The part of the cat which causes allergies in people is a protein produced mainly in the cat’s saliva and sebaceous glands called ‘Fel d 1’. It is produced in the cat’s skin. In addition Fel d 4 is present in the cat’s saliva. These proteins are called ‘allergens’ from the standpoint of people who are allergic to them.
‘Proteins’ consist of long chains of animo acid residues. Yes, it gets very technical and scientific, but you asked. We don’t know the exact molecular structure of this protein.
These allergens bind to allergic antibodies in allergic cells which produce chemicals such as histamine which in turn cause the allergic symptoms.
We don’t know the purpose of these proteins with regard to the cat’s physiology. But the fact that they are in the cat’s saliva makes it very effective in causing allergies. This is because cats groom themselves a lot. They deposit their saliva on their coats. The saliva dries and the Fel d 1 floats off around the room. It is in the air and on furniture.
This is why people who are allergic to cats get the itches even when they are a considerable distance from the cat. They just have to walk into a home where there is a cat and they can itch depending on the severity of the allergy.
I have never been allergic to cats but years ago a male stray cat regularly visited me. He was not neutered and he produced a lot of Fel D 1. I was slightly allergic to him despite loving him.
Male cats who are not neutered produce the highest levels of the protein while kittens produce less than adults and females produce less than males. Neutered males produce a similar level to that of females. Females, whether intact or spayed produce similar levels of the protein.
There is a lot of discussion on the internet and interest in cat breeds which might be more suited to allergic people because they produce less of this protein. Supporters of the Siberian cat say with confidence that the breed is suited to people who are allergic to cats. They claim that the cat breed is ‘hypoallergenic’. However, my research does not support this assertion. However, perhaps they have a lower production of Fel d 1 than normal.
Another ‘breed’ (unrecognised by the cat associations) which may be less prone to provoke an allergic reaction in humans is the Savannah cat. The high filial variant of this cat, the F3-F1s, is arguably the Ashera GD, an Allerca cat which was promoted as being the only domestic cat suited to people who are allergic to cats. The business did not catch on.
It is a perverse twist of nature that the world’s most common pet causes an allergic reaction in around 10% of people.
Sources: Myself and Wikipedia to fill in some of the gaps.