Interpretation of the temperature dependence of rate constants in biosensor studies

A comparison is made between Arrhenius and transition-state analyses of the temperature dependence of rate constants reported in four published biosensor studies. Although the Eyring transition-state theory seemingly affords a more definitive solution to the problem of characterizing the activation energetics, the analysis is equivocal because of inherent assumptions about reaction mechanism and the magnitude of the transmission coefficient. In view of those uncertainties it is suggested that a preferable course of action entails reversion to the empirical Arrhenius analysis with regard to the energy of activation and a preexponential factor. The former is essentially equivalent to the enthalpy of activation, whereas the magnitude of the latter indicates directly the extent of disparity between the frequency of product formation and the universal frequency factor (temperature multiplied by the ratio of the Boltzmann and Planck constants) and hence the likelihood of a more complicated kinetic mechanism than that encompassed by the Eyring transition-state theory. (C) 2004 Elsevier Inc. All rights reserved.

Electronic energy-transfer rate constants for geometrical isomers of a bichromophoric macrocyclic complex

The rate of electronic energy transfer (EET) between a naphthalene donor and an anthracene acceptor in [ZnL3]-(ClO4)(2) and [ZnL4](ClO4)(2) was determined by time-resolved fluorescence measurements, where L 3 and L 4 are the geometrical isomers of 6-[(anthracen-9-ylmethyl)amino]-trans-6,13-dimethyl-1,4,8,11-tetraazacyclotetradecane-13-amine (L-2), substituted with either a naphthalen-1-ylmethyl or naphthalen-2-ylmethyl donor, respectively. The energy transfer rate constant, k(EET), was determined to be (0.92 +/- 0.02) x 10(9) s(-1) for the naphthalen-1-ylmethyl-substituted isomer, while that for the naphthalen-2-ylmethyl-substituted isomer is somewhat faster, with k(EET) = (1.31 +/- 0.01) x 10(9) s(-1). The solid-state structure of [(ZnLCl)-Cl-3]ClO4 has been determined, and using molecular modeling calculations, the likely distributions of solution conformations in CH3CN have been evaluated for both complexes. The calculated conformational distributions in the common trans-III N-based isomeric form gave Forster EET rate constants that account for the differences observed and are in excellent agreement with the experimental values. It is shown that the full range of conformers must be considered to accurately reproduce the observed EET kinetics.

Interpretation of the temperature dependence of equilibrium and rate constants

The objective of this review is to draw attention to potential pitfalls in attempts to glean mechanistic information from the magnitudes of standard enthalpies and entropies derived from the temperature dependence of equilibrium and rate constants for protein interactions. Problems arise because the minimalist model that suffices to describe the energy differences between initial and final states usually comprises a set of linked equilibria, each of which is characterized by its own energetics. For example, because the overall standard enthalpy is a composite of those individual values, a positive magnitude for AHO can still arise despite all reactions within the subset being characterized by negative enthalpy changes: designation of the reaction as being entropy driven is thus equivocal. An experimenter must always bear in mind the fact that any mechanistic interpretation of the magnitudes of thermodynamic parameters refers to the reaction model rather than the experimental system For the same reason there is little point in subjecting the temperature dependence of rate constants for protein interactions to transition-state analysis. If comparisons with reported values of standard enthalpy and entropy of activation are needed, they are readily calculated from the empirical Arrhenius parameters. Copyright (c) 2006 John Wiley & Sons, Ltd.

Temperature dependence of the thrombin-catalyzed proteolysis of prothrombin

Measurement of the temperature-dependence of thrombin-catalyzed cleavage of the Arg(155)-Ser(156) and Arg(284)-Thr(285) peptide bonds in prothrombin and prothrombin-derived substrates has yielded Arrhenius parameters that are far too large for classical mechanistic interpretation in terms of a simple hydrolytic reaction. Such a difference from the kinetic behavior exhibited in trypsin- and chymotrypsin-catalyzed proteolysis of peptide bonds is attributed to contributions by enzyme exosite interactions as well as enzyme conformational equilibria to the magnitudes of the experimentally determined Arrhenius parameters. Although the pre-exponential factor and the energy of activation deduced from the temperature-dependence of rate constants for proteolysis by thrombin cannot be accorded the usual mechanistic significance, their evaluation serves a valuable role by highlighting the existence of contributions other than those emanating from simple peptide hydrolysis to the kinetics of proteolysis by thrombin and presumably other enzymes of the blood coagulation system. (C) 2004 Elsevier B.V. All rights reserved.

