pH variation of the kinetic parameters and the catalytic mechanism of malic enzyme.

The pH variation of the kinetic parameters for the oxidative decarboxylation of L-malate and decarboxylation of oxalacetate catalyzed by malic enzyme has been used to gain information on the catalytic mechanism of this enzyme. With Mn2+ as the activator, an active-site residue with a pK of 5.4 must be protonated for oxalacetate decarboxylation and ionized for the oxidative decarboxylation of L-malate. With Mg2+ as the metal, this pK is 6, and, at high pH, V/K for L-malate decreases when groups with pKs of 7.8 and 9 are deprotonated. The group at 7.8 is a neutral acid (thought to be water coordinated to Mg2+), while the group at 9 is a cationic acid such as lysine. The V profile for reaction of malate shows these pKs displaced outward by 1.4 pH units, since the rate-limiting step is normally TPNH release, and the chemical reaction, which is pH sensitive, is 25 times faster. TPN binding is decreased by ionization of a group with pK 9.3 or protonation of a group with pK 5.3. The pH variation of the Km for Mg shows that protonation of a group with pK 8.7 (possibly SH) decreases metal binding in the presence of malate by a factor of 1400, and in the absence of malate by a factor of 20. A catalytic mechanism is proposed in which hydride transfer is accompanied by transfer of a proton to the group with pK 5.4-6, and enolpyruvate is protonated by water coordinated to the Mg2+ (pK 7.8) after decarboxylation and release of CO2.     

Least-squares estimation of batch culture kinetic parameters

This article concerns the development of a simple and effective least-squares procedure for estimating the kinetic parameters in Monod expressions from batch culture data. The basic approach employed in this work was to translate the problem of parameter estimation to a mathematical model containing a single decision variable. The resulting model was then solved by an efficient one-dimensional search algorithm which can be adapted to any microcomputer or advanced programmable calculator. The procedure was tested on synthetic data (substrate concentrations) with different types and levels of error. The effect of endogeneous respiration on the estimated values of the kinetic parameters was also assessed. From the results of these analyses the least-squares procedure developed was concluded to be very effective.     

Optimal parametric sensitivity control for the estimation of kinetic parameters in bioreactors

In this paper the well-known problem of optimal input design is considered. In particular, the focus is on input design for the estimation of kinetic parameters in bioreactors. The problem is formulated as follows: given the model structure (f,g), which is assumed to be affine in the input, and the specific parameter of interest theta;(k) find a feedback law that maximizes the sensitivity of the model output to the parameter under different flow conditions in the bioreactor and, possibly, minimize the input or state costs. Analytical solutions to these problems are presented. As an example a bioreactor with a biomass that grows according to the well-known Monod kinetics is considered.     

Characterization of nicotinamidases: steady state kinetic parameters, classwide inhibition by nicotinaldehydes, and catalytic mechanism

Nicotinamidases are metabolic enzymes that hydrolyze nicotinamide to nicotinic acid. These enzymes are widely distributed across biology, with examples found encoded in the genomes of Mycobacteria, Archaea, Eubacteria, Protozoa, yeast, and invertebrates, but there are none found in mammals. Although recent structural work has improved our understanding of these enzymes, their catalytic mechanism is still not well understood. Recent data show that nicotinamidases are required for the growth and virulence of several pathogenic microbes. The enzymes of Saccharomyces cerevisiae, Drosophila melanogaster, and Caenorhabditis elegans regulate life span in their respective organisms, consistent with proposed roles in the regulation of NAD(+) metabolism and organismal aging. In this work, the steady state kinetic parameters of nicotinamidase enzymes from C. elegans, Sa. cerevisiae, Streptococcus pneumoniae (a pathogen responsible for human pneumonia), Borrelia burgdorferi (the pathogen that causes Lyme disease), and Plasmodium falciparum (responsible for most human malaria) are reported. Nicotinamidases are generally efficient catalysts with steady state k(cat) values typically exceeding 1 s(-1). The K(m) values for nicotinamide are low and in the range of 2 -110 μM. Nicotinaldehyde was determined to be a potent competitive inhibitor of these enzymes, binding in the low micromolar to low nanomolar range for all nicotinamidases tested. A variety of nicotinaldehyde derivatives were synthesized and evaluated as inhibitors in kinetic assays. Inhibitions are consistent with reaction of the universally conserved catalytic Cys on each enzyme with the aldehyde carbonyl carbon to form a thiohemiacetal complex that is stabilized by a conserved oxyanion hole. The S. pneumoniae nicotinamidase can catalyze exchange of (18)O into the carboxy oxygens of nicotinic acid with H(2)(18)O. The collected data, along with kinetic analysis of several mutants, allowed us to propose a catalytic mechanism that explains nicotinamidase and nicotinic acid (18)O exchange chemistry for the S. pneumoniae enzyme involving key catalytic residues, a catalytic transition metal ion, and the intermediacy of a thioester intermediate.     

