Kinetics of a model of autocatalysis, coupling of a reaction in which the enzyme acts on one of its substrates.

A global kinetic analysis is presented of a model of an enzyme autocatalytic process, to which a reaction is coupled, in which the enzyme acts upon one of its substrates. The kinetic equations of both the transient phase and the steady state are derived for this mechanism. In addition, we determine the corresponding kinetic equations for several particular cases which are characterized by certain relations between the rate constants. Finally, a kinetic data analysis is proposed for one of these particular cases. It can easily be extended to any of the other cases.     

Formulation,construction and analysis of kinetic models of metabolism: A review of modelling frameworks

Kinetic models are critical to predict the dynamic behaviour of metabolic networks. Mechanistic kinetic models for large networks remain uncommon due to the difficulty of fitting their parameters. Recent modelling frameworks promise new ways to overcome this obstacle while retaining predictive capabilities. In this review, we present an overview of the relevant mathematical frameworks for kinetic formulation, construction and analysis. Starting with kinetic formalisms, we next review statistical methods for parameter inference, as well as recent computational frameworks applied to the construction and analysis of kinetic models. Finally, we discuss opportunities and limitations hindering the development of larger kinetic reconstructions.     

Investigation of the mechanism of nicotine demethylation in Nicotiana through 2H and 15N heavy isotope effects: implication of cytochrome P450 oxidase and hydroxyl ion transfer

Heavy-atom isotope effects for the N-demethylation of nicotine have been determined in vivo in static-phase biosynthetically incompetent plant cell cultures of Nicotiana species. A (2)H kinetic isotope effect of 0.587 and a (15)N kinetic isotope effect of 1.0028 were obtained. An identical (15)N kinetic isotope effect of 1.0032 was obtained for the nicotine analogue, N-methyl-2-phenylpyrrolidine. The magnitude of the (15)N heavy-atom isotope effect indicates that the fission of the CN bond is not rate limiting for demethylation. The theoretical calculation of heavy-atom isotope effects for a model of the reaction pathway based on cytochrome P450 best fits the measured kinetic isotope effect to the addition of hydroxyl ion to iminium to form N-hydroxymethyl, for which the computed (2)H- and (15)N kinetic isotope effects are 0.689 and 1.0081, respectively. This large inverse (2)H kinetic isotope effect is not compatible with the initial abstraction of the H from the methyl group playing a significant kinetic role in the overall kinetic limitation of the reaction pathway, since computed values for this step (4.54 and 0.9995, respectively) are inconsistent with the experimental data.     

Kinetics of the trypsinogen activation by enterokinase and trypsin

A global kinetic analysis of the mechanisms of the trypsinogen activation by enterokinase and trypsin is presented. The kinetic equations of both the transient-phase and the steady-state of these mechanisms are presented. In addition, we here derive the corresponding kinetic equations for the case in which the condition of rapid equilibrium prevails and we propose a kinetic data analysis. The significance of this approach to the treatment of other zymogen activation processes is discussed.     

Human erythrocyte glutathione reductase: chemical mechanism and structure of the transition state for hydride transfer

Kinetic parameters and primary deuterium kinetic isotope effects for NADH and five pyridine nucleotide substrates have been determined at pH 8.1 for human erythrocyte glutathione reductase. DV/KNADH and DV are equal to 1.4 and are pH independent below pH 8.1, but DV decreases to 1.0 at high pH as a group exhibiting a pK of 8.6 is deprotonated. This result suggests that as His-467' is deprotonated, the rate of the isotopically insensitive oxidative half-reaction is specifically decreased and becomes rate-limiting. For all substrates, equivalent V and V/K primary deuterium kinetic isotope effects are observed at pH values below 8.1. The primary deuterium kinetic isotope effect on V, but not V/K, is sensitive to solvent isotopic composition. The primary tritium kinetic isotope effects agree well with the corresponding value calculated from the primary deuterium kinetic isotope effects by using the Swain-Schaad relationship. This suggests that the primary deuterium kinetic isotope effects observed in these steady-state experiments are the intrinsic primary deuterium kinetic isotope effects for hydride transfer. The magnitude of the primary deuterium kinetic isotope effect is dependent on the redox potential of the pyridine nucleotide substrate used, varying from approximately 1.4 for NADH and -320 mV reductants to 2.7 for thioNADH to 4.2-4.8 for 3-acetylpyridine adenine dinucleotide (3APADH). The alpha-secondary tritium kinetic isotope effects also increase as the redox potential of the pyridine nucleotide substrate becomes more positive. Together, these data indicate that the transition state for hydride transfer is very early for NADH and becomes later for thioNADH and 3APADH, as predicted by Hammond's postulate.(ABSTRACT TRUNCATED AT 250 WORDS)     

Simultaneous determination of thermodynamic and kinetic data by isothermal titration calorimetry

