Michaelis-Menten Expression Research Articles

Variations in Enzyme Concentrations During High-Temperature Composting of Livestock and Poultry Manure and Study on Enzymatic Reaction Mechanisms

Cow, pig, and chicken manure were collected from farms located in the proximity of Lanzhou University, Lanzhou City, Gansu Province, and were used as raw materials. Before composting, straws at a concentration of 10% were used as bulking agent. Different parameters were monitored during the composting process. Specifically, we analyzed changes in catalase, invertase, urease, and cellulase concentrations. In addition, the mechanisms of enzymatic reactions at high-temperatures were determined. The results showed that: (1) at the first stages of composting, the initial contents of catalase were 48.21±1.11, 45.04±0.85, and 44.29±0.65/0.002 mol·L−1·g−1, for cow, pig, and chicken manure, respectively. As composting proceeded, the content of catalase gradually increased. On the 6th day, catalase contents reached their maximum values, with numbers of 55.21±0.58, 57.28±0.14, and 62.18±0.45 mol·L−1·g−1, correspondingly. In addition, when composting ended, catalase content followed the order (chicken manure > cow manure > pig manure, with values of 34.33±0.58, 29.31±0.79, and 28.42±0.89/0.002 mol·L−1·g−1), in the same order; (2) According to the Michaelis-Menten expression, temperature greatly affects enzymatic reactions. Our data indicated that content of catalase, urease, sucrose, and cellulose, as well as number of microorganisms and compost temperature were positively correlated.

A quantitative analysis of cell-specific contributions and the role of anesthetics to the neurovascular coupling

The neurovascular coupling (NVC) connects neuronal activity to hemodynamic responses in the brain. This connection is the basis for the interpretation of functional magnetic resonance imaging data. Despite the central role of this coupling, we lack detailed knowledge about cell-specific contributions and our knowledge about NVC is mainly based on animal experiments performed during anesthesia. Anesthetics are known to affect neuronal excitability, but how this affects the vessel diameters is not known. Due to the high complexity of NVC data, mathematical modeling is needed for a meaningful analysis. However, neither the relevant neuronal subtypes nor the effects of anesthetics are covered by current models. Here, we present a mathematical model including GABAergic interneurons and pyramidal neurons, as well as the effect of an anesthetic agent. The model is consistent with data from optogenetic experiments from both awake and anesthetized animals, and it correctly predicts data from experiments with different pharmacological modulators. The analysis suggests that no downstream anesthetic effects are necessary if one of the GABAergic interneuron signaling pathways include a Michaelis-Menten expression. This is the first example of a quantitative model that includes both the cell-specific contributions and the effect of an anesthetic agent on the NVC.

Enzyme Kinetics at the Molecular Level

The celebrated Michaelis-Menten (MM) expression provides a fundamental relation between the rate of enzyme catalysis and substrate concentration. The validity of this classical expression is, however, restricted to macroscopic amounts of enzymes and substrates and, thus, to processes with negligible fluctuations. Recent experiments have measured fluctuations in the catalytic rate to reveal that the MM equation, though valid for bulk amounts, is not obeyed at the molecular level. In this mini-review, we show how new statistical measures of fluctuations in the catalytic rate identify a regime in which the MM equation is always violated. This regime, characterized by temporal correlations between enzymatic turnovers, is absent for a single enzyme and unobservably short in the classical limit.

Effect of Substrate Number Fluctuations in Stochastic Enzyme Kinetics.

Conventional studies on enzyme kinetics assume that the substrate concentration remains constant. However, for catalytic reactions taking place in intracellular compartments, the substrate molecules are fed in and out of the compartment and are catalyzed into product molecules within the compartment. In this work, we use a chemical master equation approach to study the stochastic kinetics of a single enzyme for different reaction pathways with one or more intermediate states. We obtain velocity expressions that deviate from the Michaelis–Menten expression. We study the coefficient of variation, which is a measure of the noise strength as a function of the mean substrate concentration for systems where there is influx or/and outflux of substrate molecules. Our results show that the noise strength decreases with the increase in the substrate concentration and finally remains the same when the substrate is present in abundance.

