Interaction of transketolase from human tissues with substrates

The Michaelis constant values for substrates of transketolase from human tissues were determined over a wide range of substrate concentrations. It is shown that K _m values determined by other authors are significantly overestimated and explained why this is so.     

Accurate kinetic parameter estimation during progress curve analysis of systems with endogenous substrate production

We have identified an error in the published integral form of the modified Michaelis–Menten equation that accounts for endogenous substrate production. The correct solution is presented and the error in both the substrate concentration, S, and the kinetic parameters V_m, K_m, and R resulting from the incorrect solution was characterized. The incorrect integral form resulted in substrate concentration errors as high as 50% resulting in 7–50% error in kinetic parameter estimates. To better reflect experimental scenarios, noise containing substrate depletion data were analyzed by both the incorrect and correct integral equations. While both equations resulted in identical fits to substrate depletion data, the final estimates of V_m, K_m, and R were different and K_m and R estimates from the incorrect integral equation deviated substantially from the actual values. Another observation was that at R = 0, the incorrect integral equation reduced to the correct form of the Michaelis–Menten equation. We believe this combination of excellent fits to experimental data, albeit with incorrect kinetic parameter estimates, and the reduction to the Michaelis–Menten equation at R = 0 is primarily responsible for the incorrectness to go unnoticed. However, the resulting error in kinetic parameter estimates will lead to incorrect biological interpretation and we urge the use of the correct integral form presented in this study. Biotechnol. Bioeng. 2011;108: 2499–2503. © 2011 Wiley Periodicals, Inc.     

Estimating Kinetic Parameters when the Amount of Enzyme Added to an Assay Is Not a Controlled Variable: NITROGENASE ACTIVITY OF INTACT LEGUMES

Reliable estimates of Michaelis constants (K_m) and inhibitor constants may be obtained, in the absence of control over the amount of enzyme being added to any assay system, provided the following constraints are met. Michaelis-Menten kinetics are obeyed. Two rate measurements must be made with the same sample of enzyme: at low and high substrate concentration for determining K_m or minus and plus an inhibitor for determining inhibitor constants. The Michaelis constant may be calculated from the equation [Formula: see text] Inhibitor constants are derived graphically from Lineweaver-Burk or Dixon plots, once the K_m has been calculated. The above technique has been applied to study of the acetylene-reducing ability of intact legume plants. The apparent K_m for acetylene reduction by nitrogenase in legume nodules is ~1/100 atmosphere in the absence of nitrogen and ~1/40 atmosphere in its presence.     

A convenient analysis of Michaelis enzyme kinetic progress curves based on second derivatives

A simple method is described for the estimation of the Michaelis parameters, K_m and V_m, from a single progress curve at a single substrate concentration without the need to follow the reaction to completion. By measuring the substrate concentration and the time when the second derivative is at a minimum, K_m and V_m can be easily obtained.     

Multiphase catalysis. II. Hollow fiber catalysts

A theory of diffusion control within hollow fiber catalysts is derived for three different types of coordinate geometries: Cartesian, cylindrical, and spherical. Effectiveness factors are calculated and formulas for reactant conversion in both a fixed-bed and a contimunuous-feed stirred-tank reactor are derived. The apparent Michaelis constant, K_m′, is a measure of the amount of diffusion control within the catalysts. When K_m′ is equal to K_m, the true Michaelis constant, there is no diffusion control. In all other cases K_m′ is greater than K_m. Hollow fibers are attractive alternatives to spherical microcapsules for the encapsulation of enzymes.     

Kinetic behavior of penicillin acylase immobilized on acrylic carrier

The usefulness of Lilly's kinetic equation to describe penicillin G hydrolysis performed by immobilized penicillin acylase onto the acrylic carrier has been shown. Based on the experimental results characteristic kinetic constants have been estimated. The effect of noncompetitive inhibition of 6-amino penicillanic acid has not been found. Five components of reaction resistance have been defined. These components were also estimated for the reaction of the native enzyme as well as the Boehringer preparation.List of Symbols C _E g/m³ enzyme concentration - C _P,C _Q mol/m³ product concentrations - C _S mol/m³ substrate concentration - C _SO mol/m³ initial substrate concentration - K _A mol/m³ constant which defines the affinity of a substrate to the enzyme - K _iS mol/m³ substrate inhibitory constant - K _iP mol/m³ PhAA inhibitory constant - K _iQ mol/m³ 6-APA inhibitory constant - k ₃ mol/g/min constant rate of dissociation of the active complex - R(1) concentrational component of reaction resistance - R(2) resistance component derived from substrate affinity - R(3) resistance component due to the inhibition of the enzyme by substrate - R(4) resistance component due to the inhibition of the enzyme by PhAA - R(5) resistance component due to inhibition of the enzyme by 6-APA - r = dC_s/dt mol/m³ min rate of reaction - t min reaction time - (i) relative resistance of reaction     

