A cometabolic kinetics model incoroporating enzyme inhibition, inactivation, and recovery: II. Trichloroethylene degradaation experiments

A Cometabolism enzyme kinetics model has been presented which takes into account changes in bacterial activity associated with enzyme inhibitiion, inactivation, inactivation of enzyme resulting from product toxicty, and respondent synthesis of new enzyme. Although this process is inherently unsteady-state, the model assumes that cometabolic degradation of a compound exhibiting product toxicity can be modeled as pseudo-steady-staate under certain conditions. In its simplified from, the model also assumes that enzyme inactivation is directly propoertional to nongrawth substrate oxidation, and that recovery is directly proportionla to growth substrate oxidation. In part 1, model drivation, simplification, and analyses were described. In this articles, model assuptiions are tested by analyzing data from experiments exmining trichloroethylene (TCE) degradation by the ammoniaoxidizing baceterium Nitrosomonas europaea in a quasisteady-state bioreactor. Model solution results showed steady-state bioreactor. Model solution results showed TCE to be a competitive inhibitoer of ammonia oxidation, with TCE affinity for ammonia monooxygenase (AMO) being about four times greater than that of ammonia for the enzyme. Inhibition was independent fo TCE oxidation and occurred essentially instantly upon exposure to TCE. In contrast, inactivation of AMO occurred more gradually and was proportional to the rate and amount of TCE oxidized. Evaluation of other O(2)-dependent enzymes and electron transport proteins suggested that TCE-related damage was predominantly confined to AMO. In response to inhibition and/or inactivation, bacterial recovery was initiated, even in the presence of TCE, implying that membranes adn protein synthesis systems were functioning. Analysis of data and comparison of model results showed the inhibition/inactivation/recovery concept to provide a reasonable basis for understandign the effects fo TCE on AMO function and bacterial response. The model assumptions were verified except tht questions remain regarding the factores controlling recovery and its role in the long term. (c) 1995 John Wiley & Sons, Inc.     

Effect of subunit dissociation, denaturation, aggregation, coagulation, and decomposition on enzyme inactivation kinetics: I. First-order behaviour

Enzyme inactivation kinetics typically follows what would appear to be simple first-order behavior. However, the inactivation process is known to involve a number of reversible (decomposition, denaturation) as well as irreversible (decomposition, aggregation, and coagulation) reactions. These reactions can combine to form a wide variety of reaction pathways which can potentially demonstrate complex inactivation kinetics. However, it was shown that with appropriate assumptions with regard to the relative magnitudes of the various reaction rates, many complex inactivation pathways can demonstrate apparent first-order behavior. Thus, with this analysis, a more accurate interpretation of the slope of an activity versus time semi-log plot can be obtained. (c) 1992 John Wiley & Sons, Inc.     

A microscopic model of enzyme kinetics.

Many in vivo enzymatic processes, such as those of the tissue factor pathway of blood coagulation, occur in environments with facilitated substrate delivery or enzymes bound to cellular or lipid surfaces, which are quite different from the ideal fluid environment for which the Michaelis-Menten equation was derived. To describe the kinetics of such reactions, we propose a microscopic model that focuses on the kinetics of a single-enzyme molecule. This model provides the foundation for macroscopic models of the system kinetics of reactions occurring in both ideal and nonideal environments. For ideal reaction systems, the corresponding macroscopic models thus derived are consistent with the Michaelis-Menten equation. It is shown that the apparent Km is in fact a function of the mechanism of substrate delivery and should be interpreted as the substrate level at which the enzyme vacancy time equals the residence time of ES-complexes; it is suggested that our microscopic model parameters characterize more accurately an enzyme and its catalytic efficiency than does the classical Km. This model can also be incorporated into computer simulations of more complex reactions as an alternative to explicit analytical formulation of a macroscopic model.     

A novel population balance model to investigate the kinetics of in vitro cell proliferation: part I. Model development

In biotechnology and biomedicine reliable models of cell proliferation kinetics need to capture the relevant phenomena taking place during the mitotic cycle. To this aim, a novel mathematical model helpful to investigate the intrinsic kinetics of in vitro culture of adherent cells up to confluence is proposed in this work. Specifically, the attention is focused on the simulation of proliferation (increase of cell number) and maturation (increase of cell size and DNA content) till contact inhibition eventually takes place inside a Petri dish. Accordingly, the proposed model is based on a population balance (PB) approach that allows one to quantitatively describe cell cycle progression through the different phases the cells of the entire population experienced during their own life. In particular, the proposed model has been developed as a 2D, multi-staged, and unstructured PB, by considering a different sub-population of cells for any single phase of the cell cycle. These sub-populations are discriminated through cellular volume and DNA content, that both increase during the mitotic cycle. The adopted mathematical expressions of the transition rates between two subsequent phases and the temporal increase of cell volume and DNA content are thoroughly analyzed and discussed with respect to those ones available in the literature. Specifically, the corresponding uncertainties and pitfalls are pointed out, by also taking into account the difficulties and the limitations involved in the quantitative measurements currently practicable for these biological systems. A novel mathematical expression for contact inhibition in line with the PB model developed is also formulated, along with a proper comparison between modeled and measurable DNA distributions. The strategy for a reliable, independent tuning of the adjustable parameters involved in the proposed model along with its numerical solution is outlined in Part II of this work, where it is also shown how it can be profitably used to gain a deeper insight into the phenomena involved during cell cultivation under microgravity conditions.     