Photodissociation of benzene under collision-free conditions: An ab initio/Rice-Ramsperger-Kassel-Marcus study

The ab initio/Rice-Ramsperger-Kassel-Marcus (RRKM) approach has been applied to investigate the photodissociation mechanism of benzene at various wavelengths upon absorption of one or two UV photons followed by internal conversion into the ground electronic state. Reaction pathways leading to various decomposition products have been mapped out at the G2M level and then the RRKM and microcanonical variational transition state theories have been applied to compute rate constants for individual reaction steps. Relative product yields (branching ratios) for C6H5+H, C6H4+H-2, C4H4+C2H2, C4H2+C2H4, C3H3+C3H3, C5H3+CH3, and C4H3+C2H3 have been calculated subsequently using both numerical integration of kinetic master equations and the steady-state approach. The results show that upon absorption of a 248 nm photon dissociation is too slow to be observable in molecular beam experiments. In photodissociation at 193 nm, the dominant dissociation channel is H atom elimination (99.6%) and the minor reaction channel is H-2 elimination, with the branching ratio of only 0.4%. The calculated lifetime of benzene at 193 nm is about 11 mus, in excellent agreement with the experimental value of 10 mus. At 157 nm, the H loss remains the dominant channel but its branching ratio decreases to 97.5%, while that for H-2 elimination increases to 2.1%. The other channels leading to C3H3+C3H3, C5H3+CH3, C4H4+C2H2, and C4H3+C2H3 play insignificant role but might be observed. For photodissociation upon absorption of two UV photons occurring through the neutral hot benzene mechanism excluding dissociative ionization, we predict that the C6H5+H channel should be less dominant, while the contribution of C6H4+H-2 and the C3H3+C3H3, CH3+C5H3, and C4H3+C2H3 radical channels should significantly increase. (C) 2004 American Institute of Physics.

Converged quantum calculations of HO2 bound states and resonances for J=6 and 10

Bound and resonance states of HO2 are calculated quantum mechanically using both the Lanczos homogeneous filter diagonalization method and the real Chebyshev filter diagonalization method for nonzero total angular momentum J=6 and 10, using a parallel computing strategy. For bound states, agreement between the two methods is quite satisfactory; for resonances, while the energies are in good agreement, the widths are in general agreement. The quantum nonzero-J specific unimolecular dissociation rates for HO2 are also calculated. (C) 2004 American Institute of Physics.

Transition-state-theory calculations for reactions of O(3P) with halogenated olefins

The potential energy surfaces for the reactions of atomic oxygen in its ground electronic state, O(P-3), with the olefins: CF2=CCl2 and CF2=CF - CF3, have been characterized using ab initio molecular orbital calculations. Geometry optimization and vibrational frequency calculations were performed for reactants, transition states and products at the MP2 and QCISD levels of theory using the 6-31G(d) basis set. This database was then used to calculate the rate constants by means of Transition-State-Theory. To obtain a better reference and to test the reliability of the activation barriers we have also carried out computations using the CCSD(T)(fc)/6-311Gdagger, MP4(SDQ)(fc)/CBSB4 and MP2(fc)/CBSB3 single point energy calculations at both of the above levels of theory, as well as with the composite CBS-RAD procedure ( P. M. Mayer, C. J. Parkinson, D. M. Smith and L. Radom, J. Chem. Phys., 1998, 108, 604) and a modi. cation of this approach, called: CBS-RAD( MP2, MP2). It was found that the kinetic parameters obtained in this work particularly with the CBS-RAD ( MP2, MP2) procedure are in reasonable agreement with the experimental values. For both reactions it is found that the channels leading to the olefin double-bond addition predominates with respect to any other reaction pathway. However, on account of the different substituents in the alkenes we have located, at all levels of theory, two transition states for each reaction. Moreover, we have found that, for the reactions studied, a correlation exists between the activation energies and the electronic structure of the transition states which can explain the influence of the substituent effect on the reactivity of the halo-olefins.

Kinetics of reduction of lead smelting slags with solid carbon

Research techniques and a methodology have been developed that enable the reduction kinetics of molten lead smelting slags with solid carbon to be studied. The rates of reduction of PbO-FeO-Fe2O3-CaO-SiO2 slags with carbon have been measured for a range of slag compositions for PbO concentrations between 3 and 100 weight percent, and temperatures between 1423 and 1573 K. The reduction rates were determined for both graphite and coke. Within the range of process conditions examined, it has been shown that the reaction rates are almost independent of carbon reactivity, SiO2/CaO and SiO2/Fe ratio in the range of compositions investigated and are not influenced by the presence of sulphur in the slag.The apparent first order rate constants for oxygen removal increase with increasing PbO concentration and oxygen activity in the slag. The data indicate that the rate limiting reaction step for the reduction of lead slags with solid carbon is the chemical reaction at the gas/slag interface.

Unimolecular Rovibrational Bound and Resonance States for Large Angular Momentum: J=20 Calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-> H+O-2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.

