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: Rate-limiting Step Approximation01:29

Reaction Mechanisms: Rate-limiting Step Approximation

15
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...
15
Multi-Step Reactions02:31

Multi-Step Reactions

8.9K
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...
8.9K
Chemical Equilibria: Systematic Approach to Equilibrium Calculations01:21

Chemical Equilibria: Systematic Approach to Equilibrium Calculations

1.8K
Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
The first step is to identify all the chemical reactions involved, The...
1.8K
Fundamental Mathematical Principles in Pharmacokinetics: Rate and Order of Reaction01:15

Fundamental Mathematical Principles in Pharmacokinetics: Rate and Order of Reaction

1.3K
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...
1.3K
Consecutive Reactions01:22

Consecutive Reactions

12
Consecutive reactions involve a sequence where the product of a preceding reaction becomes the reactant for the subsequent one. In a simple scheme, A transforms into B, which further reacts to form C, with rate constants k1 and k2, respectively. This concept is evident in the radioactive decay series. Assuming an initial state with only A present, the conservation of matter leads to three coupled differential equations, determining the concentrations of A, B, and C over time.The rate of change...
12
The Integrated Rate Law: The Dependence of Concentration on Time02:39

The Integrated Rate Law: The Dependence of Concentration on Time

46.3K
While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
46.3K

You might also read

Related Articles

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

Sort by
Same author

Reaction, diffusion, and nonlocal interaction in high-dimensional space.

Journal of mathematical biology·2026
Same author

Correction to: Reaction, diffusion and non-local interaction.

Journal of mathematical biology·2026
Same author

Propagation and blocking of bistable waves by variable diffusion.

Journal of mathematical biology·2025
Same author

Rheocarna treatment for non-dialysis patients.

Therapeutic apheresis and dialysis : official peer-reviewed journal of the International Society for Apheresis, the Japanese Society for Apheresis, the Japanese Society for Dialysis Therapy·2025
Same author

Title: Identification of Redox State Based on the Difference in Solvation Dynamics.

ChemistryOpen·2025
Same author

Investigation of treatment volume versus circulating blood volume during Rheocarna treatment.

Therapeutic apheresis and dialysis : official peer-reviewed journal of the International Society for Apheresis, the Japanese Society for Apheresis, the Japanese Society for Dialysis Therapy·2024
Same journal

Atypical Cadherin Fat2 is Involved in Axogenesis of Cerebellar Granule Cells in Zebrafish.

Development, growth & differentiation·2026
Same journal

Sbno1 and Usp8 Cooperate to Enhance Notch Signaling in Regulating Neural Stem Cells.

Development, growth & differentiation·2026
Same journal

Computer-Aided Sperm Analysis Protocol for Evaluating Sperm Motility in Japanese Medaka.

Development, growth & differentiation·2026
Same journal

Cooperative Roles of Pds5a and Pds5b Constrain Long-Range Chromatin Interactions in Vertebrate Embryos.

Development, growth & differentiation·2026
Same journal

Derepression of a Subset of Meiotic Proteins in Primordial Germ Cells of max Mutant Zebrafish.

Development, growth & differentiation·2026
Same journal

Convergence of Cell Biology and Developmental Biology: A Report of the Joint Meeting of the 77th JSCB and the 58th JSDB.

Development, growth & differentiation·2026
See all related articles

Related Experiment Video

Updated: Mar 1, 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

8.5K

Mathematical approach to nonlocal interactions using a reaction-diffusion system.

Yoshitaro Tanaka1, Hiroko Yamamoto2, Hirokazu Ninomiya3

  • 1Department of Mathematics, Faculty of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo, Hokkaido, 060-0810, Japan.

Development, Growth & Differentiation
|June 3, 2017
PubMed
Summary
This summary is machine-generated.

Nonlocal interactions in development integrate microscopic details but obscure mechanisms. This review introduces a new method to convert these interactions into reaction-diffusion systems for clearer understanding.

Keywords:
mathematical modelingnonlocal interactionreaction-diffusion approximationreduction

More Related Videos

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
12:15

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy

Published on: April 9, 2019

9.3K
Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.8K

Related Experiment Videos

Last Updated: Mar 1, 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

8.5K
Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
12:15

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy

Published on: April 9, 2019

9.3K
Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.8K

Area of Science:

  • Developmental biology
  • Mathematical biology
  • Systems biology

Background:

  • Spatial long-range interactions, termed nonlocal interactions, are crucial in developmental processes, integrating molecular events and signaling networks.
  • While useful for pattern generation via numerical simulations, nonlocal interactions can obscure specific underlying mechanisms due to information integration.

Purpose of the Study:

  • To present a heuristic understanding of nonlocal interactions in biological systems.
  • To introduce a novel method for converting nonlocal interactions into a more tractable reaction-diffusion system.

Main Methods:

  • Review of biological and mathematical studies related to nonlocal interactions.
  • Introduction of a new method converting nonlocal interactions into reaction-diffusion systems with auxiliary variables.

Main Results:

  • Demonstration that reaction-diffusion systems with auxiliary variables can effectively represent nonlocal interactions.
  • Facilitation of pattern generation analysis without detailed microscopic event simulation.

Conclusions:

  • The proposed reaction-diffusion system approach offers a simplified yet insightful way to study complex biosystems governed by nonlocal interactions.
  • This method aids in understanding developmental pattern formation by bridging the gap between integrated nonlocal information and observable mechanisms.