Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Application of percolation theory principles to the analysis of interaction of adenylate cyclase complex proteins in cell membranes

  • 32 Accesses

  • 9 Citations


Lateral protein movement in cell membranes takes place in a medium with ‘obstacles’. These obstacles are: (a) aggregates of major integral proteins immobilized by submembraneous structures and cytoskeleton, and (b) membrane lipids in the gel phase. Hormonal activation of the adenylate cyclase complex is associated with lateral mobility of the constituent proteins. Modification of the interaction of these proteins due to variation of the ‘fluid’ lipid fraction in reticulocyte membranes has been studied. A decrease in the percentage of ‘fluid’ lipids in membranes resulted in the inhibition (up to the full cessation) of the interaction of β-adrenoreceptors with regulatory Ns-proteins. The interaction of Ns-proteins with catalytic proteins stopped as well. On the other hand, an increase in the ‘fluid’ lipid fraction led to a more intensive interaction. These facts do not arise from the functional damage of interacting proteins. Conseqently, hormonal activation of the adenylate cyclase complex depends on the fraction of ‘fluid’ lipids in the membrane. The data obtained are in conformity with the percolation theory which makes it possible to characterize long-distance protein movement in a medium (‘fluid’ lipids) containing obstacles. Thus, interacting proteins prove to diffuse within distances greatly exceeding protein sizes. As a consequence, the intrinsic activity of a β-agonist, isoproterenol, varies from 1 to 0 depending on the ‘fluid’ lipid fraction. Our findings also suggest that in vitro there are no β-receptors precoupled with Ns-proteins in rat reticulocyte membranes in the absence of guanine nucleotides.

This is a preview of subscription content, log in to check access.


  1. 1.

    Devaux PF, Seigneuret M: Specificity of lipid-protein interactions as determined by spectroscopic techniques. Biochim Biophys Acta 822:63–125, 1985

  2. 2.

    Peters R: Translational diffusion in the plasma membrane of single cells as studied by fluorescence microphotolysis. Cell Biol Int Rep 5:733–760, 1981

  3. 3.

    Pink DA, Lookman T, Macdonald AL, Zuckerman MJ, Jan N: Lateral diffusion of gramicidin-S, M-13, coat protein and glycophorin in bilayers of saturated phospholipids. Mean field and Monte-Carlo studies. Biochim Biophys Acta 687:42–56, 1982

  4. 4.

    Kapitza HG, Ruppel DA, Galla H-J, Sackmann E: Lateral diffusion of lipids and glycophorin in solid phosphatidylcholine bilayers. The role of structural defects. Biophys J 45:577–587, 1984

  5. 5.

    de Gennes PG: La percolation: un concept unificateur. La Recherche 7:919–927, 1976

  6. 6.

    Stauffer D: Scaling theory of percolation clusters. Phys Rep 54:1–74, 1979

  7. 7.

    Saxton MJ: Lateral diffusion in an archipelago: effects of impermeable patches on diffusion in a cell membrane. Biophys J 39:165–173, 1982

  8. 8.

    Petit VA, Edidin M: Lateral phase separation of lipids in plasma membranes: effect of temperature on the mobility of membrane antigens. Science 184:1183–1185, 1974

  9. 9.

    Swillens SJ: Modulation of catecholamine activation of adenylate cyclase by the number of active beta-adrenergic receptors: theoretical considerations on the role of receptor diffusion in the cell membrane. J Cyclic Nucl Res 8:71–82, 1982

  10. 10.

    Levitzki A: β-Adrenergic receptors and their mode of coupling to adenylate cyclase. Physiol Rev 66:819–854, 1986

  11. 11.

    Gilman AG: G-proteins and dual control of adenylate cyclase. Cell 36:577–579, 1984

  12. 12.

    Stiles GL, Caron MG, Lefkowitz RJ: Beta-adrenergic receptors: biochemical mechanisms of physiological regulation. Physiol Rev 64:661–743, 1984

  13. 13.

    Haest CWM: Interactions between membrane skeleton proteins and the intrinsic domain of the erythrocyte membrane. Biochim Biophys Acta 694:331–352, 1982

  14. 14.

    Harrison DR: Molecular analysis of erythropoiesis: a current appraisal. Exp Cell Res 155:321–344, 1984

  15. 15.

    Sobolev AS, Rosenkranz AA, Kazarov AR: Interaction of proteins of the adenylate cyclase complex: area-limited mobility or movement along whole membrane? Analysis with the application of the percolation theory. Biosci Rep 4:897–902, 1984

  16. 16.

    Sobolev AS, Kazarov AR, Rosenkranz AA, Ganchev Tz: A percolation threshold for lateral movement of proteins of adenylate cyclase complex. Proc Acad Sci USSR 277:501–503, 1984 (in Russian)

  17. 17.

