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Operation of the Voltage Sensor of a Human Voltage- and Ca2+-activated K+ Channel

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Operation of the voltage sensor of a human

voltage-and Ca

2+

-activated K

+

channel

Antonios Pantazisa, Vadym Gudzenkoa, Nicoletta Savallia, Daniel Sigga, and Riccardo Olcesea,b,c,1

aDepartment of Anesthesiology, Division of Molecular Medicine,bBrain Research Institute, andcCardiovascular Research Laboratory, David Geffen School of Medicine, University of California, Los Angeles, CA 90095-7115

Edited by Ramón Latorre, Centro de Neurociencias, Universidad de Valparaíso, Valparaíso, Chile, and approved January 7, 2010 (received for review October 23, 2009)

Voltage sensor domains (VSDs) are structurally and functionally conserved protein modules that consist of four transmembrane segments (S1–S4) and confer voltage sensitivity to many ion channels. Depolarization is sensed by VSD-charged residues residing in the membranefield, inducing VSD activation that facilitates channel gat-ing. S4 is typically thought to be the principal functional component of the VSD because it carries, in most channels, a large portion of the VSD gating charge. The VSDs of large-conductance, voltage- and Ca2+ -activated K+channels are peculiar in that more gating charge is carried by transmembrane segments other than S4. Considering its “decen-tralized” distribution of voltage-sensing residues, we probed the BKCa VSD for evidence of cooperativity between charge-carrying segments S2 and S4. We achieved this by optically tracking their activation by using voltage clampfluorometry, in channels with intact voltage sen-sors and charge-neutralized mutants. The results from these experi-ments indicate that S2 and S4 possess distinct voltage dependence, but functionally interact, such that the effective valence of one seg-ment is affected by charge neutralization in the other. Statistical-mechanical modeling of the experimentalfindings using allosteric interactions demonstrates two mechanisms (mechanical coupling and dynamic focusing of the membrane electricfield) that are compat-ible with the observed cross-segment effects of charge neutralization. BK

|

cooperativity

|

fluorometry

|

Slo1

|

MaxiK

B

KCachannels (also known as MaxiK) are membrane proteins

expressed in most mammalian cells (1). Their activation, by membrane potential depolarization or intracellular [Ca2+] increase (1–9) results in an exceptionally high conductance for K+. As such, they are potent regulators of diverse cellular pro-cesses, including smooth muscle tone, neuronal excitability, and neurotransmitter release (8). Four pore-formingα subunits (10), encoded by KCNMA1 (hSlo1) in humans (11), are required to assemble into a functional channel. Eachα subunit possesses an extracellular N terminus (12), seven transmembrane segments (S0–S6), and a large intracellular C-terminal region organized into domains RCK1 and RCK2 (Regulator of Conductance for K+, Fig. 1A) that confer sensitivity to Ca2+ and other intra-cellular ligands (8, 9, 13–20). Segments S1–S6 are structurally and functionally homologous to those of other voltage-gated ion channels (21), with S1–S4 comprising the VSD, whereas S5 and S6 contribute to the K+-selective pore.

Our understanding of VSD structure and function has been achieved thus far through analysis of crystal structures (22–24) as well as accessibility, electrophysiological, and optical inves-tigations in functional proteins (reviewed in ref. 25). VSDs pos-sess a high density of charged residues (Fig. 1C). Upon membrane potential depolarization, a subset of these residues may traverse the field partially or entirely, initiating conformational rear-rangements that propagate to the channel gate, facilitating ionic conductance (26–28). S4 is thought to be the principal voltage-sensing segment because, in most VSD-gated channels, it con-tributes the greatest portion of gating charge movement (29–31). S2 usually carries less charge, but it can influence VSD activation by forming state-specific electrostatic interactions with S4 (32–

36). Another important feature for VSD operation is the focusing of the electricfield by water-filled crevices that can extend into the VSD core from either side of the cell membrane (37–43), effectively increasing gating charge movement and resulting in improved voltage sensitivity.

Recently, extensive electrophysiological analysis of the role of charged VSD residues in BKCavoltage-dependent activation (44)

revealed that only one residue in the BKCa S4 senses voltage

(R213) and that a greater portion of the total gating charge movement is contributed by residues outside this segment: one in S3 (D186) and two in S2 (D153, R167) (Fig. 1B). In light of this information, we optically tracked the voltage-dependent tran-sitions of S2 and S4 in the human BKCa, by combining the cut-open

oocyte Vaseline gap (COVG) voltage clamp technique (45) with site-specific tetra-methyl-rhodamine maleimide (TMRM) label-ing andfluorometry (46–50). To probe for interactions between S2 and S4, we introduced charge-neutralizing mutations in either segment and tracked the activation of the other. We discovered that gating charge neutralization in one segment impaired the voltage dependence of the other and vice versa, demonstrating that S2 and S4 are functionally coupled. Based on the statistical-mechanical analysis of voltage-dependent BKCa activation, we

propose two different, but not mutually exclusive, mechanistic interpretations of the cooperative coupling between S2 and S4: a special manifestation of mechanical coupling and dynamic (activation-dependent) focusing of the membrane electricfield. Results

