Modeling pH effects on microbial growth: a statistical thermodynamic approach

This paper applies a statistical thermodynamic approach to the kinetics of microbial growth influenced by pH. A general equation is developed and shown to provide a good theoretical basis for the existing pH models that have been widely used to describe the effects of pH on microbial growth kinetics. Four experimental data sets are used to test the general equation developed. The four data sets exhibited a variety of functional curve shapes, for example, symmetrical and asymmetrical bell-shaped, when the specific growth rate of microorganisms is plotted as a function of pH. All four data sets are found to be well represented by the general equation. The existing pH model was, however, found to represent only one out of four data sets, i.e., the symmetrical case.     

Modeling Microbially Induced Carbon Degradation in Redox-Stratified Subsurface Environments: Concepts and Open Questions

The degradation of organic matter, including organic contaminants, in subsurface environments is controlled by the abundances and functional capabilities of the resident microorganisms. As a consequence, modeling approaches simulating the fate of organics and related changes in redox conditions have to account for the effects of microbial activity on the degradation kinetics, as well as for the spatial and temporal distributions of the chemical species (e.g., terminal electron acceptors, nutrients or toxic substances) that control microbial activity. The present paper reviews the principal modeling approaches that are used to simulate the degradation of organic matter in water-saturated porous media. Special attention is devoted to modeling the bioavailability of chemical substrates of microbial reactions, and the sequential occurrence of terminal electron accepting pathways. While the various model approaches found in the literature are capable of reproducing field data sets from various environmental settings, they are rarely compared in terms of performance and predictive ability. Most approaches incorporate simplifications or empirical rate laws, which limit their range of application. Thus, there remains a need for further development of more general, process-based modeling concepts to represent microbially mediated reactive processes.     

Dynamics of muscle glycogenolysis modeled with pH time course computation and pH-dependent reaction equilibria and enzyme kinetics

Cellular metabolites are moieties defined by their specific binding constants to H+, Mg2+, and K+ or anions without ligands. As a consequence, every biochemical reaction in the cytoplasm has an associated proton stoichiometry that is generally noninteger- and pH-dependent. Therefore, with metabolic flux, pH is altered in a medium with finite buffer capacity. Apparent equilibrium constants and maximum enzyme velocities, which are functions of pH, are also altered. We augmented an earlier mathematical model of skeletal muscle glycogenolysis with pH-dependent enzyme kinetics and reaction equilibria to compute the time course of pH changes. Analysis shows that kinetics and final equilibrium states of the closed system are highly constrained by the pH-dependent parameters. This kinetic model of glycogenolysis, coupled to creatine kinase and adenylate kinase, simulated published experiments made with a cell-free enzyme mixture to reconstitute the network and to synthesize PCr and lactate in vitro. Using the enzyme kinetic and thermodynamic data in the literature, the simulations required minimal adjustments of parameters to describe the data. These results show that incorporation of appropriate physical chemistry of the reactions with accurate kinetic modeling gives a reasonable simulation of experimental data and is necessary for a physically correct representation of the metabolic network. The approach is general for modeling metabolic networks beyond the specific pathway and conditions presented here.     

General theory of determining intraparticle active immobilized enzyme distribution and rate parameters

A general theory is presented in this article for determining the intrinsic rate constants for the main reaction and deactivation reaction, the effective diffusivity of the substrate, and the active enzyme distribution within porous solid supports from deactivation study of a continuous stirred-basket reactor (CSBR). For the parallel deactivation five reaction kinetics are considered: (a) Michaelis-Menten, (b) substrate inhibition, (c) product inhibition (competitive), (d) product inhibition (anticompetitive), and (e) zero-order kinetics. The experimental results of the system of hydrogen-peroxide-immobilized catalase on controlled-pore glass particles are analyzed to demonstrate the application of the theory developed for parallel deactivation of active immobilized enzyme (IME). For series deactivation only first-order kinetics is treated, and a numerical procedure is proposed to deter mine the rate parameters and the internal active enzyme distribution. The experimental data of the system of glucose-immobilized glucose oxidase on silica-alumina and controlled-pore glass particles are used to verify the theory.     

