PHYSIOLOGICAL REVIEWS   Vol. 79 No. 1 January 1999, pp. S47-S75
Copyright ©1999 by the American Physiological Society

CFTR: Mechanism of Anion Conduction

DAVID C. DAWSON, STEPHEN S. SMITH, AND MONIQUE K. MANSOURA

Departments of Physiology and Bioengineering, The University of Michigan, Ann Arbor, Michigan

I. CYSTIC FIBROSIS TRANSMEMBRANE CONDUCTANCE REGULATOR: A CHANNEL AND A CHANNEL REGULATOR
II. CONDUCTANCE AND PERMEABILITY
    A. Ohm's Law
    B. Conductance
    C. Reversal Potential
III. MODELS FOR ION PERMEATION: INTERPRETATION OF PERMEABILITY AND CONDUCTANCE
    A. Electrodiffusional Anion Channel
    B. Selectivity in the Nernst-Planck Channel
    C. Rate Theory Model: Ion Binding
    D. Influence of Ion Binding on Permeability and Conductance
    E. Linking the Nernst-Planck and Rate Theory Models
IV. DESIGNING AN ANION CHANNEL: ORIGINS OF ANION SELECTIVITY AND ANION BINDING
    A. Model Systems and the Role of Hydration Energy
    B. Anion Binding
V. POTENTIAL PROBES OF THE PORE
    A. Arylamino Benzoates
    B. Sulfonylureas
    C. Disulfonic Stilbenes
    D. Intracellular Anions and Osmolytes
    E. Permeant Ions
    F. Cysteine Accessibility
VI. STRUCTURE AND FUNCTION OF THE CONDUCTION PATH
    A. Mutagenesis: Predictions and Pitfalls
    B. Predictions for the Pore
    C. Sensing Changes in Pore Architecture
    D. Structural Elements That Are Important for Pore Properties
VII. FUTURE DIRECTIONS AND ROADS YET TO BE TRAVELED
REFERENCES

	ABSTRACT

Top References

Dawson, David C., Stephen S. Smith, and Monique K. Mansoura. CFTR: Mechanism of Anion Conduction. Physiol. Rev. 79, Suppl.: S47-S75, 1999.  The purpose of this review is to collect together the results of recent investigations of anion conductance by the cystic fibrosis transmembrane conductance regulator along with some of the basic background that is a prerequisite for developing some physical picture of the conduction process. The review begins with an introduction to the concepts of permeability and conductance and the Nernst-Planck and rate theory models that are used to interpret these parameters. Some of the physical forces that impinge on anion conductance are considered in the context of permeability selectivity and anion binding to proteins. Probes of the conduction process are considered, particularly permeant anions that bind tightly within the pore and block anion flow. Finally, structure-function studies are reviewed in the context of some predictions for the origin of pore properties.

	I. CYSTIC FIBROSIS TRANSMEMBRANE CONDUCTANCE REGULATOR: A CHANNEL AND A CHANNEL REGULATOR

Top Next References

In the years B.C., that is before cloning in 1989 of the gene that encodes the cystic fibrosis transmembrane conductance regulator (CFTR), it was well established that the inherited disease cystic fibrosis was characterized by a defect in ion transport in both secretory and absorptive epithelial cells (116-119). When the gene was identified by means of a positional cloning strategy that was not driven by any presumption about the function of the gene product, the determination of the primary structure of CFTR set off an explosion of studies aimed at defining the function of this protein. Early investigations of CFTR function were dominated by the question of whether CFTR was itself an ion channel or if, instead, it served to regulate other channels in the cell. Now, 10 years A.C., there is a substantial amount of evidence in support of the notion that CFTR functions as a Cl channel, but there is, in addition, a growing body of evidence that the presence of CFTR can exert a regulatory influence on other Cl-selective channels and cation-selective channels (6, 10, 48, 56, 61, 135, 144).

This review focuses exclusively on the anion-selective channel function of CFTR and, in particular, on the mechanism of ion conduction through the anion-selective pore. Our understanding of CFTR anion conduction mechanisms is in a primitive state. Whereas the primary structure (80, 126, 128) of the cytosolic domains of CFTR and their homology to other proteins accurately foreshadowed the regulation of channel activity by protein kinase A and ATP, the amino acid sequence of the predicted membrane-spanning segments did not provide many clues as to how the pore might be formed. Important leads have emerged from several sources, however. One is the large number of mutations that have been identified in the gene, now over 700. Mutations associated with disease of varying severity point the way to residues in the protein that may be important for conduction (107, 137, 138). Amino acid conservation across vertebrates may also identify "critical" residues (101) and, as always, we are free to apply all manner of guesses based on presumptions about the underlying physics of the conduction process.

The aim of this review is to gather together the existing information about CFTR anion conduction and to examine what all of this may suggest about the mechanisms that underlie the conduction process and are responsible for the ion selectivity of the channel. Two features of anion conduction through CFTR have emerged as particularly important. First, it appears that the entry of anions into the channel from the adjacent aqueous solution is strongly influenced by the ion-water interactions. Second, there is substantial evidence that some anions, e.g., SCN, bind tightly in the pore and that altered anion binding is a sensitive index of structural changes in the conduction path. The review focuses on these properties. We begin with a review of the measurements that are used to define channel properties and a brief consideration of the models that are used to interpret them. In the process, we will have the opportunity to address some general questions about the design of an anion-selective pore.

