Menten Mechanism Research Articles

A generic rate equation for catalysed, template-directed polymerisation

Biosynthetic networks link to growth and reproduction processes through template-directed synthesis of macromolecules such as polynucleotides and polypeptides. No rate equation exists that captures this link in a way that it can effectively be incorporated into a single computational model of the overall process. This paper describes the derivation of such a generic steady-state rate equation for catalysed, template-directed polymerisation reactions with varying monomer stoichiometry and varying chain length. The derivation is based on a classical Michaelis–Menten mechanism with template binding and an arbitrary number of chain elongation steps that produce a polymer composed of an arbitrary number of monomer types. The rate equation only requires the identity of the first dimer in the polymer sequence; for the remainder only the monomer composition needs be known. Further simplification of a term in the denominator yielded an equation requiring no positional information at all, only the monomer composition of the polymer; this equation still gave an excellent estimate of the reaction rate provided that either the monomer concentrations are at least half-saturating, or the polymer is very long.

Enzymatic Hydrolysis of N-Benzoyl-l-Tyrosine p-Nitroanilide by α-Chymotrypsin in DMSO-Water/AOT/n-Heptane Reverse Micelles. A Unique Interfacial Effect on the Enzymatic Activity

The reverse micelle (RM) media are very good as 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 water-dimethyl sulfoxide (DMSO) mixtures encapsulated in 1,4-bis-2-ethylhexylsulfosuccinate (AOT)/n-heptane RMs on the enzymatic hydrolysis of N-benzoyl-L-tyrosine p-nitroanilide (Bz-Try-pNA) by α-chymotrypsin (α-CT). The reaction was first studied in homogeneous media at different DMSO-water mixture compositions and in DMSO-water/AOT/n-heptane RMs. The hydrolysis rates of Bz-Try-pNA catalyzed by α-CT were determined by UV-vis spectroscopy. The reaction follows the Michaelis-Menten mechanism and the kinetic parameters: kcat, KM, and kcat/KM were evaluated under different conditions. In this homogeneous media, DMSO plays an important role in the solubilization process of the peptide which is almost insoluble in water, but it has a tremendous impact on the inactivation of α-CT. It is shown that the enzyme dissolved in a 20% molar ratio of the DMSO-water mixture does not present enzymatic activity. Dynamic light scattering has been used to assess the formation of DMSO-water/AOT/heptane RMs at different DMSO compositions. The results also show that there is preferential solvation of the AOT RM interface by water molecules. To test the use of these RMs as nanoreactors, the kinetic parameters for the enzymatic reaction in these systems have been evaluated. The parameters were determined at fixed W(S) {W(S) = ([water] + [DMSO])/[AOT] = 20} at different DMSO-water compositions. The results show that the Michaelis-Menten mechanism is valid for α-CT in all the RM systems studied and that the reaction takes place at the RM interface. Surprisingly, it was observed that the enzyme encapsulated by the RMs show catalytic effects with similar kcat/KM values at any DMSO composition investigated, which evidence that DMSO molecules are localized far from the RM interface.

Cysteine endoprotease activity of human ribosomal protein S4 is entirely due to the C-terminal domain, and is consistent with Michaelis–Menten mechanism

BackgroundIt is known that tandem domains of enzymes can carry out catalysis independently or by collaboration. In the case of cysteine proteases, domain sequestration abolishes catalysis because the active site residues are distributed in both domains. The validity of this argument is tested here by using isolated human ribosomal protein S4, which has been recently identified as an unorthodox cysteine protease. MethodsCleavage of the peptide substrate Z-FR↓-AMC catalyzed by recombinant C-terminal domain of human S4 (CHS4) is studied by fluorescence-monitored steady-state and stopped-flow kinetic methods. Proteolysis and autoproteolysis were analyzed by electrophoresis. ResultsThe CHS4 domain comprised of sequence residues 116–263 has been cloned and ovreexpressed in Escherichia coli. The purified domain is enzymatically active. Barring minor differences, steady-state kinetic parameters for catalysis by CHS4 are very similar to those for full-length human S4. Further, stopped-flow transient kinetics of pre-steady-state substrate binding shows that the catalytic mechanism for both full-length S4 and CHS4 obeys the Michaelis–Menten model adequately. Consideration of the evolutionary domain organization of the S4e family of ribosomal proteins indicates that the central domain (residues 94–170) within CHS4 is indispensable. ConclusionThe C-terminal domain can carry out catalysis independently and as efficiently as the full-length human S4 does. SignificanceLocalization of the enzyme function in the C-terminal domain of human S4 provides the only example of a cysteine endoprotease where substrate-mediated intramolecular domain interaction is irrelevant for catalytic activity.

