Comprehensive Physiology Wiley Online Library
For Librarians For Authors Editors About

Principles of Membrane Transport

David C. Dawson

10.1002/cphy.cp060401

Source: Supplement 19: Handbook of Physiology, The Gastrointestinal System, Intestinal Absorption and Secretion

Originally published: 1991

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Transport Energetics
1.1 Cell Composition: Keeping Away From Equilibrium
1.2 Thermodynamic Taxonomy of Transport
1.3 Electrochemical Potential and Driving Force for Passive Transport
1.4 Units for Electrochemical Potential Difference
1.5 Nature of Driving Forces
1.6 Analysis of Transport: Uncovering Coupled Processes
1.7 Energetics of Coupled Transport
2 Transport Mechanisms
2.1 Tracer Flows
2.2 Equations of Motion for Solute Flow
2.3 Solubility‐Diffusion Model
2.4 Ion Permeability of a Lipid Bilayer: Why We Have Ion Channels
2.5 Simplest Ion Channel: A Waterlike Pore
2.6 Toward More Realistic Models
2.7 Channel Gating
2.8 Carriers as Channels With Special Gating Properties
3 Ion Transport and Bioelectricity
3.1 Introduction to Equivalent Circuits and Two Forms of Ohm's Law
3.2 Sign Conventions for Voltage and Current
3.3 Voltage Clamping
3.4 Equivalent Circuits for Cell Membranes
3.5 Current‐Voltage Relations: Ion Channels, Ion Conductance, and Cell Membrane
3.6 Effect of Pumps on Membrane Potential
3.7 Special Properties of Epithelial Cell Layers
Figure 1. Figure 1.

Hypothetical cell possessing a variety of energy‐converting transport proteins: a Na+ ‐K+ ‐ATPase, a Na+ ‐K+ ‐2Cl− cotransporter, a Na+ ‐H+ exchanger, a Na+‐amino acid (AA) cotransporter, and a Na+ ‐Ca2+ exchanger. For completeness leak pathways for Na+, K+, and Cl− are shown.
Figure 2. Figure 2.

Membrane separates 2 solutions containing Na+, K+, and Cl−. In presence of gradients of concentration and electrical potential, what is the direction of passive force on each ion? For Na+ the answer is straightforward, because both gradients would tend to move ion in same direction. In case of Cl− only an electrical gradient exists. For K+ the situation is more complicated, since gradients of concentration and electrical potential are opposed. To determine net passive driving force, 2 opposing forces must be expressed in the same units (see text for details). Vm, membrane potential.
Figure 3. Figure 3.

A–C: examples of energy barrier diagrams, which are a useful way of visualizing transport processes from the standpoint of reaction rate theory. Each profile represents a plot of standard chemical potential (standard free energy) vs. distance. Peaks and troughs represent changes in nature of molecular interaction of transported species with the environment. G01 and G02 represent standard free energies of initial and final states, respectively, and G0p represents peak standard free energy associated with barrier separating the 2 states. D: diagrammatic representation of influence of a potential difference on energy profile for a translocation from site 1 to site 2. Note that energy barrier governing forward and backward rates as well as the equilibrium distribution is influenced by potential. Parameters δ12 and δ21 represent fractional distances for forward and reverse rates, respectively, where δ12 + δ21 = δ = 1 in this example. Potential gradient is assumed to be linear. Note that ΔG012 = G0p − G01, ΔG021 = G0p − G02 and ΔG0 = G02 − G01. See text for abbreviations. [Redrawn from Moczydlowski 85.]
Figure 4. Figure 4.

A: concentration profiles for solubility‐diffusion transport processes. Three hypothetical solutes are present in identical concentrations (C) in bathing solutions but have partition coefficients of 1, 3, and 1/3. Profiles are shown in presence and in absence of concentration gradient. B: energy barriers for solubility‐diffusion. Diffusion barriers in bathing solutions are depicted to emphasize general similarity of solute movement in aqueous solution and membrane. In actual fact, however, in absence of unstirred layers, movement of solute to membrane surface would be by convection (stirring) not diffusion. C: a simple two‐barrier, one‐well model for transmembrane diffusion. Peak barrier height (ΔG0p) determines the permeability. Also indicated is energy minimum (ΔG0m), which determines equilibrium partition coefficient, and peak‐to‐well difference (ΔG0u), which determines rate of intramembrane diffusion.
Figure 5. Figure 5.

Schematic representation of origin of electrostatic energy (“Born energy”) required to move an ion from an aqueous region into an oil or lipid membrane.
Figure 6. Figure 6.

