What's Wrong with the Hodgkin-Huxley Model? An Exercise in Critical Thinking

Abstract

Critical thinking is fundamental to science: let us examine an assumption of the Hodgkin-Huxley model of excitable membranes. The circuit elements of the HH model are a capacitance C and parallel ionic conductances g in series with their electromotive forces. HH assumes that C is constant while the gs vary with voltage and time. This assumption, adapted to voltage-sensitive ion channels, places the entire burden of explaining channel function on the gs. While the assumption of constant C—and its dimensionless coefficient, dielectric permittivity ε—is a good approximation for a membrane patch, its application at the macromolecular nanoscale is dubious, considering the ubiquitous presence of branched-chain amino acids—isoleucine, leucine and valine—in the channels. The sidechains of these amino acids (and no others) strongly affect ε in certain molecules with structures resembling channel segments. These ferroelectric liquid crystals, such as 4'-3M2CPOOB, exhibit ε values as high as 3000 in their ferroelectric state. Changes in channel ε affect all electrostatic interactions, including the mutual repulsions between the positively charged residues in S4 segments, key components of voltage sensors. The Channel Activation by Electrostatic Repulsion (CAbER) hypothesis assumes the resting channel, at a high electric field, is in a polar, far-from-equilibrium state with high ε, and that threshold depolarization converts it to a nonpolar state with much lower ε. The consequently increased Coulomb repulsion between arginines and lysines explains the observed outward motion of the S4 segments, which then drives the opening of the pore domain to stochastic ion currents. Does critical thinking support constant-C or CAbER? Problem: Two proton charges on a helix of radius 0.80 nm are 0.45 nm apart axially, with an angular separation of 300°. What is their repulsion energy (kJ/mol) when ε is 500? When it is 4? Further reading: HR Leuchtag, Voltage-Sensitive Ion Channels, Springer, 2008.