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Related Concept Videos

Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
Reaction Mechanisms: Rate-limiting Step Approximation01:29

Reaction Mechanisms: Rate-limiting Step Approximation

The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...
Multi-Step Reactions02:31

Multi-Step Reactions

Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...
Rate-Determining Steps03:08

Rate-Determining Steps

Relating Reaction Mechanisms
In a multistep reaction mechanism, one of the elementary steps progresses significantly slower than the others. This slowest step is called the rate-limiting step (or rate-determining step). A reaction cannot proceed faster than its slowest step, and hence, the rate-determining step limits the overall reaction rate.
The concept of rate-determining step can be understood from the analogy of a 4-lane freeway with a short-stretch of traffic-bottleneck caused due to...
Reaction Mechanisms03:06

Reaction Mechanisms

Chemical reactions often occur in a stepwise fashion, involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs.
For instance, the decomposition of ozone appears to follow a mechanism with two steps:
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...

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: December 4, 2017

Reaction-diffusion master equation in the microscopic limit.

Stefan Hellander1, Andreas Hellander, Linda Petzold

  • 1Department of Information Technology, Uppsala University, Box 337, SE-75105 Uppsala, Sweden.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 12, 2012
PubMed
Summary
This summary is machine-generated.

The reaction-diffusion master equation (RDME) accurately models biochemical reactions at coarse scales but fails at very fine scales. This study explains why the RDME breaks down and quantifies its limits for accurate stochastic modeling.

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In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging

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Area of Science:

  • Biochemistry
  • Computational Biology
  • Chemical Physics

Background:

  • Stochastic modeling is crucial for understanding biochemical reaction networks.
  • Particle-tracking Smoluchowski and on-lattice reaction-diffusion master equation (RDME) are common frameworks.
  • RDME accuracy initially increases with finer mesh size but eventually decreases.

Purpose of the Study:

  • To provide a general argument for the breakdown of the RDME at fine scales.
  • To establish a quantifiable limit for voxel size where RDME agrees with the Smoluchowski model.
  • To review and discuss modifications to RDME for improved microscale accuracy.

Main Methods:

  • General theoretical analysis of RDME limitations.
  • Quantification of voxel size limits in 2D and 3D.
  • Review of recent RDME modifications.

Main Results:

  • The RDME has a fundamental breakdown point at very fine lattice spacings.
  • A hard limit on voxel size is identified, beyond which RDME disagrees with the Smoluchowski model.
  • The limits are quantified for both two and three-dimensional systems.

Conclusions:

  • The RDME is not universally accurate for all scales in stochastic reaction-diffusion modeling.
  • Understanding the RDME's limitations is critical for reliable biochemical network simulations.
  • Recent modifications aim to extend RDME validity to smaller scales.