Microscopic reversibility or detailed balance in ion channel models

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.

Automatic kinetic model generation and selection based on concentration versus time curves

“…An application of Feinberg's theorem (and also the detailed description with examples of the concepts) can be found in Ref. 45.…”

Automatic model generation

“…An application of Feinberg's theorem (and also the detailed description with examples of the concepts) can be found in Ref. [15].…”

Statistics and Related Topics in Single-Molecule Biophysics

“…On the one hand, for stationary molecular fluctuations in chemico-thermodynamic equilibrium, one wants to test the preservation of detailed balance [96, 97, 98]. On the other hand, for a molecular process with unknown mechanism, one wants to discover whether it is chemically driven [99].…”