Efficient and cost-effective experimental determination of kinetic constants and data: the success of a Bayesian systematic approach to drug transport, receptor binding, continuous culture and cell transport kinetics

Details about the parameters of kinetic systems are crucial for progress in both medical and industrial research, including drug development, clinical diagnosis and biotechnology applications. Such details must be collected by a series of kinetic experiments and investigations. The correct design of the experiment is essential to collecting data suitable for analysis, modelling and deriving the correct information. We have developed a systematic and iterative Bayesian method and sets of rules for the design of enzyme kinetic experiments. Our method selects the optimum design to collect data suitable for accurate modelling and analysis and minimises the error in the parameters estimated. The rules select features of the design such as the substrate range and the number of measurements. We show here that this method can be directly applied to the study of other important kinetic systems, including drug transport, receptor binding, microbial culture and cell transport kinetics. It is possible to reduce the errors in the estimated parameters and, most importantly, increase the efficiency and cost-effectiveness by reducing the necessary amount of experiments and data points measured. (C) 2003 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

A comparison of the reactivity of germylene and dimethylgermylene with some methylgermanes. Direct kinetic and quantum chemical studies

Time-resolved studies of germylene, GeH2, and dimethygermylene, GeMe2, generated by the 193 nm laser flash photolysis of appropriate precursor molecules have been carried out to try to obtain rate coefficients for their bimolecular reactions with dimethylgermane, Me2GeH2, in the gas-phase. GeH2 + Me2GeH2 was studied over the pressure range 1-100 Torr with SF6 as bath gas and at five temperatures in the range 296-553 K. Only slight pressure dependences were found (at 386, 447 and 553 K). RRKM modelling was carried out to fit these pressure dependences. The high pressure rate coefficients gave the Arrhenius parameters: log(A/cm(3) molecule(-1)s(-1)) = -10.99 +/- 0.07 and E-a = -(7.35 +/- 0.48) kJ mol(-1). No reaction could be found between GeMe2 + Me2GeH2 at any temperature up to 549 K, and upper limits of ca. 10(-14) cm(3) molecule(-1)s(-1) were set for the rate coefficients. A rate coefficient of (1.33 +/- 0.04) x 10(-11)cm(3) molecule(-1)s(-1) was also obtained for GeH2 + MeGeH3 at 296 K. No reaction was found between GeMe2 and MeGeH3. Rate coefficient comparisons showed, inter alia, that in the substrate germane Me-for-H substitution increased the magnitudes of rate coefficients significantly, while in the germylene Me-for-H substitution decreased the magnitudes of rate coefficients by at least four orders of magnitude. Quantum chemical calculations (G2(MP2,SVP)// B3LYP level) supported these findings and showed that the lack of reactivity of GeMe2 is caused by a positive energy barrier for rearrangement of the initially formed complexes. Full details of the structures of intermediate complexes and the discussion of their stabilities are given in the paper.

Surprisingly slow reaction of dimethylsilylene with dimethylgermane: time-resolved kinetic studies and related quantum chemical calculations

Time-resolved studies of silylene, SiH2, and dimethylsilylene, SiMe2, generated by the 193 nm laser flash photolysis of appropriate precursor molecules have been carried out to obtain rate constants for their bimolecular reactions with dimethylgermane, Me2GeH2, in the gas phase. SiMe2 + Me2GeH2 was studied at five temperatures in the range 299-555 K. Problems of substrate UV absorption at 193 nm at temperatures above 400 K meant that only three temperatures could be used reliably for rate constant measurement. These rate constants gave the Arrhenius parameters log(A/cm(3) molecule(-1) s(-1)) = -13.25 +/- 0.16 and E-a = -(5.01 +/- 1.01) kJ mol(-1). Only room temperature studies of SiH2 were carried out. These gave values of (4.05 +/- 0.06) x 10(-10) cm(3) molecule(-1) s(-1) (SiH2 + Me2GeH2 at 295 K) and also (4.41 +/- 0.07) x 10(-10) cm(3) molecule(-1) s(-1) (SiH2 + MeGeH3 at 296 K). Rate constant comparisons show the surprising result that SiMe2 reacts 12.5 times slower with Me2GeH2 than with Me2SiH2. Quantum chemical calculations (G2(MP2,SVP)//B3LYP level) of the model Si-H and Ge-H insertion processes of SiMe2 with SiH4/MeSiH3 and GeH4/MeGeH3 support these findings and show that the lower reactivity of SiMe2 with Ge-H bonds is caused by a higher secondary barrier for rearrangement of the initially formed complexes. Full details of the structures of intermediate complexes and the discussion of their stabilities are given in the paper. Other, related, comparisons of silylene reactivity are also presented.