Energy profile for hypothetical channels that can contain 1 or 2 ions. WB is electrostatic, or Born, energy and Wchem is energy due to local interactions of ion with channel. [Based on suggestions by Dani 107 and Andersen and Procopio 4.]
Figure 7. Figure 7.

State diagram that depicts all possible states of a channel that may be occupied simultaneously by 2 ions. OO, unoccupied; KO, singly occupied left; OK, singly occupied right; KK, doubly occupied. Rate coefficients (k) reflect physical processes involved in transitions between states: ion entry into and exit from singly or doubly occupied channels and translocation from one site to another within channel.
Figure 8. Figure 8.

Representative recording of current through a single K+ channel showing dwell times, to and tc, in open and closed states (N. W. Richards and D. C. Dawson, unpublished observations).
Figure 9. Figure 9.

Hypothetical scheme for “carrier type” solute translocation that relates kinetic process of binding, translocation, and unbinding of a solute A to sequential changes in energy profile for a membrane‐spanning protein. Binding of A to protein on side 1 (A1X1) induces a conformational change that results in profile A2X2, which facilitates unloading of A into side 2. Unbound protein X2 spontaneously reverts to original configuration.

[Adapted from Läuger 72.]
Figure 10. Figure 10.

Equivalent circuits for an ion channel in absence and in presence of a concentration gradient. Electrode resistances are denoted re. In current‐passing loop value of re is assumed to be small with respect to that of variable resistance. In voltage‐sensing loop values of re could be relatively high, but an ideal voltmeter has a high internal resistance, so that no current flows in the loop. The series or “access” resistance between tips of voltage‐sensing electrodes and membrane surface is not considered. Vm, membrane potential; Im, membrane current; gK, membrane conductance; EK ≡ RT/F ln[K]1/[K]2.
Figure 11. Figure 11.

A: physical set up for determining current‐voltage relation for battery. B: incorrect equivalent circuit that does not recognize the internal resistance of the battery. C: correct circuit contains, in addition to an emf, a dissipative element (Rb), which represents tendency of battery itself to dissipate free energy. See text for other abbreviations.
Figure 12. Figure 12.

This diagram illustrates how 4 possible conventions for polarity of voltage (V) or current (I) result from 4 possible ways in which a voltmeter and an ammeter can be connected in a circuit. Note that actual direction of current flow (shown by arrows) is identical in each case, but this current can be measured as a “positive” or “negative” value. R, resistance; E, electromotive force (emf).
Figure 13. Figure 13.

Diagram of a voltage clamp circuit designed to control membrane potential (Vm) by passing current across the membrane (Im) and varying dissipative (IR) contribution to membrane potential. Electrode resistances are denoted as re. Rm, membrane resistance.
Figure 14. Figure 14.

A: hypothetical cell that contains conductive leak pathways for Na+, K+ and Cl− and maintains electrochemical potential gradients for these ions by virtue of energy converters. B: equivalent circuit for cell membrane neglecting contribution of an electrogenic pump (Na+‐K+‐ATPase). C: equivalent circuit including influence of pump, which is considered here to function as a constant current source. See text for abbreviations.
Figure 15. Figure 15.

Diagramatic representation of relation of cell membrane potential to values of ionic emfs, showing result for 2 initial conditions of either increasing or decreasing membrane chloride conductance (gCl). Initial conditions are assumed to be ENa, EK, and ECl equal to 60 mV, 90 mV, and 30 mV, respectively, and gNa, gK, and gCl are 0.1 μS, 0.5 μS, and 3 μS, respectively, so that resting Vm is ∼53 mV inside negative. Increasing gCl depolarizes Vm, because ECl < Vm. If Vm is depolarized to a value < ECl, however, then an increase in gCl hyperpolarizes Vm, because ECl > Vm. See text for other abbreviations.
Figure 16. Figure 16.

Current‐voltage (I‐V) relations for membrane, as diagrammed in Fig. 14B, and each of 3 ion conductances. For simplicity I‐V relations are drawn assuming that cell ion conductances are voltage independent. Note that because pump current is neglected resting potential is at point where 3 currents sum to zero. See text for abbreviations.
Figure 17. Figure 17.

Koefoed‐Johnsen‐Ussing model for active Na+ transport and a simple equivalent circuit representation of series membrane system. See text for abbreviations.
Figure 18. Figure 18.

Hypothetical series membrane arrangement consisting of a K+‐selective membrane in series with a membrane containing conductances for both K+ and Cl− and equivalent circuit representation. Orientation of ECl was chosen arbitrarily. See text for abbreviations.


Figure 1.

