Michaelis-Menten Type Research Articles

Dynamic analysis of a modified Leslie-Gower model with Michaelis-Menten prey harvesting and additive allee effect on predator population

In the current study, the dynamics of a Leslie-Gower model have been studied considering the Allee effect in the growth of the predator and the Michaelis-Menten type harvesting effect on the prey from biological and theoretical perspectives. Key findings highlight how these effects influence the existence of positive equilibria, with local stability properties and potential bifurcation behaviors examined using the center manifold theorem and linearization. Criteria for saddle-node bifurcation are established through Sotomayor’s theorem, while the direction and stability of Hopf bifurcation are explored via the first Lyapunov exponent. An optimal control model is developed to promote sustainable ecosystem development, utilizing the harvesting rate as a control parameter. Further, a few numerical simulations validate our significant findings using phase portrait diagrams.

Nonlinear effects of partitioning and diffusion limitation on the efficiency of three-layer enzyme bioreactors and potentiometric biosensors

The nonlinear effects of the partitioning and diffusion limitation on the efficiency of enzyme-based bioreactors and potentiometric biosensors are investigated analytically and numerically using a three-layer mathematical model involving the Michaelis–Menten type reaction in the transient and steady states. Analytical expressions of the steady state substrate and reaction product concentrations and the bioreactor effectiveness as well as biosensor output potential are presented for the first and zero-order reaction rates. Mathematical modelling of the diffusion limiting membrane and the conditions under which the same values of the steady state characteristics are obtained when simulating the treated system at different values of the diffusion and distribution coefficients are investigated. The effective diffusion coefficients in the total diffusion layer consisting of the diffusion limiting membrane and the outer diffusion (Nernst) layer are applied to reduce the three-layer model to the corresponding two-layer model. The dynamics and behaviour of the substrate consumption rate, product emission rate, effectiveness factor and the output potential are numerically investigated.

Dynamics of a slow-fast Leslie-Gower predator-prey model with prey harvesting.

For the Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting, the known results are on the saddle-node bifurcation and the Hopf bifurcation of codimensions 1, the Bogdanov-Takens bifurcations of codimensions 2 and 3, and on the cyclicity of singular slow-fast cycles. Here, we focus on the global dynamics of the model in the slow-fast setting and obtain much richer dynamical phenomena than the existing ones, such as global stability of an equilibrium; an unstable canard cycle exploding to a homoclinic loop; coexistence of a stable canard cycle and an inner unstable homoclinic loop; and, consequently, coexistence of two canard cycles: a canard explosion via canard cycles without a head, canard cycles with a short head and a beard and a relaxation oscillation with a short beard. This last one should be a new dynamical phenomenon. Numerical simulations are provided to illustrate these theoretical results.

Dynamic Analysis of a Fractional-Modified Leslie-Gower Model with Predator Harvesting

This paper presents an investigation of a modified Leslie-Gower predator-prey model that incorporates fractional discrete-time Michaelis-Menten type prey harvesting. The analysis focuses on the topology of nonnegative interior fixed points, including their existence and stability dynamics. We derive conditions for the occurrence of flip and Neimark-Sacker bifurcations using the center manifold theorem and bifurcation theory. Numerical simulations, conducted with a computer package, are presented to demonstrate the consistency of the theoretical findings. Overall, our study sheds light on the complex dynamics that arise in this model and highlights the importance of considering fractional calculus in predator-prey systems with harvesting.

Dynamical Analysis of a Discrete Amensalism System with Michaelis–Menten Type Harvesting for the Second Species

Dynamical Analysis of a Discrete Amensalism System with Michaelis–Menten Type Harvesting for the Second Species

Periodic Dynamics of a Reaction-Diffusion-Advection Model with Michaelis–Menten Type Harvesting in Heterogeneous Environments

Periodic Dynamics of a Reaction-Diffusion-Advection Model with Michaelis–Menten Type Harvesting in Heterogeneous Environments

Oxidative transformation of methionine by pyridinium chlorochromate in aqueous DMF medium: A kinetic study

The Kinetics of Oxidative transformation of Methionine by pyridinium chlorochromate in aqueous DMF medium, containing perchloric acid has been studied. The rate of reaction was found to be of first order dependence on PCC, Methionine, and H+ ion Concentration. Michaelis–Menten type kinetics is observed respect to substrate. The increase in the rate of reaction with increase in acidity indicates the involvement of a protonated chromium(VI) species in the rate-determining step. The product of oxidation has been identified as methionine sulfoxide. The rate of reaction increased with increase in dielectric constant of the reaction medium. The plots of logkobs versus (D-1) / (2D+1) are non linear Indicating that there is an involvement of positive ion-dipole in the rate determining step. The activation parameters have been evaluated. On the basis of the experimental findings, a suitable mechanism and rate law has been proposed.

