The Pentose Phosphate Pathway in Saccharomyces cerevisiae
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This CellML model is known to run in both PCEnv and COR, however at present it does not seem to be recreating the published results - possibly beause we need to include a description of a glucose pulse in the CellML model. We are continuing to work on the model. The units have been checked and they are consistent.
Model Structure
Metabolic networks are highly complex nonlinear reaction systems whose functions are tightly co-ordinated and regulated by feedback mechanisms to meet the physiological demands of living organisms. Dynamic mathematical models of metabolic networks allow prediction as to how metabolism will respond to manipulation.
The pentose phosphate pathway can provide an alternative to glycolysis plus the TCA cycle for the complete oxidation of glucose. However, it is thought that its main role is not glucose oxidation, but to provide the cell with a source of NADPH for biosynthetic reactions and to supply pentose phosphate for the synthesis of nucleotides.
In 1999, Sam Vaseghi, Anja Baumeister, Manfred Rizzi and Matthias Reuss published a kinetic model of the pentose phosphate pathway in the yeast Saccharomyces cerevisiae (see below). They studied the in vivo dynamics of the pathway under conditions of continuous culture in order to elucidate important regulation phenomena responsible for co-ordinating the fluxes between glycolysis and the pentose phosphate pathway. They constructed the model by combining knowledge about enzyme kinetics with the stoichiometry of metabolic pathways based on the same principles used by Rizzi et al in their model of glycolysis (1997) (see The Glycolysis Pathway Model, 1997).
The complete original paper reference is cited below:
In Vivo Dynamics of the Pentose Phosphate Pathway in Saccharomyces cerevisiae
, Sam Vaseghi, Anja Baumeister, Manfred Rizzi and Matthias Reuss, 1999,
Metabolic Engineering
, 1, 128-140. (A PDF version of the article is available to subscribers on the Metabolic Engineering website.) PubMed ID: 10935926
The raw CellML description of the pentose phosphate pathway model can be downloaded in various formats as described in . For an example of a more complete documentation of another real reaction pathway, see The Bhalla Iyengar EGF Pathway Model, 1999.
the conventional rendering of the pentose phosphate pathway in Saccharomyces cerevisiae
A rendering of the pentose phosphate pathway in Saccharomyces cerevisiae. Metabolites are represented by rounded rectangles, catalysts are represented by ellipses and reactions by arrows. The action of the inhibitor MgATP on the enzymes G6PDH and 6PGDH is represented by dashed lines.
In CellML, models are thought of as connected networks of discrete components. These components may correspond to physiologically separated regions or chemically distinct objects, or may be useful modelling abstractions. This model has 36 components representing chemically distinct objects (15 metabolites, 10 enzymes one inhibitor and 10 reactions) and one component defined for modelling convenience which stores the universal variable time. Because this model has so many components, its CellML rendering would be complex. For an example of a CellML rendering of a reaction pathway see The Bhalla Iyengar EGF Pathway Model, 1999.
$\frac{d \mathrm{C\_6PG}}{d \mathrm{time}}=\mathrm{rG6PDH}-\mathrm{r6PGDH}+\mathrm{mu}\mathrm{C\_6PG}$
$\frac{d \mathrm{C\_Ru5P}}{d \mathrm{time}}=\mathrm{r6PGDH}-\mathrm{rR5PI}+\mathrm{rRu5PE}+\mathrm{mu}\mathrm{C\_Ru5P}$
$\frac{d \mathrm{C\_R5P}}{d \mathrm{time}}=\mathrm{rR5PI}-\mathrm{rTKL1}+\mathrm{rRPPK}+\mathrm{mu}\mathrm{C\_R5P}$
$\frac{d \mathrm{C\_X5P}}{d \mathrm{time}}=\mathrm{rRu5PE}-\mathrm{rTKL1}+\mathrm{rTKL2}+\mathrm{mu}\mathrm{C\_X5P}$
$\frac{d \mathrm{C\_S7P}}{d \mathrm{time}}=\mathrm{rTKL1}-\mathrm{rTAL}+\mathrm{mu}\mathrm{C\_S7P}$
$\frac{d \mathrm{C\_E4P}}{d \mathrm{time}}=\mathrm{rTAL}-\mathrm{rTKL2}+\mathrm{rPKDA}+\mathrm{mu}\mathrm{C\_E4P}$
