Efficient and accurate experimental design for enzyme kinetics: Bayesian studies reveal a systematic approach

In areas such as drug development, clinical diagnosis and biotechnology research, acquiring details about the kinetic parameters of enzymes is crucial. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. We demonstrate that a Bayesian approach (the use of prior knowledge) can produce major gains quantifiable in terms of information, productivity and accuracy of each experiment. Developing the use of Bayesian Utility functions, we have used a systematic method to identify the optimum experimental designs for a number of kinetic model data sets. This has enabled the identification of trends between kinetic model types, sets of design rules and the key conclusion that such designs should be based on some prior knowledge of K-M and/or the kinetic model. We suggest an optimal and iterative method for selecting features of the design such as the substrate range, number of measurements and choice of intermediate points. The final design collects data suitable for accurate modelling and analysis and minimises the error in the parameters estimated. (C) 2003 Elsevier Science B.V. All rights reserved.

Gas-phase kinetics

Commentary on: 'Rates of pyrolysis and bond energies of substituted organic iodides' (Part 1), E.T. Butler and M. Polanyi, Trans Faraday Society, 1943, 39, 19.

A temperature-dependent relative-rate study of the OH initiated oxidation of n-butane: the kinetics of the reactions of the 1-and 2-butoxy radicals

The kinetics of the reactions of 1-and 2-butoxy radicals have been studied using a slow-flow photochemical reactor with GC-FID detection of reactants and products. Branching ratios between decomposition, CH3CH(O-.)CH2CH3 CH3CHO + C2H5, reaction (7), and reaction with oxygen, CH3CH(O-.)CH2CH3 + O-2 -> CH3C(O)C2H5 + HO2, reaction (6), for the 2-butoxy radical and between isomerization, CH3CH2CH2CH2O. -> CH2CH2CH2CH2OH, reaction (9), and reaction with oxygen, CH3CH2CH2CH2O. + O-2 -> C3H7CHO + HO2, reaction (8), for the 1-butoxy radical were measured as a function of oxygen concentration at atmospheric pressure over the temperature range 250-318 K. Evidence for the formation of a small fraction of chemically activated alkoxy radicals generated from the photolysis of alkyl nitrite precursors and from the exothermic reaction of 2-butyl peroxy radicals with NO was observed. The temperature dependence of the rate constant ratios for a thermalized system is given by k(7)/k(6) = 5.4 x 1026 exp[(-47.4 +/- 2.8 kJ mol(-1))/RT] molecule cm(-3) and k(9)/k(8) = 1.98 x 10(23) exp[(-22.6 +/- 3.9 kJ mol(-1))/RT] molecule cm(-3). The results agree well with the available experimental literature data at ambient temperature but the temperature dependence of the rate constant ratios is weaker than in current recommendations.

A pressure-jump time-resolved x-ray diffraction study of cubic-cubic transition kinetics in monoolein

In the past two decades, the geometric pathways involved in the transformations between inverse bicontinuous cubic phases in amphiphilic systems have been extensively theoretically modeled. However, little experimental data exists on the cubic-cubic transformation in pure lipid systems. We have used pressure-jump time-resolved X-ray diffraction to investigate the transition between the gyroid Q(II)(G) and double-diamond Q(II)(D) phases in mixtures of 1-monoolein in 30 wt% water. We find for this system that the cubic-cubic transition occurs without any detectable intermediate structures. In addition, we have determined the kinetics of the transition, in both the forward and reverse directions, as a function of pressure-jump amplitude, temperature, and water content. A recently developed model allows (at least in principle) the calculation of the activation energy for lipid phase transitions from such data. The analysis is applicable only if kinetic reproducibility is achieved, at least within one sample, and achievement of such kinetic reproducibility is shown here, by carrying out prolonged pressure-cycling. The rate of transformation shows clear and consistent trends with pressure-jump amplitude, temperature, and water content, all of which are shown to be in agreement with the effect of the shift in the position of the cubic-cubic phase boundary following a change in the thermodynamic parameters.

