Smooth Muscle pp 699-721 | Cite as

Influx and Efflux Measurements

  • E. E. Daniel


Radioisotopes are convenient tracers of ion movements in a wide variety of tissues. The sensitivity and selectivity of determination of such tracers have led to widespread use of these methods. The measurement of radioisotope tracers is, despite some problems, much simpler than the interpretation of such experiments. In a simple biological system, such as a giant axon, interpretation requires consideration of movements of tracers between at least two compartments, bath and axoplasm, and it is reasonable to assume that the resistance to tracer flow is concentrated at the plasma membrane. Furthermore, there can be access to both compartments; i.e., tracer can be administered into or withdrawn from the bath or the axoplasm. Indeed, the axon can be perfused internally. However, the presence of Schwann cell and myelin layers around a single nerve fiber add complexity and inaccessibility, as would the numerous compartments, t-tubules, various components of the sarcoplasmic reticulum, mitochondria, and various portions of the sarcomere in a single skeletal muscle fiber. In smooth muscle, matters are much more complex than in the squid axon: There is gross inhomogeneity of the extracellular spaces as to size of the interstices, constituents (e.g., collagen, elastic fibers), and possibly as to electrical charge. There is also often inhomogeneity as to cell types (e.g., fibroblasts and other connective tissue cells, nerves, and axons), cell organization (e.g., bundles, nexal and ephaptic connections), and cell substructures (nuclei, mitochondria, smooth and rough endoplasmic reticulum, caveolae intracellulares). There is no direct access to any compartment except the bath, so distribution of tracer must usually be inferred from analyses of uptake and efflux curves.1


Frog Skin Compartmental Analysis Unstirred Layer Unstriated Muscle Efflux Measurement 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, J., Tomlinson, R. W. S., and Osborn, S. B. 1962. An interpretation of radioisotope turnover data. Preliminary Communication,Lancet, 949–950.Google Scholar
  2. Andreoli, T. E. and Troutman, S. L. 1971. An analysis of unstirred layers in series with “tight” and “porous” lipid bilayer membranes. J. Gen. Physiol, 57:464–478.PubMedCrossRefGoogle Scholar
  3. Atkins, G. L. 1972. Short communications. Biochem. 727:437–438.Google Scholar
  4. Barry, P. H. and Hope, A. B. 1969a. Electroosmosis in membranes: Effects of unstirred layers and transport numbers. I. Theory. Biophys. 9:700–757.CrossRefGoogle Scholar
  5. Barry, P. H. and Hope, A. B. 1969b. Electroosmosis in membranes: Effects of unstirred layers and transport numbers. II. Experimental. Biophys. 9:729–757.CrossRefGoogle Scholar
  6. Berman, M. 1963. The formulation and testing of models. Ann. N.Y. Acad. Sci., 108:182–194.PubMedCrossRefGoogle Scholar
  7. Brading, A. F. 1971. Analysis of the effluxes of sodium, potassium and chloride ions from smooth muscle in normal and hypertonic solutions. J. Physiol, 214: 393–416.PubMedGoogle Scholar
  8. Brinley, F. J., Jr. 1965. Sodium potassium and chloride concentrations and fluxes in the isolated giant axon of Humarus. J. Neurophysiol, 28:742–772.Google Scholar
  9. Britton, H. G. 1965. Fluxes in passive, monovalent and polyvalent carrier systems.J. Theor. Biol, 70:28–52.Google Scholar
  10. Burg, M. B. and Orloff, J. 1963. Effect of strophanthidin on fluxes of potassium in rabbit kidney slices. Am. J. Physiol, 206:483–491.Google Scholar
