Showing papers on "Michaelis–Menten kinetics published in 2015"

One hundred years of Michaelis–Menten kinetics☆

Abstract: The year 2013 marked the centenary of the paper of Leonor Michaelis and Maud Menten (Michaelis and Menten, 1913), and the 110th anniversary of the doctoral thesis of Victor Henri (Henri, 1903). These publications have had an enormous influence on the progress of biochemistry, and are more often cited in the 21st century than they were in the 20th. Henri laid the groundwork for the understanding of enzyme mechanisms, but his experimental design was open to criticism. He reached essentially correct conclusions about the action of invertase, but he took no steps to control the hydrogen-ion concentration, and he took no account of the spontaneous mutarotation of the glucose produced in the reaction. Michaelis and Menten corrected these shortcomings, and in addition they introduced the initial-rate method of analysis, which has proved much simpler to apply than the methods based on time courses that it replaced. In this way they defined the methodology for steady-state experiments that has remained standard for 100 years.

Enzyme Dynamics from NMR Spectroscopy

Abstract: CONSPECTUS: Biological activities of enzymes, including regulation or coordination of mechanistic stages preceding or following the chemical step, may depend upon kinetic or equilibrium changes in protein conformations. Exchange of more open or flexible conformational states with more closed or constrained states can influence inhibition, allosteric regulation, substrate recognition, formation of the Michaelis complex, side reactions, and product release. NMR spectroscopy has long been applied to the study of conformational dynamic processes in enzymes because these phenomena can be characterized over multiple time scales with atomic site resolution. Laboratory-frame spin-relaxation measurements, sensitive to reorientational motions on picosecond-nanosecond time scales, and rotating-frame relaxation-dispersion measurements, sensitive to chemical exchange processes on microsecond-millisecond time scales, provide information on both conformational distributions and kinetics. This Account reviews NMR spin relaxation studies of the enzymes ribonuclease HI from mesophilic (Escherichia coli) and thermophilic (Thermus thermophilus) bacteria, E. coli AlkB, and Saccharomyces cerevisiae triosephosphate isomerase to illustrate the contributions of conformational flexibility and dynamics to diverse steps in enzyme mechanism. Spin relaxation measurements and molecular dynamics (MD) simulations of the bacterial ribonuclease H enzymes show that the handle region, one of three loop regions that interact with substrates, interconverts between two conformations. Comparison of these conformations with the structure of the complex between Homo sapiens ribonuclease H and a DNA:RNA substrate suggests that the more closed state is inhibitory to binding. The large population of the closed conformation in T. thermophilus ribonuclease H contributes to the increased Michaelis constant compared with the E. coli enzyme. NMR spin relaxation and fluorescence spectroscopy have characterized a conformational transition in AlkB between an open state, in which the side chains of methionine residues in the active site are disordered, and a closed state, in which these residues are ordered. The open state is highly populated in the AlkB/Zn(II) complex, and the closed state is highly populated in the AlkB/Zn(II)/2OG/substrate complex, in which 2OG is the 2-oxoglutarate cosubstrate and the substrate is a methylated DNA oligonucleotide. The equilibrium is shifted to approximately equal populations of the two conformations in the AlkB/Zn(II)/2OG complex. The conformational shift induced by 2OG ensures that 2OG binds to AlkB/Zn(II) prior to the substrate. In addition, the opening rate of the closed conformation limits premature release of substrate, preventing generation of toxic side products by reaction with water. Closure of active site loop 6 in triosephosphate isomerase is critical for forming the Michaelis complex, but reopening of the loop after the reaction is (partially) rate limiting. NMR spin relaxation and MD simulations of triosephosphate isomerase in complex with glycerol 3-phosphate demonstrate that closure of loop 6 is a highly correlated rigid-body motion. The MD simulations also indicate that motions of Gly173 in the most flexible region of loop 6 contribute to opening of the active site loop for product release. Considered together, these three enzyme systems illustrate the power of NMR spin relaxation investigations in providing global insights into the role of conformational dynamic processes in the mechanisms of enzymes from initial activation to final product release.

