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Re-examination of the Surface Charge Hypothesis

Jin Bong Park¹, Hee Jeong Kim¹, Pan Dong Ryu¹ and Edward Moczydlowski²

¹ Department of Pharmacology, College of Veterinary Medicine and School of Agricultural Biotechnology, Seoul National University, Suwon 441-744, Korea
² Department of Pharmacology and Department of Cellular and Molecular Physiology, Yale University School of Medicine, New Haven, CT 06520

Address correspondence to Edward Moczydlowski, Yale University School of Medicine, 333 Cedar St., New Haven, CT 06520-8066. Fax: (203) 436-4886; E-mail: edward.moczydlowski{at}yale.edu

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Incorporation of BK Ca²⁺–activated K⁺ channels into planar bilayers composed of negatively charged phospholipids such as phosphatidylserine (PS) or phosphatidylinositol (PI) results in a large enhancement of unitary conductance (g_ch) in comparison to BK channels in bilayers formed from the neutral zwitterionic lipid, phospatidylethanolamine (PE). Enhancement of g_ch by PS or PI is inversely dependent on KCl concentration, decreasing from 70% at 10 mM KCl to 8% at 1,000 mM KCl. This effect was explained previously by a surface charge hypothesis (Moczydlowski, E., O. Alvarez, C. Vergara, and R. Latorre. 1985. J. Membr. Biol. 83:273–282), which attributed the conductance enhancement to an increase in local K⁺ concentration near the entryways of the channel. To test this hypothesis, we measured the kinetics of block by external and internal Ba²⁺, a divalent cation that is expected to respond strongly to changes in surface electrostatics. We observed little or no effect of PS on discrete blocking kinetics by external and internal Ba²⁺ at 100 mM KCl and only a small enhancement of discrete and fast block by external Ba²⁺ in PS-containing membranes at 20 mM KCl. Model calculations of effective surface potential sensed by the K⁺ conduction and Ba²⁺-blocking reactions using the Gouy-Chapman-Stern theory of lipid surface charge do not lend support to a simple electrostatic mechanism that predicts valence-dependent increase of local cation concentration. The results imply that the conduction pore of the BK channel is electrostatically insulated from the lipid surface, presumably by a lateral distance of separation (>20 Å) from the lipid head groups. The lack of effect of PS on apparent association and dissociation rates of Ba²⁺ suggest that lipid modulation of K⁺ conductance is preferentially coupled through conformational changes of the selectivity filter region that determine the high K⁺ flux rate of this channel relative to other cations. We discuss possible mechanisms for the effect of anionic lipids in the context of specific molecular interactions of phospholipids documented for the KcsA bacterial potassium channel and general membrane physical properties proposed to regulate membrane protein conformation via energetics of bilayer stress.

Key Words: electrostatics • Gouy-Chapman theory • lipid modulation • phospholipid • Slowpoke

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Ion transport proteins are responsible for movement of ions across a cell membrane that separates the external and internal aqueous milieu by 40 Å. The two membrane interfaces on the outside and inside of the cell exist as charged surfaces due to the presence of ionized chemical groups on protein, carbohydrate, and lipid. Discrete charges located at the membrane–water interface give rise to an electrostatic surface potential that varies in a complex fashion according to the distribution and density of fixed charges, electrolyte composition, and distance from the charged groups (McLaughlin, 1989; Honig and Nicholls, 1995). Because local concentrations of ionic substrates (e.g., Na⁺, K⁺, H⁺, Ca²⁺, Cl^-) near the membrane are determined by this complex surface potential map, surface charge is considered to play an important role in modulating ion channel function (Green and Andersen, 1991; Latorre et al., 1992; Hille, 2001).

One of the first experiments to identify functional effects of lipid surface charge showed that the unitary conductance of the gramicidin cation channel is increased 4.3-fold, from 15 pS in phosphatidylcholine (PC)^* to 65 pS in a phosphatidylserine (PS) membrane under conditions of 100 mM CsCl (Apell et al., 1979). According to electrostatic theory, the radius of the cylindrical gramicidin channel, 6–13 Å (Killian, 1992; Woolf and Roux, 1996), is close to the Debye length (_D 10 Å in 0.1 M salt solution) that determines the distance dependence of surface potential decay. Thus, this small peptide channel effectively "senses" the large increase in local Cs⁺ concentration that occurs near the surface of the PS membrane and responds with a proportionate increase in Cs⁺ conductance. Indeed, careful titration of phospholipid surface charge by changes in pH and mixtures of PC plus PS (Rostovtseva et al., 1998) showed that the effect of surface charge on gramicidin conductance is primarily explained by the Gouy-Chapman-Stern (GCS) theory of membrane surface potential (Eisenberg et al., 1979; McLaughlin et al., 1981).

In comparison to the test case of gramicidin, the effects of lipids and membrane surface charge on the activities of large ion channel proteins are considerably more complex. Using the planar bilayer system to measure the unitary conductance of the sarcoplasmic reticulum (SR) K⁺ channel in membranes formed from neutral zwitterionic lipids or negatively charged lipids, Bell and Miller (1984) observed a substantial enhancing effect of PS at KCl concentrations <400 mM. From a theoretical analysis based on GCS theory, they concluded that the cation entryway of the SR K⁺ channel behaved as if it sensed the local K⁺ concentration at a distance of 10–20 Å away from the electrified membrane interface. Such evidence that an ion channel may respond to less than the full value of the membrane surface potential has led to the idea that the mass disposition of a large channel protein may effectively "insulate" a channel's conducting pore from the electrostatic properties of the membrane surface.

