Simultaneous estimation ofV max,Km, and the rate of endogenous substrate production (R) from substrate depletion data

The nonlinear and 3 linearized forms of the integrated Michaelis-Menten equation were evaluated for their ability to provide reliable estimates of uptake kinetic parameters, when the initial substrate concentration (S₀) is not error-free. Of the 3 linearized forms, the one where t/(S₀–S) is regressed against ln(S₀/S)/(S₀–S) gave estimates ofV _max and K_m closest to the true population means of these parameters. Further, this linearization was the least sensitive of the 3 to errors (±1%) in S₀. Our results illustrate the danger of relying on r² values for choosing among the 3 linearized forms of the integrated Michaelis-Menten equation. Nonlinear regression analysis of progress curve data, when S₀ is not free of error, was superior to even the best of the 3 linearized forms. The integrated Michaelis-Menten equation should not be used to estimateV _max and K_m when substrate production occurs concomitant with consumption of added substrate. We propose the use of a new equation for estimation of these parameters along with a parameter describing endogenous substrate production (R) for kinetic studies done with samples from natural habitats, in which the substrate of interest is an intermediate. The application of this new equation was illustrated for both simulated data and previously obtained H₂ depletion data. The only means by whichV _max, K_m, and R may be evaluated from progress curve data using this new equation is via nonlinear regression, since a linearized form of this equation could not be derived. Mathematical components of computer programs written for fitting data to either of the above nonlinear models using nonlinear least squares analysis are presented.     

Discrimination between rival laccase inhibition models from data sets with one inhibitor concentration using a penalized likelihood analysis and Akaike weights

Laccase from the white-rot fungus Fomes fomentarius was used for the biodegradation of ferulic acid (FA) in the presence of chloride anions. The initial reaction rates of substrate depletion were obtained by reverse-phase HPLC determination of remaining FA since substrate and reaction products have absorption peaks at similar wavelengths. Modelling of time-course data was accomplished by discrimination of the best enzyme inhibition equation from an initial set of seven different models based on Michaelis–Menten kinetics: competitive; uncompetitive; non-competitive; mixed; mixed hyperbolic; mixed parabolic; mixed hyperbolic and parabolic. Corrected Akaike information criterion was used to evaluate the relative merit of each kinetic model in order to rank them and find the more likely one. The discrimination results showed that the models with higher probabilities were the competitive and mixed inhibition types, but Akaike weights supported the selection of competitive inhibition (CI). After optimization by nonlinear regression, laccase kinetic parameters of FA biodegradation in the presence of chloride anions were: V_max?=?0.11?μmol?min^?1?mg^?1, K_m?=?44?μmol?L^?1 and a CI constant K_ic?=?14?mmol?L^?1.     

Modeling and kinetic parameter estimation of alcohol dehydrogenase‐catalyzed hexanol oxidation in a microreactor

A mathematical model for hexanol oxidation catalyzed by NAD⁺‐dependent alcohol dehydrogenase from baker's yeast in a microreactor was developed and compared with the model when the reaction takes place in a macroscopic reactor. The enzyme kinetics was modeled as a pseudo‐homogeneous process with the double substrate Michaelis–Menten rate expression. In comparison with the kinetic parameters estimated in the cuvette, a 30‐fold higher maximum reaction rate and a relatively small change in the saturation constants are observed for the kinetic parameters estimated in the continuously operated tubular microreactor (V_m1=197.275 U/mg, K_m^hexanol=9.420 mmol/L, and K_m1^NAD+=0.187 mmol/L). Kinetic measurements performed in the microreactor, estimated from the initial reaction rate experiments at the residence time of 36 s, showed no product inhibition, which could be explained by hydrodynamic effects and the continuous removal of inhibiting products. The Fourier amplitude sensitivity test method was applied for global kinetic parameter analysis, which shows a significant increase in the sensitivity of K_m1^NAD+ in the microreactor. Independent experiments performed in the microreactor were used to validate and to verify the developed mathematical model.     

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.     

