Microscopic Reversibility or Detailed Balance in Ion Channel Models

TL;DR

This paper examines ion channel models that are claimed to obey detailed balance, demonstrating that with proper transformations and conditions, these models inherently satisfy thermodynamic consistency despite initial violations of mass conservation.

Contribution

It shows that ion channel models violating mass conservation can be transformed into mass-conserving models that still satisfy detailed balance conditions.

Findings

Transformations restore mass conservation in ion channel models.

Full detailed balance conditions lead to consistent reaction rate relations.

Models initially violating mass conservation can be aligned with thermodynamic principles.

Abstract

Mass action type deterministic kinetic models of ion channels are usually constructed in such a way as to obey the principle of detailed balance (or, microscopic reversibility) for two reasons: first, the authors aspire to have models harmonizing with thermodynamics, second, the conditions to ensure detailed balance reduce the number of reaction rate coefficients to be measured. We investigate a series of ion channel models which are asserted to obey detailed balance, however, these models violate mass conservation and in their case only the necessary conditions (the so-called circuit conditions) are taken into account. We show that ion channel models have a very specific structure which makes the consequences true in spite of the imprecise arguments. First, we transform the models into mass conserving ones, second, we show that the full set of conditions ensuring detailed balance (formulated by Feinberg) leads to the same relations for the reaction rate constants in these special cases, both for the original models and the transformed ones.