x(t)

=.=. 4ae initial guess for 4ae initial guess for ss andand mm

(3(3mm is the max. specific growth rate can be achievedis the max. specific growth rate can be achieved

when CC when CC ss s is saturation constant or the value of limitings is saturation constant or the value of limiting

substrate conc. at which 3substrate conc. at which 3ss e1ual to the half of 3e1ual to the half of 3mmu 4inimi8e4inimi8e DD(-2- (-2- predicted predicted))55 using solver function inusing solver function in

*xcel by varying *xcel by varying ss andand mm

+

==ss

sm x

sk

s x

dt

dx r µ


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Yield ,oefficient -eterminationYield ,oefficient -etermination

-atio of cell or *thanol concentration to substrate concentration.-atio of cell or *thanol concentration to substrate concentration.

Enowing YEnowing Yx/sx/s will give you an idea for how much additionalwill give you an idea for how much additionalyeast cell mass, on average, is produced for a given amount ofyeast cell mass, on average, is produced for a given amount ofsugar substrate consumed.sugar substrate consumed.

s well allowed you to calculate a lower bound on thes well allowed you to calculate a lower bound on theexperimental stoichiometric coefficient,experimental stoichiometric coefficient, , and therefore to, and therefore to

calculate ranges for ethanol and $Gcalculate ranges for ethanol and $G55 production. production.(Yeast $ell) $IHB5GI(Yeast $ell) $IHB5GI JJ ($G5 $H=$H5GH) (Yeast $ells) ($G5 $H=$H5GH) (Yeast $ells)

ss

x x

ds

dx Y

o

o

s

x −−

==

Y ps

= dP

ds= P − P7s7 − s


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Error in &ineweaver'(ur)Error in &ineweaver'(ur)

ParametersParameters *rror in *rror in ss andand mm relative to error in slope and y2intercept ofrelative to error in slope and y2intercept of

linear fitlinear fit

-andom *rror in y valuesK-andom *rror in y valuesK

+9*' of slopeK+9*' of slopeK

+9*' of y2interceptK+9*' of y2interceptK

( )( )5

L5

−

−

= ∑ n y y

s ii

x y

( )∑ −=

5

x x

ss

i

x y

b

( )∑∑

−=

5

5

x x n

x ss

i

i

x y a


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&ower (ound on&ower (ound on ..

/stoichiometric coefficient0/stoichiometric coefficient0

"east Ce''# + C6H12O6 → ϒ "CO2 + CH3CH2OH# + "east Ce''s#

Where$ theoretica''%$ ϒ * 2

ssume all yeast generated is attributable only to sugarssume all yeast generated is attributable only to sugarcomplete consumptioncomplete consumption

$onservation of mass re1uires that the remaining product be$onservation of mass re1uires that the remaining product be

e1uimolar amounts $Ge1uimolar amounts $G55 and ethanoland ethanol

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Fermentation Lecture