The reference state and the metric structure of biological networks: a network thermodynamic study

Convection-diffusion is used as an example to examine the recently discovered metric structure underlying nonequilibrium thermodynamics and its dependence on the reference state in a nonlinear, coupled energy conversion system. The properties of convection-diffusion systems have been examined using L. Peusner´s formulation. In a chosen reference state, these systems are linear, reciprocal 2-ports and therefore have associated with them an orthogonal coordinate system which yields the metric for the system. The relationship of the metrics for the separate elements to that of a series combination is also explored. By combining them in series, the reference state which would yield this property for the composite is more complicated and often inaccessible to the experimenter. The organization of epithelial membranes has its basis in these very fundamental considerations. It is noted that the results are a contribution to complex systems theory and illustrate the role that engineering principles play in the theoretical biology of complexity