  11. Burg, M. B., Groilman, E. T., and Orloff, J. 1964. Sodium and potassium flux of separated renal tubles. Am. J. Physiol., 206:483–491.PubMedGoogle Scholar
  12. Carslaw, H. S. and Jaeger, J. C. 1950. Conduction of Heat in Solids. The University Press, Oxford.Google Scholar
  13. Cass, A. and Finkelstein, A. 1970. Water permeability of thin lipid membranes. J. Gen. Physiol, 50: 1765–1784.CrossRefGoogle Scholar
  14. Cook, D. A. and Taylor, G. S. 1971. The use of the APL/360 system in pharmacology. A computer assisted analysis of efflux data. Comput. Biomed. Res., 4:157–166.PubMedCrossRefGoogle Scholar
  15. Cram, W. J. 1969. Short term influx as a measure of influx across the plasmalemma. Plant. Physiol, 44:1013–1015.PubMedCrossRefGoogle Scholar
  16. Crank, J. 1957.The Mathematics of Diffusion. Oxford University Press, London.Google Scholar
  17. Creese, R. 1968. Sodium fluxes in diaphragm muscle and the effects of insulin and serum proteins. J. Physiol, 797:255–278.Google Scholar
  18. 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
  19. Creese, R., Hashish, S. E. E., and Scholes, N. W. 1958. Potassium movements in contracting diaphragm muscle.J. Physiol, 143:301–324.Google Scholar
  20. Curran, P. F. and Cereijido, M. 1965. K fluxes in frog skin. Gen. Physiol, 48:1011–1033.CrossRefGoogle Scholar
  21. Dainty, J. 1963. Water relations of plant cells. Advances Bot. Res., 7:279–376.CrossRefGoogle Scholar
  22. Dainty, J. and Ginzburg, B. Z. 1964. The reflection coefficient of plant cell membranes for certain solutes. Biochim. Biophys. Acta, 79:129–137.PubMedGoogle Scholar
  23. Dainty, J. and House, C. R. 1966a. Unstirred layers in frog skin. J. Physiol, 182:66–78.PubMedGoogle Scholar
  24. Dainty, J. and House, C. R. 1966b. An examination of the evidence for membrane pores in frog skin. J.Physiol, 755:172–184.Google Scholar
  25. Daniel, E. E. and Robinson, K. 1970. Sodium exchange and net movement in rat uteri at 25°C. Can. J. Physiol Pharmacol, 48:598–624.PubMedCrossRefGoogle Scholar
  26. Daniel, E. E. and Robinson, K. 1971a. Effects of inhibitors of active transport on 22Na and 42K movements and on nucleotide levels in rat uteri at 25°C. Can. J. Physiol Pharmacol, 49:178–204.PubMedCrossRefGoogle Scholar
  27. Daniel, E. E. and Robinson, K. 1971b. Effects of inhibitors of metabolism on adenine nucleotides and on 22Na and 42K and net movements in rat uteri at 25°C. Can. J. Physiol Pharmacol, 49:205–239.PubMedCrossRefGoogle Scholar
  28. Daniel, E. E. and Robinson, K. 1971c. The effect of temperature on sodium movements in rat uteri at 25°C. Can. J. Physiol Pharmacol, 49:240–262.PubMedCrossRefGoogle Scholar
  29. Diamond, J. M. 1966. Non-linear osmosis. J. Physiol, 755:58–82.Google Scholar
  30. Dick, D. A. T. and Lea, E. J. A. 1967. The partition of sodium fluxes in isolated oocytes. J. Physiol, 191:289–308.Google Scholar
  31. DiSanto, A. R. and Wagner, J. G. 1972. Potential erroneous assignment of non-linear data to the classical linear two-compartment open model. J. Pharmaceutical Sci., 61:552–555.CrossRefGoogle Scholar
  32. Dunant, Y. and Cuthbert, A. W. 1970. Diffusion of drugs through stationary water layers as the rate limiting process in their action at membrane receptors. Br. J. Pharmac., 40:508–521.CrossRefGoogle Scholar
  33. Fenichel, I. R. and Horowitz, S. B. 1970. On the ratio of osmotic to tracer permability in a homogeneous liquid membrane.J. Phys. Chem., 74:2966–2969.CrossRefGoogle Scholar
