Menten Mechanism Research Articles

Inference of complex reaction mechanisms applying model reduction techniques

Both structural (number of species and reactions) and temporal (extremely diverse reaction rates) aspects of complexity are considered when describing large chemical reaction networks. A consistent way to make model reduction is to construct the invariant manifold, which describes the asymptotic system behavior. Preliminary approximations to SIM (Slow Invariant Manifold) are constructed using the model reduction techniques (MRTs): the Quasi-Equilibrium Manifold (QEM), the Spectral Quasi-Equilibrium Manifold (SQEM), and the Intrinsic Low-Dimension Manifold (ILDM). In this paper, the activities of the concerned species and the overall dynamics of the system are examined. Two examples are used to demonstrate the techniques: the Michaelis–Menten mechanism, which is a single reaction mechanism, and a multi-route route reaction mechanism. The behavior of each species on the available route is covered separately. As a result, the reduced invariant solution curve of several approaches is illustrated, along with a comparison of these methods in various graphs. Sensitivity analysis is applied using the SimBiology toolbox in MATLAB to monitor the role of each parameter involved. All the results of model reduction techniques are simulated through MATLAB.

Steady State Kinetics for Enzymes with Multiple Binding Sites Upstream of the Catalytic Site

The Michaelis–Menten mechanism, which describes the binding of a substrate to an enzyme, is a simplification of the process on a molecular scale. A more detailed model should include the binding of the substrate to precatalytic binding sites (PCBSs) prior to the transition to the catalytic site. Our work shows that the incorporation of PCBSs, in steady-state conditions, generates a Michaelis–Menten-type expression, in which the kinetic parameters KM and Vmax adopt more complex expressions than in the model without PCBSs. The equations governing reaction kinetics can be seen as generalized symmetries, relative to time translation actions over the state space of the underlying chemical system. The study of their structure and defining parameters can be interpreted as looking for invariants associated with these time evolution actions. The expression of KM decreases as the number of PCBSs increases, while Vmax reaches a minimum when the first PCBSs are incorporated into the model. To evaluate the trend of the dynamic behavior of the system, numerical simulations were performed based on schemes with different numbers of PCBSs and six conditions of kinetic constants. From these simulations, with equal kinetic constants for the formation of the Substrate/PCBS complex, it is observed that KM and Vmax are lower than those obtained with the Michaelis–Menten model. For the model with PCBSs, the Vmax reaches a minimum at one PCBS and that value is maintained for all of the systems evaluated. Since KM decreases with the number of PCBSs, the catalytic efficiency increases for enzymes fitting this model. All of these observations are consistent with the general equation obtained. This study allows us to explain, on the basis of the PCBS to KM and Vmax ratios, the effect on enzyme parameters due to mutations far from the catalytic site, at sites involved in the first enzyme/substrate interaction. In addition, it incorporates a new mechanism of enzyme activity regulation that could be fundamental to search for new activity-modulating sites or for the design of mutants with modified enzyme parameters.

Approximation of intra-particle reaction/diffusion effects of immobilized enzyme system following reverse Michaelis–Menten (rMM) mechanism: third degree polynomial and Akbari–Ganji methods

Two approximate analytical expressions based on third degree polynomial and Akbari–Ganji’s method (AGM) were derived for the reaction/diffusion controlled kinetics of an immobilized enzyme (IE) systems. The approximation methods predict substrate concentration profile and effectiveness factor (eta) in a porous spherical particle. The reaction is assumed to follow reverse Michaelis–Menten (rMM) kinetics. The approximate methods predictions were comparable to that of numerical solution (using the Matlab finite difference function, bvp4c) at wide range of {phi }^{2} and {y}_{o} especially at low {phi }^{2} and high {y}_{o} (polynomial equation) and low {phi }^{2} and low {y}_{o} (AGM equation). Although the approximate solution was derived for rMM kinetics, the results can be used to describe other important enzymatic reaction kinetics such as simple Michaelis–Menten (MM) kinetics and MM with competitive product inhibition kinetics. A necessary design equation should be satisfied when using polynomial or AGM approximation for different enzyme kinetic equations. In this work, two examples of enzymatic reactions of industrial interest were studied, namely glucose-fructose isomerization follows rMM kinetics and hydrolysis of lactose follows Michaelis–Menten (MM) equation with competitive product (galactose) inhibition. Predictions of the developed third degree polynomial and AGM approximation equations agree with that of numerical solution, the percentage relative error for the effectiveness factor was less than 11 in comparison with the numerical solution. Good agreement between approximate and numerical estimations demonstrates the validity of these approximation methods.

Novel carbon nanozymes with enhanced phosphatase-like catalytic activity for antimicrobial applications

In this work, Sulfur and Nitrogen co-doped carbon nanoparticles (SN-CNPs) were synthesized by hydrothermal method using dried beet powder as the carbon source. TEM and AFM images indicated that these SN-CNPs form a round-shape ball with an approximate diameter of 50 nm. The presence of Sulfur and Nitrogen in these carbon-based nanoparticles was confirmed by FTIR and XPS analyses. These SN-CNPs were found to have strong phosphatase-like enzymatic activity. The enzymatic behavior of SN-CNPs follows the Michaelis–Menten mechanism with greater vmax and much lower Km values compared to alkaline phosphatase. Their antimicrobial properties were tested on E. coli and L. lactis, with MIC values of 63 μg mL−1 and 250 μg mL−1, respectively. SEM and AFM images of fixed and live E. coli cells revealed that SN-CNPs strongly interacted with the outer membranes of bacterial cells, significantly increasing the cell surface roughness. The chemical interaction between SN-CNPs and phospholipid modeled using quantum mechanical calculations further support our hypothesis that the phosphatase and antimicrobial properties of SN-CNPs are due to the thiol group on the SN-CNPs, which is a mimic of the cysteine-based protein phosphatase. The present work is the first to report carbon-based nanoparticles with strong phosphatase activity and propose a phosphatase natured antimicrobial mechanism. This novel class of carbon nanozymes has the potential to be used for effective catalytic and antibacterial applications.Graphical abstract

Optimization and Determination of Kinetic Parameters of the Synthesis of 5-Lauryl-hydroxymethylfurfural Catalyzed by Lipases

Hydroxymethylfurfural esters (HMF-esters) have great potential for additive development; for this reason, the goal of this work was to study the optimization of the esterification conversion of HFM and lauric acid using two lipases: the Novozym 435® biocatalyst and immobilized lipase from Thermomyces lanuginosus (TL). For the optimization of conversion, a three-level three-factorial Box–Behnken experimental design was used. The models achieved a good fit (R2 over 90%) for reactions catalyzed with Novozym 435® and immobilized TL lipase. The best conversion, 78.4%, was achieved with immobilized TL lipase using 30 mM HMF, 16 U of biocatalytic activity, and 50 °C. The kinetic parameters without inhibition by the substrate were determined using the Michaelis–Menten mechanism, whereby VMax for both biocatalysts reached the highest values at 50 °C, and the highest enzyme–substrate affinities (low Km) were reached at temperatures of 30 °C and 40 °C. It can be concluded that immobilized TL lipase has the potential to catalyze this reaction since, under optimal reaction conditions, an 80.6% conversion (value predicted) could be achieved.

Chemistry students’ conceptual difficulties and problem solving behavior in chemical kinetics, as a component of an introductory physical chemistry course

Abstract The identification of undergraduate chemistry students’ conceptual difficulties and common mistakes with basic concepts and problems in chemical kinetics provided the aim for this study, which involved 2nd-year/4th semester students who had passed the chemical kinetics component of a physical chemistry course. The study involved the analysis, evaluation and interpretation of students’ answers to the final examination in chemical kinetics. Three achievement groups, for the various topics, were identified: Group A, high achievement (mean ≈ 85%): (a) the steps in a chain-reaction mechanism, (b) integrated 1st- and 2nd-order rate laws; and (c) the Lindemann–Hinshelwood mechanism. Group B, intermediate achievement (mean ≈ 74%): (a) half-life, (b) instantaneous rate and the extent of reaction variable (ξ), (c) the Michaelis–Menten mechanism, and (d) theoretical rate law not asking for a final formula. Group C, low achievement (mean ≈ 54%): (a) experimental rate law and the reaction rate constant on the basis of an experimental-data table, (b) extracting the theoretical rate law, and (c) the Arrhenius equation. Students’ errors and misconceptions have also been identified. Successful students tended to respond well to straightforward questions on the theory of the subject, but had difficulties when solving problems. It is essential that teachers understand the potential of their students, especially possible misconceptions they may hold, and the teaching approaches that may contribute to overcoming the student difficulties. Problems in chemical kinetics can be very demanding both in terms of algebraic manipulations and conceptually. Teaching should focus on problem solving, with the emphasis on students themselves trying to solve the problems.

Reaction-path statistical mechanics of enzymatic kinetics.

We introduce a reaction-path statistical mechanics formalism based on the principle of large deviations to quantify the kinetics of single-molecule enzymatic reaction processes under the Michaelis-Menten mechanism, which exemplifies an out-of-equilibrium process in the living system. Our theoretical approach begins with the principle of equal a priori probabilities and defines the reaction path entropy to construct a new nonequilibrium ensemble as a collection of possible chemical reaction paths. As a result, we evaluate a variety of path-based partition functions and free energies by using the formalism of statistical mechanics. They allow us to calculate the timescales of a given enzymatic reaction, even in the absence of an explicit boundary condition that is necessary for the equilibrium ensemble. We also consider the large deviation theory under a closed-boundary condition of the fixed observation time to quantify the enzyme-substrate unbinding rates. The result demonstrates the presence of a phase-separation-like, bimodal behavior in unbinding events at a finite timescale, and the behavior vanishes as its rate function converges to a single phase in the long-time limit.

Fast reactions with non-interacting species in stochastic reaction networks.

We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total amounts). This makes their analysis complex. We examine stochastic reaction networks with non-interacting species that often appear in examples of interest (e.g. in the two-substrate Michaelis Menten mechanism). Non-interacting species typically appear as intermediate (or transient) chemical complexes that are depleted at a fast rate. We embed the Markov process of the reaction network into a one-parameter family under a two time-scale approach, such that molecules of non-interacting species are degraded fast. We derive simplified reaction networks where the non-interacting species are eliminated and that approximate the scaled Markov process in the limit as the parameter becomes small. Then, we derive sufficient conditions for such reductions based on the reaction network structure for both homogeneous and time-varying stochastic settings, and study examples and properties of the reduction.

On the quasi-steady-state approximation in an open Michaelis-Menten reaction mechanism.

The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis–Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the system with substrate inflow. We analyze quasi-steady-state scenarios for the open system attributable to singular perturbations, as well as less restrictive conditions. For both settings we obtain distinguished invariant manifolds and time scale estimates, and we highlight the special role of singular perturbation parameters in higher order approximations of slow manifolds. We close the paper with a discussion of distinguished invariant manifolds in the global phase portrait.

Electrochemical activity of the polycrystalline cerium oxide films for hydrogen peroxide detection

Abstract Polycrystalline cerium oxide thin films (15 nm) deposited on a glassy carbon substrate were used as an electrode in a mediator-free, non-enzymatic electrochemical sensor for hydrogen peroxide. The electrode surface was characterized by X-ray photoelectron spectroscopy, resonant photoelectron spectroscopy, scanning electron microscopy and atomic force microscopy. The electrode sensitivity, detection limit and pH range of sensor stability were determined by applying electrochemical techniques: cyclic voltammetry and chronoamperometry. It was found that the sensor reactivity to H2O2 is directly related to the presence of electroactive cerium centres of 3+ character on the electrode surface. The Michaelis–Menten mechanism of catalase-like activity of ceria film is suggested as an explanation of the data and discussed. The results confirmed the sensing abilities of technologically well-accessible nanostructured cerium oxide films for hydrogen peroxide detection without using a mediator, i.e. the enzymatic properties of CeO2/GC electrode.

Au@Cu2O core@shell nanocrystals as dual-functional catalysts for sustainable environmental applications

This work reports the synthesis of Au@Cu2O core@shell nanocrystals with controllable shell thicknesses and demonstrates their use as the dual-functional catalyst that can continuously operate under illumination and darkness conditions for efficient E. coli inactivation. On account of the peroxidase mimics of the Au core and Fenton reactivity of the Cu2O shell, the Au@Cu2O nanocrystals exhibit intrinsic peroxidase-like property with the reaction kinetics in accordance with the typical Michaelis–Menten mechanism. On the other hand, time-resolved photoluminescence spectra suggest the prevalence of pronounced charge separation for Au@Cu2O nanocrystals, an important advantage that is favourable for photocatalysis. By combining the photocatalytic capability with the peroxidase mimics features, Au@Cu2O nanocrystals can perform practical photocatalytic decomposition of E. coli under visible light illumination but still show vital activity towards E. coli inactivation after light illumination was turned off. The current study delivers a new catalyst configuration by exploiting the multiple functionalities of nanosized Au and Cu2O for advanced environmental and energy conversion applications.

Enhanced Peroxidase-like Activity of Mo6+-Doped Co3O4 Nanotubes for Ultrasensitive and Colorimetric l-Cysteine Detection

Doping with transition metal ions has been regarded as one of the most effective means to optimize the catalytic efficiency of metal oxides. In this work, a general approach for the fabrication of Mo6+-doped Co3O4 (Mo–Co3O4) nanotubes for peroxidase mimicking has been demonstrated via an electrospinning method combined with a calcination process. The prepared Mo–Co3O4 nanotubes exhibited a higher peroxidase-like catalytic activity than pure Co3O4 nanotubes, and the highest catalytic activity is achieved when the molar fraction of Mo is 2.0%. The catalytic kinetic of Mo–Co3O4 nanotubes follows a typical Michaelis–Menten mechanism, representing a strong affinity to H2O2 and 3,3′,5,5′-tetramethylbenzidine (TMB) substrates. Because of the high catalytic efficiency of the Mo–Co3O4 nanotubes, we have developed a facile and efficient strategy for the sensitive colorimetric determination of l-cysteine with a low detection limit of 24.2 nM. This detection limit is superior to many previous reported enzyme-like det...

Lipase catalyzed glycerolysis of ratfish liver oil at stirred tank basket reactor: A kinetic approach

Abstract The kinetics of the lipase (Novozym 435) catalyzed glycerolysis of ratfish liver oil has been studied at pilot plant scale. A model derived from a generalized Michaelis–Menten mechanism was developed to describe the rates of disappearance of triacylglycerols and diacylglyceryl ethers. Positive discrimination of the immobilized lipase against diacylglyceryl ether was accurately determined in the different data sets studied. More than 1.5 times faster glycerolysis of triacylglycerol compared to that of diacylglyceryl ethers was observed in each set of experiments investigated. Reutilization of the same batch of the biocatalysts was carried out in a stirred tank basket reactor to evaluate the enzyme inactivation. A first-order model for deactivation of the lipase was fit to the data sets. Three different sets of enzymatic glycerolysis were carried out. In all cases rapid inactivation of the immobilized lipase was observed. The half life of Novozym 435 under the glycerolysis conditions studied was approximately 145 h which indicates a deleterious effect of the reaction conditions assayed on lipase activity. After 5 lipase reutilizations of 24 h each, lipase was washed with hexane/ethanol 50/50 w/w but original lipase activity could not be fully restored.

Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism

In this paper, mathematical models of immobilized enzyme system that follow the Michaelis-Menten mechanism for both reversible and irreversible reactions are discussed. This model is based on the diffusion equations containing the non-linear term related to Michaelis-Menten kinetics. An approximate analytical technique employing the modified Adomian decomposition method is used to solve the non-linear reaction diffusion equation in immobilized enzyme system. The concentration profile of the substrate is derived in terms of all parameters. A simple expression of the substrate concentration is obtained as a function of the Thiele modulus and the Michaelis constant. The numerical solutions are compared with our analytical solutions for slab, cylinder and spherical pellet shapes. Satisfactory agreement for all values of the Thiele modulus and the Michaelis constant is noted. Graphical results and tabulated data are presented and discussed quantitatively to illustrate the solution.

Influence of Amine-Based Cationic Gemini Surfactants on Catalytic Activity of α-Chymotrypsin

The α-chymotrypsin activity was tested in aqueous media with the presence of novel cationic amine–based gemini surfactant, with different spacer chain lengths and head group size, and also compared with the cationic cetyltrimethylammonium bromide (CTAB) and cetyltriphenylphosphonium bromide (CTPB) surfactants and aqueous buffer only. The p-nitrophenyl acetate (PNPA) hydrolysis rate was monitored in the presence of the surfactant concentration at 30°C. Most of these gemini surfactants gave higher catalytic activity as compared to cationic CTAB and CTPB. The highest superactivity was measured in the presence of gemini 16-12-16, [dodecanediyl-1,12-bis(cetyldimethylammonium bromide)] surfactant at pH 7.5. The catalytic reaction follows the Michaelis–Menten mechanism. The catalytic rate constants, kcat, show the same profile that the catalytic affinity; KM being enhanced with increasing space chain length. The results are favorable for considering that the amine-based gemini surfactant influences more than both the aqueous and cationic micellar media.

Activity of α‐Chymotrypsin in Cationic and Nonionic Micellar Media: Ultraviolet and Fluorescence Spectroscopic Approach

ABSTRACTα‐Chymotrypsin (α‐CT) activity was measured in aqueous buffer with the following alkyltriphenylphosphonium bromide surfactants in the series cetyl, tetradecyl, and dodecyl as a tail length. For the sake of comparison with mixed micellar investigation on activity of α‐CT, cationic cetyltriphenylphosphonium bromide (CTPB) and nonionic surfactant Triton X‐100, Brij‐56, Brij‐35, Tween 20, and Igepal Co‐210 have been used. The p‐nitrophenyl acetate (PNPA) hydrolysis rate was determined at the surfactant concentration of both cationic and mixed micellar systems by a UV–vis spectrophotometer. The catalytic reaction follows the Michaelis–Menten mechanism, and the catalytic efficiency (kcat/KM) was evaluated for both homogeneous and mixed‐micellar media. The maximum catalytic efficiency was observed at 5 mM concentration of CTPB, but the highest catalytic efficiency, 572 M−1 s−1, was measured in the presence of mixed micellar (7.5 mM CTPB + 2.5 mM Tween‐20). The fluorescence (FL) spectra showed the differences of α‐CT conformations in the presence of cationic surfactants. The FL results suggest that the influence of cationic surfactant on proteolysis arises from the interaction with the α‐CT. The binding constant, ksv, of α‐CT with cationic aggregates was determined in the buffer using the Stern–Volmer equation by the fluorescence spectroscopic approach.

Cooperativity in CYP2E1 metabolism of acetaminophen and styrene mixtures

Risk assessment for exposure to mixtures of drugs and pollutants relies heavily on in vitro characterization of their bioactivation and/or metabolism individually and extrapolation to mixtures assuming no interaction. Herein, we demonstrated that in vitro CYP2E1 metabolic activation of acetaminophen and styrene mixtures could not be explained through the Michaelis–Menten mechanism or any models relying on that premise. As a baseline for mixture studies with styrene, steady-state analysis of acetaminophen oxidation revealed a biphasic kinetic profile that was best described by negative cooperativity (Hill coefficient=0.72). The best-fit mechanism for this relationship involved two binding sites with differing affinities (Ks=830μM and Kss=32mM). Introduction of styrene inhibited that reaction less than predicted by simple competition and thus provided evidence for a cooperative mechanism within the mixture. Likewise, acetaminophen acted through a mixed-type inhibition mechanism to impact styrene epoxidation. In this case, acetaminophen competed with styrene for CYP2E1 (Ki=830μM and Ksi=180μM for catalytic and effector sites, respectively) and resulted in cooperative impacts on binding and catalysis. Based on modeling of in vivo clearance, cooperative interactions between acetaminophen and styrene resulted in profoundly increased styrene activation at low styrene exposure levels and therapeutic acetaminophen levels. Current Michaelis–Menten based toxicological models for mixtures such as styrene and acetaminophen would fail to detect this concentration-dependent relationship. Hence, future studies must assess the role of alternate CYP2E1 mechanisms in bioactivation of compounds to improve the accuracy of interpretations and predictions of toxicity.