Receptor-mediated cell attachment and detachment kinetics. I. Probabilistic model and analysis.

The kinetics of receptor-mediated cell adhesion to a ligand-coated surface play a key role in many physiological and biotechnology-related processes. We present a probabilistic model of receptor-ligand bond formation between a cell and surface to describe the probability of adhesion in a fluid shear field. Our model extends the deterministic model of Hammer and Lauffenburger (Hammer, D.A., and D.A. Lauffenburger. 1987. Biophys. J. 52:475-487) to a probabilistic framework, in which we calculate the probability that a certain number of bonds between a cell and surface exists at any given time. The probabilistic framework is used to account for deviations from ideal, deterministic behavior, inherent in chemical reactions involving relatively small numbers of reacting molecules. Two situations are investigated: first, cell attachment in the absence of fluid stress; and, second, cell detachment in the presence of fluid stress. In the attachment case, we examine the expected variance in bond formation as a function of attachment time; this also provides an initial condition for the detachment case. Focusing then on detachment, we predict transient behavior as a function of key system parameters, such as the distractive fluid force, the receptor-ligand bond affinity and rate constants, and the receptor and ligand densities.(ABSTRACT TRUNCATED AT 250 WORDS)     

A minimal model of non-hyperbolic enzyme and receptor kinetics

A simplified version of P.W. Kühl's Recovery Model [Biochem. J. 298 (1994) 171-180] has been developed in which the duration of the recovery phase of receptor or enzyme (macro)molecule was assumed to be a random value distributed exponentially like other model parameters. The model has been shown to retain all the properties of the original Recovery Model except for its ability to yield asymmetric dose-response curves (if plotted in semi-logarithmic scale). Due to its simplicity, the present model is applicable for routine fitting to experimental data. In enzyme kinetics, the model yields a diversity of non-hyperbolic dose-response curves both with higher and lower steepness than that of Henri-type ones. In receptor kinetics, the diversity of dose-response curves is further increased due to virtually no restraints being imposed on the efficacies of any state of the macromolecule.     

Influence of chemical modification on enzyme inactivation kinetics and stability

Enzymes are placed in different categories depending on the effect of chemical modification on their inactivation kinetics and residual activity. This is done using a series-type mechanism involving degraded but stable enzyme states. The major distinction in the three basic categories is the effect of modification on residual activity. Each category is further sub-divided depending on the effect of modification on the values of the deactivation rate constants. The classification provides for a framework for comparison of a wide variety of enzyme deactivation data. Structure-function relations are provided wherever possible.     

Kinetic modeling of a multiple immobilized enzyme system. I. Development and testing of the model

A kinetic model for the reaction sequence catalyzed by coimmobilized invertase and glucose oxidase with a sucrose substrate in a tubular reactor has been developed. The computerized mathematical model employs and orthogonal collection technique for solving oxidase were coimmobilized in poly(2-hydroxyethlmethacrylate) gels and used in a continuous flow packed-bed tubular reactor system. In addition to describing the development of the kinetic model, this article compares experimentally determined reactor effluent concentrations for various sucrose feed solutions to those predicted by the model. Variations between experimental and predicted reactor effluent concentrations were found to be on the micromolar level for sucrose feed concentrations as low as 1.38mM.     

A nonlinear compartmental model of Sr metabolism. I. Non-steady-state kinetics and model building

A model of Sr metabolism was developed by using plasma and urinary Sr kinetic data obtained in groups of postmenopausal women who received four different oral doses of Sr and collected during the Sr administration period (25 days) and for 28 days after cessation of treatment. A nonlinear compartmental formalism that is appropriate for study of non-steady-state kinetics and allows dissociation of variables pertaining to Sr metabolism (system 1) from those indirectly operating on it (system 2) was used. At each stage of model development, the dose-dependent model response was fitted to the four sets of data considered simultaneously (1 set per dose). A seven-compartment model with internal Sr distribution and intestinal, urinary, and bone metabolic pathways was selected. It includes two kinds of nonlinearities: those accounting for saturable intestinal and bone processes, which behave as intrinsic nonlinearities because they are directly dependent on Sr, and extrinsic nonlinearities (dependent on system 2), which suggest the cooperative involvement of plasma Sr changes in modulating some intestinal and bone mineral metabolic pathways. With the set of identified parameter values, the initial steady-state model predictions are relevant to known physiology, and some peculiarities of model behavior for long-term Sr administration were simulated.     