An investigation of the germylene addition reaction, GeH2+C2H2: Time-resolved gas-phase kinetic studies and quantum chemical calculations of the reaction energy surface

Time resolved studies of germylene, GeH2, generated by laser flash photolysis of 3,4-dimethylgermacyclopentene-3, have been carried out to obtain rate constants for its bimolecular reaction with acetylene, C2H2. The reaction was studied in the gas-phase over the pressure range 1-100 Tort, with SF6 as bath gas, at 5 temperatures in the range 297-553 K. The reaction showed a very slight pressure dependence at higher temperatures. The high pressure rate constants (obtained by extrapolation at the three higher temperatures) gave the Arrhenius equation: log(k(infinity)/cm(3) molecule(-1) s(-1)) (-10.94 +/- 0.05) + (6.10 +/- 0.36 kJ mol(-1))/RTln10. These Arrhenius parameters are consistent with a fast reaction occurring at approximately 30% of the collision rate at 298 K. Quantum chemical calculations (both DFT and ab initio G2//B3LYP and G2//QCISD) of the GeC2H4 potential energy surface (PES), show that GeH2 + C2H2 react initially to form germirene which can isomerise to vinylgermylene with a relatively low barrier. RRKM modelling, based on a loose association transition state, but assuming vinylgermylene is the end product (used in combination with a weak collisional deactivation model) predicts a strong pressure dependence using the calculated energies, in conflict with the experimental evidence. The detailed GeC2H4 PES shows considerable complexity with ten other accessible stable minima (B3LYP level), the three most stable of which are all germylenes. Routes through this complex surface were examined in detail. The only product combination which appears capable of satisfying the (P-3) + C2H4.C2H4 was confirmed as a product by GC observed lack of a strong pressure dependence is Ge(P-3) + C2H4. C2H4 was confirmed as a product by GC analysis. Although the formation of these products are shown to be possible by singlet-triplet curve crossing during dissociation of 1-germiranylidene (1-germacyclopropylidene), it seems more likely (on thermochernical grounds) that the triplet biradical, (GeCH2CH2.)-Ge-., is the immediate product precursor. Comparisons are made with the reaction of SiH2 with C2H2.

Gas phase kinetic and quantum chemical studies of the reactions of silylene with the methylsilanes. Absolute rate constants, temperature dependences, RRKM modelling and potential energy surfaces

Time resolved studies of silylene, SiH2, generated by the 193 nm laser. ash photolysis of phenylsilane, have been carried out to obtain rate coefficients for its bimolecular reactions with methyl-, dimethyl- and trimethyl-silanes in the gas phase. The reactions were studied over the pressure range 3 - 100 Torr with SF6 as bath gas and at five temperatures in the range 300 - 625 K. Only slight pressure dependences were found for SiH2 + MeSiH3 ( 485 and 602 K) and for SiH2 + Me2SiH2 ( 600 K). The high pressure rate constants gave the following Arrhenius parameters: [GRAPHICS] These are consistent with fast, near to collision-controlled, association processes. RRKM modelling calculations are consistent with the observed pressure dependences ( and also the lack of them for SiH2 + Me3SiH). Ab initio calculations at both second order perturbation theory (MP2) and coupled cluster (CCSD(T)) levels, showed the presence of weakly-bound complexes along the reaction pathways. In the case of SiH2 + MeSiH3 two complexes, with different geometries, were obtained consistent with earlier studies of SiH2 + SiH4. These complexes were stabilised by methyl substitution in the substrate silane, but all had exceedingly low barriers to rearrangement to product disilanes. Although methyl groups in the substrate silane enhance the intrinsic SiH2 insertion rates, it is doubtful whether the intermediate complexes have a significant effect on the kinetics. A further calculation on the reaction MeSiH + SiH4 shows that the methyl substitution in the silylene should have a much more significant kinetic effect ( as observed in other studies).