Separation of Ba-137m from Cs-137 using new ion exchanger Na-2(H2O)(4)(H3O)[Al(OH)(6)Mo6O18]

A new polyoxometalate of chemical formula, Na-2(H2O)(4)(H3O)[Al(OH)(6)Mo6O18] (1) containing Anderson type large anion has been synthesized and characterized by single-crystal X-ray structure determination and IR spectroscopic studies. The crystal of 1 is triclinic, spacegroup P-1 with cell dimensions, a = 6.365(9) angstrom, b = 10.37(1) angstrom, c = 10.44(1) angstrom and alpha = 65.41(1), beta = 77.18(1), gamma = 86.58(1) and Z = 1. The compound 1 behaves as an ion exchanger and is stable in thermal, radiation and chemical environments. Radiochemical separation of the short-lived daughter Ba-137m (t(1/2) = 2.50 min) from its long-lived parent Cs-137 using this newly designed and synthesized ion exchanger has been developed.

6,6 '-bis-(5,6-diethyl-[1,2,4]triazin-3-yl)-2,2 '-bipyridyl the first example of a new class of quadridentate hetercyclic extraction reagents for the separation of americium(III) and europium(III)

The synthesis of the first example of a new class of tetradentate reagents for the efficient separation of americium(Ill) and europium(111) is reported together with the structure of the complex formed with europium(III), (C) 2004 Elsevier B.V. All rights reserved.

Separation of lanthanides and actinides(III) using tridentate benzimidazole, benzoxazole and benzothiazole ligands

The ability of new hydrophobic tridentate ligands based on 2,6-bis(benziinidazol-2-yl)pyridine, 2,6-bis(benzoxazol-2-yl)pyridine and 2,6-bis(benzothiazol-2-yl)pyridine to selectively extract americium(III) from europium(III) was measured. The most promising ligand-2,6-bis(benzoxazol-2-yl)-4-(2-decyl-1-tetradecyloxy)pyridine L-9 was found to give separation factors (SFAm/Eu) of up to 70 when used to extract cations from 0.02-0.10 M HNO3 into TPH in synergy with 2-bromodecanoic acid. Six structures of lanthanide complexes with 2,6-bis(benzoxazol-2-yl)pyridine L-6 were then determined to evaluate the types of species that are likely to be involved in the separation process. Three structural types were observed, namely [LnL(6)(NO3)(3)(H2O)2], 11-coordinate only for La, [LnL(6) (NO3)(3) (CH3CN)], 10-coordinate for Pr, Nd and Eu and [LnL(6) (NO3)(3)(H2O)], L 10-coordinate for Eu and Gd. Quantum Mechanics calculations were carried out on the tridentate ligands to elucidate the conformational preferences of the ligands in the free state and protonated and diprotonated forms and to assess the electronic properties of the ligands for comparison with other terdentate ligands used in lanthanide/actinide separation processes.

Some new strategies for the chemical separation of actinides and lanthanides

A future goal in nuclear fuel reprocessing is the conversion or transmutation of the long-lived radioisotopes of minor actinides, such as americium, into short-lived isotopes by irradiation with neutrons. In order to achieve this transmutation, it is necessary to separate the minor actinides(III), [An(Ill)], from the lanthanides(III), [Ln(Ill)], by solvent extraction (partitioning), because the lanthanides absorb neutrons too effectively and hence limit neutron capture by the transmutable actinides. Partitioning using ligands containing only carbon, hydrogen, nitrogen and oxygen atoms is desirable because they are completely incinerable and thus the final volume of waste is minimised [1]. Nitric acid media will be used in the extraction experiments because it is envisaged that the An(III)/Ln(III) separation process could take place after the PUREX process. There is no doubt that the correct design of a molecule that is capable of acting as a ligand or extraction reagent is required for the effective separation of metal ions such as actinides(III) from lanthanides. Recent attention has been directed towards heterocyclic ligands with for the preferential separation of the minor actinides. Although such molecules have a rich chemistry, this is only now becoming sufficiently well understood in relation to the partitioning process [2]. The molecules shown in Figures I and 2 will be the principal focus of this study. Although the examples chosen here are used rather specific, the guidelines can be extended to other areas such as the separation of precious metals [3].