Hypothetical cell possessing a variety of energy‐converting transport proteins: a Na+ ‐K+ ‐ATPase, a Na+ ‐K+ ‐2Cl− cotransporter, a Na+ ‐H+ exchanger, a Na+‐amino acid (AA) cotransporter, and a Na+ ‐Ca2+ exchanger. For completeness leak pathways for Na+, K+, and Cl− are shown.



Figure 2.

Membrane separates 2 solutions containing Na+, K+, and Cl−. In presence of gradients of concentration and electrical potential, what is the direction of passive force on each ion? For Na+ the answer is straightforward, because both gradients would tend to move ion in same direction. In case of Cl− only an electrical gradient exists. For K+ the situation is more complicated, since gradients of concentration and electrical potential are opposed. To determine net passive driving force, 2 opposing forces must be expressed in the same units (see text for details). Vm, membrane potential.



Figure 3.

A–C: examples of energy barrier diagrams, which are a useful way of visualizing transport processes from the standpoint of reaction rate theory. Each profile represents a plot of standard chemical potential (standard free energy) vs. distance. Peaks and troughs represent changes in nature of molecular interaction of transported species with the environment. G01 and G02 represent standard free energies of initial and final states, respectively, and G0p represents peak standard free energy associated with barrier separating the 2 states. D: diagrammatic representation of influence of a potential difference on energy profile for a translocation from site 1 to site 2. Note that energy barrier governing forward and backward rates as well as the equilibrium distribution is influenced by potential. Parameters δ12 and δ21 represent fractional distances for forward and reverse rates, respectively, where δ12 + δ21 = δ = 1 in this example. Potential gradient is assumed to be linear. Note that ΔG012 = G0p − G01, ΔG021 = G0p − G02 and ΔG0 = G02 − G01. See text for abbreviations. [Redrawn from Moczydlowski 85.]



Figure 4.

A: concentration profiles for solubility‐diffusion transport processes. Three hypothetical solutes are present in identical concentrations (C) in bathing solutions but have partition coefficients of 1, 3, and 1/3. Profiles are shown in presence and in absence of concentration gradient. B: energy barriers for solubility‐diffusion. Diffusion barriers in bathing solutions are depicted to emphasize general similarity of solute movement in aqueous solution and membrane. In actual fact, however, in absence of unstirred layers, movement of solute to membrane surface would be by convection (stirring) not diffusion. C: a simple two‐barrier, one‐well model for transmembrane diffusion. Peak barrier height (ΔG0p) determines the permeability. Also indicated is energy minimum (ΔG0m), which determines equilibrium partition coefficient, and peak‐to‐well difference (ΔG0u), which determines rate of intramembrane diffusion.



Figure 5.

Schematic representation of origin of electrostatic energy (“Born energy”) required to move an ion from an aqueous region into an oil or lipid membrane.



Figure 6.

Energy profile for hypothetical channels that can contain 1 or 2 ions. WB is electrostatic, or Born, energy and Wchem is energy due to local interactions of ion with channel. [Based on suggestions by Dani 107 and Andersen and Procopio 4.]



Figure 7.

State diagram that depicts all possible states of a channel that may be occupied simultaneously by 2 ions. OO, unoccupied; KO, singly occupied left; OK, singly occupied right; KK, doubly occupied. Rate coefficients (k) reflect physical processes involved in transitions between states: ion entry into and exit from singly or doubly occupied channels and translocation from one site to another within channel.



Figure 8.

Representative recording of current through a single K+ channel showing dwell times, to and tc, in open and closed states (N. W. Richards and D. C. Dawson, unpublished observations).



Figure 9.

Hypothetical scheme for “carrier type” solute translocation that relates kinetic process of binding, translocation, and unbinding of a solute A to sequential changes in energy profile for a membrane‐spanning protein. Binding of A to protein on side 1 (A1X1) induces a conformational change that results in profile A2X2, which facilitates unloading of A into side 2. Unbound protein X2 spontaneously reverts to original configuration.

[Adapted from Läuger 72.]


Figure 10.

Equivalent circuits for an ion channel in absence and in presence of a concentration gradient. Electrode resistances are denoted re. In current‐passing loop value of re is assumed to be small with respect to that of variable resistance. In voltage‐sensing loop values of re could be relatively high, but an ideal voltmeter has a high internal resistance, so that no current flows in the loop. The series or “access” resistance between tips of voltage‐sensing electrodes and membrane surface is not considered. Vm, membrane potential; Im, membrane current; gK, membrane conductance; EK ≡ RT/F ln[K]1/[K]2.



Figure 11.