Tuning Enzyme Kinetics through Designed Intermolecular Interactions Far from the Active Site

Abstract: Enzyme–DNA nanostructures were designed to introduce new substrate–enzyme interactions into their reactions, which altered enzyme kinetics in a predictable manner. The designed enzymes demonstrate a new strategy of enzyme engineering based on the rational design of intermolecular interactions outside of the active site that enhance and control enzyme kinetics. Binding interactions between tetramethylbenzidine and DNA attached to horseradish peroxidase (HRP) resulted in a reduced Michaelis constant (KM) for the substrate. The enhancement increased with stronger interactions in the micromolar range, resulting in a 2.6 fold increase in kcat/KM. The inhibition effect of 4-nitrobenzoic hydrazide on HRP was also significantly enhanced by tuning the binding to HRP–DNA. Lastly, binding of a nicotinamide adenine dinucleotide (NAD(H)) cofactor mimic, nicotinamide mononucleotide (NMN(H)), to an aldo-keto reductase (AdhD) was enhanced by introducing NMN(H)–DNA interactions.

New trends and perspectives in nonlinear intracellular dynamics: one century from Michaelis–Menten paper

Abstract: One century after the seminal work by Leonor Michaelis and Maud Menten devoted to the theoretical study of the enzymatic reactions, in this paper, we give an overview of the most recent trends concerning the mathematical modeling of several enzymatic mechanisms, focusing on its asymptotic analysis, which needs the use of advanced mathematical tools, such as center manifold theory, normal forms, and bifurcation theory. Moreover, we present some perspectives, linking the models here presented with similar models, arising from different research fields.

On the relationships between the Michaelis–Menten kinetics, reverse Michaelis–Menten kinetics, equilibrium chemistry approximation kinetics, and quadratic kinetics

Abstract: The Michaelis–Menten kinetics and the reverse Michaelis–Menten kinetics are two popular mathematical formulations used in many land biogeochemical models to describe how microbes and plants would respond to changes in substrate abundance However, the criteria of when to use either of the two are often ambiguous Here I show that these two kinetics are special approximations to the equilibrium chemistry approximation (ECA) kinetics, which is the first-order approximation to the quadratic kinetics that solves the equation of an enzyme–substrate complex exactly for a single-enzyme and single-substrate biogeochemical reaction with the law of mass action and the assumption of a quasi-steady state for the enzyme–substrate complex and that the product genesis from enzyme–substrate complex is much slower than the equilibration between enzyme–substrate complexes, substrates, and enzymes In particular, I show that the derivation of the Michaelis–Menten kinetics does not consider the mass balance constraint of the substrate, and the reverse Michaelis–Menten kinetics does not consider the mass balance constraint of the enzyme, whereas both of these constraints are taken into account in deriving the equilibrium chemistry approximation kinetics By benchmarking against predictions from the quadratic kinetics for a wide range of substrate and enzyme concentrations, the Michaelis–Menten kinetics was found to persistently underpredict the normalized sensitivity ∂ ln v / ∂ ln k2+ of the reaction velocity v with respect to the maximum product genesis rate k2+, persistently overpredict the normalized sensitivity ∂ ln v / ∂ ln k1+ of v with respect to the intrinsic substrate affinity k1+, persistently overpredict the normalized sensitivity ∂ ln v / ∂ ln [E]T of v with respect the total enzyme concentration [E]T, and persistently underpredict the normalized sensitivity ∂ ln v / ∂ ln [S]T of v with respect to the total substrate concentration [S]T Meanwhile, the reverse Michaelis–Menten kinetics persistently underpredicts ∂ ln v / ∂ ln k2+ and ∂ ln v / ∂ ln [E]T, and persistently overpredicts ∂ ln v / ∂ ln k1+ and ∂ ln v / ∂ ln [S]T In contrast, the equilibrium chemistry approximation kinetics always gives consistent predictions of ∂ ln v / ∂ ln k2+, ∂ ln v / ∂ ln k1+, ∂ ln v / ∂ ln [E]T, and ∂ ln v / ∂ ln [S]T, indicating that ECA-based models will be more calibratable if the modeled processes do obey the law of mass action Since the equilibrium chemistry approximation kinetics includes advantages from both the Michaelis–Menten kinetics and the reverse Michaelis–Menten kinetics and it is applicable for almost the whole range of substrate and enzyme abundances, land biogeochemical modelers therefore no longer need to choose when to use the Michaelis–Menten kinetics or the reverse Michaelis–Menten kinetics I expect that removing this choice ambiguity will make it easier to formulate more robust and consistent land biogeochemical models

Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation

Abstract: Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.