Hill coefficients of dietary polyphenolic enzyme inhibitiors: can beneficial health effects of dietary polyphenols be explained by allosteric enzyme denaturing?

Inspired by a recent article by Prinz, suggesting that Hill coefficients, obtained from four parameter logistic fits to dose–response curves, represent a parameter allowing distinction between a general allosteric denaturing process and real single site enzyme inhibition, Hill coefficients of a number of selected dietary polyphenol enzyme inhibitions were compiled from the available literature. From available literature data, it is apparent that the majority of polyphenol enzyme interactions reported lead to enzyme inhibition via allosteric denaturing rather than single site inhibition as judged by their reported Hill coefficients. The results of these searches are presented and their implications discussed leading to the suggestion of a novel hypothesis for polyphenol biological activity termed the insect swarm hypothesis.     

Kinetic analysis of high-concentration isopropanol biodegradation by a solvent-tolerant mixed microbial culture

The ability of a previously enriched microbial population to utilize isopropanol (IPA) as the sole carbon source within a minimal salts medium is studied. The advantage of prior enrichment procedures for the improvement of IPA biodegradation performance is demonstrated for an IPA concentration of up to 24 g L(-1). Results showing the interrelationship between temperature and substrate utilization and inhibition levels at temperatures of between 2 degrees C and 45 degrees C are examined. Models of inhibition based on enzyme kinetics are assessed via nonlinear analysis, in order to accurately represent the growth kinetics of this solvent-tolerant mixed culture. The model that best describes the data is the Levenspiel substrate inhibition model, which can predict the maximum substrate level above which growth is completely limited. This is the first report of IPA treatment of up to 24 g L(-1) by an aerobic solvent-tolerant population.     

Biokinetic models for representing the complete inhibition of microbial activity at high substrate concentrations.

This paper reintroduces the Wayman and Tseng model for representing substrate inhibition effects on specific growth rate by further documenting its potential predictive capabilities. It also introduces a modification to this model in which an Andrews inhibition function is used in place of the Monod noninhibitory substrate function. This modification better represents the relationship between specific growth rate and substrate concentration for those substrates that show Andrews type inhibition at lower substrate concentrations, rather than the Monod type noninhibitory behavior described in the model of Wayman and Tseng. Results from nonlinear, least squares regression analysis are used to evaluate the ability of these models to empirically represent experimental data (both new and from the literature). The statistical goodness of fit is evaluated by comparing the regression results against those obtained using other empirical models. Finally, possible mechanisms of toxicity responsible for the observed inhibition trends are used to further justify use of these empirical models. The dominant mechanism considered to be relevant for conceptually explaining complete inhibition at high concentrations of solvents is the deterioration of cell membrane integrity. Literature citations are used to support this argument. This work should lead to improvements in the mathematical modeling of contaminant fate and transport in the environment and in the simulation of microbial growth and organic compound biodegradation in engineered systems.     

A method of graphically analyzing substrate-inhibition kinetics

A model of substrate inhibition for enzyme catalysis was extended to describe the kinetics of photosynthetic production of ethylene by a recombinant cyanobacterium, which exhibits light-inhibition behavior similar to the substrate-inhibition behavior in enzyme reactions. To check the validity of the model against the experimental data, the model equation, which contains three kinetic parameters, was transformed so that a linear plot of the data could be made. The plot yielded reasonable linearity, and the parameter values could be estimated from the plot. The linear-plot approach was then applied to other inhibition kinetics including substrate inhibition of enzyme reactions and inhibitory growth of bacteria, whose analyses would otherwise require nonlinear least-squares fits or data measured in constrained ranges. Plots for three totally different systems all showed reasonable linearity, which enabled visual validation of the assumed kinetics. Parameter values evaluated from the plots were compared with results of nonlinear least-squares fits. A normalized linear plot for all the results discussed in this work is also presented, where dimensionless rates as a function of dimensionless concentration lie in a straight line. The linear-plot approach is expected to be complementary to nonlinear least-squares fits and other currently used methods in analyses of substrate-inhibition kinetics. Copyright 1999 John Wiley & Sons, Inc.     

