Human

Are cells not computers in some way? We are made of cells and cells work with chromosomes. Chromosomes are coded with ATGC pairs and each triplet is capable of creating proteins.

And the activation and deactivation of some triplet happens on response to presence of proteins. So, chromosomes are code and input and output is proteins. So, if our fundamental building blocks are computable in nature, what does it make us?

Physical systems are computable only in approximation. And quantum uncertainty throws another wrench into it. We also know that arbitrarily small rounding errors in the computation can lead to arbitrarily large differences with the actual system down the road. No, cells are not computers (in the sense of the Turing model). (However, that doesn’t mean that one can’t still consider them to be mechanistic and “soulless”.)

I meant to say in the way that there is well defined set of alphabets (A, T, G, C) and each triplet of these alphabet is responsible for specific protein to be created and combination of such protein make each cell what it is. (There are 20 different proteins for humans and we have four alphabets coming in triplets. So, if it was pair or quadreplets responsible for proteins, it would have too much or too little. They are not perfect but given the condition, there is some balance)

A single alphabet change in specific places can cause genetic defects like sickle cell anemia. And activation of which one has to generate protein (execute) is dependent on presence of certain things encoded as proteins again.

And viruses when enter a cell, the cell starts to execute viral genetic material. Even if these are not exactly Turing compatible, do they not mimic many aspects of computation?

There are some aspects that have some similarity to computation, but also many that are not. If your aim is “aren’t we really just computers”, that doesn’t actually work.

That’s not to say that computers couldn’t do what the brain does, including consciousness and emotions, but that wouldn’t have any particular relation to how DNA/RNA and protein synthesis works.