  34. Freeman, D. J. and Daniel, E. E. 1973. Calcium movement in vascular smooth muscle and its detection using lanthanum as a tool. Can. J. Physiol. Pharmacol., 51:900–913.PubMedCrossRefGoogle Scholar
  35. Fried, J. 1968. Compartmental analysis of kinetic processes in multicellular systems: A necessary condition. Phys. Med. Biol, 13:31–43.CrossRefGoogle Scholar
  36. Garfield, R. E. 1973. Ultrastructural aspects of sodium transport in rat myometrium. Ph.D. Thesis, University of Alberta.Google Scholar
  37. Glass, H. I. and De Garreta, A. C. 1971. The quantitative limitations of exponential curve fitting. Phys. Med. Biol., 16:119–130.PubMedCrossRefGoogle Scholar
  38. Goodford, P. J. 1966. An interaction between potassium and sodium in the smooth muscle of the guinea pig taenia coli. J. Physiol, 186:11–26.PubMedGoogle Scholar
  39. Goodford, P. J. and Hermansen, K. 1961. Sodium and potassium movements in the unstriated muscle of the guinea pig taenia coli. J. Physiol, 158:426–448.PubMedGoogle Scholar
  40. Gutknecht, J. 1968. Permeability of valonia to water and solutes: Apparent absence of aqueous membrane pores. B.B.Ä., 163:20–29.Google Scholar
  41. Harris, E. J. 1965. The chloride permeability of frog sartorius. J. Physiol, 176:123–135.PubMedGoogle Scholar
  42. Harris, E. J. and Burn, G. P. 1949. The transfer of sodium and potassium ions between muscle and the surrounding medium. Trans. Faraday Soc., 45:508–528.CrossRefGoogle Scholar
  43. Hart, R. W. and Hangham, M. E. 1970. The influence of noninstantaneous mixing on the measurement of fluxes of solute and water across a biological membrane. Bull Math. Biophys., 32:1–24.PubMedCrossRefGoogle Scholar
  44. Helfferich, F. 1962.Ion Exchange. New York, McGraw-Hill.Google Scholar
  45. Hersey, S. J. and High, W. L. 1972. Effect of unstirred layers on oxygenation of frog gastric mucosa. Am. J. Physiol, 223:903–909.PubMedGoogle Scholar
  46. Hill, A. V. 1929. The diffusion of oxygen and lactic acid through tissues.Proc. R. Soc. B, 104:41–96.Google Scholar
  47. Hodgson, B. J. and Daniel, E. E. 1972. The effects of excitatory drugs on potassium fluxes in uterine smooth muscle. Can. J. Physiol Pharmacol, 50:725–730.PubMedGoogle Scholar
  48. Hodgson, B. J. and Daniel, E. E. 1973. Calcium and contraction in the pregnant rat uterus. Can. J. Physiol Pharmacol, 50:725–730.Google Scholar
  49. Hodgson, B. J., Kidwai, A. M., and Daniel, E. E. 1972. Uptake of lanthanum by smooth muscle. Can. J. Physiol. Pharmacol, 50:730–733.PubMedGoogle Scholar
  50. Holleman, D. F. 1972. Biological half-time and tracer experiments. Int. J. Appl Radiation and Isotopes, 23:341.CrossRefGoogle Scholar
  51. Holz, R. and Finkelstein, A. 1970. The water and non-electrolyte permeability induced in thin lipid membranes by the polyene antibiotics nystatin and amphotericin B. J. Gen. Physiol, 56:105–145.CrossRefGoogle Scholar
  52. Huxley, A. F. 1960. Appendix 2 to article by Solomon, A. K. Compartmental methods in kinetic analysis. In: Mineral Metabolism, Vol. 1, Part A, pp. 163–166. Ed. by Comar, C. L. and Bronner, F. Academic Press, New York.Google Scholar
  53. Julius, R. S. 1972. The sensitivity of exponentials and other curves to their parameters. Comp. Biomed. Res.,5:473–478.CrossRefGoogle Scholar
  54. Keynes, R. D. 1954. The ionic fluxes in frog muscle. Proc. Roy. Soc. B, 142: 359–382.CrossRefGoogle Scholar
