“There need to be” need or needs?

Which is correct and why?

• There need to be other reactions.
• There needs to be other reactions.

What exactly is the grammatical structure here? I try looking up need vs needs and get esamples of simple nouns to the left and complications for particles and infinitives and whatnot: “Joe needs to wash.” “Joe doesn’t need to wash.”

What’s the case here? Is “need to be” all together the verb? Is “there” used in the same gramatical role as “Joe” or is it fundimentally different?

The first sentence is correct:

There need to be other reactions.

Since "there" is an adverb, it cannot be the subject of a sentence. Another way of writing the same sentence is:

Other reactions need to be there.

In this case it is clear that "other reactions" is the subject of the sentence. It is plural, and therefore only "need to" agrees with it. The confusion comes from the fact that subjects are typically found at the beginning of the sentence.

You can find more information about subjects here.