The Journal of Membrane Biology

, Volume 74, Issue 2, pp 139–153 | Cite as

Electrical and biochemical properties of an enzyme model of the sodium pump

  • J. Brian Chapman
  • Edward A. Johnson
  • J. Mailen Kootsey


The electrochemical properties of a widely accepted six-step reaction scheme for the Na+, K+-ATPase have been studied by computer simulation. Rate coefficients were chosen to fit the nonvectorial biochemical data for the isolated enzyme and a current-voltage (I–V) relation consistent with physiological observations was obtained with voltage dependence restricted to one (but not both) of the two translocational steps. The vectorial properties resulting from these choices were consistent with physiological activation of the electrogenic sodium pump by intracellular and extracellular sodium (Na+) and potassium (K+) ions. The model exhibited K+/K+ exchange but little Na+/Na+ exchange unless the energy available from the splitting of adenosine triphosphate (ATP) was reduced, mimicking the behavior seen in squid giant axon. The vectorial ionic activation curves were voltage dependent, resulting in large shifts in apparent Km's with depolarization. At potentials more negative than the equilibrium or reversal potential transport was greatly diminished unless the free energy of ATP splitting was reduced. While the pump reversal potential is at least 100 mV hyperpolarized relative to the resting potential of most cells, the voltage-dependent distribution of intermediate forms of the enzyme allows the possibility of considerable slope conductance of the pumpI–V relation in the physiological range of membrane potentials. Some of the vectorial properties of an electrogenic sodium pump appear to be inescapable consequences of the nonvectorial properties of the isolated enzyme. Future application of this approach should allow rigorous quantitative testing of interpretative ideas concerning the mechanism and stoichiometry of the sodium pump.