According to this interpretation, various types of channel proteins would be differentially insulated from membrane surface charge. At one extreme, both the K⁺ conductance and Ca²⁺ sensitivity of the large conductance Ca²⁺-activated K⁺ channel (BK) are greatly enhanced in PS versus phosphatidylethanolamine (PE) bilayers (Moczydlowski et al., 1985). On the other hand, unitary conductance and the apparent blocking affinity of external divalent cations (Ca²⁺) and external decarbamoylsaxitoxin²⁺ are virtually unaffected by incorporation of voltage-gated Na⁺ channels (Na_V) into negatively charged bilayers containing PS, as compared with a neutral lipid mixture of PE/PC (Green et al., 1987a; Guo et al., 1987; Worley et al., 1992). [Incidentally, the voltage activation process of the rat brain Na_V channel is quite sensitive to bilayer PS as measured by shifts of the voltage-activation midpoint with increasing Ca²⁺ concentration and ionic strength (Cukierman et al., 1988; Cukierman, 1991).] In the case of L-type voltage–activated Ca²⁺ channels (Ca_V), only a small conductance increase is observed in PS bilayers when Na⁺ is the current carrier, but not when Ba²⁺ carries the current (Coronado and Affolter, 1986). These studies would suggest that conduction pores of large channel proteins are variably shielded from the electrostatic surface potential generated beyond the edge of the protein–lipid interface; however, the molecular basis of this phenomenon is poorly understood.

Since the protein complex of the tetrameric BK channel is larger in mass than structurally related Na_V and Ca_V channel complexes, it is surprising that BK conductance is enhanced to a greater degree by negatively charged phospholipids. To explore the basis of this apparent paradox, we decided to reexamine the surface charge hypothesis previously used to explain the effect of PS on conductance of the BK channel (Moczydlowski et al., 1985). The association rate of a charged blocking ion to a site in the ion conduction pathway of a channel protein is generally expected to be proportional to the local concentration of the blocking ion in equilibrium with the binding site (Green et al., 1987b; Guo et al., 1987; MacKinnon et al., 1989; Escobar et al., 1993). Studies have shown that the apparent blocking affinity of charged peptide toxins, organic cations, and inorganic cation blockers is often dependent on electrostatic interactions between the blocking ion and the channel protein (Bell and Miller, 1984; Worley et al., 1986; MacKinnon and Miller, 1989; MacKinnon et al., 1989; Stocker and Miller, 1994; Escobar et al., 1993). Therefore, measurements of cation-blocking kinetics in membranes composed of charged versus neutral lipids can be used to monitor the relative fraction of membrane surface potential that falls in the vicinity of the entrance of an ion channel. In this study, we used Ba²⁺ and TEA⁺, two well-known blockers of K⁺ channels, as probes of phospholipid surface charge sensed by the rat muscle BK channel. We find that K⁺ conductance of the BK channel is enhanced more strongly by negatively charged phospholipids than the affinity or kinetics of pore-blocking cations. These observations suggest that lipid interactions with the BK channel are more complex than expected for a simple electrostatic mechanism based on surface charge. We propose that certain K⁺ channels may be subject to lipid-dependent tuning of protein conformational changes associated with rate-determining barriers to ion movement.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Planar Lipid Bilayers and Measurement of Surface Charge Density
Planar lipid bilayers were formed on a 0.2-mm diameter hole in a polystyrene partition by spreading a solution of phospholipid (25 mg/ml) in decane with a small glass rod. The lipid composition of neutral bilayers (PE membrane) was 100% 1-palmitoyl-2-oleoyl PE and that of negatively charged bilayers (PS membrane) was 80% 1-palmitoyl-2-oleoyl phosphatidylserine plus 20% PE. In some experiments, negatively charged bilayers composed of 80% phosphatidylinositol (PI) from bovine liver plus 20% PE were also used (PI membrane). Lipid mixtures rather than pure PS or PI were used because addition of 20% PE improved bilayer stability during channel incorporation and long duration experiments. Phospholipids were purchased from Avanti Polar Lipids.

The negative charge density of phospholipid bilayers was measured with the use of the K⁺ ionophore nonactin as described previously (McLaughlin et al., 1970). This method gave the following values of surface charge density in units of e^-/nm²: 0.04 ± 0.01 (mean ± SE, n = 5), 0.98 ± 0.04 (n = 4), and 1.07 ± 0.06 (n = 3) for PE, PS, and PI membranes, respectively. Based on a molecular surface area of 0.7 nm² per phospholipid molecule (Loosley-Millman et al., 1982), the expected value of charge density for a membrane containing 80% negatively charge lipid is 1.143 e^-/nm². Our measured values correspond to 3% (PE), 69% (PS membrane), and 75% (PI membrane) in percentage of negatively charged lipid. These results are close to expectation; similar deviations from theoretical charge densities were found in previous studies (Bell and Miller, 1984; Coronado and Affolter, 1986; Rostovtseva et al., 1998).

Channel Incorporation and Electrical Recording
Membrane vesicles for bilayer incorporation of large conductance Ca²⁺-activated K⁺ channels (BK) were prepared from rat skeletal muscle using a sucrose density step gradient as described previously (Guo et al., 1987). The polystyrene partition on which the bilayer was formed was a cup and well-type chamber (Warner Instruments). The solution on both sides of the partition contained 10 mM HEPES adjusted to pH 7.2 with 7 mM KOH and the following range of KCl concentrations: 3, 10, 20, 30, 50, 100, 200, 500, 700, and 1,000 mM. Ca²⁺ was added to the same chamber (cis) as the membrane vesicles to a free concentration of 100 µM (0.6 mM CaCl₂ plus 0.5 mM EGTA) for the experiments of Figs. 1 and 2 or 200 µM CaCl₂ (without EGTA) for all other experiments. A cis-internal orientation of BK channel incorporation was confirmed by an increase in open state probability with increasing positive voltage applied on the cis side. For Ba²⁺-blocking experiments, BaCl₂ was added to the external (trans) side at 0.5–60 mM or to the internal (cis) side at 1–100 µM. For TEA⁺-blocking experiments, TEA chloride was added to the external side at 0.03–1 mM.

