Method

We considered 25 enzymatic reactions that affect the urea cycle as shown in Table 1 to build the model.

Table 1 25 enzymatic reactions we considered when we built the model.

Enzyme	Reaction formula	Enzyme number
OTC	carbamoyl phosphate + L-ornithine → L-citrulline + Pi	EC: 2.1.3.3 (argF,argI)
ASS	L-citrulline + L-aspartate + ATP → N-(L-arginino)succinate + AMP + PPi	EC: 6.3.4.5 (argG)
ASL	N-(L-arginino)succinate → fumarate + L-arginine	EC: 4.3.2.1 (argH)
ARG	L-arginine + H2O → L-ornithine + urea	EC: 3.5.3.1 (rocF)
CPS	L-glutamine + HCO3- + H2O + 2ATP → L-glutamate + carbamoyl phosphate + 2ADP + Pi	EC: 6.3.5.5
GOGAT	L-glutamine + 2-oxoglutarate + NADPH + H+ → 2 L-glutamate + NADP+	EC: 1.4.1.13
GS	L-glutamate + NH3 + ATP → L-glutamine + ADP + Pi	EC: 6.3.1.2
GLU	L-glutamine + H2O = L-glutamate + NH3	EC: 3.5.1.2
GDH	2-oxoglutarate + NH3 + NADPH + H+ = L-glutamate + NADP+ + H2O	EC: 1.4.1.4
AAA	acetyl-CoA + L-glutamate → CoASH + N-acetyl-L-glutamate	EC: 2.3.1.1 (argA)
AGK	N-acetyl-L-glutamate + ATP → N-acetyl-L-glutamate 5-phosphate + ADP	EC: 2.7.2.8 (argB)
AGPR	N-acetyl-L-glutamate 5-phosphate + NADPH + H+ → N-acetyl-L-glutamate 5-semialdehyde + NADP+ + Pi	EC: 1.2.1.38 (argC)
AOT	N-acetyl-L-glutamate 5-semialdehyde + L-glutamate → N-acetylornithine + 2-oxoglutarate	EC: 2.6.1.11 (argD)
AO	N-acetylornithine + H2O → L-ornithine + acetate	EC: 3.5.1.16 (argE)
FH	fumarate + H2O → L-malate	EC: 4.2.1.2
MDH	L-malate + NAD+ → oxaloacetate + NADH + H+	EC: 1.1.1.37
AST	oxaloacetate + L-glutamate = L-asparate + 2-oxoglutarate	EC: 2.6.1.1
CS	acetyl-CoA + oxaloacetate + H2O → citrate + CoASH	EC: 2.3.3.1
AH	citrate → isocitrate	EC: 4.2.1.3
IDH	isocitrate + NADP+ → 2-oxoglutarate + NADPH + H+ + CO2	EC: 1.1.1.42
OGDH	2-oxoglutarate + Enzyme N6-(lipoyl)lysine → [dihydrolipoyllysine-residue succinyl transferase]S-succinyldihydrolopiyllysine + CO2	EC: 1.2.4.2
DST	[dihydrolipoyllysine-residue succinyl transferase]S-succinyldihydrolopiyllysine +CoASH → succinyl-CoA + Enzyme N6-(dihydrolipoyl)lysine	EC: 2.3.1.61
E3	Enzyme N6-(dihydrolipoyl)lysine + NAD+ = Enzyme N6-(lipoyl)lysine + NADH + H	EC: 1.8.1.4
SCS	succinate + ADP + Pi → succinate + CoASH + ATP	EC: 6.2.1.5
SDH	succinate + FAD → fumarate + CoASH + FADH2	EC: 1.3.99.1

*Abbreviations of enzymes: OTC, ornithine transcarbamoylase; ASS, argininosuccinate synthase; ASL, argininosuccinate lyase; ARG, arginase; CPS, carbamoyl phosphate synthetase; GOGAT, glutamate synthase; GS, glutamine synthetase; GLU, glutaminase; GDH, glutamate dehydrogenase; AAT, amino-acid N-acetyltransferase; AGK, acetylglutamate kinase; AGPR, N-acetyl-γ-glutamylphosphate reductase; AOT, acetylornithine transaminase; AO, acetylornithine deacetylase; FH, fumarate hydratase; MDH, malate dehydrogenase; AST, asparate aminotransferase; CS, citrate (Si)-synthase; AH, aconitate hydratase; IDH, isocitrate dehydrogenase; OGDH, oxoglutarate dehydrogenase; DST, dihydrolipoyllysine-residue succinyltransferase; E3, dihydrolipoyl dehydrogenase; SCS, succinyl-CoA synthetase; SDH, succinate dehydrogenase Reversible and irreversible reactions are indicated, in the reaction equations, by the symbols = and →, respectively.