Kinetics of nitrification and denitrification reactions

Nitrification and denitrification are important microbiological reactions of nitrogen. In this work, the kinetics of these reactions have been investigated based on a Monod-type expression involving two growth limiting substrates: ammonium nitrogen and dissolved oxygen for nitrification and nitrate nitrogen and dissolved organic carbon for denitrification. The kinetic constants and yield coefficients were evaluated for both these reactions. Past experimental work was used to determine the constants for the nitrification reaction. For the denitrification reaction, experiments were performed in a stirred tank reactor under conditions such that only one substrate was growth limiting. Steady-state values of the substrate concentrations in the reactor were determined at various dilution rates. These data were analyzed to obtain the kinetic and stoichiometric constants. From these constants it was concluded that in the range of nitrate nitrogen concentrations encountered in waste water, the denitrification reaction can be considered a first-order reaction. It was also found that three times as much organic carbon is required as nitrate nitrogen for complete nitrogen removal.     

Online optimization of surface plasmon resonance-based biosensor experiments for improved throughput and confidence

The emergence of surface plasmon resonance-based optical biosensors has facilitated the identification of kinetic parameters for various macromolecular interactions. Normally, these parameters are determined from experiments with arbitrarily chosen periods of macromolecule and buffer injections, and varying macromolecule concentrations. Since the choice of these variables is arbitrary, such experiments may not provide the required confidence in identified kinetic parameters expressed in terms of standard errors. In this work, an iterative optimization approach is used to determine the above-mentioned variables so as to reduce the experimentation time, while treating the required standard errors as constraints. It is shown using multiple experimental and simulated data that the desired confidence can be reached with much shorter experiments than those generally performed by biosensor users.     

Chymotrypsin-catalyzed peptide synthesis. Kinetic analysis of the kinetically controlled peptide-bond formation

The kinetics of peptide-bond formation catalyzed by delta-chymotrypsin has been studied for a number of peptide products of different length using fixed concentrations of the acyl component (Ac-Phe-OMe, Ac-Ala-Ala-Phe-OMe, or Ac-Ala-Ala-Tyr-OMe) and varying concentration of the amino component (H-Ala-NH2 or H-Ala-Ala-NH2). The time course of the reactions was followed by monitoring ester consumption and peptide product formation by analytical HPLC. On the basis of a plausible four-centre mechanistic model, the theoretical time course of these reactions was calculated using rate and equilibrium constants determined by separate kinetic experiments. The excellent agreement observed between the theoretical and the experimental time courses supports the proposed mechanism and provides evidence for the validity of the present kinetic approach. By focusing attention on the rate constants which are critical for efficient synthesis, this mechanistic information constitutes a valuable basis for the use of the enzymatic peptide synthesis in preparative applications.     

An evolutionary approach to enzyme kinetics: Optimization of ordered mechanisms

A theoretical investigation is presented which allows the calculation of rate constants and phenomenological parameters in states of maximal reaction rates for unbranched enzymic reactions. The analysis is based on the assumption that an increase in reaction rates was an important characteristic of the evolution of the kinetic properties of enzymes. The corresponding nonlinear optimization problem is solved taking into account the constraint that the rate constants of the elementary processes do not exceed certain upper limits. One-substrate-one-product reactions with two, three and four steps are treated in detail. Generalizations concern ordered uni-uni-reactions involving an arbitrary number of elementary steps. It could be shown that depending on the substrate and product concentrations different types of solutions can be found which are classified according to the number of rate constants assuming in the optimal state submaximal values. A general rule is derived concerning the number of possible solutions of the given optimization problem. For high values of the equilibrium constant one solution always applies to a very large range of the concentrations of the reactants. This solution is characterized by maximal values of the rate constants of all forward reactions and by non-maximal values of the rate constants of all backward reactions. Optimal kinetic parameters of ordered enzymic mechanisms with two substrates and one product (bi-uni-mechanisms) are calculated for the first time. Depending on the substrate and product concentrations a complete set of solutions is found. In all cases studied the model predicts a matching of the concentrations of the reactants and the corresponding Michaelis constants, which is in good accordance with the experimental data. It is discussed how the model can be applied to the calculation of the optimal kinetic design of real enzymes.     

