Accurate pseudoanalytical solution for steady-state biofilms

An extremely accurate pseudoanalytical solution for the flux of substrate into a steady-state biofilm is developed. The standard deviations between the substrate fluxes computed from the pseudoanalytical solution and the numerical solution were less than 2.6%. Additional advantages of the pseudoanalytical solution are that it has no inaccuracies around S(min) (*) = 1 and it is composed of single continuous functions applicable to the whole S(min) (*) region.     

A general solution for the steady-state kinetics of immobilized enzyme systems

A power series solution is presented which describes the steady-state concentration profiles for substrate and product molecules in immobilized enzyme systems. Diffusional effects and product inhibition are incorporated into this model. The kinetic consequences of diffusion limitation and product inhibition for immobilized enzymes are discussed and are compared to kinetic behavior characteristic of other types of effects, such as substrate inhibition and substrate activation.     

Effect of biofilm growth on steady-state biofilm models

The results of numerical simulations for a growing biological film are presented to justify the use of steady-state biofilm models for approximating the behavior of both unlimited and shear-limited biofilms. For an unlimited biofilm we show that although the total biofilm thickness may continue to increase over time, the active biofilm volume will reach a constant value. We also show that the profile of active microorganisms within the biofilm will become constant with respect to the biofilm/fluid interface and simply move outward as the biofilm thickness increases. For a shear-limited biofilm we similarly show that once a "limiting" thickness has been reached the active biofilm volume, substrate consumption, and profile of active microorganisms within the biofilm will also be independent of the biofilm thickness.     

Microcomputer tools for steady-state enzyme kinetics

Three programs useful for the investigation of steady–statekinetics have been developed. Two provide the solution to thesteady–state rate equation; the first of these is a straightforwardimplementation of the rules developed by Chou. The second isa very efficient procedure for evaluating King–Altmandiagrams and can be used for quite large mechanisms. The thirdprogram provides the numeric solution for a specific mechanismand set of initial conditions; it is well suited to extremelylarge models. Received on April 1, 1985; accepted on April 19, 1985     

Saturation kinetics for steady-state pulmonary CO transfer

Steady-state diffusing capacity of the lungs for carbon monoxide (DLCO) was measured in 13 anesthetized, paralyzed dogs ventilated at constant tidal volume and rate, using four different inspired CO levels (190, 600, 1,110, and 2,000 ppm). DLCO increased and reached a maximum as the inspired CO level was raised from 190 to 600 ppm. Further increases in inspired CO concentration were accompanied by a decrease in inspired CO concentration were accompanied by a decrease in DLCO. CO dead space and Pao2 remained constant at all inspired O2 levels. In some experiments a second set of measurements was made, the results of which were similar to those of the first set. The results cannot be explained by changes in CO back pressure, pulmonary capillary volume, or reaction rate of CO with hemoglobin, but can be explained if there is carrier-mediated CO transport in the alveolar capillary membrane.     

Microcomputer simulation of steady-state enzyme kinetics for educational purposes

A BASIC program to assist the instruction of steady-state enzymekinetics has been developed for the IBM PC microcomputer. Itspurpose is to simulate laboratory experiments in order to minimizethe time required to obtain kinetic data from which studentsdeduce kinetic mechanisms and determine kinetic constants ofenzyme-catalyzed reactions. The program randomly selects a kineticscheme from various sequential, ping pong, and iso reactionsequences as well as values for the kinetic constants. The schemeand kinetic constants are unknown to the student at this time;the only thing he or she knows is the stoichiometry of the catalyzedreaction which can have two or three substrates and products.The student is prompted to enter values for concentrations ofsubstrates and products; several different concentrations foreach substrate and product can be entered in a single experiment.The program then calculates, displays and prints (if desired)the corresponding initial steadystate velocities. The studentcan perform as many experiments as desired until enough informationis obtained to determine the kinetic mechanism and to calculatevalues for the kinetic constants. Received on March 10, 1986; accepted on May 6, 1986     

Modeling biofilm kinetics for a low-loaded expanded-bed anaerobic reactor

The effect of surface coverage of biomass on biofilm kinetics in an expanded-bed, granular activated carbon an aerobic reactor was evaluated. Acetate was used as the sole organic carbon source. An assumption of 10% surface coverage of biofilm was examined and compared to 100% coverage. Best estimated values of k(a) and K(sa) did not differ significantly from one case to the other. The confidence region analysis also showed that the biofilm was fully penetrated in the expanded-bed reactor for the case of 10% coverage, as well as when 100% coverage was assumed. Because the biofilm was fully penetrated, a model having no internal diffusion resistance and using the best estimates of k(a) and K(sa) obtained from the 10 and 100% coverage assumptions was capable of giving good predictions of effluent acetate concentrations for an in dependent experiment having a reduced liquid detention time. Consideration of biofilm surface-loading criteria demonstrated how the results can be applied to other reactors for the purpose of predicting when the extent of surface coverage and internal diffusion resistance are not significant factors in biofilm modeling.     