A CFD Model for Prediction of the Role of Biomass Growth and Decay on the Aerobic Biodegradation of BTEX Fate and Transport in an Unconfined Aquifer System

This paper investigates the importance of considering biomass growth and decay for predicting a field scale microbial degradation of BTEX plume in an unconfined aquifer system in the Pump station area of Tehran oil refinery (TOR), Iran. A two-dimensional finite volume model has been presented to predict multi-species reactive transport incorporating physical, chemical and biological processes in the saturated zone of the aquifer. A multi-purpose commercial software called PHOENICS was modified to solve model equations. A complex Monod approach considering microbial growth and decay employed to describe the biodegradation of BTEX. The results of Monod approach was compared to those results obtained by three kinetics models including zero-order, first-order and Michaelis-Menten expressions that do not support biomass growth and decay. Monod approach predicted a further spreading of the plume. Other kinitics models underestimated the concentrations of BTEX plume, due to neglecting a high bacterial population and increased uptake rate. They are not appropriate to simulate tansport of biodegradable BTEX in the study aquifer. The model predictions agree well with the field measurements with an average error of 5%; describing that the Monod kinetics was well able to simulate the behaviour of the BTEX plume due to supporting bacterial population and considering oxygen as the electron acceptor.

Extracting signal from noise: kinetic mechanisms from a Michaelis–Menten‐like expression for enzymatic fluctuations

Enzyme-catalyzed reactions are naturally stochastic, and precision measurements of these fluctuations, made possible by single-molecule methods, promise to provide fundamentally new constraints on the possible mechanisms underlying these reactions. We review some aspects of statistical kinetics: a new field with the goal of extracting mechanistic information from statistical measures of fluctuations in chemical reactions. We focus on a widespread and important statistical measure known as the randomness parameter. This parameter is remarkably simple in that it is the squared coefficient of variation of the cycle completion times, although it places significant limits on the minimal complexity of possible enzymatic mechanisms. Recently, a general expression has been introduced for the substrate dependence of the randomness parameter that is for rate fluctuations what the Michaelis-Menten expression is for the mean rate of product generation. We discuss the information provided by the new kinetic parameters introduced by this expression and demonstrate that this expression can simplify the vast majority of published models.

Oxygen Dependency of Neutrophilic Fe(II) Oxidation by Leptothrix Differs from Abiotic Reaction

Neutrophilic Fe(II) oxidizing microorganisms are found in many natural environments. It has been hypothesized that, at low oxygen concentrations, microbial iron oxidation is favored over abiotic oxidation. Here, we compare the kinetics of abiotic Fe(II) oxidation to oxidation in the presence of the bacterium Leptothrix cholodnii Appels isolated from a wetland sediment. Rates of Fe(II) oxidation were determined in batch experiments at 20°C, pH 7 and oxygen concentrations between 3 and 120 μmol/l. The reaction progress in experiments with and without cells exhibited two distinct phases. During the initial phase, the oxygen dependency of microbial Fe(II) oxidation followed a Michaelis-Menten rate expression (KM = 24.5 ± 10 μmol O2/l, vmax = 1.8 ± 0.2 μmol Fe(II)/(l min) for 108 cells/ml). In contrast, abiotic rates increased linearly with increasing oxygen concentrations. At similar oxygen concentrations, initial Fe(II) oxidation rates were faster in the experiments with bacteria. During the second phase, the accumulated iron oxides catalyzed further oxidative iron precipitation in both abiotic and microbial reaction systems. That is, abiotic oxidation also dominated the reaction progress in the presence of bacteria. In fact, in some experiments with bacteria, iron oxidation during the second phase proceeded slower than in the absence of bacteria, possibly due to an inhibitory effect of extracellular polymeric substances on the growth of Fe(III) oxides. Thus, our results suggest that the competitive advantage of microbial iron oxidation in low oxygen environments may be limited by the autocatalytic nature of abiotic Fe(III) oxide precipitation, unless the accumulation of Fe(III) oxides is prevented, for example, through a close coupling of Fe(II) oxidation and Fe(III) reduction.

