On stochastic differential equations and equilibrium distribution: a conditional moment approach

In the recent past there have been several attempts to obtain the equilibrium distribution of multiple populations and their moments in the context of some biological or ecological processes (e.g., Matis and Kiffe in Biometrics 52:155, 1996; Matis and Kiffe in Environ Ecol Stat 9:237, 2002; Renshaw in J Math Appl Med Biol, 15:1, 1998). In particular, the method of cumulant truncation (Matis and Kiffe in Biometrics 52:155, 1996) is a pioneering work in this field. However it requires solving a large number of cumulant functions even in the case of two simultaneous differential equations. Besides the solutions are approximate and depend on the precision of the software. Renshaw (Math Biosci 168:57, 2000) provided a nice extension of the univariate truncated saddle point procedure to multivariate scenarios. But this approach involves a multivariate Newton-Raphson type iterative algorithm whose performance and convergence are critically dependent on the choice of the initial values. In the present paper we propose a new and simple approach to obtain the equilibrium distribution of populations and their conditional moments in a system of differential equations of any dimension. Our proposed method, which is a natural extension of the classical variational matrix approach, has several advantages which are discussed in detail in the paper; among other things it includes the derivation of additional conditions which can be interpreted as environmental surrogates.     

Interaction of plastic particles with heavy metals and the resulting toxicological impacts: a review

Environmental Science and Pollution Research - Interactions of plastic particles with different organic/inorganic pollutants including heavy metals impact their ecotoxicological potential, and...     

Complete degradation of butyl benzyl phthalate by a defined bacterial consortium: role of individual isolates in the assimilation pathway

Two bacterial strains, in consortium, were isolated by enrichment techniques from municipal waste-contaminated soil, which utilized butyl benzyl phthalate (BBP) as the sole carbon source. One of the isolates was identified as Arthrobacter sp. strain WY and the other one as Acinetobacter sp. strain FW based on the morphological, nutritional and biochemical characteristics and 16S rRNA sequence analysis. Various metabolites of BBP engendered by Arthrobacter sp. strain WY were isolated and identified by a combination of chromatographic and spectrophotometric analyses, which revealed a pathway involving monobutylphthalate (MBuP), monobenzyl phthalate (MBzP), phthalic acid and protocatechuic acid. The protocatechuic acid in turn was processed by ortho-cleavage dioxygenase to form beta-carboxy-cis,cis-muconate, ultimately leading to the TCA cycle. The Arthrobacter sp. strain WY could not utilize the hydrolyzed alcohols of BBP. On the other hand, the Acinetobacter sp. strain FW, which by itself could not utilize BBP as the sole carbon source, is capable of utilizing the hydrolyzed alcohols of BBP. Benzyl alcohol was found to be metabolized by the Acinetobacter sp. strain FW via benzaldehyde, benzoic acid and catechol. Catechol was further degraded by ortho-cleavage dioxygenase to cis,cis-muconic acid and subsequently to muconolactone leading to beta-ketoadipate pathway. Moreover, the Acinetobacter sp. strain FW metabolized 1-butanol through butyraldehyde and butyric acid leading to the tricarboxylic acid cycle via beta-oxidation pathway. This is the first report on the complete degradation of BBP by a defined consortium describing the role of its individual constituents in the BBP assimilation pathway.     

Excess chromium alters uptake and translocation of certain nutrients in citrullus

Citrullus plants were grown in refined sand with varying levels of chromium to determine their tolerance limit to excess chromium. The plants were maintained in control nutrient solution for 24 days and on the 25th day chromium as dichromate was added at 0.05, 0.1, 0.2, 0.3 and 0.4 mM. A control set of plants was grown in the same nutrient solution without chromium. At chromium levels >0.2 mM plants showed growth depression, with chlorosis and loss of turgor of middle leaves. Affected leaves had narrow lamina; tendrils were thin, short and did not have coiling property. Later chlorosis became severe and changed to necrosis in patches. Petiole along with lamina became wilted, rugged and hung down due to complete loss of water. At lower chromium concentration, (0.05, 0.1 and 0.2 mM) only depression in growth was observed. With increase in chromium concentration of nutrient solution accumulation of chromium in different parts of Citrullus was increased. Increase in concentrations of phosphorus, manganese and decrease in iron, copper, zinc and sulphur were observed in leaves. Toxicity of chromium was greater at 0.2-0.4 mM, compared to lower concentrations. Threshold of toxicity and toxicity of Cr in old leaves were, respectively, 0.9 and 3.9 microg g(-1) dry matter of citrullus.     