Kinetic determinations of molecular interactions using Biacore--minimum data requirements for efficient experimental design

Reliable kinetic estimates can be obtained from significantly less data than is commonly used today, particularly in the characterization of 1:1 interactions involving low molecular weight compounds and proteins. We have designed a rational and cost-effective strategy to determine kinetic constants using Biacore's surface plasmon resonance-based biosensors and show that the number of measurements necessary for accurate kinetic determinations can be greatly reduced, increasing sample throughput and saving sample material. Simulated and measured data for a range of possible 1:1 interactants were studied to find the minimum requirements of a data set for kinetic analysis. The results showed that kinetic constants in the region 10(4) < k(a) < 10(7) M(-1) s(-1) (association) and 10(-4) < k(d) < 10(-1) s(-1) (dissociation) could easily be determined in a 1:1 interaction model. Owing to the information-dense nature of Biacore data, only two sample concentrations were necessary to reliably determine the kinetics. A standard sample concentration series consisting of 10-fold dilutions between approximately 10 microM and approximately 1 nM consistently provided at least two concentrations with sufficient information about the interaction in this region. Determinations of the constants became increasingly unreliable outside this region. If the rate constants prove to be outside the specified region or the data fits poorly to the 1:1-MTL model, more experiments are required. General recommendations for the design of a cost-effective assay to deliver reliable kinetic measurements are provided.     

Optimization of surface plasmon resonance experiments: Case of high mobility group box 1 (HMGB1) interactions

Surface plasmon resonance (SPR) is a powerful technique for evaluating protein–protein interactions in real time. However, inappropriately optimized experiments can often lead to problems in the interpretation of data, leading to unreliable kinetic constants and binding models. Optimization of SPR experiments involving “sticky” proteins, or proteins that tend to aggregate, represents a typical scenario where it is important to minimize errors in the data and the kinetic analysis of those data. This is the case of High Mobility Group Box 1 and the receptor of advanced glycation end products. A number of improvements in protein purification, buffer composition, immobilization conditions, and the choice of flow rate are shown to result in substantial improvements in the accurate characterization of the interactions of these proteins and the derivation of the corresponding kinetic constants.     

Understanding glucose transport by the bacterial phosphoenolpyruvate:glycose phosphotransferase system on the basis of kinetic measurements in vitro

The kinetic parameters in vitro of the components of the phosphoenolpyruvate:glycose phosphotransferase system (PTS) in enteric bacteria were collected. To address the issue of whether the behavior in vivo of the PTS can be understood in terms of these enzyme kinetics, a detailed kinetic model was constructed. Each overall phosphotransfer reaction was separated into two elementary reactions, the first entailing association of the phosphoryl donor and acceptor into a complex and the second entailing dissociation of the complex into dephosphorylated donor and phosphorylated acceptor. Literature data on the K(m) values and association constants of PTS proteins for their substrates, as well as equilibrium and rate constants for the overall phosphotransfer reactions, were related to the rate constants of the elementary steps in a set of equations; the rate constants could be calculated by solving these equations simultaneously. No kinetic parameters were fitted. As calculated by the model, the kinetic parameter values in vitro could describe experimental results in vivo when varying each of the PTS protein concentrations individually while keeping the other protein concentrations constant. Using the same kinetic constants, but adjusting the protein concentrations in the model to those present in cell-free extracts, the model could reproduce experiments in vitro analyzing the dependence of the flux on the total PTS protein concentration. For modeling conditions in vivo it was crucial that the PTS protein concentrations be implemented at their high in vivo values. The model suggests a new interpretation of results hitherto not understood; in vivo, the major fraction of the PTS proteins may exist as complexes with other PTS proteins or boundary metabolites, whereas in vitro, the fraction of complexed proteins is much smaller.     

k-Cone analysis: determining all candidate values for kinetic parameters on a network scale

The absence of comprehensive measured kinetic values and the observed inconsistency in the available in vitro kinetic data has hindered the formulation of network-scale kinetic models of biochemical reaction networks. To meet this challenge we present an approach to construct a convex space, termed the k-cone, which contains all the allowable numerical values of the kinetic constants in large-scale biochemical networks. The definition of the k-cone relies on the incorporation of in vivo concentration data and a simplified approach to represent enzyme kinetics within an established constraint-based modeling approach. The k-cone approach was implemented to define the allowable combination of numerical values for a full kinetic model of human red blood cell metabolism and to study its correlated kinetic parameters. The k-cone approach can be used to determine consistency between in vitro measured kinetic values and in vivo concentration and flux measurements when used in a network-scale kinetic model. k-Cone analysis was successful in determining whether in vitro measured kinetic values used in the reconstruction of a kinetic-based model of Saccharomyces cerevisiae central metabolism could reproduce in vivo measurements. Further, the k-cone can be used to determine which numerical values of in vitro measured parameters are required to be changed in a kinetic model if in vivo measured values are not reproduced. k-Cone analysis could identify what minimum number of in vitro determined kinetic parameters needed to be adjusted in the S. cerevisiae model to be consistent with the in vivo data. Applying the k-cone analysis a priori to kinetic model development may reduce the time and effort involved in model building and parameter adjustment. With the recent developments in high-throughput profiling of metabolite concentrations at a whole-cell scale and advances in metabolomics technologies, the k-cone approach presented here may hold the promise for kinetic characterization of metabolic networks as well as other biological functions at a whole-cell level.     

