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Related Concept Videos

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

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Related Experiment Video

Updated: Jul 4, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Optimal parameterization of nonequilibrium generalized master equations from discrete-time experimental data.

Chih-Wei Joshua Liu, Jérémie Klinger, Grant M Rotskoff

    Arxiv
    |July 3, 2026
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a new method to analyze complex molecular systems using discrete-time generalized master equations (GMEs). This approach accurately captures system memory, offering a powerful alternative to traditional Markov state models (MSMs) for experimental and simulation data.

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    Last Updated: Jul 4, 2026

    An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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    Published on: December 4, 2017

    Spin Saturation Transfer Difference NMR (SSTD NMR): A New Tool to Obtain Kinetic Parameters of Chemical Exchange Processes
    11:44

    Spin Saturation Transfer Difference NMR (SSTD NMR): A New Tool to Obtain Kinetic Parameters of Chemical Exchange Processes

    Published on: November 12, 2016

    Area of Science:

    • Biophysics
    • Computational Chemistry
    • Chemical Kinetics

    Background:

    • Kinetic analyses often rely on coarse-grained models, but complex systems frequently violate assumptions of Markovianity and thermodynamic equilibrium.
    • Memory effects are common in coarse-grained descriptions, posing challenges for traditional Markov state models (MSMs).
    • Generalized master equations (GMEs) can capture memory but are difficult to parameterize and often approximate in discrete time.

    Purpose of the Study:

    • To develop a maximum-likelihood-based procedure for parameterizing formally exact, physically feasible, discrete-time GMEs.
    • To provide a statistically principled method for analyzing biomolecular kinetics from experimental and simulation data, both in and out of equilibrium.

    Main Methods:

    • Adapted optimal transport algorithms to construct conditional-maximum-likelihood estimators for discrete-time GMEs.
    • Developed estimators for exact Nakajima-Zwanzig memory kernels and time-convolutionless GME propagators.
    • Applied the method to Förster-resonance energy-transfer experiments, nanoparticle tracking, and protein folding simulations.

    Main Results:

    • Successfully parameterized discrete-time GMEs from experimental and simulation data.
    • Recovered key kinetic parameters including relaxation rates, irreversibilities, dwell times, and first-passage times.
    • Demonstrated the ability to capture memory effects in complex systems.

    Conclusions:

    • Discrete-time GMEs offer a physically and statistically rigorous framework for kinetic analysis.
    • This method provides a viable alternative to MSMs for studying complex biomolecular systems.
    • The developed procedure enables accurate kinetic parameter estimation from diverse experimental and simulation data.