Transport similarity: dimensional analysis of diffusion at cellular level.

Scale dependent variables in animals of different sizes can be studied by means of dimensional analysis and biological similarity criteria. The aim of this report is to demonstrate a transport similarity at the cellular level, based on two postulates derived from Fick's law of diffusion; the constancy of the "concentration gradient" between two compartments separated by a membrane; and the invariance of the "diffusion coefficient" of a given substance in homologous cells. A general equation for a transport similarity was deduced from these two postulates and it was then possible to calculate the corresponding "reduced exponents" as functions of body weight, which, in turn, can be compared with the empirical allometric exponents of Huxley's power equation. The biological meaning of the theoretically predicted reduced exponents of the transport similarity are discussed and the predicted values are compared with the experimental findings.