A Topological Method for Vector-Valued and Nth Order Nonlinear Boundary Value Problems

The use of topological methods in the analysts of second order nonlinear boundary value problems (BVP for short) in Rn of the form (E) [see pdf for notation] (C) [see pdf for notation] has recently attracted the interest of many authors (e.g. [1], [4], [5],[8],[11]) for the case in which n = 1. The prevalent approaches have been the topological method of Wazewski [1,8], the shooting method via the maximum principle, and the Kneser-Hukuhara continuum theorem [1]. A common ingredient in these approaches is the use of upper and lower solutions to obtain bounds on the solutions

Stability and Generalized Hopf Bifurcation Through a Reduction Principle

We are interested in obtaining an analysis of the bifurcating periodic orbits arising in the generalized Hopf bifurcation problems in Rn. The existence of these periodic orbits has often been obtained by using such techniques as the Liapunov-Schmidt method or topological degree arguments (see [5] and its references). Our approach, on the other hand, is based upon stability properties of the equilibrium point of the unperturbed system. Andronov et. al. [1] showed the fruitfulness of this approach in studying bifurcation problems in R2 (for more recent papers see Negrini and Salvadori 161 and Bernfeld and Salvadori [2]). In the case of R2, in contrast to that of Rn, n \u3e 2, the stability arguments can be effectively applied because of the Poincaré-Bendixson theory. Bifurcation problems in Rn can be reduced to that of R2 when two dimensional invariant manifolds are known to exist. The existence of such manifolds occurs, for example when the unperturbed system contains only two purely imaginary eigenvalues

Effects of Diabetes and Insulin on α-amylase Messenger RNA Levels in Rat Parotid Glands

Previous studies have shown that amylase levels are reduced significantly in the pancreas and parotid gland of diabetic rats and that insulin reverses this effect and increases the secretory protein levels. In the pancreas, these changes in amylase protein levels are accompanied by parallel changes in amylase mRNA levels. In the present study, the effects of diabetes and subsequent insulin treatments on contents (per cell) of amylase protein and its mRNA in parotid glands were compared in rats rendered diabetic with an injection of a beta-cell toxin, streptozotocin (STZ). Both amylase protein and its mRNA contents were reduced significantly in diabetic rats, compared with control rats, and this reduction was reversed following insulin injections of diabetic rats. In insulin-injected diabetic rats, amylase protein contents increased before a detectable increase in amylase mRNA levels was seen. The mRNA contents of a non-secretory protein, actin, did not change during diabetogenesis or subsequent insulin treatments. The reductions in parotid contents of amylase and its mRNA in diabetic rats and the reversal of these changes by insulin are similar to those changes that occur in the pancreas under the same conditions. However, the magnitude of these changes in parotid glands was much smaller than in the pancreas, and the effect of insulin on amylase mRNA synthesis was not as immediate as in the latter gland.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67977/2/10.1177_00220345900690081001.pd

The transformation of Saperda calcarata (Coleoptera: Cerambycidae) into a cellulose digester through the inclusion of fungal enzymes in its diet

The larvae of the aspen borer, Saperda calcarata , which feed on the inner bark and sapwood of living aspen stems, are unable to digest cellulose. However, they can be transformed into cellulose digesters by adding the active cellulase complex of the fungus, Penicillium funiculosum to their diet. S. calcarata larvae are preadapted to exploit the digestive potential of ingested microbial enzymes. We argue that ingested fungal enzymes may be responsible for cellulose digestion in many, perhaps most or even all, cellulose digesting cerambycid beetles.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47768/1/442_2004_Article_BF00377333.pd

Characterization of Digestive Enzymes of Bruchid Parasitoids–Initial Steps for Environmental Risk Assessment of Genetically Modified Legumes

Genetically modified (GM) legumes expressing the α-amylase inhibitor 1 (αAI-1) from Phaseolus vulgaris L. or cysteine protease inhibitors are resistant to several bruchid pests (Coleoptera: Chrysomelidae). In addition, the combination of plant resistance factors together with hymenopteran parasitoids can substantially increase the bruchid control provided by the resistance alone. If the strategy of combining a bruchid-resistant GM legume and biological control is to be effective, the insecticidal trait must not adversely affect bruchid antagonists. The environmental risk assessment of such GM legumes includes the characterization of the targeted enzymes in the beneficial species and the assessment of the in vitro susceptibility to the resistance factor. The digestive physiology of bruchid parasitoids remain relatively unknown, and their susceptibility to αAI-1 has never been investigated. We have detected α-amylase and serine protease activities in all five bruchid parasitoid species tested. Thus, the deployment of GM legumes expressing cysteine protease inhibitors to control bruchids should be compatible with the use of parasitoids. In vitro inhibition studies showed that sensitivity of α-amylase activity to αAI-1 in the parasitoids was comparable to that in the target species. Direct feeding assays revealed that harmful effects of α-amylase inhibitors on bruchid parasitoids cannot be discounted and need further evaluation

Impact of down-regulation of starch branching enzyme IIb in rice by artificial microRNA- and hairpin RNA-mediated RNA silencing

The inactivation of starch branching IIb (SBEIIb) in rice is traditionally associated with elevated apparent amylose content, increased peak gelatinization temperature, and a decreased proportion of short amylopectin branches. To elucidate further the structural and functional role of this enzyme, the phenotypic effects of down-regulating SBEIIb expression in rice endosperm were characterized by artificial microRNA (amiRNA) and hairpin RNA (hp-RNA) gene silencing. The results showed that RNA silencing of SBEIIb expression in rice grains did not affect the expression of other major isoforms of starch branching enzymes or starch synthases. Structural analyses of debranched starch showed that the doubling of apparent amylose content was not due to an increase in the relative proportion of amylose chains but instead was due to significantly elevated levels of long amylopectin and intermediate chains. Rices altered by the amiRNA technique produced a more extreme starch phenotype than those modified using the hp-RNA technique, with a greater increase in the proportion of long amylopectin and intermediate chains. The more pronounced starch structural modifications produced in the amiRNA lines led to more severe alterations in starch granule morphology and crystallinity as well as digestibility of freshly cooked grains. The potential role of attenuating SBEIIb expression in generating starch with elevated levels of resistant starch and lower glycaemic index is discussed