A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Formation mechanisms of secondary organic aerosols in relation to laser printer emissions

Due to their large surface area, complex chemical composition and high alveolar deposition rate, ultrafine particles (UFPs) (< 0.1 ìm) pose a significant risk to human health and their toxicological effects have been acknowledged by the World Health Organisation. Since people spend most of their time indoors, there is a growing concern about the UFPs present in some indoor environments. Recent studies have shown that office machines, in particular laser printers, are a significant indoor source of UFPs. The majority of printer-generated UFPs are organic carbon and it is unlikely that these particles are emitted directly from the printer or its supplies (such as paper and toner powder). Thus, it was hypothesised that these UFPs are secondary organic aerosols (SOA). Considering the widespread use of printers and human exposure to these particles, understanding the processes involved in particle formation is of critical importance. However, few studies have investigated the nature (e.g. volatility, hygroscopicity, composition, size distribution and mixing state) and formation mechanisms of these particles. In order to address this gap in scientific knowledge, a comprehensive study including state-of-art instrumental methods was conducted to characterise the real-time emissions from modern commercial laser printers, including particles, volatile organic compounds (VOCs) and ozone (O3). The morphology, elemental composition, volatility and hygroscopicity of generated particles were also examined. The large set of experimental results was analysed and interpreted to provide insight into: (1) Emissions profiles of laser printers: The results showed that UFPs dominated the number concentrations of generated particles, with a quasi unimodal size distribution observed for all tests. These particles were volatile, non-hygroscopic and mixed both externally and internally. Particle microanalysis indicated that semi-volatile organic compounds occupied the dominant fraction of these particles, with only trace quantities of particles containing Ca and Fe. Furthermore, almost all laser printers tested in this study emitted measurable concentrations of VOCs and O3. A positive correlation between submicron particles and O3 concentrations, as well as a contrasting negative correlation between submicron particles and total VOC concentrations were observed during printing for all tests. These results proved that UFPs generated from laser printers are mainly SOAs. (2) Sources and precursors of generated particles: In order to identify the possible particle sources, particle formation potentials of both the printer components (e.g. fuser roller and lubricant oil) and supplies (e.g. paper and toner powder) were investigated using furnace tests. The VOCs emitted during the experiments were sampled and identified to provide information about particle precursors. The results suggested that all of the tested materials had the potential to generate particles upon heating. Nine unsaturated VOCs were identified from the emissions produced by paper and toner, which may contribute to the formation of UFPs through oxidation reactions with ozone. (3) Factors influencing the particle emission: The factors influencing particle emissions were also investigated by comparing two popular laser printers, one showing particle emissions three orders of magnitude higher than the other. The effects of toner coverage, printing history, type of paper and toner, and working temperature of the fuser roller on particle number emissions were examined. The results showed that the temperature of the fuser roller was a key factor driving the emission of particles. Based on the results for 30 different types of laser printers, a systematic positive correlation was observed between temperature and particle number emissions for printers that used the same heating technology and had a similar structure and fuser material. It was also found that temperature fluctuations were associated with intense bursts of particles and therefore, they may have impact on the particle emissions. Furthermore, the results indicated that the type of paper and toner powder contributed to particle emissions, while no apparent relationship was observed between toner coverage and levels of submicron particles. (4) Mechanisms of SOA formation, growth and ageing: The overall hypothesis that UFPs are formed by reactions with the VOCs and O3 emitted from laser printers was examined. The results proved this hypothesis and suggested that O3 may also play a role in particle ageing. In addition, knowledge about the mixing state of generated particles was utilised to explore the detailed processes of particle formation for different printing scenarios, including warm-up, normal printing, and printing without toner. The results indicated that polymerisation may have occurred on the surface of the generated particles to produce thermoplastic polymers, which may account for the expandable characteristics of some particles. Furthermore, toner and other particle residues on the idling belt from previous print jobs were a very clear contributing factor in the formation of laser printer-emitted particles. In summary, this study not only improves scientific understanding of the nature of printer-generated particles, but also provides significant insight into the formation and ageing mechanisms of SOAs in the indoor environment. The outcomes will also be beneficial to governments, industry and individuals.

A phenomenological model for the structure-composition relationship of the high Tc cuprates based on simple chemical principles

A simple phenomenological model for the relationship between structure and composition of the high Tc cuprates is presented. The model is based on two simple crystal chemistry principles: unit cell doping and charge balance within unit cells. These principles are inspired by key experimental observations of how the materials accommodate large deviations from stoichiometry. Consistent explanations for significant HTSC properties can be explained without any additional assumptions while retaining valuable insight for geometric interpretation. Combining these two chemical principles with a review of Crystal Field Theory (CFT) or Ligand Field Theory (LFT), it becomes clear that the two oxidation states in the conduction planes (typically d8 and d9) belong to the most strongly divergent d-levels as a function of deformation from regular octahedral coordination. This observation offers a link to a range of coupling effects relating vibrations and spin waves through application of Hund’s rules. An indication of this model’s capacity to predict physical properties for HTSC is provided and will be elaborated in subsequent publications. Simple criteria for the relationship between structure and composition in HTSC systems may guide chemical syntheses within new material systems.