Iteration model of starch hydrolysis by amylolytic enzymes.

An elaborate computer program to simulate the process of starch hydrolysis by amylolytic enzymes was been developed. It is based on the Monte Carlo method and iteration kinetic model, which predict productive and non-productive amylase complexes with substrates. It describes both multienzymatic and multisubstrate reactions simulating the "real" concentrations of all components versus the time of the depolymerization reaction the number of substrates, intermediate products, and final products are limited only by computer memory. In this work, it is assumed that the "proper" substrate for amylases is the glucoside linkages in starch molecules. Dynamic changes of substrate during the simulation adequately influence the increase or decrease of reaction velocity, as well as the kinetics of depolymerization. The presented kinetic model, can be adapted to describe most enzymatic degradations of a polymer. This computer program has been tested on experimental data obtained for alpha- and beta-amylases.     

Application of the median method to the determination of kinetic constants for competitive enzyme inhibition

A procedure was developed to determine kinetic constants for competitive inhibition (Km, Ki, Vmax) by the median method. Simulated experiments were used to compare the accuracy and precision of kinetic constants determined by the median method with unweighted and weighted least-squares analysis. The median method was superior to unweighted least-squares analysis. The weighted least-squares method was superior to the median method when the error was normally distributed but the median method was superior when two or more outliers were present. The dependence of the accuracy and precision of kinetic constants obtained by the median method on several experimentally important parameters, including the number of experimental points, the number and range of substrate concentrations, and the number and range of inhibitor concentrations, was determined.     

Kinetic modeling and fitting software for interconnected reaction schemes: VisKin

Reaction kinetics for complex, highly interconnected kinetic schemes are modeled using analytical solutions to a system of ordinary differential equations. The algorithm employs standard linear algebra methods that are implemented using MatLab functions in a Visual Basic interface. A graphical user interface for simple entry of reaction schemes facilitates comparison of a variety of reaction schemes. To ensure microscopic balance, graph theory algorithms are used to determine violations of thermodynamic cycle constraints. Analytical solutions based on linear differential equations result in fast comparisons of first order kinetic rates and amplitudes as a function of changing ligand concentrations. For analysis of higher order kinetics, we also implemented a solution using numerical integration. To determine rate constants from experimental data, fitting algorithms that adjust rate constants to fit the model to imported data were implemented using the Levenberg-Marquardt algorithm or using Broyden-Fletcher-Goldfarb-Shanno methods. We have included the ability to carry out global fitting of data sets obtained at varying ligand concentrations. These tools are combined in a single package, which we have dubbed VisKin, to guide and analyze kinetic experiments. The software is available online for use on PCs.     

The direct linear plot. A new graphical procedure for estimating enzyme kinetic parameters

A new plot is described for analysing the results of kinetic experiments in which the Michaelis-Menten equation is obeyed. Observations are plotted as lines in parameter space, instead of points in observation space. With appropriate modifications the plot is applicable to most problems of interest to the enzyme kineticist. It has the following advantages over traditional methods of plotting kinetic results: it is very simple to construct, because it is composed entirely of straight lines and requires no calculation or mathematical tables; the kinetic constants are read off the plot directly, again without calculation; it may be used during the course of an experiment to judge the success of the experiment, and to modify the experimental design; it provides clear and accurate information about the quality of the observations, and identifies aberrant observations; it provides a clear indication of the precision of the kinetic constants; constructed with care, it provides unbiased estimates of the kinetic constants, the same as those provided by a computer program; it may be used to simulate results for illustrative purposes very rapidly and simply.     

