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.

Direct time-resolved study of the gas-phase reactions of germylene with ethyl- and diethylgermane: absolute rate constants, temperature dependences, and mechanism

Time-resolved studies of germylene, GeH2, generated by the 193 nm laser flash photolysis of 3,4-dimethyl-1-germacyclopent-3-ene, have been carried out to obtain rate constants for its bimolecular reactions with ethyl- and diethylgermanes in the gas phase. The reactions were studied over the pressure range 1-100 Torr with SF6 as bath gas and at five temperatures in the range 297-564 K. Only slight pressure dependences were found for GeH2 + EtGeH3 (399, 486, and 564 K). The high pressure rate constants gave the following Arrhenius parameters: for GeH2 + EtGeH3, log A = -10.75 +/- 0.08 and E-a = -6.7 +/- 0.6 kJ mol(-1); for GeH2 + Et2GeH2, log A = -10.68 +/- 0.11 and E-a = -6.95 +/- 0.80 kJ mol(-1). These are consistent with fast, near collision-controlled, association processes at 298 K. RRKM modeling calculations are, for the most part, consistent with the observed pressure dependence of GeH2 + EtGeH3. The ethyl substituent effects have been extracted from these results and are much larger than the analogous methyl substituent effects in the SiH2 + methylsilane reaction series. This is consistent with a mechanistic model for Ge-H insertion in which the intermediate complex has a sizable secondary barrier to rearrangement.

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.

Time-resolved gas-phase kinetic and quantum chemical studies of the reaction of silylene with oxygen

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reaction with O-2. The reaction was studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at five temperatures in the range 297-600 K. The second order rate constants at 10 Torr were fitted to the Arrhenius equation: log(k/cm(3) molecule(-1) s(-1)) = (-11.08 +/- 0.04) + (1.57 +/- 0.32 kJ mol(-1))/RT ln10 The decrease in rate constant values with increasing temperature, although systematic is very small. The rate constants showed slight increases in value with pressure at each temperature, but this was scarcely beyond experimental uncertainty. From estimates of Lennard-Jones collision rates, this reaction is occurring at ca. 1 in 20 collisions, almost independent of pressure and temperature. Ab initio calculations at the G3 level backed further by multi-configurational (MC) SCF calculations, augmented by second order perturbation theory (MRMP2), support a mechanism in which the initial adduct, H2SiOO, formed in the triplet state (T), undergoes intersystem crossing to the more stable singlet state (S) prior to further low energy isomerisation processes leading, via a sequence of steps, ultimately to dissociation products of which the lowest energy pair are H2O + SiO. The decomposition of the intermediate cyclo-siladioxirane, via O-O bond fission, plays an important role in the overall process. The bottleneck for the overall process appears to be the T -> S process in H2SiOO. This process has a small spin orbit coupling matrix element, consistent with an estimate of its rate constant of 1 x 10(9) s(-1) obtained with the aid of RRKM theory. This interpretation preserves the idea that, as in its reactions in general, SiH2 initially reacts at the encounter rate with O-2. The low values for the secondary reaction barriers on the potential energy surface account for the lack of an observed pressure dependence. Some comparisons are drawn with the reactions of CH2 + O-2 and SiCl2 + O-2.

Time-resolved gas-phase kinetic and quantum chemical studies of the reaction of silylene with nitric oxide

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reaction with NO. The reaction was studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas at five temperatures in the range 299-592 K. The second-order rate constants at 10 Torr fitted the Arrhenius equation log(k/cm(3) molecule(-1) s(-1)) = (- 11.66 +/- 0.01) + (6.20 +/- 0.10 kJ mol(-1))IRT In 10 The rate constants showed a variation with pressure of a factor of ca. 2 over the available range, almost independent of temperature. The data could not be fitted by RRKM calculations to a simple third body assisted association reaction alone. However, a mechanistic model with an additional (pressure independent) side channel gave a reasonable fit to the data. Ab initio calculations at the G3 level supported a mechanism in which the initial adduct, bent H2SiNO, can ring close to form cyclo-H2SiNO, which is partially collisionally stabilized. In addition, bent H2SiNO can undergo a low barrier isomerization reaction leading, via a sequence of steps, ultimately to dissociation products of which the lowest energy pair are NH2 + SiO. The rate controlling barrier for this latter pathway is only 16 kJ mol(-1) below the energy of SiH2 + NO. This is consistent with the kinetic findings. A particular outcome of this work is that, despite the pressure dependence and the effects of the secondary barrier (in the side reaction), the initial encounter of SiH2 with NO occurs at the collision rate. Thus, silylene can be as reactive with odd electron molecules as with many even electron species. Some comparisons are drawn with the reactions of CH2 + NO and SiCl2 + NO.