PH Wave-Front Propagation in the Urea-Urease Reaction

The urease-catalyzed hydrolysis of urea displays feedback that results in a switch from acid (pH ∼3) to base (pH ∼9) after a controllable period of time (from 10 to >5000 s). Here we show that the spatially distributed reaction can support pH wave fronts propagating with a speed of the order of 0.1−1 mm min−1. The experimental results were reproduced qualitatively in reaction-diffusion simulations including a Michaelis-Menten expression for the urease reaction with a bell-shaped rate-pH dependence. However, this model fails to predict that at lower enzyme concentrations, the unstirred reaction does not always support fronts when the well-stirred reaction still rapidly switches to high pH.

Mode of Regulation and the Insulation of Bacterial Gene Expression

A gene can be said to be insulated from environmental variations if its expression level depends only on its cognate inducers, and not on variations in conditions. We tested the insulation of the lac promoter of E. coli and of synthetic constructs in which the transcription factor CRP acts as either an activator or a repressor, by measuring their input function-their expression as a function of inducers-in different growth conditions. We find that the promoter activities show sizable variation across conditions of 10%-100% (SD/mean). When the promoter is bound to its cognate regulator(s), variation across conditions is smaller than when it is unbound. Thus, mode of regulation affects insulation: activators seem to show better insulation at high expression levels, and repressors at low expression levels. This may explain the Savageau demand rule, in which E. coli genes needed often in the natural environment tend to be regulated by activators, and rarely needed genes by repressors. The present approach can be used to study insulation in other genes and organisms.

Two-Dimensional Reaction Free Energy Surfaces of Catalytic Reaction: Effects of Protein Conformational Dynamics on Enzyme Catalysis

We introduce a two-dimensional (2D) multisurface reaction free energy description of the catalytic cycle that explicitly connects the recently observed multi-time-scale conformational dynamics as well as dispersed enzymatic kinetics to the classical Michaelis-Menten equation. A slow conformational motion on a collective enzyme coordinate Q facilitates the catalytic reaction along the intrinsic reaction coordinate X, providing a dynamic realization of Pauling's well-known idea of transition-state stabilization. The catalytic cycle is modeled as transitions between multiple displaced harmonic wells in the XQ space representing different states of the cycle, which is constructed according to the free energy driving force of the cycle. Subsequent to substrate association with the enzyme, the enzyme-substrate complex under strain exhibits a nonequilibrium relaxation toward a new conformation that lowers the activation energy of the reaction, as first proposed by Haldane. The chemical reaction in X is thus enslaved to the down hill slow motion on the Q surface. One consequence of the present theory is that, in spite of the existence of dispersive kinetics, the Michaelis-Menten expression of the catalysis rate remains valid under certain conditions, as observed in recent single-molecule experiments. This dynamic theory builds the relationship between the protein conformational dynamics and the enzymatic reaction kinetics and offers a unified description of enzyme fluctuation-assisted catalysis.

Depicting combinatorial complexity with the molecular interaction map notation

To help us understand how bioregulatory networks operate, we need a standard notation for diagrams analogous to electronic circuit diagrams. Such diagrams must surmount the difficulties posed by complex patterns of protein modifications and multiprotein complexes. To meet that challenge, we have designed the molecular interaction map (MIM) notation (http://discover.nci.nih.gov/mim/). Here we show the advantages of the MIM notation for three important types of diagrams: (1) explicit diagrams that define specific pathway models for computer simulation; (2) heuristic maps that organize the available information about molecular interactions and encompass the possible processes or pathways; and (3) diagrams of combinatorially complex models. We focus on signaling from the epidermal growth factor receptor family (EGFR, ErbB), a network that reflects the major challenges of representing in a compact manner the combinatorial complexity of multimolecular complexes. By comparing MIMs with other diagrams of this network that have recently been published, we show the utility of the MIM notation. These comparisons may help cell and systems biologists adopt a graphical language that is unambiguous and generally understood.