A method for estimating the turbulent kinetic energy dissipation rate from a vertically pointing Doppler lidar, and independent evaluation from balloon-borne in situ measurements

A method of estimating dissipation rates from a vertically pointing Doppler lidar with high temporal and spatial resolution has been evaluated by comparison with independent measurements derived from a balloon-borne sonic anemometer. This method utilizes the variance of the mean Doppler velocity from a number of sequential samples and requires an estimate of the horizontal wind speed. The noise contribution to the variance can be estimated from the observed signal-to-noise ratio and removed where appropriate. The relative size of the noise variance to the observed variance provides a measure of the confidence in the retrieval. Comparison with in situ dissipation rates derived from the balloon-borne sonic anemometer reveal that this particular Doppler lidar is capable of retrieving dissipation rates over a range of at least three orders of magnitude. This method is most suitable for retrieval of dissipation rates within the convective well-mixed boundary layer where the scales of motion that the Doppler lidar probes remain well within the inertial subrange. Caution must be applied when estimating dissipation rates in more quiescent conditions. For the particular Doppler lidar described here, the selection of suitably short integration times will permit this method to be applicable in such situations but at the expense of accuracy in the Doppler velocity estimates. The two case studies presented here suggest that, with profiles every 4 s, reliable estimates of ϵ can be derived to within at least an order of magnitude throughout almost all of the lowest 2 km and, in the convective boundary layer, to within 50%. Increasing the integration time for individual profiles to 30 s can improve the accuracy substantially but potentially confines retrievals to within the convective boundary layer. Therefore, optimization of certain instrument parameters may be required for specific implementations.

Coupling aerosol surface and bulk chemistry with a kinetic double layer model (K2-SUB): oxidation of oleic acid by ozone

We present a kinetic double layer model coupling aerosol surface and bulk chemistry (K2-SUB) based on the PRA framework of gas-particle interactions (Poschl-Rudich-Ammann, 2007). K2-SUB is applied to a popular model system of atmospheric heterogeneous chemistry: the interaction of ozone with oleic acid. We show that our modelling approach allows de-convoluting surface and bulk processes, which has been a controversial topic and remains an important challenge for the understanding and description of atmospheric aerosol transformation. In particular, we demonstrate how a detailed treatment of adsorption and reaction at the surface can be coupled to a description of bulk reaction and transport that is consistent with traditional resistor model formulations. From literature data we have derived a consistent set of kinetic parameters that characterise mass transport and chemical reaction of ozone at the surface and in the bulk of oleic acid droplets. Due to the wide range of rate coefficients reported from different experimental studies, the exact proportions between surface and bulk reaction rates remain uncertain. Nevertheless, the model results suggest an important role of chemical reaction in the bulk and an approximate upper limit of similar to 10(-11) cm(2) s(-1) for the surface reaction rate coefficient. Sensitivity studies show that the surface accommodation coefficient of the gas-phase reactant has a strong non-linear influence on both surface and bulk chemical reactions. We suggest that K2-SUB may be used to design, interpret and analyse future experiments for better discrimination between surface and bulk processes in the oleic acid-ozone system as well as in other heterogeneous reaction systems of atmospheric relevance.

Kinetic multi-layer model of gas-particle interactions in aerosols and clouds (KM-GAP): linking condensation, evaporation and chemical reactions of organics, oxidants and water

We present a novel kinetic multi-layer model for gas-particle interactions in aerosols and clouds (KM-GAP) that treats explicitly all steps of mass transport and chemical reaction of semi-volatile species partitioning between gas phase, particle surface and particle bulk. KM-GAP is based on the PRA model framework (Pöschl-Rudich-Ammann, 2007), and it includes gas phase diffusion, reversible adsorption, surface reactions, bulk diffusion and reaction, as well as condensation, evaporation and heat transfer. The size change of atmospheric particles and the temporal evolution and spatial profile of the concentration of individual chemical species can be modelled along with gas uptake and accommodation coefficients. Depending on the complexity of the investigated system, unlimited numbers of semi-volatile species, chemical reactions, and physical processes can be treated, and the model shall help to bridge gaps in the understanding and quantification of multiphase chemistry and microphysics in atmo- spheric aerosols and clouds. In this study we demonstrate how KM-GAP can be used to analyze, interpret and design experimental investigations of changes in particle size and chemical composition in response to condensation, evaporation, and chemical reaction. For the condensational growth of water droplets, our kinetic model results provide a direct link between laboratory observations and molecular dynamic simulations, confirming that the accommodation coefficient of water at 270 K is close to unity. Literature data on the evaporation of dioctyl phthalate as a function of particle size and time can be reproduced, and the model results suggest that changes in the experimental conditions like aerosol particle concentration and chamber geometry may influence the evaporation kinetics and can be optimized for eðcient probing of specific physical effects and parameters. With regard to oxidative aging of organic aerosol particles, we illustrate how the formation and evaporation of volatile reaction products like nonanal can cause a decrease in the size of oleic acid particles exposed to ozone.

