Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

394
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
394
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

390
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.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
390
Constraints and Statical Determinacy01:26

Constraints and Statical Determinacy

1.1K
In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
1.1K
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

384
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,...
384
Modeling with Differential Equations01:25

Modeling with Differential Equations

154
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
154
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

423
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
423

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Diclofenac and acetaminophen dim the acute-phase response but amplify expression of the iron regulator hepcidin in liver cancer cells.

Cell systems·2025
Same author

A linear pathway for inositol pyrophosphate metabolism revealed by 18O labeling and model reduction.

PLoS computational biology·2025
Same author

Pools of Independently Cycling Inositol Phosphates Revealed by Pulse Labeling with <sup>18</sup>O-Water.

Journal of the American Chemical Society·2025
Same author

Phase separation of initiation hubs on cargo is a trigger switch for selective autophagy.

Nature cell biology·2025
Same author

Characterizing the pharmacological interaction of the antimalarial combination artefenomel-piperaquine in healthy volunteers with induced blood-stage Plasmodium falciparum to predict efficacy in patients with malaria.

BMC medicine·2024
Same author

Population Pharmacokinetic Modeling of Adavosertib (AZD1775) in Patients with Solid Tumors.

Journal of clinical pharmacology·2024

Related Experiment Video

Updated: Mar 20, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.2K

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

Marcus Rosenblatt1, Jens Timmer2, Daniel Kaschek1

  • 1Institute of Physics, Albert Ludwig University of Freiburg Freiburg, Germany.

Frontiers in Cell and Developmental Biology
|June 1, 2016
PubMed
Summary

This study introduces a graph theory algorithm to derive non-negative, analytical steady-state expressions for biological models. This method improves parameter estimation by avoiding multiple solutions and ensuring optimization success.

Keywords:
biochemical reaction networksmulti-stabilitymultiplicitynon-linear ODE modelsparameter estimationpositive solutionssteady-statesuccess rate

More Related Videos

Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

10.2K
Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure
07:15

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Published on: April 25, 2025

1.2K

Related Experiment Videos

Last Updated: Mar 20, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.2K
Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

10.2K
Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure
07:15

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Published on: April 25, 2025

1.2K

Area of Science:

  • Systems Biology
  • Computational Biology
  • Biochemical Engineering

Background:

  • Ordinary differential equation (ODE) models are crucial for analyzing dynamical systems in biology.
  • Parameter estimation in complex biological ODE models is challenging due to high dimensionality.
  • Incorporating steady-state information reduces parameter space dimensionality but can lead to complex, non-linear equations or negative parameter values.

Purpose of the Study:

  • To develop a novel algorithm for deriving non-negative, analytical steady-state expressions for ODE models.
  • To address challenges associated with parameter estimation in biological systems.
  • To improve the success rate of parameter optimization in biochemical reaction networks.

Main Methods:

  • Utilized graph theory to identify and remove cyclic dependencies between dynamical variables.
  • Developed an algorithm to derive analytical steady-state expressions that are guaranteed to be non-negative.
  • Applied the method to biochemical reaction networks with mass-action, Hill-type kinetics, and inhibition terms.

Main Results:

  • The algorithm successfully derives non-negative, analytical steady-state expressions, avoiding issues with negative parameter constraints.
  • The method inherently prevents multiple steady-state solutions, simplifying optimization.
  • Parameter estimation using the derived expressions demonstrated a high success rate compared to other methods.

Conclusions:

  • The graph theory-based approach provides a robust and efficient method for incorporating steady-state information in ODE model parameter estimation.
  • This technique is broadly applicable to common biochemical network structures.
  • The developed algorithm enhances the reliability and success of parameter optimization in systems biology.