Complex Kinetic Data Research Articles

Case Study 2: Practical Analytical Considerations for Conducting In Vitro Enzyme Kinetic Studies.

Characterization of enzyme kinetics in an experiment is dependent on measurement of a change in concentration of either the substrate (loss of parent) or the product (formation of metabolite). Modern analytical techniques such as ultrahigh pressure liquid chromatography, high resolution mass spectrometry, etc. have allowed accurate characterization of minute changes in concentration. Therefore, complex kinetic data such as a sigmoidal phase at low substrate concentrations or terminal half-life in a PK curve can be evaluated by stretching the limits of analytical quantification. This chapter presents some elementary dos and don'ts and provides insight into some of the underlying principles for utilizing the best possible analytical techniques when investigating enzyme kinetics. The objective of this case study is to answer the following questions: (a) Why is it necessary to determine lower and upper limits of quantification (LLOQ and ULOQ, respectively) of a bioanalytical assay, specifically for enzyme kinetic assays? How do you utilize LLOQ and ULOQ to correctly interpret your kinetic data? (b) Why should one use a linear fit and not a quadratic fit for standard curves? (c) Is quantification of an analyte possible without a reference standard? Can one assume equal signal intensities regardless of analytical technique (MS, UV)? (d) In the absence of reference standards, can you still determine kinetic constants? (e) With the need to keep substrate depletion at less than 20% for linearity assumptions, does bioanalytical variability matter? (f) What buffer do you use for your enzyme systems? How do you choose your buffer ? Does choice of bioanalytical methods (LC, MS) dictate your choice of buffer ?

Kinetic analysis of particle-size based complex kinetic processes

Complex kinetic data arbitrarily created by measuring (calorimetrically) crystallization of mixed selenium powders with different defined particle sizes were evaluated by the three standard approaches to complex kinetic analysis. Performance of the three tested approaches was tested by comparison with the kinetic results obtained for the separate powder fractions. The additivity of the kinetic signals was verified. Single-process methods of kinetic analysis provided qualitative and quantitative information about the temperature dependence of activation energy E and estimation of the ratio between intensities of the involved sub-processes I1/I2. Mathematic deconvolution approach well reflected the correct model-free and model-based kinetics for the partial overlaps. However, it required iterative processing and additional supplemental information about the nature of the sub-processes in case of the evaluation of fully overlapping data. Kinetic deconvolution based on single-curve non-linear optimization utilizing the fixed E values obtained independently provided very good results for both, partial and full overlaps.

Catalytic reactions of dioxygen with ethane and methane on platinum clusters: Mechanistic connections, site requirements, and consequences of chemisorbed oxygen

C2H6 reactions with O2 only form CO2 and H2O on dispersed Pt clusters at 0.2–28 O2/C2H6 reactant ratios and 723–913K without detectable formation of partial oxidation products. Kinetic and isotopic data, measured under conditions of strict kinetic control, show that CH4 and C2H6 reactions involve similar elementary steps and kinetic regimes. These kinetic regimes exhibit different rate equations, kinetic isotope effects and structure sensitivity, and transitions among regimes are dictated by the prevalent coverages of chemisorbed oxygen (O*). At O2/C2H6 ratios that lead to O*-saturated surfaces, kinetically-relevant CH bond activation steps involve O*O* pairs and transition states with radical-like alkyls. As oxygen vacancies (∗) emerge with decreasing O2/alkane ratios, alkyl groups at transition states are effectively stabilized by vacancy sites and CH bond activation occurs preferentially at O** site pairs. Measured kinetic isotope effects and the catalytic consequences of Pt cluster size are consistent with a monotonic transition in the kinetically-relevant step from CH bond activation on O*O* site pairs, to CH bond activation on O** site pairs, to O2 dissociation on ** site pairs as O* coverage decrease for both C2H6 and CH4 reactants. When CH bond activation limits rates, turnover rates increase with increasing Pt cluster size for both alkanes because coordinatively unsaturated corner and edge atoms prevalent in small clusters lead to more strongly-bound and less-reactive O* species and lower densities of vacancy sites at nearly saturated cluster surfaces. In contrast, the highly exothermic and barrierless nature of O2 activation steps on uncovered clusters leads to similar turnover rates on Pt clusters with 1.8–8.5nm diameter when this step becomes kinetically-relevant at low O2/alkane ratios. Turnover rates and the O2/alkane ratios required for transitions among kinetic regimes differ significantly between CH4 and C2H6 reactants, because of the different CH bond energies, strength of alkylO* interactions, and O2 consumption stoichiometries for these two molecules. Vacancies emerge at higher O2/alkane ratios for C2H6 than for CH4 reactants, because their weaker CH bonds lead to faster scavenging of O* and to lower O* coverages, which are set by the kinetic coupling between CH and OO activation steps. The elementary steps, kinetic regimes, and mechanistic analogies reported here for C2H6 and CH4 reactions with O2 are consistent with all rate and isotopic data, with their differences in CH bond energies and in alkyl binding, and with the catalytic consequences of surface coordination and cluster size. The rigorous mechanistic interpretation of these seemingly complex kinetic data and cluster size effects provides useful kinetic guidance for larger alkanes and other catalytic surfaces based on the thermodynamic properties of these molecules and on the effects of metal identity and surface coordination on oxygen binding and reactivity.

