So there's not functionality for this exactly in MeTA, but the current tools should be able to give you output from which you can extract these sorts of things.
The first step would be to parse your sentence using something like the
sr_parser object. This will give you a constituency parse tree denoting the (inferred) phrase structure of the sentence. Then, you can look at the nodes of the tree that is returned to identify the subject and predicate and extract the noun/noun phrase from both.
An alternative method, which MeTA doesn't yet implement, would be to use a dependency parse, which gives more direct access to this sort of thing. I would recommend SpaCy or Stanford Dependencies for a good implementation of a dependency parser.
You could also extract dependency parses from constituency parses using a method like described in this paper.