In my opinion, I do not think DNN has a close relation with brain or neuron. In my case, I would prefer to regard the relevance between these two terms as a coincidence rather than a kind of inspiration. 

Firstly, I want to consider the structure which make them work. In my experience of coding, I gradually discover that all the complicated algorithm repeat the same structure. First breaking a complicated problem into many easier subunits, and then design functions for each unit. Finally, combining them all together and then we get that expected algorithm. And between the gap of each subunit, we need to give them a kind of connection to make the whole stuff works. That is the input and output of taken by each function. And for the case of DNN, those inputs and outputs are vectors or arrays filled with numbers. For brain and neuron, it also works in a similar way. The neurons in our bodies communicates with each other through the electrical signal, and with those neurons, our brains can process a very complicated algorithm and then give us the useful information. They both works in a structure built with multiple layers. But I think it is not because that DNN is inspired by the brain/neuron so it has this structure. It is because it has to use this structure which is similar to the brain/neuron to make itself possible so it got its name.

Secondly, I want to compare how they respectively achieve ‘learning’ and ‘intelligence’. For DNN, it learn things in a very inflexible way. It evaluates itself with a fixed algorithm. It knows if it makes progress by a fixed algorithm. It makes a change and tries to perform better according to a fixed algorithm. All the stuff is related to algorithm, calculus and numbers. When we code, we always try to transform how we think in natural language and then translate the natural language in to programming language. In this case, we also do this, it is convenient and useful. However, it is sometime more complicated then the thought in our brain, and it is sometimes limited in one situation and lack of flexibility. For example, DNN can only work in a fixed pattern, it can only get the answer from the calculation, just like the score for our exam. But in the real world, we seldom judge someone or something only by its score. And sometimes we really do so because some limitation in the real world. But there is no limitation in our brain when we are thinking. So I think there is still a remarkable difference between DNN and brain/neuron.