Fix: no flux in TCA when maximizing ATP production

[feiranl]

Description of the issue:

When using minimal media as the set up and maximizing ATP as the objective for simulation, TCA is skipped while glycine-serine cycle is utilized due to a higher ATP yield on this pathway.

matlab model 8.5.0 main branch
load('yeast-GEM.mat')
model = minimal_Y6(model)
model = changeRxnBounds(model,'r_4046',1000,'u');
model = changeRxnBounds(model,'r_4046',0,'l');
model = changeObjective(model,'r_4046',1);
sol=optimizeCbModel(model,'max','one')

current rxn|flux|equation

rxn	flux	equation
r_0226	17	ADP[m] + 3 H+[c] + phosphate[m] => ATP[m] + 2 H+[m] + H2O[m]
r_0438	24	ferrocytochrome c[m] + 1.266 H+[m] + 0.25 oxygen[m] => ferricytochrome c[m] + 0.633 H+[c] + 0.5 H2O[m]
r_0439	12	2 ferricytochrome c[m] + 1.266 H+[m] + ubiquinol-6[m] => 2 ferrocytochrome c[m] + 2.532 H+[c] + ubiquinone-6[m]
r_0445	4	formate[c] + NAD[c] => carbon dioxide[c] + NADH[c]
r_0446	-4	ATP[c] + formate[c] + THF[c] <=> 10-formyl-THF[c] + ADP[c] + phosphate[c]
r_0450	1	D-fructose 1,6-bisphosphate[c] <=> dihydroxyacetone phosphate[c] + glyceraldehyde 3-phosphate[c]
r_0467	1	D-glucose 6-phosphate[c] <=> D-fructose 6-phosphate[c]
r_0471	2	2-oxoglutarate[c] + ammonium[c] + H+[c] + NADPH[c] => H2O[c] + L-glutamate[c] + NADP(+)[c]
r_0486	2	glyceraldehyde 3-phosphate[c] + NAD[c] + phosphate[c] <=> 1,3-bisphospho-D-glycerate[c] + H+[c] + NADH[c]
r_0501	2	L-glycine[m] + NAD[m] + THF[m] => 5,10-methylenetetrahydrofolate[m] + ammonium[m] + carbon dioxide[m] + NADH[m]
r_0502	4	L-serine[c] + THF[c] <=> 5,10-methylenetetrahydrofolate[c] + H2O[c] + L-glycine[c]
r_0503	-2	L-serine[m] + THF[m] <=> 5,10-methylenetetrahydrofolate[m] + H2O[m] + L-glycine[m]
r_0534	1	ATP[c] + D-glucose[c] => ADP[c] + D-glucose 6-phosphate[c] + H+[c]
r_0658	2	isocitrate[m] + NAD[m] => 2-oxoglutarate[m] + carbon dioxide[m] + NADH[m]
r_0659	-2	isocitrate[c] + NADP(+)[c] <=> 2-oxoglutarate[c] + carbon dioxide[c] + NADPH[c]
r_0725	4	5,10-methenyl-THF[c] + H2O[c] <=> 10-formyl-THF[c] + H+[c]
r_0732	4	5,10-methylenetetrahydrofolate[c] + NADP(+)[c] <=> 5,10-methenyl-THF[c] + NADPH[c]
r_0770	8	H+[c] + NADH[c] + ubiquinone-6[m] => NAD[c] + ubiquinol-6[m]
r_0773	4	H+[m] + NADH[m] + ubiquinone-6[m] => NAD[m] + ubiquinol-6[m]
r_0886	1	ATP[c] + D-fructose 6-phosphate[c] => ADP[c] + D-fructose 1,6-bisphosphate[c] + H+[c]
r_0891	2	3-phosphonato-D-glycerate(3-)[c] + NAD[c] => 3-phospho-hydroxypyruvate[c] + H+[c] + NADH[c]
r_0892	2	1,3-bisphospho-D-glycerate[c] + ADP[c] <=> 3-phosphonato-D-glycerate(3-)[c] + ATP[c]
r_0917	2	3-phospho-serine[c] + H2O[c] => L-serine[c] + phosphate[c]
r_0918	2	3-phospho-hydroxypyruvate[c] + L-glutamate[c] => 2-oxoglutarate[c] + 3-phospho-serine[c]
r_1054	1	dihydroxyacetone phosphate[c] <=> glyceraldehyde 3-phosphate[c]
r_1110	17	ADP[c] + ATP[m] <=> ADP[m] + ATP[c]
r_1112	-2	2-oxoglutarate[c] + citrate[m] <=> 2-oxoglutarate[m] + citrate[c]
r_1128	-2	citrate[c] + isocitrate[m] <=> citrate[m] + isocitrate[c]
r_1166	1	D-glucose[e] => D-glucose[c]
r_1245	17	H+[c] + phosphate[c] => H+[m] + phosphate[m]
r_1277	-6	H2O[e] <=> H2O[c]
r_1672	6	carbon dioxide[e] =>
r_1696	-4	carbon dioxide[c] <=> carbon dioxide[m]
r_1697	6	carbon dioxide[c] <=> carbon dioxide[e]
r_1714	-1	D-glucose[e] <=>
r_1811	4	L-glycine[c] <=> L-glycine[m]
r_1965	-2	ammonium[c] <=> ammonium[m]
r_1978	6	oxygen[c] <=> oxygen[m]
r_1979	6	oxygen[e] <=> oxygen[c]
r_1992	-6	oxygen[e] <=>
r_2045	-2	L-serine[c] <=> L-serine[m]
r_2096	-27	H2O[c] <=> H2O[m]
r_2100	6	H2O[e] <=>
r_4046	21	ATP[c] + H2O[c] => ADP[c] + H+[c] + phosphate[c]

