MATHEMATICAL METHODS IN WATER QUALITY CONTROL

In this paper we intend to summarize the most important mathematical statistical methods which play a basic role in water quality control. In the first section we will use a random variable model and it will be shown how to observe the changing of water quality by testing homogeneity. In the second section we will compare the means of the random variables. A few new idea will be introduced in the third and fourth sections based on stochastic process models

Penicillin-binding proteins of protoplast and sporoplast membranes of Streptomyces griseus strains

Membrane-bound penicillin-binding proteins (PBPs) of two Streptomyces griseus strains that sporulate well in liquid and solid medium have been investigated during the course of their life-cycle. The PBP patterns were analyzed by sodium dodecylsulphate polyacrylamide-gel electrophoresis and fluorography. One strain (No. 45 H) has only a single band (mol wt: 27,000) in early log phase, and two additional PBPs of higher mol wt (69,000 and 80,000) in the late log phase. The other strain (No. 2682) possessed two bands with mol wts 27,000 and 38,000 which did not change during its vegetative phase. In strain No. 2682, a new PBP with a mol wt of 58,000 appeared in spore membranes while one of those (mol wt 38,000) present in mycelial membranes disappeared. Our results suggest that appearance of the new PBP in the spore may be associated with the sporulation process. The major PBP band (mol wt: 27,000) present in all stages of the life cycle of these strains, may be characteristic of S. griseus while the other PBPs reflect certain stages of the life cycle. A new method was developed for the production of spore protoplasts by consecutive enzymatic treatments.

Estrogen induces estrogen receptor alpha-dependent cAMP response element-binding protein phosphorylation via mitogen activated protein kinase pathway in basal forebrain cholinergic neurons in vivo

In addition to classical genomic mechanisms, estrogen also exerts nonclassical effects via a signal transduction system on neurons. To study whether estrogen has a nonclassical effect on basal forebrain cholinergic system, we measured the intensity of cAMP response element-binding protein (CREB) phosphorylation (pCREB) in cholinergic neurons after administration of 17 beta-estradiol to ovariectomized (OVX) mice. A significant time-dependent increase in the number of pCREB-positive cholinergic cells was detected after estrogen administration in the medial septum-diagonal band (MS-DB) and the substantia innominata ( SI). The increase was first observed 15 min after estrogen administration. The role of classical estrogen receptors (ERs) was evaluated using ER knock-out mice in vivo. The estrogen-induced CREB phosphorylation in cholinergic neurons was present in ER beta knock-out mice but completely absent in ER beta knock-out mice in MS-DB and SI. A series of in vitro studies demonstrated that estrogen acted directly on cholinergic neurons. Selective blockade of the mitogen activated protein kinase (MAPK) pathway in vivo completely prevented estrogen-induced CREB phosphorylation in cholinergic neurons in MS-DB and SI. In contrast, blockade of protein kinase A (PKA) was effective only in SI. Finally, studies in intact female mice revealed levels of CREB phosphorylation within cholinergic neurons that were similar to those of estrogen-treated OVX mice. These observations demonstrate an ER alpha-mediated nonclassical effect of estrogen on the cholinergic neurons and that these actions are present under physiological conditions. They also reveal the role of MAPK and PKA-MAPK pathway activation in nonclassical estrogen signaling in the basal forebrain cholinergic neurons in vivo

How Gaussian competition leads to lumpy or uniform species distributions

A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource spectrum, or their distribution is 'lumped' (or 'clumped'), consisting of clusters of species with similar resource use that are separated by gaps in resource space. Which of these outcomes will occur crucially depends on the competition kernel, which reflects the shape of the resource utilization pattern of the competing species. Most models considered in the literature assume a Gaussian competition kernel. This is unfortunate, since predictions based on such a Gaussian assumption are not robust. In fact, Gaussian kernels are a border case scenario, and slight deviations from this function can lead to either uniform or lumped species distributions. Here we illustrate the non-robustness of the Gaussian assumption by simulating different implementations of the standard competition model with constant carrying capacity. In this scenario, lumped species distributions can come about by secondary ecological or evolutionary mechanisms or by details of the numerical implementation of the model. We analyze the origin of this sensitivity and discuss it in the context of recent applications of the model.Comment: 11 pages, 3 figures, revised versio

Glutamate Uptake Triggers Transporter-Mediated GABA Release from Astrocytes

Background: Glutamate (Glu) and c-aminobutyric acid (GABA) transporters play important roles in regulating neuronal activity. Glu is removed from the extracellular space dominantly by glial transporters. In contrast, GABA is mainly taken up by neurons. However, the glial GABA transporter subtypes share their localization with the Glu transporters and their expression is confined to the same subpopulation of astrocytes, raising the possibility of cooperation between Glu and GABA transport processes. Methodology/Principal Findings: Here we used diverse biological models both in vitro and in vivo to explore the interplay between these processes. We found that removal of Glu by astrocytic transporters triggers an elevation in the extracellular level of GABA. This coupling between excitatory and inhibitory signaling was found to be independent of Glu receptor-mediated depolarization, external presence of Ca2+ and glutamate decarboxylase activity. It was abolished in the presence of non-transportable blockers of glial Glu or GABA transporters, suggesting that the concerted action of these transporters underlies the process. Conclusions/Significance: Our results suggest that activation of Glu transporters results in GABA release through reversal of glial GABA transporters. This transporter-mediated interplay represents a direct link between inhibitory and excitatory neurotransmission and may function as a negative feedback combating intense excitation in pathological conditions such as epilepsy or ischemia

Where Two Are Fighting, the Third Wins: Stronger Selection Facilitates Greater Polymorphism in Traits Conferring Competition-Dispersal Tradeoffs

A major conundrum in evolution is that, despite natural selection, polymorphism is still omnipresent in nature: Numerous species exhibit multiple morphs, namely several abundant values of an important trait. Polymorphism is particularly prevalent in asymmetric traits, which are beneficial to their carrier in disruptive competitive interference but at the same time bear disadvantages in other aspects, such as greater mortality or lower fecundity. Here we focus on asymmetric traits in which a better competitor disperses fewer offspring in the absence of competition. We report a general pattern in which polymorphic populations emerge when disruptive selection increases: The stronger the selection, the greater the number of morphs that evolve. This pattern is general and is insensitive to the form of the fitness function. The pattern is somewhat counterintuitive since directional selection is excepted to sharpen the trait distribution and thereby reduce its diversity (but note that similar patterns were suggested in studies that demonstrated increased biodiversity as local selection increases in ecological communities). We explain the underlying mechanism in which stronger selection drives the population towards more competitive values of the trait, which in turn reduces the population density, thereby enabling lesser competitors to stably persist with reduced need to directly compete. Thus, we believe that the pattern is more general and may apply to asymmetric traits more broadly. This robust pattern suggests a comparative, unified explanation to a variety of polymorphic traits in nature.ope