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BIOMD0000000090 - Wolf2001_Respiratory_Oscillations

 

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Reference Publication
Publication ID: 11423122
Wolf J, Sohn H, Heinrich R, Kuriyama H.
Mathematical analysis of a mechanism for autonomous metabolic oscillations in continuous culture of Saccharomyces cerevisiae.
FEBS Lett. 2001 Jun; 499(3): 230-234
Humboldt University, Institute of Biology, Theoretical Biophysics, Berlin, Germany. wolf@rz.hu-berlin.de  [more]
Model
Original Model: BIOMD0000000090.xml.origin
Submitter: Rainer Machne
Submission ID: MODEL9728951048
Submission Date: 22 Feb 2007 21:19:56 UTC
Last Modification Date: 05 Jul 2012 14:48:26 UTC
Creation Date: 23 Jan 2007 15:42:43 UTC
Encoders:  Rainer Machne
set #1
bqbiol:occursIn Taxonomy Saccharomyces cerevisiae
bqbiol:isVersionOf Gene Ontology sulfate assimilation, phosphoadenylyl sulfate reduction by phosphoadenylyl-sulfate reductase (thioredoxin)
Notes

This model by Jana Wolf et al. 2001 is the first mechanistic model of respiratory oscillations in Saccharomyces cerevisae. It is based on the assumption that feedback inhibition of cysteine on the sulfate transporters leads to oscillations in this pathway and causes oscillations in respiratory activity via inhibition of cytochrome c oxidase by hydrogen disulfide. The model is qualitative/semi-quantitative and reproduces the respiratory oscillation pattern quite well. It is based on very coarse-grained representations of the mitochondrial tricarboxylic acid cycle and the mitochondrial electron transport chain (oxidative phosphorylation). The sulfate assimilatory pathways also contains some significant simplifcations.

The model corresponds to Fig. 2B of the paper, with a slight phase shift of the oscillations. No initial conditions were given in the paper, and thus they were chosen arbitrarily in a range that lies within the basin of attraction of the limit cycle oscillations. Species IDs correspond to IDs used by the authors, while SBML names are more common abbreviations.

Caveats:
1) Equilibrated transport:
The model assumes fast equilibration between mitochondria and cytoplasm for the metabolites NADH, NAD+, H2S and Acetyl-CoA.
2) Cytosolic mass conservation ATP/ADP:
The model uses mass conservation for cytosolic adenosine nucleotides with is however not encoded in the stoichiometry, but is implied by the lumped reaction v4. This reaction combines the enzymatic reactions of phosphoadenylyl-sulfate reductase (thioredoxin) (yeast protein Met16p, EC 1.8.4.8) and sulfite reductase (NADPH) (subunits Met5p and Met10p, EC 1.8.1.2). EC 1.8.4.8 also has adenosine-3',5'-bismonophosphate (PAP, not to confuse with ID pap in this model, standing for PAPS) as a product. PAP is the substrate for enzyme 3'(2'),5'-bisphosphate nucleotidase (Met22p, EC:3.1.3.7) which would revover AMP (and Pi). Then AMP can be assumed to be equilibrated with ATP and ADP via adenylate kinase, as often used in metabolic models. This AMP production is implied in the mass conservation for cytosolic adenosine phosphates. Accounting for these reactions explicitly does not change the dynamics of the model significantly. An according version can be obtained from the SBML creator (Rainer Machne, mailto:raim@tbi.univie.ac.at).
3) Redox balance:
The enzyme sulfite reductase (NADPH) (subunits Met5p and Met10p, EC 1.8.1.2, part of reaction v4) actually uses NADPH, and the authors assume equilibration of NADH and NADPH. But actually S. cerevisiae specifically is missing the according enzyme transhydrogenase (EC 1.6.1.1 or EC 1.6.1.2). EC 1.8.4.8 also oxidizes thioredoxin and would actually require an additional NADPH for thioredoxin recovery (reduction). This would slightly affect the redox balance of the model.
4) Energy balance:
Reaction v7 lumps NAD-dependent alcohol dehydrogenase (EC 1.1.1.1), aldehyde dehydrogenase (NAD+) (EC 1.2.1.3) and acetyl-CoA synthase (EC 6.2.1.1). The latter reaction would actually consume ATP as a co-factor, producing AMP+PPi, and this is not included in the model. This would slightly bias the model's energy balance.


