Hopf bifurcation in an age-structured predator-prey system with Beddington-DeAngelis functional response and constant harvesting.

In this paper, an age-structured predator-prey system with Beddington-DeAngelis (B-D) type functional response, prey refuge and harvesting is investigated, where the predator fertility function f(a) and the maturation function ß ( a ) are assumed to be piecewise functions related to their maturation period τ . Firstly, we rewrite the original system as a non-densely defined abstract Cauchy problem and show the existence of solutions. In particular, we discuss the existence and uniqueness of a positive equilibrium of the system. Secondly, we consider the maturation period τ as a bifurcation parameter and show the existence of Hopf bifurcation at the positive equilibrium by applying the integrated semigroup theory and Hopf bifurcation theorem. Moreover, the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are studied by applying the center manifold theorem and normal form theory. Finally, some numerical simulations are given to illustrate of the theoretical results and a brief discussion is presented.

Alcohol dehydrogenases from Kluyveromyces marxianus: heterologous expression in Escherichia coli and biochemical characterization.

BACKGROUND: Kluyveromyces marxianus has recently become a species of interest for ethanol production since it can produce ethanol at high temperature and on a wide variety of substrates. However, the reason why this yeast can produce ethanol at high temperature is largely unknown. RESULTS: The ethanol fermentation capability of K. marxianus GX-UN120 at 40°Ð¡ was found to be the same as that of Saccharomyces cerevisiae at 34°Ð¡. Zymogram analysis showed that alcohol dehydrogenase 1 (KmAdh1) was largely induced during ethanol production, KmAdh4 was constitutively expressed at a lower level and KmAdh2 and KmAdh3 were almost undetectable. The genes encoding the four alcohol dehydrogenases (ADHs) were cloned from strain GX-UN120. Each KmADH was expressed in Escherichia coli and each recombinant protein was digested with enterokinase to remove the fusion protein. The optimum pH of the purified recombinant KmAdh1 was 8.0 and that of KmAdh2, KmAdh3 and KmAdh4 was 7.0. The optimum temperatures of KmAdh1, KmAdh2, KmAdh3 and KmAdh4 were 50, 45, 55 and 45°C, respectively. The K(m) values of the recombinant KmAdh1 and KmAdh2 were 4.0 and 1.2 mM for acetaldehyde and 39.7 and 49.5 mM for ethanol, respectively. The V(max) values of the recombinant KmAdh1 and KmAdh2 were 114.9 and 21.6 µmol min⁻¹ mg⁻¹ for acetaldehyde and 57.5 and 1.8 µmol min⁻¹ mg⁻¹ for ethanol, respectively. KmAdh3 and KmAdh4 catalyze the oxidation reaction of ethanol to acetaldehyde but not the reduction reaction of acetaldehyde to ethanol, and the K(m) values of the recombinant KmAdh3 and KmAdh4 were 26.0 and 17.0 mM for ethanol, respectively. The V(max) values of the recombinant KmAdh3 and KmAdh4 were 12.8 and 56.2 µmol min⁻¹ mg⁻¹ for ethanol, respectively. CONCLUSION: These data in this study collectively indicate that KmAdh1 is the primary ADH responsible for the production of ethanol from the reduction of acetaldehyde in K. marxianus. The relatively high optimum temperature of KmAdh1 may partially explain the ability of K. marxianus to produce ethanol at high temperature. Understanding the biochemical characteristics of KmAdhs will enhance our fundamental knowledge of the metabolism of ethanol fermentation in K. marxianus.