On the choice of the optimal periodic operation for a continuous fermentation process

In this contribution we investigate the impact of the forcing waveform on the productivity of a continuous bioreactor governed by an unstructured, nonlinear kinetic model. The (periodic) forcing is applied on the substrate concentration in the feed. To this end, some alternative waveforms commonly encountered in practice are evaluated and their performance is compared. An analytical/numerical approach is used. The preliminary analytical step is based on the π‐criterion that gives useful information for small amplitudes. The extension to larger amplitudes, when significant improvements are expected, is then performed through a continuation‐optimization procedure. It is found that the choice of the specific waveform has an impact on the performance of the process and there is no unique best forcing for any process condition, but its choice depends on the operating parameters and the forcing amplitude and frequency values. Further, the influence of the waveform functions on the wash‐out conditions are extensively examined. The analysis shows that all the waveforms examined in this work may lead to significant enlargement of the nontrivial regime with respect to a steady state operation. In particular, square‐wave forcing leads in practice to the extinction of the wash‐out conditions for any feed substrate concentration and for a well defined choice of the forcing parameters. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

The dynamics of two-species allelopathic competition with optimal harvesting

This paper analyses a bionomic model of two competitive species in the presence of toxicity with different harvesting efforts. An interesting dynamics in the first quadrant is analysed and two saddle-node bifurcations are detected for different bifurcation parameters. It is noted that under certain parametric restrictions, the model has a unique positive equilibrium point that is globally asymptotically stable whenever it is locally stable. It is also noted that the model can have zero, one or two feasible equilibria appearing through saddle-node bifurcations. The non-existence of a limit cycle in the interior of the first quadrant is also discussed using the Poincare–Dulac criteria. The saddle-node bifurcations are studied using Sotomayor's theorem. Numerical simulations are carried out to validate the analytical findings. The conditions for the existence of bionomic equilibria are discussed and an optimal harvesting policy is derived using Pontryagin's maximum principle.     

Cycles in cannibalistic egg-larval interactions

A model of a cannibalistic larval-egg interaction such as occurs in Tribolium is developed which leads to a system of nonlinear Volterra integral equations. I determine the local stability properties of the unique equilibrium point of the model. A Hopf bifurcation analysis shows that the model always undergoes a subcritical bifurcation when stability is lost. Numerical solutions confirm the presence of multiple attractors over a range of parameter values. The form of the cycles observed in the numerical solutions is analogous to that observed in laboratory populations of Tribolium.     

The occurrence and distribution of certain polypeptides within the human carotid body

Summary Both carotid bodies from 26 patients coming to necropsy were fixed in 10% neutral buffered formalin and sections 4 m thick were stained for various peptides by use of the immunogold technique. The results show that the human carotid body contains met- and leu-enkephalin, substance P, vasoactive intestinal peptide (VIP), neurotensin and bombesin. The distribution of these six peptides within the carotid body differs. Thus met- and leu-enkephalin are both present predominantly within glomic chief cells but with a marked tendency to favour the dark variant of these cells. Substance P and VIP both show a weak immunoreactivity in comparison to the enkephalins and are present in all three variants of chief cell. Neurotensin shows the weakest immunoreactivity of all and is restricted to a few glomic chief cells in a minority of cases. Bombesin also shows a weak immunoreactivity in glomic chief cells but a strong reaction in glomic arteries and arterioles. In these vessels bombesin appears to be confined to smooth muscle cells in the media but we cannot say whether it is secreted by them or merely bound to receptor sites on their membranes. These findings are related to quantitative data on the concentration of peptides in the human carotid body from a previous paper with which we were associated.     

Oscillations in a system with material cycling

We study a system of two integrodifierential equations which models the evolution of a biotic species feeding on an abiotic resource. We also consider nutrient recycling with time delay. By Hopf bifurcation theory we prove the existence of stable oscillations for a range of values of the input of nutrients.Work performed within the activity of the research group Evolution Equations and Physico-Mathematical Applications, M.P.I. (Italy), and under the auspices of G.N.F.M., C.N.R. (Italy)     

Cannibalism as a life boat mechanism

Under certain conditions a cannibalistic population can survive when food for the adults is too scarce to support a non-cannibalistic population. Cannibalism can have this lifeboat effect if (i) the juveniles feed on a resource inaccessible to the adults; and (ii) the adults are cannibalistic and thus incorporate indirectly the inaccessible resource. Using a simple model we conclude that the mechanism works when, at low population densities, the average yield, in terms of new offspring, due to the energy provided by one cannibalized juvenile is larger than one.     