To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

In summary, you are entitled to use this encoded model in absolutely any manner you deem suitable, verbatim, or with modification, alone or embedded it in a larger context, redistribute it, commercially or not, in a restricted way or not.


To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

Model
Publication ID: 11423122 Submission Date: 22 Feb 2007 21:19:56 UTC Last Modification Date: 05 Jul 2012 14:48:26 UTC Creation Date: 23 Jan 2007 15:42:43 UTC
Mathematical expressions
Reactions
v1 v13 v2 v10
v14 v3 v4 v5
v6 v7 v15 v17
v18 v8 v9 vET1
vET2 v16 vSYNT vLEAK
v12      
Rules
Assignment Rule (variable: ADP) Assignment Rule (variable: ADP_mit) Assignment Rule (variable: NAD) Assignment Rule (variable: S2)
Physical entities
Compartments Species
external SO4_ex EtOH_ex O2_ex
     
cytosol ATP APS PPi
PAPS SO4 EtOH
ADP H2S CYS
NADH NAD AcCoA
OAH Ho  
mitochondria O2 H2O S1
S2 C1 C2
ADP_mit ATP_mit Hm
Global parameters
k_v0 k2 k3 k4
k5 k6 k7 k8
k9 k_v10 k11 k12
k_v13 k14 k15 k16
k17 k18 n m
Ka Kc a Ac
Am S N Kh
Reactions (21)
 
 v1 [SO4_ex] → [SO4];   {CYS}
 
 v13 [EtOH_ex] → [EtOH];  
 
 v2 [SO4] + [ATP] → [APS] + [PPi];  
 
 v10 [O2_ex] → [O2];  
 
 v14 [O2] → [O2_ex];  
 
 v3 [APS] + [ATP] → [PAPS] + [ADP];  
 
 v4 [PAPS] + 3.0 × [NADH] → [H2S] + 3.0 × [NAD];  
 
 v5 [H2S] + [OAH] → [CYS];  
 
 v6 [CYS] → ;  
 
 v7 [EtOH] + 2.0 × [NAD] → [AcCoA] + 2.0 × [NADH];  
 
 v15 [AcCoA] → [OAH];  
 
 v17 [H2S] → ;  
 
 v18 [OAH] → ;  
 
 v8 [S2] + [AcCoA] → [S1];  
 
 v9 [S1] + 4.0 × [NAD] → [S2] + 4.0 × [NADH];  
 
 vET1 [C1] + [Hm] + [NADH] → [C2] + [Ho] + [NAD];   {H2S} , {O2}
 
 vET2 [C2] + [O2] → [C1] + [H2O];   {H2S} , {NADH}
 
 v16 [ADP] + [ATP_mit] → [ADP_mit] + [ATP];  
 
 vSYNT [Ho] + [ADP_mit] → [Hm] + [ATP_mit];   {H2S} , {NADH} , {O2}
 
 vLEAK [Ho] → [Hm];  
 
 v12 [ATP] → [ADP];  
 
Rules (4)
 
 Assignment Rule (name: A2c) ADP = Ac-A3c
 
 Assignment Rule (name: A2m) ADP_mit = Am-A3m
 
 Assignment Rule (name: N1) NAD = N-N2
 
 Assignment Rule (name: S2) S2 = S-S1
 
 external Spatial dimensions: 3.0  Compartment size: 1.0
 
 SO4_ex
Compartment: external
Initial concentration: 0.0
Constant
 
 EtOH_ex
Compartment: external
Initial concentration: 0.0
Constant
 
 O2_ex
Compartment: external
Initial concentration: 0.0
Constant
 
 cytosol Spatial dimensions: 3.0  Compartment size: 1.0
 
 ATP
Compartment: cytosol
Initial concentration: 1.5  (Units: substance)
 