The cis and trans compartments were connected to the amplifier via Ag/AgCl electrodes and KCl-agar bridges. BK channel activity was measured at room temperature (22°C) using a BC525A bilayer amplifier (Warner Instruments). Single-channel current data was stored on VCR tape via a digital data recorder (VR-10; Instrutech) for off-line analysis. The stored data was replayed either at 200 or 10 Hz using an 8-pole Bessel filter and digitized at 2 kHz using a PC-based data acquisition system from Axon Instruments, Inc.

Measurement of Single-channel Conductance and Blocking Parameters
Single-channel current amplitude was measured in the voltage range of -80 to 80 mV using pClamp 6 analysis software from Axon Instruments, Inc. that facilitated accurate measurement of mean closed state (defined as zero current) and mean open state current levels. Single-channel conductance was calculated from linear slopes of individual current-voltage datasets obtained at different K⁺ concentrations. Fast block by external Ba²⁺ and TEA⁺ was measured as the apparent reduction of unitary current. Time-averaged open state probability in the absence and presence of the discrete blocker, Ba²⁺, was measured for current records at 20 mV as the total time in the open state divided by the duration of the record. Dwell time histograms containing a minimum of 250 Ba²⁺-blocked or unblocked events were constructed from long records filtered at 10 Hz. A filter setting of 10 Hz imposed an effective dead time of 18 ms for the shortest detectable closed or blocked state event. This procedure eliminated the contribution of gating closures (Vergara and Latorre, 1983) since the longest component of closed state gating events typically had a time constant of 2 ms under these conditions. This method effectively isolated consistently sampled populations of Ba²⁺-blocked events that were fit to a sum of two exponentials and Ba²⁺-unblocked events that were fit to a single exponential function. The use of a dead time of 18 ms for the shortest acceptable blocked event results in a small artificial lengthening (<10%) of the measured unblocked duration due to exclusion of a small number of short-lived Ba²⁺-blocked states. We did not correct for this error, since this sampling effect only results in an 10% underestimate of the true association rate for Ba²⁺.

Modeling of Surface Charge Effects
To first explore how underlying rate constants of ion translocation might be quantitatively affected in a PS vs. PE membrane, we fit conductance vs. [K⁺] data to a simple discrete-state kinetic model of a symmetrical two-site channel with double occupancy (Andersen, 1989). Nonlinear least squares fitting was performed using SigmaPlot 2000 software (SPSS, Inc.).

To assess the relative effect of PS in enhancing K⁺ conductance and block by Ba²⁺ (and TEA⁺) by a surface charge mechanism, we calculated the expected local ion concentration at a distance, x, from the surface of a phospholipid membrane from the Boltzmann distributions for a monovalent cation (e.g., K⁺, TEA⁺) and a divalent cation (e.g., Ba²⁺):

(1)

(2)

where [K⁺]_local and [Ba²⁺]_local are the respective local concentrations of K⁺ and Ba²⁺, [K⁺]_bulk and [Ba²⁺]_bulk are the respective bulk concentrations of K⁺ and Ba²⁺ far from the membrane, _x, is the electrostatic potential at a distance x from the membrane surface, F is the Faraday, R is the gas constant, and T is the absolute temperature. The electrostatic potential at the membrane surface, _{x = 0} or ₀, was calculated from the Grahame (1947) equation of Gouy-Chapman theory as outlined in McLaughlin et al. (1981) and Latorre et al. (1992):

(3)

Eq. 3 relates ₀ to the membrane surface density of negative charge, , and the indicated sum over the bulk concentrations, C_i, of i ions of valence z_i in the aqueous phase (e.g., K⁺, Cl⁺, Ba²⁺), where _r is the dielectric constant of water and ₀ is the permittivity of free space. To simplify the calculations, 10 mM HEPES-KOH used as the buffer in all solutions was approximated as 7 mM KCl. The density of negative surface charge at the membrane surface, , is further equal to the theoretical surface density of negatively charged PS in a phospholipid membrane containing 80% PS, {PS} in e^-/nm², multiplied by a factor to correct for the known binding association constants of K⁺ to PS (K₁ = 0.15 M^-1), Ba²⁺ to PS (K₂ = 20 M^-1), and Ca²⁺ to PS (K₂ = 12 M^-1) as described (Eisenberg et al., 1979; McLaughlin et al., 1981; Latorre et al., 1992):

(4)

In Eq. 4, we used {PS} = 1.143 e^-/nm² as the theoretical unneutralized surface density of 80% PS. [K⁺]₀ and [Ba²⁺]₀ are given, respectively, by Eqs. 1 and 2 at x = 0 Å from the surface. The potential at the membrane surface, ₀, was numerically computed by solving Eqs. 3 and 4 with the root function of Mathcad 8 software (MathSoft).

The decay of the surface potential as a function of linear distance from the membrane was computed according to McLaughlin (1989):

(5)

where =[exp(F₀/2RT) - 1]/[exp(F₀/2RT + 1]. The reciprocal Debye length, _D^-1, is given by:

(6)

where I is the ionic strength of the solution. Eq. 5 is not strictly applicable to solutions of mixed electrolytes containing both monovalent and divalent cations. For this reason, we limited distance calculations based on Eq. 5 to solution conditions where BaCl₂ is <1 mM and is only a minor contribution to the total ionic strength. Under these conditions, monovalent ion interactions predominate and Eq. 5 is a good approximation of the distance function.

