Stochastic chemical kinetics and the quasi-steady-state assumption : application to the stochastic simulation algorithm and chemical master equation

Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical efficiency is obtained by respecting the vastly different time scales characterizing the system and then by advancing only the slow reactions exactly, based on a suitable approximation to the fast reactions. We considerably extend these works by applying the QSSA to numerical methods for the direct solution of the chemical master equation (CME) and, in particular, to the finite state projection algorithm [Munsky and Khammash, J. Chem. Phys. 124, 044104 (2006)], in conjunction with Krylov methods. In addition, we point out some important connections to the literature on the (deterministic) total QSSA (tQSSA) and place the stochastic analogue of the QSSA within the more general framework of aggregation of Markov processes. We demonstrate the new methods on four examples: Michaelis–Menten enzyme kinetics, double phosphorylation, the Goldbeter–Koshland switch, and the mitogen activated protein kinase cascade. Overall, we report dramatic improvements by applying the tQSSA to the CME solver.

Development of a colorimetric assay for heparanase activity suitable for kinetic analysis and inhibitor screening

The role that heparanase plays during metastasis and angiogenesis in tumors makes it an attractive target for cancer therapeutics. Despite this enzyme’s significance, most of the assays developed to measure its activity are complex. Moreover, they usually rely on labeling variable preparations of the natural substrate heparan sulfate, making comparisons across studies precarious. To overcome these problems, we have developed a convenient assay based on the cleavage of the synthetic heparin oligosaccharide fondaparinux. The assay measures the appearance of the disaccharide product of heparanase-catalyzed fondaparinux cleavage colorimetrically using the tetrazolium salt WST-1. Because this assay has a homogeneous substrate with a single point of cleavage, the kinetics of the enzyme can be reliably characterized, giving a Km of 46 μM and a kcat of 3.5 s−1 with fondaparinux as substrate. The inhibition of heparanase by the published inhibitor, PI-88, was also studied, and a Ki of 7.9 nM was determined. The simplicity and robustness of this method, should, not only greatly assist routine assay of heparanase activity but also could be adapted for high-throughput screening of compound libraries, with the data generated being directly comparable across studies.

Evolving genetic regulatory networks performing as stochastic switches

Recent studies have shown that small genetic regulatory networks (GRNs) can be evolved in silico displaying certain dynamics in the underlying mathematical model. It is expected that evolutionary approaches can help to gain a better understanding of biological design principles and assist in the engineering of genetic networks. To take the stochastic nature of GRNs into account, our evolutionary approach models GRNs as biochemical reaction networks based on simple enzyme kinetics and simulates them by using Gillespie’s stochastic simulation algorithm (SSA). We have already demonstrated the relevance of considering intrinsic stochasticity by evolving GRNs that show oscillatory dynamics in the SSA but not in the ODE regime. Here, we present and discuss first results in the evolution of GRNs performing as stochastic switches.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.

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.

Carbon dioxide reforming of methane to produce synthesis gas over metal-supported catalysts: State of the art

Carbon dioxide reforming of methane produces synthesis gas with a low hydrogen to carbon monoxide ratio, which is desirable for many industrial synthesis processes. This reaction also has very important environmental implications since both methane and carbon dioxide contribute to the greenhouse effect. Converting these gases into a valuable feedstock may significantly reduce the atmospheric emissions of CO2 and CH4. In this paper, we present a comprehensive review on the thermodynamics, catalyst selection and activity, reaction mechanism, and kinetics of this important reaction. Recently, research has centered on the development of catalysts and the feasible applications of this reaction in industry. Group VIII metals supported on oxides are found to be effective for this reason. However, carbon deposition causing catalyst deactivation is the major problem inhibiting the industrial application of the CO2/CH4 reaction. Ni-based catalysts impregnated on certain supports show carbon-free operation and thus attract much attention. To develop an effective catalyst for CO2 reforming of CH4 and accelerate the commercial application of the reaction, the following are identified to be the most important areas for future work: (1) selection of metal and support and studying the effect of their interaction on catalyst activity; (2) the effect of different promoter on catalyst activity; (3) the reaction mechanism and kinetics; and (4) pilot reactor performance and scale-up operation.