Reactions of silylene with unreactive molecules. 2. nitrogen: gas-phase kinetic and theoretical studies

Time-resolved studies of the reaction of silylene, SiH2, with N-2 have been attempted at 296, 417, and 484 K, using laser flash photolysis to generate and monitor SiH2. No conclusive evidence for reaction could be found even with pressures of N-2 of 500 Torr. This enables us to set upper limits of ca. 3 x 10(-15) cm(3) molecule(-1) s(-1) for the second-order rate constants. A lower limit for the activation energy, E-a, of ca. 47 kJ mol(-1) is also derived. Ab initio calculations at the G3 level indicate that the only SiH2N2 species of lower energy than the separated reactants is the H2Si...N-2 donor-acceptor (ylid) species with a relative enthalpy of -26 kJ mol(-1), insufficient for observation of reaction under the experimental conditions. Ten bound species on the SiH2N2 surface were found and their energies calculated as well as those of the potential dissociation products: HSiN + NH((3)Sigma(-)) and HNSi + NH((3)Sigma(-)). Additionally two of the transition states involving cyclic-SiH2N2 (siladiazirine) were explored. It appears that siladiazirine is neither thermodynamically nor kinetically stable. The findings indicate that Si-N-d bonds (where N-d is double-bonded nitrogen) are not particularly strong. An unexpected cyclic intermediate was found in the isomerization of silaisocyanamide to silacyanamide.

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).

Metal complexes of a dipyridine octaazamacrocycle: stability constants, structural and modelling studies

Two 28-membered octaazamacrocycles, [28]py(2)N(6) and Me-2[28]py(2)N(6), have been synthesized. The protonation constants of the N-methyl. derivative and the stability constants of its complexes with Ni2+, Cu2+, Zn2+, Cd2+, and Pb2+ were determined at 25degreesC in 0.10 mol dm(-3) KNO3. The high overall basicity of Me-2[28]py(2)N(6) is ascribed to the weaker repulsion between protonated contiguous charged ammonium sites separated by propyl chains. These studies together with NMR, UV-vis and EPR spectroscopies indicated the presence of mono- and di-nuclear species, The single crystal structure of the complex [Ni-2([28]py(2)N(6))(H2O)(4)]Cl-4.3H(2)O was determined, and showed each nickel centre in a distorted octahedral co-ordination environment. The nickel centres are held within the macrocycle at a large distance of 6.991(g) Angstrom from each other. The formation of mononuclear complexes was evaluated theoretically via molecular mechanics (MM) and molecular dynamics (MD) calculations and showed that these large macrocycles have sufficient flexibility to encapsulate metal ions with different stereo-electronic sizes. Structures for small and large metal ions are proposed.

Metal complexes of cyclen and cyclam derivatives useful for medical applications: a discussion based on thermodynamic stability constants and structural data

A series of the most common chelators used in magnetic resonance imaging ( MRI) and in radiopharmaceuticals for medical diagnosis and tumour therapy, H(4)dota, H(4)teta, H(8)dotp and H(8)tetp, is examined from a chemical point of view. Differences between 12- and 14-membered tetraazamacrocyclic derivatives with methylcarboxylate and methylphosphonate pendant arms and their chelates with divalent first-series transition metal and trivalent lanthanide ions are discussed on the basis of their thermodynamic stability constants, X- ray structures and theoretical studies.

Acid dissociation of 2,2 '-dipyridylamine in non-aqueous medium when chelated to some Ru(II)N-4 cores

[Ru(2,2'-bipyridine)(2)(Hdpa)](BF4)(2) center dot 2H(2)O (1), [Ru(1,10-phenanthroline)(2)(Hdpa)] (PF6)(2) center dot CH2Cl2 (2) and [Ru(4,4,4',4'-tetramethyl-2,2'- bisoxazoline)(2)(Hdpa)] (PF6)(2) (3) are synthesized where Hdpa is 2,2'-dipyridylamine. The X-ray crystal structures of 1 and 2 have been determined. Hdpa in 1 and 2 is found to bind the metal via the two pyridyl N ends. Comparing the NMR spectra in DMSO-d(6), it is concluded that 3 has a similar structure. The pK(a) values (for the dissociation of the NH proton in Hdpa) of free Hdpa and its complexes are determined in acetonitrile by exploiting molar conductance. These correlate linearly with the chemical shift of the NH proton in the respective entities. (C) 2007 Elsevier B.V. All rights reserved.