	II. CONDUCTANCE AND PERMEABILITY

Top Previous Next References

For the purpose of this review, an ion channel is defined as a purely dissipative, conducting element, i.e., one that can be represented by a resistor in an equivalent circuit and that functions in a purely permissive fashion. Like a valve, it permits ions to flow when it is open, but that flow must be driven by an external driving force, i.e., an ion concentration gradient or an electrical potential difference. A purely dissipative element has no ability to couple free energy, derived from ATP hydrolysis or an ion gradient for example, to the flow of something else. This expectation for an ion channel was a source of some consternation for those who attempted to predict the function of CFTR from its primary structure and apparent topology. The presence of two domains (NBF1 and NBF2) that were likely to hydrolyze ATP provoked an image that was more that of a pump or transporter than that of an ion channel (see Fig. 1). It now seems likely, however, that the hydrolysis of ATP at NBF1 and NBF2 is a crucial step in regulating the opening and closing of the CFTR Cl channel (5, 9, 72, 141, 158). This review focuses on the conduction properties of the open channel, but the reader should not lose sight of the fact that ATP hydrolysis could have functions other than opening and closing a Cl-conducting pore, particularly with regard to the emerging role of CFTR as a regulator of other channels, and as yet poorly defined relationships to ATP transport (1, 60, 122, 123, 135). In addition, Linsdell and Hanrahan (94) recently reported an apparent ATP-dependent asymmetry in the conduction of organic anions through CFTR that may point to some additional mode of ion transport by CFTR.

View larger version (39K): [in this window] [in a new window]   FIG. 1.   Diagrammatic representation of domain topology of cystic fibrosis transmembrane conductance regulator (CFTR) showing location of charged residues in predicted transmembrane segments.

The most economical description of the behavior of an ion channel is Ohm's law in which the flow of ions, expressed as an electric current (i), is written as the product of the conductance of the channel () and the total electrochemical driving force, i.e.

(1)

where  is the conductance of a single channel (in pS), V_m is the membrane potential (in mV) referenced to the outside of the cell, and E_rev is the reversal potential defined as the value of V_m (in mV) at which i = 0. The value of E_rev is determined by the gradients of permeant ions across the membrane as described below. The dissipative or passive nature of the flow process is captured in the driving force term, V_m  E_rev; if the net electrochemical force is zero, then ion flow is zero. In the presence of a net driving force, the magnitude of flow is determined by the conductance , a concise description of the series of events that results in ion translocation, i.e., 1) the movement of the ion from the aqueous solution into the channel, 2) translocation of the ion through the channel pore, and 3) the exit of the ion on the other side. In any investigation of channel conduction properties, the behavior of these two parameters, channel conductance and the E_rev for single-channel current, are the principal basis for inferring ion translocation mechanisms. Both can provide important information about the environment of the pore as experienced by permeating ions.

Conductance is measured by determining the i-V_m relation for the channel, a plot of the single-channel current at different voltages as indicated in Figure 2. If this plot were a straight line, the definition of  would be straightforward; it would simply be the voltage-independent slope of the i-V plot. This is rarely the case in general, however. Most i-V relations will, under some ionic condition, exhibit nonlinearities described as either inward or outward rectification. For a nonlinear i-V plot, the slope varies with voltage; hence, the "slope conductance" is voltage dependent. (It is important to remember that this means that the conductance of the open channel varies with voltage as distinct from the voltage dependence of macroscopic conductance arising from voltage-dependent gating.) For a nonlinear i-V plot, the slope conductance is a useful description of the shape of the i-V plot, but it does not meet the criterion for an Ohmic conductance (38). This is easily seen if one considers an i-V relation such as that shown in Figure 2 that exhibits marked outward rectification such that the slope of the i-V plot in the lower left quadrant approaches zero. The slope conductance of the channel is thus zero, despite the fact that the flow of inward current indicates that the Ohmic conductance must be nonzero. The Ohmic or "chord conductance" is the most appropriate measure of channel conduction properties and is defined by measuring the slope of a chord connecting any operating point of interest on the i-V relation with E_rev . This chord would describe the "instantaneous" trajectory of i and V if, for example, a perturbation in V was made around the operating point and i was recorded during a time during which  did not vary. Clearly, at V_m = E_rev , the slope conductance and the chord conductance are identical.

View larger version (14K): [in this window] [in a new window]   FIG. 2.   Plot of current (i) vs. voltage (Vm) for a hypothetical single channel that exhibits strong outward rectification such that inward current becomes voltage independent at hyperpolarized potentials. Lines represent conductance as defined by slope (dashed line) or chord (dotted line) at Vm = 100 mV.

The reversal potential for the current flowing through a single channel is the voltage at which the total driving force for ion flow is zero so that the current is zero. In the presence of a single permeant ion, the current must reverse when V_m is equal to the equilibrium potential for that ion. Thus, for a Cl-selective channel, in the presence of a single permeant anion (Cl), Ohm's law can be written as

(2)

where E_Cl = (RT/zF) ln ([Cl]_o/[Cl]_i), where [Cl]_o and [Cl]_i are extracellular and intracellular Cl concentrations, respectively, so that E_rev is that value of V_m at which the electrochemical potential difference for Cl (_Cl) is zero, i.e., thermodynamic equilibrium.

If more than one permeant ion is present, E_rev is the voltage at which the net current due to the algebraic summation of all permeant ion fluxes is zero. Hence, E_rev in this condition depends on the concentration of all of the permeant ions and their relative abilities to permeate the channel. In the context of studies of anion permeation, the parameter of interest is most often the shift in E_rev when all or a portion of the Cl bathing the channel is replaced by a substitute ion. The behavior of E_rev when a permeant ion is substituted for Cl is most commonly interpreted in terms of an expression for E_rev that assumes the following form if there are two permeant anions, for example, Cl and a "substitute" anion S

(3)

E'_rev is the new value of E_rev after equimolar substitution of S for Cl outside the cell ([Cl]'_o + [S]_o = [Cl]_o). [Cl]'_o, [Cl]_i , and [S]_o represent the respective concentrations of Cl and the substitute anion outside and inside the cell, and may be thought of as an empirical parameter that provides a quantitative measure of the "similarity" of the substitute ion to Cl. It can be seen that the new value of the E_rev is determined by the concentrations of both permeant ions and that the contribution of the substitute ion is weighted by the "similarity factor" . Clearly, in the limit 0, E_rev approaches the equilibrium potential for Cl (E_Cl), and S is judged to be rather unlike Cl in its permeation.