Kinetics of inhibition in the biodegradation of monoaromatic hydrocarbons in presence of heavy metals

The toxicity and inhibitory effects of heavy metals such as cadmium, nickel and zinc on alkylbenzene removal were evaluated with a Bacillus strain. The kinetics of alkylbenzene biodegradation with the different heavy metals at various concentrations were modeled using the Andrews equation which yielded a good fit between model and experimental data. Additional experiments undertaken with a Pseudomonas sp. in presence of nickel confirmed a good fit between experimental data and the Andrews model for this strain as well. The heavy metals inhibition constants (Ki) were calculated for different combinations of volatile organic compounds (VOC) and heavy metals. The present approach provides a method for evaluating and quantifying the inhibition effect of heavy metals on the biodegradtion of pollutants by specific microbial strains.     

Fuel alcohol production by Zymomanas anaerobia: Kinetics

Process kinetics of a strain of Zymomonas anaerobia,which recently was shown to posses a high potential for ethanol production,are described applying the formal macroapproach The effect of ethanol inhibition on microbial growth,substrate utilization and alcohol production was investigated in detail. Growth rate and yield coefficients were affected by the ethanol concentration Several mathematical model functions from literature were tested for the quantification of experimental batch data. As none of these models was able to describe the entire growth phase a modified model using formal kinetics was developed for the rates of growth,substrate utilization and product formation (see Eqs. 10, 14, 18).     

Mathematical modelling and kinetic study for CD production catalysed by Toruzyme® and CGTase from Bacillus firmus strain 37

A new mathematical model was developed for the kinetics of α-, β- and γ-cyclodextrin production, expanding an existing model that only included the production of β- and γ-cyclodextrins, because a detailed kinetic modelling of the reactions involved allows the manipulation of the process yields. The kinetic behaviour of the commercial enzyme Toruzyme^® was studied with maltodextrin as substrate at different concentrations and for CGTase from Bacillus firmus strain 37 at a concentration of 100 g L⁻¹. The mathematical model showed a proper fit to the experimental data, within the 24-h period studied, confirming that the considered hypotheses represent the kinetic behaviour of the enzymes in the reaction medium. The kinetic parameters generated by the model allowed reproducing previous observed qualitative tendencies as it can be seen that changing experimental conditions in the reaction process such as enzyme and substrate concentrations results in large changes in the enzyme kinetics and using high substrate concentrations does not guarantee the highest conversion rates due to enzyme inhibition and reverse reactions. In addition, this new mathematical model complements previous qualitative observations enabling the manipulation of the direct and reverse reactions catalysed by the enzyme by adjusting the reaction conditions, to target quantitative results of increased productivity and better efficiency in the production of a desired cyclodextrin.

     

Effects of spatial variation of cells and nutrient and product concentrations coupled with product inhibition on cell growth in a polymer scaffold.

The effects of spatial variation of cells and nutrient and product concentration, in combination with product inhibition in cell growth kinetics on chondrocyte generation in a polymer scaffold, are analyzed. Experimental studies reported previously have demonstrated spatial dependence in the cultivation of chondrocytes. In the present study, the cell-polymer system is assumed to consist of two distinct phases. The cells, fluid, polymer matrix, and extracellular matrix comprise one phase, and the other phase consists of a fluid and polymer matrix. The only two species in the fluid considered to affect cell growth are the nutrient and product. The multiphase transport process of these two species in the cell-polymer system is described by the species continuity equations and corresponding boundary conditions for each individual phase. A volume-averaging approach is utilized for this system to derive averaged species continuity equations for the nutrient and product concentrations. The volume-averaging approach allows for a single species in a two-phase system to be represented by a single averaged continuity equation. Competitive product inhibition, saturation kinetics of substrate, and cell population control are assumed to affect the cell growth kinetics. A modified Contois growth kinetic model is used to represent the three factors that affect cell growth. A parameter analysis is performed and the results are compared qualitatively with experimental data found in the literature.     

