@tanguatlay,
"Each (of the three emotion systems) are connected to a specific neurobiology in the brain. "
Here's a tip for you to make it easier to determine which word to use. Remove the words in brackets - what would the answer be now? Simple, really. "Each" is connected... ".
The same tip goes for determining which to use in the following:
Him (and I) went to the store.
Him did not
went to the store. I went to the store.
They gave it to her (and I). No. They gave it to her but didn't give it to I.
Write the sentence as if it were just the one person.