The kinetics of the 2π+2π photodimerisation reactions of single-crystalline derivatives of trans-cinnamic acid: a study by infrared microspectroscopy

The kinetics of the photodimerisation reactions of the 2- and 4-β-halogeno-derivatives of trans-cinnamic acid (where the halogen is fluorine, chlorine or bromine) have been investigated by infrared microspectroscopy. It is found that none of the reactions proceed to 100% yield. This is in line with a reaction mechanism developed by Wernick and his co-workers that postulates the formation of isolated monomers within the solid, which cannot react. β-4-Bromo and β-4-chloro-trans-cinnamic acids show approximately first order kinetics, although in both cases the reaction accelerates somewhat as it proceeds. First order kinetics is explained in terms of a reaction between one excited- and one ground-state monomer molecule, while the acceleration of the reaction implies that it is promoted as defects are formed within the crystal. By contrast β-2-chloro-trans-cinnamic acid shows a strongly accelerating reaction which models closely to the contracting cube equation. β-2-Fluoro- and β-4-fluoro-trans-cinnamic acids show a close match to first order kinetics. The 4-fluoro-derivative, however, shows a reaction that proceeds via a structural intermediate. The difference in behaviour between the 2-fluoro- and 4-fluoro-derivative may be due to different C–HF hydrogen bonds observed within these single-crystalline starting materials.

The kinetics of the gas-phase decomposition of the 2-methyl-2-butoxyl and 2-methyl-2-pentoxyl radicals

The kinetics of the title reactions have been studied by relative-rate methods as a function of temperature. Relative-rate coefficients for the two decomposition channels of 2-methyl-2-butoxyl have been measured at five different temperatures between 283 and 345 K and the observed temperature dependence is consistent with the results of some previous experimental studies. The kinetics of the two decomposition channels of 2-methyl-2-pentoxyl have also been investigated, as a function of temperature, relative to the estimated rate of isomerisation of this radical. Room-temperature rate coefficient data for the two decomposition channels of both 2-methyl-2-pentoxyl and 2-methyl-2-butxoyl (after combining the relative rate coefficient for this latter with a value for the rate coefficient of the major channel, extrapolated from the data presented by Batt et al., Int. J. Chem. Kinet., 1978, 10, 931) are shown to be consistent with a non-linear kinetic correlation, for alkoxyl radical decomposition rate data, previously presented by this laboratory (Johnson et al., Atmos. Environ., 2004, 38, 1755-1765).

Correlation-type structure activity relationships for the kinetics of gas-phase RO2 self-reactions and reaction with HO2

Structure activity relationships (SARs) are presented for the gas-phase reactions of RO2 with HO2, and the self- and cross-reactions of RO2. For RO2+HO2 the SAR is based upon a correlation between the logarithm of the measured rate coefficient and a calculated ionisation potential for the molecule R-CH=CH2, R being the same group in both the radical and molecular analogue. The correlation observed is strong and only for one RO2 species does the measured rate coefficient deviate by more than a factor of two from the linear least-squares regression line. For the self- and cross-reactions of RO2 radicals, the SAR is based upon a correlation between the logarithm of the measured rate coefficient and the calculated electrostatic potential (ESP) at the equivalent carbon atom in the RH molecule to which oxygen is attached in RO2, again R being the same group in the molecule and the radical. For cases where R is a simple alkyl-group, a strong linear correlation observed. For RO2 radicals which contain lone pair-bearing substituents and for which the calculated ESP<-0.05 self-reaction rate coefficients appear to be insensitive to the value of the ESP. For RO2 of this type with ESP>-0.05 a linear relationship between log k and the ESP is again observed. Using the relationships, 84 out of the 85 rate coefficients used to develop the SARs are predicted to within a factor of three of their measured values. A relationship is also presented that allows the prediction of the Arrhenius parameters for the self-reactions of simple alkyl RO2 radicals. On the basis of the correlations, predictions of room-temperature rate coefficients are made for a number of atmospherically important peroxyl-peroxyl radical reactions. (C) 2003 Elsevier Ltd. All rights reserved.