The determination of  is relatively straightforward; one measures the shift in E_rev , E_rev , associated with the equimolar substitution of the ion S for Cl. When Cl is the only permeant anion, the E_rev is given by E_Cl . Now, if a portion of the external Cl is replaced by the substitute ion S, then the new value of E_rev , E'_rev, before S has entered the cell in any significant amount, is given by Equation 3, so that the substitution of S for Cl in the external bath produces a shift in E_rev , E_rev given by the difference between E'_rev and E_Cl (assuming that [Cl]_i is constant)

(4)

and  can be calculated directly from E_rev , [Cl]'_o, and [S]_o .

The mechanistic interpretation of , however, is complicated by the fact that its value is not completely independent of the mechanism of ion permeation through the channel. Generally, is defined as being equal to the ratio of the "permeabilities" for Cl and the substituted ion, i.e.

(5)

where P_S and P_Cl are the respective permeabilities. But, what are the permeabilities and how are they related to the underlying physics of the permeation process?

For channels in which the fluxes of permeant ions are not coupled, i.e., those that obey the Ussing flux-ratio criterion (149-151), permeabilities can be thought of as tracer rate coefficients that would be measured if the unidirectional flow of a labeled form of Cl or S were measured in the condition at V_m = 0 (38). This corresponds with the general notion of permeability as applied to both electrolytes and nonelectrolytes and would apply to channels that contain, at most, one ion at a time. For channels that can be occupied by more than one ion at a time, however, the flows of permeant ions can be coupled. That is to say, the gradient of S can drive the flow of Cl, and vice versa. In such channels, the mechanistic interpretation of permeability is more complicated. Nevertheless, the operational definition of the permeability ratio provided by Equation 3 is empirically useful and is widely used to evaluate anion selectivity. In the context of macroscopic, multichannel i-V relationships, the E_rev has the important property of being independent of channel gating (the number of open channels), because it is defined as the voltage at which the ionic current is zero.

	III. MODELS FOR ION PERMEATION: INTERPRETATION OF PERMEABILITY AND CONDUCTANCE

Top Previous Next References

The goal of measurements of channel permeability and conductance is to obtain information about the mechanism of ion permeation. Permeant ions serve as probes or "reporters" of channel properties because the nature of their interaction with the channel will depend on their physical properties as well as the structure and physical properties of the pore. Thus the interpretation of permeability or conductance, or the relation between these two parameters, is dependent on adopting some physical model that describes the three-step process of permeation: leaving water and entering the channel, translocating within the channel, and exiting on the other side. The state of an ion in the aqueous solution bathing the channel is perhaps best depicted using the language of coordination chemistry (8, 26, 30, 103). The ion is coordinated or stabilized by a layer of water molecules with which it interacts strongly. The water molecules in this primary or "inner" hydration sphere, because of their association with the central ion, interact more strongly with other water molecules that form a secondary or "outer" hydration sphere. The energy of interaction between the ion and the inner sphere water molecules is appreciable, but the complex is nevertheless kinetically labile, and individual water molecules exchange with rates on the order of 10¹² s. For an ion to enter a channel, the highly favorable interaction with coordinating water molecules must be partly or completely replaced by interactions with the channel. The crystal structure of the bacterial K channel, for example, suggests that within the selectivity filter the K ion is completely (or nearly completely) dehydrated and is tetrahedrally coordinated by carbonyl oxygens contributed by the peptide backbones of the four subunits (45). It has been suggested that such dehydration could occur in a stepwise fashion so that the overall rate of the process is increased (24, 32, 40, 49). Andersen and Koeppe (4) envisioned the process by which an ion enters a channel in the following way. A hydrated ion diffuses through the aqueous bath up to the mouth of the channel where it forms an "encounter complex" and then an outer sphere complex with the channel mouth. The next step involves loss of some or all of the waters of hydration in exchange for solvation of the ion by polar groups within the channel (43, 115, 131). This is followed by diffusional translocation within the pore and exit on the other side, involving again the exchange of ion-channel interaction for ion-water interaction. The essence of the permeation process, as suggested by Doyle et al. (45), is that the energy of interaction of the ion with the channel must be sufficient to balance the energy required to dehydrate the ion, but the ion must, nevertheless, remain mobile within the channel. In K channels (45, 108) and perhaps CFTR (147), the limitation on mobility induced by tight binding is overcome by ion-ion repulsion due to multiple ion occupancy. The description of the three-step process of ion permeation has been dominated by two types of model, one based on simple electrodiffusion and the other based on the theory of absolute reaction rates, which we outline here only in their simplest forms.

In its simplest form, the electrodiffusion model views the process of ion translocation within the channel as identical to the diffusion of ions in water so that it can be described by the Nernst-Planck (N-P) equation (38, 37). The movement of ions between the aqueous solution and the "ends" of the channel is viewed as an equilibrium distribution in which the ion "partitions" between water and the channel interior. The permeability of the channel to an ion i is defined operationally as the rate coefficient for the unidirectional flow of a labeled form of i (tracer) through the channel in the condition V_m = 0 given by the rate of unidirectional tracer flow (J_i) divided by the tracer concentration (C_i) (see Ref. 38 for detailed discussion). The N-P equation, together with the equilibrium boundary assumptions, predicts that the permeability (P_i) is given by

(6)

where A is the cross-sectional area of the channel, _i is the equilibrium partition coefficient between the aqueous solution and the channel interior, D_i is the diffusion coefficient for i in the channel, and l is the length of the channel (so that the units of P are cm³/s) (38). Note that the units for P_i reflect the fact that the area is incorporated in the definition. If the area is factored out, the units become centimeters per second. The permeability of the channel to ion i is proportional to the partition coefficient (propensity to partition into the channel) and the diffusion coefficient (mobility within the channel) but is independent of the concentration of i in the bath. The concentration independence of the permeability is a reflection of the fact that the simple N-P model views the interior of the pore as similar to a dilute aqueous solution in which ions do not interact. In practical terms, this means that the channel is rarely occupied by an ion (37) and never by more than one ion. Thus there is no "competition" between ions for entry into the pore, nor is there any coupling between the flows of permeant ions.

