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Related Concept Videos

The Equilibrium Binding Constant and Binding Strength02:18

The Equilibrium Binding Constant and Binding Strength

The equilibrium binding constant (Kb) quantifies the strength of a protein-ligand interaction. Kb can be calculated as follows when the reaction is at equilibrium:
The Equilibrium Binding Constant and Binding Strength02:18

The Equilibrium Binding Constant and Binding Strength

The equilibrium binding constant (Kb) quantifies the strength of a protein-ligand interaction. Kb can be calculated as follows when the reaction is at equilibrium:
Calculating the Equilibrium Constant02:46

Calculating the Equilibrium Constant

The equilibrium constant for a reaction is calculated from the equilibrium concentrations (or pressures) of its reactants and products. If these concentrations are known, the calculation simply involves their substitution into the Kc expression.
For example, gaseous nitrogen dioxide forms dinitrogen tetroxide according to this equation:
Homogeneous Equilibria for Gaseous Reactions02:15

Homogeneous Equilibria for Gaseous Reactions

Homogeneous Equilibria for Gaseous Reactions
For gas-phase reactions, the equilibrium constant may be expressed in terms of either the molar concentrations (Kc) or partial pressures (Kp) of the reactants and products. A relation between these two K values may be simply derived from the ideal gas equation and the definition of molarity. According to the ideal gas equation:
The Equilibrium Constant03:10

The Equilibrium Constant

Consider the oxidation of sulfur dioxide:
Complexation Equilibria: Overview01:23

Complexation Equilibria: Overview

Complexation reactions take place when dative or coordinate covalent bonds form between metal ions and ligands. The compounds formed in these reactions are called coordination compounds. The number of bonds formed between the metal ion and the ligands is called its coordination number. Generally, most metal ions in an aqueous solution are solvated by water molecules and thus exist as aqua complexes.
The equilibrium constant of the complexation reaction is represented as the formation constant...

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Single-Molecule Measurement of Protein Interaction Dynamics Within Biomolecular Condensates
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Determining equilibrium constants for dimerization reactions from molecular dynamics simulations.

Djurre H De Jong1, Lars V Schäfer, Alex H De Vries

  • 1Groningen Biomolecular Science and Biotechnology Institute, University of Groningen, Nijenborgh 7, 9747 AG, Groningen, The Netherlands.

Journal of Computational Chemistry
|April 7, 2011
PubMed
Summary

Calculating binding free energy for molecular simulations is now feasible. This study resolves discrepancies in methods, providing a new formula applicable to various concentrations and particle numbers, validated by simulations.

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Area of Science:

  • Computational chemistry and biophysics
  • Statistical mechanics

Background:

  • Free energy calculations from equilibrium molecular dynamics (MD) simulations are increasingly feasible.
  • Calculating binding free energy for dimerization reactions, like transmembrane alpha-helices, using MD is challenging.
  • Existing methods based on Boltzmann statistics and the law of mass action yield contradictory results.

Purpose of the Study:

  • To develop a unified theory resolving discrepancies in free energy calculations from MD simulations.
  • To provide a correct formula for dimerization free energy applicable to systems with two molecules.
  • To extend the theory for high concentrations and arbitrary numbers of monomers and dimers.

Main Methods:

  • Development of a new theoretical framework for free energy calculations.
  • Application of the theory to simulation systems with varying particle numbers.
  • Comparison of results with reference free energy values from radial distribution functions.

Main Results:

  • A new formula for dimerization free energy: ΔG ∝ ln(P(1) /P(0) ) for two-molecule systems.
  • The theory accurately describes systems at high concentrations, overcoming limitations of dilute approximations.
  • Full agreement was observed between simulation results and theoretical predictions for binding free energies and dimerization statistics.

Conclusions:

  • The developed theory resolves the conflict between different free energy calculation approaches in MD simulations.
  • The new formula provides a robust method for determining binding free energies, applicable to various simulation conditions.
  • This work offers rigorous error estimates and validates the approach with Lennard-Jones system simulations.