evolving petri nets to represent metabolic pathways
Given concentrations of metabolites over a sequence of time steps, the metabolic pathway prediction problem seeks a set of reactions and rate constants for them that could yield the concentration-time data. Such metabolic pathways can be modeled with Petri nets: bipartite graphs whose nodes are called places and transitions and in which tokens move from place to place through the transitions. Thus the pathway prediction problem can be addressed by searching a space of Petri nets, and such a search can be undertaken evolutionarily.Here, a genetic algorithm performs such a search. The GA seeks only the net's structure; a hill-climbing step applied as part of evaluation approximates parameters associated with the net's transitions. On one contrived problem instance, the GA sometimes identifies the pathway used to generate the given data, but on a second contrived instance, apparently no harder, it fails. On an instance drawn from real biology---the pathway for phospholipid synthesis---the genetic algorithm identifies a Petri net whose pathway is very similar, but not identical to, the real one. In all three cases, the GA develops Petri nets that represent pathways that closely reproduce the target concentration-time data.
petri nets metabolic pathways genetic algorithms evolutionary search