A: physical set up for determining current‐voltage relation for battery. B: incorrect equivalent circuit that does not recognize the internal resistance of the battery. C: correct circuit contains, in addition to an emf, a dissipative element (Rb), which represents tendency of battery itself to dissipate free energy. See text for other abbreviations.



Figure 12.

This diagram illustrates how 4 possible conventions for polarity of voltage (V) or current (I) result from 4 possible ways in which a voltmeter and an ammeter can be connected in a circuit. Note that actual direction of current flow (shown by arrows) is identical in each case, but this current can be measured as a “positive” or “negative” value. R, resistance; E, electromotive force (emf).



Figure 13.

Diagram of a voltage clamp circuit designed to control membrane potential (Vm) by passing current across the membrane (Im) and varying dissipative (IR) contribution to membrane potential. Electrode resistances are denoted as re. Rm, membrane resistance.



Figure 14.

A: hypothetical cell that contains conductive leak pathways for Na+, K+ and Cl− and maintains electrochemical potential gradients for these ions by virtue of energy converters. B: equivalent circuit for cell membrane neglecting contribution of an electrogenic pump (Na+‐K+‐ATPase). C: equivalent circuit including influence of pump, which is considered here to function as a constant current source. See text for abbreviations.



Figure 15.

Diagramatic representation of relation of cell membrane potential to values of ionic emfs, showing result for 2 initial conditions of either increasing or decreasing membrane chloride conductance (gCl). Initial conditions are assumed to be ENa, EK, and ECl equal to 60 mV, 90 mV, and 30 mV, respectively, and gNa, gK, and gCl are 0.1 μS, 0.5 μS, and 3 μS, respectively, so that resting Vm is ∼53 mV inside negative. Increasing gCl depolarizes Vm, because ECl < Vm. If Vm is depolarized to a value < ECl, however, then an increase in gCl hyperpolarizes Vm, because ECl > Vm. See text for other abbreviations.



Figure 16.

Current‐voltage (I‐V) relations for membrane, as diagrammed in Fig. 14B, and each of 3 ion conductances. For simplicity I‐V relations are drawn assuming that cell ion conductances are voltage independent. Note that because pump current is neglected resting potential is at point where 3 currents sum to zero. See text for abbreviations.



Figure 17.

Koefoed‐Johnsen‐Ussing model for active Na+ transport and a simple equivalent circuit representation of series membrane system. See text for abbreviations.



Figure 18.

Hypothetical series membrane arrangement consisting of a K+‐selective membrane in series with a membrane containing conductances for both K+ and Cl− and equivalent circuit representation. Orientation of ECl was chosen arbitrarily. See text for abbreviations.