The conductance of the N-P channel in the presence of symmetric solutions and in the condition V_m = 0 can be derived in several ways (38, 37) and is given by

(7)

where (_i)_o is the single-channel conductance, P_i is the permeability as defined by Equation 6, and [i]_b is the symmetric bath concentration of the permeant ion i. As might be anticipated for a channel in which ions move independently, the conductance of the channel is directly proportional to the permeability multiplied by the ion concentration. This relationship prompts us to view permeability and conductance of the N-P channel as being related parameters that measure different things. Permeability is best thought of as describing the experience of a single ion as it traverses the channel, whereas conductance is a measure of the rate of ionic throughput per unit driving force. Thus, if the concentration of i in the bath were reduced to zero, the permeability of the N-P channel measured using radiotracer flow would be unchanged, but the conductance would vanish. Conductance is proportional to permeability, but also depends on the abundance of the permeating ion in the conduction path.

It is possible to get an idea of the sort of prediction that this type of model makes for CFTR conduction properties by letting the CFTR pore be a right circular cylinder with a length of 50 Å and a diameter of 5 Å (37, 38). The single-channel permeability can be estimated from Equation 6 by setting  equal to unity and using the value of D_Cl for diffusion in free solution (D_Cl = 10⁵ cm²/s). This yields a value of P_Cl = 3.9 × 10¹⁴ cm³/s. Inserting this into Equation 7 and setting [Cl]_b = 100 mM yields a value of 14 pS for , the single-channel conductance at V_m = 0. Although this must be considered the crudest of approximations, it is remarkable that the value is within a factor of 3 of the actual value of 6 pS, suggesting that the description of ion translocation as a diffusional process provides a reasonable starting place for thinking about anion conduction in CFTR.

The ability to selectively conduct a particular ion is perhaps the most important physiological feature of an ion channel. Selectivity can be defined by comparing permeability ratios or conductance ratios, and for the simple N-P channel, these two approaches yield identical results, i.e., for two permeant ions A and B

(8)

where the first term _A/_B has been referred to as the "equilibrium selectivity" in as much as it would compare the ratio of the probabilities that the channel would be occupied by ion A or B under equilibrium conditions. The second term D_A/D_B has been referred to as the "nonequilibrium selectivity" because in the N-P model it reflects the relative restriction to ion flow within the channel, due for example to steric constraints.

Eisenman and co-workers (39, 50, 162) developed a unified theory of equilibrium ion selectivity that provides a useful framework for thinking about permeability ratios. The theory focused on the underlying forces that are expected to determine the equilibrium distribution of an ion between an aqueous solution and the channel interior. Eisenman and co-workers (39, 50, 162) reasoned that such a distribution would be determined by the balance between the energies associated with ion-water and ion-channel interactions, respectively. To remove an ion from aqueous solution and place it inside a channel, the work required to overcome the highly favorable interaction of the ion with surrounding, polar water molecules must be balanced by favorable interactions with the peptide backbone or amino acid side chains that line the channel interior. Eisenman and co-workers recognized that if both ion-water and ion-channel interactions were viewed as being dominated by electrostatic forces, then both would vary inversely with the radius of the ion. The smaller the ionic radius, the larger would be both the hydration energy and the energy of interaction with charged or polar moieties in the channel. In the original Eisenman model, the balance between this tug of war is decided by the apparent "field strength" of the portion of the channel interacting with the ion. If a channel exhibited a "high field strength" behavior, then the ion-channel energy would be the dominant influence on , and smaller ions would have a greater tendency to partition into the channel so that the predicted selectivity sequence for a high field strength anion channel would be in the order of increasing ionic radius, i.e., F > Cl > Br > NO₃ > I.

In contrast, if the intrachannel environment is characterized by a "weak field strength," then the energetics of the partitioning process will be dominated by hydration energies, i.e., the smaller the ion, the more likely that it will be retained in the aqueous solution, and the selectivity sequence will be in the order of decreasing ionic radius: I > NO₃ > Br > Cl > F.

For a weak field strength channel, the larger the ion, the more likely that it will escape its hydration shell and enter the channel. Variations in the field strength of the site produce five intermediate sequences. Although this simple equilibrium model ignored some of the complexities of the ion dehydration and channel solvation processes (see Ref. 43), for example, the effect of an "optimal fit" into a cavity within the protein which stabilizes the ion (7), it served to focus attention on the importance of the balance between ion-water and ion-channel interactions in determining selectivity. The fact that the permeability selectivity sequence for CFTR more closely resembles that for the weak field strength model foreshadowed the importance of anion dehydration as an important factor in determining the sequence of anion permeation through CFTR (6).

The simple N-P channel is a direct extension of the continuum model for the electrodiffusional movement of ions in a dilute aqueous solution, and it does not allow for any interactions between permeating ions. The predicted permeability is concentration independent, and conductance is predicted to be a linear function of ion concentration. Evidence obtained from a wide variety of channels, however, including CFTR, suggests that ions interact with biological channels in a way such as to prolong the dwell time of ions in the channel over that which would be expected for an equivalent volume of aqueous solution. This situation is modeled by assuming that a permeating ion associates transiently with "binding sites" that form part of the conduction path. Models incorporating ion binding can account for concentration-dependent ion permeability and the saturable relation between single-channel conductance and ion concentration, and also observations that suggest that ion flows can be coupled (38, 67, 68). The single-channel conductance of CFTR is a saturable function of [Cl]_o in symmetric solutions with a mean affinity constant (K_1/2) of ~38 mM (146). In addition, CFTR Cl conductance can be blocked by SCN (101), and in the presence of mixtures of SCN and Cl, CFTR conductance exhibits an anomalous dependence on the mole fraction of SCN (147). These observations provide strong evidence for the binding of permeant anions in the pore of CFTR.