Numerical Matrices Method for Nonlinear System Identification and Description of Dynamics of Biochemical Reaction Networks

A flexible Numerical Matrices Method (NMM) for nonlinear system identification has been developed based on a description of the dynamics of the system in terms of kinetic complexes. A set of related methods are presented that include increasing amounts of prior information about the reaction network structure, resulting in increased accuracy of the reconstructed rate constants. The NMM is based on an analytical least squares solution for a set of linear equations to determine the rate parameters. In the absence of prior information, all possible unimolecular and bimolecular reactions among the species in the system are considered, and the elements of a general kinetic matrix are determined. Inclusion of prior information is facilitated by formulation of the kinetic matrix in terms of a stoichiometry matrix or a more general set of representation matrices. A method for determination of the stoichiometry matrix beginning only with time-dependent concentration data is presented. In addition, we demonstrate that singularities that arise from linear dependencies among the species can be avoided by inclusion of data collected from a number of different initial states. The NMM provides a flexible set of tools for analysis of complex kinetic data, in particular for analysis of chemical and biochemical reaction networks.

Can a two-state MWC allosteric model explain hemoglobin kinetics?

We have analyzed the nanosecond-millisecond kinetics of ligand binding and conformational changes in hemoglobin. The kinetics were determined from measurements of precise time-resolved optical spectra following nanosecond photodissociation of the heme-carbon monoxide complex. To fit the data, it was necessary to extend the two-state allosteric model of Monod, Wyman, and Changeux (MWC) to include geminate ligand rebinding and nonexponential tertiary relaxation within the R quaternary structure. Considerable simplification of the model is obtained by using a linear free energy relation for the rates of quaternary transitions, and by incorporating concepts from recent studies on the physics of geminate rebinding and conformational changes in myoglobin. The model, described by 85 coupled differential equations, quantitatively explains a demanding set of complex kinetic data. Moreover, with the same set of kinetic parameters it simultaneously fits the equilibrium data on ligand binding and the distribution of ligation states. The present results, together with those from single-crystal oxygen binding studies, indicate that the two-state MWC allosteric model has survived its most critical tests.

The use of neural networks for fitting complex kinetic data

In this paper the use of neural networks for fitting complex kinetic data is discussed. To assess the validity of the approach two different neural network architectures are compared with the traditional kinetic identification methods for two cases: the homogeneous esterification reaction between propionic anhydride and 2-butanol, catalysed by sulphuric acid, and the heterogeneous liquid-liquid toluene mononitration by mixed acid. A large set of experimental data obtained by adiabatic and heat flux calorimetry and by gas chromatography is used for the training of the neural networks. The results indicate that the neural network approach can be used to deal with the fitting of complex kinetic data to obtain an approximate reaction rate function in a limited amount of time, which can be used for design improvement or optimisation when, owing to small production levels or time constraints, it is not possible to develop a detailed kinetic analysis.

18] Compartmental analysis of enzyme-catalyzed reactions

This chapter discusses the compartmental analysis of the chemistry of enzyme catalyzed reactions. It presents a background to the development and evolution of chemistry of enzyme catalyzed reactions. The chapter illustrates an example in which the analysis of the time-resolved kinetics of a restriction endonuclease-catalyzed reaction is accomplished by compartmental analysis using methodology developed by Berman and colleagues. Traditionally, in the analysis of complex kinetic data, a model is proposed and the corresponding differential equations are written and solved numerically. This sequence must be repeated for succeeding models. The process is tedious, computationally intensive, and, therefore, not often employed except for simple systems. High turnover and low substrate affinity are the signatures of the enzymes of intermediary metabolism. In the analysis of enzyme kinetics by the steady-state approach, it is the differential (rate) equation that is directly analyzed. With the approach of Berman, the kinetic data are analyzed first to determine the relations between compartments using an interactive program for model simulation and data analysis. Subsequently, the compartmental model is interpreted in terms of chemical processes. These processes are represented as transfers of species from one compartment to another. A compartment may be a unique chemical species, or it may be several chemical species. The program SAAM/CONSAM, an interactive program for simulation, analysis, and modeling, has the advantage that models may be easily developed and modified. The chapter presents an application of this type of kinetic analysis to a restriction endonuclease using Bam HI as a model system and shows that the cleavage process may be easily resolved into separate binding and hydrolytic steps.