References
 1. Almers, W., and E. W. McCleskey. Non‐selective conductance in calcium channels of frog muscle: calcium selectivity in a single‐file pore. J. Physiol. Lond. 353: 585–608, 1984.
 2. Almers, W., E. W. McCleskey, and P. T. Palade. A nonselective cation conductance in frog muscle membrane blocked by micromolar external calcium ions. J. Physiol. Lond. 353: 565–583, 1984.
 3. Altimirano, A. A., and J. M. Russell. Coupled Na/K/Cl efflux: “reverse” unidirectional fluxes in squid giant axons. J. Gen. Physiol. 89: 669–686, 1987.
 4. Andersen, O. S., and J. Procopio. Ion movement through gramicidin A channels: on the importance of the aqueous diffusion resistance and ion‐water interactions. Acta Physiol. Scand. Suppl. 481: 27–35, 1980.
 5. Andreoli, T. E., J. F. Hoffman, D. D. Fanestil, and S. G. Schultz. Physiology of Membrane Disorders. New York: Plenum, 1986.
 6. Apell, H.‐J., R. Borlinghaus, and P. Lauger. Fast charge translocations associated with partial reactions of the Na,K pump. II. Microscopic analysis of transient currents. J. Membr. Biol. 97: 179–191, 1987.
 7. Aronson, P. S. Identifying secondary active solute transport in epithelia. Am. J. Physiol. 240 (Renal Fluid Electrolyte Physiol. 9): F1–F11, 1981.
 8. Aronson, P. S. Electrochemical driving forces for secondary active transport: energetics and kinetics of Na+‐H+ exchange and Na+‐glucose cotransport. In: Electrogenic Transport: Fundamental Principles and Physiological Implications, edited by M. P. Blaustein and M. Lieberman. New York: Raven, 1984, p. 49–70.
 9. Aronson, P. S., J. Nee, and M. A. Suhm. Modifier role of internal H+ in activating the Na+‐H+ exchanger in renal microvillus membrane vesicles. Nature Lond. 299: 161–163, 1982.
 10. Berg, H. C. Random Walks in Biology. Princeton, NJ: Princeton Univ. Press, 1983.
 11. Bezanilla, F. Gating of sodium and potassium channels. J. Membr. Biol. 88: 97–111, 1985.
 12. Bezanilla, F., and C. M. Armstrong. Negative conductance caused by entry of sodium and cesium ions into the potassium channels of squid axons. J. Gen. Physiol. 60: 588–608, 1972.
 13. Bockris, J. O., and A. K. N. Reddy. Modern Electrochemistry. New York: Plenum, 1970, vol. 1.
 14. Borlinghaus, R., H.‐J. Apell, and P. Lauger. Fast charge translocations associated with partial reactions of the Na, K‐pump. I. Current and voltage transients after photochemical release of ATP. J. Membr. Biol. 97: 161–178, 1987.
 15. Britton, H. G. Induced uphill and downhill transport: relationship to the Ussing criterion. Nature Lond. 198: 190–191, 1963.
 16. Britton, H. G. The Ussing relationship and chemical reactions: possible applications to enzymatic investigations. Nature Lond. 205: 1323–1324, 1965.
 17. Britton, H. G. Relationship between the number of interacting particles and flux‐ratio. Nature Lond. 209: 296, 1966.
 18. Carslaw, H. S., and J. C. Jaeger. Conduction of Heat in Solids (2nd ed.). Oxford, UK: Clarendon, 1959.
 19. Colquhoun, D., and A. G. Hawkes. The principles of the stochastic interpretation of ion‐channel mechanisms. In: Single‐Channel Recording, edited by B. Sakmann and E. Neher, New York: Plenum, 1983, chapt. 9, p. 139–175.
 20. Coronado, R., R. Rosenberg, and C. Miller. Ionic selectivity, saturation, and block in an K+‐selective channel from sacroplasmic reticulum. J. Gen. Physiol. 76: 425–446, 1980.
 21. Curran, P. F., and S. G. Schultz. Transport across membranes: general principles. Handbook of Physiology. Alimentary Canal. Washington, DC: Am. Physiol. Soc., 1968, sect. 6, vol. III, chapt. 65, p. 1217–1243.
 22. Dani, J. A. Ion‐channel entrances influence permeation: net charge, size, shape, and binding considerations. Biophys. J. 49: 607–618, 1986.
 23. Dawson, D. C. Tracer flux ratios: a phenomenological approach. J. Membr. Biol. 31: 351–358, 1977.
 24. Dawson, D. C. Thermodynamic aspects of radiotracer flow. In: Biological Transport of Radiotracers, edited by L. G. Colombetti. Boca Raton, FL: CRC, 1982, chapt. 6, p. 79–95.
 25. Dawson, D. C. Properties of epithelial potassium channels. In: Current Topics in Membranes and Transport. New York: Academic, 1987, vol. 28, p. 41–71.
 26. Denbigh, K. The Principles of Chemical Equilibrium (3rd ed). New York: Cambridge Univ. Press, 1971.