The N-P theory can be modified to incorporate the effects of ion binding in the permeation path (33, 88, 89), but a conceptually simpler approach is based on the Theory of Absolute Reaction Rates or Eyring Rate Theory (51). In this formalism, ion movement is viewed as a series of hopping events. Diffusion in aqueous solution, for example, is envisioned as a series of hops of an ion from one point in a lattice of water molecules to another. Each point in the lattice of water molecules could be viewed as a binding site of sorts, and translocation involves a series of hops from one site to the next and so on. It is, therefore, straightforward to extend this formalism to an ion that hops from water into a channel, moves across the channel, and hops out on the other side.

Although elements of the rate theory approach to ion conduction have been questioned (89), this formalism has become a popular way of envisioning ion transport through pores for several reasons. First, because it describes ion movement as a series of hopping events driven by thermal energy and the electric field, rate theory lends itself naturally to describing ion translocation in a setting in which it is envisioned that ions move by hopping from one site to the next and can associate more or less strongly with each site. Second, because the formalism is basically that of reaction rate kinetics and compartmental analysis, it lends itself very well to thinking about permeability, which is best thought of in terms of the behavior of a labeled form of the ion (tracer) that is present in low molar abundance (36, 38). Most importantly, the rate theory model provides an intuitively useful framework for understanding the difference in the behavior of permeability and conductance in channels that bind ions. Here, we briefly outline the development of the simplest model for an ion channel, that in which the channel can accommodate only one ion at a time. More complex models can be envisioned (32, 95), but the simple model is intuitively accessible and contains sufficient complexity to introduce the most widely utilized generalizations that are derived from this approach. The derivations are presented here in a highly condensed form. The details can be found in Reference 38 and a variety of other sources (67, 85, 106, 160).

Rate theory models are most properly regarded as models for the process of ion conduction rather than as models for the structure of the channel. Accordingly, the process of ion translocation through a single-site, one ion channel is represented by the diagram shown in Figure 3 in which crossing the channel requires two hops. In the first, an ion located in the "capture volume" in the aqueous solution adjacent to the mouth of the channel hops into the channel and is able to interact with a "binding site." In the second hop, the ion leaves the binding site and exits the channel, entering the aqueous bath on the trans-side. The permeation process is represented as surmounting a series of two energy barriers, each of which depicts in a very general way the forces that impact the ion translocation events. As indicated in section IIIB, these are envisioned as representing the difference in the energies associated with ion-water and ion-channel interactions. For example, the height of the barrier to anion entry is presumably related in part to the fact that the ion must be at least partially dehydrated, but the height of this barrier would be diminished by favorable ion-channel interactions. The depth of the energy well representing the site reflects the apparent affinity of the ion for some sort of binding site, and the depth of this well also contributes to the energy barrier to ion exit from the channel. Shown in the diagram is a symmetric two-barrier, one-site energy profile for a channel that can be occupied by only one ion at a time.

View larger version (20K): [in this window] [in a new window]   FIG. 3.   Diagrammatic representation of a 2-barrier 1-site model for an ion channel that allows for a description of ion entry process as an energy barrier representing process of dehydrating ion and solvation by channel and accounts for binding of ions within channel by including an energy well. Gp , peak height; Gw , depth of energy well; Gb, energy in ion bath, defined as zero.

The properties of the channel are specified in four unidirectional rate coefficients, k_1m , k_m1 , k_m2 , and k_2m , the magnitudes of which depend on the height of the relevant energy barrier (Fig. 3). The relationship is assumed to be exponential and of the form exp(G_p /RT), where G_p is the peak barrier height. The preexponential term is taken to be the frequency of thermal vibration given by kT/h, where k is Boltzmann's constant, T is absolute temperature, and h is Planck's constant so that at 25°C, kT/h is equal to ~6 × 10¹² s¹. One criticism of the rate theory approach is based on the fact that this preexponential term is taken to be independent of the ion and its physical environment (21). The four rate coefficients are written as

(9)

(10)

(11)

(12)

where the terms in G represent the height of the barrier that must be overcome in one hop, i.e., G_1p = G_p  G_b , G_mp = G_p  G_w , and G_2p = G_p  G_b . The preexponential factor is sometimes multiplied by a transmission coefficient, but the latter is usually set equal to unity (67).

The net fluxes of the ion into, and out of, the channel must be equal in the steady state so that if these are written as the difference between the relevant one-way hopping rates we obtain

(13)

where J_1m , J_m1 , J_m2 , and J_2m are the unidirectional fluxes into or out of the channel in molar units. Influx into the channel, for example, J^Cl_1m, is written as

(14)

here v is the capture volume from which ions may enter the channel, [Cl]₁ is the Cl concentration within this volume, k_1m is the unidirectional rate coefficient for the entry process, and f_o is the probability that the channel is occupied. The product of v and [Cl]₁ is the number of moles of Cl ions in the capture volume so that multiplying by the entry rate coefficient in units of s¹ yields the flux in units of mol/s. The term (1  f_o) is the probability that the channel is unoccupied, and multiplying by this factor applies the constraint that ions may only enter an empty channel.

Efflux from the channel, e.g., J^Cl_m1, is written as

(15)

where N_A is Avogadro's number and k_m1 is the rate coefficient for Cl exit. Multiplying by f_o expresses the fact that ions may only exit an occupied channel.

Combining Equations 13-15 and solving for f_o when [Cl]₁ = [Cl]₂ = [Cl]_b yields

(16)

(16a)

As expected for a single-site binding process, the occupancy of the channel saturates as [Cl]_b is increased and the K_1/2 for the process is proportional to the ratio of the sum of the off rates and the sum of the on rates. Inserting expressions for the rate coefficients for a symmetric 2B1S channel yields

(17)

where G_w is the "depth" of the energy well measured with respect to the external bath. Note that because a value for the capture volume v is not easily specified, (1/v N_A) is usually set at 1 M so that values of G_w are referenced to a 1 M standard state (28), i.e.

(18)

where C*_b = 1 M.

The saturable occupancy of the 2B1S channel has important implications for the interpretation of permeability and conductance measurements. Permeability, as noted earlier, is best defined in terms of a one-way tracer flow measurement through a channel that is always open so that the permeability P_Cl can be defined as

(19)

where J^Cl₁₂ is the unidirectional flow of Cl from side 1 to side 2 as would be determined in a tracer flow experiment, and is given by

(20)

The one-way flow of Cl through the channel is equal to the rate of Cl entry (J_1m) multiplied by the fraction of entering ions that exit on side 2. Substituting from Equations 14-20 yields

(21)

Here P_Cl is seen to be the product of two terms, the right most reflecting the intrinsic hopping rates into and out of the channel and the left most pertaining to the concentration-dependent loading of the channel. Clearly, as [Cl]_b is increased, P_Cl declines. This is because a tracer ion moving from side 1 to side 2 must compete with unlabeled ions for the binding site in the channel. The maximum value for P_Cl defined in this way, denoted as P⁰_Cl, is found when [Cl]_b = 0 and is given by

(22)

It is useful to think of P⁰_Cl as the "intrinsic" permeability of the channel, i.e., that which reflects only the rate coefficients for entry into and exit from an empty channel. Thus the permeability of a channel defined by a tracer flux measurement is equal to the intrinsic permeability multiplied by a factor that accounts for the fact that tracer may enter only unoccupied channels so that P_Cl will equal P⁰_Cl only in the limit [Cl]_b = 0.

The conductance of the 2B1S channel in the presence of symmetric Cl can be derived from the relation

(23)

where (_Cl)₀ is the conductance of the channel at V_m = 0, P_Cl is the permeability determined at V_m = 0 by a tracer flow measurement, and [Cl]_b is the symmetric Cl concentration. Inserting the expression for P_Cl from Equation 21 yields

(24)

which can be written as

(25)

It can be seen that _Cl is proportional to the intrinsic channel permeability P⁰_Cl but is a saturable function of [Cl]_b . If [Cl]_b << K_1/2 , then

(26)

At low concentrations of Cl, channel conductance is a linear function of [Cl]_b as it is for the N-P channel (Eq. 8). This makes intuitive sense in as much as conductance, a measure of ionic throughput, requires not only that the channel be permeable to the ion, but also that the ion be present. If the intrinsic permeability (P⁰_Cl) is constant, then for [Cl]_b << K_1/2 , as the abundance of the permeant ion increases the current that can be driven by an applied voltage increases linearly, just as it would in the N-P channel in which ions do not influence each other. As [Cl]_b becomes comparable to K_1/2 , however, the effects of channel occupancy become apparent. Successive increments in [Cl]_b produce smaller and smaller increases in  as increasing channel occupancy reduces the probability that the channel will be available to an entering ion. When [Cl]_b >> K_1/2 ,  is independent of [Cl]_b , and the conductance approaches a maximum given by

(27)

In this condition, the channel is occupied virtually 100% of the time, and throughput is limited by the rate of exit of ions from a loaded channel. This can be seen clearly if the expressions for K_1/2 and P⁰_Cl are inserted in Equation 27, i.e.

(28)

(_Cl)_max is seen to be proportional to the intrinsic exit rate, k_m2 , multiplied by the fraction of exiting ions that entered on the opposite side. For the symmetric case considered here, however, k_1m = k_2m so that

(29)

because in the symmetric case, regardless of the barrier heights, 50% of the exiting ions will have entered from the opposite side and, therefore, must represent conducted ions.

The dependence of _Cl on ion binding is readily apparent from Equation 25, which shows that _Cl exhibits a saturable dependence on ion concentration, and Equation 27, which shows that (_Cl)_max is directly proportional to K_1/2 so that high-affinity binding (low K_1/2) implies reduced conductance. In the symmetric model, it is particularly apparent that the maximum value of the conductance is inversely proportional to the well-to-peak energy embedded in the term k_m2 so that tighter binding (increased well depth) decreases the rate of ion exit from the channel. All of this makes intuitive sense from the perspective that conductance is a measure of throughput, of net ionic flow per unit voltage. Any ion that "sticks" in the channel will impede flow and reduce the maximum rate of throughput. A tightly binding, permeant ion will block or impede the flow of other ions that bind less tightly. From this perspective, highly conductive ions and "blocking" ions clearly represent two points on a continuum. For the purpose of illustration, we can examine some of the predictions of the admittedly over-simplified symmetric 2B1S model for CFTR with two equally spaced barriers and one well. The value of K_1/2 for the saturable dependence of  on [Cl]_b of 38 mM reported by Tabcharani et al. (146) would predict a well depth of about 3.3RT, with respect to a 1 M standard state. The well-to-peak energy that governs maximal conductance would be ~14.5RT if  = 10 pS (symmetric [Cl]_b = 100 mM), yielding a peak barrier height of 11.2RT. The behavior of SCN is particularly interesting because it is highly permeant but also blocks the channel. A permeability ratio P_SCN/P_Cl of 3.3 translates into a difference in the peak barrier height of 1.2RT. The tighter binding of SCN would be compatible with a well depth of 6RT for this ion (Fig. 4).

View larger version (12K): [in this window] [in a new window]   FIG. 4.   Representative macroscopic current (I)-voltage (V) plots recorded from a Xenopus oocyte expressing wild-type human CFTR. Shown are plots in presence of 105 mM external Cl (Clo) and after replacing 98% of Clo with external SCN (SCNo). Note that in presence of SCN reversal potential shifts to left as expected if PSCN > PCl , but conductance is dramatically reduced.