Suppression of testicular steroidogenesis in rats by the organochlorine insecticide Aldrin

Treatment with Aldrin, an organochlorine insecticide, for 13 and 26 days caused suppression of 3beta-hydroxysteroid dehydrogenase (3beta-HSD) and 17beta-hydroxysteroid dehydrogenase (17beta-HSD) activities, along with accumulation of cholesterol in the testicular tissues of adult rats. The same treatment also resulted in a reduction in the nuclear diameter of Leydig cells (LCND) and diameter of seminiferous tubules. A decrease in the weight of testes, seminal vesicles and ventral prostate was also noted. HCG administration in the long-term (26 days) treatment restored the steroidogenic enzymes activity and the nuclear diameter of the Leydig cells. It also reduced the accumulation of tissue cholesterol towards the vehicle-injected controls. The inhibition of steroidogenesis in the testes possibly reflects a decrease in pituitary gonadotrophin release after the treatment with Aldrin.     

A study of ground water contamination by arsenic in the residential area of Behala, Calcutta due to industrial pollution

Due to the discharge of industrial effluent after production of the insecticide Paris-Green [Copper acetoarsenite Cu(CH(3)COO)(2).3Cu(AsO(2))(2)] by a local factory at the P. N. Mitra Lane, Behala, ground water has become contaminated with arsenic. More than seven thousand people were using this arsenic contaminated tube-well water for drinking and house-hold purposes. Many people of the area were hospitalised and symptoms of arsenic toxicity were visible amongst a large number of the population. Analytical study reveals that soil around the area of effluent dumping point, which is at the middle of the locality, contains a very high concentration of arsenic and copper. For the last 20 years this factory had been producing 20 tons of Paris-Green per year and had been dumping its effluent in that area. It seems, the effluent treatment for arsenic removal was not adequate and finally arsenic percolated to the underground aquifers. Consequently, arsenic concentration in the ground water is very high. Both arsenite and arsenate are present in ground water. An alternate source of water other than the ground water is immediately necessary for the people of P. N. Mitra Lane.     

Hydrogeochemical behavior of arsenic-enriched groundwater in the deltaic environment: comparison between two study sites in West Bengal, India

Groundwaters have been collected from deltaic areas of West Bengal (Chakdaha and Baruipur blocks) to record their hydrogeochemical characteristics, and to verify the mechanism of arsenic (As) release. The data reveals that shallow (<70 m) groundwaters in both areas are of Ca-Mg-HCO(3) type; however deeper (>70 m) groundwaters in Baruipur areas are slightly enriched with Na, Cl and SO(4), indicating possible saline water intrusion. The groundwater is anoxic (mean Eh: -124 and -131 mV) with high levels of As (mean: 116 and 293 mug/L), Fe (mean: 4.74 and 3.83 mg/L), PO(4) (mean: 3.73 and 3.21 mg/L) and Mn (mean: 0.37 and 0.49 mg/L), respectively for Chakdaha and Baruipur areas. The observed values of As and bicarbonate (mean: 409 and 499 mg/L) in the shallow aquifer are indicative of redox processes (e.g., oxidation of organic matter) favouring the release of As. Moreover, the presence of DOC in the shallow aquifer suggests that organic matter is young and reactive, and may actively engage in redox driven processes. Our study further confirms that both Fe- and Mn-reduction processes are the dominant mechanisms for As release in these groundwaters.