Improved assay for catalase based upon steady-state substrate concentration

A modification of the polarographic assay for catalase is described that is based upon automatic titration of a buffered H₂O₂-catalase reaction mixture with a more concentrated H₂O₂ solution such that there is no significant change in the volume of the reaction mixture. The recorded rate of addition of the titrant required to maintain a steady-state substrate concentration yields enzyme activity measurements in terms of actual reaction rate instead of the less satisfactory rate constant for H₂O₂ decomposition, as is the case for most extant assays for catalase. An additional advantage of the new method is that the reaction can be easily carried out at considerably lower temperature and substrate concentrations than can be employed practicably in other types of assays for this enzyme. Both of these features are desirable to minimize the formation of inactive catalase-H₂O₂ complexes. The improved assay works satisfactorily for measuring catalase activity in rat tissue homogenates.     

Microscopic diffusion-reaction coupling in steady-state enzyme kinetics

The theory of diffusion-controlled processes is applied to describe the steady state of a reversible enzymatic reaction with special emphasis on the effects of enzyme saturation. A standard macroscopic steady-state treatment requires only that the average diffusional influx of substrate equals the net reaction flux as well as the average diffusional efflux of product. In contrast, the microscopic diffusion-reaction coupling used here takes properly into account the conditional concentration distributions of substrate and product: Only when the enzyme is unoccupied will there be a diffusional association flux; when the enzyme is occupied, the concentration distributions will relax towards their homogeneous bulk values. In this way the relaxation effects of the non-steady state will be constantly reoccurring as the enzyme shifts between unoccupied and occupied states. Thus, one is forced to describe the steady state as the weighted sum of properly time-averaged non-stationary conditional distributions. The consequences of the theory for an appropriate assessment of the parameters obtained in Lineweaver-Burk plots are discussed. In general, our results serve to justify the simpler macroscopic coupling scheme. However, considerable deviations between the standard treatment and our analysis can occur for fast enzymes with an essentially irreversible product release.     

Nonlinear steady-state kinetics of chloramphenicol acetyltransferase.

Steady-state kinetic analysis of chloramphenicol acetyltransferase showed that medium effects (higher temperatures or pH, higher ionic strengths, or lower values for dielectric constant) altered the kinetic behaviour of the enzyme with acetyl-CoA as substrate, but did not significantly affect behaviour with chloramphenicol. This was manifest as an increase in the degree of the rate equation to a 2:2 function. This is interpreted in terms of perturbations to the enzyme at or near the acetyl-CoA binding region of the enzyme.     

The computerized derivation of steady-state rate equations for enzyme kinetics.

A FORTRAN 77 program is described for the derivation of steady-state rate equations for enzyme kinetics. Input is very simple and consists of the two enzyme forms and the two rate constants for each step in the mechanism. The program may be run interactively or off-line. The results are produced after collecting together the algebraic coefficients of like concentration terms, taking account of sign. A fully interactive BASIC version running on a BBC Microcomputer is also available. Details of the programs have been deposited as Supplementary Publication SUP 50126 (45 pages) with the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies may be obtained as indicated in Biochem. J. (1984) 217, 5.     

Microcomputer analysis of hyperbolic and non-hyperbolic steady-state kinetics

A BASIC computer program has been developed which has been used to show that bovine lens aldose reductase with NADPH as substrate follows a 1:1 function, while rabbit lens hexokinase has a rate equation of minimum degree 2:2, and bovine lens polyol dehydrogenase has a rate equation of minimum degree 1:2 with xylitol as substrate. The parameter estimates obtained are very close to those from the BMDP3R curvefitting program on an ICL 2980 mainframe computer, with identical conclusions as to the minimum degree of the rate equation. The computer program can be run on any microcomputer with high resolution graphics in less than 48 K of random access memory.     

