Michaelis-Menten Mechanism Research Articles

Stochastic mapping of the Michaelis-Menten mechanism

The Michaelis-Menten mechanism is an extremely important tool for understanding enzyme-catalyzed transformation of substrates into final products. In this work, a computationally viable, full stochastic description of the Michaelis-Menten kinetic scheme is introduced based on a stochastic equivalent of the steady-state assumption. The full solution derived is free of restrictions on amounts of substance or parameter values and is used to create stochastic maps of the Michaelis-Menten mechanism, which show the regions in the parameter space of the scheme where the use of the stochastic kinetic approach is inevitable. The stochastic aspects of recently published examples of single-enzyme kinetic studies are analyzed using these maps.

Kinetics of enzymatic deacetylation of chitosan

The current paper reports on an investigation of the kinetics of chitosan deacetylation by chitin deacetylase isolated from Absidia orchidis vel coerulea. The reaction rate was correlated with the concentration of GlcNHAc units of the polymer. It is shown that the process follows the Michaelis–Menten mechanism. Modification of the Michaelis–Menten equation by introducing the activity of the enzyme instead of its concentration was tested and found to give a better approximation to the experimental data than the original Michaelis–Menten model. Parameters for both the original and the modified Michaelis–Menten equations are also proposed.

Asymptotic behaviour near a nonlinear sink

In this paper, we will develop an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Moreover, we will address the writing of one component of a solution in terms of the other in the case of a planar system. Examples will be given, notably the Michaelis-Menten mechanism of enzyme kinetics.

KINETICS OF P - NITROPHENYL ACETATE HYDROLYSIS CATALYZED BY α- CHYMOTRYPSIN IN PRESENCE OF POLYETHYLENE GLYCOL

The effect of poly (ethyleneglycol) (PEG) addition on the rate of p-nitrophenyl acetate (PNPA) catalyzed by a- chymotrypsin has been measured in TRIS buffer at pH = 7.4. The presence of PEG (up to 30 % p/v) leads to an increase in the rate of the process. The effect of PEG is evident both, in the pre-steady state and steady state stages of the process. The reaction follows a Michaelis-Menten mechanism under all the conditions employed. The Michaelis constant slightly decreases and the catalytic rate constant slightly increases with PEG concentration over all the polymer concentration range employed (up to 30%). The decrease in the Michaelis constant suggests that the effect of the polymer is due to crowding.

Esterification of benzoic acid and glycerol to α-monobenzoate glycerol in solventless media using an industrial free Candida antarctica lipase B

The enzymatic reaction of benzoic acid and glycerol in the absence of organic solvents to obtain the 1- or 3-monobenzoate glycerol (α-MBG) is studied. Esterification runs were batch wise performed with a concentration of enzyme of 30 g/L, changing the initial concentration of the acid in glycerol from 20 to 60 g/L, and temperature from 50 to 70 °C. In these conditions, the most active lipase among those tested for this synthesis was lipase B isozyme from Candida antarctica (CALB), obtaining conversion values higher than 80% and a significant selectivity to α-MBG. Unlike the synthesis in organic media, water did not have an inhibitory behaviour; hence control of water activity was unnecessary. Temperature and benzoic acid act synergically as deactivating factors. Considering the aforementioned, a kinetic model according to a Michaelis–Menten mechanism is proposed. This model considers a partial enzymatic deactivation mechanism with two terms, one of them accounting for the deactivating action of the acid.

Kinetic study of Saccharomyces pastorianus (carlsbergensis) multiplication.

In this paper we derive an approximating model for the kinetic reaction of the processes in yeast multiplication. The model comprising a Michaelis-Menten mechanism for yeast's feeding and other two elementary reactions for multiplication and degradation of the yeasts were qualitatively compared with a series of experimental results for yeast fermentation. The analysis given an estimate for the minimum number of experiments required to obtain good estimates for the parameters of the yeast fermentation process.

