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Related Concept Videos

Diffusion01:12

Diffusion

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...
Diffusion01:21

Diffusion

Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
Protein Diffusion in the Membrane01:24

Protein Diffusion in the Membrane

Proteins show rotational as well as lateral diffusion across the membrane. The lateral diffusion of proteins was confirmed through the cell fusion experiment where mouse and human cells were fused, resulting in hybrid cells. When the human and mouse cells fused, the specific membrane proteins on human and mouse cells were marked with the red and green-fluorescent markers, respectively. Initially, the red and green fluorescence was located on the respective hemisphere of the cell. As time...
Fast Reactions01:27

Fast Reactions

Fast reactions occurring in times shorter than the time needed to mix reactants pose a unique challenge for investigation. In a liquid-phase continuous-flow system, reactants A and B are swiftly pushed into the mixing chamber, where mixing occurs within 1 ms. The reaction mixture then flows through an observation tube, and one measures light absorption to determine species concentrations at various points of the tube. This method is most appropriate when relatively large volumes of reactants...
Temperature Dependence on Reaction Rate02:55

Temperature Dependence on Reaction Rate

The Collision Theory
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. This premise is the basis for a theory that explains many observations regarding chemical kinetics, including factors affecting reaction rates.
The collision theory is based on the postulates that (i) the reaction rate is proportional to the rate of reactant collisions, (ii) the reacting species collide in an orientation allowing contact between...
Consecutive Reactions01:22

Consecutive Reactions

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...

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Related Experiment Video

Updated: Jun 26, 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

Cross-diffusion and pattern formation in reaction-diffusion systems.

Vladimir K Vanag1, Irving R Epstein

  • 1Department of Chemistry and Volen Center for Complex Systems, MS015, Brandeis University, 415 South St., Waltham, MA 02454, USA. vanag@brandeis.edu

Physical Chemistry Chemical Physics : PCCP
|January 30, 2009
PubMed
Summary
This summary is machine-generated.

Cross-diffusion, where one chemical’s concentration gradient drives another’s flux, significantly impacts reaction-diffusion systems. This phenomenon can create spatial patterns, even when not initially present among reacting species.

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Last Updated: Jun 26, 2026

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Spot Variation Fluorescence Correlation Spectroscopy for Analysis of Molecular Diffusion at the Plasma Membrane of Living Cells

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Area of Science:

  • Chemical kinetics and physical chemistry.
  • Non-equilibrium thermodynamics and complex systems.

Background:

  • Cross-diffusion is often overlooked in reaction-diffusion systems.
  • Its coefficients can be substantial, particularly in systems with ions, micelles, or complex formations.
  • Excluded volume effects also highlight the importance of cross-diffusion.

Purpose of the Study:

  • To highlight the significance of cross-diffusion in reaction-diffusion systems.
  • To demonstrate the role of cross-diffusion in pattern formation.
  • To explore pattern formation induced by nonreactive species via cross-diffusion.

Main Methods:

  • Review of experimental evidence for significant cross-diffusion coefficients.
  • Model calculations to investigate pattern formation.
  • Analysis of systems with and without cross-diffusion among reactive species.

Main Results:

  • Cross-diffusion coefficients can exceed diagonal diffusion coefficients.
  • Cross-diffusion can induce spatial and spatiotemporal pattern formation in simple systems.
  • Nonreactive species can also drive pattern formation through cross-diffusive fluxes.

Conclusions:

  • Cross-diffusion is a crucial factor in reaction-diffusion systems, not to be neglected.
  • It plays a key role in the emergence of complex spatial structures.
  • Understanding cross-diffusion opens new avenues for controlling pattern formation in chemical systems.