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

Cooperative Allosteric Transitions01:58

Cooperative Allosteric Transitions

Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...
Stability of Conjugated Dienes01:28

Stability of Conjugated Dienes

Introduction
A comparison of the enthalpies of hydrogenation of dienes reveals that conjugated dienes release less heat on hydrogenation, rendering them more stable than their nonconjugated analogs.
Step-Growth Polymerization: Overview01:03

Step-Growth Polymerization: Overview

Step-growth or condensation polymerization is a stepwise reaction of bi or multifunctional monomers to form long-chain polymers. As all the monomers are reactive, most of the monomers are consumed at the early stages of the reaction to form small chains of reactive oligomers, which then combine to form long polymer chains in the late stages. Hence, the reaction has to proceed for a long time to achieve high molecular weight polymers.
Many natural and synthetic polymers are produced by...
Molecular Weight of Step-Growth Polymers01:08

Molecular Weight of Step-Growth Polymers

Step growth polymerization involves bi or multifunctional monomers. Bifunctional monomers react to form linear step growth polymers, whereas multifunctional monomers react to form non-linear or branched polymers.
As the step-growth polymerization involves step-wise condensation of monomers, the molecular weight also builds up eventually. Consequently, high molecular weight polymers are obtained at the late stages of the polymerization, where 99% of monomers have been consumed.
The extent of the...
Determination of Molar Masses of Polymers I01:24

Determination of Molar Masses of Polymers I

Polymerization produces macromolecules with a range of chain lengths due to the random nature of molecular growth processes. As chains form and terminate at different stages, a single polymer sample contains molecules of varying sizes rather than a uniform structure. This variability is described using average molar masses and distribution-related parameters, which together provide a comprehensive understanding of polymer characteristics.The distribution of molar masses plays a critical role in...
[3,3] Sigmatropic Rearrangement of 1,5-Dienes: Cope Rearrangement01:21

[3,3] Sigmatropic Rearrangement of 1,5-Dienes: Cope Rearrangement

The Cope rearrangement is classified as a [3,3] sigmatropic shift in 1,5-dienes, leading to a more stable, isomeric 1,5-diene. The reaction involves a concerted movement of six electrons, four from two π bonds and two from a σ bond, via an energetically favorable chair-like transition state.

You might also read

Related Articles

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

Sort by
Same author

Structure and dynamics in the low-density phase of a two-dimensional cellular automaton model of traffic flow.

Physical review. E·2026
Same author

Surface optimization governs the local design of physical networks.

Nature·2026
Same author

Observing network dynamics through sentinel nodes.

Nature communications·2025
Same author

Privacy preserving optimization of communication networks.

Nature communications·2025
Same author

Effect of preferential node deletion on the structure of networks that evolve via preferential attachment.

Physical review. E·2025
Same author

Reply to: Evolutionary rescue effect can disappear under non-neutral mutations-a reply to Zhang et al. (2022).

Nature communications·2024
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

Related Experiment Video

Updated: Jun 18, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Stochastic analysis of dimerization systems.

Baruch Barzel1, Ofer Biham

  • 1Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces moment equations for modeling dimerization processes, offering simplified analytical solutions for monomer and dimer concentrations. This approach accurately captures stochastic fluctuations in small systems, outperforming traditional rate equations.

More Related Videos

Single-Molecule Measurement of Protein Interaction Dynamics Within Biomolecular Condensates
06:48

Single-Molecule Measurement of Protein Interaction Dynamics Within Biomolecular Condensates

Published on: January 5, 2024

Sedimentation Equilibrium of a Small Oligomer-forming Membrane Protein: Effect of Histidine Protonation on Pentameric Stability
09:49

Sedimentation Equilibrium of a Small Oligomer-forming Membrane Protein: Effect of Histidine Protonation on Pentameric Stability

Published on: April 2, 2015

Related Experiment Videos

Last Updated: Jun 18, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Single-Molecule Measurement of Protein Interaction Dynamics Within Biomolecular Condensates
06:48

Single-Molecule Measurement of Protein Interaction Dynamics Within Biomolecular Condensates

Published on: January 5, 2024

Sedimentation Equilibrium of a Small Oligomer-forming Membrane Protein: Effect of Histidine Protonation on Pentameric Stability
09:49

Sedimentation Equilibrium of a Small Oligomer-forming Membrane Protein: Effect of Histidine Protonation on Pentameric Stability

Published on: April 2, 2015

Area of Science:

  • Biophysics
  • Chemical Kinetics
  • Computational Biology

Background:

  • Dimerization, the binding of two monomers into a dimer, is a fundamental biological process.
  • Traditional rate equations accurately model dimerization with large molecule counts but fail in low-copy-number systems dominated by fluctuations.
  • Stochastic methods like master equations and Monte Carlo simulations are computationally intensive and lack analytical solutions for small systems.

Purpose of the Study:

  • To develop a simplified stochastic treatment for dimerization processes using moment equations.
  • To derive analytical solutions for copy numbers and reaction rates in both steady-state and time-dependent dimerization.
  • To analyze various dimerization scenarios, including those with and without dissociation, and heterodimer formation.

Main Methods:

  • Utilized recently introduced moment equations for a simplified stochastic analysis of dimerization.
  • Derived analytical solutions for monomer and dimer copy numbers and reaction rates.
  • Investigated three distinct dimerization models: simple dimerization, dimerization with dissociation, and heterodimer formation.

Main Results:

  • Obtained analytical solutions for dimerization kinetics, applicable to both steady-state and time-dependent scenarios.
  • The moment equations provide accurate predictions in the stochastic limit, validating against master equation results.
  • Demonstrated the method's effectiveness across different dimerization types, including heterodimer formation.

Conclusions:

  • Moment equations offer a computationally efficient and analytically tractable approach to modeling stochastic dimerization.
  • This method bridges the gap between deterministic rate equations and complex stochastic simulations for small molecule systems.
  • The derived analytical solutions have potential applications in various physical and biological contexts involving molecular interactions.