Patient resuscitated after cardiopulmonary arrest exhibits abnormally increased phenytoin metabolic rate due to unknown factors: a case report

BackgroundFosphenytoin (FOS) is a prodrug of phenytoin (PHT) with a metabolism that exhibits Michaelis–Menten-type kinetics. Genetic polymorphisms of the metabolic enzymes of PHT make it challenging to predict its plasma concentrations. High plasma PHT concentrations are typically problematic, and several causes have been elucidated. In contrast, cases of patients with low PHT plasma concentrations that did not increase despite the administration of appropriate PHT doses have been reported, and the causes may include changes in plasma protein-binding rates, genetic mutations, and concomitant use of drugs that induce liver enzymes; however, even these factors do not explain the low PHT plasma concentrations in some cases.Case presentationWe encountered the case of a patient with plasma PHT concentrations that were continuously < 0.7 µg/mL after daily use of FOS for seizures that occurred after cardiopulmonary arrest. We analyzed the protein-unbound fraction, urinary metabolites, and related genes to investigate the cause. False negatives due to the measurement method, errors in dosage and administration method, and increased excretion of PHT were excluded. Hepatic metabolic activity of PHT increased to 4.6–6.1 times the normal level. The S/R ratio of 5-(p-hydroxyphenyl)-5-phenylhydantoin-glucuronide, a major PHT metabolite, was normal at 15.2, suggesting increased activities of CYP2C9 and CYP2C19. Furthermore, the protein-unbound fraction of PHT was 5.2–6.9%, CYP2C19*17 was wild type, and there was no concomitant drug use to induce both enzymes.ConclusionsThe low PHT plasma concentration in this patient was found to be caused by increased hepatic metabolic activity that could not be explained by known factors. Careful monitoring is necessary to consider the possibility of increased hepatic metabolic activity in similar cases.

Kinetic and mechanistic studies in the Oxidative regeneration of carbonyl compounds from oximes by diethylammonium chlorochromate

The oxidative deoximination of several aldo- and keto-oximes by diethylammonium chlorochromate (DEACC), in dimethylsulphoxide (DMSO) exhibited a first order dependence on DEACC. A Michaelis-Menten type kinetics was observed with respect to oximes. The oxidation of ketoximes is slower than that of aldoximes. The rates of oxidation of aldoximes correlated well in terms of Pavelich-Taft dual substituent-parameter equation. The low positive value of polar reaction constant indicated a nucleophilic attack by a chromate-oxygen on the carbon. The reaction is subject to steric hindrance by the alkyl groups. The reaction of acetaldoxime has been studied in nineteen different organic solvents. The solvent effect has been analysed by multiparametric equations. A mechanism involving the formation of a cyclic intermediate, in the rate-determining step is suggested.

A kinetic and mechanistic study of oxidation of N-Acetyl-DL-Methionine by pyridinium chlorochromate in aqueous DMF medium

The Kinetics of Oxidative transformation of N-Acetyl-DL-Methionine by pyridinium chlorochromate in aqueous DMF medium, containing perchloric acid has been studied at 40 ℃. The rate of reaction was found to be of first order dependence on PCC, N-Acetyl-DL-Methionine, and H+ ion Concentration. Michaelis–Menten type kinetics is observed respect to substrate. The increase in the rate of reaction with increase in acidity indicates the involvement of a protonated chromium(VI) species in the rate-determining step. The product of oxidation has been identified as N-Acetyl-DL-Methionine sulfoxide. The rate of reaction increased with increase in dielectric constant of the reaction medium. The activation parameters have been evaluated. On the basis of the experimental findings, a suitable mechanism and rate law has been proposed.

Identification of UDP-glucuronosyltransferase (UGT) isoforms involved in the metabolism of Chlorophenols (CPs)

Chlorophenols (CPs) are a group of pollutants that pose a great threat to the environment, they are widely used in industrial and agricultural wastes, pesticides, herbicides, textiles, pharmaceuticals and plastics. Among CPs, pentachlorophenol was listed as one of the persistent organic pollutants (POPs) by the Stockholm convention. This study aims to identify the UDP-glucosyltransferase (UGT) isoforms involved in the metabolic elimination of CPs. CPs’ mono-glucuronide was detected in the human liver microsomes (HLMs) incubation mixture with co-factor uridine-diphosphate glucuronic acid (UDPGA). HLMs-catalyzed glucuronidation metabolism reaction equations followed Michaelis-Menten or substrate inhibition type. Recombinant enzymes and chemical reagents inhibition experiments were utilized to phenotype the main UGT isoforms involved in the glucuronidation of CPs. UGT1A6 might be the major enzyme in the glucuronidation of mono-chlorophenol isomer. UGT1A1, UGT1A6, UGT1A9, UGT2B4 and UGT2B7 were the most important five UGT isoforms for metabolizing the di-chlorophenol and tri-chlorophenol isomers. UGT1A1 and UGT1A3 were the most important UGT isoforms in the catalysis of tetra-chlorophenol and pentachlorophenol isomers. Species differences were investigated using rat liver microsomes (RLMs), pig liver microsomes (PLMs), dog liver microsomes (DLMs), and monkey liver microsomes (MyLMs). All these results were helpful for elucidating the metabolic elimination and toxicity of CPs.