A mathematical model of tumor oxygen and glucose mass transport and metabolism with complex reaction kinetics.

Hypoxia imparts radioresistance to tumors, and various approaches have been developed to enhance oxygenation, thereby improving radiosensitivity. This study explores the influence of kinetic and physical factors on substrate metabolism in a tumor model, based on a Krogh cylinder. In tissue, aerobic metabolism is assumed to depend on glucose and oxygen, represented by the product of Michaelis-Menten expressions. For the base case, an inlet pO(2) of 40 mmHg, a hypoxic limit of 5 mmHg, and a tissue/capillary radius ratio of 10 are used. For purely aerobic metabolism, a hypoxic fraction of 0.16 and volume-average pO(2) of 8 mmHg are calculated. Reducing the maximum oxygen rate constant by 9%, decreasing the tissue cylinder radius by 5%, or increasing the capillary radius by 8% abolishes the hypoxic fraction. When a glycolytic term is added, concentration profiles are similar to the base case. Using a distribution of tissue/capillary radius ratios increases the hypoxic fraction and reduces sensitivity to the oxygen consumption rate, compared to the case with a single tissue/capillary radius ratio. This model demonstrates that hypoxia is quite sensitive to metabolic rate and geometric factors. It also predicts quantitatively the effects of inhibited oxygen metabolism and enhanced mass transfer on tumor oxygenation.

Kinetic analysis of a tod-lux bacterial reporter for toluene degradation and trichloroethylene cometabolism.

Kinetics of toluene and trichloroethylene (TCE) degradation and bioluminescence from the bioreporter Pseudomonas putida B2 and TVA8 were investigated utilizing batch and continuous culture, respectively. Degradation was modeled using a Michaelis-Menten expression for the competition of two substrates for a single enzyme system, and bioluminescence was modeled assuming a luciferase enzyme saturational dependence on toluene as the inducer and growth substrate. During the batch experiments, bioluminescence increased at approximately 90 namp/min for initial toluene concentrations of 10 to 50 mg/L, but more slowly at higher toluene concentrations, suggesting maximum promoter induction at below 10 mg/L and toxic effects above 50 mg/L toluene. TCE degradation did not occur until toluene depletion, presumably due to competition between toluene and TCE for the toluene dioxygenase enzyme. During continuous culture, bioluminescence transiently increased, then gradually decreased in response to increasing step changes in toluene feed concentration. Bioluminescence in the CSTR appeared to be limited by growth substrate and/or inducer.

Voltammetric studies on mechanisms of dopamine efflux in the presence of substrates and cocaine from cells expressing human norepinephrine transporter.

The effects of substrates m-tyramine and beta-phenethylamine, as well as cocaine, on the DA efflux from a cell line stably expressing the human norepinephrine transporter (hNET) were investigated by using rotating disk electrode voltammetry. Both the substrates and cocaine induced apparent DA efflux in a concentration-dependent manner. Their EC50 values for inducing DA efflux were similar to their IC50 values for inhibiting DA uptake. The substrate-induced DA efflux was inhibited by various NET blockers, enhanced by raising the internal [Na+] with Na+,K+-ATPase inhibition, but was insensitive to membrane potential-altering agents valinomycin, veratridine, and high [K+]. The initial rate of m-tyramine-induced DA efflux was related to preloaded [DA] in a manner defined by a Michaelis-Menten expression. In contrast, DA efflux in the presence of cocaine displayed a much slower efflux rate, lower efficacy, was not stimulated by elevated internal [Na+], and was nonsaturable with preloaded [DA]. Single exponential kinetic analysis of the entire time course of the DA efflux showed that the apparent first-order rate constant for m-tyramine-induced DA efflux declined with increased preloaded [DA], whereas that for the DA efflux in the presence of cocaine was unchanged with varying preloaded [DA]. These results suggest that the substrates stimulate the NET-dependent DA efflux by increasing the accessibility of the NET to internal DA, whereas cocaine "uncovers" NET-independent DA efflux by reducing the accessibility of diffused/leaked external DA to the NET.