This issue can be fixed by modify the reversibility of r_2045 as done in GECKO paper.

matlab 
model = changeRxnBounds(model,'r_2045',0,'l');
sol=optimizeCbModel(model,'max','one')

updated rxn|flux|equation

ID	NAME	EQUATION
r_0226	15	ADP[m] + 3 H+[c] + phosphate[m] => ATP[m] + 2 H+[m] + H2O[m]
r_0300	2	acetyl-CoA[m] + H2O[m] + oxaloacetate[m] => citrate[m] + coenzyme A[m] + H+[m]
r_0366	2	2-phospho-D-glyceric acid[c] <=> H2O[c] + phosphoenolpyruvate[c]
r_0438	24	ferrocytochrome c[m] + 1.266 H+[m] + 0.25 oxygen[m] => ferricytochrome c[m] + 0.633 H+[c] + 0.5 H2O[m]
r_0439	12	2 ferricytochrome c[m] + 1.266 H+[m] + ubiquinol-6[m] => 2 ferrocytochrome c[m] + 2.532 H+[c] + ubiquinone-6[m]
r_0450	1	D-fructose 1,6-bisphosphate[c] <=> dihydroxyacetone phosphate[c] + glyceraldehyde 3-phosphate[c]
r_0451	2	fumarate[m] + H2O[m] <=> (S)-malate[m]
r_0467	1	D-glucose 6-phosphate[c] <=> D-fructose 6-phosphate[c]
r_0486	2	glyceraldehyde 3-phosphate[c] + NAD[c] + phosphate[c] <=> 1,3-bisphospho-D-glycerate[c] + H+[c] + NADH[c]
r_0505	2	dihydrolipoamide[m] + NAD[m] => H+[m] + lipoamide[m] + NADH[m]
r_0534	1	ATP[c] + D-glucose[c] => ADP[c] + D-glucose 6-phosphate[c] + H+[c]
r_0658	2	isocitrate[m] + NAD[m] => 2-oxoglutarate[m] + carbon dioxide[m] + NADH[m]
r_0713	2	(S)-malate[m] + NAD[m] <=> H+[m] + NADH[m] + oxaloacetate[m]
r_0770	2	H+[c] + NADH[c] + ubiquinone-6[m] => NAD[c] + ubiquinol-6[m]
r_0773	8	H+[m] + NADH[m] + ubiquinone-6[m] => NAD[m] + ubiquinol-6[m]
r_0831	2	coenzyme A[m] + S(8)-succinyldihydrolipoamide[m] => dihydrolipoamide[m] + succinyl-CoA[m]
r_0832	2	2-oxoglutarate[m] + H+[m] + lipoamide[m] => carbon dioxide[m] + S(8)-succinyldihydrolipoamide[m]
r_0886	1	ATP[c] + D-fructose 6-phosphate[c] => ADP[c] + D-fructose 1,6-bisphosphate[c] + H+[c]
r_0892	2	1,3-bisphospho-D-glycerate[c] + ADP[c] <=> 3-phosphonato-D-glycerate(3-)[c] + ATP[c]
r_0893	2	3-phosphonato-D-glycerate(3-)[c] <=> 2-phospho-D-glyceric acid[c]
r_0961	2	coenzyme A[m] + NAD[m] + pyruvate[m] => acetyl-CoA[m] + carbon dioxide[m] + NADH[m]
r_0962	2	ADP[c] + H+[c] + phosphoenolpyruvate[c] => ATP[c] + pyruvate[c]
r_1021	2	succinate[m] + ubiquinone-6[m] <=> fumarate[m] + ubiquinol-6[m]
r_1022	2	ADP[m] + phosphate[m] + succinyl-CoA[m] => ATP[m] + coenzyme A[m] + succinate[m]
r_1054	1	dihydroxyacetone phosphate[c] <=> glyceraldehyde 3-phosphate[c]
r_1110	17	ADP[c] + ATP[m] <=> ADP[m] + ATP[c]
r_1166	1	D-glucose[e] => D-glucose[c]
r_1245	17	H+[c] + phosphate[c] => H+[m] + phosphate[m]
r_1277	-6	H2O[e] <=> H2O[c]
r_2034	2	H+[c] + pyruvate[c] => H+[m] + pyruvate[m]
r_1672	6	carbon dioxide[e] =>
r_1696	-6	carbon dioxide[c] <=> carbon dioxide[m]
r_1697	6	carbon dioxide[c] <=> carbon dioxide[e]
r_1714	-1	D-glucose[e] <=>
r_1978	6	oxygen[c] <=> oxygen[m]
r_1979	6	oxygen[e] <=> oxygen[c]
r_1992	-6	oxygen[e] <=>
r_2096	-23	H2O[c] <=> H2O[m]
r_2100	6	H2O[e] <=>
r_4046	19	ATP[c] + H2O[c] => ADP[c] + H+[c] + phosphate[c]
r_4262	2	citrate[m] <=> isocitrate[m]