Passive air sampling theory for semivolatile organic compounds

The mathematical modelling underlying passive air sampling theory can be based on mass transfer coefficients or rate constants. Generally, these models have not been inter-related. Starting with basic models, the exchange of chemicals between the gaseous phase and the sampler is developed using mass transfer coefficients and rate constants. Importantly, the inter-relationships between the approaches are demonstrated by relating uptake rate constants and loss rate constants to mass transfer coefficients when either sampler-side or air-side resistance is dominating chemical exchange. The influence of sampler area and sampler volume on chemical exchange is discussed in general terms and as they relate to frequently used parameters such as sampling rates and time to equilibrium. Where air-side or sampler-side resistance dominates, an increase in the surface area of the sampler will increase sampling rates. Sampling rates are not related to the sampler/air partition coefficient (K-SV) when air-side resistance dominates and increase with K-SV when sampler-side resistance dominates.

Mechanisms of acetohydroxyacid synthases

Acetohydroxyacid synthases are thiamin diphosphate- (ThDP-) dependent biosynthetic enzymes found in all autotrophic organisms. Over the past 4-5 years, their mechanisms have been clarified and illuminated by protein crystallography, engineered mutagenesis and detailed single-step kinetic analysis. Pairs of catalytic subunits form an intimate dimer containing two active sites, each of which lies across a dimer interface and involves both monomers. The ThDP adducts of pyruvate, acetaldehyde and the product acetohydroxyacids can be detected quantitatively after rapid quenching. Determination of the distribution of intermediates by NMR then makes it possible to calculate individual forward unimolecular rate constants. The enzyme is the target of several herbicides and structures of inhibitor-enzyme complexes explain the herbicide-enzyme interaction.

How an enzyme answers. multiple-choice questions

Acetohydroxyacid synthase (AHAS) is the first common enzyme in the pathway for the biosynthesis of branched-chain amino acids. Interest in the enzyme has escalated over the past 20 years since it was discovered that AHAS is the target of the sulfonylurea and imidazolinone herbicides. However, several questions regarding the reaction mechanism have remained unanswered, particularly the way in which AHAS I chooses' its second substrate. A new method for the detection of reaction intermediates enables calculation of the microscopic rate constants required to explain this phenomenon.

Cyclopropane-1,1-dicarboxylate is a slow-, tight-binding inhibitor of rice ketol-acid reductoisomerase

Ketol-acid reductoisomerase (EC 1.1.1.86) catalyses the second reaction in the biosynthesis of the branched-chain amino acids. The reaction catalyzed consists of two stages, the first of which is an alkyl migration from one carbon atom to its neighbour. The likely transition state is therefore a cyclopropane derivative, and cyclopropane-1,1-dicarboxylate(CPD) has been reported to inhibit the Escherichia coli enzyme. In addition, this compound causes the accumulation of the substrate of ketol-acid reductoisomerase in plants. Here, we investigate the inhibition of the purified rice enzyme. The cDNA was cloned, and the recombinant protein was expressed in E. coli, purified and characterized kinetically. The purified enzyme is strongly inhibited by cyclopropane-1,1-dicarboxylate, with an inhibition constant of 90 nM. The inhibition is time-dependent and this is due to the low rate constants for formation (2.63 X 10(5) M-1 min(-1)) and dissociation (2.37 x 10(-2) min(-1)) of the enzyme-inhibitor complex. Other cyclopropane derivatives are much weaker inhibitors while dimethylmalonate is moderately effective. (c) 2004 Elsevier Ireland Ltd. All rights reserved.

Evaluation of performance reference compounds in polyethylene-based passive air samplers

Polyethylene-based passive air samplers (PSDs) were loaded with performance reference compounds (PRCs) and deployed in a wind tunnel to examine the effects of wind speed on sampler performance. PRCs could be loaded reproducibly into PSDs, with coefficients of variation only exceeding 20% for the more volatile compounds. When PSDs were exposed to low (0.5-1.5 m s(-1)) and high (3.5-4.5 m s(-1)) wind speeds, PRC loss rate constants generally increased with increasing wind speed and decreased with increasing sampler/air partition coefficients. PSD-based air concentrations calculated using PRC loss rate constants and sampler/air partition coefficients and air concentrations measured using active samplers compared closely. PRCs can be used to account for the effect of differences in wind speeds on sampler performance and measure air concentrations with reasonable accuracy. (c) 2006 Elsevier Ltd. All rights reserved.

