People like to think of blobs interacting and not interacting, but really a cell is more of a crowded mess, see this image for a sense of scale:

http://media.tumblr.com/525082e14ba810bc539c61a646fdba93/tum...

Now picture everything in that image swirling around incredibly fast, with some parts of it (the yellow fibers) more stationary and everything else randomly zooming/bouncing around. There is no equivalent in computation.

A logic may appear to emerge from that jumble, but it's not going to behave very predictably. It takes years of work to be able to predict mechanistically just a tiny aspect of one system, much less the whole cell.

The DNA example you describe is a fascinating area, but it took ~30-50 years to get that understanding, and we still find out new things about it all the time! Now that's a really easy system to study, you can isolate its components, you have clean readouts (new DNA generated, sequencing etc.). How about everything upstream of that? The signaling chain going from the cell surface to the DNA to turn on a gene is quite long, picture at least 3 links with yet another 3 links each, which themselves have separate, independent links back into the DNA.

That's not to say we can't make assumptions and make some progress, see Marcus Colvert's lab:

https://covert.stanford.edu

But it's really, really hard, and an FSA is a quite incomplete way of describing it. Looking at the paper you sent, a useful MFA would have to be insanely large to be useful, and defining all the terms is just an impossibly large task.