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Nonlinear Pharmacokinetics: Michaelis-Menten Equation01:18

Nonlinear Pharmacokinetics: Michaelis-Menten Equation

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The Michaelis–Menten equation is a fundamental model for describing capacity-limited kinetics in drug metabolism. It offers insights into the rate of decline of plasma drug concentration Cp over time, with Vmax and KM as pivotal parameters.
Vmax represents the maximum achievable process rate, while KM, known as the Michaelis constant, signifies the drug concentration at which the process rate reaches half its maximum. This relationship between Vmax, KM, and Cp gives rise to three distinct...
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Introduction to Enzyme Kinetics01:19

Introduction to Enzyme Kinetics

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Enzyme kinetics studies the rates of biochemical reactions. Scientists monitor the reaction rates for a particular enzymatic reaction at various substrate concentrations. Additional trials with inhibitors or other molecules that affect the reaction rate may also be performed.
The experimenter can then plot the initial reaction rate or velocity (Vo) of a given trial against the substrate concentration ([S]) to obtain a graph of the reaction properties. For many enzymatic reactions involving a...
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Enzyme Kinetics01:19

Enzyme Kinetics

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Enzymes speed up reactions by lowering the activation energy of the reactants. The speed at which the enzyme turns reactants into products is called the rate of reaction. Several factors impact the rate of reaction, including the number of available reactants. Enzyme kinetics is the study of how an enzyme changes the rate of a reaction.
Scientists typically study enzyme kinetics with a fixed amount of enzyme in the controlled environment of a test tube. When more reactant, or substrate, is...
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Two-Compartment Open Model: Extravascular Administration01:12

Two-Compartment Open Model: Extravascular Administration

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The two-compartment model for extravascular administration represents a drug's absorption and distribution process. It features a central compartment, where the drug is first absorbed, and a peripheral compartment, which illustrates the drug's distribution throughout the body. The rate of change in drug concentration in the central compartment is calculated by three exponents: absorption, distribution, and elimination.
The absorption exponent (ka) indicates the speed at which the drug...
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Multi-Step Reactions02:31

Multi-Step Reactions

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Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

962
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
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Related Experiment Video

Updated: Dec 2, 2025

Steady-state, Pre-steady-state, and Single-turnover Kinetic Measurement for DNA Glycosylase Activity
14:27

Steady-state, Pre-steady-state, and Single-turnover Kinetic Measurement for DNA Glycosylase Activity

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Stochastic time-dependent enzyme kinetics: Closed-form solution and transient bimodality.

James Holehouse1, Augustinas Sukys1, Ramon Grima1

  • 1School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom.

The Journal of Chemical Physics
|November 3, 2020
PubMed
Summary

We developed a new approximate solution for enzyme kinetics, revealing transient bimodality in substrate distribution not seen in deterministic models. This method accurately captures enzyme number fluctuations for better Michaelis-Menten reaction modeling.

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Area of Science:

  • Biochemistry
  • Chemical Kinetics
  • Computational Biology

Background:

  • The Michaelis-Menten mechanism is fundamental to enzyme kinetics.
  • Stochastic effects are crucial in understanding enzyme-catalyzed reactions, especially at low molecule numbers.
  • Existing approximations may not fully capture the dynamics of enzyme number fluctuations.

Purpose of the Study:

  • To derive an approximate closed-form solution for the chemical master equation of the Michaelis-Menten reaction.
  • To investigate the time-dependent probability distributions of substrate and enzyme molecules.
  • To compare the derived solution with existing approximations, particularly regarding enzyme number fluctuations.

Main Methods:

  • Derivation of a closed-form solution to the chemical master equation under specific assumptions (dissociation probability >> product formation).
  • Analysis of time-dependent marginal probability distributions for substrate and enzyme numbers.
  • Stochastic simulation of elementary reaction steps for validation.

Main Results:

  • An approximate closed-form solution was obtained for the Michaelis-Menten reaction mechanism.
  • Transient bimodality in substrate distribution was identified under specific conditions (high initial substrate, high binding frequency), a phenomenon absent in deterministic models.
  • The derived solution demonstrates improved accuracy over a wider parameter range compared to the discrete stochastic Michaelis-Menten approximation, particularly by accounting for enzyme number fluctuations.

Conclusions:

  • The derived closed-form solution provides a more accurate description of the Michaelis-Menten reaction dynamics by incorporating enzyme number fluctuations.
  • Transient bimodality is a key stochastic feature that can emerge in enzyme kinetics under certain conditions.
  • This work offers a refined computational tool for studying enzyme mechanisms with greater fidelity.