Modeling animal guts as chemical reactors

Chemical-reactor theory recognizes three ideal reactor types: batch reactors, which are filled with reactants, continuously stirred during the reaction, and then emptied of products after a given reaction period; plug-flow reactors (PFR's), in which reactants continuously enter and products continuously exit with no mixing along the flow path; and continuous-flow, stirred-tank reactors (CSTR's), in which reactants continuously enter and products continuously leave a stirred vessel. Performance equations for these reactors, together with kinetic models for simple enzymatic catalysis and microbially mediated (autocatalytic) digestive fermentation, reveal necessary functional relationships among initial concentrations of the limiting food component, gut volume, throughput time or gut holding time, and digestive reaction kinetics. We use these models to suggest optimization constraints for digestion, analogous to those of optimal foraging theory. Two general predictions are possible. To sustain the greatest digestive production rate in minima of throughput time and gut volume, an animal dependent on its own digestive enzymes should function as a PFR. Animals fermenting refractory materials should combine a CSTR and a PFR in series at all but the slowest throughput rates, when a PFR will suffice. We make specific predictions for deposit feeders because they digest little of the ingested volume, greatly simplifying digestive performance equations and making them ideal subjects for initial tests of our models. The majority conform to the prediction of PFR guts, but some deposit feeders apparently use CSTR-PFR series (terebellimorph polychaetes) and batch processing (asteroids and ophiuroids). We suggest that terebellimorph polychaetes may use the CSTR to overcome digestive-rate constraints imposed by diffusion limitations; asteroids and ophiuroids may use a variety of foraging modes to obtain the highest-quality foods available. We also apply reactor theory to mammalian fermenters because empirical feeding information is extensive. Specifically, we compare the dynamics of foregut versus hindgut fermentation. Foregut fermenters should optimize fermentation with respect to ingested foods and optimize subsequent catalytic digestion with respect to fermentation products. In contrast, hindgut fermenters should optimize foregut catalytic digestion and then optimize fermentation of the residue. According to the principles of dynamic programming, the first digestive stag