The absolute permeabilities measured for the 2B1S channel will also be sensitive to ion binding, as shown by Equation 21. The same effect that reduces maximum conductance will also cause tracer ions to experience more difficulty in finding an unoccupied channel as [Cl]_b is raised. Permeability has a unique value as a comparative tool, however, in that it is possible, in principle, to compare the permeability of the channel with two different ions under identical conditions. The simplest way to envision such a comparison is in terms of a double-label, tracer flow experiment. For example, the one-way fluxes of ³⁶Cl and labeled SCN could be determined simultaneously, in the presence of bathing solutions containing unlabeled Cl or SCN in any combination. The unidirectional flows of both tracer ions would be reduced by occupancy of the channel by Cl or SCN, but to an identical extent. That is to say, in the ratio P_SCN/P_Cl (determined at V_m = 0), the term describing channel occupancy would be identical for either ion and would cancel out so that the measured ratio would be equal to the ratio of the intrinsic permeabilities of the channel to Cl and SCN.

This result is particularly important with regard to the use of E_rev values to estimate permeability ratios (see sect. IIC). It is useful to think of E_rev shifts as measuring the ratios of intrinsic permeabilities (38). As shown in Equation 22 for the 2B1S model, the intrinsic permeability is given by the rate coefficient for ion entry into the channel multiplied by the fraction of entering ions that exit on the trans-side. This fraction is independent of well depth, however, because any change in depth will affect the probability of an ion leaving the channel in either direction equally. On the other hand, the intrinsic permeability is very sensitive to barrier height, in the simple 2B1S model, the barrier to entry into the channel. Thus the permeability ratios, estimated from shifts in E_rev , for a 2B1S channel will be relatively insensitive to well depth (ion binding) and highly sensitive to peak height (ease of entering the channel), as recognized by Bezanilla and Armstrong (11). This prediction is consonant with the fact that the E_rev , because it is determined at zero current, is not dependent on the rate of ionic throughput. Channel conductance, on the other hand, measures the time-average rate of ion flow and is expected to be very sensitive to anion binding in the channel. Thus it is useful, although not completely accurate, to think of permeability ratios as comparing the ease with which anions leave the aqueous solution and enter the pore, whereas the relative conductance can report the tightness of binding to sites in the conduction pathway. The dichotomy between permeability ratios and conductance ratios for CFTR is well illustrated by the behavior of SCN. Figure 4 shows two macroscopic i-V relations recorded from a Xenopus oocyte expressing wild-type CFTR, one recorded in the presence of 105 mM [Cl]_o and the other recorded after replacing 90% of the Cl by SCN. In the presence of SCN, the E_rev shifted to more negative values, indicating that P_SCN/P_Cl > 1, but the conductance measured at the reversal potential is dramatically reduced. This behavior is predicted for an anion that enters the channel more readily than Cl but sticks tightly once inside. As always, one must approach with caution any attempt to generalize such predictions to real channels, in particular those that can be occupied by more than one permeant ion (67, 68, 147), but they provide a useful guide or zeroth approximation.

The simplest N-P model, as presented here, represents a limiting case in which the interior of the channel is viewed as an equivalent volume of aqueous solution where ions move without interacting with the channel or each other. It is important to point out, however, that the physical parameters that characterize the permeability of the N-P channel can be readily interpreted within the framework of the simple rate theory description. The permeability of the N-P channel to an ion i is given by

(30)

where A is the channel area, _i is the channel/bulk solution partition coefficient, D_i is the intracellular diffusion coefficient, and x is the length of the channel.

The partition coefficient for the simple 2B1S channel (Fig. 3) is a function of the well depth, G_w  G_b , i.e.

(31)

The intramembrane diffusion coefficient D_i can be written as (12, 67)

(32)

so that in the product _iD_i , the term representing the well depth (G_w) drops out, i.e.

(33)

Thus, for any permeability ratio, say P_j/P_i , we obtain the result that

(34)

permeability ratios are not sensitive to ion binding. But what then are the properties of a free solution or N-P channel expressed in the language of rate theory? The hallmark of the simplest N-P channel is short residence time for the ion within the channel. The channel is never seen by an entering ion as being occupied, and there is no saturation of channel conductance as the concentration of permeant ions in the bath is raised. The free solution 2B1S channel, therefore, is one characterized by a shallow or no energy well. For example, in relation to Figure 3, if G_w = G_b so that the well depth is zero, the K_1/2 for the dependence of  on concentration is 1,000 mM. If the concentrations of permeant ions in the bathing solution are significantly less than the K_1/2 , then the conductance exhibits a simple linear dependence on the permeability given by Equations 7 and 26.

Finally, we note that there is perhaps a subtle deception effected by the tendency, within the rate theory formalism, to view well depth and peak height as independent parameters. This seems unlikely to be the case in general, and one might expect, for example, that channel modifications that reduced the binding of ions by reducing the ion-channel interaction energy might also influence the peak height, which is expected to depend in large part on the balance between ion-water and ion-channel interactions. This effect is, in fact, seen in CFTR mutations like G314E, which destabilizes relative anion binding, but also reduces single-channel conductance rather than increasing single-channel conductance as would be expected if only the well depth were affected (Mansoura and Dawson, unpublished data).

	IV. DESIGNING AN ANION CHANNEL: ORIGINS OF ANION SELECTIVITY AND ANION BINDING

Top Previous Next References

Studies of anion conduction by CFTR and several other anion channels have established two important properties of the anion conduction path. First, compared with cation channels, anion channels tend to be rather nonselective. Second, certain anions bind within the pore such that they act as blockers of the channel (13, 58, 101, 146, 147, 157). These two characteristics have been derived from a comparison of permeability ratios and conductance ratios for permeant ions, the former reflecting primarily the relative ease with which an anion enters the channel and the latter reporting the tightness of anion binding. Representative values for permeability and conductance ratios for several anion channels are compiled in Table 1. Although it is not possible to specify exactly how these properties arise, studies of CFTR as well as other anion channels, viewed in light of the known properties of anions and water, provide the basis for some provocative speculation.

