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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...
Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
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...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Population Growth00:57

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.

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Related Experiment Video

Updated: May 9, 2026

Molecular Diffusion in Plasma Membranes of Primary Lymphocytes Measured by Fluorescence Correlation Spectroscopy
12:06

Molecular Diffusion in Plasma Membranes of Primary Lymphocytes Measured by Fluorescence Correlation Spectroscopy

Published on: February 1, 2017

Diffusion rate determines balance between extinction and proliferation in birth-death processes.

Hilla Behar1, Alexandra Agranovich, Yoram Louzoun

  • 1Department of Mathematics, Bar Ilan University, Ramat Gan, Israel. hilla.behar2@gmail.com

Mathematical Biosciences and Engineering : MBE
|August 3, 2013
PubMed
Summary

Catalyst-induced growth processes, common in biology, show complex spatial patterns. Reactant density peaks at intermediate diffusion rates, influencing population survival and dynamics.

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Last Updated: May 9, 2026

Molecular Diffusion in Plasma Membranes of Primary Lymphocytes Measured by Fluorescence Correlation Spectroscopy
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From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope

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Area of Science:

  • Multidisciplinary science
  • Chemical kinetics
  • Population dynamics

Background:

  • Spatially extended catalyst-induced growth processes are prevalent across biology, from ecology to molecular signaling.
  • These systems can display extinction-proliferation transitions based on parameter variations.
  • Incorporating stochasticity, discrete reactants, and spatial distribution leads to non-uniform patterns.

Purpose of the Study:

  • To investigate the asymptotic behavior of spatially extended catalyst-induced growth systems.
  • To understand how factors like reactant aggregation, spatial distribution, and diffusion influence population survival.
  • To provide a generic explanation for observed population dynamics.

Main Methods:

  • Monte Carlo simulations
  • Percolation theory-based estimations

Main Results:

  • Non-uniform reactant distribution emerges even with uniform parameters.
  • Population survival depends on aggregate size/shape, spatial distribution, and diffusion rate.
  • Reactant density is maximal at intermediate diffusion rates, decreasing at extremes.

Conclusions:

  • The study offers new insights into population dynamics in chemical, biological, and ecological systems.
  • Spatial structure and diffusion rates are critical determinants of long-term reactant population survival.
  • A universal explanation for density-diffusion rate relationships is provided.