 APS
Compartment: cytosol
Initial concentration: 0.5  (Units: substance)
 
 PPi
Compartment: cytosol
Initial concentration: 0.0
Constant
 
 PAPS
Compartment: cytosol
Initial concentration: 0.4  (Units: substance)
 
 SO4
Compartment: cytosol
Initial concentration: 0.4  (Units: substance)
 
 EtOH
Compartment: cytosol
Initial concentration: 4.0  (Units: substance)
 
  ADP
Compartment: cytosol
Initial concentration: 0.5  (Units: substance)
 
 H2S
Compartment: cytosol
Initial concentration: 0.5  (Units: substance)
 
 CYS
Compartment: cytosol
Initial concentration: 0.3  (Units: substance)
 
 NADH
Compartment: cytosol
Initial concentration: 2.0  (Units: substance)
 
  NAD
Compartment: cytosol
Initial concentration: 0.0  (Units: substance)
 
 AcCoA
Compartment: cytosol
Initial concentration: 0.3  (Units: substance)
 
 OAH
Compartment: cytosol
Initial concentration: 1.5  (Units: substance)
 
 Ho
Compartment: cytosol
Initial concentration: 0.0
Constant
 
 mitochondria Spatial dimensions: 3.0  Compartment size: 1.0
 
 O2
Compartment: mitochondria
Initial concentration: 7.0  (Units: substance)
 
 H2O
Compartment: mitochondria
Initial concentration: 0.0
Constant
 
 S1
Compartment: mitochondria
Initial concentration: 1.5  (Units: substance)
 
  S2
Compartment: mitochondria
Initial concentration: 0.5  (Units: substance)
 
 C1
Compartment: mitochondria
Initial concentration: 0.0
Constant
 
 C2
Compartment: mitochondria
Initial concentration: 0.0
Constant
 
  ADP_mit
Compartment: mitochondria
Initial concentration: 0.5  (Units: substance)
 
 ATP_mit
Compartment: mitochondria
Initial concentration: 1.5  (Units: substance)
 
 Hm
Compartment: mitochondria
Initial concentration: 0.0
Constant
 
Global Parameters (28)
 
   k_v0
Value: 1.6
Constant
 
   k2
Value: 0.2
Constant
 
   k3
Value: 0.2
Constant
 
   k4
Value: 0.2
Constant
 
   k5
Value: 0.1
Constant
 
   k6
Value: 0.12
Constant
 
   k7
Value: 10.0
Constant
 
   k8
Value: 10.0
Constant
 
   k9
Value: 10.0
Constant
 
   k_v10
Value: 80.0
Constant
 
   k11
Value: 10.0
Constant
 
   k12
Value: 5.0
Constant
 
   k_v13
Value: 4.0
Constant
 
   k14
Value: 10.0
Constant
 
   k15
Value: 5.0
Constant
 
   k16
Value: 10.0
Constant
 
   k17
Value: 0.02
Constant
 
   k18
Value: 1.0
Constant
 
   n
Value: 4.0
Constant
 
   m
Value: 4.0
Constant
 
   Ka
Value: 1.0
Constant
 
   Kc
Value: 0.1
Constant
 
   a
Value: 0.1
Constant
 
   Ac
Value: 2.0
Constant
 
   Am
Value: 2.0
Constant
 
   S
Value: 2.0
Constant
 
   N
Value: 2.0
Constant
 
   Kh
Value: 0.5
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000090

Curator's comment: (updated: 22 Feb 2007 16:47:19 GMT)

Figure 2B in the paper has been reproduced by the odeSolver.

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