Kinetics of enzymatic reactions in lipid membranes containing domains

An appreciable part of enzymes operating in vivo is associated with lipid membranes. The function of such enzymes can be influenced by the presence of domains containing proteins and/or composed of different lipids. The corresponding experimental model-system studies can be performed under well controlled conditions, e.g., on a planar supported lipid bilayer or surface-immobilized vesicles. To clarify what may happen in such systems, we propose general kinetic equations describing the enzyme-catalyzed substrate conversion occurring via the Michaelis–Menten (MM) mechanism on a membrane with domains which do not directly participate in reaction. For two generic situations when a relatively slow reaction takes place primarily in or outside domains, we take substrate saturation and lateral substrate–substrate interactions at domains into account and scrutinize the dependence of the reaction rate on the average substrate coverage. With increasing coverage, depending on the details, the reaction rate reaches saturation via an inflection point or monotonously as in the conventional MM case. In addition, we show analytically the types of reaction kinetics occurring primarily at domain boundaries. In the physically interesting situation when the domain growth is fast on the reaction time scale, the latter kinetics are far from conventional. The opposite situation when the reaction is fast and controlled by diffusion has been studied by using the Monte Carlo technique. The corresponding results indicate that the dependence of the reaction kinetics on the domain size may be weak.

Kinetics of Enzymatic Degradation of High Molecular Weight Polysaccharides through a Nanopore: Experiments and Data-Modeling

The enzymatic degradation of long polysaccharide chains is monitored by nanopore detection. It follows a Michaelis-Menten mechanism. We measure the corresponding kinetic constants at the single molecule level. The simulation results of the degradation process allowed one to account for the oligosaccharide size distribution detected by a nanopore.

Mechanistic description of survival of irradiated cells: repair kinetics in Padé linear-quadratic or differential Michaelis–Menten model

Biophysical models for repair mechanisms for cell surviving fractions \(S_\mathrm{F}(D)\) after exposure to radiation are studied. The principal focus is on a novel theory, the Pade-linear quadratic (PLQ), or equivalently, the differential Michaelis–Menten radiobiological model, which predicts \(S_\mathrm{F}(D)\) as a function of the absorbed dose \(D\) in the form \(S_\mathrm{F}(D)=\exp {\{-(\alpha D+\beta D^2)/(1+\gamma D)\}}\), with a clear biological and clinical meaning of the three parameters \(\alpha , \beta \) and \(\gamma \). It is shown that this functional form in the PLQ model emerges directly from the simultaneous fulfillment of the requirements for the correct asymptotic behaviors of the repair function at low and high doses. Moreover, this automatically secures the purely exponential cell kill modes at both small and large \(D\), as also encountered in the corresponding experimental data for cell surviving fractions. Further, it is demonstrated that the PLQ-based repair function, given by a rectangular hyperbola, coincides with the reaction velocity for enzyme catalysis from the Michaelis–Menten mechanism. This repair velocity is the halved harmonic mean of the low- and high-dose asymptotes of the catalytic repair function. Such circumstances constitute a firm mechanistic basis of the PLQ model, which is shown to exhibit excellent agreement with measurements. Robust applications of the PLQ model are anticipated, especially in hypofractionted radiotherapy, such as stereotactic radiosurgery.