Cool stuff. I used to study genetics and systems biology and I really enjoyed “thinking computationally” about what it was cells and organisms were doing, especially during development. I do find, though, that practitioners of the more formal sciences (computer science, mathematics, physics) who find their way to biology have a tendency to parachute into some existing problem, come up with a relatively simple model that predicts some things correctly by conveniently ignoring a lot of experimental data, getting it published, and declaring the problem solved (this basically). Some of the papers linked in the OP come off this way, although I have only skimmed them so perhaps I am being ungenerous.
I think the situation is that the concept of “computability” and “computational models” are simple and predictable, but can explain complex behavior like we see in biological systems. Whether or not the concept of computability can construct these complex systems, however, is another question entirely. I’m hopeful that the field of self-organization can shed some light on this issue of constructing complex systems that work. FWIW I like this short interview with De Landa as an intro to this way of thinking.
Note: Luca Cardelli was also involved with the early days of Haskell and related paradigms of function programming in the 70’s (early 70’s?). It seems his FP-influences have transferred nicely to biology, a turn of events that both fascinates and boggles me. Anyway, if you want to challenge your understanding of “computability”, some of his papers might stretch your thinking - they certainly have stretched mine :)