Alternative algebraic rate‐integration approach for progress‐curve analysis of enzyme kinetics

A recent article of Zavrel et al. in this journal (Eng. Life Sci. 2010, 10, 191–200) described a comparison of several computer programs for progress‐curve analysis with respect to different computational approaches for parameter estimation. The authors applied both algebraic and dynamic parameter estimations, although they omitted time‐course analysis through the integrated rate equation. Recently, it was demonstrated that progress‐curve analysis through the integrated rate equation can be considered a simple and useful alternative for enzymes that obey the generalized Michaelis–Menten reaction mechanism. To complete this gap, the time‐dependent solution of the generalized Michaelis–Menten equation is here fitted to the progress curves from the Zavrel et al. reference article. This alternative rate‐integration approach for determining the kinetics parameters of Michaelis–Menten‐type enzymes yields the values with the greatest accuracy, as compared with the results obtained by other (algebraic or dynamic) parameter estimations.     

Kinetics of phosphate absorption by mycorrhizal and non-mycorrhizal Scots pine seedlings

Kinetics of net phosphate (P_i) uptake was measured on intact ectomycorrhizal and non‐mycorrhizal Pinus sylvestris seedlings using a semihydroponic cultivation method. The depletion of P_i in a nutrient solution was assessed over a 160–0.2 μM P_i gradient. Growth of the pine seedlings was P limited and measurements were performed 7 and 9 weeks after inoculation. Three ectomycorrhizal fungi were studied: Paxillus involutus, Suillus bovinus and Thelephoraterrestris. P_i uptake was extremely fast in plants colonised by P. involutus. The P_i concentration dropped below 0.2 μM within 4–5 h. In plants colonised with S. bovinus this occurred in 5–6 h and in plants associated with T. terrestris 8 h were needed to run through the whole concentration range. Non‐mycorrhizal plants of similar size and nutrient status decreased P_i to a concentration between 1 and 2 μM in 18 h. Data were curve fitted to a two‐phase Michaelis‐Menten equation. The apparent kinetic constants, K_m and V_max, for the high affinity P_i uptake system of the pine roots could be estimated accurately. V_max of this system was up to 7 times higher in pines associated with P. involutus than in non‐mycorrhizal seedlings. The intact extraradical mycelium greatly increased the absorption surface area of the roots (V_max). Non‐mycorrhizal plants had a K_m between 7.8 and 16.4 μM P_i. Plants mycorrhizal with P. involutus had K_m values between 2.4 and 7.2, plants colonised with S. bovinus had a K_m between 5.1 and 12.3, and seedlings associated with T. terrestris had a K_m from 4.6 to 10.1 μM P_i. All 3 ectomycorrhizal fungi had a strong impact on the P_i absorption capacity of the pine seedlings. The results also demonstrated that there is substantial heterogeneity in kinetic parameters among the different mycorrhizal root systems.     

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     

Efficient biokinetic experimental designs

Of the experimental methods available for obtaining data to estimate the biological kinetic parameters μ_m, K_s, and Yeach requires considerable experimental effort, yet often yields somewhat imprecise estimates of the parameters, particularly K_s. Therefore it would be worthwhile to seek ways to get parameter estimates of greater precision using less experimental effort. The precision of parameter estimates is strongly dependent, upon the settings of the independent, variables used in the experiments. This dependence is explained and an attempt made to show how experimental settings can be determined that lead efficiently to precise parameter estimates with minimal effort.     

Theoretical analysis of intrinsic reaction kinetics and the behavior of immobilized enzymes system for steady-state conditions

Mathematical modeling of immobilized enzymes under different kinetics mechanism viz. simple Michaelis–Menten, uncompetitive substrate inhibition, total competitive product inhibition, total non-competitive product inhibition and reversible Michaelis–Menten reaction are discussed. These five kinetic models are based on reaction diffusion equations containing non-linear terms related to Michaelis–Menten kinetics of the enzymatic reaction. Modified Adomian decomposition method is employed to derive the general analytical expressions of substrate and product concentration for all these five mechanisms for all possible values of the parameters Φ_S (Thiele modulus for substrate), Φ_P (Thiele modulus for product) and α (dimensionless inhibition degree). Also we have presented the general analytical expressions for the mean integrated effectiveness factor for all values of parameters. Analytical results are compared with the numerical results and also with the limiting case results, which are found to be good in agreement.     