A D-optimal designed population pharmacokinetic study of itraconazole capsules and solution in adults with cystic fibrosis

Background: Oral itraconazole (ITRA) is used for the treatment of allergic bronchopulmonary aspergillosis in patients with cystic fibrosis (CF) because of its antifungal activity against Aspergillus species. ITRA has an active hydroxy-metabolite (OH-ITRA) which has similar antifungal activity. ITRA is a highly lipophilic drug which is available in two different oral formulations, a capsule and an oral solution. It is reported that the oral solution has a 60% higher relative bioavailability. The influence of altered gastric physiology associated with CF on the pharmacokinetics (PK) of ITRA and its metabolite has not been previously evaluated. Objectives: 1) To estimate the population (pop) PK parameters for ITRA and its active metabolite OH-ITRA including relative bioavailability of the parent after administration of the parent by both capsule and solution and 2) to assess the performance of the optimal design. Methods: The study was a cross-over design in which 30 patients received the capsule on the first occasion and 3 days later the solution formulation. The design was constrained to have a maximum of 4 blood samples per occasion for estimation of the popPK of both ITRA and OH-ITRA. The sampling times for the population model were optimized previously using POPT v.2.0.[1] POPT is a series of applications that run under MATLAB and provide an evaluation of the information matrix for a nonlinear mixed effects model given a particular design. In addition it can be used to optimize the design based on evaluation of the determinant of the information matrix. The model details for the design were based on prior information obtained from the literature, which suggested that ITRA may have either linear or non-linear elimination. The optimal sampling times were evaluated to provide information for both competing models for the parent and metabolite and for both capsule and solution simultaneously. Blood samples were assayed by validated HPLC.[2] PopPK modelling was performed using FOCE with interaction under NONMEM, version 5 (level 1.1; GloboMax LLC, Hanover, MD, USA). The PK of ITRA and OH‑ITRA was modelled simultaneously using ADVAN 5. Subsequently three methods were assessed for modelling concentrations less than the LOD (limit of detection). These methods (corresponding to methods 5, 6 & 4 from Beal[3], respectively) were (a) where all values less than LOD were assigned to half of LOD, (b) where the closest missing value that is less than LOD was assigned to half the LOD and all previous (if during absorption) or subsequent (if during elimination) missing samples were deleted, and (c) where the contribution of the expectation of each missing concentration to the likelihood is estimated. The LOD was 0.04 mg/L. The final model evaluation was performed via bootstrap with re-sampling and a visual predictive check. The optimal design and the sampling windows of the study were evaluated for execution errors and for agreement between the observed and predicted standard errors. Dosing regimens were simulated for the capsules and the oral solution to assess their ability to achieve ITRA target trough concentration (Cmin,ss of 0.5-2 mg/L) or a combined Cmin,ss for ITRA and OH-ITRA above 1.5mg/L. Results and Discussion: A total of 241 blood samples were collected and analysed, 94% of them were taken within the defined optimal sampling windows, of which 31% where taken within 5 min of the exact optimal times. Forty six per cent of the ITRA values and 28% of the OH-ITRA values were below LOD. The entire profile after administration of the capsule for five patients was below LOD and therefore the data from this occasion was omitted from estimation. A 2-compartment model with 1st order absorption and elimination best described ITRA PK, with 1st order metabolism of the parent to OH-ITRA. For ITRA the clearance (ClItra/F) was 31.5 L/h; apparent volumes of central and peripheral compartments were 56.7 L and 2090 L, respectively. Absorption rate constants for capsule (kacap) and solution (kasol) were 0.0315 h-1 and 0.125 h-1, respectively. Comparative bioavailability of the capsule was 0.82. There was no evidence of nonlinearity in the popPK of ITRA. No screened covariate significantly improved the fit to the data. The results of the parameter estimates from the final model were comparable between the different methods for accounting for missing data, (M4,5,6)[3] and provided similar parameter estimates. The prospective application of an optimal design was found to be successful. Due to the sampling windows, most of the samples could be collected within the daily hospital routine, but still at times that were near optimal for estimating the popPK parameters. The final model was one of the potential competing models considered in the original design. The asymptotic standard errors provided by NONMEM for the final model and empirical values from bootstrap were similar in magnitude to those predicted from the Fisher Information matrix associated with the D-optimal design. Simulations from the final model showed that the current dosing regimen of 200 mg twice daily (bd) would provide a target Cmin,ss (0.5-2 mg/L) for only 35% of patients when administered as the solution and 31% when administered as capsules. The optimal dosing schedule was 500mg bd for both formulations. The target success for this dosing regimen was 87% for the solution with an NNT=4 compared to capsules. This means, for every 4 patients treated with the solution one additional patient will achieve a target success compared to capsule but at an additional cost of AUD $220 per day. The therapeutic target however is still doubtful and potential risks of these dosing schedules need to be assessed on an individual basis. Conclusion: A model was developed which described the popPK of ITRA and its main active metabolite OH-ITRA in adult CF after administration of both capsule and solution. The relative bioavailability of ITRA from the capsule was 82% that of the solution, but considerably more variable. To incorporate missing data, using the simple Beal method 5 (using half LOD for all samples below LOD) provided comparable results to the more complex but theoretically better Beal method 4 (integration method). The optimal sparse design performed well for estimation of model parameters and provided a good fit to the data.