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

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...
Reaction Mechanisms: Rate-limiting Step Approximation01:29

Reaction Mechanisms: Rate-limiting Step Approximation

The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...
Reversible or Opposing Reactions01:26

Reversible or Opposing Reactions

Reversible or opposing reactions play a crucial role in understanding the dynamic nature of chemical processes. While kinetics focuses on how reactions proceed, thermodynamics emphasizes that most reactions do not reach completion. Instead, a reverse reaction starts occurring over time, and when its rate equals that of the forward reaction, a dynamic equilibrium is established.For example, consider a simple chemical process where A forms B reversibly. The rate constants for the forward and...
Multi-Step Reactions02:31

Multi-Step Reactions

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...
Predicting Reaction Outcomes02:24

Predicting Reaction Outcomes

Kinetics describes the rate and path by which a reaction occurs. In contrast, thermodynamics deals with state functions and describes the properties, behavior, and components of a system. It is not concerned with the path taken by the process and cannot address the rate at which a reaction occurs. Although it does provide information about what can happen during a reaction process, it does not describe the detailed steps of what appears on an atomic or a molecular level. On the other hand,...
Fundamental Mathematical Principles in Pharmacokinetics: Rate and Order of Reaction01:15

Fundamental Mathematical Principles in Pharmacokinetics: Rate and Order of Reaction

In pharmacokinetics, the rates and order of reactions play a crucial role in understanding how the body processes drugs and help us comprehend drug absorption, distribution, metabolism, and elimination. A critical concept in pharmacokinetics is the rate constant, which quantifies the speed of a reaction. It provides valuable information about the kinetics of drug elimination. The rate constant allows us to determine the rate at which drugs are eliminated from the body.
Pharmacokinetic reactions...

You might also read

Related Articles

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

Sort by
Same author

A method for the calculation of multi-layer shielding buildup factors based on extra-trees regression and equivalent iteration.

Journal of radiological protection : official journal of the Society for Radiological Protection·2026
Same author

Problems, Progress and Perspectives in Mathematical and Computational Biology.

Bulletin of mathematical biology·2026
Same author

Host size and parasite density impact on the efficacy and reproductive output of Pyemotes zhonghuajia, a biological control agent of potato tuber moth.

Experimental & applied acarology·2026
Same author

Inferring structure and parameters of stochastic reaction networks with logistic regression.

PloS one·2026
Same author

Instructed Diffuser With Temporal Condition Guidance for Offline Reinforcement Learning.

IEEE transactions on pattern analysis and machine intelligence·2026
Same author

An efficient point kernel method for rapid dose evaluation in dynamic virtual environment.

Journal of radiological protection : official journal of the Society for Radiological Protection·2025
Same journal

Slow Evolution Towards Generalism in a Model of Variable Dietary Range.

Bulletin of mathematical biology·2026
Same journal

CBINN: Cancer Biology-Informed Neural Network for Unknown Parameter Estimation and Missing Physics Identification.

Bulletin of mathematical biology·2026
Same journal

A Cost-Sensitive Behavioral Modeling Analysis of the Early Identification and Control of Infectious Diseases.

Bulletin of mathematical biology·2026
Same journal

Tracking Dynamics of Superspreading Through Contacts, Exposures, and Transmissions in Edge-Based Network Epidemics.

Bulletin of mathematical biology·2026
Same journal

The Exact Hypergeometric Posterior Method for Accurate Inference of Population Size from Mark-Recapture Data.

Bulletin of mathematical biology·2026
Same journal

Modeling, Analysis, and Optimal Control of Leukemic Cell Population Dynamics Under Therapy.

Bulletin of mathematical biology·2026
See all related articles

Related Experiment Video

Updated: May 11, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Stochastic analysis of reaction-diffusion processes.

Jifeng Hu1, Hye-Won Kang, Hans G Othmer

  • 1School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA.

Bulletin of Mathematical Biology
|May 31, 2013
PubMed
Summary
This summary is machine-generated.

This study develops a new computational algorithm for simulating reaction-diffusion systems, improving efficiency and accuracy in modeling chemical and biological processes across scales.

More Related Videos

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

Related Experiment Videos

Last Updated: May 11, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

Area of Science:

  • Computational Biology
  • Chemical Kinetics
  • Systems Biology

Background:

  • Reaction and diffusion processes are fundamental to modeling chemical and biological systems across diverse scales.
  • Existing methods for simulating these processes face challenges in accuracy and computational efficiency, particularly in spatially discretized systems.

Purpose of the Study:

  • To develop a novel computational algorithm for simulating reaction-diffusion systems.
  • To introduce methods for estimating compartment size and measuring fluctuations in discretized systems.
  • To enhance the efficiency and applicability of the Gillespie method for complex compartmental systems.

Main Methods:

  • Development of a master equation for spatially discretized reaction-diffusion systems.
  • Introduction of an estimator for optimal compartment size in simulations.
  • Proposal of a measure for quantifying fluctuations in discretized systems.
  • Implementation of a modified Gillespie algorithm with reaction aggregation and optimized tree search for computational cells.

Main Results:

  • The developed master equation provides a framework for modeling reaction-diffusion dynamics in discretized spaces.
  • The proposed estimator and fluctuation measure aid in accurate simulation setup and analysis.
  • The novel computational algorithm significantly improves the efficiency of simulating compartmental reaction-diffusion systems.

Conclusions:

  • The new algorithm and methods offer a more robust and efficient approach to simulating complex reaction-diffusion systems.
  • This work provides valuable tools for researchers in computational biology, chemical kinetics, and systems biology.
  • Addressing issues in general systems simulation is crucial for advancing our understanding of chemical and biological processes.