Optimal design of experiments for the estimation of precise hyperbolic kinetic and binding parameters

Optimal designs were evaluated for the estimation of precise parameters in kinetic and binding experiments in which the concentration dependence of the response (reaction velocity or bound ligand concentration) is characterized by a hyperbola. The designs were evaluated by maximizing the determinant of the appropriate information matrix. It is demonstrated that highest precision is obtained by replicating basic two-point designs. However, the calculated optimal designs should serve only as guidelines and not rules for experimentation.In the presence of constant variance, half of the observations should be obtained at the highest practically attainable concentration. In kinetic studies, the remaining measurements should yield half of the maximally attainable velocity. In binding experiments, the second half of observations for either bound (b) or free (f) ligand concentrations should be made at a total concentration of c = P + K (K is the dissociation constant, and P the binding capacity).With constant coefficient of variation (constant relative error), kinetic experiments should be performed, at equal frequency, at the highest and lowest attainable concentration. Half of the binding experiments should be made at their lowest precision: at the highest possible concentration when b is measured, and at the smallest feasible concentration when f is obtained. The other half of the readings should be taken at c = P ? K (if P > K) for the measurement of b, and at c = P + K for observations of f.Deviations from the calculated optimal designs result in diminished efficiency (increased variance) of the estimated parameters. The reduction can be substantial with some frequently used experimental designs, especially when the number of observations is not very small. Therefore, the first few readings could consider the validation of the model, but additional measurements should follow the guidelines presented here.     

The catalytic mechanism of carbonic anhydrase. Hydrogen-isotope effects on the kinetic parameters of the human C isoenzyme.

1. The steady-state kinetics of the interconversion of CO2 and HCO3 catalyzed by human carbonic anhydrase C was studied using 1H2O and 2H2O as solvents. The pH-independent parts of the parameters k(cat) and Km are 3-4 times larger in 1H2O than in 2H2O for both directions of the reaction, while the ratios k(cat)/Km show much smaller isotope effects. With either CO2 or HCO3 as substrate the major pH dependence is observed in k(cat), while Km appears independent of pH. The pKa value characterizing the pH-rate profiles is approximately 0.5 unit larger in 2H2O than in 1H2O. 2. The hydrolysis of p-nitrophenyl acetate catalyzed by human carbonic anhudrase C is approximately 35% faster in 2H2O than in 1H2O. In both solvents the pKa values of the pH-rate profiles are similar to those observed for the CO2-HCO3 interconversion. 3. It is tentatively proposed that the rate-limiting step at saturating concentrations of CO2 or HCO3 is an intramolecular proton transfer between two ionizing groups in the active site. It cannot be decided whether the transformation between enzyme-bound CO2 and HCO3 involves a proton trnasfer or not.     

Temperature- and pressure-dependent stopped-flow kinetic studies of jack bean urease. Implications for the catalytic mechanism

Urease, a Ni-containing metalloenzyme, features an activity that has profound medical and agricultural implications. The mechanism of this activity, however, has not been as yet thoroughly established. Accordingly, to improve its understanding, in this study we analyzed the steady-state kinetic parameters of the enzyme (jack bean), K (M) and k (cat), measured at different temperatures and pressures. Such an analysis is useful as it provides information on the molecular nature of the intermediate and transition states of the catalytic reaction. We measured the parameters in a noninteracting buffer using a stopped-flow technique in the temperature range 15-35?°C and in the pressure range 5-132?MPa, the pressure-dependent measurements being the first of their kind performed for urease. While temperature enhanced the activity of urease, pressure inhibited the enzyme; the inhibition was biphasic. Analyzing K (M) provided the characteristics of the formation of the ES complex, and analyzing k (cat), the characteristics of the activation of ES. From the temperature-dependent measurements, the energetic parameters were derived, i.e. thermodynamic ΔH (o) and ΔS (o) for ES formation, and kinetic ΔH ( ≠ ) and ΔS ( ≠ ) for ES activation, while from the pressure-dependent measurements, the binding ΔV (b) and activation [Formula: see text] volumes were determined. The thermodynamic and activation parameters obtained are discussed in terms of the current proposals for the mechanism of the urease reaction, and they are found to support the mechanism proposed by Benini et al. (Structure?7:205-216; 1999), in which the Ni-Ni bridging hydroxide-not the terminal hydroxide-is the nucleophile in the catalytic reaction.     

