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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.