BackgroundThermodynamic and binding kinetic data increasingly support and guide the drug optimization process.MethodsBecause ITC thermograms contain binding thermodynamic and kinetic information, an efficient protocol for the simultaneous extraction of thermodynamic and kinetic data for 1:1 protein ligand reactions from AFFINImeter kinITC in one single experiment are presented.ResultsThe effort to apply this protocol requires the same time as for the standard protocol but increases the precision of both thermodynamic and kinetic data.ConclusionsThe protocol enables reliable extraction of both thermodynamic and kinetic data for 1:1 protein-ligand binding reactions with improved precision compared to the ‘standard protocol’.General significanceThermodynamic and kinetic data are recorded under exactly the same conditions in solution without any labeling or immobilization from a protein sample that is not 100% active and would otherwise render the extraction of kinetic parameters impossible.     

Synthesis and characterisation of novel chromogenic substrates for human pancreatic alpha-amylase

Derivatives of maltose and maltotriose were chemically synthesised as substrates for human pancreatic alpha-amylases and subjected to kinetic analysis. Rates measured were shown to reflect both hydrolysis and transglycosylation reactions. 4-O-Methylated derivatives of these substrates underwent only hydrolysis, thereby simplifying kinetic analyses. These modified substrates may be used for the detection and kinetic analysis of alpha-amylases, and are useful in rapidly screening for novel alpha-amylase inhibitors and for subsequent kinetic characterisation.     

Scanning molecular sieve chromatography of interacting protein systems. III. Effect of kinetic parameters on the large zone boundary profiles for local equilibration between mobile and stationary phases.

Large zone reaction boundary profiles for molecular sieve chromatography as affected by kinetic parameters have been simulated for local equilibration between the mobile and stationary phases. Our studies of monomer-dimer and monomer-tetramer systems indicate that in a slowly equilibrating system, the kinetic controls operating between the mobile and stationary phases contribute most significantly to the overall boundary profile. In a rapidly equilibrating system, however, the kinetic parameters kij and kji operating in the mobile phase are the principal determinants of the reaction boundary, while the kinetic effects of kii and k-ii between the mobile and stationary phases are minimal.     

Malate dehydrogenases. The lack of evidence for dissociation of the dimeric enzyme in kinetic analyses

The kinetic parameters of beef heart cytoplasmic and pig heart mitochondrial malate dehydrogenases have been examined over a wide range of enzyme concentration. No significant changes are observed in these properties. In conjunction with active enzyme sedimentation and sedimentation equilibrium experiments, it is concluded that there is no evidence for dissociation of the dimeric enzyme at any enyzme level in the kinetic analyses. Thus, if dissociation occurs, it must be too slow to be of significance in determining the kinetic properties of the enzyme. It is shown that unless a subunit and its dimeric form have identical kinetic and substrate binding characteristics, the kinetic parameters should change as a function of enzyme concentration.     

Substrate utilization kinetic model for biological treatment process

The applicability of Contois' kinetic equation to aerobic and anaerobic treatments of organic wastes is investigated. A refractory coefficient to account for the nonbiodegradable portion of the organic substrates in the digester is incorporated into the kinetic equation. The kinetic equation is applied to the data for aerobic digestions of organic substrates and for anaerobic treatment of dairy wastes. They all show a very good fit of the kinetic equation to the data. Furthermore, the kinetic parameters and the refractory coefficients are shown to be independent of influent organic substrate concentration. This study confirms previous reports that the effluent quality of biological treatment systems for organic wastes depends on influent organic waste concentration. The effect of temperature on the kinetic parameters and the refractory coefficient for anaerobic treatment of sewage sludge are studied. It shows that the kinetic parameters vary with temperature, while the refractory coefficient remains fairly constant. Equations to predict biodegradable treatment efficiency and volumetric substrate utilization rate are also briefly discussed.     

Kinetic chain lengths in highly cross-linked networks formed by the photoinitiated polymerization of divinyl monomers: a gel permeation chromatography investigation

Highly cross-linked networks formed by the photoinitiated polymerization of multifunctional monomers are finding application in the field of biomaterials because of their chemical versatility, reaction control, and ability to polymerize under physiological conditions. Typically, degradation is introduced into these networks via the cross-links and leads to the release of nondegradable but water-soluble kinetic chains formed during the chain polymerization process. In this study, gel permeation chromatography (GPC) was used to characterize kinetic chain length distributions in highly cross-linked systems that are being developed for orthopedic applications. By polymerizing divinyl monomers to various conversions and subsequently degrading them, we investigated the aspects of network structural evolution related to kinetic chain formation. In general, the average kinetic chain length increased with conversion until the onset of autodeceleration, when the kinetic chains decreased in length as the propagation reaction became diffusion-controlled. The distribution of kinetic chains also changed when different initiation conditions (i.e., initiator concentration and incident light intensity) were used, and a decrease in the kinetic chain lengths was observed at higher initiation rates. Finally, kinetic chain lengths were examined as a function of depth in thick samples polymerized with different light intensities and with a photobleaching initiator. Light attenuation through the sample led to different initiation rates as a function of depth and, consequently, spatial heterogeneity in the network structure as measured by the distributions of kinetic chains.     

