A new rapid and simple method to determine the kinetics of electrode reactions of biologically relevant compounds from the half-peak width of the square-wave voltammograms

A new method is introduced to determine the kinetic parameters of electron transfer reactions of biologically important compounds, based on the measurements of the half-peak width (DeltaE(p/2)) of the square-wave voltammograms. A simple surface (diffusionless) redox reaction, and a simple electrode reaction occurring from dissolved state are considered as model systems. In the region of quasireversible electron transfer, the half-peak widths of theoretical square-wave voltammograms are linear functions of the logarithm of the dimensionless kinetic parameter ln(K) that characterizes the rate of the electron transfer reaction. The dimensionless kinetic parameter K is defined as K=k(s)(fD)(-0.5) for the redox reaction taking place from dissolved state, whereas for the surface redox reaction K is defined as K=k(s)/f (k(s) is the standard rate constant of electron transfer, f is the SW frequency, and D is the diffusion coefficient). A set of linear regression equations for the dependences DeltaE(p/2)vs. ln(K) are derived, which can be used for rapid and precise determination of the charge-transfer kinetic parameters. The estimated values for the standard rate constants of various biologically relevant redox systems using this approach are in very good agreement with the experimental values determined by other square-wave voltammetric methods. The square-wave voltammetric half-peak width method can be used as a simple and reliable alternative to other voltammetric methods developed for the kinetic characterization of electron transfer rates.     

Kinetics of bacterial processes in natural aquatic systems based on biomass as determined by high-resolution flow cytometry

The two primary kinetic constants for describing the concentration dependency of nutrient uptake by microorganisms are shown to be maximal rate of substrate uptake and, rather than the Michaelis constant for transport, specific affinity. Of the two, the specific affinity is more important for describing natural aquatic microbial processes because it can be used independently at small substrate concentrations. Flow cytometry was used to evaluate specific affinities in natural populations of aquatic bacteria because it gives a convenient measure of biomass, which is an essential measurement in the specific-affinity approach to microbial kinetics. Total biomass, biomass in various filter fractions, and the specific affinity of the bacteria in each fraction were determined in samples from a near-arctic lake. The partial growth rate of the pelagic bacteria from the 25 micrograms/liter of dissolved amino acids present (growth rate from the amino acid fraction alone) was determined to be 0.78 per day. By measuring activity in screened and whole-system populations, the biomass of the bacteria associated with particles was computed to be 427 micrograms/liter.     

Co-immobilized Nitrosomonas europaea and Nitrobacter agilis cells: validation of a dynamic model for simultaneous substrate conversion and growth in kappa-carrageenan gel beads

A dynamic model for two microbial species immobilized in a gel matrix is presented and validated with experiments. The model characterizes the nitrification of ammonia with Nitrosomonas europaea and Nitrobacter agilis co-immobilized in K-carrageenan gel beads. The model consists of kinetic equations for the microorganisms and mass transfer equations for the substrates and products inside and outside the gel beads. The model predicts reactor bulk concentrations together with the substrate consumption rate, product formation, and biomass growth inside the gel beads as a function of time. A 50-day experiment with immobilized cells in a 3.3-dm(3) air-lift loop reactor was carried out to validate the model. The parameter values for the model were obtained from literature and separate experiments. The experimentally determined reactor bulk concentrations and the biomass distribution of the two microorganisms in the gel beads were well predicted by the model. A sensitivity analysis of the model for the given initial values indicated the most relevant parameters to be the maximum specific growth rate of the microorganisms, the diffusion coefficient of oxygen, and the radius of the beads. The dynamic model provides a useful tool for further study and possible control of the nitrification process. (c) 1994 John Wiley & Sons, Inc.     

