  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.
