wolf1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000090). Biomodels 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." JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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Abstract
Autonomous metabolic oscillations were observed in aerobic continuous culture of Saccharomyces cerevisiae. Experimental investigation of the underlying mechanism revealed that several pathways and regulatory couplings are involved. Here a hypothetical mechanism including the sulfate assimilation pathway, ethanol degradation and respiration is transformed into a mathematical model. Simulations confirm the ability of the model to produce limit cycle oscillations which reproduce most of the characteristic features of the system.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
Id Name Spatial dimensions Size
c0 external 3.0 1.0
c1 cytosol 3.0 1.0
c2 mitochondria 3.0 1.0
Id Name Initial quantity Compartment Fixed
A2c ADP 0.5 c1 (cytosol)
A2m ADP_mit 0.5 c2 (mitochondria)
A3c ATP 1.5 c1 (cytosol)
A3m ATP_mit 1.5 c2 (mitochondria)
C1 C1 0.0 c2 (mitochondria)
C2 C2 0.0 c2 (mitochondria)
H2O H2O 0.0 c2 (mitochondria)
Hm Hm 0.0 c2 (mitochondria)
Ho Ho 0.0 c1 (cytosol)
N1 NAD 0.0 c1 (cytosol)
N2 NADH 2.0 c1 (cytosol)
PPi PPi 0.0 c1 (cytosol)
S1 S1 1.5 c2 (mitochondria)
S2 S2 0.5 c2 (mitochondria)
aco AcCoA 0.3 c1 (cytosol)
aps APS 0.5 c1 (cytosol)
cys CYS 0.3 c1 (cytosol)
eth EtOH 4.0 c1 (cytosol)
eth_ex EtOH_ex 0.0 c0 (external)
hyd H2S 0.5 c1 (cytosol)
oah OAH 1.5 c1 (cytosol)
oxy O2 7.0 c2 (mitochondria)
oxy_ex O2_ex 0.0 c0 (external)
pap PAPS 0.4 c1 (cytosol)
sul SO4 0.4 c1 (cytosol)
sul_ex SO4_ex 0.0 c0 (external)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
v1 v1 sul_ex > sul

c0 * k_v0 / (1 + pow(cys / Kc, n))
v10 v10 oxy_ex > oxy

c0 * k_v10
v11a vET1 C1 + Hm + N2 > C2 + Ho + N1

c2 * k11 * N2 * oxy / ((a * N2 + oxy) * (1 + pow(hyd / Kh, m)))
v11a2 vET2 C2 + oxy > C1 + H2O

c2 * k11 * N2 * oxy / ((a * N2 + oxy) * (1 + pow(hyd / Kh, m)))
v11b vSYNT Ho + A2m > Hm + A3m

c2 * 3 * k11 * N2 * oxy / ((a * N2 + oxy) * (1 + pow(hyd / Kh, m))) * A2m / (Ka + A2m)
v12 v12 A3c > A2c

c1 * k12 * A3c
v13 v13 eth_ex > eth

c0 * k_v13
v14 v14 oxy > oxy_ex

c2 * k14 * oxy
v15 v15 aco > oah

c1 * k15 * aco
v16 v16 A2c + A3m > A2m + A3c

c2 * k16 * A3m * A2c
v17 v17 hyd > ∅

c1 * k17 * hyd
v18 v18 oah > ∅

c1 * k18 * oah
v2 v2 sul + A3c > aps + PPi

c1 * k2 * sul * A3c
v3 v3 aps + A3c > pap + A2c

c1 * k3 * aps * A3c
v4 v4 pap + {3.0}N2 > hyd + {3.0}N1

c1 * k4 * pap * N2
v5 v5 hyd + oah > cys

c1 * k5 * hyd * oah
v6 v6 cys > ∅

c1 * k6 * cys
v7 v7 eth + {2.0}N1 > aco + {2.0}N2

c1 * k7 * eth * N1
v8 v8 S2 + aco > S1

c2 * k8 * aco * S2
v9 v9 S1 + {4.0}N1 > S2 + {4.0}N2

c2 * k9 * S1 * N1
vLEAK vLEAK Ho > Hm

0

Global parameters

Id Value
Ac 2.0
Am 2.0
Ka 1.0
Kc 0.1
Kh 0.5
N 2.0
S 2.0
a 0.1
k11 10.0
k12 5.0
k14 10.0
k15 5.0
k16 10.0
k17 0.02
k18 1.0
k2 0.2
k3 0.2
k4 0.2
k5 0.1
k6 0.12
k7 10.0
k8 10.0
k9 10.0
k_v0 1.6
k_v10 80.0
k_v13 4.0
m 4.0
n 4.0

Local parameters

Id Value Reaction

Assignment rules

Definition
S2 = S - S1
N1 = N - N2
A2m = Am - A3m
A2c = Ac - A3c

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments