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Membrane Transport in Single Cells

Michael L. Jennings, Mark A. Milanick

10.1002/cphy.cp140107

Source: Supplement 31: Handbook of Physiology, Cell Physiology

Originally published: 1997

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Examples of Preparations of Single Cells
1.1 Large Cells that Can Be Studied Individually
1.2 Blood Cells
1.3 Cells Prepared by Dissociating Intact Tissue
1.4 Permanent Cell Lines and Expression Systems
2 Methods for Measuring Transport
2.1 Tracer Influx and Efflux: Definition of Flux
2.2 Definition of Permeability Coefficient
2.3 Unstirred Layers
2.4 Multiple Intracellular Compartments
2.5 Optical Methods for Measuring Transport
2.6 Ion‐Sensitive Microelectrodes
2.7 Membrane Potential
2.8 Nuclear Magnetic Resonance
3 Transport Mechanisms
3.1 Rationale for Investigating Transport Mechanisms
3.2 Catalytic Cycles
4 Anion Exchanger
4.1 Red Blood Cell Anion Transport
4.2 Electrically Silent Obligatory Exchange
4.3 Kinetic Mechanism of Anion Exchange
4.4 Intrinsic Asymmetries
4.5 Electrical Properties of the Exchange Pathway
5 Sodium Pump
5.1 Electrically Silent and Electrogenic Na Pump Modes
5.2 Pump Stoichiometry
5.3 Kinetic Mechanism of the Na Pump
5.4 Electrical Properties of the Na Pump
5.5 Summary of Transport Mechanisms
6 Integrative Transport Studies in Single Cells: Cell‐Volume Regulation
6.1 Pump‐Leak Paradigm
6.2 Volume‐Sensitive Transport Processes
6.3 Detection of Cell Volume
6.4 Transduction of Volume Signal to Transport Proteins
Figure 1. Figure 1.

Some examples of preparations of individual cells that have been used extensively for transport studies. A. Cardiac myocytes from guinea pig. B. Endothelial cells from cow. C. Enterocytes from chick. D. Oocytes from Xenopus. E. Erythrocytes from human. F. Smooth muscle cells from cow.
Figure 2. Figure 2.

Unidirectional influx and efflux under conditions of no net flux. Lower graph: Tracer is allowed to equilibrate before efflux is measured. Upper graph: Tracer influx reaches only 20% of the extracellular specific activity before the cells are washed to begin efflux measurement. In both cases, unidirectional influx and efflux are equal. The tracer influx appears to be more rapid than efflux in the lower part of the figure because the initial intracellular specific activity (DPM/nmol) is much less than the original extracellular specific activity in the influx experiment. Therefore, each DPM that crosses the membrane at the beginning of the efflux experiment represents more K+ ions than in the beginning of the influx experiment. See text for further discussion.
Figure 3. Figure 3.

A. Schematic model of a ping‐pong system that exchanges squares for circles. The outward‐facing conformations are striped. Starting at the top and proceeding clockwise: empty transporter with site facing outside. Outside square binding to transporter. Translocation of the square so that the square now has access to the inside. Release of the square to the inside. The steps for the circle are similar. Note that there is no conformation that has both a square and a circle bound. The dashed line in the middle illustrates slippage; this allows for movement of the square in the absence of the circle by allowing the empty transporter to move the empty site. More details on the specifics of each conformation are presented in Figure 4. B. Schematic model of a non‐ping‐pong system that exchanges squares for circles. The outward‐facing conformations are striped. Starting at the right top and proceeding counterclockwise: empty transporter with both sites facing outside. Outside square binding to transporter. Translocation of the sites and the square to the inside Binding of inside circle to the transporter, which promotes the release of the square to the inside. Translocation of the sites and the circle to the outside, with subsequent release of circle to the outside. Note that there is a conformation that has both a square and a circle bound (lower left), in contrast to the ping‐pong model. Other non‐ping‐pong models are possible by varying the order of addition of the substrates, of release of the substrates, and of translocation of one or the other sites. In all cases, the essential feature is the existence of at least one conformation with both substrates bound.
Figure 4. Figure 4.

Schematic representation of the ping‐pong mechanism for coupled exchange. The four states of the system are shown. All transitions between these states are reversible. The following is the sequence of states in the influx of a substrate, that is, half of a complete catalytic cycle. A. The empty outward‐facing state. This state has no substrate bound at the transport site, but an extracellular substrate has diffusional access to the site. Intracellular substrate cannot bind to this state. B. The loaded outward‐facing state. This state is formed when a substrate moves from the bulk extracellular medium and binds to the outward‐facing transport site. At present this site has a kinetic rather than a physical definition, because the detailed structure of the protein is unknown. The outward‐facing site is wherever the substrate is immediately before the rate‐limiting inward translocation step. C. The loaded inward‐facing state. After formation of the loaded outward‐facing state, the protein‐substrate complex undergoes a conformational change that allows the substrate diffusional access to the intracellular medium. The structural differences between the inward‐facing and outward‐facing states are unknown. D. The unloaded inward‐facing state. This state is formed when the substrate moves from the inward facing transport site to the bulk intracellular solution. Extracellular substrate can no longer reach the transport site of this state of the protein.
Figure 5. Figure 5.

Effect of membrane potential on electroneutral 1:1 anion exchange. The anion exchange flux is plotted as a function of membrane potential. Upper: In this example, the transporter is intrinsically symmetric and the membrane potential is varied between −100 mV and +100 mV. The three curves represent three different amounts of charge translocated through the membrane potential difference in the rate‐limiting step. Note that, because the transporter is intrinsically symmetric, it is not possible to distinguish between positive and negative charge movement in the translocation step. Lower: In this example, it is assumed that a full net negative charge moves through the transmembrane potential difference in the translocation step. The three curves refer to different intrinsic asymmetries, represented as the ratio of outward to inward translocation rate constants at a membrane potential of zero. The curves are normalized to the same maximum exchange flux. Note that the sign of the net charge translocated can be determined only if there is independent knowledge of the intrinsic asymmetry of the exchanger. For example, if a full net positive charge were translocated, and if °kio/°koi = 10, the flux would have exactly the same dependence on potential as it would if there were a full net negative charge translocated and °kio/°koi = 0.1 (dotted curve).
Figure 6. Figure 6.

The difference between an electrogenic system and a system that responds to membrane potential. Upper panel: Addition of an inhibitor to an electrogenic system will alter the membrane potential. Lower panel: In contrast, changes of membrane potential can alter the rate of a transport system (as indicated by the change in arrow size). Electrogenicity and voltage dependence are two different characteristics. For some range of membrane potentials, all electrogenic systems will be altered by membrane potential. However, as discussed in the text, there are conditions where electrogenic systems may be membrane potential independent and electroneutral systems can be membrane potential dependent.
Figure 7. Figure 7.

Inhibition of the Na pump could alter membrane potential for two different reasons. Upper panel: The Na pump directly contributes to the membrane potential and thus inhibition of the pump rapidly leads to dissipation of the membrane potential. Lower panel: The Na pump does not directly contribute to the membrane potential. However, inhibition of the pump will lead to alterations in the Na and K gradients, and these will alter the membrane potential. Since the changes in ion gradients are relatively slow, the time course for membrane potential change will be relatively slow. Thus, when attempting to determine if a new system is electroneutral or electrogenic, one needs to determine if changes in membrane potential reflect direct operation of the transporter or are secondary to ion changes caused by the transporter.
Figure 8. Figure 8.

Possible changes of proton concentration in response to a coupled process that directly moves protons in exchange for K (A and B) and directly moves Na in exchange for K (C and D). The experimental preparation is inside‐out vesicles from red blood cells treated so that the primary conductive pathway is protons. The Na pump mediates K efflux under these conditions in response to ATP in the bath. In A, Na pump mediates an electroneutral K/H exchange. H influx will directly elevate the intravesicular H. The increase in intracellular H will lead to an increased H efflux from the vesicles. Eventually, the proton influx through the Na pump will be balanced by the increased passive H efflux and there will be no further change of H. In B, the Na pump mediates an electrogenic 2K/1 Na exchange and does not directly move H. Operation of the pump leads to an inside negative potential. Because the primary conductive pathway in these vesicles is H, the inside negative potential will lead to a conductive influx of H. The H influx will elevate the intravesicular H and the measured result will be similar to that observed in A. The increase in intracellular H will lead to an increased H efflux from the vesicles. Eventually, the proton influx in response to the electrogenic Na pump will be balanced by the increased passive H efflux and there will be no further change of H. In C, addition of TPP will not alter the H concentration. Since operation of the pump has not changed the membrane potential, addition of TPP should not alter the H flux mediated by the pump nor the passive pathway. Thus, there will be no change in H. In D, addition of TPP will alter the H concentration. TPP will short‐circuit the membrane potential change. Thus, the membrane potential will return to its value in the absence of ATP. Thus, there will be no driving force for passive H efflux and the H concentration will return toward basal values.
Figure 9. Figure 9.

Simplied kinetic scheme for Na/K exchange by the Na pump. T is the pump. The conformation with the empty transport site having access to the intracellular solution is __T and having access to the extracellular solution is T—P__. After addition of ATP and Nain, the terminal phosphate is covalently attached to the pump, ADP is released, and Na is translocated. Following Na release, Kout can bind. The transport site returns to the inside to release K and the covalent Pi bond is broken, releasing Pi (to the inside). Not explicitly shown are the occluded states 51,77. During translocation, there is a conformation where K ions are trapped inside the pump and have access to neither the inside nor the outside.
Figure 10. Figure 10.

Slightly less simple kinetic scheme for the Na pump. This scheme incorporates two additional points. (1) The middle pathway from T—P___to__T(ATP) can occur in the absence of Kout and is the pathway for uncoupled Na efflux. See text for a more complete discussion of the uncoupled Na pathway. (2) ATP with low affinity (and without hydrolysis) accelerates the K translocation steps. Thus, ATP can bind to the lower pathway. Whether this ATP effect occurs at the separate physical site from where the terminal phosphate of ATP is transferred to the pump remains to be determined. Most kinetic results are consistent with only one physical site for ATP, but do not rule out models of two physically distinct ATP sites.
Figure 11. Figure 11.

Cyclic diagrams for different transport mechanisms for the exchange of Nai for Ko. For all diagrams the rate constants from k1 to k6 are in the clockwise direction and the rate constants for k−1 to k−6 are in the counterclockwise direction. T is the transporter protein. a. A ping‐pong mechanism. The conformation with the empty transport site having access to the intracellular solution is ___T and having access to the extracellular solution is T___. Steps 3 and 6 are the release of product. b. Non‐ping‐pong mechanism no. 1. A key feature of non‐ping‐pong mechanisms is the formation of a ternary complex, TNak, which has both substrates bound. There are a variety of possible non‐ping‐pong models based on different (or random) ordered binding and release. In this model, steps 1 and 3 are the addition of substrate. Step 4 represents the translocation of k, and step 2 the translocation of Na. In this model, steps 5 and 6 are release of product. A major difference in the cyclic diagrams between this model and that shown in a is that Ko adds before Nai is released in this model. c. A ping‐pong mechanism with slippage. The addition of step 7 allows the interconversion of T___to ___T in the absence of Ko; thus the transporter can cycle (and transport) Na in the absence of Ko or K in the absence of Na. This step is referred to as uncoupled Na flux in the Na pump field and is called slippage in the anion exchanger field. d. Non‐ping‐pong mechanism no. 1 with slippage. The addition of step 7 allows transporter to cycle (and transport) Na in the absence of Ko.
Figure 12. Figure 12.

Cyclic diagram for non‐ping‐pong model #2. A key feature of non‐ping‐pong mechanisms is the formation of a ternary complex, TNaK, which has both substrates bound. In this model, Ko adds before Nai. (See Fig. 11 for more details.) This model fits with the oligomycin data because Ko and I are not mutually exclusive and Nao and Nai are not mutually exclusive.
Figure 13. Figure 13.

The rate of some exchanges predict the rate of other exchanges for a ping‐pong model of the Na pump. A. The Na efflux/K influx exchange mode. B. Na efflux / Na influx exchange mode (which involves some of the same steps as in Na/K exchange, as indicated by the similar type of line). C. K efflux / K influx exchange mode (which involves some of the same steps as in Na/K exchange, as indicated by the similar type of line). D. K efflux /Na influx exchange (pump reversal). For the simple scheme diagrammed, the slowest steps from the other three exchange modes must govern the rate of the reverse mode. E. Possible alternative explanation for why K/Na exchange is slow is that there is a conformational change between the Na binding forms and the K binding forms. Since Na and K compete on both sides, this explanation is less likely than the possibility that it is difficult to achieve optimal concentrations of ADP and Pi for pump reversal (see text).
Figure 14. Figure 14.

Some examples of shapes of I–V (current vs. membrane potential) curves with Erev = − 250 mV.

Adapted from DeWeer [35]. These curves were drawn manually to illustrate the following possibilities: (1) There can be a large range of voltage where current is independent of membrane potential (see text for more details). (2) Near Erev the current may be very small. (3) Away from Erev there are no thermodynamic constraints on the shape of the curve (though it can't cross the voltage axis again). For a more detailed discussion of I–V curve shapes, see, for example, Hansen et al. 87, DeWeer 35, and Läuger 143
Figure 15. Figure 15.

Cyclic diagram of electroneutral Na/Na exchange mode of the Na pump. This model provides explicit consideration of radioactive tracers, ADP (for example, 3H or 14C, ADP) and Na (for example, 22Na or 24Na). The ATP/ADP exchange rate is determined by the rate of appearance of ATP from ADP. Na/Na exchange is measured by the appearance of Nao. While the protein is assumed to treat Na22, Na23, and Na24 exactly the same, this explicit treatment of the tracers allows for easier consideration of some properties of the cycle. The outer loop (square) is the cycle required for Na/Na exchange. The outer loop is also one possible cycle that gives ATP/ADP exchange. The inner loop (upper triangle) is the cycle that allows for ATP/ADP exchange in the absence of Nao.
Figure 16. Figure 16.

Flux vs. membrane potential simulations for different values of δ, the electric field asymmetry factor. These cures were drawn for a simple two‐step reaction scheme shown at the tip of the figure. The rate equation is Flux = 1/[1/k1 + 1/k−1 + 1/k2 + 1/k −2 + k−1/(k1k2) + k2/(k−1k−2)], see Gadsby et al., 1993 66. For this simulation, all the rate constants were set to 1 at Em = O. The voltage dependence (of step 2) was modeled as k2 = ko2 exp((δ,/25) and k−2 = ko−2 exp (− (1 − δ,)/25). As δ tend toward zero, a plateau is achieved at negative potentials. The δ values are indicated.
Figure 17. Figure 17.

Flux vs. membrane potential simulations for different values of rate constants k2 = k−2. Upper: These curves were drawn for a simple two‐step reaction scheme shown at the top of Figure 16, with the rate equation Flux= 1/[1/k1 + 1/k−1 + 1/k2 + 1/k−2 + k−1/(k1k2) + k2/(k−1k−2)]. For this simulation, δ = 0.5, k1 = k−1 = 1 and the k2 and k−2 values at Em = 0 are as indicated. Lower: When k2 = k−2=1000 plateaus in the range from −50 to −100 mV, over a large range the flux eventually declines. This is because no matter how fast k2 and k−2 are at Em = 0 (that is, ko2 and ko−2), at extreme potentials k2 and k−2 must become rate limiting; compare Hilgemann 93.
Figure 18. Figure 18.

Flux vs. membrane potential stimulations for a two‐step model in which both steps are voltage dependent. Solid line: the overall flux as a function of membrane potential. Dashed lines: the rates of the voltage‐dependent steps. Note that at extreme potentials, the voltage‐dependent steps become rate limiting and therefore dominate the rate of the overall cycle.


Figure 1.

Some examples of preparations of individual cells that have been used extensively for transport studies. A. Cardiac myocytes from guinea pig. B. Endothelial cells from cow. C. Enterocytes from chick. D. Oocytes from Xenopus. E. Erythrocytes from human. F. Smooth muscle cells from cow.



Figure 2.

Unidirectional influx and efflux under conditions of no net flux. Lower graph: Tracer is allowed to equilibrate before efflux is measured. Upper graph: Tracer influx reaches only 20% of the extracellular specific activity before the cells are washed to begin efflux measurement. In both cases, unidirectional influx and efflux are equal. The tracer influx appears to be more rapid than efflux in the lower part of the figure because the initial intracellular specific activity (DPM/nmol) is much less than the original extracellular specific activity in the influx experiment. Therefore, each DPM that crosses the membrane at the beginning of the efflux experiment represents more K+ ions than in the beginning of the influx experiment. See text for further discussion.



Figure 3.

A. Schematic model of a ping‐pong system that exchanges squares for circles. The outward‐facing conformations are striped. Starting at the top and proceeding clockwise: empty transporter with site facing outside. Outside square binding to transporter. Translocation of the square so that the square now has access to the inside. Release of the square to the inside. The steps for the circle are similar. Note that there is no conformation that has both a square and a circle bound. The dashed line in the middle illustrates slippage; this allows for movement of the square in the absence of the circle by allowing the empty transporter to move the empty site. More details on the specifics of each conformation are presented in Figure 4. B. Schematic model of a non‐ping‐pong system that exchanges squares for circles. The outward‐facing conformations are striped. Starting at the right top and proceeding counterclockwise: empty transporter with both sites facing outside. Outside square binding to transporter. Translocation of the sites and the square to the inside Binding of inside circle to the transporter, which promotes the release of the square to the inside. Translocation of the sites and the circle to the outside, with subsequent release of circle to the outside. Note that there is a conformation that has both a square and a circle bound (lower left), in contrast to the ping‐pong model. Other non‐ping‐pong models are possible by varying the order of addition of the substrates, of release of the substrates, and of translocation of one or the other sites. In all cases, the essential feature is the existence of at least one conformation with both substrates bound.



Figure 4.

Schematic representation of the ping‐pong mechanism for coupled exchange. The four states of the system are shown. All transitions between these states are reversible. The following is the sequence of states in the influx of a substrate, that is, half of a complete catalytic cycle. A. The empty outward‐facing state. This state has no substrate bound at the transport site, but an extracellular substrate has diffusional access to the site. Intracellular substrate cannot bind to this state. B. The loaded outward‐facing state. This state is formed when a substrate moves from the bulk extracellular medium and binds to the outward‐facing transport site. At present this site has a kinetic rather than a physical definition, because the detailed structure of the protein is unknown. The outward‐facing site is wherever the substrate is immediately before the rate‐limiting inward translocation step. C. The loaded inward‐facing state. After formation of the loaded outward‐facing state, the protein‐substrate complex undergoes a conformational change that allows the substrate diffusional access to the intracellular medium. The structural differences between the inward‐facing and outward‐facing states are unknown. D. The unloaded inward‐facing state. This state is formed when the substrate moves from the inward facing transport site to the bulk intracellular solution. Extracellular substrate can no longer reach the transport site of this state of the protein.



Figure 5.

Effect of membrane potential on electroneutral 1:1 anion exchange. The anion exchange flux is plotted as a function of membrane potential. Upper: In this example, the transporter is intrinsically symmetric and the membrane potential is varied between −100 mV and +100 mV. The three curves represent three different amounts of charge translocated through the membrane potential difference in the rate‐limiting step. Note that, because the transporter is intrinsically symmetric, it is not possible to distinguish between positive and negative charge movement in the translocation step. Lower: In this example, it is assumed that a full net negative charge moves through the transmembrane potential difference in the translocation step. The three curves refer to different intrinsic asymmetries, represented as the ratio of outward to inward translocation rate constants at a membrane potential of zero. The curves are normalized to the same maximum exchange flux. Note that the sign of the net charge translocated can be determined only if there is independent knowledge of the intrinsic asymmetry of the exchanger. For example, if a full net positive charge were translocated, and if °kio/°koi = 10, the flux would have exactly the same dependence on potential as it would if there were a full net negative charge translocated and °kio/°koi = 0.1 (dotted curve).



Figure 6.

The difference between an electrogenic system and a system that responds to membrane potential. Upper panel: Addition of an inhibitor to an electrogenic system will alter the membrane potential. Lower panel: In contrast, changes of membrane potential can alter the rate of a transport system (as indicated by the change in arrow size). Electrogenicity and voltage dependence are two different characteristics. For some range of membrane potentials, all electrogenic systems will be altered by membrane potential. However, as discussed in the text, there are conditions where electrogenic systems may be membrane potential independent and electroneutral systems can be membrane potential dependent.



Figure 7.

Inhibition of the Na pump could alter membrane potential for two different reasons. Upper panel: The Na pump directly contributes to the membrane potential and thus inhibition of the pump rapidly leads to dissipation of the membrane potential. Lower panel: The Na pump does not directly contribute to the membrane potential. However, inhibition of the pump will lead to alterations in the Na and K gradients, and these will alter the membrane potential. Since the changes in ion gradients are relatively slow, the time course for membrane potential change will be relatively slow. Thus, when attempting to determine if a new system is electroneutral or electrogenic, one needs to determine if changes in membrane potential reflect direct operation of the transporter or are secondary to ion changes caused by the transporter.



Figure 8.

Possible changes of proton concentration in response to a coupled process that directly moves protons in exchange for K (A and B) and directly moves Na in exchange for K (C and D). The experimental preparation is inside‐out vesicles from red blood cells treated so that the primary conductive pathway is protons. The Na pump mediates K efflux under these conditions in response to ATP in the bath. In A, Na pump mediates an electroneutral K/H exchange. H influx will directly elevate the intravesicular H. The increase in intracellular H will lead to an increased H efflux from the vesicles. Eventually, the proton influx through the Na pump will be balanced by the increased passive H efflux and there will be no further change of H. In B, the Na pump mediates an electrogenic 2K/1 Na exchange and does not directly move H. Operation of the pump leads to an inside negative potential. Because the primary conductive pathway in these vesicles is H, the inside negative potential will lead to a conductive influx of H. The H influx will elevate the intravesicular H and the measured result will be similar to that observed in A. The increase in intracellular H will lead to an increased H efflux from the vesicles. Eventually, the proton influx in response to the electrogenic Na pump will be balanced by the increased passive H efflux and there will be no further change of H. In C, addition of TPP will not alter the H concentration. Since operation of the pump has not changed the membrane potential, addition of TPP should not alter the H flux mediated by the pump nor the passive pathway. Thus, there will be no change in H. In D, addition of TPP will alter the H concentration. TPP will short‐circuit the membrane potential change. Thus, the membrane potential will return to its value in the absence of ATP. Thus, there will be no driving force for passive H efflux and the H concentration will return toward basal values.



Figure 9.

Simplied kinetic scheme for Na/K exchange by the Na pump. T is the pump. The conformation with the empty transport site having access to the intracellular solution is __T and having access to the extracellular solution is T—P__. After addition of ATP and Nain, the terminal phosphate is covalently attached to the pump, ADP is released, and Na is translocated. Following Na release, Kout can bind. The transport site returns to the inside to release K and the covalent Pi bond is broken, releasing Pi (to the inside). Not explicitly shown are the occluded states 51,77. During translocation, there is a conformation where K ions are trapped inside the pump and have access to neither the inside nor the outside.



Figure 10.

Slightly less simple kinetic scheme for the Na pump. This scheme incorporates two additional points. (1) The middle pathway from T—P___to__T(ATP) can occur in the absence of Kout and is the pathway for uncoupled Na efflux. See text for a more complete discussion of the uncoupled Na pathway. (2) ATP with low affinity (and without hydrolysis) accelerates the K translocation steps. Thus, ATP can bind to the lower pathway. Whether this ATP effect occurs at the separate physical site from where the terminal phosphate of ATP is transferred to the pump remains to be determined. Most kinetic results are consistent with only one physical site for ATP, but do not rule out models of two physically distinct ATP sites.



Figure 11.

Cyclic diagrams for different transport mechanisms for the exchange of Nai for Ko. For all diagrams the rate constants from k1 to k6 are in the clockwise direction and the rate constants for k−1 to k−6 are in the counterclockwise direction. T is the transporter protein. a. A ping‐pong mechanism. The conformation with the empty transport site having access to the intracellular solution is ___T and having access to the extracellular solution is T___. Steps 3 and 6 are the release of product. b. Non‐ping‐pong mechanism no. 1. A key feature of non‐ping‐pong mechanisms is the formation of a ternary complex, TNak, which has both substrates bound. There are a variety of possible non‐ping‐pong models based on different (or random) ordered binding and release. In this model, steps 1 and 3 are the addition of substrate. Step 4 represents the translocation of k, and step 2 the translocation of Na. In this model, steps 5 and 6 are release of product. A major difference in the cyclic diagrams between this model and that shown in a is that Ko adds before Nai is released in this model. c. A ping‐pong mechanism with slippage. The addition of step 7 allows the interconversion of T___to ___T in the absence of Ko; thus the transporter can cycle (and transport) Na in the absence of Ko or K in the absence of Na. This step is referred to as uncoupled Na flux in the Na pump field and is called slippage in the anion exchanger field. d. Non‐ping‐pong mechanism no. 1 with slippage. The addition of step 7 allows transporter to cycle (and transport) Na in the absence of Ko.



Figure 12.

Cyclic diagram for non‐ping‐pong model #2. A key feature of non‐ping‐pong mechanisms is the formation of a ternary complex, TNaK, which has both substrates bound. In this model, Ko adds before Nai. (See Fig. 11 for more details.) This model fits with the oligomycin data because Ko and I are not mutually exclusive and Nao and Nai are not mutually exclusive.