Kinetic-mechanistic studies of lipase-polymer micelle binding and catalytic degradation: Enzyme interfacial activation

Relatively small and uniformly sized block copolymer micelles from low polydispersity poly (ethylene glycol) (PEG) block poly (ε-caprolactone) (PCL) (PEG45-b-PCL60) give 1H NMR spectra useful for direct micelle characterization and kinetic-mechanistic studies. P. cepacia lipase catalyzed PEG45-b-PCL60 micelle degradations were followed by 1H NMR and GPC to obtain simultaneous evaluation of the micelle composition, degradation kinetics and appearance of the water soluble hydrolysis products. Analysis and simulation of the concentration versus time profiles for P. cepacia lipase catalyzed PEG45-b-PCL60 micelle degradation show that the process conforms to a Michaelis–Menten mechanism (E + M⇌EM → P + E) with enzyme-micelle complex product inhibition (EM + P⇌EMP). Formation and tight binding of the lipase enzyme-micelle complex, activation of lipase catalysis and sequential micelle degradation are characteristics of PEG45-b-PCL60 micelle degradation which parallel features of enzyme interfacial activation associated with lipase catalyzed hydrolysis of lipids in membranes.

A binomial stochastic kinetic approach to the Michaelis–Menten mechanism

This Letter presents a new method that gives an analytical approximation of the exact solution of the stochastic Michaelis–Menten mechanism without computationally demanding matrix operations. The method is based on solving the deterministic rate equations and then using the results as guiding variables of calculating probability values using binomial distributions. This principle can be generalized to a number of different kinetic schemes and is expected to be very useful in the evaluation of measurements focusing on the catalytic activity of one or a few individual enzyme molecules.

Inference of analytical thermodynamic models for biological networks

We present an automated algorithm for inferring analytical models of closed reactive biochemical mixtures, on the basis of standard approaches borrowed from thermodynamics and kinetic theory of gases. As input, the method requires a number of steady states (i.e. an equilibria cloud in phase–space), and at least one time series of measurements for each species. Validations are discussed for both the Michaelis–Menten mechanism (four species, two conservation laws) and the mitogen-activated protein kinase–MAPK mechanism (eleven species, three conservation laws).

Kinetics of Enzyme Action on Surface-Attached Substrates: A Practical Guide to Progress Curve Analysis in Any Kinetic Situation

In the present work, exact kinetic equations describing the action of an enzyme in solution on a substrate attached to a surface have been derived in the framework of the Michaelis-Menten mechanism but without resorting to the often-used steady-state approximation. The here-derived kinetic equations are cast in a workable format, allowing us to introduce a simple and universal procedure for the quantitative analysis of enzyme surface kinetics that is valid for any kinetic situation. The results presented here should allow experimentalists studying the kinetics of enzyme action on immobilized substrates to analyze their data in a perfectly rigorous way.

Overexpression, purification, and biochemical and spectroscopic characterization of copper-containing nitrite reductase from Sinorhizobium meliloti 2011. Study of the interaction of the catalytic copper center with nitrite and NO

The entire nirK gene coding for a putative copper-nitrite reductase (Nir) from Sinorhizobium meliloti 2011 (Sm) was cloned and overexpressed heterologously in Escherichia coli for the first time. The spectroscopic and molecular properties of the enzyme indicate that SmNir is a green Nir with homotrimeric structure (42.5kDa/subunit) containing two copper atoms per monomer, one of type 1 and the other of type 2. SmNir follows a Michaelis–Menten mechanism and is inhibited by cyanide. EPR spectra of the as-purified enzyme exhibit two magnetically different components associated with type 1 and type 2 copper centers in a 1:1 ratio. EPR characterization of the copper species obtained upon interaction of SmNir with nitrite, and catalytically-generated and exogenous NO reveals the formation of a Cu-NO EPR active species not detected before in closely related Nirs.

Immobilization of commercial laccase on spent grain

The aim of this work was to assess the possibility of using beer spent grain (a byproduct of beer's brewing industry) as a carrier for laccase immobilization. Both adsorption (on spent grain – SG and on digested spent grain – DSG) and covalent binding (using glycidol and glycidol followed by ethylenediamine on DSG) were used. The effect of different immobilization conditions on the immobilization yields and recovered activities such as contact time, enzyme concentration and pH was evaluated. For the best conditions, immobilization yields, recovered activities and thermal, operational and storage stabilities were also evaluated. Finally, the Michaelis–Menten mechanism was applied and the parameter with respect to ABTS oxidation was determined.Enzyme immobilization on DSG led to the best enzyme activities (recovered activities as high as 90%) and to high storage and operational stabilities (10 cycles). Thermal stability was also improved and the half-life of immobilized laccase in SG increased from 0.64h to 1.1h at 70°C.