Scanning molecular sieve chromatography of interacting protein systems. III. Effect of kinetic parameters on the large zone boundary profiles for local equilibration between mobile and stationary phases

Large zone reaction boundary profiles for molecular sieve chromatography as affected by kinetic parameters have been simulated for local equilibration between the mobile and stationary phases. Our studies of monomer-dimer and monomer-tetramer systems indicate that in a slowly equilibrating system, the kinetic controls operating between the mobile and stationary phases contribute most significantly to the overall boundary profile. In a rapidly equilibrating system, however, the kinetic parameters k(ij) and k(ji) operating in the mobile phase are the principal determinants of the reaction boundary, while the kinetic effects of k(ii) and k-(ii) between the mobile and stationary phases are minimal.     

Multiscale kinetic analysis of proteins

The stochasticity of molecular motion results in the existence of multiple kinetically relevant pathways in many biomolecular mechanisms. Because it is highly demanding to characterize them for complex systems, mechanisms are often described with a single-pathway perspective. However, kinetic network analysis and sub-ensemble experimental insight are increasingly demonstrating not only the existence of competing pathways but also the importance of kinetic selection in biology. This review focuses on advances in multiscale kinetic analysis of proteins, which connects molecular level information from simulations to macroscopic data to characterize mechanistic reaction networks and the reactive flux through them. We describe a range of methods used and highlight several examples where kinetic modeling has revealed functional importance of pathway heterogeneity.     

Kinetics of autocatalytic zymogen activation measured by a coupled reaction: pepsinogen autoactivation

A kinetic study was performed of a model for an autocatalytic zymogen activation process involving both intra- and intermolecular routes, to which a chromogenic reaction in which the active enzyme acts upon one of its substrates was coupled to continuously monitor the reaction. Kinetic equations describing the evolution of species involved in the system with time were obtained. These equations are valid for any zymogen autocatalytic activation process under the same initial conditions. Experimental design and kinetic data analysis procedures to evaluate the kinetic parameters, based on the derived kinetic equations, are suggested. In addition, a dimensionless distribution coefficient was defined, which shows mathematically whether the intra- or the intermolecular route prevails once the kinetic parameters involved in the system are known. The validity of the results obtained was checked using simulated curves for the species involved. As an example of application of the method, the system is experimentally illustrated by the continuous monitoring of pepsinogen transformation to pepsin.     

Efflux of cholesterol from different cellular pools

Free cholesterol is very efficiently removed from cells by 2-hydroxypropyl-beta-cyclodextrins. The efflux of cholesterol occurs from two distinct kinetic pools: the half-times (t(1/2)) for the two pools in CHO-K1 cells are 15 +/- 5 s and 21 +/- 6 min and they represent 25% +/- 5% and 75% +/- 5% of the readily exchangeable cell cholesterol, respectively. In this study we have determined that the fast pool and the majority of the slow kinetic pool for cholesterol efflux are apparently present in the plasma membrane. Numerous agents that inhibit intracellular cholesterol trafficking are unable to affect either the size or the t(1/2) for efflux of either kinetic pool. In contrast, treatment of the cells with N-ethylmaleimide (NEM), exogenous lipases such as sphingomyelinase and phospholipase C, calcium ionophore A23187, or heat resulted in the dramatic increase in the size of the fast kinetic pool of cholesterol. These changes in the kinetics of cholesterol efflux are not specific to the nature of the extracellular acceptor indicating that they are a consequence of changes in the cell plasma membrane. The above treatments disrupt the normal organization of the lipids in the plasma membrane via either hydrolysis or randomization. The phosphatidylcholine and sphingomyelin present in the plasma membrane are critical for maintaining the two kinetic pools of cholesterol; any alteration in the amount or the location of these phospholipids results in an enhancement of efflux by redistributing cholesterol into the fast kinetic pool.     

