  In this paper, we use a variety of mathematical techniques to explore
existence, local stability, and global stability of equilibria in abstract
models of mitochondrial metabolism. The class of models constructed is defined
by the biological description of the system, with minimal mathematical
assumptions. The key features are an electron transport chain coupled to a
process of charge translocation across a membrane. In the absence of charge
translocation these models have previously been shown to behave in a very
simple manner with a single, globally stable equilibrium. We show that with
charge translocation the conclusion about a unique equilibrium remains true,
but local and global stability do not necessarily follow. In sufficiently low
dimensions - i.e. for short electron transport chains - it is possible to make
claims about local and global stability of the equilibrium. On the other hand,
for longer chains, these general claims are no longer valid. Some particular
conditions which ensure stability of the equilibrium for chains of arbitrary
length are presented.
