The tau of continuous feeding on simple foods

Chemical reactor theory under the premise of maximization of net rate of nutrient absorption has been used to predict throughput time, tau, of digesta in animals. Animals that feed on hexoses, such as many vertebrate fruit and nectar eaters, are of central interest in testing reactor theory because they use no hydrolysis before absorption and, hence, should provide valuable, simplified test cases. Graphical methods based on batch reactors and used to make such predictions in the past can give optimal gut throughput times (tauopt) identical with predictions from continuous plug-flow reactor models derived here: in animals with passive, linear uptake alone, tauopt should decline as hexose concentration of food increases. If saturating active uptake is involved, however, a minimum in tauopt (maximum in ingestion rate) is predicted at intermediate hexose concentration, the exact location of this minimum depending on costs of ingestion as well as on uptake kinetics. That is, tauopt first falls to a minimum with increasing hexose concentration and then increases. Optimal throughput time rises as uptake sites become saturated because there is little gross gain and no net gain from increased ingestion rate when uptake already is nearly saturated. It also rises with increasing costs of ingestion. The continuous-time analytic solutions provided here further make the novel and very general prediction of high sensitivity to decreasing tau below tauopt.