Figure 13.

The rate of some exchanges predict the rate of other exchanges for a ping‐pong model of the Na pump. A. The Na efflux/K influx exchange mode. B. Na efflux / Na influx exchange mode (which involves some of the same steps as in Na/K exchange, as indicated by the similar type of line). C. K efflux / K influx exchange mode (which involves some of the same steps as in Na/K exchange, as indicated by the similar type of line). D. K efflux /Na influx exchange (pump reversal). For the simple scheme diagrammed, the slowest steps from the other three exchange modes must govern the rate of the reverse mode. E. Possible alternative explanation for why K/Na exchange is slow is that there is a conformational change between the Na binding forms and the K binding forms. Since Na and K compete on both sides, this explanation is less likely than the possibility that it is difficult to achieve optimal concentrations of ADP and Pi for pump reversal (see text).



Figure 14.

Some examples of shapes of I–V (current vs. membrane potential) curves with Erev = − 250 mV.

Adapted from DeWeer [35]. These curves were drawn manually to illustrate the following possibilities: (1) There can be a large range of voltage where current is independent of membrane potential (see text for more details). (2) Near Erev the current may be very small. (3) Away from Erev there are no thermodynamic constraints on the shape of the curve (though it can't cross the voltage axis again). For a more detailed discussion of I–V curve shapes, see, for example, Hansen et al. 87, DeWeer 35, and Läuger 143


Figure 15.

Cyclic diagram of electroneutral Na/Na exchange mode of the Na pump. This model provides explicit consideration of radioactive tracers, ADP (for example, 3H or 14C, ADP) and Na (for example, 22Na or 24Na). The ATP/ADP exchange rate is determined by the rate of appearance of ATP from ADP. Na/Na exchange is measured by the appearance of Nao. While the protein is assumed to treat Na22, Na23, and Na24 exactly the same, this explicit treatment of the tracers allows for easier consideration of some properties of the cycle. The outer loop (square) is the cycle required for Na/Na exchange. The outer loop is also one possible cycle that gives ATP/ADP exchange. The inner loop (upper triangle) is the cycle that allows for ATP/ADP exchange in the absence of Nao.



Figure 16.

Flux vs. membrane potential simulations for different values of δ, the electric field asymmetry factor. These cures were drawn for a simple two‐step reaction scheme shown at the tip of the figure. The rate equation is Flux = 1/[1/k1 + 1/k−1 + 1/k2 + 1/k −2 + k−1/(k1k2) + k2/(k−1k−2)], see Gadsby et al., 1993 66. For this simulation, all the rate constants were set to 1 at Em = O. The voltage dependence (of step 2) was modeled as k2 = ko2 exp((δ,/25) and k−2 = ko−2 exp (− (1 − δ,)/25). As δ tend toward zero, a plateau is achieved at negative potentials. The δ values are indicated.



Figure 17.

Flux vs. membrane potential simulations for different values of rate constants k2 = k−2. Upper: These curves were drawn for a simple two‐step reaction scheme shown at the top of Figure 16, with the rate equation Flux= 1/[1/k1 + 1/k−1 + 1/k2 + 1/k−2 + k−1/(k1k2) + k2/(k−1k−2)]. For this simulation, δ = 0.5, k1 = k−1 = 1 and the k2 and k−2 values at Em = 0 are as indicated. Lower: When k2 = k−2=1000 plateaus in the range from −50 to −100 mV, over a large range the flux eventually declines. This is because no matter how fast k2 and k−2 are at Em = 0 (that is, ko2 and ko−2), at extreme potentials k2 and k−2 must become rate limiting; compare Hilgemann 93.



Figure 18.

Flux vs. membrane potential stimulations for a two‐step model in which both steps are voltage dependent. Solid line: the overall flux as a function of membrane potential. Dashed lines: the rates of the voltage‐dependent steps. Note that at extreme potentials, the voltage‐dependent steps become rate limiting and therefore dominate the rate of the overall cycle.

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Article Title: Membrane Transport in Single Cells
 

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Michael L. Jennings, Mark A. Milanick. Membrane Transport in Single Cells. Compr Physiol 2011, Supplement 31: Handbook of Physiology, Cell Physiology: 261-308. First published in print 1997. doi: 10.1002/cphy.cp140107