Effect of subunit dissociation, denaturation, aggregation, coagulation, and decomposition on enzyme inactivation kinetics: II. Biphasic and grace period behavior

A model previously developed to characterize enzymatic in activation behavior was used to explain the non-first-order biphasic and grace period phenomena that are often observed with oligomeric enzymes. Luciferase and urease were used as model enzyme such as luciferase, the oligomer initially dissociates reversibly into two native monomer species. These native monomers can then reversibly denature and irreversibly aggregate and coagulate. With the hexamer, urease, two trimers are formed that can subsequently aggregate to form an inactive hexamer. The dissociated monomer species of luciferase do not possess catalytic activity, so the inactivation mechanism, is biphasic; the first slope of a first-order kinetic plot is influenced by the reversible oligomer/monomer/denatured-monomer transition. Whereas the second slope is associated with either irreversible aggregation or coagulation. In contrast, the trimer of urease has the same activity as the hexamer; therefore, during the intitial hexamer-trimer transition, little activity loss occurs. However, as the trimer concentration increases, activity decreases as a result of trimer aggregation. As a result, grace period inactivation behavior is observed. (c) 1992 John Wiley & Sons, Inc.     

Staphylococcal L-asparaginase: enzyme kinetics.

The ph optimum of purified staphylococcal L-asparaginase (EC 3.5.1.1) was found to be between 8.6 and 8.8. The temperature optimum was 30 degrees-32 degrees C and the highest reaction rate occurred at 30 degrees C. The KM of the enzyme calculated from Lineweaver-Burk plot was 3.71 x 10(-2) M. Besides L-asparaginase, the substrate specificity of enzyme was restricted to N-alpha-acetyl-L-asparagine. D-asparagine, L-aspartic acid and D-glutamic acid were competitive inhibitors. Hg2+ and Cu2+ cations strongly inhibited the enzyme while Na+ and K+ cations strongly stimulated activity. Two SH-groups could be detected after enzyme denaturation with guanidine.     

UDPglucose pyrophosphorylase from Xanthomonas spp. Characterization of the enzyme kinetics, structure and inactivation related to oligomeric dissociation

The genes encoding for UDPglucose pyrophosphorylase in two Xanthomonas spp. were cloned and overexpressed in Escherichia coli. After purification to electrophoretic homogeneity, the recombinant proteins were characterized, and both exhibited similar structural and kinetic properties. They were identified as dimeric proteins of molecular mass 60kDa, exhibiting relatively high specific activity ( approximately 80Units/mg) for UDPglucose synthesis. Both enzymes utilized UTP or TTP as substrate with similar affinity. The purified Xanthomonas enzyme was inactivated after dilution into the assay medium. Studies of crosslinking with the bifunctional lysyl reagent bisuberate suggest that inactivation occurs by enzyme dissociation to monomers. UTP effectively protects the enzyme against inactivation, from which a dissociation constant of 15microM was calculated for the interaction substrate-enzyme. The UTP binding to the enzyme would induce conformational changes in the protein, favoring the subunits interaction to form an active dimer. This view was reinforced by protein modeling of the Xanthomonas enzyme on the basis of the prokaryotic UDPglucose pyrophosphorylase crystallographic structure. The in silico approach pointed out two main critical regions in the enzyme involved in subunit-subunit interaction: the region surrounding the catalytic-substrate binding site and the C-term.     

A computer program for enzyme kinetics that combines model discrimination, parameter refinement and sequential experimental design.

A method of model discrimination and parameter estimation in enzyme kinetics is proposed. The experimental design and analysis of the model are carried out simultaneously and the stopping rule for experimentation is deduced by the experimenter when the probabilities a posteriori indicate that one model is clearly superior to the rest. A FORTRAN77 program specifically developed for joint designs is given. The method is very powerful, as indicated by its usefulness in the discrimination between models. For example, it has been successfully applied to three cases of enzyme kinetics (a single-substrate Michaelian reaction with product inhibition, a single-substrate complex reaction and a two-substrate reaction). By using this method the most probable model and the estimates of the parameters can be obtained in one experimental session. The FORTRAN77 program is deposited as Supplementary Publication SUP 50134 (19 pages) at the British Library (Lending Division), Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1986) 233, 5.     

Anaerobic digestion model no. 1-based distributed parameter model of an anaerobic reactor: I. Model development

This work presents a distributed parameter model of the anaerobic digestion process. The model is based on the Anaerobic digestion model no. 1 (ADM1) and was developed to simulate anaerobic digestion process in high-rate reactors with significant axial dispersion, such as in upflow anaerobic sludge bed (UASB) reactors. The model, which was named ADM1d, combines ADM1's kinetics of biomass growth and substrate transformation with axial dispersion material balances. ADM1d uses a hyperbolic tangent function to describe biomass distribution within a one compartment model. A comparison of this approach with a two-compartment, sludge bed - liquid above the bed, model showed similar simulation results while the one-compartment model had less equations. A comparison of orthogonal collocation and finite difference algorithms for numerical solution of ADM1d showed better stability of the finite difference algorithm.