Voltage-Dependent Conformational Changes Reported from the S2 BKCa Domain.Having characterized the voltage-dependent rear-rangements of S4 (51, 52), we sought to resolve those of S2, which contains residues that make a significant contribution to BKCa

gating charge displacement (44). Fig. 2A and B shows K+currents

and TMRM fluorescence deflections (ΔF/F), implying

con-formational rearrangements, simultaneously recorded from BKCa

channels labeled at the extracellular tip of S2 (position 145). Thefitting of ionic conductance and ΔF/F isotherms with a Boltzmann distribution (see SI Text) for S2- and S4-labeled channels (Fig. 2 C and F) provides information on the voltage dependence of ionic conductance and VSD segment motions. The voltage-dependent movements of S2 exhibited a half-acti-vation potential (Vhalf) of approximately−58 mV and effective

charge (z) of 0.57 e0. The conformational rearrangements of S4

(Fig. 2E) had a Vhalf of −79 mV and a z of 0.79 e0 (Fig. 2F),

similar to previously published measurements (51). The meas-ured time-course of their activation was 5–6 ms (Fig. 2E), an

Author contributions: A.P., V.G., N.S., D.S., and R.O. designed research; A.P., V.G., N.S., and R.O. performed research; D.S. contributed new reagents/analytic tools; A.P., V.G., N.S., D.S., and R.O. analyzed data; and A.P., D.S., and R.O. wrote the paper.

The authors declare no conflict of interest. This article is a PNAS Direct Submission.

1To whom correspondence should be addressed. E-mail: rolcese@ucla.edu.

This article contains supporting information online atwww.pnas.org/cgi/content/full/ 0911959107/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.0911959107 PNAS | March 2, 2010 | vol. 107 | no. 9 | 4459–4464

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order of magnitude slower than those of S2ΔF/F (130-300 μs, Fig. 2B). The difference in the voltage dependence of S2 and S4—also encountered in channels with neutralized voltage-sensing charges —and kinetics strongly supports that the reported TMRM fluo-rescence deflections were segment-specific.

Neutralizing Voltage-Sensing Residues Impairs the Voltage-Dependent Transitions of Their Segment.As the neutralization of charged res-idues D153 (S2) and R213 (S4) significantly decreased BKCa

gating charge movement (44), neutralizing these residues should perturb the voltage dependence of the transmembrane segments bearing them. D153 was mutated to the uncharged residue glu-tamine in a BKCaclone with a TMRM label at the extracellular tip

of S2. Macroscopic K+currents from these channels were only observed at extremely depolarized potentials, typically above 180 mV (Fig. 3A). Brief (10 ms) depolarizations up to 300 mV elicited outward K+current up to 200μA, unlike in mock-injected oocytes (≈6 μA at 300 mV). The resolved ΔF/F (Fig. 3B) had extremely shallow voltage dependence, barely exhibiting satu-ration within the range of testable membrane potential (±300 mV, Fig. 3C). The maximum effective charge this data could be fitted with was 0.16e0. This marked loss of valence (>78%) is compat-ible with the prominent role of D153 in the voltage dependence of BKCachannel activation. The residual voltage dependence likely

arose from another gating charge in S2, R167 (44).

Channels with a neutralized voltage-sensing charge in S4 (R213G) also required extremely depolarized potentials to exhibit macroscopic K+conductance (Fig. 3D). The voltage dependence ofΔF/F observed from position 202, at the short extracellular S3– S4 linker, differed from those of channels with an intact S4 in two ways: (i) it exhibited a reduction in effective charge by 70% and (ii) was shifted by 160 mV toward depolarized potentials (Fig. 3 E andF). Sequence homology (Fig. 1C), hydropathy analysis (12), and NMR spectroscopy (53) suggest that the extracellular linker between S3 and S4 in BKCais only three residues long. Thus, the

voltage-evoked movements of S3, which bears the voltage-sensing D186 (44), could contribute to the fluorescence deflections reported from position 202.

