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Related Concept Videos

Diffusion01:21

Diffusion

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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...
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Protein Diffusion in the Membrane01:24

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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...
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Passive Diffusion: Overview and Kinetics01:17

Passive Diffusion: Overview and Kinetics

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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...
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Distribution and Dispersion00:54

Distribution and Dispersion

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To understand intra-specific interactions in populations, scientists measure the spatial arrangement of species individuals. This geographic arrangement is known as the species distribution or dispersion. Highly territorial species exhibit a uniform distribution pattern, in which individuals are spaced at relatively equal distances from one another. Species that are highly tied to particular resources, such as food or shelter, tend to concentrate around those resources, and thus exhibit a...
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Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models00:57

Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models

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Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
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Gene Flow02:39

Gene Flow

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Gene flow is the transfer of genes among populations, resulting from either the dispersal of gametes or from the migration of individuals.
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Related Experiment Video

Updated: Jun 7, 2025

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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Speed and Shape of Population Fronts with Density-Dependent Diffusion.

Beth M Stokes1, Tim Rogers1, Richard James2

  • 1Department of Mathematical Sciences, University of Bath, Bath, UK.

Bulletin of Mathematical Biology
|November 9, 2024
PubMed
Summary

Animal range expansion speed depends on how easily populations spread at low densities. Density-dependent diffusion models reveal that low-density diffusion strength critically impacts wave propagation speed and shape.

Keywords:
Density dependent diffusionTravelling waves

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Last Updated: Jun 7, 2025

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Area of Science:

  • Mathematical Biology
  • Ecology
  • Population Dynamics

Background:

  • Animal movement patterns are increasingly understood to be influenced by population density.
  • Reaction-diffusion models are commonly used to study animal range expansion.

Purpose of the Study:

  • To investigate travelling wave solutions in reaction-diffusion models with density-dependent diffusion.
  • To determine how population diffusion at low densities affects range expansion speed.

Main Methods:

  • Analysis of travelling wave solutions in reaction-diffusion models.
  • Investigation of density-dependent diffusion effects.
  • Application of linear analysis and variational approaches.

Main Results:

  • The speed of population fronts is critically dependent on the strength of diffusion at low population densities.
  • For strong low-density diffusion, wave speed aligns with predictions from linear analysis.
  • For weak or absent low-density diffusion, linear analysis is insufficient; variational methods provide speed and shape.

Conclusions:

  • Density-dependent diffusion is a crucial factor in animal range expansion dynamics.
  • The behavior of population fronts at low densities significantly influences overall expansion speed.
  • Variational approaches offer valuable insights into population front dynamics when linear analysis fails.