Isn't this what the entire field of bioinformatics supposed to be about? I know a few people who left it because it doesn't pay as well (in the US) as your average software engineering job.
What OP seems to be talking about is systems modelling, where you model the network of genes and proteins (genomics and proteomics) using tools partly derived from modelling of computer networks.
In other words, a bioinformatician is to a computer scientist what a computational biologist is to a data scientist.
Using biological systems to do computing is more in the realm of "biological computers".