Base-induced decomposition of alkyl hydroperoxides in the gas phase. Part 3. Kinetics and dynamics in HO-+CH3OOH, C2H5OOH, and tert-C4H9OOH reactions

The E-CO(2) elimination reactions of alkyl hydroperoxides proceed via abstraction of an (x-hydrogen by a base: X- + (RRHCOOH)-R-1-H-2 -> HX + (RRC)-R-1-C-2=O + HO-. Efficiencies and product distributions for the reactions of the hydroxide anion with methyl, ethyl, and tert-butyl hydroperoxides are studied in the gas phase. On the basis of experiments using three isotopic analogues, HO- + CH3OOH, HO- + CD3OOH, and H18O- + CH3OOH. the overall intrinsic reaction efficiency is determined to be 80% or greater. The E(CO)2 decomposition is facile for these methylperoxide reactions, and predominates over competing proton transfer at the hydroperoxide moiety. The CH3CH2OOH reaction displays a similar E(CO)2 reactivity, whereas proton transfer and the formation of HOO- are the exclusive pathways observed for (CH3)(3)COOH, which has no (x-hydrogen. All results are consistent with the E-CO(2) mechanism, transition state structure, and reaction energy diagrams calculated using the hybrid density functional B3LYP approach. Isotope labeling for HO- + CH3OOH also reveals some interaction between H2O and HO- within the E(CO)2 product complex [H2O center dot center dot center dot CH2=O center dot center dot center dot HO-]. There is little evidence, however. for the formation of the most exothermic products H2O + CH2(OH)O-, which would arise from nuclephilic condensation of CH2=O and HO-. The results suggest that the product dynamics are not totally statistical but are rather direct after the E-CO(2) transition state. The larger HO- + CH3CH2OOH system displays more statistical behavior during complex dissociation.

Detoxification enzyme activities (CYP1A1 and GST) in the skin of humpback whales as a function of organochlorine burdens and migration status

The activities of glutathione-s-transferase (GST) and cytochrome P-450 1A1 (CYP1A1) enzymes were measured in freshly extracted epidermis of live-biopsied, migrating, southern hemisphere humpback whales (Megaptera novaeangliae). The two quantified enzyme activities did not correlate strongly with each other. Similarly, neither correlated strongly with any of the organochlorine compound groups previously measured in the superficial blubber of the sample biopsy core, likely reflecting the anticipated low levels of typical aryl-hydrocarbon receptor ligands. GST activity did not differ significantly between genders or between northward (early migration) or southward (late migration) migrating cohorts. Indeed, the inter-individual variability in GST measurements was relatively low. This observation raises the possibility that measured activities were basal activities and that GST function was inherently impacted by the fasting state of the sampled animals, as seen in other species. These results do not support the implementation of CYP1A1 or GST as effective biomarkers of organochlorine contaminant burdens in southern hemisphere populations of humpback whales as advocated for other cetacean species. Further investigation of GST activity in feeding versus fasting cohorts may, however, provide some insight into the fasting metabolism of these behaviourally adapted populations.

A novel fluorescent probe involving a graphene quantum dot-enzyme hybrid system for the analysis of hydroquinone in the presence of toxic resorcinol and catechol

An efficient method for the analysis of hydroquinone at trace levels in water samples has been developed in the form of a fluorescent probe based on graphene quantum dots (GQDs). The analytical variable, fluorescence quenching, was generated from the formation of benzoquinone intermediates, which formed during the catalytic oxidation of hydroquinone by horseradish peroxidase (HRP). In general, the reaction mechanism involved hydroquinone, as an electron acceptor, which affected the surface state of GQDs via an electron transfer effect. The water-soluble GQDs were directly prepared by the pyrolysis of citric acid and with the use of the mentioned hybrid enzyme system, the detection limit for hydroquinone was as low as 8.4 × 10−8 M. Furthermore, this analysis was almost unaffected by other phenol and quinine compounds, such as phenol, resorcinol and other quinines, and therefore, the developed GQD method produced satisfactory results for the analysis of hydroquinone in several different lake water samples.

Developments in psoriasis and psoriatic arthritis

Psoriasis and psoriatic arthritis are common conditions for which treatment options have until recently been extremely limited. Recent advances in our understanding of the immunology and genetics underlying these conditions have been rapid, and have contributed to the development of new therapies for these diseases. This article discusses the current state of the art in our understanding of the aetiopathogenesis of psoriasis and psoriatic arthritis, and current therapies for the diseases.