Coordination and separation studies of the uranyl ion with iso-butyramide based ligands: Synthesis and structures of [UO2(NO3)(2)((C3H7CON)-C-i{(C4H9)-C-i}(2))(2)] and [UO2(C6H5COCHCOC6H5)(2)((C3H7CON)-C-i{(C3H7)-C-i}(2))]

The coordination chemistry of iso-butyramide based ligands such as: (C3H7CON)-C-i((C3H7)-C-i)(2), (C3H7CON)-C-i(C4H9)(2) and (C3H7CON)-C-i((C4H9)-C-i)(2) with [UO2(NO3)(2) center dot 6H(2)O], [UO2(OO)(2) center dot 2H(2)O] {where OO = C4H3SCOCHCCCF3 (TTA), C6H5COCHCOCF3 (BTA) and C6H5COCHCOC6H5 (DBM)), [Th(NO3)(4) center dot 6H(2)O] and [La(NO3)(3) center dot 6H(2)O] has been evaluated. Structures for the compounds [UO2(NO3)(2)CC3H7CON{(C4H9)-C-i}(2))(2)] and [UO2(C6H5COCHCOC6H5)(2)((C3H7CON)-C-i{(C3H7)-C-i)(2))] have been determined by single crystal X-ray diffraction methods. Preliminary separation studies from nitric acid medium using the amide (C3H7CON)-C-i((C4H9)-C-i)(2) with U(VI), Th(IV) and La(Ill) ions showed the selective precipitation of uranyl ion from the mixture. Thermal study of the compound [UO2(NO3)(2)((C3H7CON)-C-i((C4H9)-C-i)(2))(2)] in air revealed that the ligands can be destroyed completely on incineration. (C) 2008 Elsevier Ltd. All rights reserved.

Phase mixing and phase separation accompanying the catalytic oxidation of CO on Ir{100}

The co-adsorption of CO and O on the unreconstructed (1 x 1) phase of Ir {100} was examined by low energy electron diffraction (LEED) and temperature programmed desorption (TPD). When CO is adsorbed at 188 K onto the Ir{100} surface precovered with 0.5 ML O, a mixed c(4 x 2)-(2O + CO) overlayer is formed. All CO is oxidised upon heating and desorbs as CO2 in three distinct stages at 230 K, 330 K and 430 K in a 2:1:2 ratio. The excess oxygen left on the surface after all CO has reacted forms an overlayer with a LEED pattern with p(2 x 10) periodicity. This overlayer consists of stripes with a local p(2 x 1)-O arrangement of oxygen atoms separated by stripes of uncovered It. When CO is adsorbed at 300 K onto the surface precovered with 0.5 ML O an apparent (2 x 2) LEED pattern is observed. LEED IV analysis reveals that this pattern is a superposition of diffraction patterns from islands of c(2 x 2)-CO and p(2 x 1)-O structures on the surface. Heating this co-adsorbed overlayer leads to the desorption of CO, in two stages at 330 K and 430 K; the excess CO (0.1 ML) desorbs at 590 K. LEED IV structural analysis of the mixed c(4 x 2) O and CO overlayer shows that both the CO molecules and the O atoms occupy bridge sites. The O atoms show significant lateral displacements of 0.14 angstrom away from the CO molecules; the C-O bond is slightly expanded with respect to the gas phase (1.19 angstrom); the modifications of the Ir substrate with respect to the bulk-terminated surface are very small. (c) 2006 Elsevier B.V. All rights reserved.