  55. Keynes, R. D. and Swan, R. C. 1959. The effect of external sodium concentration on the sodium fluxes in frog skeletal muscle. J. Physiol, 147:591–625.PubMedGoogle Scholar
  56. Krejci, I. and Daniel, E. E. 1970a. Effect of contraction on movements of calcium 45 into and out of rat myometrium. Am. J. Physiol, 219:256–262.PubMedGoogle Scholar
  57. Krejci, I. and Daniel, E. E. 1970b. Effects of altered external calcium contractions on fluxes of calcium 45 in rat myometrium. Am. J. Physiol, 219:263–269.PubMedGoogle Scholar
  58. Lakshminarayanaiah, N. 1969.Transport Phenomena in Membranes. Academic Press, New York.Google Scholar
  59. Lanczos, C. 1956.Applied analysis. Prentice-Hall, Englewood Cliffs, New Jersey.Google Scholar
  60. Leb, D. E., Hoshiko, T., Lindley, B. D., and Dugan, J. A. 1965. Effects of alkali metal cations on the potential across toad and bullfrog urinary bladder. J. Gen. Physiol, 48:527–540.PubMedCrossRefGoogle Scholar
  61. Lieb, W. R. and Stein, W. D. 1972a. The influence of unstirred layers on the kinetics of carrier-mediated transport.J. Theor. BioL, 36:641–645.PubMedCrossRefGoogle Scholar
  62. Lieb, W. R. and Stein, W. D. 1972b. Carrier and non-carrier models for sugar transport in the human red blood cells.Biochim. Biophys. Acta, 265: 187–207.PubMedCrossRefGoogle Scholar
  63. McLennan, H. 1956. The diffusion of potassium, inulin, and thiocyanate in the extracellular spaces of mammalian muscle. Biochim. Biophys. Acta, 21:472–481.PubMedCrossRefGoogle Scholar
  64. McLennan, H. 1957. The diffusion of potassium, sodium, sucrose and inulin in the extracellular spaces of mammalian tissues. Biochim. Biophys. Acta, 24: 1–8.PubMedCrossRefGoogle Scholar
  65. Miller, D. M. 1972. The effect of unstirred layers on the measurement of transport rates in individual cell. Biochem. Biophys. Acta, 266:85–90.PubMedCrossRefGoogle Scholar
  66. Myhill, J. 1967. Investigation of the effects of data error in the analysis of biological tracer data. Biophys. J., 7:903–911.PubMedCrossRefGoogle Scholar
  67. Myhill, J. 1969. Investigation of the effects of data error in the analysis of biological tracer data from three- compartment systems. J. Theor. Biol., 25:218–231.CrossRefGoogle Scholar
  68. Myhill, J., Wadsworth, G. P., and Brownell, G. L. 1965. Investigations of an operator method in the analysis of biological tracer data. Biophysics. J, 5:89–107.CrossRefGoogle Scholar
  69. Naftalin, R. J. 1970. A model for sugar transport across red cell membranes without carriers. Biochim. Biophys. Acta, 211:65–78.PubMedCrossRefGoogle Scholar
  70. Naftalin, R. J. 1971. The role of unstirred layers in control of sugar movements across red cell membranes. Biochim. Biophys. Acta, 233:635–643.PubMedCrossRefGoogle Scholar
  71. Paton, W. D. M. and Waud, D. R. 1964. A quantitative investigation of the relationship between rate of access of a drug to receptor and the rate of onset or offset of action. Namyn-Schmiedebergs Arch. Exp. Path. u. Pharmak., 248:124–143.CrossRefGoogle Scholar
  72. Perl, W. 1960. A method for curve-fitting for exponential functions.Int. J. Appl. Radiat., 8:222.CrossRefGoogle Scholar
  73. Rangachari, P. S. K. 1972. Metabolic requirements for coupled Na+-K+ exchange and spontaneous contractions in the rat myometrium. PhD. Thesis, University of Alberta.Google Scholar
  74. Rangachari, P. S. K., Paton, D. M. and Daniel, E. E, 1972a. Aerobic and glycolytic support of sodium pumping and contraction in rat myometrium.Am. J. Physiol., 223:1009–1015.PubMedGoogle Scholar