 27. De Weer, P. Na,K‐ATPase: reaction mechanisms and ion translocating steps. In: Current Topics in Membranes and Transport. New York: Academic, 1983, vol. 19, p. 599–623.
 28. De Weer, P. Electrogenic pumps: theoretical and practical considerations. In: Electrogenic Transport: Fundamental Principles and Physiological Implications, edited by M. P. Blaustein and M. Lieberman, New York: Raven, 1984, p. 1–15.
 29. De Weer, P., and R. F. Rakowski. Current generated by backward‐running electrogenic Na pump in squid giant axons. Nature Lond. 309: 450–452, 1984.
 30. Einstein, A. Investigations on the Theory of the Brownian Movement. New York: Dover, 1956.
 31. Eisenman, G., and J. A. Dani. An introduction to molecular architecture and permeability of ion channels. Annu. Rev. Biophys. Chem. 16: 205–226, 1987.
 32. Eisenman, G., and R. Horn. Ionic selectivity revisited: the role of kinetic and equilibrium processes in ion permeation through channels. J. Membr. Biol. 76: 197–225, 1983.
 33. Finkelstein, A. Discussion paper. In: Carriers and Channels in Biological Systems, edited by A. E. Shamoo. New York: Ann. NY Acad. Sci. 1975, p. 244–245.
 34. Finkelstein, A. Water and nonelectrolyte permeability of lipid bilayer membranes. J. Gen. Physiol. 68: 127–135, 1976.
 35. Finkelstein, A. Nature of the water permeability increase induced by antidiuretic hormone (ADH) in toad urinary bladder and related tissues. J. Gen. Physiol. 68: 137–143, 1976.
 36. Finkelstein, A. Water Movement Through Lipid Bilayers, Pores and Plasma Membranes: Theory and Reality. New York: Wiley, 1987.
 37. Finkelstein, A., and O. S. Andersen. The gramicidin A channel: a review of its permeability characteristics with special reference to the single‐file aspect of transport. J. Membr. Biol. 59: 155–171, 1981.
 38. Finkelstein, A., and A. Mauro. Equivalent circuits as related to ionic systems. Biophys. J. 3: 215–237, 1963.
 39. Finkelstein, A., and A. Mauro. Physical principles and formalisms of electrical excitability. Handbook of Physiology. The Nervous System. Cellular Biology of Neurons. Bethesda, MD: Am. Physiol. Soc., 1977, sect. 1, vol. I, pt. 1, chapt. 6, p. 161–213.
 40. Finkelstein, A., and P. A. Rosenberg. Single‐file transport: implications for ion and water movement through gramicidin A channels. In: Membrane Transport Processes, edited by C. F. Stevens and R. W. Tsien. New York: Raven, 1979, vol. 3, p. 73–88.
 41. Gadsby, D. C., J. Kimura, and A. Noma. Voltage dependence of Na/K pump current in isolated heart cells. Nature Lond. 315: 63–65, 1985.
 42. Goldman, D. E. Potential, impedance, and rectificaiton in membranes. J. Gen. Physiol. 27: 37–60, 1943.
 43. Guggenheim, E. A. Thermodynamics (5th ed.). Amsterdam: North‐Holland, 1967.
 44. Halm, D. R., and D. C. Dawson. Cation activation of the basolateral sodium‐potassium pump in turtle colon. J. Gen. Physiol. 82: 315–329, 1983.
 45. Hess, P., and R. W. Tsien. Mechanism of ion permeation through calcium channels. Nature Lond. 309: 453–456, 1984.
 46. Hille, B. Ionic selectivity of Na and K channels of nerve membranes. In: Membranes. Lipid Bilayers and Biological Membranes: Dynamic Properties, edited by G. Eisenman, New York: Dekker, 1975, chapt. 4, p. 255–323.
 47. Hille, B. Ionic Channels of Excitable Membranes. Sunderland, MA: Sinauer, 1984.
 48. Hille, B., and W. Schwarz. Potassium channels as multiion single‐file pores. J. Gen. Physiol. 72: 409–442, 1978.
 49. Hodgkin, A. L., and A. F. Huxley. Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J. Physiol. Lond. 116: 449–472, 1952.
 50. Hodgkin, A. L., and A. F. Huxley. The components of membrane conductance in the giant axon of Loligo. J. Physiol. Lond. 116: 473–496, 1952.
 51. Hodgkin, A. L., and A. F. Huxley. The dual effect of membrane potential on sodium conductance in giant axon of Loligo. J. Physiol. Lond. 116: 497–506, 1952.
 52. Hodgkin, A. L., and A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. Lond. 117: 500–544, 1952.
 53. Hodgkin, A. L., and A. F. Huxley. Measurement of current‐voltage relations in the membrane of the giant axon of Loligo. J. Physiol. Lond. 116: 424–448, 1952.
 54. Horie, M., H. Irisawa, and A. Noma. Voltage‐dependent magnesium block of adenosine‐triphosphate‐sensitive potassium channel in guinea‐pig ventricular cells. J. Physiol. Lond. 387: 251–272, 1987.
