What do all these things have in common?

DETERMINING KINETIC PARAMETERS OF SACCHAROMYCES

CEREVISIAE GROWTH IN A

BATCH STIRRED-TANK REACTOR

Joyanne SchneiderCH EN 4903

November 28, 2006

OverviewOverview

•Problem Statement and SetupProblem Statement and Setup

•TheoryTheory

•Results and DiscussionResults and Discussion

•Conclusions and Conclusions and RecommendationsRecommendations

•Questions and AnswersQuestions and Answers

Problem Statement and SetupProblem Statement and Setup

Biochemical company wanted to obtain growth Biochemical company wanted to obtain growth kinetics of a genetically modified yeast strain kinetics of a genetically modified yeast strain analogous to analogous to S. cerevisae S. cerevisae for use in for use in recombinant technologyrecombinant technology::

volumetric mass transfer coefficient (kLa) volumetric mass transfer coefficient (kLa) specific respiration rate, OUR specific respiration rate, OUR yield coefficient Yyield coefficient YX/SX/S

maximum specific growth rate (μmaximum specific growth rate (μmaxmax) ) specific glucose uptake rate, Rspecific glucose uptake rate, Rvv

Problem Statement and Setup: Problem Statement and Setup: New Brunswick BSTR ApparatusNew Brunswick BSTR Apparatus

Problem Statement and Setup:Problem Statement and Setup: ConditionsConditions

Temperature: 37 degrees CelsiusTemperature: 37 degrees Celsius pH: 6.5pH: 6.5 Agitation Rate: 500 RMPAgitation Rate: 500 RMP Air Flow Rate: 800 cc/minAir Flow Rate: 800 cc/min Startup: 1.5 L Deionized water Startup: 1.5 L Deionized water 40 g/L glucose 40 g/L glucose 10 g/L of yeast extract10 g/L of yeast extract 20 g/L of Bacto Peptone 20 g/L of Bacto Peptone

Thoery: PhasesThoery: Phases

Lag Phase (minimize)Lag Phase (minimize)

Acceleration PhaseAcceleration Phase

Exponential Growth PhaseExponential Growth Phase

Deceleration PhaseDeceleration Phase

Stationary PhaseStationary Phase

Death PhaseDeath Phase

Theory: kTheory: kLLa without cellsa without cells

Using Henry’s Law: Using Henry’s Law:

After re-aeration begins, After re-aeration begins,

Oxygen Transfer Rate

0

20

40

60

80

100

120

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16Time, hr

% O

2 S

atu

rati

on

HxyP

)*( CCaLk

dtdC

Theory: kTheory: kLLa without cells, a without cells, cont.cont.

Dividing both sides by C*, separating Dividing both sides by C*, separating variables, and integrating:variables, and integrating:

Determining kLa

-7-6-5-4-3-2-10

-0.0018 -0.0016 -0.0014 -0.0012 -0.001 -0.0008 -0.0006 -0.0004 -0.0002 0

Time, hr

ln(1

-C/C

*)

)()*

1( taLk

CCLn

Theory: OUR and kTheory: OUR and kLLa with cellsa with cellsDuring de-aeration, During de-aeration,

During re-aeration, During re-aeration,

OUR and kLa Determination

0

10

20

30

40

50

60

0 0.05 0.1 0.15 0.2 0.25

Time, hr

% O

2 s

atu

rati

on

OURdtCCd *)/(

)*

1(*)/(

CCkLaOUR

dtCCd

Theory: OUR and kLa with cells Theory: OUR and kLa with cells cont.cont.

Once OUR is determined, kOnce OUR is determined, kLLa can be determined by plotting a can be determined by plotting change in percent saturation plus specific respiration rate change in percent saturation plus specific respiration rate versus one minus percent saturation, 1-C/C*.versus one minus percent saturation, 1-C/C*.

Determining kLa

0

500

1000

1500

2000

2500

0 10 20 30 40 50 60 70 801-C/C*

d(C

/C*)

/dt

+

OU

R

Theory: Yield CoefficientTheory: Yield Coefficient

Yield is given by,Yield is given by,

where where ΔΔX is the change in cell X is the change in cell

concentration and concentration and ΔΔ S is the change in substrate S is the change in substrate (glucose) concentration.(glucose) concentration.

Glucose and cell concentrations obtained every half-Glucose and cell concentrations obtained every half-hour using HPLC and spectrometry (absorbance), hour using HPLC and spectrometry (absorbance), respectively.respectively.

SX

SXY

/

Theory:Theory:μμmaxmax

Monod Equation:Monod Equation:

μμ is the specific growth rate is the specific growth rate μμmaxmax is the maximum specific growth rate is the maximum specific growth rate S is the substrate (glucose) concentrationS is the substrate (glucose) concentration KKss is the Monod constant is the Monod constant

μμmaxmax is the asymptote of is the asymptote of μμ plotted as a function plotted as a function

of Sof S

SsKS

max

Theory: Theory: μμmaxmax (cont.)(cont.)