New insights into activation and substrate recognition of polyhydroxyalkanoate synthase from Ralstonia eutropha

The polyhydroxyalkanoate synthase of Ralstonia eutropha (PhaC_Re) shows a lag time for the start of its polymerization reaction, which complicates kinetic analysis of PhaC_Re. In this study, we found that the lag can be virtually eliminated by addition of 50 mg/L TritonX-100 detergent into the reaction mixture, as well as addition of 2.5 g/L Hecameg detergent as previously reported by Gerngross and Martin (Proc Natl Sci USA 92: 6279–6283, 1995). TritonX-100 is an effective lag eliminator working at much lower concentration than Hecameg. Kinetic analysis of PhaC_Re was conducted in the presence of TritonX-100, and PhaC_Re obeyed Michaelis–Menten kinetics for (R)-3-hydroxybutyryl-CoA substrate. In inhibitory assays using various compounds such as adenosine derivatives and CoA derivatives, CoA free acid showed competitive inhibition but other compounds including 3′-dephospho CoA had no inhibitory effect. Furthermore, PhaC_Re showed a considerably reduced reaction rate for 3′-dephospho (R)-3-hydroxybutyryl CoA substrate and did not follow typical Michaelis–Menten kinetics. These results suggest that the 3′-phosphate group of CoA plays a critical role in substrate recognition by PhaC_Re.     

Protein adsorption on Ion exchange resin: Estimation of equilibrium isotherm parameters from batch kinetic data

The simple Langmuir isotherm is frequently employed to describe the equilibrium behavior of protein adsorption on a wide variety of adsorbents. The two adjustable parameters of the Langmuir isotherm—the saturation capacity, orq _m, and the dissociation constant,K _d—are usually estimated by fitting the isotherm equation to the equilibrium data acquired from batch equilibration experiments. In this study, we have evaluated the possibility of estimatingq _m andK _d for the adsorption of bovine serum albumin to a cation exchanger using batch kinetic data. A rate model predicated on the kinetic form of the Langmuir isotherm, with three adjustable parameters (q _m,K _d, and a rate constant), was fitted to a single kinetic profile. The value ofq _m determined as the result of this approach was quantitatively consistent with theq _m value derived from the traditional batch equilibrium data. However, theK _d value could not be retrieved from the kinetic profile, as the model fit proved insensitive to this parameter. Sensitivity analysis provided significant insight into the identifiability of the three model parameters.     

Evaluation of droplet-based microfluidic platforms as a convenient tool for lipases and esterases assays

Abstract

The accurate estimation of kinetic parameters is of fundamental importance for biochemical studies for research and industry. In this paper, we demonstrate the application of a modular microfluidic system for execution of enzyme assays that allow determining the kinetic parameters of the enzymatic reactions such as V_max – the maximum rate of reaction and K_M – the Michaelis constant. For experiments, the fluorogenic carbonate as a probe for a rapid determination of the kinetic parameters of hydrolases, such as lipases and esterases, was used. The microfluidic system together with the method described yields the kinetic constants calculated from the concentration of enzymatic product changes via a Michaelis–Menten model using the Lambert function W(x). This modular microfluidic system was validated on three selected enzymes (hydrolases).     

Different temperature sensitivity and kinetics of soil enzymes indicate seasonal shifts in C,N and P nutrient stoichiometry in acid forest soil

Acid forest soils in the Bohemian Forest in Central Europe are biogeochemically imbalanced in organic C, N and P processing. We hypothesized that these imbalances can be due to different temperature sensitivities of soil enzyme activities and their affinities to substrate in litter and organic soil horizons. We measured potential activities of five main soil enzymes (β-glucosidase, cellobiohydrolase, Leu-aminopeptidase, Ala-aminopeptidase, and phosphatase) responsible for organic carbon, nitrogen and phosphorus acquisition. We also modeled potential in situ enzyme activities and nutrient release based on continuous in situ temperature measurements. We determined basic kinetic parameters (K_m, V_max), enzyme efficiencies (k_cat) and temperature sensitivities (E_a and Q₁₀) according to Michaelis–Menten kinetic and modified Arrhenius models. Our results showed significant differences in substrate affinities between the litter and organic soil horizons. Higher aminopeptidase affinity (lower K_m) in the litter soil horizon can lead to leaching of peptidic compounds to lower soil horizons. β-Glucosidase and phosphatase showed high temperature response following the Arrhenius model. However, both aminopeptidases showed no or even decreased activity with increasing temperature. The aminopeptidase temperature insensitivity means that peptidic compounds are degraded at the same or even lower rate in warmer and colder periods of the year in acid forest soils. This imbalance results in different release of available nutrients from plant litter and soil organic matter which may affect bacterial and fungal community composition and nutrient leaching from these ecosystems.     

