Metabolic Model Describing Growth of Substrate Uptake

By

Idelfonso Arrieta

Anant Kumar Upadhyayula

Objectives Explain the Growth of substrate uptake

Simulate a range of metabolic responses obtained from Trigonopsis variabilis by simple biochemical reactions produced in a cell

1 of 2

Objectives Understand the behavior of yeast under

different growth conditions

Simulate the growth of any yeast under discontinuous conditions

1 of 2

Introduction The yeast Trigonopsis variabilis has been reported to be a

potent producer of this enzyme.

Aerobic metabolism of all yeast is determined by relative sizes of the sugar transport rate into the cell and the Pyruvate transport into the mitochondrion.

Introduction

Fermentation models are normally divided into two classes

1. Unstructured models where the biomass is described by one variable

2. Structured models where intracellular metabolic pathways are considered.

SugarTransport

S sug r

Generic Yeast cell with Main Metabolic Pathways

S’

RIGrowth

RI’

Cell membrane

Mitochondrialmembrane

Glycolisis

RespiratoryIntermediatesystems

rigr r

OHCO 22

2COEthanol

rimit r

et r

'rimit r TCA

Cycle

Description of the model structure

The model describes seven major steps in yeast metabolism:

Sugar transport across the plasma membrane. Sugar conversion to growth macromolecules.

Glycolytic conversion of sugar to pyruvate Pyruvate conversion to growth macromolecules.

Description of the model structure

Pyruvate conversion to ethanol product Pyruvate transport across the mithocondrial

membrane. Respiration of pyruvate to carbon dioxide

and water.

Assumptions Cell matter and culture medium form a distributed system The limiting substrate is both the carbon and energy

source. The composition and metabolic activity assumed constant

such that biomass may be described by a single variable X. The redox state of the cell is assumed to be the same as

that of the substrate. ATP generation is only a result of fermentation and

respiration.

Assumptions All growth yields (g biomass/g substrate) are constant

since YATP (g biomass/mol ATP), the PO ratio (mol ATP/atom oxygen), and growth stoichiometry.

The carbon content of the intermediates for biosynthesis of cell material is provided from both sugar and pyruvate.

Assumptions Saturation of the respiratory capacity is the only

controlling factor in fermentation and respiration.

ATP is a product of energy-producing reactions and is only a hypothetical value in this model.

Biochemical Reactions Sequence

(mM) cell theinsideion Concentrat Substrate:

(mM)ion Concentrat Substrate:

(g/l)ion Concentrat Biomass:

:

S

S

x

Where

SxSx

Biochemical Reactions Sequence

2

(mM)ion concentrat ate triphosphadenosine alHypothetic :

(mM) cell theinsideion concentrat Pyruvate :

(mM) cell theinsideion concentrat Substrate:

)(g/lion concentrat Biomass :

,

..

pir

ATP

RI

S

x

where

ATPpirRIpirxSx

Biochemical Reactions Sequence

(nM) iummithocondrion concentrat Pyrovate:

(mM) cell theinsideion concentrat Pyruvate :

(g/l)ion concentrat Biomass :

:

IR

RI

x

where

IRxRIx

(mM)ion concentrat dedinucleoti

adeninenicotamide alhypothetic :

:

4232

NADH

where

ATPNADHOHCOxIRx

Biochemical Reactions Sequence

2COEtRI

Biochemical Reactions Sequence

)ATP 1-mol x (gn consumptio ATP the torelated yield Biomass :/

)1-gS (mmol biomass of isbiosynthes for the used pyruvate of Mass :2

)1-gS (mmol biomass of isbiosynthes for the used Substrate of Mass:1

:

2

/

1.2.1

ATPxY

xa

xa

where

x

ATPxYRIaSax

Rate Equations

1. Balance to S (Glucose in the culture medium)

SsKS.xk

dtdS

1

It is consumed through the cellular membrane

1K Maximum Substrate Uptake rate

mmol S

1.1 hg

Rate Equations2.Balance to S’(Glucose inside the cell)It is consumed by the transportation of S through the cellular Membrane

2.1'*'*.1

'1 aRIaSgrkSglyc

kSsK

SkdtdS

x

k

grk Kinetic constant in the Growth reactions

.glyck Kinetic constant of the glycolysis process

Rate Equations

2.1'.

