All diagrams in supply, synthesis and cofactors
BH4 synthesis and cofactor recycling
Making BH4, recycling it after hydroxylases and redox salvage are distinct. The hydroxylase cofactor cycle is not identical to NOS redox salvage.
BH4 synthesis and cofactor recycling
Scoped educational mechanism

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BH4 is made through GCH1, PTPS and SPR-dependent reactions and serves several enzymes. Aromatic-amino-acid hydroxylation generates a hydroxylated pterin intermediate; PCD and QDPR participate in regeneration. NOS has a different redox cycle, and oxidised BH2 can be reduced through DHFR-dependent salvage. These routes should not be collapsed into one chemical loop. Inherited biochemical disorders require their own clinical and laboratory assessment; ordinary ADHD does not by itself demonstrate such a disorder.
What the diagram shows
BH4 is made through GCH1, PTPS and SPR-dependent reactions and serves several enzymes. Aromatic-amino-acid hydroxylation generates a hydroxylated pterin intermediate; PCD and QDPR participate in regeneration. NOS has a different redox cycle, and oxidised BH2 can be reduced through DHFR-dependent salvage. These routes should not be collapsed into one chemical loop. Inherited biochemical disorders require their own clinical and laboratory assessment; ordinary ADHD does not by itself demonstrate such a disorder.