Summary of the genes shown in those illustrations:
(Copied, paraphrased and modified from a website entitled "Tetrahydrobiopterin Deficiency")

The most well-established function of BH4 in humans is as the cofactor for the aromatic amino acid hydroxylase enzymes phenylalanine hydroxylase (PAH), tyrosine hydroxylase (TH), and tryptophan hydroxylase (TPH); the latter 2 are key enzymes in biogenic amine biosynthesis (including serotonin and dopamine). In addition to the hydroxylation of aromatic amino acids, BH4 serves as the cofactor for nitric oxide synthase and glyceryl-ether monooxygenase.

BH4 is synthesized from guanosine triphosphate (GTP) in at least 4 enzymatic steps by the action of 3 different enzymes. GTP cyclohydrolase I (GTPCH), the first enzyme in BH4 biosynthesis, catalyzes the formation of 7,8-dihydroneopterin triphosphate from GTP in a single reaction step. GTPCH is subject to feedback inhibition by BH4 which does so by binding GTPCH feedback regulatory protein.

In the next step, 6-pyruvoyl-tetrahydropterin synthase (PTPS) catalyzes the conversion of 7,8-dihydroneopterin triphosphate to 6-pyruvoyl-tetrahydropterin.

Sepiapterin reductase (SR) is a nicotinamide adenine dinucleotide phosphate, reduced form, (NADPH) oxidoreductase. It is required for the final 2-step reduction of the diketo intermediate 6-pyruvoyl-tetrahydropterin to BH4. Because patients with SR deficiency seem to make pterins, it is clear other enzymes can function in the pathway. Among these may be various aldo-keto reductase (AKR) family and short-chain dehydrogenase/reductase (SDR) family proteins, including an alpha-hydroxysteroid dehydrogenase and aldose reductase.

During the enzymatic hydroxylation of aromatic amino acids, molecular oxygen is consumed and BH4 is peroxidated and oxidized. The pterin intermediate is subsequently reduced back to BH4 by 2 enzymes and a reduced pyridine nucleotide (ie, NADH) in a complex recycling reaction.

Molecular oxygen (O2) is first bound to BH4 to form an unstable 4 a-peroxy-tetrahydrobiopterin. The monooxygenation of aromatic amino acids is thus concomitant with oxidation of BH4 to 4 a-hydroxy-tetrahydrobiopterin (pterin-4 a-carbinolamine). Pterin-4 a-carbinolamine is subsequently dehydrated to quinonoid-dihydrobiopterin (q-dihydrobiopterin) and water by the specific and highly efficient pterin-4 a-carbinolamine dehydratase (PCD). In the last step of BH4 recycling, q-dihydrobiopterin is reduced back to BH4 by the NADH-dependent dihydropteridine reductase (DHPR).

GTP Cyclohydrolase I (aka GCH, GCH1, GTPCH)
C. e. gene: cat-4 / F32G8.6

GTP Cyclohydrolase feedback regulatory protein (aka GFRP)
C. e. gene: Y38C1AA.13 (currently a predicted pseudogene)

Pyruvoyl Tetrahydropterin Synthetase (aka PTPS, PTS, 6-Pyruvoyl Tetrahydropterin Synthetase)
C. e. gene: ptps-1 / B0041.6

Sepiapterin Reductase (aka SR, Pyruvoyl tetrahydropterin reductase)
C. e. gene: no obvious homolog
Many candidate reductase/dehydrogenases that could function as an SR enzyme, including short-chain dehydrogenases: dhs-11, dhs-15, dhs-21, dhs -25, dhs-13

Enzymes (& C. elegans genes) in Tetrahydrobiopterin (BH4) regeneration / recycling pathway:

Pterin-4-alpha-carbinolamine dehydratase (aka PCD, PCBD, DCoH)
C. e. gene: pcbd-1 / T10B11.1

Dihydropteridine reductase (aka DHPR, Quinoid dihydropteridine reductase, QDPR)
C. e. gene: qdpr-1 / T03F6.1