Staphylococcus aureus sortase transpeptidase SrtA: insight into the kinetic mechanism and evidence for a reverse protonation catalytic mechanism

The Staphylococcus aureus transpeptidase SrtA catalyzes the covalent attachment of LPXTG-containing virulence and colonization-associated proteins to cell-wall peptidoglycan in Gram-positive bacteria. Recent structural characterizations of staphylococcal SrtA, and related transpeptidases SrtB from S. aureus and Bacillus anthracis, provide many details regarding the active site environment, yet raise questions with regard to the nature of catalysis and active site cysteine thiol activation. Here we re-evaluate the kinetic mechanism of SrtA and shed light on aspects of its catalytic mechanism. Using steady-state, pre-steady-state, bisubstrate kinetic studies, and high-resolution electrospray mass spectrometry, revised steady-state kinetic parameters and a ping-pong hydrolytic shunt kinetic mechanism were determined for recombinant SrtA. The pH dependencies of kinetic parameters k(cat)/K(m) and k(cat) for the substrate Abz-LPETG-Dap(Dnp)-NH(2) were bell-shaped with pK(a) values of 6.3 +/- 0.2 and 9.4 +/- 0.2 for k(cat) and 6.2 +/- 0.2 and 9.4 +/- 0.2 for k(cat)/K(m). Solvent isotope effect (SIE) measurements revealed inverse behavior, with a (D)2(O)k(cat) of 0.89 +/- 0.01 and a (D)2(O)(k(cat)/K(m)) of 0.57 +/- 0.03 reflecting an equilibrium SIE. In addition, SIE measurements strongly implicated Cys184 participation in the isotope-sensitive rate-determining chemical step when considered in conjunction with an inverse linear proton inventory for k(cat). Last, the pH dependence of SrtA inactivation by iodoacetamide revealed a single ionization for inactivation. These studies collectively provide compelling evidence for a reverse protonation mechanism where a small fraction (ca. 0.06%) of SrtA is competent for catalysis at physiological pH, yet is highly active with an estimated k(cat)/K(m) of >10(5) M(-)(1) s(-)(1).     

An oxygraphic method for determining kinetic properties and catalytic mechanism of aromatic amino acid hydroxylases

We have developed a simple and versatile oxygraphic assay procedure that can be used for determination of kinetic constants and enzyme reaction mechanisms of wild-type and mutant aromatic amino acid hydroxylases. The oxygen concentration and rate of oxygen consumption were measured continuously throughout the enzyme reaction, while aliquots of the reaction mixture were removed at regular intervals for measurement of other substrates and products. Using (6R)-tetrahydrobiopterin as electron donor in the phenylalanine hydroxylase (PAH) reaction, a stable stoichiometry of 1:1 was obtained between the amount of oxygen consumed and the tyrosine formation. In comparison, low and variable coupling efficiency values between oxygen consumption and tyrosine formation were found using the parent unsubstituted tetrahydropterin. The application of this assay procedure to study mechanisms of disease-associated mutations was also demonstrated. Thus, the phenylketonuria-associated PAH mutant R158Q had a coupling efficiency of about 80%, compared to the wild-type enzyme under similar conditions. Furthermore, the amount of H(2)O(2) produced in the reaction catalyzed by R158Q PAH was about four times higher than the amount produced by the wild-type PAH, demonstrating a possible pathogenetic mechanism of the mutant enzyme.     

A catalytic mechanism for benzylamine oxidase from pig plasma. Stopped-flow kinetic studies

1. Ammonium ion is shown to decrease the rate constants for Schiff's base formation and formation of a reduced intermediate during the catalytic cycle of benzylamine oxidase from pig plasma. The rat constant for reoxidation of the reduced intermediate is also inhibited whilst the rate constant for conversion of the oxidised enzyme form back to native enzyme is stimulated by ammonium ion. 2. Ammonium ion changes the electron paramagnetic resonance spectrum of the cupric centres in the enzyme, indicating that ammonia binds to the copper. 3. A catalytic mechanism for benzylamine oxidase is proposed on the basis of these and other results. This mechanism includes a novel step in which a hydroxyl coordinated to copper acts as a nucleophyle to facilitate hydride ion transfer to oxygen during the reoxidation process.     

