Quantum Mechanical Model for Passive Transport through Bilayer Lipid Membranes

  • Leonor Cruzeiro
  • Kelo M. C. Da Silva
Part of the NATO ASI Series book series (NSSA, volume 91)


Unmodified bilayer lipid membranes (BLMs) are known to be low dielectric media with a correspondingly low ionic conductivity. The mathematical treatment of ion diffusion through them is usually done in classical thermodynamical terms through the so-called Generalized Nernst-Planck equation1,2:
$$ \Phi =-D(\frac{dc}{dx}+zc\frac{df}{dx}+c\frac{dv}{dx}) $$
where Ф is the ion flux per unit area, D is the diffusion coefficient of the ion in the membrane, C is the ion concentration in the membrane, ø is the electrical potential, z is the valency of the ion, V is the potential energy of the ion in the membrane and x is the coordinate normal to the membrane surface.


Phase Transition Lipid Bilayer Potential Energy Function High Energy Barrier Bilayer Thickness 
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Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • Leonor Cruzeiro
    • 1
  • Kelo M. C. Da Silva
    • 1
  1. 1.Lab. BiomecânicaInstituto Gulbenkian de CiênciaOeiras CodexPortugal

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