Tracer dynamics and the determination of pool-sizes and turnover factors in metabolic systems

Abstract

Tracer dynamics constitutes a theory aimed to simplify a physico-biologically significant interpretation of tracer data, especially of such data as are accessible at the supply of radioactive isotopes to metabolic systems; this communication gives a simplified survey of the theory. An essential problem is to find out how and when the behaviour of the “tracer” (i.e. of the small amount of radioactive isotopes supplied to the system) is representative of the properties of the “mother substance” (i.e. of the isotopes naturally present in the system). In a previous paper it has been shown that only incidentally can the tracer fluxes be expected to be definitely related to the properties of the mother substance, and in the present analysis the following question is treated: Do there exist any “averages” of tracer properties which are not only representative of the mother substance but also generally valid and accessible to experimental estimations? From this point of view an attempt at a “time-statistical” approach is outlined, in terms of time-averages of certain tracer properties. It results in an ergodic theorem, which gives a general and simple relationship between the tracer and the mother substance. As practical consequences of the analysis we get simple equations for the determination of “pool-sizes” and for the determination of certain tracer dynamic parameters that characterise the “turnovers” of the considered metabolites; the common conception of “turnover” is in the general case experimentally non-observable, and the corresponding properties of the mother substance must accordingly be described in other variables. The theory gives fairly precise advice how to perform tracer experiments and appears applicable under experimentally modest conditions. It is also shown that the tracer dynamics contains the classic physico-chemical kinetics as a special case: the tracer dynamic description of metabolic systems is accordingly consistent with the conceptual background of the well established kinetics of chemical reactions.