Kinetic multi-layer model of gas-particle interactions in aerosols and clouds (KM-GAP): linking condensation, evaporation and chemical reactions of organics, oxidants and water

We present a novel kinetic multi-layer model for gas-particle interactions in aerosols and clouds (KMGAP) that treats explicitly all steps of mass transport and chemical reaction of semi-volatile species partitioning between gas phase, particle surface and particle bulk. KMGAP is based on the PRA model framework (P¨oschl-Rudich- Ammann, 2007), and it includes gas phase diffusion, reversible adsorption, surface reactions, bulk diffusion and reaction, as well as condensation, evaporation and heat transfer. The size change of atmospheric particles and the temporal evolution and spatial profile of the concentration of individual chemical species can be modeled along with gas uptake and accommodation coefficients. Depending on the complexity of the investigated system and the computational constraints, unlimited numbers of semi-volatile species, chemical reactions, and physical processes can be treated, and the model shall help to bridge gaps in the understanding and quantification of multiphase chemistry and microphysics in atmospheric aerosols and clouds. In this study we demonstrate how KM-GAP can be used to analyze, interpret and design experimental investigations of changes in particle size and chemical composition in response to condensation, evaporation, and chemical reaction. For the condensational growth of water droplets, our kinetic model results provide a direct link between laboratory observations and molecular dynamic simulations, confirming that the accommodation coefficient of water at 270K is close to unity (Winkler et al., 2006). Literature data on the evaporation of dioctyl phthalate as a function of particle size and time can be reproduced, and the model results suggest that changes in the experimental conditions like aerosol particle concentration and chamber geometry may influence the evaporation kinetics and can be optimized for efficient probing of specific physical effects and parameters. With regard to oxidative aging of organic aerosol particles, we illustrate how the formation and evaporation of volatile reaction products like nonanal can cause a decrease in the size of oleic acid particles exposed to ozone.

Electron acceleration and parallel electric fields due to kinetic Alfvén waves in plasma with similar thermal and Alfvén speeds

We investigate electron acceleration due to shear Alfven waves in a collissionless plasma for plasma parameters typical of 4–5RE radial distance from the Earth along auroral field lines. Recent observational work has motivated this study, which explores the plasma regime where the thermal velocity of the electrons is similar to the Alfven speed of the plasma, encouraging Landau resonance for electrons in the wave fields. We use a self-consistent kinetic simulation model to follow the evolution of the electrons as they interact with a short-duration wave pulse, which allows us to determine the parallel electric field of the shear Alfven wave due to both electron inertia and electron pressure effects. The simulation demonstrates that electrons can be accelerated to keV energies in a modest amplitude sub-second period wave. We compare the parallel electric field obtained from the simulation with those provided by fluid approximations.

The cleft ion fountain: a two-dimensional kinetic model

The transport of ionospheric ions from a source in the polar cleft ionosphere through the polar magnetosphere is investigated using a two-dimensional, kinetic, trajectory-based code. The transport model includes the effects of gravitation, longitudinal magnetic gradient force, convection electric fields, and parallel electric fields. Individual ion trajectories as well as distribution functions and resulting bulk parameters of density, parallel average energy, and parallel flux for a presumed cleft ionosphere source distribution are presented for various conditions to illustrate parametrically the dependences on source energies, convection electric field strengths, ion masses, and parallel electric field strengths. The essential features of the model are consistent with the concept of a cleft-based ion fountain supplying ionospheric ions to the polar magnetosphere, and the resulting plasma distributions and parameters are in general agreement with recent low-energy ion measurements from the DE 1 satellite.