Key Words

Na+, K+-ATPase sodium pump electrogenic computer simulation enzyme kinetics thermodynamics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Atkinson, D.E. 1977. Cellular Energy Metabolism and its Regulation. Academic Press, New YorkGoogle Scholar
  2. Attwell, D., Cohen, I., Eisner, D.A. 1979. Membrane potential stability conditions for a cell with a restricted extra-cellular space.Proc. R. Soc. London B 206:145–161Google Scholar
  3. Bockris, J.O'M., Reddy, A.K.N. 1970. Modern electrochemistry: An Introduction to an Interdisciplinary Area. Plenum Press, New YorkGoogle Scholar
  4. Boudart, M. 1976. Consistency between kinetics and thermodynamics.J. Phys. Chem. 80:2869–2870Google Scholar
  5. Brinley, F.J., Mullins, L.J. 1968. Sodium fluxes in internally dialyzed squid axons.J. Gen. Physiol. 52:181–211Google Scholar
  6. Brown, H., Di Francesco, D., Noble, D., Noble, S. 1980. The contribution of potassium accumulation to outward currents in frog atrium.J. Physiol. (London) 306:127–149Google Scholar
  7. Caldwell, P.C., Hodgkin, A.L., Keynes, R.D., Shaw, T.I. 1960. Partial inhibition of the active transport of cations in the giant axons ofLoligo.J. Physiol. (London) 152:591–600Google Scholar
  8. Chapman, J.B. 1973. On the reversibility of the sodium pump in dialyzed squid axons. A method for determining the free energy of ATP breakdown?J. Gen. Physiol. 62:643–646Google Scholar
  9. Chapman, J.B. 1982. A kinetic interpretation of “variable” stoichiometry for an electrogenic sodium pump obeying chemiosmotic principles.J. Theor. Biol. 95:665–678Google Scholar
  10. Chapman, J.B. 1983. Thermodynamics and kinetics of electrogenic pumps.In: Electrogenic Transport. Fundamental Principles and Physiological Implications. M.P. Blaustein and M. Lieberman, editors. Raven Press, New York (in press)Google Scholar
  11. Chapman, J.B., Johnson, E.A. 1978. The reversal potential for an electrogenic sodium pump: A method for determining the free energy of ATP breakdown?J. Gen. Physiol. 72:403–408Google Scholar
  12. Chapman, J.B., Kootsey, J.M., Johnson, E.A. 1979. A kinetic model for determining the consequences of electrogenic active transport in cardiacmuscle.J. Theor. Biol. 80:405–424Google Scholar
  13. Chapman, J.B., McKinnon, I.R. 1978. Consistency between thermodynamics and kinetic models of ion transport processes.Proc. Aust. Soc. Biophys. 2:3–7Google Scholar
  14. Chapman, K.M. 1980. The sodium pump as a current source: Linear thermodynamic equations for the transmembrane potential and its transient responses to changes in transport rate.Physiologist 76:18aGoogle Scholar
  15. Chipperfield, A.R., Whittham, R. 1974. Evidence that ATP is hydrolysed in a one step reaction of the sodium pump.Proc. R. Soc. London B 187:269–280Google Scholar
  16. Daut, J., Rudel, R. 1981. Cardiac glycoside binding to the Na/K-ATPase in the intact myocardial cell: Electrophysiological measurement of chemical kinetics.J. Mol. Cell. Cardiol. 13:777–782Google Scholar
  17. Fried, I. 1973. The chemistry of electrode processes. Academic Press, LondonGoogle Scholar
  18. Gadsby, D.C., Cranefield, P.F. 1979a. Direct measurement of changes in sodium pump current in canine cardiac Purkinje fibers.Proc. Natl. Acad. Sci. USA 76:1783–1787Google Scholar
  19. Gadsby, D.C., Cranefield, P.F. 1979b. Electrogenic sodium extrusion in cardiac Purkinje fibers.J. Gen. Physiol. 73:819–837Google Scholar
  20. Garay, R.P., Garrahan, P.J. 1973. The interactions of sodium and potassium with the sodium pump in red cells.J. Physiol. (London) 231:297–325Google Scholar
  21. Garrahan, P.J., Glynn, I.M. 1967a. Factors affecting the relative magnitudes of the sodium: potassium and sodium: sodium exchanges catalysed by the sodium pump.J. Physiol. (London) 192:189–216Google Scholar
  22. Garrahan, P.J., Glynn, I.M. 1967b. The incorporation of inorganic phosphate into adenosine triphosphate by reversal of the sodium pump.J. Physiol. (London) 192:237–256Google Scholar
  23. Gradmann, D., Hansen, U.-P., Slayman, C.L. 1981. Reaction kinetic analysis of current-voltage relationships for electrogenic pumps inNeurospora andAcetabularia.Curr. Top. Membr. Transp. 16:257–276Google Scholar
  24. Guidotti, G. 1979. Coupling of ion transport to enzyme activity.In: The Neurosciences, Fourth Study Program. I.O. Schmitt and F.G. Worden, editors. pp. 831–840. MIT Press, Boston, Mass.Google Scholar