The enzymatic mechanism of glucuronidation catalyzed by two purified rat liver steroid UDP-glucuronosyltransferases

A kinetic analysis of two homogeneous rat liver steroid (3 alpha-hydroxysteroid and 17 beta-hydroxysteroid) UDP-glucuronosyltransferases was conducted using bisubstrate kinetic analysis, product inhibition studies, and dead-end competitive inhibition studies. Double reciprocal plots of initial velocity versus substrate concentration, using bisubstrate kinetic analysis, gave a sequential mechanism. Product inhibition studies were compatible with either a rapid equilibrium, random-order kinetic mechanism or an ordered Theorell-Chance mechanism. Results of dead-end competitive inhibition studies excluded an ordered Theorell-Chance mechanism. The cumulative results are consistent with a rapid equilibrium random-order sequential kinetic mechanism for the glucuronidation of testosterone by purified 17 beta-hydroxysteroid UDP-glucuronosyltransferase and of androsterone by purified 3 alpha-hydroxysteroid UDP-glucuronosyltransferase.     

Rapid determination of kinetic constants by competitive spectrophotometry

The use of competitive spectrophotometry to measure kinetic constants for enzyme-catalyzed reactions is described. The equation for the progress curve characterizing the kinetic behavior of an enzyme acting simultaneously on two alternative substrates is derived. By the addition of a competition term to the integrated Michaelis-Menten equation, the kinetic constants of an alternative substrate can be evaluated by measuring the competition with a substrate of known kinetic constants in a single experiment. Studies are presented involving the enzymes leucine aminopeptidase (LAP) and carboxypeptidase A (CPA). The results obtained with LAP and CPA showed that the kinetic constants determined using competitive spectrophotometry were in agreement with values cited in the literature or with values determined by single substrate enzyme kinetics.     

iSCHRUNK – In Silico Approach to Characterization and Reduction of Uncertainty in the Kinetic Models of Genome-scale Metabolic Networks

Accurate determination of physiological states of cellular metabolism requires detailed information about metabolic fluxes, metabolite concentrations and distribution of enzyme states. Integration of fluxomics and metabolomics data, and thermodynamics-based metabolic flux analysis contribute to improved understanding of steady-state properties of metabolism. However, knowledge about kinetics and enzyme activities though essential for quantitative understanding of metabolic dynamics remains scarce and involves uncertainty. Here, we present a computational methodology that allow us to determine and quantify the kinetic parameters that correspond to a certain physiology as it is described by a given metabolic flux profile and a given metabolite concentration vector. Though we initially determine kinetic parameters that involve a high degree of uncertainty, through the use of kinetic modeling and machine learning principles we are able to obtain more accurate ranges of kinetic parameters, and hence we are able to reduce the uncertainty in the model analysis. We computed the distribution of kinetic parameters for glucose-fed E. coli producing 1,4-butanediol and we discovered that the observed physiological state corresponds to a narrow range of kinetic parameters of only a few enzymes, whereas the kinetic parameters of other enzymes can vary widely. Furthermore, this analysis suggests which are the enzymes that should be manipulated in order to engineer the reference state of the cell in a desired way. The proposed approach also sets up the foundations of a novel type of approaches for efficient, non-asymptotic, uniform sampling of solution spaces.     

Kinetic and chemical mechanism of arylamine N-acetyltransferase from Mycobacterium tuberculosis

Arylamine N-acetyltransferases (NATs) are cytosolic enzymes that catalyze the transfer of the acetyl group from acetyl coenzyme A (AcCoA) to the free amino group of arylamines and hydrazines. Previous studies have reported that overexpression of NAT from Mycobacterium smegmatis and Mycobacterium tuberculosis may be responsible for increased resistance to the front-line antitubercular drug, isoniazid, by acetylating and hence inactivating the prodrug. We report the kinetic characterization of M. tuberculosis NAT which reveals that substituted anilines are excellent substrates but that isoniazid is a very poor substrate for this enzyme. We propose that the expression of NAT from M. tuberculosis (TBNAT) is unlikely to be a significant cause of isoniazid resistance. The kinetic parameters for a variety of TBNAT substrates were examined, including 3-amino-4-hydroxybenzoic acid and AcCoA, revealing K m values of 0.32 +/- 0.03 and 0.14 +/- 0.02 mM, respectively. Steady-state kinetic analysis of TBNAT reveals that the enzyme catalyzes the reaction via a bi-bi ping-pong kinetic mechanism. The pH dependence of the kinetic parameters reveals that one enzyme group must be deprotonated for optimal catalytic activity and that two amino acid residues at the active site of the free enzyme are involved in binding and/or catalysis. Solvent kinetic isotope effects suggest that proton transfer steps are not rate-limiting in the overall reaction for substituted aniline substrates but become rate-limiting when poor hydrazide substrates are used.     

The kinetics of rat liver and heart mitochondrial beta-hydroxybutyrate dehydrogenase.

The kinetic mechanisms of the beta-hydroxybutyrate dehydrogenase from rat heart and liver mitochondria were investigated. Both enzymes, show an Ordered Bi Bi mechanism and there are no major differences in the kinetic constants. In both cases, the solubilized enzyme, re-activated with phosphatidylcholine, shows kinetic properties very similar to those of the enzyme bound to the mitochondrial membrane.