Compartmental Analysis of Ion Movements

Abstract

Tracers, and in particular the radioactive ones, provide a powerful tool for the study of the kinetics and the distribution of ions in a biological system. The interpretation of the data from tracer experiments is usually performed in terms of a multi- compartmental model. However, these physical models are only useful if they consist of a limited number of compartments. The final purpose of compartmental analysis is the determination of the parameters that describe the physical model, i.e., the number and size of the compartments and the rate constants of the exchange of ions between the different compartments. If the number and the size of the compartments and their interconnections are known, it is possible to determine the rate constatits from the experimental data, provided they are sufficiently extensive. Such an experimental situation is, however, rather exceptional and therefore we most often can only deduce from the experimental data a mathematical model, i.e., a mathematical description. However, the same experimental data can usually be represented by different mathematical models. Moreover, it is not possible to derive from a mathematical model a unique physical model. One can only infer the minimal number of compartments which is compatible with the experimental results. Unless other criteria are valid, this minimal number is to be preferred. If, in addition, the experimental data are sufficiently extensive, all the rate constants can be calculated and a unique physical model is obtained. If in contrast the experimental data are limited, one has to neglect some of the connections between the compartments in order to determine the remaining parameters of the system. These restrictions cannot be deduced from the tracer experiments and have to be determined from other characteristics of the system. If such knowledge is lacking, the restrictions in the model may be chosen arbitrarily and consequently the resulting model is not the only possible one.