One approach to identifying the critical design criteria for an anion channel is to examine the behavior of model systems for which the structure is more or less established. One candidate for such a comparison is the channel formed by the antibiotic gramicidin (43, 90). It has been proposed that the channel is formed from a dimer consisting of two helical peptides joined at the amino-terminal ends. Each helix consists of 15 alternating L- and D-amino acids, containing 6.3 peptide units per turn. This arrangement dictates that the lining of the channel is formed by the carbon, oxygen, nitrogen, and hydrogen atoms of the polypeptide backbone, whereas the side chains face the surrounding lipid. The channel contains no charged groups, but it is, nevertheless, highly cation selective. Another interesting model is the channel(s) that is formed when designed, amphiphilic peptides are incorporated into a lipid bilayer. Lear et al. (86) synthesized 21-residue peptides composed of leucine and serine, (LSSLLSL)₃ , that, when incorporated into a lipid bilayer, gave rise to cation-selective channels, again in the absence of any charge on the peptide. Although anions and cations are predicted to interact differently with a peptide structure because of the difference in their net charge, Levitt (90) called attention to the fact that the cation selectivity of gramicidin could arise in part from the fact that more work is required to dehydrate an anion than a cation of comparable size (12, 16, 25, 102, 103). Cox et al. (30) compared the free energy required to transfer anions and cations from water to dimethylformamide, a compound which might be viewed as a model peptide. They found that the transfer of univalent cations was favored over that of anions by anywhere from 2 to 13 kcal/mol, although this difference reflects, in part, stronger interactions of cations with the aprotic solvent (35, 100). Levitt (90) proposed that anion selectivity might require either the placement of positive charges in the channel or that the effective diameter of the channel be sufficiently large that the anion could migrate through the channel while retaining some of its waters of hydration. A similar conclusion was reached by Dorman et al. (43) who used a Monte Carlo approach to simulate permeation energetics in the gramicidin channel. They considered interaction between anions and cations and the peptide backbone of the channel as well as ion-water interactions and concluded that the lack of anion permeation was primarily attributable to the increased energy required to remove the anion from water so that anion permeation might require a larger cross section so as to accommodate the more highly hydrated anions. This perspective seems to fit, in a general way, the findings for a number of anion channels that are, as a group, relatively nonselective and in which permeability ratios, which measure the ability of an anion to enter the channel, fall in the order predicted on the basis of hydration energy, i.e., a "weak field strength" site sequence according to Eisenman and Horn (50) (Table 1).

There is evidence that positive charges may be important for anion selectivity. The structure of the transmembrane segments presumed to line the pores of the GABA_A receptor and the glycine receptor (GlyR) both contain arginines near the cytoplasmic and extracellular ends that have been implicated in anion/cation discrimination. When Langosch et al. (83) incorporated the presumed pore-lining GlyR M2 peptides into planar bilayers, they observed multiple unitary conductance events, some anion selective but some cation selective. A modified peptide, however, in which the terminal arginines were replaced by glutamic acids led to the formation of cation-selective channels. Reddy et al. (121) reported that peptides modeled after the M2 segment of GlyR, when incorporated into planar bilayers formed at the tip of a patch pipette, gave rise to channel events that exhibited distinct anion selectivity (P_Cl/P_K = 5.6). In contrast, an identical peptide in which the flanking arginines were replaced with glutamic acids produced cation-selective channel events (P_K/P_Cl = 5.3). Furthermore, a tethered tetramer of M2 GlyR peptides also formed anion-selective channels (P_Cl/P_K = 9.0). Oblatt-Montal et al. (111) assayed the channel-forming abilities of peptides modeled after the first six membrane-spanning segments of CFTR. Only two, transmembrane segment (TM) 2 and TM6, gave rise to channel-like activity. Both of these peptides contain arginines and/or lysines near their ends.

The importance of the arginine residues in GlyR was also apparent in a mutant form, R271Q, associated with the inherited disease hyperekplexia, which exhibited a diminished single-channel conductance (84). Arginine has also been implicated in anion selectivity in the glutamate receptor channel. The so-called "Q/R site" in the glutamine R2 subunit was identified as being important for calcium permeation and also block by polyamines (18, 19). It was also found, however, that the Q to R substitution increased the relative anion permeability such that, in the presence of high external calcium, the ratio P_Cl/P_Cs was 1.4, i.e., with regard to these two similarly sized ions, the channel behaved as if it was anion selective.

There is evidence that the membrane-spanning peptides that appear to be important for the conduction path of anion-selective channels can induce anion permeation in cell membranes. Wallace et al. (154) reported that if apical membranes of Madin-Darby canine kidney monolayers were exposed to a GlyR M2 peptide modified to contain four lysine residues at the carboxy terminus, Cl secretion was induced. Recently, Lencer et al. (87) reported that a class of compounds called cryptdins, which are related to neutrophil defensins, induced Cl secretion in monolayers of T84 cells. The most active peptide, cryptdin 3, contains eight arginines and three lysines.

The importance of the structural context in which charges that line the pore may act to influence permeability and conductance was highlighted by the experiments of Galzi et al. (57), who attempted to design anion-selective variants of a GABA receptor (GABAR)/GlyR homolog, the acetylcholine receptor. In the acetylcholine receptor (AChR) M2 segment, glutamates at position 237 are thought to contribute to a cytoplasmic ring of negative charge, whereas the corresponding position in the GABAR and GlyR M2 receptor is occupied by an alanine. The adjacent residue (238) is an arginine in GABAR and GlyR M2 and a lysine in the AChR M2. Replacing glutamate-237 with alanine resulted in an anion-selective channel, but only if an additional neutral residue (proline or alanine) was inserted between positions 236 and 237 to bring the length of the M2 segment or the MI-M2 linker into register with that of GABAR and GlyR. This important result strongly suggests that although anion to cation selectivity is likely to be charge dependent, the structural context in which potential permeant ions experience these charges can be critical. The results obtained by Mansoura et al. (101) in studies of mutant CFTR suggest that a similar caution will apply to the results of charge substitution experiments in the CFTR Cl channel.