Effect of Human Serum Albumin on the Kinetics of 4-Methylumbelliferyl-β-D-N-N′-N″ Triacetylchitotrioside Hydrolysis Catalyzed by Hen Egg White Lysozyme

The effect of human serum albumin (HSA) addition on the rate of hydrolysis of the synthetic substrate 4-methylumbelliferyl-β-D-N-N'-N″ triacetylchitotrioside ((NAG)(3)-MUF) catalyzed by hen egg white lysozyme has been measured in aqueous solution (citrate buffer 50mM pH=5.2 at 37°C). The presence of HSA leads to a decrease in the rate of the process. The reaction follows a Michaelis-Menten mechanism under all the conditions employed. The catalytic rate constant decreases tenfold when the albumin concentration increases, while the Michaelis constant remains almost constant in the albumin concentration range employed. Ultracentrifugation experiments indicate that the main origin of the observed variation in the kinetic behavior is related to the existence of an HSA-lysozyme interaction. Interestingly, the dependence of the catalytic rate constant with albumin concentration parallels the decrease of the free enzyme concentration. We interpret these results in terms of the presence in the system of two enzyme populations; namely, the HSA associated enzyme which does not react and the free enzyme reacting as in the absence of albumin. Other factors such as association of the substrate to albumin or macromolecular crowding effects due to the presence of albumin are discarded. Theoretical modeling of the structure of the HSA-lysozyme complex shows that the Glu35 and Asp52 residues located in the active site of lysozyme are oriented toward the HSA surface. This conformation will inactivate lysozyme molecules bound to HSA.

Michaelis-Menten relations for complex enzymatic networks.

Most biological processes are controlled by complex systems of enzymatic chemical reactions. Although the majority of enzymatic networks have very elaborate structures, there are many experimental observations indicating that some turnover rates still follow a simple Michaelis-Menten relation with a hyperbolic dependence on a substrate concentration. The original Michaelis-Menten mechanism has been derived as a steady-state approximation for a single-pathway enzymatic chain. The validity of this mechanism for many complex enzymatic systems is surprising. To determine general conditions when this relation might be observed in experiments, enzymatic networks consisting of coupled parallel pathways are investigated theoretically. It is found that the Michaelis-Menten equation is satisfied for specific relations between chemical rates, and it also corresponds to a situation with no fluxes between parallel pathways. Our results are illustrated for a simple model. The importance of the Michaelis-Menten relationship and derived criteria for single-molecule experimental studies of enzymatic processes are discussed.

Demonstration of the receptor-mediated hepatic uptake of dextran in mice.

To establish a rationale of designing a drug targeting system using dextran conjugation, the disposition behaviour of dextran itself was investigated in mice. At a high dose (100 mg kg-1), [14C]dextran was retained in the blood circulation for a considerably long period. However, [14C]dextran rapidly disappeared from the plasma and accumulated in the liver (up to 60% of dose in 1 h) after a dose of 1 mg kg-1. Cellular localization of [14C]dextran in the liver following intravenous administration was examined and the contribution of parenchymal cells was demonstrated as well as the case of galactosylated bovine serum albumin (Gal-BSA). Pharmacokinetic analysis based on a physiological model including Michaelis-Menten type uptake mechanisms revealed that the Michaelis constant Km,l of [14C]dextran was 100 times greater than that of Gal-BSA. Coadministration of Gal-BSA delayed the hepatic uptake of [14C]dextran and the simulation based on the physiological model suggested that [14C]dextran was taken up by the same mechanism as Gal-BSA. These results suggested that dextran conjugation of a drug might lead to its undesirable accumulation in the liver at a low dose and an appropriate modification of dextran, such as carboxymethylation, would be required in such cases.