  25. Hall, J.E., Mead, C.A., Szabo, G. 1973. A barrier model for current flow in lipid bilayer membranes.J. Membrane Biol. 11:75–97Google Scholar
  26. Hammes, G.G., Schimmel, P.R. 1970. Rapid reactions and transient states.In: The Enzymes, 3rd ed. P.D. Boyer, editor. Vol. II, Ch. 2. Academic Press, New YorkGoogle Scholar
  27. Hansen, U.-P., Gradmann, D., Slayman, C.L. 1981. Interpretation of current-voltage relationships for “active” ion transport systems: I. Steady-state reaction-kinetic analysis of class-I mechanisms.J. Membrane Biol. 63:165–190Google Scholar
  28. Hassinen, I.E., Hiltunen, K. 1975. Respiratory control in isolated perfused rat heart. Role of the equilibrium relations between the mitochondrial electron carriers and the adenylate system.Biochim. Biophys. Acta 408:319–330Google Scholar
  29. Hoffman, P.G., Tosteson, D.C. 1971. Active sodium and potassium transport in high potassium and low potassium sheep red cells.J. Gen. Physiol. 58:438–466Google Scholar
  30. Jack, J.J.B., Noble, D., Tsien, R.W. 1975. Electric current flow in excitable cells. Oxford University Press, OxfordGoogle Scholar
  31. Jakobsson, E. 1980. Interactions of cell volume, membrane potential, and membrane transport parameters.Am. J. Physiol. 238:C196-C206Google Scholar
  32. Johnson, E.A., Chapman, J.B., Kootsey, J.M. 1980. Some electrophysiological consequences of electrogenic sodium and potassium transport in cardiac muscle: A theoretical study.J. Theor. Biol. 87:737–756Google Scholar
  33. Jorgensen, P.L. 1980. Sodium and potassium ion pump in kidney tubules.Physiol. Rev. 60:864–917Google Scholar
  34. Keizer, J. 1975. Thermodynamic coupling in chemical reactions.J. Theor. Biol. 49:323–335Google Scholar
  35. Keynes, R.D., Swan, R.C. 1959. The effect of external sodium concentration on the sodium fluxes in frog skeletal muscle.J. Physiol. (London) 147:591–625Google Scholar
  36. Kootsey, J.M., Johnson, E.A., Chapman, J.B. 1981. Electrochemical inhomogeneity in ungulate Purkinje fibers: Model of electrogenic transport and electrodiffusion in clefts.Adv. Physiol. Sci. 8:83–92Google Scholar
  37. Lauger, P., Stark, G. 1970. Kinetics of carrier-mediated ion transport across lipid bilayer membranes.Biochim. Biophys. Acta 211:458–466Google Scholar
  38. Lieberman, M., Sawanobori, T., Kootsey, J.M., Johnson, E.A. 1975. A synthetic strand of cardiac muscle. Its passive properties.J. Gen. Physiol. 65:527–550Google Scholar
  39. Michael, L.H., Schwartz, A., Wallick, E.T. 1979. Nature of the transport adenosine triphosphatase-digitalis complex: XIV. Inotropy and cardiac glycoside interaction with cat ventricular muscle.Mol. Pharmacol. 16:135–146Google Scholar
  40. Mitchell, P. 1977. Epilogue: From Energetic abstraction to biochemical mechanism.Symp. Soc. Gen. Microbiol. 27:383–423Google Scholar
  41. Mobley, B.A., Page, E. 1972. The surface area of sheep cardiac Purkinje fibers.J. Physiol. (London) 220:547–563Google Scholar
  42. Mullins, L.J., Frumento, A.S. 1963. The concentration dependence of sodium efflux from muscle.J. Gen. Physiol. 46:629–654Google Scholar
  43. Rapoport, S.I. 1970. The sodium-potassium exchange pump: Relation of metabolism to electrical properties of the cell. I. Theory.Biophys. J. 10:246–259Google Scholar
  44. Sachs, J.R. 1977. Kinetic evaluation of the Na−K pump reaction mechanism.J. Physiol. (London) 273:489–514Google Scholar
  45. Scriven, D.R.L. 1981. Modeling repetitive firing and bursting in a small unmyelinated nerve fiber.Biophys. J. 35:715–730Google Scholar
  46. Skou, J.C. 1957. The influence of some cations on an adenosinetriphosphatase from peripheral nerves.Biochim. Biophys. Acta 23:394–401Google Scholar
  47. Skou, J.C. 1975. The (Na++K+) activated enzyme system and its relationship to transport of sodium and potassium.Q. Rev. Biophys. 7:401–434Google Scholar
  48. Tanford, C. 1981. Equilibrium state of ATP-driven ion pumps in relation to physiological ion concentration gradients.J. Gen. Physiol. 77:223–229Google Scholar
  49. Veech, R.L., Lawson, J.W.R., Cornell, N.W., Krebs, H.A. 1979. Cytosolic phosphorylation potential.J. Biol. Chem. 254:6538–6547Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1983

Authors and Affiliations

  • J. Brian Chapman
    • 1
    • 2
  • Edward A. Johnson
    • 1
    • 2
  • J. Mailen Kootsey
    • 1
    • 2
  1. 1.Departments of PhysiologyMonash UniversityClaytonAustralia
  2. 2.Duke University Medical CenterDurham

Personalised recommendations