Comparative kinetic behavior of nitrifiers with different growth environments

A batch feed study using nitrifiers that had been continuously acclimated under a low-ammonia environment showed that a sudden change of ammonia concentration resulted in sluggish physiological adaptation and biochemical reaction of nitrifiers (i.e., indicated by the parameter specific oxygen utilization rate). When the one-stage continuous-stirred tank reactor (CSTR) system was maintained at a short microbial cell residence time and a high volumetric loading rate, an accumulation of nitrite occurred. Under such circumstances, ammonia and nitrite oxidation both limit overall nitrification at different stages of the process. Batch studies with biomass respectively removed from the front and rear reactors (i.e., high-ammonia and low-ammonia growth environments) of a two-stage CSTR system showed that the estimated kinetic parameters for nitrifiers with the low-ammonia growth environment were 0.3-0.8-fold lower than those for nitrifiers with the high-ammonia growth environment, possibly leading to inaccurate model simulation results. Accordingly, biomass removed from a CSTR system that had been operated continuously to grow bacteria under a high-substrate environment should be loaded into the batch reactor if the batch reactor method is to be used to estimate kinetic parameters.     

Estimation of kinetic parameters in a structured yeast model using regularisation.

In this work, a procedure for estimating kinetic parameters in biochemically structured models was developed. The approach is applicable when the structure of a kinetic model has been set up and the kinetic parameters should be estimated. The procedure consists of five steps. First, initial values were found in or calculated from literature. Hereafter using sensitivity analysis the most sensitive parameters were identified. In the third step physiological knowledge was combined with the parameter sensitivities to manually tune the most sensitive parameters. In step four, a global optimisation routine was applied for simultaneous estimation of the most sensitive parameters identified during the sensitivity analysis. Regularisation was included in the simultaneous estimation to reduce the effect of insensitive parameters. Finally, confidence intervals for the estimated parameters were calculated. This parameter estimation approach was demonstrated on a biochemically structured yeast model containing 11 reactions and 37 kinetic constants as a case study.     

Measurement of minimum substrate concentration (Smin) in a recycling fermentor and its prediction from the kinetic parameters of Pseudomonas strain B13 from batch and chemostat cultures.

The minimum substrate concentration required for growth, Smin, was measured for Pseudomonas sp. strain B13 with 3-chlorobenzoate (3CB) and acetate in a recycling fermentor. The substrates were provided alone or in a mixture. Smin values predicted with kinetic parameters from resting-cell batches and chemostat cultures differed clearly from the values measured in the recycling fermentor. When 3CB and acetate were fed as single substrates, the measured Smin values were higher than the individual Smin values in the mixture. The Smin in the mixture reflected the relative energy contributions of the two substrates in the fermentor feed. The energy-based maintenance coefficients during zero growth in the recycling fermentor were comparable for all influent compositions (mean +/- standard deviation, 0.34 +/- 0.07 J mg [dry weight]-1 h-1). Maintenance coefficient values for acetate were significantly higher in chemostat experiments than in recycling-fermentor experiments. 3CB maintenance coefficients were comparable in both experimental systems. The parameters for 3CB consumption kinetics varied remarkably with the experimental growth conditions in batch, chemostat, and recycling-fermentor environments. The results demonstrate that the determination of kinetic parameters in the laboratory for prediction of microbial activity in complex natural systems should be done under conditions which best mimic the system under consideration.     

A New Rate Law Describing Microbial Respiration

The rate of microbial respiration can be described by a rate law that gives the respiration rate as the product of a rate constant, biomass concentration, and three terms: one describing the kinetics of the electron-donating reaction, one for the kinetics of the electron-accepting reaction, and a thermodynamic term accounting for the energy available in the microbe's environment. The rate law, derived on the basis of chemiosmotic theory and nonlinear thermodynamics, is unique in that it accounts for both forward and reverse fluxes through the electron transport chain. Our analysis demonstrates how a microbe's respiration rate depends on the thermodynamic driving force, i.e., the net difference between the energy available from the environment and energy conserved as ATP. The rate laws commonly applied in microbiology, such as the Monod equation, are specific simplifications of the general law presented. The new rate law is significant because it affords the possibility of extrapolating in a rigorous manner from laboratory experiment to a broad range of natural conditions, including microbial growth where only limited energy is available. The rate law also provides a new explanation of threshold phenomena, which may reflect a thermodynamic equilibrium where the energy released by electron transfer balances that conserved by ADP phosphorylation.     

