Artificial neural networks have basically nothing to do with actual biological neurons. First, neuroscientists do not have even a decent understanding of biological neurons: you cannot say that neural networks mimic neurons when we don't understand biological neurons. Of the bajillion things we do know neurons do, neural networks do on the order of 1% of those things. On the flip side, neural networks do a ton of things that biological neurons do not (like backpropagation(!)* ).
* In fairness, Hinton hypothesizes the brain has a way of doing backprop, but what he talks about only barely resembles actual backprop.