Functionalised zinc oxide nanowire gas sensors : enhanced NO2 gas sensor response by chemical modification of nanowire surfaces

Surface coating with an organic self-assembled monolayer (SAM) can enhance surface reactions or the absorption of specific gases and hence improve the response of a metal oxide (MOx) sensor toward particular target gases in the environment. In this study the effect of an adsorbed organic layer on the dynamic response of zinc oxide nanowire gas sensors was investigated. The effect of ZnO surface functionalisation by two different organic molecules, tris(hydroxymethyl)aminomethane (THMA) and dodecanethiol (DT), was studied. The response towards ammonia, nitrous oxide and nitrogen dioxide was investigated for three sensor configurations, namely pure ZnO nanowires, organic-coated ZnO nanowires and ZnO nanowires covered with a sparse layer of organic-coated ZnO nanoparticles. Exposure of the nanowire sensors to the oxidising gas NO2 produced a significant and reproducible response. ZnO and THMA-coated ZnO nanowire sensors both readily detected NO2 down to a concentration in the very low ppm range. Notably, the THMA-coated nanowires consistently displayed a small, enhanced response to NO2 compared to uncoated ZnO nanowire sensors. At the lower concentration levels tested, ZnO nanowire sensors that were coated with THMA-capped ZnO nanoparticles were found to exhibit the greatest enhanced response. ΔR/R was two times greater than that for the as-prepared ZnO nanowire sensors. It is proposed that the ΔR/R enhancement in this case originates from the changes induced in the depletion-layer width of the ZnO nanoparticles that bridge ZnO nanowires resulting from THMA ligand binding to the surface of the particle coating. The heightened response and selectivity to the NO2 target are positive results arising from the coating of these ZnO nanowire sensors with organic-SAM-functionalised ZnO nanoparticles.

Zeolite supported gold nanoparticles for selective photooxidation of aromatic alcohols under visible light irradiation

With new photocatalysts of gold nanoparticles supported on zeolite supports (Au/zeolite), oxidation of benzyl alcohol and its derivatives into the corresponding aldehydes can proceed well with a high selectivity (99%) under visible light irradiation at ambient temperature. Au/zeolite photocatalysts were characterized by UV/Vis, XPS, TEM, XRD, EDS, BET, IR, and Raman techniques. The Surface Plasmon Resonance (SPR) effect of gold nanoparticles, the adsorption capability of zeolite supports, and the molecular polarities of aromatic alcohols were demonstrated to have an essential correlation with the photocatalytic performances. In addition, the effects of light intensity, wavelength range, and the role of molecular oxygen were investigated in detail. The kinetic study indicated that the visible light irradiation required much less apparent activation energy for photooxidation compared with thermal reaction. Based on the characterization data and the photocatalytic performances, we proposed a possible photooxidation mechanism.

Bacterially mediated iron cycling and associated biogeochemical processes in a subtropical shallow coastal aquifer: implications for groundwater quality

Bacterially mediated iron redox cycling exerts a strong influence on groundwater geochemistry, but few studies have investigated iron biogeochemical processes in coastal alluvial aquifers from a microbiological viewpoint. The shallow alluvial aquifer located adjacent to Poona estuary on the subtropical Southeast Queensland coast represents a redox-stratified system where iron biogeochemical cycling potentially affects water quality. Using a 300 m transect of monitoring wells perpendicular to the estuary, we examined groundwater physico-chemical conditions and the occurrence of cultivable bacterial populations involved in iron (and manganese, sulfur) redox reactions in this aquifer. Results showed slightly acidic and near-neutral pH, suboxic conditions and an abundance of dissolved iron consisting primarily of iron(II) in the majority of wells. The highest level of dissolved iron(III) was found in a well proximal to the estuary most likely a result of iron curtain effects due to tidal intrusion. A number of cultivable, (an)aerobic bacterial populations capable of diverse carbon, iron, or sulfur metabolism coexisted in groundwater redox transition zones. Our findings indicated aerobic, heterotrophic respiration and bacterially mediated iron/sulfur redox reactions were integral to carbon cycling in the aquifer. High abundances of dissolved iron and cultivable iron and sulfur bacterial populations in estuary-adjacent aquifers have implications for iron transport to marine waters. This study demonstrated bacterially mediated iron redox cycling and associated biogeochemical processes in subtropical coastal groundwaters using culture-based methods.

The surface-structure sensitivity of dioxygen activation in the anatase-photocatalyzed oxidation reaction

The reaction pathways by which oxygen is incorporated into the substrate in the photocatalytic oxidation of terephthalic acid (TPTA) are vastly different on {001} and {101} facets of an anatase single crystal. This was established by controlling the percentage of {101} and {001} facets, isotopically tracing the origins of the hydroxy group, and studying dioxygen consumption and variance in the concentration of hydroxylation intermediate.

