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

Rate Law and Reaction Order02:33

Rate Law and Reaction Order

11.3K
The rate of a reaction is affected by the concentrations of reactants. Rate laws (differential rate laws) or rate equations are mathematical expressions describing the relationship between the rate of a chemical reaction and the concentration of its reactants.
For example, in a generic reaction aA + bB ⟶ products, where a and b are stoichiometric coefficients, the rate law can be written as:
rate = k[A]m[B]n
[A] and [B] represent the molar concentrations of reactants, and k is the rate...
11.3K
Diffusion01:12

Diffusion

217.9K
Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
217.9K
Concentration and Rate Law03:03

Concentration and Rate Law

38.2K
The rate of a reaction is affected by the concentrations of reactants. Rate laws (differential rate laws) or rate equations are mathematical expressions describing the relationship between the rate of a chemical reaction and the concentration of its reactants.
For example, in a generic reaction aA + bB ⟶ products, where a and b are stoichiometric coefficients, the rate law can be written as:
38.2K
Second Law of Thermodynamics02:49

Second Law of Thermodynamics

26.9K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
26.9K
Scientific Laws and Theories02:31

Scientific Laws and Theories

87.9K
Scientific Laws
87.9K
Determining Order of Reaction02:53

Determining Order of Reaction

61.9K
Rate laws describe the relationship between the rate of a chemical reaction and the concentration of its reactants. In a rate law, the rate constant k and the reaction orders are determined experimentally by observing how the rate of reaction changes as the concentrations of the reactants are changed. A common experimental approach to the determination of rate laws is the method of initial rates. This method involves measuring reaction rates for multiple experimental trials carried out using...
61.9K

You might also read

Related Articles

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

Sort by
Same author

Universal Precision Limits in General Open Quantum Systems.

Physical review letters·2026
Same author

Macroscopic particle transport in dissipative long-range bosonic systems.

Nature communications·2026
Same author

Thermodynamic entropic uncertainty relation.

Physical review. E·2025
Same author

Fundamental Precision Limits in Finite-Dimensional Quantum Thermal Machines.

Physical review letters·2025
Same author

Quantum-computer-based verification of quantum thermodynamic uncertainty relation.

Physical review. E·2025
Same author

Thermomajorization Mpemba Effect.

Physical review letters·2025
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles

Related Experiment Video

Updated: Jan 29, 2026

From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope
15:10

From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope

Published on: October 9, 2014

11.9K

Diffusion-dynamics laws in stochastic reaction networks.

Tan Van Vu1, Yoshihiko Hasegawa1

  • 1Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.

Physical Review. E
|February 21, 2019
PubMed
Summary
This summary is machine-generated.

Diffusion

More Related Videos

Quantification of Protein Interaction Network Dynamics using Multiplexed Co-Immunoprecipitation
07:57

Quantification of Protein Interaction Network Dynamics using Multiplexed Co-Immunoprecipitation

Published on: August 21, 2019

9.1K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

4.1K

Related Experiment Videos

Last Updated: Jan 29, 2026

From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope
15:10

From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope

Published on: October 9, 2014

11.9K
Quantification of Protein Interaction Network Dynamics using Multiplexed Co-Immunoprecipitation
07:57

Quantification of Protein Interaction Network Dynamics using Multiplexed Co-Immunoprecipitation

Published on: August 21, 2019

9.1K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

4.1K

Area of Science:

  • Computational Biology
  • Chemical Kinetics
  • Systems Biology

Background:

  • Cellular processes rely on chemical reactions involving diffusing molecules.
  • Stochastic reaction networks model these complex biological systems.
  • Previous studies suggest diffusion significantly impacts gene regulatory network fluctuations.

Purpose of the Study:

  • To elucidate the universal relationship between diffusion and stochastic dynamics in reaction networks.
  • To determine conditions under which diffusion's effects can be neglected.
  • To understand diffusion's influence on the fluctuations within biological systems.

Main Methods:

  • Utilizing the reaction-diffusion master equation (RDME) approximation.
  • Analyzing complex balanced networks and their steady-state distributions.
  • Deriving conditions for Poisson-like steady-state distributions.
  • Investigating linear reaction networks.

Main Results:

  • Steady-state distributions in complex balanced networks are independent of diffusion.
  • Diffusion can be ignored in networks with Poisson-like steady-state distributions.
  • A necessary and sufficient condition for such distributions was derived.
  • For linear networks, RDME simplifies to the chemical master equation, negating diffusion's effect at any time.

Conclusions:

  • Diffusion's impact on stochastic dynamics is system-dependent.
  • Provides criteria for neglecting diffusion in modeling biological systems.
  • Clarifies the role of diffusion in gene regulatory networks and beyond.