Linear rate-equilibrium relations arising from ion channel-bilayer energetic coupling Academic Article uri icon


MeSH Major

  • Gramicidin
  • Ion Channels
  • Lipid Bilayers
  • Membrane Lipids


  • Linear rate-equilibrium (RE) relations, also known as linear free energy relations, are widely observed in chemical reactions, including protein folding, enzymatic catalysis, and channel gating. Despite the widespread occurrence of linear RE relations, the principles underlying the linear relation between changes in activation and equilibrium energy in macromolecular reactions remain enigmatic. When examining amphiphile regulation of gramicidin channel gating in lipid bilayers, we noted that the gating process could be described by a linear RE relation with a simple geometric interpretation. This description is possible because the gating process provides a well-understood reaction, in which structural changes in a bilayer-embedded model protein can be studied at the single-molecule level. It is thus possible to obtain quantitative information about the energetics of the reaction transition state and its position on a spatial coordinate. It turns out that the linear RE relation for the gramicidin monomer-dimer reaction can be understood, and the quantitative relation between changes in activation energy and equilibrium energy can be interpreted, by considering the effects of amphiphiles on the changes in bilayer elastic energy associated with channel gating. We are not aware that a similar simple mechanistic explanation of a linear RE relation has been provided for a chemical reaction in a macromolecule. RE relations generally should be useful for examining how amphiphile-induced changes in bilayer properties modulate membrane protein folding and function, and for distinguishing between direct (e.g., due to binding) and indirect (bilayer-mediated) effects.

publication date

  • August 2, 2011



  • Academic Article



  • eng

PubMed Central ID

  • PMC3150884

Digital Object Identifier (DOI)

  • 10.1073/pnas.1103192108

PubMed ID

  • 21768343

Additional Document Info

start page

  • 12717

end page

  • 22


  • 108


  • 31