Improved processing of the steady-state evoked potential

Two related procedures for estimating the parameters of steady-state evoked potentials (SSEPs) are introduced. The first procedure involves an initial stage of digital bandpass filtering followed by a Discrete Fourier Transform analysis. In the second method, a high resolution method based on parametric modelling is applied to the filtered data. The digital pre-filter consists of a non-phase shifting Chebychev bandpass filter. The parametric modelling method considers the evoked-response-plus-noise distribution to consist of a set of exponentially damped sinusoids. The frequency, amplitude, phase and damping factors of these components are estimated by calculating the mean of the forward and backward prediction filters and linear regression.We compared the signal-to-noise ratio (SNR) of the new procedures to the conventional Discrete Fourier Transform method for Monte Carlo simulations utilizing known sinusoids buried in white noise, known sinusoids buried in human EEG noise and for a sample of visual evoked potential data. Both of the new methods produce substantially more accurate and less variable estimates of test sinusoid amplitude. For VEP recording, the EEG background noise level is reduced by 5–6 dB over that obtained with the DFT. The new methods also provide approximately 5 dB better SNR than the DFT for detection of sinusoids based on the Rayleigh statistic. The parametric modelling approach is particularly suited for the analysis of very short data records including cycle-by-cycle analysis of the SSEP.     

Haloalkane dehalogenases: steady-state kinetics and halide inhibition

The substrate specificities and product inhibition patterns of haloalkane dehalogenases from Xanthobacter autotrophicus GJ10 (XaDHL) and Rhodococcus rhodochrous (RrDHL) have been compared using a pH-indicator dye assay. In contrast to XaDHL, RrDHL is efficient toward secondary alkyl halides. Using steady-state kinetics, we have shown that halides are uncompetitive inhibitors of XaDHL with 1, 2-dichloroethane as the varied substrate at pH 8.2 (Cl-, Kii = 19 +/- 0.91; Br-, Kii = 2.5 +/- 0.19 mM; I-, Kii = 4.1 +/- 0.43 mM). Because they are uncompetitive with the substrate, halide ions do not bind to the free form of the enzyme; therefore, halide ions cannot be the last product released from the enzyme. The Kii for chloride was pH dependent and decreased more than 20-fold from 61 mM at pH 8.9 to 2.9 mM at pH 6.5. The pH dependence of 1/Kii showed simple titration behavior that fit to a pKa of approximately 7.5. The kcat was maximal at pH 8.2 and decreased at lower pH. A titration of kcat versus pH also fits to a pKa of approximately 7.5. Taken together, these data suggest that chloride binding and kcat are affected by the same ionizable group, likely the imidazole of a histidyl residue. In contrast, halides do not inhibit RrDHL. The Rhodococcus enzyme does not contain a tryptophan corresponding to W175 of XaDHL, which has been implicated in halide ion binding. The site-directed mutants W175F and W175Y of XaDHL were prepared and tested for halide ion inhibition. Halides do not inhibit either W175F or W175Y XaDHL.     

Identification of enzyme inhibitory mechanisms from steady-state kinetics

Enzyme inhibitors are used in many areas of the life sciences, ranging from basic research to the combat of disease in the clinic. Inhibitors are traditionally characterized by how they affect the steady-state kinetics of enzymes, commonly analyzed on the assumption that enzyme-bound and free substrate molecules are in equilibrium. This assumption, implying that an enzyme-bound substrate molecule has near zero probability to form a product rather than dissociate, is valid only for very inefficient enzymes. When it is relaxed, more complex but also more information-rich steady-state kinetics emerges. Although solutions to the general steady-state kinetics problem exist, they are opaque and have been of limited help to experimentalists.Here we reformulate the steady-state kinetics of enzyme inhibition in terms of new parameters. These allow for assessment of ambiguities of interpretation due to kinetic scheme degeneracy and provide an intuitively simple way to analyze experimental data. We illustrate the method by concrete examples of how to assess scheme degeneracy and obtain experimental estimates of all available rate and equilibrium constants. We suggest simple, complementary experiments that can remove ambiguities and greatly enhance the accuracy of parameter estimation.     

Development and experimental evaluation of a steady-state, multispecies biofilm model

A steady-state model for quantifying the space competition in multispecies biofilms is developed. The model includes multiple active species, inert biomass, substrate utilization and diffusion within the biofilm, external mass transport, and detachment phenomena. It predicts the steady-state values of biofilm thickness, species distribution, and substrate fluxes. An experimental evaluation is carried out in completely mixed biofilm reactors in which slow-growing nitrifying bacteria compete with acetate-utilizing heterotrophs. The experimental results show that the model successfully describes the space competition. In particular, increasing acetate concentrations causes NH(4) (+)-N fluxes to decrease, because nitrifiers are forced deeper into the biofilm, where they experience greater mass-transport resistance.