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Related Concept Videos

Catalysis01:27

Catalysis

Catalysis influences the rate of chemical reactions by providing an alternative reaction pathway with lower activation energy. A catalyst speeds up a reaction, but it is not consumed during the process. The fundamental principle of catalysis is the ability of a catalyst to alter the reaction mechanism, often introducing a more efficient pathway than the uncatalyzed process.In a catalyzed reaction, the catalyst participates directly in the reaction mechanism. It interacts with reactants to form...
Catalysis02:50

Catalysis

The presence of a catalyst affects the rate of a chemical reaction. A catalyst is a substance that can increase the reaction rate without being consumed during the process. A basic comprehension of a catalysts’ role during chemical reactions can be understood from the concept of reaction mechanisms and energy diagrams.
Catalytically Perfect Enzymes01:07

Catalytically Perfect Enzymes

The theory of catalytically perfect enzymes was first proposed by W.J. Albery and J. R. Knowles in 1976. These enzymes catalyze biochemical reactions at high-speed. Their catalytic efficiency values range from 108-109 M-1s-1. These enzymes are also called 'diffusion-controlled' as the only rate-limiting step in the catalysis is that of the substrate diffusion into the active site. Examples include triose phosphate isomerase, fumarase, and superoxide dismutase.
Turnover Number and Catalytic Efficiency01:19

Turnover Number and Catalytic Efficiency

The turnover number of an enzyme is the maximum number of substrate molecules it can transform per unit time. Turnover numbers for most enzymes range from 1 to 1000 molecules per second. Catalase has the known highest turnover number, capable of converting up to 2.8×106 molecules of hydrogen peroxide into water and oxygen per second. Lysozyme has the lowest known turnover number of half a molecule per second.
Chymotrypsin is a pancreatic enzyme that breaks down proteins during digestion. The...
Half-life of a Reaction02:42

Half-life of a Reaction

The half-life of a reaction (t1/2) is the time required for one-half of a given amount of reactant to be consumed. In each succeeding half-life, half of the remaining concentration of the reactant is consumed. For example, during the decomposition of hydrogen peroxide, during the first half-life (from 0.00 hours to 6.00 hours), the concentration of H2O2 decreases from 1.000 M to 0.500 M. During the second half-life (from 6.00 hours to 12.00 hours), the concentration decreases from 0.500 M to...
Consecutive Reactions01:22

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Consecutive reactions involve a sequence where the product of a preceding reaction becomes the reactant for the subsequent one. In a simple scheme, A transforms into B, which further reacts to form C, with rate constants k1 and k2, respectively. This concept is evident in the radioactive decay series. Assuming an initial state with only A present, the conservation of matter leads to three coupled differential equations, determining the concentrations of A, B, and C over time.The rate of change...

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Extinction Training During the Reconsolidation Window Prevents Recovery of Fear
11:17

Extinction Training During the Reconsolidation Window Prevents Recovery of Fear

Published on: August 24, 2012

Extinction times in autocatalytic systems.

Peter D Drummond1, Timothy G Vaughan, Alexei J Drummond

  • 1Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, Victoria, Australia. pdrummond@swin.edu.au

The Journal of Physical Chemistry. A
|September 14, 2010
PubMed
Summary

Autocatalytic systems, crucial in biology and chemistry, face extinction risks from limited reactants and degradation. This study provides an exact formula for extinction time, approximated by an Arrhenius-like expression.

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Area of Science:

  • Chemical kinetics
  • Biochemical systems
  • Population dynamics

Background:

  • Autocatalytic processes are fundamental in diverse systems, from chemical reactions to organism replication.
  • Deterministic models suffice for large reactant numbers, but fluctuations dominate dynamics with limited supply.
  • Spontaneous degradation coupled with fluctuations can drive autocatalytic populations to extinction.

Purpose of the Study:

  • To investigate the dynamics of reversible autocatalytic processes (X + Y ⇌ 2X) with a surplus of Y.
  • To analyze the impact of spontaneous degradation (X → Z) on the autocatalytic reactant population.
  • To derive an exact analytical expression for the mean extinction time of the reactant X.

Main Methods:

  • Utilizing the Poisson representation to analyze the stochastic dynamics.
  • Focusing on the limit of a surplus of reactant Y.
  • Studying the degradation process X → Z.

Main Results:

  • An exact analytical expression for the mean extinction time of population X was derived.
  • The derived exact result can be closely approximated by an Arrhenius-like formula.
  • This approximation highlights an effective activation energy between quasi-stationary and extinct states.

Conclusions:

  • Fluctuations significantly influence autocatalytic systems with limited reactants and degradation.
  • The study provides a precise method to quantify extinction time in such systems.
  • An Arrhenius-like approximation offers a simplified yet accurate representation of the extinction dynamics.