The Agouti (agouti signaling protein, ASIP) gene produces a protein that regulates the distribution of black pigment (eumelanin) within the hair shaft.
The dominant allele 'A' produces hair shafts with alternating bands of yellow and black colour, ending with black tips, while the recessive allele 'a' produces a cat that is self-colored (solid) when 2 copies of a are present. The effect of the agouti protein on orange pigment is limited, thus tabby striping may still be seen on cats that are a/a for agouti.
The Agouti gene is responsible for the tabby coat markings. If a cat carries the Agouti gene (genotype AA or Aa), its coat shows the typical markings of 'tabby'. If the cat is non-Agouti (aa), the coat is single-coloured (solid).
The Charcoal gene (Apb) is very special as it is originates from the Asian Leopard cat Agouti gene. This explains why it is only seen in Bengal cats. Coat markings of a dark face mask and a dark thick dorsal stripe (cape) are also known as 'Zorro markings'.
Charcoal cats would have Apb/a at the agouti gene.