Advertisement

Smooth Muscle pp 663-671 | Cite as

Compartmental Analysis of Ion Movements

  • R. Casteels
  • G. Droogmans

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.

Keywords

Tracer Experiment Compartmental Analysis Intracellular Sodium Exponential Component Semilogarithmic Plot 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brownell, G. L. and Callahan, A. B. 1963. Transform methods for tracer data analysis. Ann. N.Y. Acad. Sci, 705:172–181.Google Scholar
  2. Casteels, R. 1969. Calculation of the membrane potential in smooth muscle cells of the guinea-pig’s taenia coli by the Goldman equation. J. Physiol., 205:193–208.PubMedGoogle Scholar
  3. Creese, R., Neil, M. W., and Stephenson, G. 1956. Effect of cell variation on potassium exchange of muscle. Trans. Faraday Soc., 52:1022–1032.CrossRefGoogle Scholar
  4. Feurzeig, W. and Tyler, S. A. 1950. A note on exponential fitting of empirical curves. Argonne Nat. Lab. Quart. Rep., ANL, 4401:14–29.Google Scholar
  5. Gardner, D. G. 1963. Resolution of multi-component exponential decay curves using Fourier transforms. Ann. N.Y. Acad. Sci., 108:195–203.PubMedCrossRefGoogle Scholar
  6. Goodford, P. J. and Leach, E. H. 1966. The extracellular space in the smooth muscle of the guinea-pig’s taenia coli. J. Physiol., 186:1–10.PubMedGoogle Scholar
  7. Haas, H. G. 1962. Zur Kinetik des lonenaustausch in mehrphasigen Systemen. Pflügers Arch., 275:341–357.Google Scholar
  8. Householder, A. S. 1950. On Prony’s method of fitting exponential decay curves and multiple-hit survival curves. Oak Ridge Nat. Lab. ORNL, 455:1–15.Google Scholar
  9. Huxley, A. F. 1960. Appendix 2 to chapter by Solomon, A. K. In: Mineral Metabolism, Vol. 1, Part A, pp. 163–166. Ed. by Comar, C. L. and Bronner, F. Academic Press, New York and London.Google Scholar
  10. Mancini, P. and Pilo, A. 1970. A computer program for multiexponential fitting by the peeling method. Comput. Biomed. Res., 3:1–14.PubMedCrossRefGoogle Scholar
  11. Myhill, J. 1967. Investigation of the effect of data error in the analysis of biological tracer data. Biophys. J., 7:903–911.PubMedCrossRefGoogle Scholar
  12. Myhill, J., Wadsworth, G. P., and Brownell, G. L. 1965. Investigation of an operator method in the analysis of biological tracer data. Biophys. 5:89–107.CrossRefGoogle Scholar
  13. Peslin, R., Dawson, S., and Mead, J. 1971. Analysis of multicomponent exponential curves by the Post-Widder’s equation. J. Appl. Physiol, 30: 462–472.PubMedGoogle Scholar
  14. Pizer, S. M., Ashare, A. B., Callahan, A. B., and Brownell, G. L. 1969. Fourier transform analysis of tracer data. In: Concepts and Models of Biomathematics, Vol. 1. Ed. by Heinmets, F. Dekker, Maidenhead.Google Scholar
  15. Van Liew, H. D. 1962. Semilogarithmic plots of data which reflect a continuum of exponential processes. Science,138:682–683.PubMedCrossRefGoogle Scholar
  16. Van Liew, H. D. 1967. Graphic analysis of aggregates of linear and exponential processes. J. Theor. Biol., 75:43–53.CrossRefGoogle Scholar
  17. Whittaker, E. T. and Robinson, G. 1944. The Calculus of Observations. Blackie and Son, London.Google Scholar
  18. Worsley, B. H. and Lax, L. C. 1962. Selection of numerical technique for analyzing experimental data of the decay type with reference to the use of tracers in biological systems. Biochim. Biophys. Acta, 59:1–24.PubMedCrossRefGoogle Scholar
  19. Zierler, K. L. 1966. Interpretation of tracer washout curves from a population of muscle fibers. J. Gen. Physiol., 49:423–431PubMedCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1975

Authors and Affiliations

  • R. Casteels
    • 1
  • G. Droogmans
    • 1
  1. 1.Institute of PhysiologyUniversity of LouvainLouvainBelgium

Personalised recommendations