The best response we have received to the question, "Does solving the Steiner tree problem shed any light on the biochemical pathway chart?" is below.
Yes. Random approaches to solving interconnectivity problems are useless for all but the most trivial cases. If one doesn't have (n!) time to wait around for a solution, the application of intelligently devised heuristic methods is required. For smallish Steiner Tree problems with fewer nodes, an intelligent agent can trivially generate good solutions by quickly sketching a few lines. For something with the intricate complexity and functionality requirements of a set of biochemical pathways, substantial amounts of careful planning and explicit coordination, not to mention raw and inexplicable artifice, would be required to establish it. I don't think solutions to the Steiner Tree Problem does this justice in the least. It's apparent that nodes in the biochemical pathway are cascade-dependent, with subsequent events (nodes) relying on the successful execution of previous ones. In that way, there are very specific constraints on how nodes must interconnect. Simply finding an efficient method for connecting nodes will just not do. The constraints on the functional interconnectivity of dependent nodes are explicit in the configuration. This problem (evolution of biochemical pathways) is massively more sophisticated than a Steiner Tree or a Traveling Salesman Problem. If solving a simple spanning problem requires intelligent input (in order to avoid waiting until cosmic heat death for a solution) then it stands to reason that a substantially more complex and constrained process would also necessitate a craft, and one of the highest order.
Chance Ratcliff
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