A model of chlorophyll a destruction by Calanus spp. and implications for the estimation of ingestion rates using the gut fluorescence method

Chlorophyll a (chl a) destruction by groups of Calanus spp. with different long-term in situ feeding histories was compared. For copepods that had fed during both pre- and early-bloom conditions, degrees of chl a destruction were relatively constant at high ingestion rates and increased as ingestion rates decreased. Assuming that 2 pools of chlorophyll bleaching enzymes (CBEs) were involved in the destruction of chl a (one derived from the copepods and one from the ingested algae), a new model was developed to describe the kinetics of chl a destruction. In this model, the CBE activity of each pool was described using a Michaelis-Menten expression and the total CBE activity was given by the sum of the 2 expressions. Parameter estimates of V(c)(max), the maximum activity of the copepod CBE, were higher for the early-bloom copepods than for the pre-bloom copepods, suggesting that the former had a higher destructive capacity. Estimates of R(p)(max), the phytoplankton 'CBE activity coefficient' which is analogous to V(max), were similar between the 2 groups of experiments. This is reasonable since most of the food fed to the copepods was healthy, actively growing diatoms. The model could also describe the kinetics of chl a destruction for Calanus spp. that had fed during late-bloom conditions. For the late-bloom data, V(c)(max) and R(p)(max) values were higher than for the pre- and early-bloom copepods and phytoplankton. This suggests that the late-bloom copepods and the in situ phytoplankton that they ate had higher destructive capacities, perhaps because the spring-bloom was more advanced. Expressions were derived from the new model to describe the relationship between real ingestion rate (I(r)) and apparent ingestion rate (I(a)), over a range of I(a) values, where the latter are values which would have been determined using gut fluorescence methodology. Correction factors (I(r)/I(a)) varied by a factor of less than 2 (for I(a) values ranging from 0.1 to 100 ng chi a ind.-1 h-1) between different groups of copepods (pre-, early- and late-bloom) and sources of algae (actively growing and senescent). In future it will be important to validate this model under controlled conditions (e.g. using single species of copepods and phytoplankton food) and to assess whether correction factors derived from our model are generally applicable, if results of studies using gut fluorescence methods are to be interpreted properly.

The kinetics of nitrogen utilization in the oceanic mixed layer: Nitrate and ammonium interactions at nanomolar concentrations

The concentration‐dependent uptake of nitrate (NO3) and its inhibit ion by ammonium (NH4) were surveyed in surface waters of the North Atlantic Ocean. Low‐level NO3 determinations combined with conventional tracer methods provided the first comprehensive data set on NO3 utilization kinetics at nanomolar concentrations. Uptake followed saturation kinetics described by the Michaelis‐Menten equation. The half‐saturation parameter for uptake (KN) ranged 2–3 orders of magnitude, covarying with ambient NO3 concentrations. KN concentrations in oceanic waters averaged ~20–30 nM. NH4 half‐saturation parameters could only be approximated (i.e. KA + A), but observations suggested that KA and KN were of similar magnitude in oceanic waters. Maximum uptake rates of nitrate, pm(N), and ammonium, pm(A), covaried, but pm(A) almost always exceeded p,(N); in oceanic waters, the disparity was an order of magnitude or greater. Most of the variability in pm(N) and pm(A) could be explained by variations in phytoplankton biomass and temperature. The slope of the uptake vs. concentration relationship, a, was also investigated but was highly variable and could not be related to any of the oceanographic properties observed; αA was generally greater than αN. Kinetics analysis showed that NH4 is preferentially utilized over NO3 over the full spectrum of nitrogen concentrations, nanomolar to micromolar.The inhibition of NO3 uptake by NH4 was also parameterized using the Michaelis‐Menten expression. The inhibition half‐saturation parameter (Ki) covaried with KN, but Ki concentrations in oceanic waters (~40– 50 nM) always exceeded Kn. Maximum inhibition (Im) was rarely complete (i.e. Imn < 1), even at 2,000 nM ammonium. Overall, results suggest that nitrogen utilization parameters currently used in ecosystem models of the open ocean should be re‐examined.