 55. Hume, J. R. Component of whole cell Ca current due to electrogenic Na‐Ca exchange in cardiac myocytes. Am. J. Physiol. 252 (Heart Circ. Physiol. 21): H666–H670, 1987.
 56. Jack, J. J. B., D. Noble, and R. W. Tsien. Electric Current Flow in Excitable Cells. Oxford, UK: Clarendon, 1975.
 57. Jacquez, J. A. Application of tracers to the study of membrane transport processes. In: Physiology of Membrane Disorders, edited by T. E. Andreoli, J. F. Hoffman, D. D. Fanestil, and S. G. Schultz. New York: Plenum, 1986, chapt. 8, p. 133–150.
 58. Jauch, P., and P. Lauger. Electrogenic properties of the sodium‐alanine cotransporter in pancreatic acinar cells. II. Comparison with transport models. J. Membr. Biol. 94: 117–127, 1986.
 59. Jauch, P., O. H. Petersen, and P. Lauger. Electrogenic properties of the sodium‐alanine cotransporter in pancreatic acinar cells. I. Tight‐seal whole‐cell recordings. J. Membr. Biol. 94: 99–115, 1986.
 60. Kaplan, J. H. Sodium ions and the sodium pump: transport and enzymatic activity. Am. J. Physiol. 245 (Gastrointest Liver Physiol. 8): G327–G333, 1983.
 61. Kaplan, J. H. Ion movements through the sodium pump. Annu. Rev. Physiol. 47: 535–544, 1985.
 62. Katchalsky, A., and P. F. Curran. Nonequilibrium Thermodynamics in Biophysics. Cambridge, MA: Harvard Univ. Press, 1965, p. 1–248.
 63. Kimmich, G. A., and J. Randles. Energetics of sugar transport by isolated intestinal epithelial cells: effects of cytochalasin B. Am. J. Physiol. 237 (Cell Physiol. 6): C56–C63, 1979.
 64. Kimura, J., A. Noma, and H. Irisawa. Na‐Ca exchange current in mammalian heart cells. Nature Lond. 319: 596–597, 1986.
 65. Kirk, K. L., and D. C. Dawson. Basolateral potassium channel in turtle colon. J. Gen. Physiol. 82: 297–313, 1983.
 66. Kirk, K. L., D. R. Halm, and D. C. Dawson. Active sodium transport by turtle colon via an electrogenic Na‐K exchange pump. Nature Lond. 287: 237–239, 1980.
 67. Koefoed‐Johnsen, V., and H. H. Ussing. The nature of the frog skin potential. Acta Physiol. Scand. 42: 298–308, 1958.
 68. Krasne, S. Ion selectivity in membrane permeation. Physiology of Membrane Disorders, edited by T. E. Andreoli, J. F. Hoffman, and D. D. Fanestil. New York: Plenum, 1978, chapt. 12, p. 217–241.
 69. Krasne, S., and G. Eisenman. The molecular basis of ion selectivity. In: Membranes: Lipid Bilayers and Antibiotics, edited by G. Eisenman, New York: Dekker, 1973, vol. 2, p. 277–328.
 70. Latorre, R., and C. Miller. Conduction and selectivity in potassium channels. J. Membr. Biol. 71: 11–30, 1983.
 71. Läuger, P. Ion transport through pores: a rate‐theory analysis. Biochim. Biophys. Acta 311: 423–441, 1973.
 72. Läuger, P. Transport of noninteracting ions through channels. In: Membrane Transport Processes, edited by C. F. Stevens and R. W. Tsien. New York: Raven, 1979, vol. 3, p. 17–27.
 73. Läuger, P. Kinetic properties of ion carriers and channels. J. Membr. Biol. 57: 163–178, 1980.
 74. Läuger, P., and P. Jauch. Microscopic description of voltage effects on ion‐driven cotransport systems. J. Membr. Biol. 91: 275–284, 1986.
 75. Läuger, P., and B. Neumcke. Theoretical analysis of ion conductance in lipid bilayer membranes. In: Membranes: Lipid Bilayers and Antibiotics, edited by G. Eisenman, New York: Dekker, 1973, vol. 2, p. 1–59.
 76. Levitt, D. G. Kinetics of movement in narrow channels. In: Ion Channels: Molecular and Physiological Aspects, edited by W. D. Stein. New York: Academic. In press.
 77. Levitt, D. G. Electrostatic calculations for an ion channel I. Energy and potential profiles and interactions between ions. Biophys. J. 22: 209–219, 1978.
 78. Levitt, D. C. Electrostatic calculations for an ion channel II. Kinetic behavior of the gramicidin A channel. Biophys. J. 22: 221–248, 1978.
 79. Levitt, D. G. Comparison of Nernst‐Planck and reaction‐rate models for multiply occupied channels. Biophys. J. 37: 575–587, 1982.
 80. Levitt, D. G. Interpretation of biological ion channel flux data‐reaction‐rate versus continuum theory. Annu. Rev. Biophys. Chem. 15: 29–57, 1986.
 81. Macey, R. I. Mathematical models of membrane transport processes. In: Physiology of Membranes Disorders, edited by T. E. Andreoli, J. E. Hoffman, D. D. Fanestil, and S. G. Schultz. New York: Plenum, 1986, chapt. 7, p. 111–131.