Chemical variability of groundwater samples collected from a Coal Seam Gas exploration well, Maramarua, New Zealand

A pilot study has produced 31 groundwater samples from a coal seam gas (CSG) exploration well located in Maramarua, New Zealand. This paper describes sources of CSG water chemistry variations, and makes sampling and analytical recommendations to minimize these variations. The hydrochemical character of these samples is studied using factor analysis, geochemical modelling, and a sparging experiment. Factor analysis unveils carbon dioxide (CO2) degassing as the principal cause of sample variation (about 33%). Geochemical modelling corroborates these results and identifies minor precipitation of carbonate minerals with degassing. The sparging experiment confirms the effect of CO2 degassing by showing a steady rise in pH while maintaining constant alkalinity. Factor analysis correlates variations in the major ion composition (about 17%) to changes in the pumping regime and to aquifer chemistry variations due to cation exchange reactions with argillaceous minerals. An effective CSG water sampling program can be put into practice by measuring pH at the well head and alkalinity at the laboratory; these data can later be used to calculate the carbonate speciation at the time the sample was collected. In addition, TDS variations can be reduced considerably if a correct drying temperature of 180°C is consistently implemented.

Deformation with coupled chemical diffusion

The deformation of rocks is commonly intimately associated with metamorphic reactions. This paper is a step towards understanding the behaviour of fully coupled, deforming, chemically reacting systems by considering a simple example of the problem comprising a single layer system with elastic-power law viscous constitutive behaviour where the deformation is controlled by the diffusion of a single chemical component that is produced during a metamorphic reaction. Analysis of the problem using the principles of non-equilibrium thermodynamics allows the energy dissipated by the chemical reaction-diffusion processes to be coupled with the energy dissipated during deformation of the layers. This leads to strain-rate softening behaviour and the resultant development of localised deformation which in turn nucleates buckles in the layer. All such diffusion processes, in leading to Herring-Nabarro, Coble or “pressure solution” behaviour, are capable of producing mechanical weakening through the development of a “chemical viscosity”, with the potential for instability in the deformation. For geologically realistic strain rates these chemical feed-back instabilities occur at the centimetre to micron scales, and so produce structures at these scales, as opposed to thermal feed-back instabilities that become important at the 100–1000 m scales.

Infrared study of CO adsorption on reduced and oxidised silica-supported copper catalysts

FTIR spectra are reported of CO adsorbed on silica-supported copper catalysts prepared from copper(II) acetate monohydrate. Fully oxidised catalyst gave bands due to CO on CuO, isolated Cu2+ cations on silica and anion vacancy sites in CuO. The highly dispersed CuO aggregated on reduction to metal particles which gave bands due to adsorbed CO characteristic of both low-index exposed planes and stepped sites on high-index planes. Partial surface oxidation with N2O or H2O generated Cu+ adsorption sites which were slowly reduced to Cu° by CO at 300 K. Surface carbonate initially formed from CO was also slowly depleted with time with the generation of CO2. The results are consistent with adsorbed carbonate being an intermediate in the water-gas shift reaction of H2O and CO to H2 and CO2.

A combined environmental scanning electron microscopy and Raman microscopy study of methanol oxidation on silver(I) oxide

The techniques of environmental scanning electron microscopy (ESEM) and Raman microscopy have been used to respectively elucidate the morphological changes and nature of the adsorbed species on silver(I) oxide powder, during methanol oxidation conditions. Heating Ag2O in either water vapour or oxygen resulted firstly in the decomposition of silver(I) oxide to polycrystalline silver at 578 K followed by sintering of the particles at higher temperature. Raman spectroscopy revealed the presence of subsurface oxygen and hydroxyl species in addition to surface hydroxyl groups after interaction with water vapour. Similar species were identified following exposure to oxygen in an ambient atmosphere. This behaviour indicated that the polycrystalline silver formed from Ag2O decomposition was substantially more reactive than silver produced by electrochemical methods. The interaction of water at elevated temperatures subsequent to heating silver(I) oxide in oxygen resulted in a significantly enhanced concentration of subsurface hydroxyl species. The reaction of methanol with Ag2O at high temperatures was interesting in that an inhibition in silver grain growth was noted. Substantial structural modification of the silver(I) oxide material was induced by catalytic etching in a methanol/air mixture. In particular, "pin-hole" formation was observed to occur at temperatures in excess of 773 K, and it was also recorded that these "pin- holes" coalesced to form large-scale defects under typical industrial reaction conditions. Raman spectroscopy revealed that the working surface consisted mainly of subsurface oxygen and surface Ag=O species. The relative lack of sub-surface hydroxyl species suggested that it was the desorption of such moieties which was the cause of the "pin-hole" formation.