Ontogeny of substance P-, CGRP-, and VIP-containing nerve fibers in the amphibian carotid labyrinth of the bullfrog,Rana catesbeiana

Summary The ontogeny of substance P, CGRP (calcitonin gene-related peptide), and VIP (vasoactive intestinal polypeptide) containing nerve fibers in the carotid labyrinth of the bullfrog, Rana catesbeiana, was examined by the peroxidase-antiperoxidase method. The time of appearance of these three peptides was different for each. First, CGRP fibers appeared in the wall of the carotid arch and external carotid arteries, and in a thin septum between these two arteries at an early stage of larval development (stage III). At stage V, substance P immunoreactive fibers appeared, and VIP fibers were detected at the early metamorphic stage (stage XXII). Up to the completion of metamorphosis, the number of these fibers remained low. From 1 to 5 weeks after metamorphosis, substance P, CGRP, and VIP fibers increased in number to varying degrees. By 8 weeks after metamorphosis, the distribution and abundance of these fibers closely resembled those of the adults. Some CGRP and VIP immunoreactive glomus cells were found at the stages immediately before and after the completion of metamorphosis. These findings suggest that substance P, CGRP, and VIP fibers during larval development and metamorphosis may be nonfunctional, and start to participate in vascular regulation only after metamorphosis. The transient CGRP and VIP in some glomus cells may be important for the development of the labyrinth, or may take part in vascular regulation through the close apposition of the glomus and smooth muscle cells (g-s connection).     

Some epidemiological models with nonlinear incidence

Epidemiological models with nonlinear incidence rates can have very different dynamic behaviors than those with the usual bilinear incidence rate. The first model considered here includes vital dynamics and a disease process where susceptibles become exposed, then infectious, then removed with temporary immunity and then susceptible again. When the equilibria and stability are investigated, it is found that multiple equilibria exist for some parameter values and periodic solutions can arise by Hopf bifurcation from the larger endemic equilibrium. Many results analogous to those in the first model are obtained for the second model which has a delay in the removed class but no exposed class.Research supported in part by Centers for Disease Control Contract 200-87-0515. Support services provided at University House Research Center at the University of IowaResearch supported in part by NSERC A-8965 and the University of Victoria President's Committee on Faculty Research and Travel     

Oscillatory coexistence in a food chain model with competing predators

A food chain model with two predators feeding on a single prey in a chemostat is studied. Using a multiparameter bifurcation analysis, we find parameters values for which there is stable oscillatory coexistence of the predators. It is also shown how these coexistent states provide a transition between two possible states of competitive exclusion. It is shown that the competitive exclusion principle need not hold if one or more of the predators has oscillatory behavior in the absence of other predators.This work was partially supported by National Science Foundation Grant MCS 83-01881     

Biogenic Amine-Stimulated Cyclic Adenosine-3'',5''-Monophosphate Formation in the Rat Carotid Body

The subcutaneous injection of isoprenaline, salbutamol, histamine, and adrenaline to rats, which were subsequently killed by microwave irradiation, resulted in a rapid increase in the cyclic AMP content of the carotid body. On the other hand, noradrenaline, dopamine, adenosine, and 5-hydroxytryptamine, at doses at least 100 times greater than that of isoprenaline, did not significantly alter the cyclic nucleotide content in vivo. The response to isoprenaline was dose related, with an ED50 of 15 micrograms X kg-1, and reached a peak level 1-1.5 min after injection. Incubation of intact carotid bodies with isoprenaline (10(-5) M) in vitro also resulted in a 10-fold increase in cyclic AMP content. The in vivo response to isoprenaline could be blocked stereo-selectively by propranolol, and ICI 118.551, a beta 2-selective antagonist, blocks the isoprenaline-elicited increase in cyclic AMP completely at a dose of 30 micrograms X kg-1; whereas betaxolol, a beta 1-selective antagonist, was ineffective, even at a dose of 300 micrograms X kg-1. Hypoxia (5% oxygen in 95% N2) did not result in a significant increase in the cyclic AMP content, nor did it significantly alter the isoprenaline-stimulated increase in the cyclic AMP content of the rat carotid body. These results suggest that some catecholamines may stimulate cyclic AMP formation by interacting with a beta 2-adrenoceptor in the rat carotid body.