Michaelis−Menten Equation and Detailed Balance in Enzymatic Networks

Many enzymatic reactions in biochemistry are far more complex than the celebrated Michaelis-Menten scheme, but the observed turnover rate often obeys the hyperbolic dependence on the substrate concentration, a relation established almost a century ago for the simple Michaelis-Menten mechanism. To resolve the longstanding puzzle, we apply the flux balance method to predict the functional form of the substrate dependence in the mean turnover time of complex enzymatic reactions and identify detailed balance (i.e., the lack of unbalanced conformational current) as a sufficient condition for the Michaelis-Menten equation to describe the substrate concentration dependence of the turnover rate in an enzymatic network. This prediction can be verified in single-molecule event-averaged measurements using the recently proposed signatures of detailed balance violations. The finding helps analyze recent single-molecule studies of enzymatic networks and can be applied to other external variables, such as force-dependence and voltage-dependence.

Nitrate reduction associated with respiration in Sinorhizobium meliloti 2011 is performed by a membrane-bound molybdoenzyme

The purification and biochemical characterization of the respiratory membrane-bound nitrate reductase from Sinorhizobium meliloti 2011 (Sm NR) is reported together with the optimal conditions for cell growth and enzyme production. The best biomass yield was obtained under aerobic conditions in a fed-batch system using Luria-Bertani medium with glucose as carbon source. The highest level of Sm NR production was achieved using microaerobic conditions with the medium supplemented with both nitrate and nitrite. Sm NR is a mononuclear Mo-protein belonging to the DMSO reductase family isolated as a heterodimeric enzyme containing two subunits of 118 and 45 kDa. Protein characterization by mass spectrometry showed homology with respiratory nitrate reductases. UV-Vis spectra of as-isolated and dithionite reduced Sm NR showed characteristic absorption bands of iron-sulfur and heme centers. Kinetic studies indicate that Sm NR follows a Michaelis-Menten mechanism (K (m) = 97 ± 11 μM, V = 9.4 ± 0.5 μM min(-1), and k (cat) = 12.1 ± 0.6 s(-1)) and is inhibited by azide, chlorate, and cyanide with mixed inhibition patterns. Physiological and kinetic studies indicate that molybdenum is essential for NR activity and that replacement of this metal for tungsten inhibits the enzyme. Although no narGHI gene cluster has been annotated in the genome of rhizobia, the biochemical characterization indicates that Sm NR is a Mo-containing NR enzyme with molecular organization similar to NarGHI.

A Heme–Peptide Metalloenzyme Mimetic with Natural Peroxidase‐Like Activity

Mimicking enzymes with alternative molecules represents an important objective in synthetic biology, aimed to obtain new chemical entities for specific applications. This objective is hampered by the large size and complexity of enzymes. The manipulation of their structures often leads to a reduction of enzyme activity. Herein, we describe the spectroscopic and functional characterization of Fe(III)-mimochrome VI, a 3.5 kDa synthetic heme-protein model, which displays a peroxidase-like catalytic activity. By the use of hydrogen peroxide, Fe(III)-mimochrome VI efficiently catalyzes the oxidation of several substrates, with a typical Michaelis-Menten mechanism and with several multiple turnovers. The catalytic efficiency of Fe(III)-mimochrome VI in the oxidation of 2,2'-azino-di(3-ethyl-benzothiazoline-6-sulfonic acid (ABTS) and guaiacol (k(cat)/K(m)=4417 and 870 mM(-1) s(-1), respectively) is comparable to that of native horseradish peroxidase (HRP, k(cat)/K(m)=5125 and 500 mM(-1) s(-1), respectively). Fe(III)-mimochrome VI also converts phenol to 4- and 2-nitrophenol in the presence of NO(2) (-) and H(2) O(2) in high yields. These results demonstrate that small synthetic peptides can impart high enzyme activities to metal cofactors, and anticipate the possibility of constructing new biocatalysts tailored to specific functions.

Lipase activity in biphasic media: Why interfacial area is a significant parameter?