Degradation of Dimethyl Isophthalate by Viarovorax paradoxus Strain T4 Isolated from Deep-Ocean Sediment of the South China Sea

Viarovorax paradoxusT4 strain was isolated from deep-ocean sediment and demonstrated to be able to degrade dimethyl isophthalate (DMI). When DMI was utilized as the sole source of carbon and energy, it was transformed by hydrolysis initially, forming monomethyl isophthalate (MMI) and isophthalate acid (IA) as degradation intermediates. DMI and MMI were completely transformed to MMI and IA in about 100 h, respectively. Degradation of IA was completed in about 55 h. Analysis of total organic carbon in the culture medium confirmed that more than 80% of the substrate carbon was mineralized. Bacterial esterase induced by a range of substrates could be assessed using p-nitrophenyl acetate as the common substrate using crude enzyme preparation. The decreasing trend of K _m values derived from the Michaelis–Menten equation was dimethyl phthalate (DMP) > monomethyl phthalate (MMP) > dimethyl terephthalate (DMT) > Liver esterase > DMI > MMI > monomethyl terephthalate (MMT), indicating that higher K _m values were obtained by di-esters than mono-ester and the esters induced by terephthalate esters showed the highest activity. This investigation suggests that biochemical pathways for phthalate esters share many common characteristics and the esterases induced by different substrates are highly specific.     

Competition between isoprene emission and pigment synthesis during leaf development in aspen

In growing leaves, lack of isoprene synthase (IspS) is considered responsible for delayed isoprene emission, but competition for dimethylallyl diphosphate (DMADP), the substrate for both isoprene synthesis and prenyltransferase reactions in photosynthetic pigment and phytohormone synthesis, can also play a role. We used a kinetic approach based on post‐illumination isoprene decay and modelling DMADP consumption to estimate in vivo kinetic characteristics of IspS and prenyltransferase reactions, and to determine the share of DMADP use by different processes through leaf development in Populus tremula. Pigment synthesis rate was also estimated from pigment accumulation data and distribution of DMADP use from isoprene emission changes due to alendronate, a selective inhibitor of prenyltransferases. Development of photosynthetic activity and pigment synthesis occurred with the greatest rate in 1‐ to 5‐day‐old leaves when isoprene emission was absent. Isoprene emission commenced on days 5 and 6 and increased simultaneously with slowing down of pigment synthesis. In vivo Michaelis–Menten constant (K_m) values obtained were 265 nmol m^?2 (20 μm ) for DMADP‐consuming prenyltransferase reactions and 2560 nmol m^?2 (190 μm ) for IspS. Thus, despite decelerating pigment synthesis reactions in maturing leaves, isoprene emission in young leaves was limited by both IspS activity and competition for DMADP by prenyltransferase reactions.     

Posttranslational oxidative modification of (R)‐2‐(2,4‐dichlorophenoxy)propionate/α‐ketoglutarate‐dependent dioxygenases (RdpA) leads to improved degradation of 2,4‐dichlorophenoxyacetate (2,4‐D)

