I think the DNA of the neurons is very important. The production of hormones e.g. is of course very relevant for character of a person. This is definitely not stored in the connectome. Hormones are created in the brain and different organs of the body.
The production of neurotransmitter depends on genes too and is therefore not represented by the connectome alone.
We should assume that the character of a person would change a lot if the body is exchanged. On the other hand, memory and knowledge could still be very similar.
Many approaches to cryonics assume that a detailed map of the neural patterns in a brain (via brain scanning technology) may be sufficient, using future technology, to bring that person "back to life." But cognition is greatly shaped by more than just the neural pattern: it is shaped by biology - by the body. (See Noe 2009; Pfeifer et al. 2006; Lakoff & Johnson 1999.)
I admit I'm pretty unfamiliar with the cryonics literature. I assume this is a standard objection, and has standard responses. Where can I find those responses?
Thanks!