 82. Matsuda, H., A. Saigusa, and H. Irisawa. Ohmic conductance through the inwardly rectifying K channel and blocking by internal Mg2+. Nature Lond. 325: 156–159, 1987.
 83. McCleskey, E. W., and W. Almers. The Ca channel in skeletal muscle is a large pore. Proc. Natl. Acad. Sci. USA 82: 7149–7153, 1985.
 84. Mechman, S., and L. Pott. Identification of Na‐Ca exchange current in single cardiac myocytes. Nature Lond. 319: 597–599, 1986.
 85. Miller, C. (editor). Ion Channel Reconstitution. New York: Plenum, 1986.
 86. Miller, C. Trapping single ions inside single ion channels. Biophys. J. 52: 123–126, 1987.
 87. Moczydlowski, E. Single‐channel enzymology. In: Ion Channel Reconstitution, edited by C. Miller, New York: Plenum, 1986, chapt. 4, p. 75–113.
 88. Nakao, M., and D. C. Gadsby. Voltage dependence of Na translocation by the Na/K pump. Nature Lond. 323: 628–630, 1986.
 89. Orbach, E., and A. Finkelstein. The nonelectrolyte permeability of planar lipid bilayer membranes. J. Gen. Physiol. 75: 427–436, 1980.
 90. Pappone, P. A., and M. D. Cahalan. Ion permeation in cell membranes. In: Physiology of Membrane Disorders, edited by T. E. Andreoli, J. F. Hoffman, D. D. Fanestil, and S. G. Schultz. New York: Plenum, 1986, chapt. 15, p. 249–272.
 91. Parsegian, V. A. Energy of an ion crossing a low dielectric membrane: solutions to four relevant electrostatic problems. Nature Lond. 221: 844–846, 1969.
 92. Parsegian, V. A. Ion‐membrane interactions as structural forces. Ann. NY Acad. Sci. 264: 161–174, 1975.
 93. Rashin, A. A., and B. Honig. Reevaluation of the Born model for ion hydration. J. Phys. Chem. 89: 5588–5593, 1985.
 94. Robinson, R. A., and R. H. Stokes. Electrolyte Solutions. London: Butterworths, 1959.
 95. Sakmann, B., and E. Neher (editors). Single‐Channel Recording. New York: Plenum, 1983.
 96. Schultz, S. G. Basic Principles of Membrane Transport. Cambridge, MA: Cambridge Univ. Press, 1980.
 97. Schultz, S. G., and R. A. Frizzell. Ionic permeability of epithelial tissues. Biochim. Biophys. Acta 443: 181–189, 1976.
 98. Sten‐Knudsen, O. Passive transport processes. In: Membrane Transport in Biology, edited by G. Giebisch, D. C. Tosteson, and H. H. Ussing. New York: Springer‐Verlag, 1978, vol. I, chapt. 2, p. 5–113.
 99. Tanford, C. The Hydro‐Phobic Effect: Formation of Micelles of Biological Membranes (2nd ed.). New York: Wiley, 1980.
 100. Teorell, T. Transport processes and electrical phenomena in ionic membranes. Progr. Biophys. Chem. 3: 305–369, 1953.
 101. Thompson, S. M. Relations between chord and slope conductances and equivalent electromotive forces. Am. J. Physiol. 250 (Cell Physiol. 19): C333–C339, 1986.
 102. Ussing, H. H. The distinction by means of tracers between active transport and diffusion. Acta Physiol. Scand. 19: 43–56, 1949.
 103. Ussing, H. H. Some aspects of the application of tracers in permeability studies. Adv. Enzymol. 13: 21–65, 1952.
 104. Ussing, H. H. Interpretation of tracer fluxes. In: Membrane Transport in Biology, edited by G. Giebisch, D. C. Tosteson, and H. H. Ussing. New York: Springer‐Verlag, 1978, chapt. 3, p. 115–140.
 105. Ussing, H. H., and K. Zerahn. Active transport of sodium as the source of electric current in the short circuited isolated frog skin. Acta Physiol. Scand. 23: 110–127, 1951.
 106. Vandenberg, C. A. Inward rectification of a potassium channel in cardiac ventricular cells depends on internal magnesium ions. Proc. Natl. Acad. Sci. USA 84: 2560–2564, 1987.
 107. Woodbury, J. W. Eyring rate theory model of the current‐voltage relationships of ion channels in excitable membranes. In: Chemical Dynamics: Papers in Honor of Henry Eyring, edited by J. Hirschfelder, New York: Wiley, 1971, p. 601–617.
 108. Zimmerberg, J., and V. A. Parsegian. Polymer inaccessible volume changes during opening and closing of a voltage‐dependent ion channel. Nature Lond. 323: 36–39, 1986.

Contact Editor

Submit a note to the editor about this article by filling in the form below.

* Required Field

Article Title: Principles of Membrane Transport
 

How to Cite

David C. Dawson. Principles of Membrane Transport. Compr Physiol 2011, Supplement 19: Handbook of Physiology, The Gastrointestinal System, Intestinal Absorption and Secretion: 1-44. First published in print 1991. doi: 10.1002/cphy.cp060401