Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Chain Reactions01:29

Chain Reactions

19
Chain reactions involve highly reactive transient species, such as atoms or free radicals, as intermediates. These intermediates facilitate rapid reactions over an extended period. The process includes a series of steps: a reactive intermediate is consumed, reactants are converted to products, and the intermediate is regenerated. This cycle enables continuous repetition, amplifying the production of products with a small amount of intermediate. Chain reactions often utilize free radicals as...
19
Radical Anti-Markovnikov Addition to Alkenes: Mechanism01:17

Radical Anti-Markovnikov Addition to Alkenes: Mechanism

3.8K
The reaction of hydrogen bromide with alkenes in the presence of hydroperoxides or peroxides proceeds via anti-Markovnikov addition. The radical chain reaction comprises initiation, propagation, and termination steps.
The mechanism starts with chain initiation, which involves two steps. In the first chain initiation step, a weak peroxide bond is homolytically cleaved upon mild heating to form two alkoxy radicals. In the second initiation step, a hydrogen atom is abstracted by the alkoxy...
3.8K
Coupled Reactions01:17

Coupled Reactions

7.8K
Cellular processes such as building and breaking down complex molecules occur through stepwise chemical reactions. Some of these chemical reactions are spontaneous and release energy, whereas others require energy to proceed. Cells often couple the energy-releasing reaction with the energy-requiring one to carry out important cell functions. 
Energy in adenosine triphosphate or ATP molecules is easily accessible to do work. ATP powers the majority of energy-requiring cellular reactions....
7.8K
Reaction Mechanisms: Rate-limiting Step Approximation01:29

Reaction Mechanisms: Rate-limiting Step Approximation

101
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...
101
Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

12
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...
12
Radical Anti-Markovnikov Addition to Alkenes: Overview01:25

Radical Anti-Markovnikov Addition to Alkenes: Overview

3.3K
The addition of hydrogen bromide to alkenes in the presence of hydroperoxides or peroxides proceeds via an anti-Markovnikov pathway and yields alkyl bromides.
3.3K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

iFLinkC-EZ: A scalable and automatable method for the assembly of complex fusion proteins and multi-gene expression constructs based on the iFLinkC framework.

Synthetic and systems biotechnology·2026
Same author

Iterative design of a NAND hybrid riboswitch by deep batch Bayesian optimization.

Nucleic acids research·2026
Same author

The Coli Toolkit (CTK): An Extension of the Modular Yeast Toolkit for Use in <i>E. coli</i>.

ACS synthetic biology·2026
Same author

Decoding stimulus-specific regulation of promoter activity of p53 target genes.

Frontiers in cell and developmental biology·2025
Same author

Fluctuation induced network patterns in active matter with spatially correlated noise.

Soft matter·2025
Same author

Tuning Ultrasensitivity in Genetic Logic Gates Using Antisense RNA Feedback.

ACS synthetic biology·2025

Related Experiment Video

Updated: May 5, 2026

Plasmid-derived DNA Strand Displacement Gates for Implementing Chemical Reaction Networks
07:50

Plasmid-derived DNA Strand Displacement Gates for Implementing Chemical Reaction Networks

Published on: November 25, 2015

14.1K

Markov chain aggregation and its applications to combinatorial reaction networks.

Arnab Ganguly1, Tatjana Petrov, Heinz Koeppl

  • 1Department of Mathematics, University of Louisville, 231 Natural Sciences Building, Louisville, KY, USA, a0gang02@louisville.edu.

Journal of Mathematical Biology
|November 21, 2013
PubMed
Summary

This study introduces a method for simplifying complex biochemical models using aggregated Markov chains. This approach reduces computational complexity by focusing on local protein interactions, aiding in the analysis of biological systems.

More Related Videos

Optimization of Radiochemical Reactions using Droplet Arrays
10:54

Optimization of Radiochemical Reactions using Droplet Arrays

Published on: February 12, 2021

3.1K
JUMPn: A Streamlined Application for Protein Co-Expression Clustering and Network Analysis in Proteomics
07:28

JUMPn: A Streamlined Application for Protein Co-Expression Clustering and Network Analysis in Proteomics

Published on: October 19, 2021

2.7K

Related Experiment Videos

Last Updated: May 5, 2026

Plasmid-derived DNA Strand Displacement Gates for Implementing Chemical Reaction Networks
07:50

Plasmid-derived DNA Strand Displacement Gates for Implementing Chemical Reaction Networks

Published on: November 25, 2015

14.1K
Optimization of Radiochemical Reactions using Droplet Arrays
10:54

Optimization of Radiochemical Reactions using Droplet Arrays

Published on: February 12, 2021

3.1K
JUMPn: A Streamlined Application for Protein Co-Expression Clustering and Network Analysis in Proteomics
07:28

JUMPn: A Streamlined Application for Protein Co-Expression Clustering and Network Analysis in Proteomics

Published on: October 19, 2021

2.7K

Area of Science:

  • Computational Biology
  • Biochemical Systems Modeling
  • Systems Chemistry

Background:

  • Continuous-time Markov chains (CTMC) are used to model biochemical systems.
  • Current models can be computationally intensive due to large state spaces.
  • Site-graph-rewrite rules offer a compact representation of biological processes.

Purpose of the Study:

  • To develop a theory for creating aggregated Markov chains from detailed CTMC models.
  • To provide a sufficient condition for aggregate CTMC definition based on weak lumpability.
  • To demonstrate the application of this theory in reducing the complexity of biochemical models, particularly those involving protein-protein interactions.

Main Methods:

  • Definition of a variant of weak lumpability for CTMCs.
  • Analysis of de-aggregation applicability based on initial distributions.
  • Application of the theory to biochemical systems modeled with site-graph-rewrite rules.
  • Case studies on polymerization and receptor crosstalk (EGFR/insulin).

Main Results:

  • A sufficient condition for defining aggregated CTMCs is presented.
  • The measure of the original process can be recovered from the aggregated one.
  • The method effectively reduces the state space and computational complexity of biochemical models.
  • Successful application demonstrated in polymerization and EGFR/insulin signaling pathways.

Conclusions:

  • The developed theory provides an effective method for model reduction in biochemical systems.
  • Aggregated Markov chains simplify complex models by leveraging local context in protein interactions.
  • This approach enhances the computational feasibility of analyzing biological processes.