Comprehensive Physiology Wiley Online Library

Principles of Membrane Transport

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 = G0pG01, ΔG021 = G0pG02 and ΔG0 = G02G01. See text for abbreviations. [Redrawn from Moczydlowski .]

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 and Andersen and Procopio .]

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 .]
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; EKRT/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. B, 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 = G0pG01, ΔG021 = G0pG02 and ΔG0 = G02G01. See text for abbreviations. [Redrawn from Moczydlowski .]



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 and Andersen and Procopio .]



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 .]


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; EKRT/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. B, 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.

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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