Chemical master equation and Langevin regimes for a gene transcription model

Gene transcription models must take account of intrinsic stochasticity. The Chemical Master Equation framework is based on modelling assumptions that are highly appropriate for this context, and the Stochastic Simulation Algorithm (also known as Gillespie's algorithm) allows for practical simulations to be performed. However, for large networks and/or fast reactions, such computations can be prohibitatively expensive. The Chemical Langevin regime replaces the massive ordinary dierential equation system with a small stochastic dierential equation system that is more amenable to computation. Although the transition from Chemical Master Equation to Chemical Langevin Equation can be justied rigorously in the large system size limit, there is very little guidance available about how closely the two models match for a xed system. Here, we consider a transcription model from the recent literature and show that it is possible to compare rst and second moments in the two stochastic settings. To analyse the Chemical Master Equation we use some recent work of Gadgil, Lee and Othmer, and to analyse the Chemical Langevin Equation we use Ito's Lemma. We nd that there is a perfect match|both modelling regimes give the same means, variances and correlations for all components in the system. The model that we analyse involves 'unimolecular reactions', and we nish with some numerical simulations involving dimerization to show that the means and variances in the two regimes can also be close when more general 'bimolecular reactions' are involved

Noise Management by Molecular Networks

Fluctuations in the copy number of key regulatory macromolecules (“noise”) may cause physiological heterogeneity in populations of (isogenic) cells. The kinetics of processes and their wiring in molecular networks can modulate this molecular noise. Here we present a theoretical framework to study the principles of noise management by the molecular networks in living cells. The theory makes use of the natural, hierarchical organization of those networks and makes their noise management more understandable in terms of network structure. Principles governing noise management by ultrasensitive systems, signaling cascades, gene networks and feedback circuitry are discovered using this approach. For a few frequently occurring network motifs we show how they manage noise. We derive simple and intuitive equations for noise in molecule copy numbers as a determinant of physiological heterogeneity. We show how noise levels and signal sensitivity can be set independently in molecular networks, but often changes in signal sensitivity affect noise propagation. Using theory and simulations, we show that negative feedback can both enhance and reduce noise. We identify a trade-off; noise reduction in one molecular intermediate by negative feedback is at the expense of increased noise in the levels of other molecules along the feedback loop. The reactants of the processes that are strongly (cooperatively) regulated, so as to allow for negative feedback with a high strength, will display enhanced noise

Source patterns of potentially toxic elements (PTEs) and mining activity contamination level in soils of Taltal city (northern Chile)

Mining activities are among the main sources of potentially toxic elements (PTEs) in the environment which constitute a real concern worldwide, especially in developing countries. These activities have been carried out for more than a century in Chile, South America, where, as evidence of incorrect waste disposal practices, several abandoned mining waste deposits were left behind. This study aimed to understand multi-elements geochemistry, source patterns and mobility of PTEs in soils of the Taltal urban area (northern Chile). Topsoil samples (n = 125) were collected in the urban area of Taltal city (6 km2) where physicochemical properties (redox potential, electric conductivity and pH) as well as chemical concentrations for 35 elements were determined by inductively coupled plasma optical emission spectrometer. Data were treated following a robust workflow, which included factor analysis (based on ilr-transformed data), a new robust compositional contamination index (RCCI), and fractal/multi-fractal interpolation in GIS environment. This approach allowed to generate significant elemental associations, identifying pool of elements related either to the geological background, pedogenic processes accompanying soil formation or to anthropogenic activities. In particular, the study eventually focused on a pool of 6 PTEs (As, Cd, Cr, Cu, Pb, and Zn), their spatial distribution in the Taltal city, and the potential sources and mechanisms controlling their concentrations. Results showed generally low baseline values of PTEs in most sites of the surveyed area. On a smaller number of sites, however, higher values concentrations of As, Cd, Cu, Zn and Pb were found. These corresponded to very high RCCI contamination level and were correlated to potential anthropogenic sources, such as the abandoned mining waste deposits in the north-eastern part of the Taltal city. This study highlighted new and significant insight on the contamination levels of Taltal city, and its links with anthropogenic activities. Further research is considered to be crucial to extend this assessment to the entire region. This would provide a comprehensive overview and vital information for the development of intervention limits and guide environmental legislation for these pollutants in Chilean soils

Groundwater Quality, Health Risk Assessment, and Source Distribution of Heavy Metals Contamination around Chromite Mines: Application of GIS, Sustainable Groundwater Management, Geostatistics, PCAMLR, and PMF Receptor Model

Groundwater contamination by heavy metals (HMs) released by weathering and mineral dissolution of granite, gneisses, ultramafic, and basaltic rock composition causes human health concerns worldwide. This paper evaluated the heavy metals (HMs) concentrations and physicochemical variables of groundwater around enriched chromite mines of Malakand, Pakistan, with particular emphasis on water quality, hydro-geochemistry, spatial distribution, geochemical speciation, and human health impacts. To better understand the groundwater hydrogeochemical profile and HMs enrichment, groundwater samples were collected from the mining region (n = 35), non-mining region (n = 20), and chromite mines water (n = 5) and then analyzed using ICPMS (Agilent 7500 ICPMS). The ranges of concentrations in the mining, non-mining, and chromite mines water were 0.02–4.5, 0.02–2.3, and 5.8–6.0 mg/L for CR, 0.4–3.8, 0.05–3.6, and 3.2–5.8 mg/L for Ni, and 0.05–0.8, 0.05–0.8, and 0.6–1.2 mg/L for Mn. Geochemical speciation of groundwater variables such as OH−, H+, Cr+2, Cr+3, Cr+6, Ni+2, Mn+2, and Mn+3 was assessed by atomic fluorescence spectrometry (AFS). Geochemical speciation determined the mobilization, reactivity, and toxicity of HMs in complex groundwater systems. Groundwater facies showed 45% CaHCO3, 30% NaHCO3, 23.4% NaCl, and 1.6% Ca-Mg-Cl water types. The noncarcinogenic and carcinogenic risk of HMs outlined via hazard quotient (HQ) and total hazard indices (THI) showed the following order: Ni > Cr > Mn. Thus, the HHRA model suggested that children are more vulnerable to HMs toxicity than adults. Hierarchical agglomerative cluster analysis (HACA) showed three distinct clusters, namely the least, moderately, and severely polluted clusters, which determined the severity of HMs contamination to be 66.67% overall. The PCAMLR and PMF receptor model suggested geogenic (minerals prospects), anthropogenic (industrial waste and chromite mining practices), and mixed (geogenic and anthropogenic) sources for groundwater contamination. The mineral phases of groundwater suggested saturation and undersaturation. Nemerow’s pollution index (NPI) values determined the unsuitability of groundwater for domestic purposes. The EC, turbidity, PO4−3, Na+, Mg+2, Ca+2, Cr, Ni, and Mn exceeded the guidelines suggested by the World Health Organization (WHO). The HMs contamination and carcinogenic and non-carcinogenic health impacts of HMs showed that the groundwater is extremely unfit for drinking, agriculture, and domestic demands. Therefore, groundwater wells around the mining region need remedial measures. Thus, to overcome the enrichment of HMs in groundwater sources, sustainable management plans are needed to reduce health risks and ensure health safety