Chemistry / Molecular Biology

In mathematics, the tokens of our multicomputational model are abstract mathematical statements, and the “events between them” represent the application of laws of inference. In thinking about chemistry we can make a much more concrete multicomputational model: the tokens are actual individual molecules (represented say in terms of bonds) and the events are reactions between them. The token-event graph is then a “molecular-dynamics-level” representation of a chemical process. But what would a more macroscopic observer make of this? One “chemical reference frame” might combine all molecules of a particular chemical species at a given time. The result would be a fairly traditional “chemical reaction network”. (The choice of time slices might reflect external conditions; the number of microscopic paths might reflect chemical concentrations.) Within the chemical reaction network a “synthesis pathway” is much like a proof in mathematics: a path that leads from certain “inputs” in the network to a particular output. (And, yes, one can imagine “chemical undecidability” where it’s not clear if there’s any path of any length to make “this from that”.) A chemical reaction network is much like a multiway graph of the kind we’ve shown for string substitutions. And just as in that case we can define a branchial graph that describes relationships between chemical species associated with their “entanglement” through participation in reactions—and from which a kind of “chemical space” emerges in which different chemical species appear at different positions. There’s plenty to study at this “species level”. (As a simple example, small loops represent equilibria but larger ones can reflect the effect of protecting groups, or give signatures of autocatalysis.) But I suspect there’s even more to learn by looking at something closer to the underlying token-event graph. In standard chemistry, one typically characterizes the state of a chemical system at a particular time in terms of the concentrations of different chemical species. But ultimately there’s much more information in the whole token-event graph—for example about the entangled histories of individual molecules and the causal relationships between events that produced them (which at a physical level might be manifest in things like correlations in orientations or momenta of molecules). Does this matter, though? Perhaps not for chemistry as it’s done today. But in thinking about molecular computing it may be crucial—and perhaps it’s also necessary for understanding molecular biology. Processes in molecular biology today tend to be described—like chemical reactions—in terms of networks and concentrations of chemical species. (There are additional pieces having to do with the spatial structure of molecules and the possibility of “events at different places on a molecule”.) But maybe the whole “entanglement network” at the “token-event level” is also important in successfully capturing what amounts to the molecular-scale “chemical information processing” going on in molecular biology. Just as in genetics in the 1950s there was a crucial realization that information could be stored not just, say, in concentrations of molecules, but in the structure of a single molecule, so perhaps now we need to consider that information can be stored—and processed—in a dynamic network of molecular interactions. And that in addition to seeing how things behave in “chemical species space”, one also needs to consider how they behave in branchial space. And in the end, maybe it just takes a different kind of “chemical observer” (and maybe one more embedded in the system and operating at a molecular scale) to be able to understand the “overall architecture” of many of the molecular computations that go on in biology. (By the way, it’s worth emphasizing that even though branchial space is what’s associated with quantum mechanics in our model of fundamental physics we’re not thinking about the “physical quantum mechanics” of molecules here. It’s just that through the general structure of multicomputational models “quantum formalism” may end up being central to molecular computing and molecular biology even though—ironically enough—there doesn’t have to be anything “physically quantum” about them.)