	RESULTS

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Enhancement of Unitary Conductance by Negatively Charged Phospholipids
Fig. 1 A illustrates the behavior of single BK channels from rat skeletal muscle incorporated into planar bilayers formed either from pure PE, 80/20 PS/PE, or 80/20 PI/PE. As described previously (Moczydlowski et al., 1985; Park and Ryu, 1998; Turnheim et al., 1999), the BK channel exhibits a large increase in unitary conductance and open state probability in membranes containing negatively charged phospholipids. Under ionic conditions of Fig. 1 A (symmetrical: 100 mM KCl, 10 mM HEPES-KOH, pH 7.2, cis: 100 µM free Ca²⁺), K⁺ conductance is increased by 40% in a bilayer composed of 80% PS (g = 360 ± 9 pS, mean ± SE) or 80% PI (g = 356 ± 12 pS) as compared with 100% PE (g = 252 ± 10 pS). Enhancement of K⁺ conductance, measured from the linear slope of single-channel current-voltage data at low voltage (less than ±40 mV), is observed over a wide range of [K⁺] from 10 to 1,007 mM (Figs. 1 B and 2). The data of Fig. 2 also show that conductance values in PS and PI bilayers are virtually indistinguishable, suggesting that the chemical nature of the phospholipid head group is less important than its net charge in promoting this lipid-based enhancement. In Fig. 2 B, a plot of the measured ratio of unitary conductance in PS or PI bilayers to that of PE as a function of [K⁺] shows that the enhancement is inversely dependent on K⁺ concentration or ionic strength, ranging from 1.7-fold at 10 mM K⁺ to 1.1-fold at 1,007 mM K⁺. In principle, such an inverse dependence is consistent with a mechanism based on surface charge, since increasing ionic strength and K⁺ concentration acts to diminish the surface potential through screening of negative charges and binding of K⁺ to the carboxylate head groups of PS^-.

View larger version (45K): [in this window] [in a new window]   FIGURE 1. Effect of negatively charged lipids on single-channel current-voltage behavior. (A) Current records of single BK channels from rat skeletal muscle in neutral PE and negatively charged PS and PI bilayers at 20 and -20 mV. The solution on both sides of the membrane contained 107 mM K+ (100 mM KCl, 0.5 mM EGTA, 0.6 mM CaCl2, 10 mM HEPES, adjusted to pH 7.2 with KOH). Current records were low-pass filtered at 0.5 kHz and digitized at 2 kHz. The dashed line marks the zero-current or closed level marked c. Single-channel current-voltage relations in the range of -40 to 40 mV are shown in symmetrical solutions containing 10, 17, 107, 507, and 1,007 mM K+ for PE (B), PS (C), and PI (D) bilayers. Solid lines correspond to respective slope conductances from low to high K+ of 130, 169, 252, 359, and 481 pS for PE bilayers, 217, 282, 360, 454, and 519 pS for PS bilayers, and 216, 268, 356, 458, and 533 pS for PI bilayers. Data points and error bars represent mean ± SE for 3–11 single channels. Most error bars were smaller than the symbol.

View larger version (22K): [in this window] [in a new window]   FIGURE 2. Unitary conductance of the rat BK channel as function of symmetrical K+ concentration in PE, PS, and PI bilayers. (A) Conductance versus [K+]. Single-channel conductance was measured in PE, PS, or PI bilayers as described in Fig. 1. Data points correspond to the mean ± SE for 3–11 single channels. The solid line and dashed lines are respective nonlinear fits of the PE and PS data to Eq. 7 in the text. The model and best-fit parameters are given in Table I. The dotted lines are computed simulations based on Eq. 7 and the best-fit parameters for the PE data listed in Table I using [K+]local at various distances (2, 3, 5, 10, and 20 Å) from a PS membrane as calculated according to GCS theory given in MATERIALS AND METHODS. (B) Ratio of conductance data plotted in A for comparison of PS/PE or PI/PE bilayers vs. [K+]. The dotted lines are the ratio of the individual dotted line simulations in A to the fitted curve for the PE data in A.

(7)

where e is the elementary charge and k_B is the Boltzmann constant. The best-fit lines plotted according to Eq. 7 in Fig. 2 A show that this theory is capable of closely simulating the conductance-concentration data of the BK channel in PE and PS.

The values of rate constants derived from independently fitting the conductance data for PE and PS to the symmetric two-site model are given in Table I. These results show that the conductance increase observed in a PS vs. PE bilayer can be accounted for by rather modest increases in elementary rate constants. For example, the bimolecular association rates for K⁺ binding to the unoccupied (k₁, k₂) and the singly occupied channel (k₃, k₄) are increased, respectively, by 2.1-fold and 1.4-fold for PS relative to PE. Since apparent rates of K⁺ association from solution to the outer K⁺ binding sites may reflect changes in the local K⁺ concentration at the mouth of the channel, the fitting results suggest that as little as a twofold increase in the local K⁺ concentration seen by the channel in a PS membrane could be sufficient to generate the observed conductance enhancement. Table I further shows almost no change in the best-fit values for the K⁺ translocation step (k₅, k₆), suggesting that PS may not necessarily affect site-to-site ion movement within the channel. It is more difficult to draw conclusions concerning the K⁺ dissociation rate constants (k_-1, k_-2, k_-3, k_-4), since the fitting procedure yields a large uncertainty (152%) on the value of one pair of these constants in PE (k_-3, k_-4). However, a 1.5-fold increase in the k_-1, k_-2 pair and the fourfold decrease in the k_-3, k_-4 pair show that a PS membrane could potentially affect elementary rates of dissociation of K⁺ from the channel. In addition, results of Table I indicate that a possible overall effect of PS would be to produce a differential increase in apparent binding affinity of K⁺ to the unoccupied channel (K₁, K₂ = 12.2 mM for PS vs. 17.4 mM for PE) and to the singly occupied channel (K₃, K₄ = 1.24 M for PS vs. 6.85 M for PE). In principle, a change in lipid environment could alter the equilibrium binding affinity at 0 mV of a channel for ions.