Simple enzyme kinetic mechanisms that can give all possible velocity profiles with chemically reasonable rate constant values

It is shown that all rate profiles and double reciprocal plots possible for arbitrary rational functions of degree n : n can be given by enzyme mechanisms in which rate constant values are limited by physical constraints. The significance of this finding in the theory of complex kinetics is explained, and the application in the area of non-linear regression analysis of complex kinetic data and model discrimination, is discussed.

Complex kinetic data obtained with neutral proteinase and its inhibitor present in tumour-cell preparations.

Complex kinetic data obtained with neutral proteinase and its inhibitor present in tumour-cell preparations.

The interactiion of a trypsin-dependent neutral protease and its inhibitor found in tumour cells Analysis of complex kinetic data involved in a thiol-disulphide exchange mechanism

Ehrlich ascites tumour cells contain a granule-derived zymogen which on trypsin activation yields on collegenolytic neutral protease. The preparation of the granule fraction by subcellular fractionation procedure results in the preparation of a second fraction referred to as the post-granule supernatant fraction. The post-granule supernatant fraction contains a latent form of the granule-derived neutral protease and an excess of cytoplasmic inhibitor for this enzyme. The inhibitor of neutral protease is also capable of inhibiting trypsin and in each case the chemical mechanism of enzyme · inhibitor complex formation has been shown to be a reversible thiol-disulphide exchange. The post-granule supernatant fraction exhibited complex kinetic data when the interactions between the inhibitor, the latent enzymes and trypsin were examined simultaneously by incremental analysis. The data were interpreted and quantitatively analysed by computer analysis. It was demonstrated that the conventional types of analysis could not have provided meaningful interpretations of the experimental data provided by these complex-interacting systems.

Plasma Membrane-associated Adenosine Triphosphatase Activity of Isolated Cortex and Stele from Corn Roots

The plasma membrane fractions from separated cortex and stele of primary roots of corn (Zea mays L. WF9 x M14) contained cation ATPase activity at similar levels but with somewhat different properties. ATPase activity from cortex was optimum at pH 6.5, showed a simple Michaelis-Menten saturation with increasing ATP.Mg, and showed complex kinetic data for K(+) stimulation similar in character to the kinetic data for K(+)-ATPase and K(+) influx in primary roots. The results for cortex indicate that homogenates of primary roots are dominated by membranes from cortical cells.ATPase activity from stele was optimum at pH 6.5 and showed another maximum at pH 9. At pH 6.5, activity from stele had properties similar to that from cortex except that the kinetics of K(+) stimulation closely approached that expected for a Michaelis-Menten enzyme. At pH 9, the enzyme activity from stele was inhibited by 5 mug/ml oligomycin, suggesting that a significant portion of the activity was of mitochondrial origin. Sucrose density gradient analysis indicated some contamination of mitochondrial membranes in the plasma membrane fraction from stele. The results for stele are consistent with the view that stelar parenchyma cells are not deficient in ion pumps.

Studies on the partial reactions catalyzed by the (Na 2+ + L +-activated ATPase. I. Effects of simple anions and nucleoside triphosphates on the alkali-cation specificity of the p-nitrophenylphosphatase

1. 1. The K +-dependent p-nitrophenylphosphatase activity of the (Na 2+ + K +)-activated. ATPase complex is stimulated by the addition of Na + + ATP. Since oligomycin blocks the (Na + + ATP)-stimulation, but not the K +-dependent activity, the existence of a “K +-sensitive sit” and a “Na +-sensitive site” is indicated. The object of this work was to learn more about these sites through kinetic studies. 2. 2. The “K +-sensitive site” responded to Li +, Rb +, and Cs +; but the “Na +-sensitive site” showed absolute specificity for Na +. 3. 3. The order of cation specificity of the “K +-sensitive site” (K + = Rb + > Cs + > Li +), and the absolute specificity of the “Na +-sensitive site” remained constant under conditions ( e.g., change in the major anion of the assay medium) which had been used to demonstrate the changing specificity of another alkali-cation-activated enzyme (AMP deaminase). 4. 4. The “ +-sensitive site” could be demonstrated only in the presence of certain nucleoside triphosphates (ATP, ITP and CTP). Nucleoside diphosphates, nucleoside monophosphates, pyrophosphate and orthophosphate had no activating effects in the presence of Na +. 5. 5. A variety of simple anions were found to have inhibitory effects on the enzyme. Because of this, and due to the impurity of the enzyme, the complex kinetic data were of little value for mechanistic interpretations. 6. 6. Na + inhibited the enzyme both in the presence and absence of an activator cation. From the kinetic data it was not possible to determine if this inhibition was exerted at the same “Na +-sensitive site” that is involved in the (Na + + ATP)-activation of the enzyme.