$\frac{d \mathrm{C\_G6P}}{d \mathrm{time}}=\mathrm{dC\_G6P\_dt}\mathrm{dC\_G6P\_dt}=\frac{44.1}{48+1\mathrm{time}+0.45\mathrm{time}^{2}}+\frac{44.1\mathrm{time}}{(48+1\mathrm{time}+0.45\mathrm{time}^{2})(48+1\mathrm{time}+0.45\mathrm{time}^{2})}(1+0.90\mathrm{time})$
$\frac{d \mathrm{C\_NADP}}{d \mathrm{time}}=\frac{-1.48}{9.17+16.1\mathrm{time}+0.48\mathrm{time}^{2}}+\frac{1.48\mathrm{time}}{(9.17+16.1\mathrm{time}+0.48\mathrm{time}^{2})(9.17+16.1\mathrm{time}+0.48\mathrm{time}^{2})}(16.1+0.96\mathrm{time})$
$\frac{d \mathrm{C\_NADPH}}{d \mathrm{time}}=\frac{0.516}{25.39+0.37\mathrm{time}+0.5\mathrm{time}^{2}}-\frac{0.516\mathrm{time}}{(25.39+0.37\mathrm{time}+0.5\mathrm{time}^{2})(25.39+0.37\mathrm{time}+0.5\mathrm{time}^{2})}(0.37+1\mathrm{time})$
$\frac{d \mathrm{C\_MgATP}}{d \mathrm{time}}=\frac{29.83}{29.77+13.42\mathrm{time}+0.05\mathrm{time}^{2}}-\frac{29.83\mathrm{time}}{(29.77+13.42\mathrm{time}+0.05\mathrm{time}^{2})(29.77+13.42\mathrm{time}+0.05\mathrm{time}^{2})}(13.42+0.1\mathrm{time})$
$\mathrm{rG6PDH}=\mathrm{rmax\_G6PDH}\frac{\mathrm{C\_NADP}}{(\mathrm{C\_NADP}+\mathrm{K\_NADP\_1}\mathrm{I\_NADPH\_1})\mathrm{I\_MgATP\_1}}\mathrm{I\_NADPH\_1}=1.0+\frac{\mathrm{C\_NADPH}}{\mathrm{Ki\_NADPH\_1}}\mathrm{I\_MgATP\_1}=1.0+\frac{\mathrm{C\_MgATP}}{\mathrm{Ki\_MgATP\_1}}$
$\mathrm{r6PGDH}=\mathrm{rmax\_6PGDH}\frac{\mathrm{C\_NADP}}{(\mathrm{C\_NADP}+\mathrm{K\_NADP\_2}\mathrm{I\_NADPH\_2})\mathrm{I\_MgATP\_2}}\mathrm{I\_NADPH\_2}=1.0+\frac{\mathrm{C\_NADPH}}{\mathrm{Ki\_NADPH\_2}}\mathrm{I\_MgATP\_2}=1.0+\frac{\mathrm{C\_MgATP}}{\mathrm{Ki\_MgATP\_2}}$
$\mathrm{rR5PI}=1\mathrm{rmax\_R5PI}\mathrm{C\_Ru5P}$
$\mathrm{rRu5PE}=1\mathrm{rmax\_Ru5PE}\mathrm{C\_Ru5P}$
$\mathrm{rTKL1}=1\mathrm{rmax\_TKL1}\mathrm{C\_X5P}\mathrm{C\_R5P}$
$\mathrm{rTAL}=1\mathrm{rmax\_TAL}\mathrm{C\_GAP}\mathrm{C\_S7P}$
$\mathrm{rTKL2}=1\mathrm{rmax\_TKL2}\mathrm{C\_E4P}\mathrm{C\_X5P}$
$\mathrm{rPKDA}=1\mathrm{rmax\_PKDA}\frac{\mathrm{C\_E4P}}{\mathrm{C\_E4P}+\mathrm{K\_PKDA}}$
$\mathrm{rRPPK}=1\mathrm{rmax\_RPPK}\frac{\mathrm{C\_R5P}}{\mathrm{C\_R5P}+\mathrm{K\_RPPK}}$
$\mathrm{rHK}=\mathrm{qs}$
$\mathrm{rPGI}=\mathrm{qs}-\mathrm{rG6PDH}+\mathrm{mu}\mathrm{C\_G6P}+\mathrm{dC\_G6P\_dt}$
$\mathrm{qs}=\begin{cases}0.131 & \text{if $\mathrm{time}< 0.0$}\\ 0.546 & \text{otherwise}\end{cases}$
c.lloyd@auckland.ac.nz
The University of Auckland, Bioengineering Institute
Replaced the reaction element with simple MathML equations to better describe the original publication.
2008-11-03T15:02:03+13:00
In Vivo Dynamics of the Pentose Phosphate Pathway in Saccharomyces cerevisiae
1
128
140
glucose-6-phosphate
G6P
erythrose 4-phosphate
C_E4P
2007-06-20T11:42:32+12:00
Catherine
Lloyd
May
Matthias
Reuss
Catherine
Lloyd
May
Catherine Lloyd
2007-06-13T00:00:00+00:00
1999-04
Yizhi
Cai
10935926
Anja
Baumeister
6-phosphogluconate
C_6PG
This is the CellML description of Vaseghi et al's mathematical model of the pentose phosphate pathway in the yeast Saccharomyces cerevisiae (1999).
A model of the pentose phosphate pathway in the yeast Saccharomyces
cerevisiae
Metabolic Engineering
Catherine Lloyd
This CellML model is known to run in both PCEnv and COR, however at present it does not seem to be recreating the published results - possibly beause we need to include a description of a glucose pulse in the CellML model. We are continuing to work on the model. The units have been checked and they are consistent.
Catherine
Lloyd
May
2007-06-14T08:03:30+12:00
Manfred
Rizzi
100000.0
Sam
Vaseghi
Corrected some of the equations so the CellML model now reflects the model in the original publication.
The University of Auckland
The Bioengineering Institute
sedoheptulose 7-phosphate
C_S7P
ribulose 5-phosphate
C_Ru5P
Added some initial conditions to the ODEs, altered some equations to better reflect the paper, and unit balanced several equations.
xylulose 5-phosphate
C_X5P
keyword
metabolism
yeast
ribose 5-phosphate
C_R5P