We also used the model of the two-site symmetrical channel to explore the expected effect of membrane surface potential predicted by GCS theory. This was performed by using the best-fit parameters for the neutral PE bilayer (Table I) to compute the expected conductance based on the local concentration of K⁺ at various distances from the surface of a membrane containing 80% PS. This approach assumes that PS does not change any of the underlying rate constants of K⁺ conduction that hold in a PE membrane. It further assumes that PS only acts to increase the local concentration of K⁺ near the mouth of the channel. The local concentration of K⁺ at various distances from the PS membrane were calculated from GCS theory as described in MATERIALS AND METHODS, except that the bulk Ca²⁺ concentration was set equal to 100 µM and a Ca²⁺ binding association constant of 12 M^-1 (McLaughlin et al., 1981) was used to account for binding of Ca²⁺ to PS. The calculated curves at 2, 3, 5, 10, and 20 Å corresponding to the dotted lines in Fig. 2, A and B, show that a simulation based on a distance of 5 Å closely matches the observed conductance behavior in PS. [Note that the inability of the Gouy-Chapman model to simulate surface charge effects on channel conductance at low K⁺ concentration in Fig. 2 A is due to the fact that the planar geometry of this model predicts a finite surface cation concentration in this limit (Apell et al., 1979; Green and Andersen, 1991), unlike the case for a protein.] Thus, this approach leads to the suggestion that the BK channel behaves as if it senses the K⁺ concentration located at 5 Å from the surface of the PS membrane. To put this result in perspective, GCS theory predicts that the electrostatic potential at 5 Å from the surface of an 80% PS bilayer is -55 mV at 0.1 mM CaCl₂ and a bulk KCl concentration of 27 mM and -38 mV at a bulk KCl concentration of 107 mM KCl. According to the Boltzmann distribution of Eq. 1, surface potentials of this magnitude would increase the local concentration of K⁺ at the mouth of the channel by factors of 4.5 and 8.7, respectively, over that in the bulk solution.

In summary, the modeling results of Fig. 2 offer two different mechanisms and approaches to account for the enhancement of K⁺ conductance by PS. On one hand, PS might affect various intrinsic rate constants that underlie multiion conduction, perhaps by promoting a protein conformational change that perturbs elementary steps in K⁺ movement. On the other hand, PS might simply act by generating a more negative electrostatic potential at the mouth of the channel, which increases the local K⁺ concentration available for binding to the outermost K⁺ sites. However, both approaches predict a significant increase in the apparent association rate of K⁺ to the channel; i.e., a 2.1-fold increase in the k₁ (k₂) rate constant (Table I) or a 4.4- to 8.7-fold increase in local K⁺ concentration due to a partially shielded electrostatic potential.

Effect of Phosphatidylserine on Slow Block of the BK Channel by Extracellular Ba²⁺
The divalent cation Ba²⁺ is a blocker of many different K⁺ channels and has been extensively studied as a probe of multiion conduction in the BK channel (Neyton and Miller, 1988). Crystallographic analysis has also shown that Ba²⁺ binds within the selectivity filter of the KcsA K⁺ channel (Jiang and MacKinnon, 2000). Here, we used Ba²⁺ block to address questions raised by the conductance enhancement of the BK channel in PS. If a PS bilayer acts by increasing local K⁺ concentration at the mouth of the channel via a through-space electrostatic mechanism, one would expect the local Ba²⁺ concentration to be similarly increased, resulting in enhanced block. As pointed out by Bell and Miller (1984), the exponential dependence on charge valence for a Boltzmann distribution requires that the local concentration of a multivalent cation is increased more strongly by surface potential than that of a monovalent cation. Eqs. 1 and 2 lead to the following exact relationship:

(8)

Thus, according to Eq. 8, if membrane surface potential increases the local concentration of K⁺ at the mouth of a channel in a PS membrane by a factor of 4 compared with a PE membrane, the local concentration of Ba²⁺ at the mouth is predicted to increase by a factor of 16. Such an increase in [Ba²⁺]_local should be reflected in the apparent bimolecular association rate of Ba²⁺. In principle, this relationship provides a sensitive test of a surface potential mechanism.

Fig. 3 shows examples of single-channel current recorded at 20 mV from experiments in which block by extracellular Ba²⁺ at 100 mM symmetrical KCl was compared in bilayers composed of pure PE (Fig. 10 A) or 80/20 PS/PE (Fig. 10 B). As described previously (Vergara and Latorre, 1983), Ba²⁺ added to the external side of the BK channel produces a slow block characterized by the appearance of discrete blocking events. Extracellular Ba²⁺ in the millimolar range also produces a second type of fast blocking effect that is evident from the progressive decrease in apparent unitary current at 2 and 20 mM Ba²⁺ (Fig. 3). At a first glance, simple inspection of the records in Fig. 3 suggests that block by external Ba²⁺ block is not markedly different in PE vs. PS bilayers.

View larger version (17K): [in this window] [in a new window]   FIGURE 3. Effect of external Ba2+ on single BK channels in PE vs. PS bilayers. Examples of current records at 20 mV in PE (A) or PS (B) bilayers in the presence of 0, 2, or 20 mM BaCl2 on the external side. Conditions: symmetrical 100 mM KCl and 10 mM Hepes-KOH, pH 7.2, internal 200 µM CaCl2, and various concentrations of BaCl2 on the external side as indicated. Records are filtered at 20 Hz and the dashed line indicates the closed current level.