A new rate law describing microbial respiration

The rate of microbial respiration can be described by a rate law that gives the respiration rate as the product of a rate constant, biomass concentration, and three terms: one describing the kinetics of the electron-donating reaction, one for the kinetics of the electron-accepting reaction, and a thermodynamic term accounting for the energy available in the microbe's environment. The rate law, derived on the basis of chemiosmotic theory and nonlinear thermodynamics, is unique in that it accounts for both forward and reverse fluxes through the electron transport chain. Our analysis demonstrates how a microbe's respiration rate depends on the thermodynamic driving force, i.e., the net difference between the energy available from the environment and energy conserved as ATP. The rate laws commonly applied in microbiology, such as the Monod equation, are specific simplifications of the general law presented. The new rate law is significant because it affords the possibility of extrapolating in a rigorous manner from laboratory experiment to a broad range of natural conditions, including microbial growth where only limited energy is available. The rate law also provides a new explanation of threshold phenomena, which may reflect a thermodynamic equilibrium where the energy released by electron transfer balances that conserved by ADP phosphorylation.     

Methanogenic degradation kinetics of phenolic compounds in aquifer-derived microcosms

In this segment of a larger multidisciplinary study of the movement and fate of creosote derived compounds in a sand-and-gravel aquifer, we present evidence that the methanogenic degradation of the major biodegradable phenolic compounds and concomitant microbial growth in batch microcosms derived from contaminated aquifer material can be described using Monod kinetics. Substrate depletion and bacterial growth curves were fitted to the Monod equations using nonlinear regression analysis. The method of Marquardt was used for the determination of parameter values that best fit the experimental data by minimizing the residual sum of squares. The Monod kinetic constants ( _max , K _s, Y, and k _d) that describe phenol, 2-, 3-, and 4-methylphenol degradation and concomitant microbial growth were determined under conditions that were substantially different from those previously reported for microcosms cultured from sewage sludge. The K _s values obtained in this study are approximately two orders of magnitude lower than values obtained for the anaerobic degradation of phenol in digesting sewage sludge, indicating that the aquifer microorganisms have developed enzyme systems that are adapted to low nutrient conditions. The values for k _d are much less than _max, and can be neglected in the microcosms. The extremely low Y values, approximately 3 orders of magnitude lower than for the sewage sludge derived cultures, and the very low numbers of microorganisms in the aquifer derived microcosms suggest that these organisms use some unique strategies to survive in the subsurface environment.Abbreviations GC gas chromatography - HPLC high performance liquid chromatography - LBSSB likelihood based sum of squares boundaries - MPN most probable number - NLR nonlinear regression analysis - OFAG oxygen free Argon gas - PCP pentachlorophenol - RSS residual sum of squares - SRB sulfate reducing bacteria     

嗜酸氧化亚铁硫杆菌生长动力学

在确定二价铁离子为A.f生长过程中惟一限制性底物条件下,通过考察初始亚铁离子浓度、初始pH值两种影响亚铁离子氧化代谢的主要因素来研究细菌的生长特性,得到以限制性底物亚铁离子浓度为表征的细菌生长曲线。利用基于Monod方程建立的细菌生长动力学方程模型,采用Matlab软件中的Gauss-Newton算法确定了在不同条件下细菌生长动力学参数,包括最大比生长速率μm、Monod常数K及Ro,推导出了不同条件下A.f对数期以底物Fe(Ⅱ)浓度为表征的生长动力学方程。     

Kinetic models for the growth of Escherichia coli with mixtures of sugars under carbon-limited conditions