Real-Time Enzyme Kinetics by Quantitative NMR Spectroscopy and Determination of the Michaelis–Menten Constant Using the Lambert-W Function

Abstract: Enzyme kinetics is an essential part of a chemistry curriculum, especially for students interested in biomedical research or in health care fields. Though the concept is routinely performed in undergraduate chemistry/biochemistry classrooms using other spectroscopic methods, we provide an optimized approach that uses a real-time monitoring of the kinetics by quantitative NMR (qNMR) spectroscopy and a direct analysis of the time course data using Lambert-W function. The century old Michaelis–Menten equation, one of the fundamental concepts in biochemistry, relates the time derivative of the substrate to two kinetic parameters (the Michaelis constant KM and the maximum rate Vmax) and to the concentration of the substrate. The exact solution to the Michaelis–Menten equation, in terms of the Lambert-W function, is not available in standard curve-fitting tools. The high-quality of the real-time qNMR data on the enzyme kinetics enables a revisit of the concept of applying the progress curve analysis. This is pa...

Hydrolysis of a Lipid Membrane by Single Enzyme Molecules: Accurate Determination of Kinetic Parameters

Abstract: The accurate determination of the maximum turnover number and Michaelis constant for membrane enzymes remains challenging. Here, this problem has been solved by observing in parallel the hydrolysis of thousands of individual fluorescently labeled immobilized liposomes each processed by a single phospholipase A2 molecule. The release of the reaction product was tracked using total internal reflection fluorescence microscopy. A statistical analysis of the hydrolysis kinetics was shown to provide the Michaelis-Menten parameters with an accuracy better than 20 % without variation of the initial substrate concentration. The combined single-liposome and single-enzyme mode of operation made it also possible to unravel a significant nanoscale dependence of these parameters on membrane curvature.

Parallel versus Off-Pathway Michaelis–Menten Mechanism for Single-Enzyme Kinetics of a Fluctuating Enzyme

Abstract: Recent fluorescence spectroscopy measurements of the turnover time distribution of single-enzyme turnover kinetics of β-galactosidase provide evidence of Michaelis-Menten kinetics at low substrate concentration. However, at high substrate concentrations, the dimensionless variance of the turnover time distribution shows systematic deviations from the Michaelis-Menten prediction. This difference is attributed to conformational fluctuations in both the enzyme and the enzyme-substrate complex and to the possibility of both parallel- and off-pathway kinetics. Here, we use the chemical master equation to model the kinetics of a single fluctuating enzyme that can yield a product through either parallel- or off-pathway mechanisms. An exact expression is obtained for the turnover time distribution from which the mean turnover time and randomness parameters are calculated. The parallel- and off-pathway mechanisms yield strikingly different dependences of the mean turnover time and the randomness parameter on the substrate concentration. In the parallel mechanism, the distinct contributions of enzyme and enzyme-substrate fluctuations are clearly discerned from the variation of the randomness parameter with substrate concentration. From these general results, we conclude that an off-pathway mechanism, with substantial enzyme-substrate fluctuations, is needed to rationalize the experimental findings of single-enzyme turnover kinetics of β-galactosidase.

Effects of multivalency and hydrophobicity of polyamines on enzyme hyperactivation of α-chymotrypsin

Abstract: Enzyme hyperactivation using a complementary charged modulator/substrate pair has potential for enzyme applications in a wide range of research fields. Here, we report that amine compounds as well as naturally occurring polyamines, putrescine, spermidine, and spermine, enhance the enzyme activity of α-chymotrypsin (ChT) toward anionic substrates. The enzyme activity of ChT was increased by 1.6–6.9-fold in the presence of 50 mM amine compounds at pH 7.5. Analysis of the enzyme kinetics indicated that the catalytic constant ( k cat ) and specific constant ( k cat / K M ) increased in the presence of amine compounds depending on both the multivalency and hydrophobicity of the amine compounds, whereas the Michaelis constant ( K M ) remained constant. Molecular dynamics simulation suggested that the enhancement of enzyme activity of ChT was induced by weak interactions between amine compounds and ChT. These results provide extended design parameters for artificial activators for enzyme hyperactivation as well as an understanding of enzyme activity in the crude complex condition in vivo .

Partial purification and biochemical characterization of peroxidase from rosemary (Rosmarinus officinalis L.) leaves