(9)

View larger version (22K): [in this window] [in a new window]   FIGURE 4. Probability that the channel is not blocked as a function of external Ba2+ concentration in PE and PS bilayers. Inhibition of single-channel activity due to discrete block by external Ba2+ was computed from the time-averaged reduction in open-state probability from long recordings at 20 mV. The ordinate value is a normalized ratio corresponding to the probability that the channel was not blocked by Ba2+ at a given Ba2+ concentration divided by the corresponding open state probability in the absence of Ba2+. Conditions: symmetrical 10 mM HEPES-KOH, pH 7.2, 100 mM KCl (squares) or 20 mM KCl (circles), internal 200 mM CaCl2, for PE (filled symbols) or PS bilayers (open symbols). The solid and dashed lines are fits to the empirical Hill equation (Eq. 9) with parameters given in the text. The dotted lines correspond to simulations computed according to Eq. 9 using KB = 0.46 mM based on the fit to PE data at 20 mM KCl, n = 1, and [Ba2+]local calculated from GCS theory (MATERIALS AND METHODS) at various distances (0, 5, 10, 20, and 30 Å) from a PS bilayer at 20 mM KCl, and plotted as a function of bulk Ba2+ concentration.

To interpret these results, we must consider changes in electrostatic potential at the membrane surface under the ionic conditions of the experiment. Although Ba²⁺ block can be used to monitor surface potential, Ba²⁺ also acts in two ways to reduce the surface potential. As a mobile counterion, high concentrations of Ba²⁺ reduce the surface potential by electrostatic screening. Ba²⁺ can also bind directly to PS to reduce the effective negative charge density. These effects are well-described by Eqs. 3 and 4 of GCS theory (McLaughlin et al., 1981). The three-dimensional surface plots of Fig. 5 illustrate the theoretical dependence of surface potential, , on distance at 20 mM KCl (Fig. 5 A) and 100 mM KCl (Fig. 5 B) for bulk Ba²⁺ concentration ranging from 10^-6 to 10^-3 M Ba²⁺. At 20 mM KCl, the calculated potential at the surface (distance = 0) is reduced from -116 mV at 10^-6 M Ba²⁺ to -46 mV at 10^-3 M Ba²⁺. At 100 mM KCl, the respective surface potentials at these two Ba²⁺ concentrations are -91 and -44 mV. Using the approximate distance decay function of Eq. 5, Fig. 5 also shows that the electrostatic potential decays to less than -5 mV at a distance of 50 Å away from the surface in 20 mM KCl and decays to 0 mV at 50 Å in 100 mM KCl.

View larger version (48K): [in this window] [in a new window]   FIGURE 5. Three-dimensional plot of electrostatic surface potential at various distances from a membrane composed of 80% PS and 20% PE. Surface potential was calculated at 5-Å intervals in the range of 0 to 50 Å from the membrane surface at 20 mM KCl (A) or 100 mM KCl (B) in the presence of different bulk BaCl2 concentrations ranging from 10-6 to 10-3 M using GCS theory described in MATERIALS AND METHODS.

Looking more closely at Fig. 4, the small rightward shift of the Ba²⁺ titration curve in PS vs. PE at 100 mM KCl suggests that the relevant surface potential for slow block by Ba²⁺ is actually more positive in PS than PE. This cannot be easily explained by lipid surface charge since our calculations indicate that the expected positive reversal of membrane surface charge that eventually occurs due to Ba²⁺ binding to PS^- only commences at a bulk Ba²⁺ concentration above 50 mM. However, such a rightward shift could also occur if Ba²⁺ binding increases to nonblocking extracellular sites on the protein surface surrounding the pore entrance in the presence of PS. This could create an additional source of electrostatic repulsion and reduce the probability of Ba²⁺ binding to blocking site(s) in the selectivity filter.

At 20 mM KCl, the data of Fig. 4 suggests that a significant effect of lipid surface charge in the PS bilayer is present at the lower concentration range of bulk Ba²⁺. To model the effect of lipid surface charge under these conditions, we calculated expected titration curves based on Eq. 9 assuming an intrinsic blocking affinity equal to that measured in PE (K_B = 0.46 mM) and using [Ba²⁺]_local at various distances from the PS surface as calculated from GCS equations given in the MATERIALS AND METHODS. Theoretical curves for distances of 0, 5, 10, 20, and 30 Å from the membrane are shown by the dotted lines in Fig. 4. This set of simulations shows that the Ba²⁺ titration at 20 mM KCl in a PS membrane most closely matches the enhancement expected to occur at a distance of 30 Å from the surface. Thus, this analysis suggests that the slow Ba²⁺ blocking process at 20 mM KCl senses less surface potential than the K⁺ conduction process analyzed in Fig. 2.

Another important consideration in the interpretation of these experiments is the effect of binding competition between and Ba²⁺ and K⁺. Since negative surface potential simultaneously increases the local concentration of K⁺ and Ba²⁺ according to Boltzmann distributions (Eqs. 1 and 2), Ba²⁺ block in a PS bilayer could also be attenuated by increased binding competition of Ba²⁺ and K⁺ for relevant sites in the BK channel. However, since local Ba²⁺ concentration increases as the square of the local K⁺ concentration according to Eq. 8, the surface charge effect on Ba²⁺ concentration is expected to predominate over the effect of K⁺ competition. In view of the uncertainty associated with the effect of K⁺ competition, distance estimates applied to Ba²⁺ titrations using the simple GCS-based theory described above should be considered as maximal estimates of the surface charge effect on Ba²⁺ block.

