Great visualization in this post.

Could neural networks in general be compared to the way information is stored in DNA?

The encoder/decoder is in the process and the data loop would be the same as life in this metaphor. The training conditions of the NN are constrained such that it is able to store small variational changes, success accumulates by survival over many trial and error experiments. Like animals in nature DeepMind and OpenAI have shown that NN's can evolve into sophisticated local optimum solutions for specific game environments.