Steady-state kinetic studies of the negative co-operativity and flip-flop mechanism for Escherichia coli alkaline phosphatase.

1. A study of variations in experimental error of velocity measurement with substrate concentration for alkaline phosphatase reveals that the standard error is not constant or strictly proportional to velocity, but obeys a more complex dependence. 2. By using an approach based on error estimates at each individual substrate concentration, we show that the double-reciprocal plots in general are curved, necessitating a high-degree rate equation. The curves are analysed according to a recent classification of possible curve shapes for the 3:3 function, which is shown to be the lowest-degree rate equation satisfying the experimental data. 4. Other workers have supposed the enzyme to follow Michaelis-Menten kinetics, and it is shown that this assumption is approximately true at low temperatures in the absence of phosphate. 5. A study of the effects of phosphate concentration, pH and temperature on the kinetics shows that there is a gradual alteration in curve shape with these experimental variables, resulting in an apparent reduction in degree under certain special conditions, and particularly at low temperature. 6. It is shown that the steady-state kinetics do not require a flip-flop or half-of-sites reactivity mechanism as claimed, and a mechanism is proposed, a rate equation calculated and an analysis attempted. 7. An analysis of the product-inhibition effects for a linked two-sited Uni Bi enzyme is given. Alterations of asymptotic double-reciprocal slopes and limiting (1/nu) intercepts with products is discussed, and it is shown how the theory of product inhibition can be extended to complex kinetic situations to extract information as to molecular mechanism. 8. Deviations from Michaelis-Menten kinetics are expressed in terms of the magnitude of the appropriate Sylvester resultants.     

Half-time analysis of the kinetics of irreversible enzyme inhibition by an unstable site-specific reagent

The half-time method for the determination of Michaelis parameters from enzyme progress-curve data (Wharton, C.W. and Szawelski, R.J. (1982) Biochem. J. 203, 351-360) has been adapted for analysis of the kinetics of irreversible enzyme inhibition by an unstable site-specific inhibitor. The method is applicable to a model in which a product (R) of the decomposition of the site-specific reagent, retaining the chemical moiety responsible for inhibitor specificity, binds reversibly to the enzyme with dissociation constant Kr: (formula; see text). Half-time plots of simulated enzyme inactivation time-course data are shown to be unbiased, and excellent estimates of the apparent second-order rate constant for inactivation (k +2/Ki) and Kr can be obtained from a series of experiments with varying initial concentrations of inhibitor. Reliable estimates of k +2 and Ki individually are dependent upon the relative magnitudes of the kinetic parameters describing inactivation. The special case, Kr = Ki, is considered in some detail, and the integrated rate equation describing enzyme inactivation shown to be analogous to that for a simple bimolecular reaction between enzyme and an unstable irreversible inhibitor without the formation of a reversible enzyme-inhibitor complex. The half-time method can be directly extended to the kinetics of enzyme inactivation by an unstable mechanism-based (suicide) inhibitor, provided that the inhibitor is not also a substrate for the enzyme.     

The Dual Arrhenius and Michaelis–Menten kinetics model for decomposition of soil organic matter at hourly to seasonal time scales

