  Membrane transporters contribute to the regulation of the internal
environment of cells by translocating substrates across cell membranes. Like
all physical systems, the behaviour of membrane transporters is constrained by
the laws of thermodynamics. However, many mathematical models of transporters,
especially those incorporated into whole-cell models, are not thermodynamically
consistent, leading to unrealistic behaviour. In this paper we use a
physics-based modelling framework, in which the transfer of energy is
explicitly accounted for, to develop thermodynamically consistent models of
transporters. We then apply this methodology to model two specific
transporters: the cardiac sarcoplasmic/endoplasmic Ca$^{2+}$ ATPase (SERCA) and
the cardiac Na$^+$/K$^+$ ATPase.