I hereby confirm that I have:

• Tested my code with all requirements for running the model
• Done this analysis in the main branch of the repository
• Checked that a similar issue does not exist already
• If needed, asked first in the Gitter chat room about the issue

[edkerk]

While blocking reverse reaction of r_2045 might prevent this to occur, is there not another approach that makes more sense biologically? Isn't transmembrane transport of serine by diffusion, which is r_2045 representing, unlikely to be unidirectional? What about blocking reverse direction of r_0446, which has an estimated Gibbs free energy of -25 kcal/mol?

[feiranl]

I will update the reversibility for the reaction r_0446.

[edkerk]

@feiranl Did this resolve the issue?

[feiranl]

@edkerk yes, Will update that tomorrow.

[feiranl]

Flux distribution after update. Now TCA has flux when ATP is maximized.

rxn	flux	equation
r_0226	15.192	ADP [mitochondrion] + 3 H+ [cytoplasm] + phosphate [mitochondrion] -> ATP [mitochondrion] + 2 H+ [mitochondrion] + H2O [mitochondrion]
r_0300	2	acetyl-CoA [mitochondrion] + H2O [mitochondrion] + oxaloacetate [mitochondrion] -> citrate [mitochondrion] + coenzyme A [mitochondrion] + H+ [mitochondrion]
r_0366	2	2-phospho-D-glyceric acid [cytoplasm] <=> H2O [cytoplasm] + phosphoenolpyruvate [cytoplasm]
r_0438	24	ferrocytochrome c [mitochondrion] + 1.266 H+ [mitochondrion] + 0.25 oxygen [mitochondrion] -> ferricytochrome c [mitochondrion] + 0.633 H+ [cytoplasm] + 0.5 H2O [mitochondrion]
r_0439	12	2 ferricytochrome c [mitochondrion] + 1.266 H+ [mitochondrion] + ubiquinol-6 [mitochondrion] -> 2 ferrocytochrome c [mitochondrion] + 2.532 H+ [cytoplasm] + ubiquinone-6 [mitochondrion]
r_0450	1	D-fructose 1,6-bisphosphate [cytoplasm] <=> dihydroxyacetone phosphate [cytoplasm] + glyceraldehyde 3-phosphate [cytoplasm]
r_0451	2	fumarate [mitochondrion] + H2O [mitochondrion] <=> (S)-malate [mitochondrion]
r_0467	1	D-glucose 6-phosphate [cytoplasm] <=> D-fructose 6-phosphate [cytoplasm]
r_0486	2	glyceraldehyde 3-phosphate [cytoplasm] + NAD [cytoplasm] + phosphate [cytoplasm] <=> 1,3-bisphospho-D-glycerate [cytoplasm] + H+ [cytoplasm] + NADH [cytoplasm]
r_0505	2	dihydrolipoamide [mitochondrion] + NAD [mitochondrion] -> H+ [mitochondrion] + lipoamide [mitochondrion] + NADH [mitochondrion]
r_0534	1	ATP [cytoplasm] + D-glucose [cytoplasm] -> ADP [cytoplasm] + D-glucose 6-phosphate [cytoplasm] + H+ [cytoplasm]
r_0658	2	isocitrate [mitochondrion] + NAD [mitochondrion] -> 2-oxoglutarate [mitochondrion] + carbon dioxide [mitochondrion] + NADH [mitochondrion]
r_0713	2	(S)-malate [mitochondrion] + NAD [mitochondrion] <=> H+ [mitochondrion] + NADH [mitochondrion] + oxaloacetate [mitochondrion]
