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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...
Passive Diffusion: Overview and Kinetics01:17

Passive Diffusion: Overview and Kinetics

Passive diffusion is a critical process that allows small lipophilic drugs to cross the cell membrane along a concentration gradient. This mechanism's efficiency depends on four primary factors: the membrane's surface area, the drug's lipid-water partition coefficient, the concentration gradient, and the membrane's thickness.
When administered orally, drugs establish a substantial concentration gradient between the gastrointestinal (GI) lumen and the bloodstream, expediting their diffusion into...
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...
Dynamic Equilibrium02:20

Dynamic Equilibrium

A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model01:09

Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model

Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the concentration...

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Related Experiment Video

Updated: Jun 27, 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

Single-file dynamics with different diffusion constants.

Tobias Ambjörnsson1, Ludvig Lizana, Michael A Lomholt

  • 1Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. ambjorn@mit.edu

The Journal of Chemical Physics
|December 3, 2008
PubMed
Summary
This summary is machine-generated.

We studied how particles move in a line, finding their average distance traveled grows with the square root of time. This movement depends on individual particle speeds, even when particles cannot overtake each other.

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

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

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Understanding particle dynamics in confined systems is crucial for various physical phenomena.
  • Single-file diffusion, where particles cannot overtake, presents unique transport properties.
  • Previous models often assumed identical particles, limiting applicability to heterogeneous systems.

Purpose of the Study:

  • To investigate the single-file diffusion dynamics of a tagged particle in a system of N interacting particles with differing diffusion constants.
  • To derive exact solutions for the two-particle case and employ efficient simulations for larger systems.
  • To analyze the long-time behavior of the mean squared displacement (MSD) of the tagged particle.

Main Methods:

  • Exact analytical derivation of the conditional probability density function (PDF) for the two-particle system.
  • Application of the two-particle PDF to determine the tagged particle PDF.
  • Development and utilization of a computationally efficient stochastic simulation technique based on the Gillespie algorithm for N-particle systems (N large).

Main Results:

  • An exact solution for the two-particle probability density function was obtained for arbitrary initial conditions and all times.
  • For large N, stochastic simulations revealed that the tagged particle's mean squared displacement scales as the square root of time.
  • The prefactor of the MSD was found to be dependent on the individual diffusion constants of the particles, deviating from the identical particle case.

Conclusions:

  • The single-file diffusion of tagged particles with differing diffusion constants exhibits a universal square root of time scaling for the MSD at long times.
  • The prefactor of this scaling provides a signature of the underlying particle heterogeneity.
  • The simulation results align well with recent analytical predictions, validating the computational approach and theoretical findings.