Universal Turing Machine can be boiled down to two components. Infinite tape of input and an action table, a finite state machine that moves read/write head along the tape and writes to it depending on input provided by the tape.
From this point of view cells have some properties very similar to UTMs, the DNA is in an essence a tape of instructions that can be read and written to. Rest of the cell behaves similar to action table, defining rules that guide which part of DNA is read and when it happens, a moving "head" along DNA "tape".
Subquestion 1: DNA can be used for computation. Can entire cell be used for similar purposes?
Subquestion 2: If every living organism contains at least one UTM is it possible that all organism are in some sense Turing Complete?