Abstract This work focused on lipase-catalyzed triglyceride hydrolysis in biphasic media. The effect of specific interfacial area of oil-in-water emulsions on the hydrolysis activity of lipase was particularly investigated following a rigorous methodology and using two different oils, tributyrin and olive oil. The specific interfacial area was varied over several orders of magnitude by changing either the amount of emulsified oil or the average diameter of oil droplets. This work particularly focused on the effect of changing droplet size (at given amount of oil) on lipase activity. When the specific interfacial area was varied over several orders of magnitude, the specific activity of the enzyme exhibited a non-monotonic variation with a pronounced maximum. At low specific interfacial area, initial velocity increased with specific interfacial area. Inhibition of enzyme activity at a high interfacial concentration of triglyceride was observed. Experimental results were interpreted on the basis of a theoretical mechanism assuming Michaelis–Menten mechanism for enzyme catalysis, Langmuir-type adsorption isotherm for enzyme and limitation of enzyme–substrate formation by enzyme adsorption process.

Effect of Human Serum Albumin on the Kinetics of N-glutaryl-L-phenylalanine p-nitroanilide Hydrolysis Catalyzed by α-Chymotrypsin

The effect of human serum albumin (HSA) addition on the rate of hydrolysis of N-glutaryl-L-phenylalanine p-nitroanilide (GPNA) catalyzed by α-chymotrypsin has been measured in phosphate buffer saline at pH=7.4. The presence of HSA (up to 200μM) leads to a decrease in the rate of the process. The reaction follows a Michaelis-Menten mechanism under all the conditions employed. To take into account the effect of substrate depletion due to its binding to albumin ultrafiltration experiments were carried out from which the binding of GPNA to HSA was derived. After correction of the kinetic data taking into account the binding of GPNA to HSA, the activity of the enzyme, and the derived Michaelis constant and catalytic rate constant tends to remain almost independent of the presence of albumin, indicating that the depletion of the substrate due to its binding to HSA is the main factor affecting the enzyme activity.

α-Chymotrypsin catalyzed hydrolysis of p-nitrophenyl acetate in cationic microemulsions

The catalytic activity of α-chymotrypsin (α-CT) for the hydrolysis of p-nitrophenyl acetate has been studied in oil-in-water microemulsions formed by cetyltrimethylammonium bromide, n-butanol and alkanes (organic solvents). The specificity of α-chymotrypsin regarding the chain length of the organic solvent ( n-hexane, n-heptane and isooctane) in CTAB/ n-butanol microemulsions was tested in hydrolytic reactions of PNPA. The stability and activity of α-CT depend upon organic solvents. Under all the conditions employed, the reaction follows a Michaelis–Menten mechanism. The second order rate constant, k 2 was determined for α-CT catalyzed hydrolysis of p-nitrophenyl acetate at 27 °C. The chain length of oil influences the k cat and K M. The CTAB/ n-butanol/isooctane ( z = 1.07) system of o/w microemulsion shows the higher activity and stability of α-CT.

Cationic Reverse Micelles Create Water with Super Hydrogen‐Bond‐Donor Capacity for Enzymatic Catalysis: Hydrolysis of 2‐Naphthyl Acetate by α‐Chymotrypsin