    Larner AC, Ross EM: Alteration in the protein components of catecholamine-sensitive adenylate cyclase during maturation of rat reticulocytes. J Biol Chem 256:9551–9557, 1981

  18. 18.

    Bligh EG, Dyer WJ: A rapid method of total lipid extraction and purification. Can J Biochem Physiol 37:911–916, 1959

  19. 19.

    Petitou M, Tuy F, Rosenfeld C: Simplified procedure for organic phosphorus determination from phospholipids. Anal Biochem 91:350–353, 1978

  20. 20.

    McConnell HM, Wright KM, McFarland BG: Fraction of lipid in a biological membrane that is in a fluid state: spin label assay. Biochem Biophys Res Commun 47:273–278, 1972

  21. 21.

    Vistnes AI, Puskin JS: A spin label method for measuring internal volumes in liposomes or cells applied to Ca-dependent fusion of negatively charged vesicles. Biochim Biophys Acta 644:244–250, 1981

  22. 22.

    Feldman H, Rodbard P, Levin D: Mathematical theory of cross-reactive radioimmunoassay and ligand-binding systems at equilibirum. Anal Biochem 45:530–556, 1972

  23. 23.

    Hancock AA, De Lean A, Lefkowitz RJ: Quantitative resolution of beta-adrenergic receptors subtypes by selective ligand binding: application of a computerized model fitting technique. Mol Pharmacol 16:1–9, 1979

  24. 24.

    Himmelbau DM: Applied Nonlinear Programming. McGrow-Hill Book Company, New York, 1972

  25. 25.

    Houslay MD, Warren GB, Birdsall NJM, Metcalfe JG: Lipid phase-transitions control of beta-hydroxybutyrate dehydrogenase activity in defined lipid protein complexes. FEBS Lett 51:146–151, 1975

  26. 26.

    Lowry OH, Rosebrough NJ, Farr AL, Randell RJ: Protein measurement with the Folin-phenol reagent. J Biol Chem 193:265–275, 1951

  27. 27.

    Counis R, Mongongu S: Adenylate-cyclase assay with alpha-[32P]ATP as substrate: simple modification for lowering blanks. Anal Biochem 84:179–185, 1978

  28. 28.

    Morris DAN, McNeil R, Castellino FJ, Thomas JK: Interaction of lysophosphatidylcholine with phosphatidylcholine bilayers. A photophysical and NMR study. Biochim Biophys Acta 599:380–390, 1980

  29. 29.

    Prilipko LL, Kagan VE, Turin VA, Gorbunov NV, Bogdanova HD: Modification of lipids and changes of β-adrenoreceptors' properties in brain synaptosomes. Proc Acad Sci USSR 269:1260–1263, 1983 (in Russian)

  30. 30.

    Limbird LE, Macmillan SJ: Mn2+-uncoupling of the catecholamine sensitive AC system of rat rcticulocytes: parallel effects on cholera-toxin-catalyzed ADP-ribosylation of the system. Biochim Biophys Acta 677:408–416, 1981

  31. 31.

    Cassel D, Selinger Z: Catecholamine-induced release of Gpp(NH)p-[3H] from turkey erythrocyte adenylate cyclase. J Cyclic Nucl Res 3:11–22, 1977

  32. 32.

    Havlin S, Ben-Avraham D, Sompolinsky H: Scaling behaviour of diffusion on percolation clusters. Phys Rev A 27:1730–1733, 1983

  33. 33.

    Henis YI, Hekman M, Elson EL, Helmreich EJM: Lateral motion of β-receptors in membranes of cultured liver cells. Proc Natl Acad Sci USA 79:2907–2911, 1982

  34. 34.

    Kent RS, De Lean A, Lefkowitz RJ: Quantitative analysis of beta-adrenergic receptor interactions: resolution of high and low affinity states of the receptor by computer modelling of ligand-binding data. Mol Pharmacol 17:14–23, 1980

  35. 35.

    Gawlinski ET, Stanley HE: Continuum percolation in two dimensions: Monte-Carlo tests of scaling and universality for non-interacting discs. J Phys A 14:L291-L299, 1981

  36. 36.

    Axelrod D: Lateral motion of membrane proteins and biological function. J Membrane Biol 75:1–10, 1983

  37. 37.

    Levinshtein ME, Shkloviskii BI, Shur MS, Efros AL: On the relation between critical indices of percolation theory. JETP 69:386–392, 1975 (in Russian)

Download references

Author information

Correspondence to Alexander S. Sobolev.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sobolev, A.S., Kazarov, A.R. & Rosenkranz, A.A. Application of percolation theory principles to the analysis of interaction of adenylate cyclase complex proteins in cell membranes. Mol Cell Biochem 81, 19–28 (1988). https://doi.org/10.1007/BF00225649

Download citation

Key words

  • cell membrane
  • adenylate cyclase
  • percolation theory
  • protein-protein interaction