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Related Concept Videos

Diffusion01:12

Diffusion

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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...
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Diffusion01:21

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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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Phase I biotransformation reactions are integral to drug metabolism, predominantly involving oxidative, reductive, and hydrolytic transformations. Chief among these are oxidative reactions, which enhance the hydrophilicity of xenobiotics and introduce polar functional groups to facilitate their elimination from the body.
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Oxidative reactions are pivotal in metabolizing numerous compounds, including pharmaceutical drugs. These reactions often occur in carbon-heteroatom systems, such as carbon-nitrogen, carbon-sulfur, and carbon-oxygen.
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Hybrid Zones02:29

Hybrid Zones

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Hybrid zones are narrow regions where two closely related species interact, mate, and produce hybrids. Relative to either parent species, hybrids may possess distinct phenotypic or genetic differences that impact their survival and reproductive success. The genetic variances introduced by hybridization influence species diversity and speciation processes within the hybrid zone.
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Hybridization of Atomic Orbitals I03:24

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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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Related Experiment Video

Updated: Jan 26, 2026

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates
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A hybrid method for micro-mesoscopic stochastic simulation of reaction-diffusion systems.

Alireza Sayyidmousavi1, Katrin Rohlf1, Silvana Ilie1

  • 1Department of Mathematics, Ryerson University, 350 Victoria St, M5B 2K3 Toronto, Canada.

Mathematical Biosciences
|April 19, 2019
PubMed
Summary

A novel hybrid algorithm combines Reactive Multi-Particle Collision (RMPC) dynamics and Reaction-Diffusion Master Equation (RDME) for efficient simulation of reaction-diffusion systems, offering significant speed-ups.

Keywords:
Hybrid methodInhomogeneous Stochastic Simulation AlgorithmMulti-Particle Collision dynamicsReaction-diffusion systemsStochastic simulation

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Area of Science:

  • Computational chemistry
  • Chemical kinetics
  • Multiscale modeling

Background:

  • Accurate simulation of reaction-diffusion systems is crucial in various scientific fields.
  • Existing molecular-based methods can be computationally expensive.
  • Bridging micro and meso scales presents a significant modeling challenge.

Purpose of the Study:

  • To introduce a novel micro-meso hybrid algorithm for reaction-diffusion systems.
  • To leverage Reactive Multi-Particle Collision (RMPC) dynamics at the microscopic level.
  • To utilize the Reaction-Diffusion Master Equation (RDME) at the mesoscopic level.

Main Methods:

  • Developed a hybrid algorithm integrating Ghost Cell Method, RMPC, and RDME.
  • Employed the Inhomogeneous Stochastic Simulation Algorithm to solve the RDME.
  • Tested the algorithm on three distinct reaction-diffusion systems.

Main Results:

  • Achieved excellent agreement between the hybrid algorithm's results and deterministic solutions.
  • Demonstrated that RMPC dynamics can effectively model particle trajectories and reactions.
  • Showcased significant computational speed-ups through proper domain discretization compared to full RMPC.

Conclusions:

  • The proposed micro-meso hybrid algorithm provides an efficient and accurate approach for simulating reaction-diffusion systems.
  • The integration of RMPC dynamics offers advantages in speed and conservation properties.
  • Domain discretization is a key factor in optimizing the performance of the hybrid algorithm.