Oxovanadium(V) complexes of bis(phenolate) ligands with acetylacetone as co-ligand: synthesis, crystal structure, electrochemical and kinetics studies on the oxidation of ascorbic acid

Two vanadium(V) complexes, [VO(L-1)]acac)] (1) and [VO(L-2)(acac)] (2), where H2L1 = N,N-bis(2-hydroxy-3-5-di-tert-butyl-benzyl)propylamine and H2L2 = 2,2'-selenobis(4,6-di-tert-butylphenol), have been synthesized and characterized by elemental analyses, IR, V-51 NMR, both in the solid and in solution, and cyclic voltammetric studies. Single crystal X-ray studies reveal that in complex 1 the vanadium atom is octahedrally coordinated with an O5N donor environment, where the oxygen atom of the V-V=O moiety and the N atom of the ONO ligand occupy the axial sites while two oxygen atoms (O1 and O2) from the bisphenolate ligand and two oxygen atoms (O3 and O4) from the acac ligand occupy the equatorial plane. A similar bonding pattern has also been encountered for 2 with the exception that a Se atom instead of N is involved in weak bonding to the metal center. Both complexes showed reversible cyclic voltammeric responses and E-1/2 appears at -0.18 and 0.10 V versus NHE for complexes 1 and 2, respectively. The kinetics of oxidation of ascorbic acid by complex 1 were carried out in 50% MeCN-50% HO (v/v) at 25 degrees C. The high formation constant value, Q = 63 +/- 7 M-1, reveals that the reaction proceeds through the rapid formation of a H-bonded intermediate. The low k(2)Q(2)/k(1)Q(1) ratio (13.4) for 1 points out that there is extensive H-bonding between the oxygen atom of the V-V=O group and the OH group of ascorbic acid. (c) 2007 Published by Elsevier Ltd.

Self-nucleation and crystallization kinetics of double crystalline poly(p-dioxanone)-b-poly(epsilon-caprolactone) diblock copolymers

The crystallization kinetics of each constituent of poly(p-dioxanone)-b-poly(epsilon-caprolactone) diblock copolymers (PPDX-b-PCL) has been determined in a wide composition range by differential scanning calorimetry and compared to that of the equivalent homopolymers. Spherulitic growth rates were also measured by polarized optical microscopy while atomic force microscopy was employed to reveal the morphology of one selected diblock copolymer. It was found that crystallization drives structure formation and both components form lamellae within mixed spherulitic superstructures. The overall isothermal crystallization kinetics of the PPDX block at high temperatures, where the PCL is molten, was determined by accelerating the kinetics through a previous self-nucleation procedure. The application of the Lauritzen and Ho. man theory to overall growth rate data yielded successful results for PPDX and the diblock copolymers. The theory was applied to isothermal overall crystallization of previously self-nucleated PPDX ( where growth should be the dominant factor if self-nucleation was effective) and the energetic parameters obtained were perfectly matched with those obtained from spherulitic growth rate data of neat PPDX. A quantitative estimate of the increase in the energy barrier for crystallization of the PPDX block, caused by the covalently bonded molten PCL as compared to homo-PPDX, was thus determined. This energy increase can dramatically reduce the crystallization rate of the PPDX block as compared to homo-PPDX. In the case of the PCL block, both the crystallization kinetics and the self-nucleation results indicate that the PPDX is able to nucleate the PCL within the copolymers and heterogeneous nucleation is always present regardless of composition. Finally, preliminary results on hydrolytic degradation showed that the presence of relatively small amounts of PCL within PPDX-bPCL copolymers substantially retards hydrolytic degradation of the material in comparison to homo-PPDX. This increased resistance to hydrolysis is a complex function of composition and its knowledge may allow future prediction of the lifetime of the material for biomedical applications.