r_0770	2	H+ [cytoplasm] + NADH [cytoplasm] + ubiquinone-6 [mitochondrion] -> NAD [cytoplasm] + ubiquinol-6 [mitochondrion]
r_0773	8	H+ [mitochondrion] + NADH [mitochondrion] + ubiquinone-6 [mitochondrion] -> NAD [mitochondrion] + ubiquinol-6 [mitochondrion]
r_0831	2	coenzyme A [mitochondrion] + S(8)-succinyldihydrolipoamide [mitochondrion] -> dihydrolipoamide [mitochondrion] + succinyl-CoA [mitochondrion]
r_0832	2	2-oxoglutarate [mitochondrion] + H+ [mitochondrion] + lipoamide [mitochondrion] -> carbon dioxide [mitochondrion] + S(8)-succinyldihydrolipoamide [mitochondrion]
r_0886	1	ATP [cytoplasm] + D-fructose 6-phosphate [cytoplasm] -> ADP [cytoplasm] + D-fructose 1,6-bisphosphate [cytoplasm] + H+ [cytoplasm]
r_0892	2	1,3-bisphospho-D-glycerate [cytoplasm] + ADP [cytoplasm] <=> 3-phosphonato-D-glycerate(3-) [cytoplasm] + ATP [cytoplasm]
r_0893	2	3-phosphonato-D-glycerate(3-) [cytoplasm] <=> 2-phospho-D-glyceric acid [cytoplasm]
r_0961	2	coenzyme A [mitochondrion] + NAD [mitochondrion] + pyruvate [mitochondrion] -> acetyl-CoA [mitochondrion] + carbon dioxide [mitochondrion] + NADH [mitochondrion]
r_0962	2	ADP [cytoplasm] + H+ [cytoplasm] + phosphoenolpyruvate [cytoplasm] -> ATP [cytoplasm] + pyruvate [cytoplasm]
r_1021	2	succinate [mitochondrion] + ubiquinone-6 [mitochondrion] <=> fumarate [mitochondrion] + ubiquinol-6 [mitochondrion]
r_1022	2	ADP [mitochondrion] + phosphate [mitochondrion] + succinyl-CoA [mitochondrion] -> ATP [mitochondrion] + coenzyme A [mitochondrion] + succinate [mitochondrion]
r_1054	1	dihydroxyacetone phosphate [cytoplasm] <=> glyceraldehyde 3-phosphate [cytoplasm]
r_1110	17.192	ADP [cytoplasm] + ATP [mitochondrion] <=> ADP [mitochondrion] + ATP [cytoplasm]
r_1166	1	D-glucose [extracellular] -> D-glucose [cytoplasm]
r_1245	17.192	H+ [cytoplasm] + phosphate [cytoplasm] -> H+ [mitochondrion] + phosphate [mitochondrion]
r_1277	-6	H2O [extracellular] <=> H2O [cytoplasm]
r_2034	2	H+ [cytoplasm] + pyruvate [cytoplasm] -> H+ [mitochondrion] + pyruvate [mitochondrion]
r_1672	6	carbon dioxide [extracellular] ->
r_1696	-6	carbon dioxide [cytoplasm] <=> carbon dioxide [mitochondrion]
r_1697	6	carbon dioxide [cytoplasm] <=> carbon dioxide [extracellular]
r_1714	-1	D-glucose [extracellular] <=>
r_1978	6	oxygen [cytoplasm] <=> oxygen [mitochondrion]
r_1979	6	oxygen [extracellular] <=> oxygen [cytoplasm]
r_1992	-6	oxygen [extracellular] <=>
r_2096	-23.192	H2O [cytoplasm] <=> H2O [mitochondrion]
r_2100	6	H2O [extracellular] <=>
r_4046	19.192	ATP [cytoplasm] + H2O [cytoplasm] -> ADP [cytoplasm] + H+ [cytoplasm] + phosphate [cytoplasm]
r_4262	2	citrate [mitochondrion] <=> isocitrate [mitochondrion]