Abstract: Background: In this study, it is aimed to purify POD from leaves of Rosmarinus officinalis L. and determine its some biochemical properties. PODs are a group of oxidoreductase enzymes that catalyze the oxidation of a wide variety of phenolic compounds in the presence of hydrogen peroxide as an electron acceptor. Materials and Methods: In this investigation, POD was purified 9.3-fold with a yield of 32.1% from the leaves of Rosemary by ammonium sulfate precipitation and ion-exchange chromatography. The enzyme biochemical properties, including the effect of pH, temperature and ionic strength were investigated with guaiacol as an electron donor. For substrate specificity investigation of the enzyme, Michaelis constant and the maximum velocity of an enzymatic reaction values for substrates guaiacol and 3,3Ͳ, 5,5Ͳ-TetraMethyle-Benzidine were calculated from the Lineweaver-Burk graphs. Results: The POD optimum pH and temperature were 6.0 and 40°C. The POD activity was maximal at 0.3 M of sodium phosphate buffer concentration (pH 6.0). Sodium dodecyl sulphate polyacrylamide gel electrophoresis was performed for molecular weight (M w ) determination and M w of the enzyme was found to be 33 kDa. To investigate the homogeneity of the POD, native-PAGE was done and a single band was observed. Conclusion: The stability against high temperature and extreme pH demonstrated that the enzyme could be a potential POD source for various applications in the medicine, chemical and food industries.

Effects of metal ions on the catalytic degradation of dicofol by cellulase.

Abstract: A new technique whereby cellulase immobilized on aminated silica was applied to catalyze the degradation of dicofol, an organochlorine pesticide. In order to evaluate the performance of free and immobilized cellulase, experiments were carried out to measure the degradation efficiency. The Michaelis constant, Km, of the reaction catalyzed by immobilized cellulase was 9.16 mg/L, and the maximum reaction rate, Vmax, was 0.40 mg/L/min, while that of free cellulase was Km = 8.18 mg/L, and Vmax = 0.79 mg/L/min, respectively. The kinetic constants of catalytic degradation were calculated to estimate substrate affinity. Considering that metal ions may affect enzyme activity, the effects of different metal ions on the catalytic degradation efficiency were explored. The results showed that the substrate affinity decreased after immobilization. Monovalent metal ions had no effect on the reaction, while divalent metal ions had either positive or inhibitory effects, including activation by Mn2 +, reversible competition with Cd2 +, and irreversible inhibition by Pb2 +. Ca2 + promoted the catalytic degradation of dicofol at low concentrations, but inhibited it at high concentrations. Compared with free cellulase, immobilized cellulase was affected less by metal ions. This work provided a basis for further studies on the co-occurrence of endocrine-disrupting chemicals and heavy metal ions in the environment.

Application of oxo-manganese complex immobilized on ion-exchange polymeric film as biomimetic sensor for nitrite ions

Abstract: A biomimetic sensor based on oxo-bridged dinuclear manganese–phenanthroline complex immobilized into an ion-exchange polymeric film deposited on glassy carbon electrode was applied to detection of nitrite ions and studied according to their kinetics parameters. The cyclic voltammetry at the modified electrode in universal buffer showed a two electron oxidation/reduction of the couple Mn IV (μ-O) 2 Mn IV /Mn III (μ-O) 2 Mn III and electrocatalytic property toward nitrite oxidation with a decrease of the overpotential of 320 mV compared with the bare glassy carbon electrode. A plot of the anodic current vs. the nitrite ions concentration for potential fixed (+0.480) at the biomimetic sensor was linear in the 2.49 × 10 −6 to 9.90 × 10 −6 mol L −1 concentration range with a detection limit of 6.50 × 10 −6 mol L −1 . The kinetic mechanism was derived by Michaelis–Menten, then, kinetics parameters were calculated through four methods: Lineweaver–Burke, Eadie–Hofstee, Hanes–Woolf and Nonlinear curve fitting. The best results were Michaelis–Menten rate constant = 3.42 μmol L −1 , catalytic rate constant = 0.0114 s −1 , catalytic efficiency = 3.3 × 10 3 (mol L) −1 s −1 and heterogeneous electrochemical rate constant = 1.15 × 10 −5 cm s −1 .

Michaelis-Menten kinetics under non-isothermal conditions.

Abstract: We extend the celebrated Michaelis–Menten kinetics description of an enzymatic reaction taking into consideration the presence of a thermal driving force. A coupling of chemical and thermal driving forces is expected from the principle of non-equilibrium thermodynamics, and specifically we obtain an additional term to the classical Michaelis–Menten kinetic equation, which describes the coupling in terms of a single parameter. A companion equation for the heat flux is also derived, which actually can exist even in the absence of a temperature difference. Being thermodynamic in nature, this result is general and independent of the detailed mechanism of the coupling. Conditions for the experimental verification of the new equation are discussed.

Closed form solutions and dominant elimination pathways of simultaneous first-order and Michaelis-Menten kinetics.