HERSIM: a microcomputer program designed to compute the limits of conversion for real homogeneous isothermal enzymic reactors

HERSIM is a program written in BASIC designed to aid the investigatorinterested in determining the substrate conversion in a realhomogeneous isothermal enzymic reactor, for various kineticequations. The program runs after tracer data relative to aDirac impulse to the reactor have been entered, and computesthe two limits of real conversion: total segregation and maximummixedness. The kinetic constants of the reacting system areinput as data, and the variation of conversion with reactortemperature between given limits is computed as accurately asrequested. Received on November 6, 1986; accepted on March 4, 1987     

A microcomputer method for designing optimal experiments for estimating enzyme kinetic parameters

A computer program, written in BASIC, for designing optimal experiments with the aim of evaluating estimates of the parameters for any enzyme kinetic model is given. This computer program can be run on any microcomputer with less than 32 Kbytes of random access memory. The program uses the termed D-optimization design criterion, which minimizes the determinant of the variance-covariance matrix. The user only supplies the rate equation, the maximum and minimum concentrations of substrates and inhibitors, the weighting pattern, and the best possible values of the parameters. The computer supplies the optimal substrate and inhibitor concentrations (one for each parameters), for estimating the parameter values, and the determinant of the variance-covariance matrix. Likewise, the microcomputer supplies the eigenvalues and eigenvectors of information and redundancy matrices, the sensitivity and the global redundancy.     

Non-linear kinetic modelling of reversible bioconversions: Application to the transaminase catalyzed synthesis of chiral amino-alcohols

This work describes the establishment of a full kinetic model, including values of apparent kinetic parameters, for the whole cell E. coli mediated synthesis of the chiral amino-alcohol (2S,3R)-2-amino-1,3,4-butanetriol (ABT), using (S)-(−)-α-methylbenzylamine (MBA) as amino donor. The whole cell biocatalyst expressed the CV2025 ω-transaminase from Chromobacterium violaceum. Establishment of the most suitable reaction mechanism and determination of the complete forward and reverse kinetic parameter values for the reversible bioconversion where obtained using a hybrid methodology. This combined traditional initial rate experiments to identify a solution in the vicinity of the global minimum, with nonlinear regression methods to determine the exact location of the solution. The systematic procedure included selection and statistical evaluation of different kinetic models that best described the measured reaction rates and which ultimately provided new insights into the reaction mechanism; in particular the possible formation of a dead end complex between the amino donor and the cofactor enzyme complex. The hybrid methodology was combined with a microscale experimental platform, to significantly reduce both the number of experiments required as well as the time and material required for full kinetic parameter estimation. The equilibrium constant was determined to be 849, and the forward and reverse rate constants were found to be 97 and 13 min⁻¹, respectively, which greatly favoured the asymmetric synthesis of chiral ABT. Using the established kinetic model, the asymmetric synthesis of ABT was simulated, and excellent agreement was found between the experimental and predicted data over a range of reaction conditions. A sensitivity analysis combined with various simulations suggested the crucial bottleneck of the reaction was the second half reaction of the ping pong bi–bi mechanism, in part due to the low Michaelis constant of substrate l-erythrulose (ERY). The toxicity of MBA towards the transaminase was identified as another major bottleneck. The kinetic model was useful to give early insights into the most appropriate bioconversion conditions, which can improve the rate and yield of ABT formation, as well as minimizing the toxicity and inhibition effects of the substrates and products. The systematic methodology developed here is considered to be generic and useful in regard to speeding up bioconversion process design and optimization.     

The use of chromogenic reference substrates for the kinetic analysis of penicillin acylases.

Determination of kinetic parameters of penicillin acylases for phenylacetylated compounds is complicated due to the low K(m) values for these substrates, the lack of a spectroscopic signal, and the strong product inhibition by phenylacetic acid. To overcome these difficulties, a spectrophotometric method was developed, with which kinetic parameters could be determined by measuring the effects on the hydrolysis of the chromogenic reference substrate 2-nitro-5-[(phenylacetyl)amino]benzoic acid (NIPAB). To that end, spectrophotometric progress curves with NIPAB in the absence and presence of the phenylacetylated substrates and their products were measured and analyzed by numerical fitting to the appropriate equations for competing substrates with product inhibition. This analysis yielded kinetic constants for phenylacetylated substrates such as penicillin G, which are in close agreement with those obtained in independent initial velocity experiments. Using NIPAB analogs with lower k(cat)/K(m) values, kinetic parameters for the hydrolysis of cephalexin and penicillin V were determined. This method was suitable for determining the kinetic constants of penicillin acylases in periplasmic extracts from Escherichia coli, Alcaligenes faecalis, and Kluyvera citrophila. The use of chromogenic reference substrates thus appears to be a rapid and reliable method for determining kinetic constants with various substrates and enzymes.     