Kinetics of lipase-catalyzed hydrolysis of palm oil in lecithin/izooctane reversed micelles

Candida rugosa lipase has been used to investigate the hydrolysis of palm oil in a lecithin/isooctane reversed micellar system. The reaction obeys Michaelis-Menten kinetics for the initial conditions. Kinetic parameters such as maximum rate and Michaelis constant (K _m) were determined for lipase-catalyzed hydrolysis in n-hexane and isooctane. According to the K _m values, the enzyme affinity towards the substrate was increased in isooctane. The maximum degree of hydrolysis was generally decreased as the initial substrate concentration was increased. This may suggest that the hydrolysis in lecithin reversed micelles should be regarded as a one-substrate first-order reversible reaction. It is shown in this study that the proposed one-substrate first-order kinetic model can serve for the precise prediction of the degree of hydrolysis for a known reaction time or vice versa, when the initial substrate concentration is less than 0.325 mol/dm³. A disagreement with this model was found when the initial substrate concentration was higher than approximately 0.3 mol/dm³. This may be due to the effects of the products on lipase activity or even to the conversion of the reversed micellar system to other systems. Received: 16 May 1997 / Received revision: 22 October 1997 / Accepted: 24 October 1997     

Reactor design for the enzymatic isomerization of glucose to fructose

A comprehensive methodology is presented for the design of reactors using immobilized enzymes as catalysts. The design is based on material balances and rate equations for enzyme action and decay and considers the effect of mass transfer limitations on the expression of enzyme activity. The enzymatic isomerization of glucose into fructose with a commercial immobilized glucose isomerase was selected as a case study. Results obtained are consistent with data obtained from existing high-fructose syrup plants. The methodology may be extended to other cases, provided sound expressions for enzyme action and decay are available and a simple flow pattern within the reactor might be assumed.List of Symbols C kat/kg specific activity of the catalyst - D m²/s substrate diffusivity within the catalyst particle - Dr m reactor diameter - d d operating time of each reactor - E kat initial enzyme activity - E _i kat initial enzyme activity in each reactor - F m³/s process flowrate - F _i m³/s reactor feed flowrate at a given time - F ₀ m³/s initial feed flowrate to each reactor - H number of enzyme half-lives used in the reactors - K mole/m³ equilibrium constant - K _S mole/m³ Michaelis constant for substrate - K _P mole/m³ Michaelis constant for product - K _m mole/m³ apparent Michaelis constant f(K, K _s, K_p, s₀) - k mole/s · kat reaction rate constant - k _d d^–1 first-order thermal inactivation rate constant - L m reactor height - L _r m height of catalyst bed - N _R number of reactors - P _i kg catalyst weight in each reactor - p mole/m³ product concentration - R m particle radius - R _P ratio of minimum to maximum process flowrate - r m distance to the center of the spherical particle - s mole/m³ substrate concentration - s _0i mole/m³ substrate concentration at reactor inlet - s ₀ mole/m³ bulk substrate concentration - s mole/m³ apparent substrate concentration - T K temperature - t d time - t _i d operating time for reactor i - t _s d time elapsed between two successive charges of each reactor - V m³ reactor volumen - V _m mole/m³ s maximum apparent reaction rate - V _p mole/m³ s maximum reaction rate for product - V _R m³ actual volume of catalyst bed - V _r m³ calculated volume of catalyst bed - V _S mol/m³ s maximum reaction rate for substrate - v mol/m³ s initial reaction rate - v _i m/s linear velocity - v _m mol/m³ s apparent initial reaction rate f(K_m, s,V_m) - X substrate conversion - X _eq substrate conversion at equilibrium - =s/K dimensionless substrate concentration - ₀=s₀/K bulk dimensionless substrate concentration - _eq=s_eq/K dimensionless substrate concentration at equilibrium - local effectiveness factor - mean integrated effectiveness factor - Thiéle modulus - =r/R dimensionless radius - _s kg/m³ hydrated support density - substrate protection factor - s residence time     