Reverse micelles (RMs) are very good nanoreactors because they can create a unique microenvironment for carrying out a variety of chemical and biochemical reactions. The aim of the present work is to determine the influence of different RM interfaces on the hydrolysis of 2-naphthyl acetate (2-NA) by alpha-chymotrypsin (alpha-CT). The reaction was studied in water/benzyl-n-hexadecyldimethylammonium chloride (BHDC)/benzene RMs and, its efficiency compared with that observed in pure water and in sodium 1,4-bis-2-ethylhexylsulfosuccinate (AOT) RMs. Thus, the hydrolysis rates of 2-NA catalyzed by alpha-CT were determined by spectroscopic measurements. In addition, the method used allows the joint evaluation of the substrate partition constant K(p) between the organic and the micellar pseudophase and the kinetic parameters: catalytic rate constant k(cat), and the Michaelis constant K(M) of the enzymatic reaction. The effect of the surfactant concentration on the kinetics parameters was determined at constant W(0)=[H(2)O]/[surfactant], and the variation of W(0) with surfactant constant concentration was investigated. The results show that the classical Michaelis-Menten mechanism is valid for alpha-CT in all of the RMs systems studied and that the reaction takes place at both RM interfaces. Moreover, the catalytic efficiency values k(cat)/K(M) obtained in the RMs systems are higher than that reported in water. Furthermore, there is a remarkable increase in alpha-CT efficiency in the cationic RMs in comparison with the anionic system, presumably due to the unique water properties found in these confined media. The results show that in cationic RMs the hydrogen-bond donor capacity of water is enhanced due to its interaction with the cationic interface. Hence, entrapped water can be converted into "super-water" for the enzymatic reaction studied in this work.

Developing the enzyme-machine analogy: a non-mathematical approach to teaching Michaelis-Menten kinetics

The behavior of enzyme-catalyzed reactions is not made clear to many students by the standard mathematical description of enzyme kinetics. An enzyme-machine analogy is described that has made the details of the Michaelis-Menten mechanism and the associated kinetics more accessible with minimal use of mathematics. Students taught using the analogy appear to have fewer of the misconceptions than those taught using a more mathematical approach.

Michaelis–Menten mechanism for single-enzyme and multi-enzyme system under stochastic noise and spatial diffusion

The investigation of enzymatic reaction under stochastic effect and spatial effect is an interesting problem. By virtue of Monte Carlo simulation, the stochastic dynamic of enzyme and the related Michaelis–Menten mechanism with stochastic internal noise and spatial diffusion are explored in this article. (i) For the single-enzyme system, two cases, including the fast phosphorylation case [X. S. Xie, et al., J. Phys. Chem. B 109 (2005) 19068] and slow phosphorylation case [X. S. Xie, et al., Nat. Chem. Biol. 2 (2006) 87] are considered. It is found the micro enzymatic velocity rate shows a rough hyperbolic dependence on the substrate concentration, hence obeys the Michaelis–Menten law qualitatively. In addition, our result reveals that diffusion rate can adjust the Michaelis–Menten curve; especially, it is shown that increasing diffusion rate enhances the micro enzyme rate. (ii) For the multi-enzyme system, a typical example, i.e., MAPK signaling pathway is used. We apply the Michaelis–Menten mechanism to the MAPK cascade and give a simple comparison for the signaling ability between the Michaelis–Menten mechanism and the single collision mechanism [J. W. Locasale et al., PLOS Comput. Biol. 4 (2008) e1000099].

Esterification of phenolic acids catalyzed by lipases immobilized in organogels

Lipases from Rhizomucor miehei and Candida antarctica B were immobilized in hydroxypropylmethyl cellulose organogels based on surfactant-free microemulsions consisting of n-hexane, 1-propanol and water. Both lipases kept their catalytic activity, catalyzing the esterification reactions of various phenolic acids including cinnamic acid derivatives. High reaction rates and yields (up to 94%) were obtained when lipase from C. antarctica was used. Kinetic studies have been performed and apparent kinetic constants were determined showing that ester synthesis catalyzed by immobilized lipases occurs via the Michaelis-Menten mechanism.

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Starting from zero-, first-, and second-order integrated laws for chemical kinetics, some cases are shown which produce fractional orders. Taking the Michaelis-Menten mechanism as a first example, it is shown that substrate order can go from 1 to zero, depending on relative concentration of enzyme and substrate. Using other examples which show fractional orders higher than one and even negative (inhibition), it is shown that the presence of an equilibrium before or parallel to the rate determining step can be the reason for fractional orders, which is an indication of a more complex mechanism.