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A protease is a type of protein; there are several proteases, each with different functions.

If we want to refer to all those functions in general, is proteases functions correctly written? Should it be protease functions?

I mean to say functions of proteases.

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    The use of the plural noun as modifier is known here, but is quite rare (and, I'd say, unidiomatic). If you wish to emphasise that you are considering different proteases each with different subsets of functions, you're better with 'the [different] funtions of [the different] proteases'. If you will disambiguate later in the text (or disambiguation isn't important), the general term 'protease functions' may certainly be used: it means 'functions of [the] proteases' and is fine grammatically / with regard to agreement. – Edwin Ashworth Apr 5 '16 at 19:05
  • I believe that if you were talking about a set of specific proteases (whatever that means - a small group of molecules i suppose), eg if you were looking in a microscope and could see four protease molecules, and each had a different function, you would say "The proteases' functions", talking about four different functions of four different proteases, but as @EdwinAshworth says it would be clearer to say "the functions of the proteases". – Max Williams Apr 7 '16 at 10:03
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Although there are several proteases, in this case protease is a noun used attributively, and it remains singular.

Protease Functions.

Compare 'Bean salad.' A bean salad can have several sorts of bean in it and continues to be a bean salad. A cook can make a variety of bean salads. Someone with a healthy appetite can eat several bean salads with red beans and haricot beans and broad beans. They are all bean salads.

The same applies to carboxypeptidase α and β which both share Carboxypeptidase functions.

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