In natural environments, heterotrophic microorganisms encounter complex mixtures of carbon sources, each of which is present only at very low concentrations. Under such conditions no significant growth could be expected if cells utilized only one of the available carbon compounds as suggested by the principle of diauxic growth. Indeed, there is much evidence that microbial cells utilize many carbon sources simultaneously. In order to predict bacterial growth under such conditions we developed a model describing the specific growth rate as a function of the individual concentrations of several simultaneously utilized carbon substrates. Together with multisubstrate models previously published, this model was evaluated for its ability to describe growth of Escherichia coli during the simultaneous utilization of mixtures of sugars in carbon-limited continuous culture. Using the micromax and Ks constants determined for single substrate growth with six different sugars, the model was able for most experiments to adequately describe the specific growth rate of the culture, i.e., the experimentally set dilution rate, from the measured concentrations of the individual sugars. The model provides an explanation why bacteria can still grow relatively fast under environmental conditions where the concentrations of carbon substrates are usually extremely low.     

Quantitative studies of bacterial chemotaxis and microbial population dynamics

Although there is a long history of conjecture regarding the role and significance of bacterial chemotaxis in microbial ecology, only recently has a significant body of work appeared attempting to address this issue. The purpose of this paper is to provide a concise overview of this work, which combined mathematical modeling of bacterial population migration and experimental measurement of the model parameters with modeling of competitive microbial population dynamics in a nonmixed environment. Predictions from the population dynamics models, based on experimental estimates of the various motility and growth parameter values, are related to the small number of experimental observations available to date dealing with the effects of bacterial motility on competition in a nonmixed environment. Current results indicate that cell motility and chemotaxis properties can be as important to population dynamics as cell growth kinetic properties, so that greater attention to this aspect of microbial behavior is warranted in future studies of microbial ecology.     

Parameter estimation for ligand binding systems kinetics applied to 1,25-dihydroxycholecalciferol

A mathematical analysis of the kinetics of the hormone-receptor interaction was applied to the 1,25-dihydroxycholecalciferol-intestinal receptor system. The exact analytical solution and the numerical integration of the kinetic equation were installed in a Statistical Analysis System (SAS) computer program to estimate the rate constants of the reaction. Estimates of the parameters obtained by these two methods are similar, demonstrating that the numerical integration can be combined with the nonlinear regression procedure for least-squares parameter fitting using a simple SAS program. This enables estimation of kinetics rate constants when the kinetic equation cannot be solved analytically. The ratio of the rate constants (ka/kd) found by the nonlinear procedure is close to the independently determined equilibrium (Scatchard) constant in the nonlinear analysis.     

Kinetics of Sulfate Reduction in a Coastal Aquifer Contaminated with Petroleum Hydrocarbons

An integrated field and laboratory study was conducted to quantify the effect of environmental determinants on the activity of sulfate reducers in a freshwater aquifer contaminated with petroleum hydrocarbons (PHC). Within the contaminated zone, PHC-supported in␣situ sulfate reduction rates varied from 11.58±3.12 to 636±53 nmol cm⁻³ d⁻¹ and a linear increase (R ²=0.98) in reduction rate was observed with increasing in situ sulfate concentrations suggesting sulfate limitation. Half-saturation concentration (K _s) for sulfate reduction coupled to PHC mineralization was determined for the first time. At two different sites within the␣aquifer, maximum sulfate reduction rate under␣non-limiting conditions (R _max) was 5,000 nmol cm⁻³ d⁻¹, whereas the retrieved K _s values were 3.5 and 7.5 mM, respectively. The K _s values are the highest ever reported from a natural environment. Furthermore, the K _s values were significantly higher than in situ sulfate concentrations confirming sulfate limited growth. On addition of lactate and formate, sulfate reduction rate increased indicating that reactivity and bioavailability of organic substrate may also have played a role in rate inhibition in certain parts of the aquifer. Experiments with sulfide amendments show statistically minor decrease in sulfate reduction rates on addition of sulfide and analogous increase in sulfide toxicity with increasing sulfide concentrations (0.5–10 mM) was not apparent.     

