Membranes and meters

We present a mathematical examination of the measurement and representation of membrane transport systems. Confronted with a coupled, multicomponent system, the experimentalist must choose meters which project out and make measurements upon subsystems in a rational manner. With a proper choice of projection operations, a representation of the composite system can be synthesized directly from the results of measurement. Starting from a set of basic axioms governing the measurement process, we apply the tenets of operator theory to the action of meters. We derive the projection operators associated with the representation of transport systems in terms of irreversible thermodynamics. The metric structure of this representation is explored from the viewpoint of measurement and the specification of identity. By means of concrete examples and a computational algorithm, the abstract, mathematical formalism is related to standard laboratory procedures.