Changes in Activity of 5-Dehydroquinate Hydro-lyase in Relation to Lignification of Bamboo

Characterization of 5-dehydroquinate hydro-lyase extracted from bomboo shoot was carried out. The enzyme was active over a broad range of pH with no marked peak between pH 6.0 and 8.0. Michaelis constant (K_m) for dehydroquinic acid was found to be 1.3 × 10^?5 m at pH 7.4. The enzyme activity is highest in the top and tends to decrease quite gradually toward the lower parts of the bamboo shoot, and the results suggests a possible participation of the enzyme in the biosynthesis of lignin through shikimic acid pathway. 5-Dehydroquinate hydro-lyase was demonstrated to be widely distributed in woody plants.     

Diffusional and electrostatic effects on apparent kinetic parameters of reactions catalyzed by enzyme immobilized on the external surface of a support

Diffusional and electrostatic effects on the apparent maximum reaction rate V_m^app and the apparent Michaelis constant K_m^app were investigated theoretically for a system in which an enzyme immobilized on the external surface of a solid support catalyzes a reaction according to Michaelis-Menten kinetics. In such a system, the dependence of V_m^app and K_m^app on the substrate concentration can be expressed analytically. When the support and substrate carry charges of the same sign, resulting in a repulsive force between them, both V_m^app and K_m^app decrease with increasing substrate concentration, but they never decrease below the respective intrinsic values. On the other hand, when the support and substrate carry charges of opposite sign and therefore an attractive force occurs, V_m^app decreases towards its intrinsic value, while K_m^app decreases to values below its intrinsic value in the region of high substrate concentration.     

To what extent is a constant volume design worse than a minimum volume design for a series of CSTR's?

The balance equations for substrate in a cascade of CSTR's undergoing an enzyme-catalyzed reaction following Michaelis-Menten kinetics are developed in dimensionless form. Analytical expressions relating the intermediate concentrations are independently obtained for the cases of minimum overall volume and constant volume. The fractional deviations between the overall volumes following these two design criteria are calculated and presented for several values of the relevant parameters. For situations of practical interest, the fractional deviation is below 10%. Increasing values of the Michaelis-Menten parameter, K _m(or decreasing values of the number of reactors in the cascade, N) lead to lower values of the maximum deviation; this maximum deviation is attained at lower conversions of substrate when K _mis increased or N decreased.List of Symbols C _{S, i}mol.m^–3 concentration of substrate at the outlet of the i-th reactor - C _* ^{S, i} normalized concentration of substrate at the outlet of the i-th reactor - C _* ^{S, i, eq} normalized concentration of substrate at the outlet of the i-th reactor using the design criterion of constant volume - C _* ^{S, i, opt} normalized concentration of substrate at the outlet of the i-th reactor using the design criterion of minimum overall volume - C _{S, 0} mol.m^–3 concentration of substrate at the inlet to the first reactor - Da _i Damköhler number for the i-th reactor - Da _eq constant Damköhler number for each reactor of the cascade - Da _{tot, eq} overall Damköhler number for the cascade assuming equal-sized reactors - Da _{tot, min} minimum overall Damköhler number for the cascade - Er fractional deviation between the overall volumes using the two different design criteria - K _mmol. m^–3 Michaelis-Menten constant - K _* ^M dimensionless Michaelis-Menten constant - N number of reactors of the cascade - Q m³. s^–1 volumetric flow rate - V _im³ volume of the i-th reactor - v _max mol. m^–3. s^–1 reaction rate under saturation conditions of the enzyme with substrate - V _{tot, opt} m³ minimum overall volume of the cascade - V _{tot, eq} m³ overall volume of the cascade assuming equal-sized reactors     

Effects of starvation on valine and alanine transport across the intestinal mucosal border in sea bass,Dicentrarchus labrax

Summary kinetics of intestinal transport of l-alanine and l-valine (substrates of the A-system and the L-system, respectively, in mammals) across the brush-border membrane in sea bass, Dicentrarchus labrax, were studied on intact mucosa using a short-term uptake technique. When fish were starved for 4–8 weeks, total influx (mucosa-to-cell) of valine fell owing to disappearance or modification of the diffusion component. The maximum influx rate of saturable component increased but its affinity (reflected by the Michaelis constant) decreased. Alanine transport by Na⁺-dependent and diffusion pathways was unchanged after starvation Fasting also induced an almost 20% decrease in the length of intestinal microvilli.Abbreviations K _d diffusional constant - K _m Michaelis constant - V _max maximum influx rate     