  75. Rangachari, P. S. K., Paton, D. M., and Daniel, E. E. 1972b. Potassium: ATP ratios in smooth muscle. Biochim. Biophys. Acta, 274:462–465.PubMedCrossRefGoogle Scholar
  76. Rangachari, P. S. K., Paton, D. M., and Daniel, E. E. 1973. Regulation of cellular volume in rat myometrium. Biochim. Biophys. Acta, 323:297–308.PubMedCrossRefGoogle Scholar
  77. Robertson, J. S. 1957. Theory and use of tracers in determining transfer rates in biological systems. Physiol. Rev., 37:133–154.PubMedGoogle Scholar
  78. Schäfer, J. A. and Andreoli, T. E. 1972. Water transport in biological and artificial membranes. Arch. Intern. Med., 129:279–292.PubMedCrossRefGoogle Scholar
  79. Sha’afi, R. I., Rich, G. T., Sidel, V. W., Bossert, W., and Solomon, A. K. 1967. The effect of the unstirred layer on human red cell water permeability. J. Gen. Physiol., 50:1377–1399.PubMedCrossRefGoogle Scholar
  80. Smulders, A. P. and Wright, E. M. 1971. The magnitude of nonelectrolyte selectivity in the gallbladder epithehum. J. Membrane Biol, 5:297–318.CrossRefGoogle Scholar
  81. Smulders, A. P., Tormey, J. M., and Wright, E. M. 1972. The effect of osmotically induced water flows on the permeability and ultrastructure of the rabbit gallbladder. J. Membrane Biol., 7:164–197.CrossRefGoogle Scholar
  82. Sonin, A. A. and Grossman, G. 1972. Ion transport through layered ion exchange membranes. J. Phys. Chem., 76:3996–4006.CrossRefGoogle Scholar
  83. Stein, W. D. 1967. The Movements of Molecules across Cell Membranes. Vol. 6, Theoretical and Experimental Biology. Academic Press, New York.Google Scholar
  84. Thron, C. D. 1972a. Nonlinear kinetics of atropine action on the pacemaker of the isolated guinea pig atrium. J. Pharmacol. Exp. Therapeutics, 181:529–537.Google Scholar
  85. Thron, C. D. 1972b. Structure and kinetic behavior of linear multi-compartment systems. Bull. Math. Biophys., 34:211–291.CrossRefGoogle Scholar
  86. Van Breemen, C., Farinas, B., Gerba, P., and McNaughton, E. 1972. Excitation-contraction coupling in arterial smooth muscle studied by the “La method,” for measuring cellular calcium influx. Circ. Res., 30:44–54.PubMedCrossRefGoogle Scholar
  87. Van Liew, H. 1967. Graphic analysis of aggregates of linear and exponential processes. J. Theor. Biol., 16:43–53.PubMedCrossRefGoogle Scholar
  88. Weatherall, M. 1962a. Quantitative analysis of movements of potassium in rabbit auricles. Proc. R. Soc. Lond. B, 156:57–82.PubMedCrossRefGoogle Scholar
  89. Weatherall, M. 1962b. Location of fractions of potassium in rabbit auricles.Proc. R. Soc. Lond. B, 156:83–95.PubMedCrossRefGoogle Scholar
  90. Wedner, H. J. and Diamond, J. M. 1969. Contributions of unstirred layers effects to apparent electrokinetic phenomena in the gallbladder. J. Membrane Biol., 1:92–108.CrossRefGoogle Scholar
  91. Wright, E. M., Smulders, A. P., and Tormey, J. M. 1972. The role of the lateral intercellular spaces and solute polarization effects in the passive flow of water across the rabbit gallbladder. J. Membrane Biol., 7:198–219.CrossRefGoogle Scholar
  92. Zierler, K. L. 1966. Interpretation of tracer washout curves from a population of muscle fibres. J. Gen. Physiol., 49:423–431.PubMedCrossRefGoogle Scholar
  93. Zierler, K. L. 1972. Sodium flux and distribution in skeletal muscle. Scand. J. Clin. Lab. Invest., 29:343–468.PubMedCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1975

Authors and Affiliations

  • E. E. Daniel
    • 1
  1. 1.Department of PharmacologyUniversity of AlbertaEdmontonCanada

Personalised recommendations