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.

Feedforward non-Michaelis–Menten mechanism for CO2 uptake by Rubisco: Contribution of carbonic anhydrases and photorespiration to optimization of photosynthetic carbon assimilation

Rubisco, the most abundant protein serving as the primary engine generating organic biomass on Earth, is characterized by a low catalytic constant (in higher plants approx. 3s−1) and low specificity for CO2 leading to photorespiration. We analyze here why this enzyme evolved as the main carbon fixation engine. The high concentration of Rubisco exceeding the concentration of its substrate CO2 by 2–3 orders of magnitude makes application of Michaelis–Menten kinetics invalid and requires alternative kinetic approaches to describe photosynthetic CO2 assimilation. Efficient operation of Rubisco is supported by a strong flux of CO2 to the chloroplast stroma provided by fast equilibration of bicarbonate and CO2 and forwarding the latter to Rubisco reaction centers. The main part of this feedforward mechanism is a thylakoidal carbonic anhydrase associated with photosystem II and pumping CO2 from the thylakoid lumen in coordination with the rate of electron transport, water splitting and proton gradient across the thylakoid membrane. This steady flux of CO2 limits photosynthesis at saturating CO2 concentrations. At low ambient CO2 and correspondingly limited capacity of the bicarbonate pool in the stroma, its depletion at the sites of Rubisco is relieved by utilizing O2 instead of CO2, i.e. by photorespiration, a process which supplies CO2 back to Rubisco and buffers the redox state and energy level in the chloroplast. Thus, the regulation of Rubisco function aims to keep steady non-equilibrium levels of CO2, NADPH/NADP and ATP/ADP in the chloroplast stroma and to optimize the condition of homeostatic photosynthetic flux of matter and energy.

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.

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.

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.

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.

Determination of the six rate constants of a three-state enzymatic network and a noninvasive test of detailed balance

The Michaelis-Menten mechanism is unanimously recognized by experimentalists and theoreticians as the reference model for the description of enzymatic catalysis. The recent explosion in the diversity of fluorescent probes solves the problem of in situ observation of proteins and the experimental investigation of enzymatic dynamics, which determines the Michaelis constant or a small number of relaxation times, is becoming more and more common. We propose a protocol for the full characterization of enzyme kinetics in the framework of the Michaelis-Menten mechanism. The method relies on the measurement of the oscillation amplitude of the enzymatic concentrations, when the biological medium is submitted to a temperature modulation of a few degrees. Analytical expressions of all the rate constants as functions of the concentration amplitudes are derived. The noninvasive character of the perturbation and the assessable uncertainty on the rate constant values make an in situ test of detailed balance possible.

Application of the Van Slyke–Cullen irreversible mechanism in the analysis of enzymatic progress curves

For enzymatic progress curves conforming to the Michaelis–Menten mechanism E + S ⇌ ES → E + P , the minimal fitting model cast as a system of numerically integrated differential equations is the simplified, irreversible Van Slyke–Cullen mechanism E + S → ES → E + P . The best-fit value of the bimolecular association rate constant is identical to the specificity constant k cat / K M . An illustrative example involves a fluorogenic continuous assay of the HIV protease, analyzed by the differential-equation oriented software package DYNAFIT [P. Kuzmic, Anal. Biochem. 237 (1996) 260].

Deformation Model for Thioredoxin Catalysis of Disulfide Bond Dissociation by Force

We develop a theoretical model describing the effect of applied force on the rate of enzymatic dissociation of disulfide bonds (Wiita, A. P. et al., Nature 450:124–127, 2007). The timescale characterizing the extension of the 8-domain protein chain, in which every domain contains a disulfide bond, exhibits anomalous force dependence: The extension time first increases and then decreases with increasing force. This type of force dependence indicates catch-binding and is under active investigation in a variety of systems. The disulfide system presents the first example of a chemical catch-bond. The key difference between the deformation model developed here and the two-pathway model used in the original publication is the bond-deformation term in the force dependence of the dissociation rate constant. The bond-deformation concept provides a different interpretation of the phenomenon. Rather than invoking a new dissociation pathway, which is difficult to rationalize for a simple S–S bond, catch-binding is explained by a force-induced deformation in the protein system disfavoring bond dissociation by thioredoxin. The analysis of the experimental data is performed within the Michaelis–Menten kinetic mechanism of enzyme catalysis. A simplified version of the Michaelis–Menten mechanism containing only four parameters is found to provide a quantitative description of the key features of the experimental data.