Growth Kinetics of Attached Iron-Oxidizing Bacteria

A model of growth and substrate utilization for ferrous-iron-oxidizing bacteria attached to the disks of a rotating biological contactor was developed and tested. The model describes attached bacterial growth as a saturation function in which the rate of substrate utilization is determined by a maximum substrate oxidation rate constant (P), a half-saturation constant (K_s), and the concentration of substrate within the rotating biological contactor (S₁). The maximum oxidation rate constant was proportional to flow rate, and the substrate concentration in the reactor varied with influent substrate concentration (S₀). The model allowed the prediction of metabolic constants and included terms for both constant and growth-rate-dependent maintenance energies. Estimates for metabolic constants of the attached population of acidophilic, chemolithotrophic, iron-oxidizing bacteria limited by ferrous iron were: maximum specific growth rate (μ_max), 1.14 h⁻¹; half-saturation constant (K_s) for ferrous iron, 54.9 mg/liter; constant maintenance energy coefficient (m₁), 0.154 h⁻¹; growth-rate-dependent maintenance energy coefficient (m′), 0.07 h⁻¹; maximum yield (Y_g), 0.063 mg of organic nitrogen per mg of Fe(II) oxidized.     

Kinetic study of a membrane enzyme reactor

A flat-membrane dialyzer was used as enzyme reactor by introducing enzyme solution into one of the membrane-separated chambers. The apparent Michaelis constant K_m(app) of urease was always larger (ten times at [urease] = 1 mg/ml) than that of free enzyme because the permeation of substrate through the membrane was rate determining. K_m(app) for urease decreased from 125 to 20mM with increasing flow rate of the substrate solution because of the turbulent flow near the membrane. In the case of glucose oxidase or creatine kinase, the reaction rate was limited by the permeation of less permeable substrates such as oxygen or ATP. Therefore, K_m(app) of more permeable substrates such as glucose or creatine became smaller than that of free enzyme. The reaction amount calculated from the permeation data agreed well with experimental results. By designing spacers for the reactor to give turbulence to the solution, the effectiveness of the reactor was improved fivefold.     

Kinetic study of a hollow-fiber enzyme reactor

Enzymes, such as urease and uricase, were entrapped in three kinds of hollow fibers. The apparent Michaelis–Menten constants K_m(app) obtained for these enzyme reactors were always larger than K_m of free enzyme because of the permeation resistance of substrate across the hollow-fiber membrane. K_m(app) increased with increasing degree of permeation resistance across the membrane by the increase in enzyme concentration. The half-life of the entrapped urease in the continuous reaction system was 60–80% of that of free enzyme. Activation energies of hollow-fiber enzyme reactors were always smaller than that of the free enzyme, because the activation energy of permeation was smaller than that of the enzyme reaction.     

Temperature dependence of intracellular pH: Its role in the conservation of pyruvate apparentKm values of vertebrate lactate dehydrogenases

Summary When apparent Michaelis constants (K _m's) for pyruvate of M₄-lactate dehydrogenases from differently thermally adapted vertebrates are measured at the species' normal cell temperatures, a marked degree of conservation inK _m is observed, but only when the pH of the assay medium is varied in the manner in which intracellular pH varies with temperature in most animals (Fig. 2).K _m measurements performed at a constant pH do not yield this high degree of interspecific conservation inK _m (Figs. 2 and 3).The temperature dependence of intracellular pH preserves the charge states of imidazoles of protein histidines during temperature transitions. Thus under intracellular conditions the ionization state of the active site histidine of LDH will be independent of temperature, reducing the temperature dependence of pyruvate binding. This effect appears important in the contexts of short-term temperature variation experienced by an individual ectotherm and of long-term, evolutionary temperature changes important in speciation processes.These findings emphasize the importance of utilizing biologically realistic pH values in enzyme studies if major adaptive trends are to be observed.     