Kinetic implications of the occurrence of several relaxations in the conformational transition of mnemonical enzymes

If the conformational transition involved in enzyme memory occurs in several elementary steps, the time constant of the overall 'slow' relaxation is mostly determined by the individual values of the rate constants pertaining to the overall transconformation. The extent of kinetic co-operativity of the enzyme reaction, however, is mostly controlled by the degree of reversibility of the elementary steps of the conformational transition. There is then no simple relation between the time scale of the 'slow' transition and the extent of kinetic co-operativity of the enzyme reaction. A slow transition of about 10(-3) s-1 is therefore perfectly compatible with a strong positive or negative co-operativity and in particular with the negative co-operativity observed with wheat germ hexokinase LI. The relationship that has been established recently [Pettersson, G. (1986) Eur. J. Biochem. 154, 167-170] between the 'slow' enzyme relaxation and the extent of kinetic co-operativity holds only in the specific case where the transconformation occurs in one step. Owing to the possible occurrence of a multistep conformation change, the lack of this relationship means nothing as to the validity, or the invalidity, of the concept of mnemonical transition. More informative than the time scale of the 'slow' transition is its dependence with respect to glucose and glucose 6-phosphate, which both react with the enzyme. The effect of reaction products on the modulation of kinetic co-operativity is also of cardinal importance in the diagnosis of enzyme memory. Since an alternative model has been recently proposed by Pettersson (cited above) to explain the mechanistic origin of kinetic co-operativity of monomeric enzymes, the effect of products on the kinetic co-operativity predicted by this alternative model has been studied theoretically, in order to determine whether it is consistent with the experimental results obtained with wheat germ hexokinase LI. This analysis shows that the predictions of this model are in total disagreement with both the predictions of the mnemonical model and the experimental results obtained with wheat germ hexokinase LI, as well as with other enzymes. This alternative model cannot therefore be considered as a sensible explanation of the mechanistic origin of co-operativity of monomeric enzymes. It is therefore concluded that the mnemonical model which rests on numerous experimental results, obtained by different research groups, on different enzymes is the simplest and most likely explanation of the kinetic subtleties displayed by some monomeric enzymes, and in particular wheat germ hexokinase LI.     

Peroxidase-mediated oxidation of l-dopa: A kinetic approach

A kinetic model able to adequately describe the accumulation of p-topaquinone in peroxidase-mediated oxidation of l-dopa was developed, and the rate constants for both enzymatic and non-enzymatic branch were estimated either experimentally or using a computing program for detailed kinetic simulation. It is demonstrated that the accumulation of p-topaquinone in significant amounts occurred in excess of hydrogen peroxide or during auto-oxidation of l-dopa, but changes in the ratio of initial concentrations of the reactants can reduce considerably the production of this intermediate.     

The feasibility of determining kinetic constants from isothermal titration calorimetry data

Isothermal titration calorimetry (ITC) has long been established as an excellent means to determine the thermodynamic parameters of biomolecular interactions. More recently, efforts have focused on exploiting the power/time trace (the “thermogram”) resulting from ITC experiments to glean kinetic association and dissociation rates for these interactions. The success of such analyses rests on the ability of algorithms to simulate with high accuracy the output of the calorimeter. Thus, several critical factors must be taken into account: the injection protocol, the kinetics of the interaction, accurate discovery of the instrumental response to heat signals, and the addition of unrelated signals. All of these aspects of extracting kinetic constants from thermograms have been considered and addressed in the current work. To validate the resultant methods, we performed several ITC experiments, titrating small-molecule inhibitors into solutions of bovine carbonic anhydrase II or titrating lysozyme into solutions of anti-lysozyme nanobodies. We found that our methods could arrive at kinetic constants that were close to the known values for these interactions taken from other methods. Finally, the effort to improve ITC kinetic characterizations uncovered a set of best practices for both the calorimetric experiment and the subsequent analyses (termed “kinetically optimized ITC” or “KO-ITC”) that is detailed in this work.     

A new multi-wavelength model-based method for determination of enzyme kinetic parameters

Lineweaver-Burk plot analysis is the most widely used method to determine enzyme kinetic parameters. In the spectrophotometric determination of enzyme activity using the Lineweaver-Burk plot, it is necessary to find a wavelength at which only the substrate or the product has absorbance without any spectroscopic interference of the other reaction components. Moreover, in this method, different initial concentrations of the substrate should be used to obtain the initial velocities required for Lineweaver-Burk plot analysis. In the present work, a multi-wavelength model-based method has been developed and validated to determine Michaelis-Menten constants for some enzyme reactions. In this method, a selective wavelength region and several experiments with different initial concentrations of the substrate are not required. The absorbance data of the kinetic assays are fitted by non-linear regression coupled to the numeric integration of the related differential equation. To indicate the applicability of the proposed method, the Michaelis-Menten constants for the oxidation of phenanthridine, 6-deoxypenciclovir and xanthine by molybdenum hydroxylases were determined using only a single initial concentration of the substrate, regardless of any spectral overlap.