A monoaqua zinc complex. Unique acid dissociation behaviour

Using the I : 2 condensate of benzil dihydrazone and 2-acetylpyridine as the ligand L, two complexes of zinc, [ZnL(CH3COO)]PF6 (1) and [ZnL(H2O)CIO4]CIO4 H2O (2), are synthesised from Zn(CH3COO)(2).2H(2)O and Zn(CIO4)(2).6H(2)O, respectively. From X-ray crystallography, both the complexes are found to be single helical with the metal in distorted octahedral N4O2 environment. In 1, the two oxygen atoms come from the bidentate acetate while 2 is a monoaqua complex with a perchlorate anion bound to the metal in monodentate fashion. The perchlorate in 2 is not at all weakly bound [Zn-O(perchlorate) 2.256(4) A]. Still in acetonitrile solution, the coordinated perchlorate ion dissociates upon deprotonation [reaction (i)].

On defining base units in terms of fundamental constants

The definitions of the base units of the international system of units have been revised many times since the idea of such an international system was first conceived at the time of the French revolution. The objective today is to define all our units in terms of 'invariants of nature', i.e. by referencing our units to the fundamental constants of physics, or the properties of atoms, rather than the characteristics of our planet or of artefacts. This situation is reviewed, particularly in regard to finding a new definition of the kilogram to replace its present definition in terms of a prototype material artefact.

Dissociation of water on oxygen-covered Rh{111}

The adsorption of water and coadsorption with oxygen on Rh{111} under ultrahigh vacuum conditions was studied using synchrotron-based photoemission and photoabsorption spectroscopy. Water adsorbs intact on the clean surface at temperatures below 154 K. Irradiation with x-rays, however, induces fast dissociation and the formation of a mixed OH+H(2)O layer indicating that the partially dissociated layer is thermodynamically more stable. Coadsorption of water and oxygen at a coverage below 0.3 monolayers has a similar effect, leading to the formation of a hydrogen-bonded network of water and hydroxyl molecules at a ratio of 3:2. The partially dissociated layers are more stable than chemisorbed intact water with the maximum desorption temperatures up to 30 K higher. For higher oxygen coverage, up to 0.5 monolayers, water does not dissociate and an intact water species is observed above 160 K, which is characterized by an O 1s binding energy 0.6 eV higher than that of chemisorbed water and a high desorption temperature similar to the partially dissociated layer. The extra stabilization is most likely due to hydrogen bonds with atomic oxygen.

Evaluation of data for atmospheric models: master equation/RRKM calculations on the combination reaction, BrO+NO2 -> BrONO2, a conundrum

Experimental data for the title reaction were modeled using master equation (ME)/RRKM methods based on the Multiwell suite of programs. The starting point for the exercise was the empirical fitting provided by the NASA (Sander, S. P.; Finlayson-Pitts, B. J.; Friedl, R. R.; Golden, D. M.; Huie, R. E.; Kolb, C. E.; Kurylo, M. J.; Molina, M. J.; Moortgat, G. K.; Orkin, V. L.; Ravishankara, A. R. Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies, Evaluation Number 15; Jet Propulsion Laboratory: Pasadena, California, 2006)(1) and IUPAC (Atkinson, R.; Baulch, D. L.; Cox, R. A.: R. F. Hampson, J.; Kerr, J. A.; Rossi, M. J.; Troe, J. J. Phys. Chem. Ref. Data. 2000, 29, 167) 2 data evaluation panels, which represents the data in the experimental pressure ranges rather well. Despite the availability of quite reliable parameters for these calculations (molecular vibrational frequencies (Parthiban, S.; Lee, T. J. J. Chem. Phys. 2000, 113, 145)3 and a. value (Orlando, J. J.; Tyndall, G. S. J. Phys. Chem. 1996, 100,. 19398)4 of the bond dissociation energy, D-298(BrO-NO2) = 118 kJ mol(-1), corresponding to Delta H-0(circle) = 114.3 kJ mol(-1) at 0 K) and the use of RRKM/ME methods, fitting calculations to the reported data or the empirical equations was anything but straightforward. Using these molecular parameters resulted in a discrepancy between the calculations and the database of rate constants of a factor of ca. 4 at, or close to, the low-pressure limit. Agreement between calculation and experiment could be achieved in two ways, either by increasing Delta H-0(circle) to an unrealistically high value (149.3 kJ mol(-1)) or by increasing , the average energy transferred in a downward collision, to an unusually large value (> 5000 cm(-1)). The discrepancy could also be reduced by making all overall rotations fully active. The system was relatively insensitive to changing the moments of inertia in the transition state to increase the centrifugal effect. The possibility of involvement of BrOONO was tested and cannot account for the difficulties of fitting the data.