Decomposition of soil carbon stocks is one of the largest potential biotic feedbacks to climate change. Models of decomposition of soil organic matter and of soil respiration rely on empirical functions that relate variation in temperature and soil water content to rates of microbial metabolism using soil‐C substrates. Here, we describe a unifying modeling framework to combine the effects of temperature, soil water content, and soluble substrate supply on decomposition of soluble soil‐C substrates using simple functions based on process concepts. The model's backbone is the Michaelis–Menten equation, which describes the relationship between reaction velocity and soluble organic‐C and O₂ substrate concentrations at an enzyme's reactive site, which are determined by diffusivity functions based on soil water content. Temperature sensitivity is simulated by allowing the maximum velocity of the reaction (V_max) to vary according to Arrhenius function. The Dual Arrhenius and Michaelis–Menten kinetics (DAMM) model core was able to predict effectively observations from of laboratory enzyme assays of β‐glucosidase and phenol‐oxidase across a range of substrate concentrations and incubation temperatures. The model also functioned as well or better than purely empirical models for simulating hourly and seasonal soil respiration data from a trenched plot in a deciduous forest at the Harvard Forest, in northeastern United States. The DAMM model demonstrates that enzymatic processes can be intrinsically temperature sensitive, but environmental constrains of substrate supply under soil moisture extremes can prevent that response to temperature from being observed. We discuss how DAMM could serve as a core module that is informed by other modules regarding microbial dynamics and supply of soluble‐C substrates from plant inputs and from desorption of physically stabilized soil‐C pools. Most importantly, it presents a way forward from purely empirical representation of temperature and moisture responses and integrates temperature‐sensitive enzymatic processes with constraints of substrate supply.     

Biodegradation kinetics of peptone and 2,6-dihydroxybenzoic acid by acclimated dual microbial culture

This study evaluated the kinetics of simultaneous biodegradation of peptone mixture and 2,6-dihydroxybenzoic acid (2,6-DHBA) by an acclimated dual microbial culture under aerobic conditions. A laboratory-scale sequencing batch reactor was sustained at steady-state with peptone mixture feeding. During the study period, peptone mixture feeding was continuously supplemented with 2,6-DHBA. Related experimental data were derived from three sets of parallel batch reactors, the first fed with the peptone mixture, the second with 2,6-DHBA and the third one with the two substrates, after acclimation of microbial culture and simultaneous biodegradation of both organics. A mechanistic model was developed for this purpose including the necessary model components and process kinetics for the model calibration of relevant experimental data. Model evaluation provided all biodegradation characteristics and kinetics for both peptone mixture and 2,6-DHBA. It also supported the development of a dual microbial community through acclimation, with the selective growth of a second group of microorganisms specifically capable of metabolizing 2,6-DHBA as an organic carbon source.     

Saturation Behavior: a general relationship described by a simple second-order differential equation

Background  

The numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches.     

Simulated data sets for single molecule kinetics: some limitations and complications of data analysis

When the fluorescence intensity of a chromophore attached to or bound in an enzyme relates to a specific reactive step in the enzymatic reaction, a single molecule fluorescence study of the process reveals a time sequence in the fluorescence emission that can be analyzed to derive kinetic and mechanistic information. Reports of various experimental results and corresponding theoretical studies have provided a basis for interpreting these data and understanding the methodology. We have found it useful to parallel experiments with Monte Carlo simulations of potential models hypothesized to describe the reaction kinetics. The simulations can be adapted to include experimental limitations, such as limited data sets, and complexities such as dynamic disorder, where reaction rates appear to change over time. By using models that are known a priori, the simulations reveal some of the challenges of interpreting finite single-molecule data sets by employing various statistical signatures that have been identified.     

Effect of biocatalyst swelling on the operation of packed-bed immobilized enzyme bioreactor

A general mathematical model was developed for predicting the performance and simulation of a packed-bed immobilized enzyme reactor performing a reaction that follows Michaelis–Menten kinetics with competitive product inhibition. The performance of a packed-bed immobilized enzyme reactor was analyzed taking into account the effect of bed swelling on various diffusional phenomena such as axial dispersion, internal and external mass transfer limitations. The numerical solutions were compared with experimental data obtained for a packed-bed reactor operating with β-galactosidase entrapped in Ca-alginate-K-κ-carrageenan gels for lactose hydrolysis.     

Modelling of inhibition of nitrite oxidation in biological nitritation processes by free ammonia

To understand nitrite build-up in the nitritation process, the inhibition kinetics of free ammonia (FA) on nitrite oxidation were investigated. FA inhibition on nitrite oxidation was the key factor of nitrite build-up and its type was mixed inhibition. Therefore, the mixed inhibition model should be adapted to a Michaelis–Menten equation to set up a process rate equation for nitrite oxidation in the nitritation process.