Kinetics of Block by External Ba²⁺ in Neutral and Negatively Charged Bilayers
The effect of PS on the kinetics of slow Ba²⁺ block was further investigated by analyzing dwell time distributions of discrete Ba²⁺-blocking events. Fig. 6, A and B, show unblocked and blocked state histograms, respectively, of dwell times collected from a single-channel recorded in the presence of 20 mM external Ba²⁺ and filtered at 10 Hz. The population of unblocked events defined as dwell times between adjacent Ba²⁺-blocked states is well described by a single exponential function with a time constant of 623 ms (Fig. 6 A). However, the population of blocked events observed in the presence of Ba²⁺ is best fit by a sum-of-two-exponential function with 68% of the events described by a short time constant of 206 ms and 32% of the events described by a long time constant of 6.84 s (Fig. 6 B). The presence of two time constants in histograms of Ba²⁺-blocked events of the BK channel has been described previously (Sohma et al., 1996; Sugihara, 1998) and appears to reflect binding of Ba²⁺ to two different sites within the multiion conduction pathway of K⁺ channels.

View larger version (76K): [in this window] [in a new window]   FIGURE 6. Dwell time distributions of discrete blocking events associated with slow block by external Ba2+ compared for PE and PS bilayers. (A and B) Dwell time histograms compiled for a single BK channel in a PE membrane recorded at 20 mV in the presence of symmetrical 100 mM KCl, 10 mM HEPES-KOH, pH 7.2, internal 200 µM CaCl2, and external 20 mM BaCl2. Populations of unblocked (A) and blocked (B) events were kinetically isolated from normal gating events by filtering the record at 10 Hz (Vergara and Latorre, 1983) and using PClamp analysis software to automatically compile blocked and unblocked events using a 50% threshold criterion for event detection. The solid line in A is a fit to a single exponential with a lifetime of 623 ms for a population of 585 events. The solid line in B is a fit to a sum-of-two exponentials with lifetimes (amplitudes) of 206 ms (68%) and 6.84 s (32%) for 585 events. (C and D) Examples of blocked time histograms are compared for PE (C) and PS (D) bilayers at 2, 6, and 20 mM external Ba2+. The solid lines are fits to a sum of two exponentials with respective lifetimes (amplitudes) at 2, 6, and 20 mM Ba2+ for PE (C): 850 ms (82%), 2.97 s (18%); 94 ms (81%), 2.65 s (19%); 115 ms (77%), 2.7 s (23%), and for PS (D): 85 (79%), 2.1 s (21%); 105 ms (75%), 3.6 s (25%); 104 ms (74%), 3.5 s (26%).

View larger version (21K): [in this window] [in a new window]   FIGURE 7. Lifetimes of blocked state events as a function of external Ba2+ concentration compared for PE and PS bilayers. (A and B) Mean values of short (circles) and long (squares) lifetimes of Ba2+-blocked events in PE (filled symbols) and PS (open symbols) bilayers measured at various concentrations of external Ba2+ in the presence of 20 mM (A) or 100 mM (B) symmetrical KCl. (C) Corresponding plot of the ratio of the amplitudes of the short lifetime component to the long lifetime component at 20 mM KCl (circles) and 100 mM KCl (squares). Data points and error bars represent the mean ± SE of 3–9 experiments.

View larger version (19K): [in this window] [in a new window]   FIGURE 8. Ba2+ association rate measured from the dependence of reciprocal lifetime of unblocked events as a function of external Ba2+ concentration in PE and PS bilayers. (A and B) Mean values of the reciprocal lifetime of unblocked events at different concentrations of external Ba2+ and 20 mM (A) or 100 mM (B) symmetrical KCl. Note that the data points for PE and PS in A at 0.5 and 1 mM Ba2+ are superimposable. Solid lines are linear fits used to obtain the association rate constant for slow block by external Ba2+ as described in the text. The dotted lines are theoretical curves plotted according to U-1 = kon[Ba2+]local + b, showing the behavior expected for a process governed by the measured association rate in PE (kon) and the expected local concentration of Ba2+ at various distances in Å from a bilayer containing 80% PS as calculated from GCS theory (MATERIALS AND METHODS).

Fig. 9 A summarizes titrations of the Ba²⁺-dependent reduction in apparent unitary current in PE and PS bilayers measured at 20 mV in symmetrical solutions of 100 and 20 mM KCl. The decrease in unitary current is measured as the ratio, I/I₀, of single-channel current at a given concentration of Ba²⁺ to that of the same channel in the absence of external Ba²⁺. The results show that the apparent affinity of Ba²⁺ for the fast blocking(s) sites is increased in PS relative to PE at 20 and 100 mM KCl. The titration curves of Fig. 9 A were separately fit to the empirical Hill function of Eq. 9 using n = 0.7 to adequately describe the rather shallow [Ba²⁺] dependence. At 100 mM KCl, the best-fit values of the apparent blocking constants are: PE, K_B = 36.5 ± 5.9 mM; PS, K_B = 22.3 ± 1.7 mM. At 20 mM KCl, we obtain: PE, K_B = 7.2 ± 0.5 mM; PS, K_B = 2.1 ± 0.3 mM. Overall, these results support the idea that there is a small but significant effect of lipid surface charge on fast block by external Ba²⁺ since the PS-dependent enhancement of Ba²⁺ affinity as measured by K_B is greater at the lower ionic strength of 20 mM vs. 100 mM KCl. To evaluate the observed enhancement of fast Ba²⁺ block within the context of surface charge theory, we calculated a series of expected Ba²⁺-titration curves based on [Ba²⁺]_local at various distances from a PS membrane under conditions of 20 mM KCl using the procedure described above for the slow-block Ba²⁺ titration of Fig. 4. As shown by the calculated dotted line curves in Fig. 9 A, the observed enhancement of fast Ba²⁺ block in 80% PS and 20 mM KCl would be similar to that expected if the fast blocking site senses [Ba²⁺]_local at a distance of 20–30 Å from the membrane.