2'..2

1 aRIaSgrkRI

rimitK

RIkS

glyck

dt

dRI

x

3.Balance to RI (Pyruvate)

It is generated through the Glycolysis of S’ and it is consumed toward the interior of the mitochondrion to form the new cell

The experimental work with T. variabilis has shown a negligible quantity of Ethanol produced in aerobic growth conditions

Rate Equations

4. Balance to RI’ (pyruvate inside mithocondrion)

3)2

(.2

1 OIRoxKRI

rimitK

RIkdt

IdRx

It is generated by the transport of RI toward the mithocondrion.

2K Maximum pyruvate transport rate

rimitK Saturation constant for pyruvate transport across the mithocondrial membrane

oxK Oxidation constant

Rate Equations

5. Balance to x

21.1

aRI

aSgrK

dtdx

x

New cells are generated in the growth reaction

grK Kinetic constant in the growth reaction.

Rate Equations

6. Balance to oxygen inside the cell

3

2.

321 OIRoxK

SsKSK

dt

dO

x

It is consumed by the cells during the respiration

3K Maximum specific oxygen uptake rate.

oxK Oxidation constant.

Rate Equations

7. Balance to ATP

21.

/

13

2.1

/4.2

aRI

aSgrK

ATPxY

ORIoxKOP

Sglic

K

It is generated during the glycolysis and respiration process.It is consumed in the generation reaction of new cells

glycK Kinetic constant of the glycolysis process

oxK Oxidation constant.

grK Kinetic constant in the growth reaction.

Computation Procedure

) 5.1( uptakeoxygen

of rate specific alexperiment thesimilar to valueaGiven :

similar to Value :)(

) 5.1( uptakesugar

of rate specific alexperiment thesimilar to valueaGiven :

:parameters for the estimation Initial

112

3

111

2

11

1

hgOmmol

k

khmmol RI gk

hgSmmol

k

-

COMPUTATION PROCEDURES

literature

in the reported valuescalGiven typi :) (

literature

in the reported valuesTypicalGiven :) (/

literature in the reprted valuescalGiven typi :)(

)003.0( saturated

wasmembrane ialmithocondr thesuch that valuesmall aGiven :

lower than Value :)) RI .()((1

and similar to Value :) 1).((

1/

21

31112

24

21111

ATPmolxgY

OmolATPmolOP

nMk

mM

k

khgmmolmmolOk

kkhgSmmolmmolRIk

ATPx

s

imit

resp

glyc

Computation procedure

The values of the parameters included in

are calculated with the following numerical

methods: Runge-Kutta (fourth order). Comparation of theoretical data and experimental data and

the best values calculated by least squares method.

Results Since the model discussed in this paper can be used to

simulate not only an exceptional growth but also a substrate starvation process, so it cave be sued to simulate the growth of any yeast under discontinuous conditions.

The maximum specific substrate uptake rate for the rich medium is considerably greater to that of the salts medium.

The observed specific oxygen uptake rate k3 does not reach a maximum for higher concentration of of oxygen because the growth is performed under limiting conditions of oxygen(0.5%).

3k

Results The cellular yield concerning the glucose reaches a higher value in the

rich medium compared to with the salt medium, since in using the rich medium a large part of the carbonated chains that constitute the cellular matter are formed from the amino acids contained in the medium but while using the salt medium these chains should be synthesized entirely from the main substrate.

The energetic yield is much higher in the rich medium with respect to the salts medium since the cellular material synthesis requires a smaller consumption because the rich medium contains several amino acids basic for protein synthesis.

3k

conclusions

The chemically structured model is capable of expalining the cellular growth and consumption of sunstrate uptake in the yeast

The model may simulate a range of metabolic responses obtained from the T. Variabilis growth in discontinuous culture and can serve to understand the behavior of the yeast under different growth conditions.

Reference

Barford, J. P. A general model for aerobic yeast growth. Biotechnol. Bioeng.1990, 35, 907-920.

Montes, F. J., Moreno, J.A., Catalan, J., and Galan, M.A. Oxygen kinetic and metabolic parameters for the yeast Trigonopsis Variabilis. J. Chem. Tech. Biotechnol.1997,68,243-246.

Montes F.J., Catalan J., and Galan M.A. Barford, J. P. A metabolic model describing growth and substrate uptake of Trigonopsis Variabilis. Enzyme and Microbial Technol. 1998, 22, 329-334.