The homology of an $E_2$-algebra is a Gerstenhaber algebra.

How precisely is the Gerstenhaber structure related to the $E_2$-structure?

Obviously, the Gerstenhaber product is the commutative product that the $E_2$-product induces in homology.

But what precisely is the interpretation of the Gerstenhaber bracket? It cannot be the commutator of the $E_2$-product because that would be zero in homology, right?

Thanks for any hints.