Kinetics of the sequential dechlorination of 2,4,6-trichlorophenol by an anaerobic microbial population

A mathematical model was developed to describe the sequential dechlorination of 2,4,6-trichlorophenol to 2,4-dichlorophenol, 4-chlorophenol and phenol. Each compound was assumed to be degraded according a Michaelis-Menten expression. Experimental data were used to obtain the model kinetic constants and to test its validity. Good agreement between the model predictions and the experimental data was obtained.

Kinetic evaluation of an anaerobic fluidised-bed reactor treating slaughterhouse wastewater

An anaerobic fluidised-bed reactor for purification of slaughterhouse wastewater was modelled as a continuous-flow, completely-mixed homogeneous microbial system, with the feed COD as the limiting-substrate concentration. The average microbial residence time in the reactor was defined in terms of conventional sludge-retention-time. The experimental data obtained indicated that the Michaelis-Menten expression was applicable to a description of substrate utilisation (i.e. COD removal) in the anaerobic fluidised-bed system. The maximum substrate utilisation rate, k, and the Michaelis constant, K s, were determined to be 1·2/day and 0·039 g/l. The observed biomass yield in the reactor decreased with increasing sludge-retention-time. The specific methane production rate observed was a linear function of the specific substrate-utilisation rate.

Unified modeling framework of cell death due to bubbles in agitated and sparged bioreactors

A modeling framework is proposed to assess the detrimental effects of air sparging and other bubble phenomena (vortex entrainment, coalescence, bursting) on freely suspended cells in an aerated, agitated bioreactor. It is assumed that cells may be rendered nonviable by bubble breakup/coalescence within the medium, by bubble formation at the sparger, or by bubble bursting at the free surface. Some plausible mechanisms are argued from the energetic view point. The dominant parameters in each case are the cell-bubble encounter rate and the bubble breakup/bursting rate. These inactivation processes lead to a Michaelis-Menten expression for the specific cell death rate, which is shown to be linearly proportional to the specific bubble interfacial area (total bubble surface area per unit volume of media). By using published viable cell concentration data for retarded growth of mammalian cells due to sparging, the interfacial area correlation is demonstrated. The method is generalized to aerated bioreactor conditions. The article offers a unique, consistent perspective on how cell death can be viewed.

Starting D-Optimal Designs for Batch Kinetic Studies of Enzyme-Catalyzed Reactions in the Presence of Enzyme Deactivation

This paper describes a strategy for the starting experimental design of experiments required by general research in the field of biochemical kinetics. The type of experiments that qualify for this analysis involve batch reactions catalyzed by soluble enzymes where the activity of the enzyme decays with time. Assuming that the catalytic action of the enzyme obeys a Michaelis-Menten rate expression and that the deactivation of the enzyme follows a first-order decay, the present analysis employs the dimensionless, integrated form of the overall rate expression to obtain a criterion (based on the maximization of the determinant of the derivative matrix) that relates the a priori estimates of the parameters with the times at which samples should be withdrawn from the reacting mixture. The analysis indicates that the initial concentration of substrate should be as large as possible, and that the samples should be taken at times corresponding to substrate concentrations of approximately 2/3, 1/4, and I/epsilon of the initial concentration (where epsilon should be as large as possible).