Microbial activities and the versatility gained through adaptation to xenobiotic compounds are the main biological forces to counteract environmental pollution. The current results present a new adaptive mechanism that is mediated through posttranslational modifications. Strains of Delftia acidovorans incapable of growing autochthonously on 2,4‐dichlorophenoxyacetate (2,4‐D) were cultivated in a chemostat on 2,4‐D in the presence of (R)‐2‐(2,4‐dichlorophenoxy)propionate. Long‐term cultivation led to enhanced 2,4‐D degradation, as demonstrated by improved values of the Michaelis–Menten constant K_m for 2,4‐D and the catalytic efficiency k_cat/K_m of the initial degradative key enzyme (R)‐2‐(2,4‐dichlorophenoxy)propionate/α‐ketoglutarate‐dependent dioxygenases (RdpA). Analyses of the rdpA gene did not reveal any mutations, indicating a nongenetic mechanism of adaptation. 2‐DE of enzyme preparations, however, showed a series of RdpA forms varying in their pI. During adaptation increased numbers of RdpA variants were observed. Subsequent immunoassays of the RdpA variants showed a specific reaction with 2,4‐dinitrophenylhydrazine (DNPH), characteristic of carbonylation modifications. Together these results indicate that posttranslational carbonylation modified the substrate specificity of RdpA. A model was implemented explaining the segregation of clones with improved degradative activity within the chemostat. The process described is capable of quickly responding to environmental conditions by reversibly adapting the degradative potential to various phenoxyalkanoate herbicides.     

Non-thermal Effects of a Ceramics Heater Radiation on Xanthine Oxidase Activity

The non-thermal effects of ceramics heater radiation on xanthine oxidase activity have been investigated using the enzyme, substrate, and competitive inhibitors which were irradiated on cooling. The K_m and V_max in the irradiated enzyme system were reduced to 51% and 85%, of the non-irradiated control, respectively. The K_i for a competitive inhibitor, folic acid, in the irradiated enzyme system decreased to 22% of the non-irradiated control. A steady-state molecular kinetic analysis for the reaction estimates that the irradiated enzyme may be kept in a folding state, and the formation of a Michaelis complex has been accelerated, and the activated Michaelis complex has been stabilized, and that a solvation or an electrostriction of xanthine, folate, and an active center of the enzyme with water may be promoted by irradiating the components in an aqueous solution, by which modification of the enzyme activity has been regulated.     

Desulfurization of dibenzothiophene by lyophilized cells of Pseudomonas delafieldii R-8 in the presence of dodecane

Several parameters that influence the dibenzothiophene (DBT) desulfurization by lyophilized cells of Pseudomonas delafieldii R-8 were studied in the presence of dodecane. The aqueous media tested with pH range in 4.6–8.5 made no obvious difference on the desulfurization activity. The rate and extent of desulfurization were strongly dependent on the volume ratio of oil-to-water, DBT concentration and the cell concentration. The specific desulfurization rate of DBT and 4,6-dimethyl DBT (4,6-DMDBT) could reach 11.4 and 9.4 mmol sulfur kg⁻¹ dry cells (DCW) h⁻¹, respectively. The desulfurization pattern of DBT was represented by the Michaelis–Menten equation. The kinetic parameters, the limiting maximal velocity (V_max) and Michaelis constant (K_m), for desulfurization of DBT were calculated.     

Purification and Characterization of Extracellular Chitin Deacetylase from Colletotrichum lindemuthianum

Chitin deacetylase, active in the presence of acetate (96% of the enzymatic activity was retained in the presence of 100 mm sodium acetate), was purified to electrophoretic homogeneity from a culture filtrate of Colletotrichum lindemuthianum (944-fold with a recovery of 4.05%). The enzyme was induced in the medium after the eighth day of incubation simultaneously with the blackening of the medium. The molecular mass of the enzyme was 31.5 kDa and 33 kDa as judged by SDS–PAGE and gel filtration, respectively, suggesting that the enzyme is a single polypeptide. The optimum temperature was 60°C and the optimum pH was 11.5–12.0 when glycol chitin was used as substrate. The enzyme was active toward glycol chitin, partially N-deacetylated water soluble chitin, and chitin oligomers the degrees of polymerization of which were more than four, but was less active with chitin trimer and dimer, and inactive with N-acetylglucosamine. The K_m and k_cat for glycol chitin were 2.55 mm and 27.1s^?1, respectively, and those for chitin pentamer were 414 μm and 83.2s^?1, respectively. The reaction rates of the enzyme toward glycol chitin and chitin oligomers seemed to follow the Michaelis–Menten kinetics.