Studies on the kinetic mechanism of the catalytic subunit of the cAMP-dependent protein kinase

The kinetic mechanism of the catalytic subunit of the cAMP-dependent protein kinase has been investigated employing the heptapeptide Kemptide (Leu-Arg-Arg-Ala-Ser-Leu-Gly) as substrate. Initial velocity measurements performed over a wide range of ATP and Kemptide concentrations indicated that the reaction follows a sequential mechanistic pathway. In line with this, the results of product and substrate inhibition studies, the patterns of dead end inhibition obtained employing the nonhydrolyzable ATP analogue, AMP X PNP (5'-adenylylimidodiphosphate), and equilibrium binding determinations, taken in conjunction with the patterns of inhibition observed with the inhibitor protein of the cAMP-dependent protein kinase that are reported in the accompanying paper (Whitehouse, S., and Walsh, D.A. (1983) J. Biol. Chem. 258, 3682-3692), are best fit by a steady state Ordered Bi-Bi kinetic mechanism. Although the inhibition patterns obtained employing the synthetic peptide analogue in which the phosphorylatable serine was replaced by alanine were apparently incompatible with this mechanism, these inconsistencies appear to be due to some element of the structure of this latter peptide such that it is not an ideal dead end inhibitor substrate analogue. The data presented both here and in the accompanying paper suggest that both this substrate, analogue and the ATP analogue, AMP X PNP, do not fully mimic the binding of Kemptide and ATP, respectively, in their mechanism of interaction with the protein kinase. It is proposed that, as with some other kinase reactions, the configuration of the terminal anhydride bond of ATP assumes a conformation once the nucleotide is bound to the protein kinase that assists in the binding of either Kemptide or the inhibitor protein but not the alanine-substituted peptide and that AMP X PNP, because of its terminal phosphorylimido bond, cannot assume this conformation which favors protein (or peptide) binding.     

pH dependence of the kinetic parameters for the pyrophosphate-dependent phosphofructokinase reaction supports a proton-shuttle mechanism

The pH dependence of kinetic parameters for the pyrophosphate-dependent phosphofructokinase from Propionibacterium freudenreichii suggests that the enzyme catalyzes its reaction via general acid-base catalysis with the use of a proton shuttle. The base is required unprotonated in both reaction directions. In the direction of fructose 6-phosphate phosphorylation the base accepts a proton from the hydroxyl at C-1 of F6P and then donates it to protonate the leaving phosphate. Whether this occurs in one or two steps cannot be deduced from the present data. The maximum velocity of the reaction is pH independent in both reaction directions while V/K profiles exhibit pKs for binding groups (including enzyme and reactant functional groups) as well as pKs for enzyme catalytic groups. These data suggest that reactants bind only when correctly protonated and only to the correctly protonated form of the enzyme. Specifically, the requirement for two enzyme epsilon-amino groups in the protonated form for reactant binding was detected as was the requirement for the ionized phosphates of fructose 6-phosphate, fructose 1,6-bisphosphate, MgPPi and HPO4(2-). The protonation state of enzyme and reactant binding groups is in agreement with data obtained previously [Cho, Y.-K., & Cook, P. F. (1988) J. Biol. Chem. 263, 5135].     

Unscented Kalman filter with parameter identifiability analysis for the estimation of multiple parameters in kinetic models

In systems biology, experimentally measured parameters are not always available, necessitating the use of computationally based parameter estimation. In order to rely on estimated parameters, it is critical to first determine which parameters can be estimated for a given model and measurement set. This is done with parameter identifiability analysis. A kinetic model of the sucrose accumulation in the sugar cane culm tissue developed by Rohwer et al. was taken as a test case model. What differentiates this approach is the integration of an orthogonal-based local identifiability method into the unscented Kalman filter (UKF), rather than using the more common observability-based method which has inherent limitations. It also introduces a variable step size based on the system uncertainty of the UKF during the sensitivity calculation. This method identified 10 out of 12 parameters as identifiable. These ten parameters were estimated using the UKF, which was run 97 times. Throughout the repetitions the UKF proved to be more consistent than the estimation algorithms used for comparison.     

A kinetic investigation of fumarase reaction at high substrate concentrations

The hydration of fumarate to malate, catalyzed by fumarase was followed by infrared spectrometry. Substrate concentrations employed were all several orders of magnitude higher than K_m . The reciprocal plot of Lineweaver and Burke yielded an unusual curve of the type indicating auto-inhibition by substrate due perhaps to a two-point binding on the enzyme sites. The data obtained could not be treated satisfactorily by the conventional Michaelis-Menten kinetics. A slightly different type of analysis gave numerical values for some of the kinetics constants which are in reasonable agreement with published values.     

Improved non-parametric statistical methods for the estimation of Michaelis-Menten kinetic parameters by the direct linear plot.

The theoretical basis for the direct linear plot [Eisenthal & Cornish-Bowden (1974) Biochem. J. 139, 715-720], a non-parametric statistical method for the analysis of data-fitting the Michaelis-Menten equation, was reinvestigated in order to accommodate additional experimental designs and to provide estimates of precision more directly comparable with those obtained by parametric statistical methods. Methods are given for calculating upper and lower confidence limits for the estimated parameters, for accommodating replicate measurements and for comparing the results of two separate experiments. Factors that influence the proper design of experiments are discussed.