Abstract: The current study aims to provide the closed form solutions of one-compartment open models exhibiting simultaneous linear and nonlinear Michaelis–Menten elimination kinetics for single- and multiple-dose intravenous bolus administrations. It can be shown that the elimination half-time (\(t_{1/2}\)) has a dose-dependent property and is upper-bounded by \(t_{1/2}\) of the first-order elimination model. We further analytically distinguish the dominant role of different elimination pathways in terms of model parameters. Moreover, for the case of multiple-dose intravenous bolus administration, the existence and local stability of the periodic solution at steady state are established. The closed form solutions of the models are obtained through a newly introduced function motivated by the Lambert W function.

Understanding mechanisms of enzyme co-operativity: The importance of not being at equilibrium ☆

Abstract: The discovery at the end of the 1950s and the beginning of the 1960s that there were enzymes like threonine deaminase and aspartate transcarbamoylase that failed to follow the expected hyperbolic behaviour predicted by the Michaelis–Menten equation, raised several questions and induced the development of mechanisms to explain this peculiar behaviour. At that time it was already known that the binding of oxygen to haemoglobin did not follow a hyperbolic curve, but a sigmoidal one, and it was thought that a similar situation probably existed for enzymes with sigmoidal kinetics. In other words, the observed kinetic behaviour was a consequence of co-operativity in the substrate binding. Two main models were postulated: those of Monod, Wyman and Changeux in 1965 and of Koshland, Nemethy and Filmer in 1966. Both consider that the different conformations are in equilibrium and that there is a rapid equilibrium in the binding, which implies that co-operativity could only exist if there is more than one substrate binding site per enzyme molecule, that is, if the enzyme is an oligomer. What about monomeric enzymes, could they show kinetic co-operativity? Yes, but only through mechanisms that imply the existence of enzyme conformations that are not in equilibrium, and have different kinetic parameters. There are, in fact, very few examples of monomeric enzymes showing kinetic co-operativity with a natural substrate. The case of “glucokinase” (hexokinase D or hexokinase IV), a monomeric enzyme with co-operativity with respect to glucose, will be discussed.

Enzyme kinetics and transport in a system crowded by mobile macromolecules

Abstract: The dynamics of an elastic network model for the enzyme 4-oxalocrotonate tautomerase is studied in a system crowded by mobile macromolecules, also modeled by elastic networks. The system includes a large number of solvent molecules, as well as substrate and product molecules which undergo catalytic reactions with this hexameric protein. The time evolution of the entire system takes place through a hybrid dynamics that combines molecular dynamics for solute species and multiparticle collision dynamics for the solvent. It is shown that crowding leads to subdiffusive dynamics for the protein, in accord with many studies of diffusion in crowded environments, and increases orientational relaxation times. The enzyme reaction kinetics is also modified by crowding. The effective Michaelis constant decreases with crowding volume fraction, and this decrease is attributed to excluded volume effects, which dominate over effects due to reduced substrate diffusion that would cause the Michaelis constant to increase.

Hydrolysis of cellobiose to monosaccharide catalyzed by functional Lanthanum(III) metallomicelle

Abstract: A novel surfactant, 3-(dodecylimino)butan-2-one-oxime (DMBO), was synthesized. The metallomicelle La(DMBO)2 was prepared and used as a mimic of β-glucosidase to catalyze the hydrolysis of cellobiose in weakly alkaline aqueous solution at relative low temperature (80–110 °C). This study indicated that the functional metallomicelle displayed effective catalytic activity for hydrolysis of cellobiose to monosaccharide (glucose, fructose and 1,6-anhydroglucose) and glucosyl-erythrose. The conversion of cellobiose and selectivity of monosaccharide could reach 38.5% and 71.1%, respectively, for a reaction time of 10 h at pH 9.0 and 95 °C. The possible reaction pathways of cellobiose hydrolysis are proposed and the catalysis reaction rate constant kcat and Michaelis constant Km for the cellobiose hydrolysis were calculated. The apparent activation energy (Ea = 84.6 kJ mol−1) of cellobiose to monosaccharide was evaluated.

Modified Taylor solution of equation of oxygen diffusion in a spherical cell with Michaelis-Menten uptake kinetics

Abstract: This work presents the application of a modified Taylor method to obtain a handy and easily computable approximate solution of the nonlinear differential equation to model the oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. The obtained solution is fully symbolic in terms of the coefficients of the equation, allowing to use the same solution for different values of the maximum reaction rate, the Michaelis constant, and the permeability of the cell membrane. Additionally, the numerical experiments show the high accuracy of the proposed solution, resulting 1.658509453A~10−15 as the lowest mean square error for a set of coefficients. The straightforward process to obtain the solution shows that the modified Taylor method is a handy alternative to a more sophisticated method because does not involve the solving of differential equations or calculate complicated integrals.