Membrane enzyme reactor with simultaneous separation using electrophoresis

A membrane enzyme reactor with simultaneous separation was investigated. Enzymes, urease and aspartase, were immobilized by a porous polytetrafluoroethylene membrane. Electrical field was applied in the medium while the reaction was carried out. Products with electrical charge could be separated through the membrane from the reaction medium as they were formed. Reaction behavior was analyzed by a simple model considering both pore-migration and reaction in the skelton of the membrane. According to the analysis the inherent reaction rate of the immobilized enzymes decreases significantly. This is probably caused by the structural variation of enzymes. For the case of urease, the change of pH inside the membrane may also cause the decrease of the reaction rate. The model analysis showed that the enzyme content in the membrane and the residence time of the substrate in the membrane governed overall extent of reaction.List of Symbols e g (dm³)^–1 enzyme concentration in the membrane - L cm membrane thickness - K _m mM Michaelis constant - Rate mmol · min^–1 · g^–1 rate of product formation per unit weight of enzyme - S mM substrate concentration - S _in mM inlet substrate concentration - S _out mM outlet substrate concentration - u cm · min^–1 migration rate - V V voltage between the electrodes - V _m mmol · min^–1 · g^–1 maximum reaction rate - X conversion - z cm distance from the surface inside the membrane - void fraction of the porous membrane - tortuosity of the membrane - min space time     

A generalized mathematical model for the growth kinetics of Saccharomyces cerevisiae with experimental determination of parameters

A general model of the kinetics of microbial growth has been developed involving the kinetics of incorporation of substrate into biomass and the maintenance energy requirements. Results obtained from batch cultures of the yeast Saccharomyces cerevisiae growing in synthetic media at pH 5.1 and 30°C permitted all biological parameters in the model to be calculated. Values obtained for these parameters were: maximum specific glucose uptake rate (μS_m), 2.08 g/g biomass/hr; apparent Michaelis constant for glucose (K_S), 0.1 g/liter (5.5 × 10^?4M) apparent Michaelis constant for oxygen (K_L), 1.4% O₂ (3.2 × 10^?6 M) quantitative index of the Pasteur effect (b), 4.9 × 10^?4%^?1 O₂ (207 M ^?1). Under conditions of strongly substrate-repressed respiration the values obtained for Y_ATP and P/O were constant over the course of the exponential phase of growth (Y_ATP = 10.4 g biomass/mole ATP; P/O = 3 moles ATP/atom 0). Mass balances for aerobic and anaerobic cultures confirmed the results obtained form the generalized model. Results presented suggested the operation of a mechanism for regulating energy-yielding metabolism which involved an equilibrium between the systems of oxidative phosphorylation and dephosphorylation and was dependent upon the level of catbolite repression.     

The role of Mg2+ in the hydrolytic activity of the isolated chloroplast ATPase: Study by high-performance liquid chromatography

The influences of total magnesium ion concentration at different total ATP concentrations, and of total ATP concentration, for different total magnesium ion concentrations, on the enzymatic rate of the isolated chloroplast F₁ ATPase, have been followed by a chromatographic method consisting in the separation and determination of ADP. From the various series of curves, it is concluded that the experimental results (position of the maxima,K _m values) are better fitted by a mechanism involving the activation of the enzyme by magnesium ion and hydrolysis of free ATP, rather than by the classical mechanism, for which the enzyme hydrolyzes the MgATP complex and is inhibited by Mg²⁺. Although the equations giving the reaction rate are similar in the two cases, the calculated values ofK _m are widely different. The value obtained from the classical mechanism does not agree withK _D , the dissociation constant of the enzyme-substrate complex, measured by the Hummel and Dreyer method. Moreover, when the total ATP concentration tends toward the total magnesium ion concentration, the nucleotide binding to the enzyme tends toward zero, although it should be maximum if MgATP were the true substrate. Finally, the inhibitory effect of Na⁺ is more easily explained as a competition between this ion and the activating Mg²⁺, than by the classical mechanism.     

Relation of CO(2) Compensation Concentration to Apparent Photosynthesis in Maize

Significant differences in CO₂ compensation concentration measured in the field among varieties of the species Zea mays L. are reported for the first time. CO₂ compensation concentrations were significantly (P≤ 0.01) and negatively correlated with apparent photosynthesis at 300 μl CO₂/liter air. The Michaelis constant (as defined) for a leaf was significantly (P≤ 0.01) and positively correlated with apparent photosynthesis among varieties. While the first correlation is similar to behavior of CO₂ compensation among species of different photosynthetic efficiency, the latter correlation is the converse of the behavior of Km among species.