Assessment of Bacterial and Fungal Growth on Natural Substrates: Consequences for Preserving Caves with Prehistoric Paintings

The most representative bacterium (Pseudonocardia sp.) and fungus (Fusarium sp.) from the microbial communities of a cave containing paleolithic paintings were isolated and their growth on natural substrates assessed. Growth was tested at the in situ and optimal, laboratory growth temperature. Development was analyzed with and without supplemented nutrients (glucose, ammonium, phosphate, peptone). Results showed that the assayed bacterium on natural substrate was able to develop best at in situ temperature and the addition of organic nutrients and/or phosphate enhanced its growth. The growth of the assayed fungus, however, was limited by low temperature and the availability of ammonium. These results confirm a differential behavior of microorganisms between the laboratory and the natural environments and could explain previous invasion of fungi reported for some caves with prehistoric paintings.     

Influence of pH on microbial hydrogen metabolism in diverse sedimentary ecosystems

Hydrogen transformation kinetic parameters were measured in sediments from anaerobic systems covering a wide range of environmental pH values to assess the influence of pH on hydrogen metabolism. The concentrations of dissolved hydrogen were measured and hydrogen transformation kinetics of the sediments were monitored in the laboratory by monitoring hydrogen consumption progress curves. The hydrogen turnover rate constants (kt) decreased directly as a function of decreasing sediment pH, and the maximum hydrogen uptake velocities (Vmax) varied as a function of pH within each of the trophic states. Conversely, the half-saturation concentrations (Km) were independent of pH. The steady-state hydrogen concentrations were at least 2 orders of magnitude lower than the half-saturation constants for hydrogen uptake. Dissolved hydrogen concentrations were at least fivefold higher in sediments from eutrophic systems than from oligotrophic and dystrophic systems. The rates of hydrogen production determined from the assumption of steady state decreased with sediment pH. These data indicate that progressively lower pH values inhibit microbial hydrogen-producing and -consuming processes within sedimentary ecosystems.     

Influence of pH on microbial hydrogen metabolism in diverse sedimentary ecosystems.

Hydrogen transformation kinetic parameters were measured in sediments from anaerobic systems covering a wide range of environmental pH values to assess the influence of pH on hydrogen metabolism. The concentrations of dissolved hydrogen were measured and hydrogen transformation kinetics of the sediments were monitored in the laboratory by monitoring hydrogen consumption progress curves. The hydrogen turnover rate constants (kt) decreased directly as a function of decreasing sediment pH, and the maximum hydrogen uptake velocities (Vmax) varied as a function of pH within each of the trophic states. Conversely, the half-saturation concentrations (Km) were independent of pH. The steady-state hydrogen concentrations were at least 2 orders of magnitude lower than the half-saturation constants for hydrogen uptake. Dissolved hydrogen concentrations were at least fivefold higher in sediments from eutrophic systems than from oligotrophic and dystrophic systems. The rates of hydrogen production determined from the assumption of steady state decreased with sediment pH. These data indicate that progressively lower pH values inhibit microbial hydrogen-producing and -consuming processes within sedimentary ecosystems.     

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.     

Modification of A-stat for the characterization of microorganisms

Two novel modifications of continuous culture with gradual change of dilution rate (A-stat): D-stat and auxo-accelerostat were evaluated in the studies of the effect of changing individual environmental parameters (T, pH, pO(2), substrate concentration, etc.) on growth characteristics of different microorganisms. Common for those cultivation methods is that one environmental parameter is programmed to change with constant change rate (change-stat) while the others are kept constant or in the range not affecting the growth characteristics. The environment response growth curves were obtained starting with chemostat (in A-stat and D-stat) or auxostat (in auxo-accelerostat) steady-state cultures followed by change of set-point value of the desired cultivation parameter. Physiological studies of Saccharomyces sp. and Lactococcus lactis were combined with validation of the different modifications of the A-stat method based on well-known cultivation techniques: chemostat, pH-auxostat, pO(2)-auxostat CO(2)-auxostat and fed-batch. The auxo-accelerostat was shown to be very efficient for cell characterization and dynamic studies in growth environments with excess of essential substrates. Choosing the rate of change of environmental parameters was shown to be critical in comparative physiological studies of microorganisms.