Nitrogen and phosphorus uptake kinetics in cultures of two novel picoplankton groups responsible for a recent bloom event in a subtropical estuary (Indian River Lagoon, Florida)

IntroductionSuccessful management and mitigation of harmful algal blooms (HABs) requires an in-depth understanding of the physiology and nutrient utilization of the organisms responsible. We explored the preference of various nitrogen (N) and phosphorus (P) substrates by two novel groups of HAB-forming phytoplankton originating from the Indian River Lagoon (IRL), Florida: 1) a consortium of picocyanobacteria (Crocosphaera sp. and ‘Synechococcus’ sp.) and 2) ananochlorophyte (Picochlorum sp.).MethodsShort-term kinetic uptake experiments tested algal use and affinity for inorganic and organic N substrates (ammonium (NH4+), nitrate (NO3-), urea, and an amino acid (AA) mixture) through 15N and 13C isotope tracing into biomass.ResultsPicocyanobacteria exhibited Michaelis-Menten type uptake for the AA mixture only, while nanochlorophytes reached saturation for NH4+, the AA mixture, and urea at or below 25 µM-N. Both picocyanobacteria and nanochlorophyte cultures had highest affinity (Vmax/Ks) for NH4+ followed by the AA mixture and urea. Neither culture showed significant uptake of isotopically-labeled nitrate. Disappearance of glucose-6-phosphate (G6P) added to culture medium suggesting use of organic P by both cultures was confirmed by detection of alkaline phosphatase activity and the tracing of 13C-G6P into biomass.DiscussionTogether, our results suggest that these HAB-forming phytoplankton groups are able to use a variety of N and P sources including organic forms, and prefer reduced forms of N. These traits are likely favorable under conditions found in the IRL during periods of significant competition for low concentrations of inorganic nutrients. Bloom-forming phytoplankton are therefore able to subsist on organic or recycled forms of N and P that typically dominate the IRL nutrient pools.

Global Hopf Bifurcation of a Diffusive Modified Leslie–Gower Predator–Prey Model with Delay and Michaelis–Menten Type Prey Harvesting

Global Hopf Bifurcation of a Diffusive Modified Leslie–Gower Predator–Prey Model with Delay and Michaelis–Menten Type Prey Harvesting

Theory on the rate equations of Michaelis-Menten type enzyme kinetics with competitive inhibition.

We derive approximate expressions for pre- and post-steady state regimes of the velocity-substrate-inhibitor spaces of the Michaelis-Menten enzyme kinetic scheme with fully and partial competitive inhibition. Our refinement over the currently available standard quasi steady state approximation (sQSSA) seems to be valid over wide range of enzyme to substrate and enzyme to inhibitor concentration ratios. Further, we show that the enzyme-inhibitor-substrate system can exhibit temporally well-separated two different steady states with respect to both enzyme-substrate and enzyme-inhibitor complexes under certain conditions. We define the ratios fS = vmax/(KMS + e0) and fI = umax/(KMI + e0) as the acceleration factors with respect to the catalytic conversion of substrate and inhibitor into their respective products. Here KMS and KMI are the Michaelis-Menten parameters associated respectively with the binding of substrate and inhibitor with the enzyme, vmax and umax are the respective maximum reaction velocities and e0, s0, and i0 are total enzyme, substrate and inhibitor levels. When (fS/fI) < 1, then enzyme-substrate complex will show multiple steady states and it reaches the full-fledged steady state only after the depletion of enzyme-inhibitor complex. When (fS/fI) > 1, then the enzyme-inhibitor complex will show multiple steady states and it reaches the full-fledged steady state only after the depletion of enzyme-substrate complex. This multi steady-state behavior especially when (fS/fI) ≠ 1 is the root cause of large amount of error in the estimation of various kinetic parameters of fully and partial competitive inhibition schemes using sQSSA. Remarkably, we show that our refined expressions for the reaction velocities over enzyme-substrate-inhibitor space can control this error more significantly than the currently available sQSSA expressions.

High codimension bifurcations analysis in a predator-prey system with Michaelis-Menten type predator harvesting

High codimension bifurcations analysis in a predator-prey system with Michaelis-Menten type predator harvesting

Stability and Hopf bifurcation of an intraguild prey-predator fishery model with two delays and Michaelis-Menten type predator harvest.