View larger version (21K): [in this window] [in a new window]   FIGURE 9. Apparent reduction in unitary BK channel current due to fast block by external Ba2+ and TEA+ compared in PE and PS bilayers. Ordinate values (I/I0) correspond to single-channel current at the indicated Ba2+ (or TEA+) concentration (I) divided by the unitary current of the same channel (I0) in the absence of Ba2+ (or TEA+). Data point are the mean ± SE for 4–9 experiments. Fast block by external Ba2+ (A) or external TEA+ (B) measured as the apparent reduction in unitary current at 20 mV. Solid symbols, PE; open symbols, PS; circles, symmetrical 100 mM KCl; squares, symmetrical 20 mM KCl. Solid lines in A and B are fits to the empirical Hill equation (Eq. 9) as described in the text. Dotted lines in A are theoretical curves using the KB parameter obtained for the fit of the PE data at 20 mM KCl and the local concentration of Ba2+ at various distances (in Å) from a bilayer containing 80% PS as calculated from GCS theory outlined in MATERIALS AND METHODS. Dotted lines in B show similar theoretical curves based on the KB parameter for the fit to the TEA+ titration in PE bilayers and the calculated local concentration of TEA+ at various distances from a PS bilayer.

Effect of Phosphatidylserine on Slow Block of the BK Channel By Intracellular Ba²⁺
Thus far, we have considered the effect of a negatively charged membrane surface on the reactions of blockers applied to the extracellular side of the rat BK channel. Depending on the location and disposition of the outer and inner pore entrances with respect to the phospholipid surface on each side of the membrane, membrane surface charge could potentially have different effects on the kinetics of blockers added to the external vs. internal sides of the channel. Therefore, we also studied the effect of PS on slow block by Ba²⁺ added to the internal side. The BK channel is well known to exhibit a higher affinity for slow block by internal Ba²⁺ in comparison to external Ba²⁺ (Vergara and Latorre, 1983). This allows internal block to be studied at a much lower range of Ba²⁺ concentration where self-screening by Ba²⁺ is insignificant.

Fig. 10 shows examples of single-channel current recorded at 20 mV from experiments in which block by intracellular Ba²⁺ at 100 mM symmetrical KCl was compared in bilayers composed of pure PE (Fig. 10 A) or 80% PS (Fig. 10 B). Visual comparison of records taken in the presence of 3 and 10 µM Ba²⁺ suggests that the kinetics of slow Ba²⁺ block are similar in PE and PS membranes. Fig. 10 also shows little evidence of fast block at micromolar concentrations of internal Ba²⁺ in comparison to the substantial reduction of unitary current at the higher concentrations of external Ba²⁺ used in the experiments of Fig. 3.

View larger version (20K): [in this window] [in a new window]   FIGURE 10. Effect of internal Ba2+ on single BK channels in PE vs. PS bilayers. Examples of current records at 20 mV in PE (A) or PS (B) bilayers in the presence of 0, 3, or 10 µM BaCl2 on the internal side. Conditions: symmetrical 100 mM KCl and 10 mM HEPES-KOH, pH 7.4, internal 200 µM CaCl2, and various concentrations of BaCl2 on the external side as indicated. Records are filtered at 20 Hz and the dashed line indicates the closed current level.

View larger version (21K): [in this window] [in a new window]   FIGURE 11. Probability that the channel is not blocked as a function of internal Ba2+ concentration in PE and PS bilayers. Inhibition of single-channel activity due to discrete block by external Ba2+ at 20 mV was computed from the time-averaged reduction in open-state probability from long recordings. The ordinate value is a normalized ratio corresponding to the probability that the channel was not blocked by Ba2+ concentration divided by the corresponding open state probability in the absence of Ba2+. Conditions: symmetrical 10 mM HEPES-KOH, pH 7.2, 100 mM KCl, internal 200 µM CaCl2, for PE (filled circle) or PS bilayers (open circle). Solid lines are fits to the empirical Hill equation (Eq. 9) with parameters given in the text. Dotted lines correspond to simulations computed according to Eq. 9 using KB = 13 µM based on the fit to PE data and [Ba2+]local calculated from GCS theory (MATERIALS AND METHODS) at various distances (0–40 Å) from a bilayer containing 80% PS.

View larger version (18K): [in this window] [in a new window]   FIGURE 12. Dwell time distributions of discrete blocking events associated with slow block by internal Ba2+. Dwell time histograms were compiled as described in Fig. 6 for a single BK channel in a PE membrane at 20 mV in the presence of symmetrical 100 mM KCl, 10 mM HEPES-KOH, pH 7.2, internal 200 µM CaCl2, and internal 100 µM BaCl2. (A) Unblocked events. (B) Blocked events. The solid line in A is a fit to a single exponential with a lifetime of 222 ms for a population of 638 events. The solid line in B is a fit to a sum-of-two exponentials with lifetimes (amplitudes) of 127 ms (41%) and 2.73 s (59%) for 639 events.

View larger version (22K): [in this window] [in a new window]   FIGURE 13. Lifetimes of blocked (A) and reciprocal unblocked (B) events as a function of internal Ba2+ concentration in PE and PS bilayers. (A) Mean values of short (circles) and long (squares) lifetimes of Ba2+-blocked events in PE (filled symbols) and PS bilayers (open symbols) measured at various concentrations of external Ba2+ in the presence of symmetrical 100 mM KCl. (B) Mean values of the reciprocal lifetime of unblocked events at different concentrations of internal Ba2+ and symmetrical 100 mM KCl. Solid lines are linear fits used to obtain the association rate constant for slow block by internal Ba2+ as given in th