Determining Max Growth Rate

0

0.2

0.4

0.6

0.8

0 10 20 30 40

Glucose Conc. (g/L)

Gro

wth

Ra

te

(hr-1

)

Theory: Theory: μμmaxmax (cont.)(cont.)

If few samples are taken, no asymptotic If few samples are taken, no asymptotic relationshiprelationshipBecause rate of cell growth isBecause rate of cell growth is

Separating variables and integrating gives:Separating variables and integrating gives:

Plotting gives a slope of uPlotting gives a slope of umax.max.

XdtdX

gr

tLnXmax

Theory: RTheory: Rvv

The volumetric glucose uptake rate (g/(L-hr) The volumetric glucose uptake rate (g/(L-hr) is given by:is given by:

Since it is just change in glucose Since it is just change in glucose concentration per time, can just be calculated concentration per time, can just be calculated from:from:

XSX

Y

u

vR

dtdS

/

max

0

0t

ft

SfS

dtdS

Results and Discussion: Results and Discussion: kkLLa without cellsa without cells

Agitator Agitator (RPM)(RPM)

Flow Flow (cc/min)(cc/min)

kLa value (hrkLa value (hr--

11))

(95%)(95%)

Variance Variance

500500 400400 36.3+/-0.80536.3+/-0.805 0.1690.169

500500 800800 66.3+/-1.2666.3+/-1.26 0.4150.415

500500 800800 60.8+/-0.77460.8+/-0.774 0.1560.156

500500 12001200 87.0+/-1.6987.0+/-1.69 0.7390.739

100100 800800 7.94+/-0.3217.94+/-0.321 0.02700.0270

300300 800800 19.9+/-0.22519.9+/-0.225 0.1320.132

700700 800800 111.7+/-1.71111.7+/-1.71 0.7640.764

850850 800800 158+/-2.63158+/-2.63 1.791.79

Results and Discussion: Results and Discussion: OUR and kOUR and kLLa with cellsa with cells

Run Run ##

OUROUR

(1/hr)(1/hr)OUROUR

VarianceVariancekkLLaa

(hr(hr-1-1))

kkLLaa

VariancVariancee

11 1.73 1.73

+/- 1.32+/- 1.320.4570.457 74.4 74.4

+/- 3.39+/- 3.393.013.01

22 12.412.4

+/- 5.17+/- 5.176.966.96 95.195.1

+/- 3.00+/- 3.002.352.35

Results and Discussion: Results and Discussion: μμmaxmax and Y and YX/SX/S

Run Run ##

μμmaxmax

(hr(hr-1-1))

μμmaxmax VariancVariancee

YYX/SX/S YYX/SX/S VariancVariancee

11 0.1700.170

+/- 0.221+/- 0.2210.01280.0128 0.2360.236 0.008710.00871

22 0.1030.103

+/- 0.163+/- 0.1630.00830.008344

0.1500.150 0.003650.00365

Results and Discussion: Results and Discussion: RRvv

Run #Run # RRv v (g/L-hr)(g/L-hr) VarianceVariance

11 0.240 +/- 0.240 +/- 0.4720.472

0.05800.0580

22 0.3190.319

+/-0.210+/-0.2100.04060.0406

Conclusions and Conclusions and RecommendationsRecommendations

Start with growth medium as close to growth Start with growth medium as close to growth conditions as possible.conditions as possible.

Using dissolved OUsing dissolved O22 probe and percent probe and percent saturation, can’t get accurate ksaturation, can’t get accurate kLLa with cells a with cells growing (should be lower with cells than without)growing (should be lower with cells than without)

To increase kTo increase kLLa, use higher air flow rate and a, use higher air flow rate and agitation speedagitation speed

To obtain maximum yield, don’t allow the oxygen To obtain maximum yield, don’t allow the oxygen to fall below the critical saturationto fall below the critical saturation

Use more trials to get more data pointsUse more trials to get more data points

ReferencesReferences

Atkinson, B., Mavituna, F. Atkinson, B., Mavituna, F. Biochemical Engineering and Biotechnology Biochemical Engineering and Biotechnology HandbookHandbook, 2, 2ndnd ed., 1991, Macmillion Publishers, Hampshire, England. ed., 1991, Macmillion Publishers, Hampshire, England.

Asenjo, J., Merchuk, J. Asenjo, J., Merchuk, J. Bioreactor System DesignBioreactor System Design, 1995, Marcel Dekker, New , 1995, Marcel Dekker, New York.York.

Bailey, J., Ollis, D. Bailey, J., Ollis, D. Biochemical Engineering FundamentalsBiochemical Engineering Fundamentals, International ed., , International ed., 1977, McCraw-Hill, Tokyo.1977, McCraw-Hill, Tokyo.

Shuler, M., Kargi, F. Shuler, M., Kargi, F. Bioprocess Engineering: Basic ConceptsBioprocess Engineering: Basic Concepts, 2, 2ndnd ed., 2002, ed., 2002, Prentice Hall, Upper Saddle River, New Jersey.Prentice Hall, Upper Saddle River, New Jersey.

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