In this paper, we have proposed and investigated an intraguild predator-prey system incorporating two delays and a harvesting mechanism based on the Michaelis-Menten principle, and it was assumed that the two species compete for a shared resource. Firstly, we examined the properties of the relevant characteristic equations to derive sufficient conditions for the asymptotical stability of equilibria in the delayed model and the existence of Hopf bifurcation. Using the normal form method and the central manifold theorem, we analyzed the stability and direction of periodic solutions arising from Hopf bifurcations. Our theoretical findings were subsequently validated through numerical simulations. Furthermore, we explored the impact of harvesting on the quantity of biological resources and examined the critical values associated with the two delays.

Fractional dynamics and computational analysis of food chain model with disease in intermediate predator

&lt;abstract&gt; &lt;p&gt;In this paper, a fractional food chain system consisting of a Holling type Ⅱ functional response was studied in view of a fractional derivative operator. The considered fractional derivative operator provided nonsingular as well as a nonlocal kernel which was significantly better than other derivative operators. Fractional order modeling of a model was also useful to model the behavior of real systems and in the investigation of dynamical systems. This model depicted the relationship among four types of species: prey, susceptible intermediate predators (IP), infected intermediate predators, and apex predators. One of the significant aspects of this model was the inclusion of Michaelis-Menten type or Holling type Ⅱ functional response to represent the predator-prey link. A functional response depicted the rate at which the normal predator consumed the prey. The qualitative property and assumptions of the model were discussed in detail. The present work discussed the dynamics and analytical behavior of the food chain model in the context of fractional modeling. This study also examined the existence and uniqueness related analysis of solutions to the food chain system. In addition, the Ulam-Hyers stability approach was also discussed for the model. Moreover, the present work examined the numerical approach for the solution and simulation for the model with the help of graphical presentations.&lt;/p&gt; &lt;/abstract&gt;

A Simultaneous Denitrification and Fermentation Process for Nitrate Removal in a Whiteleg Shrimp (Litopenaeus vannamei) Recirculating Aquaculture System: Using Endogenous Carbon from a Biofilm

During the process of circulating aquaculture, high concentrations of nitrate will accumulate. A simultaneous denitrification and fermentation process is described to remove nitrate from a recirculating aquaculture system using endogenous carbon on a biofilm. 15N isotope technology was used to assess the nitrate removal, mainly through heterotrophic denitrification. The nitrate removal rate could be as high as 98.97%, with a final concentration of nitrate below 1 mg/L. The denitrification process obeys a Michaelis–Menten-type enzyme kinetic model, with a half saturation constant of 99.91 mg/L and a maximum nitrate removal rate of 0.39 mg L−1 h−1 at 28 °C. The functional genes narG and narH for nitrate removal were obtained from Nitrospirae spp. at proportions of 39.13% and 26.16%, respectively. The acetate, propionate and iso-valerate produced by anaerobic fermentation provided the principal electron donors for denitrification.

Light and temperature controls of aquatic plant photosynthesis downstream of a hydropower plant and the effect of plant removal

Many rivers worldwide are regulated, and the altered hydrology can lead to mass development of aquatic plants. Plant invasions are often seen as a nuisance for human activities leading to costly remedial actions with uncertain implications for aquatic biodiversity and ecosystem functioning. Mechanical harvesting is often used to remove aquatic plants and knowledge of plant growth rate could improve management decisions. Here, we used a simple light-temperature theoretical model to make a priori prediction of aquatic plant photosynthesis. These predictions were assessed through an open-channel diel change in O2 mass balance approach. A Michaelis-Menten type model was fitted to observed gross primary production (GPP) standardised at 10 °C using a temperature dependence from thermodynamic theory of enzyme kinetics. The model explained 87 % of the variability in GPP of a submerged aquatic plant (Juncus bulbosus L.) throughout an annual cycle in the River Otra, Norway. The annual net plant production was about 2.4 (1.0–3.8) times the standing biomass of J. bulbosus. This suggests a high continuous mass loss due to hydraulic stress and natural mechanical breakage of stems, as the biomass of J. bulbosus remained relatively constant throughout the year. J. bulbosus was predicted to be resilient to mechanical harvesting with photosynthetic capacity recovered within two years following 50–85 % plant removal. The predicted recovery was confirmed through a field experiment where 72 % of J. bulbosus biomass was mechanically removed. We emphasise the value of using a theoretical approach, like metabolic theory, over statistical models where a posteriori results are not always easy to interpret. Finally, the ability to predict ecosystem resilience of aquatic photosynthesis in response to varying management scenarios offers a valuable tool for estimating aquatic ecosystem services, such as carbon regulation. This tool can benefit the EU Biodiversity Strategy and UN Sustainable Development Goals.

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.