Charge Neutralization in S4 Impairs the Voltage Dependence of the Motion of S2 and Vice Versa.Although intrasubunit interactions between S2 and S4 have been reported in other voltage-gated channels (32–36), they have not been investigated using a seg-ment-specific optical technique. To probe for such interactions within the BKCa VSD, we engineered channels with

voltage-sensing charge neutralization in one segment and optically tracked the activation of the other. We first tracked the acti-vation of S2 in channels bearing a charge-neutralizing mutation in S4, R213G. As in S4-labeled R213G clones (Fig. 3D), these channels required extremely depolarized potential to produce significant macroscopic K+ current (Fig. 4A). S2

conforma-tional transitions were reported by TMRM labeling position 145 (Fig. 4B). Their voltage dependence (Fig. 4C) was distinctly shallower than that from S2-labeled channels with an intact S4 (a reduction by 0.33e0). Similarly, a loss of 0.56e0was exhibited by the ΔF/F of S4-labeled, S2-neutralized (D153Q) channels (Fig. 4D–F). These experiments directly demonstrate that when one voltage-sensing segment is impaired (S2 or S4), the func-tion of the neighboring segment is reciprocally affected sup-porting the hypothesis that the two voltage-sensing segments are functionally coupled.

The BKCaVSD Is Not a Rigid Structure.To explore the nature of the interaction between S2 and S4, we constructed statistical-mechanical models of voltage-dependent BKCa activation. The

complete expressions for the energetic terms underlying these H O O C H N2 1 K C R 2 K C R In s id e Out r a l u l l e c a r t n I a C 2+sensors

B

A

6 / 5 S 4 S 3 S 2 S 1 S 0 S r o s n e S e g a t l o V n i a m o D Pore 3 1 2 R 3 5 1 D

+

7 6 1 R

+

6 8 1 D

4

S

3

S

2

S

Fig. 1. BKCaα subunit topology and voltage-sensing residues. (A) BKCachannel α subunit membrane topology (12) and putative structure (intracellular Ca2+ sensing RCK1 and RCK2 by homology to a bacterial RCK domain (19). (B) Close-up of the BKCavoltage sensor domain (VSD) segments S2–S4, indicating the approximate positions of voltage-sensing residues D153 (S2) and D186 (S3) in red and R167 (S2) and R213 (S4) in blue (44).

Fig. 2. Voltage-dependent structural transitions and ionic conductance from S2- and S4-labeled channels. (A) Voltage pulses and characteristic evoked K+currents from BK

Cachannels labeled with TMRM at position 145 (outside S2). (B) TMRMfluorescence traces recorded during the volt-age pulses in A. Fitted activation exponentials (black) areτ = 0.130 μs for the 40 mV pulse, 220μs for 0 mV, 300 μs for −40 mV. (C) Normalized K+ conductance (G, black circles) and ΔF/F (red squares) plotted against membrane potential andfitted with Boltzmann distributions (black and red curves, respectively; seeSI Text). Boltzmann parameters: G-V Vhalf= 9.9± 2.2 mV; z = 0.86 ± 0.1 e0. F-V V

half=−58 ± 9.3 mV; z = 0.57 ± 0.05 e0. n = 8 cells. (D–F) As in A–C, for channels labeled with TMRM at position 202, in the short extracellular linker between S3 and S4. Fitted activation exponentials in E (black) areτ = 5.2 ms for the 40 mV pulse, 6.1 ms for 0 mV, 6.0 ms for−40 mV. Boltzmann parameters in F: G-V (black) Vhalf= −1.0 ± 9.0 mV; z = 1.0 ± 0.053 e0. F-V (red) V

half=−79 ± 4.2 mV; z = 0.79 ± 0.055 e0. n = 7.

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models, and thefitting regime, are inSI Text. The first tested premise is that the voltage sensor operates as a single functional unit, whereby transmembrane segments comprise a rigid struc-ture possessing uniform voltage dependence. In this context, neutralization of a voltage-sensing residue anywhere in the VSD would produce a global reduction in effective charge. This model possesses four voltage-sensing domains energetically linked to the pore (Fig. S1A, scheme I). As this model produces the same voltage dependence of activation for S2 and S4, it is unable to reproduce the experimental data, whereby S2 and S4 exhibit distinct voltage dependence (Fig. S1B–D). This result confirmed

that theΔF/F reported from S2 and S4 did not reflect the same voltage-dependent process, supporting our premise that the resolved conformational rearrangements are segment-specific. A State-Dependent Interaction Alone Is Unable to Account for S2–S4 Cooperativity. To account for the difference in the voltage dependence of activation exhibited by S2 and S4, the VSD was separated into two subdomains, S2 and S4, with distinct voltage dependence (Fig. 5A, scheme II). Their activation is mutually facilitated by cooperative energetic interactionH24, which

low-ers the free energy of the doubly activated VSD state.H24is

compatible with an electrostatic coupling between S2 and S4,

such as was demonstrated inShaker (32–34) and HERG (35, 36) K+ channels, but could also represent steric, hydrophobic, or other state-specific interactions. This model can produce dis-tinct activation curves for S2 and S4 and predicts data from channels without charge mutations well (Fig. 5B). However, it cannot account for the reduction in the effective charge of labeled segments when a charge in the neighboring segment is neutralized, instead producing steep activation curves (Fig. 5C andD). This result indicates that a different basis of interaction, more directly related to segment valence, is required. Because of the extremely shallow S2 F-V curve from S2-neutralized (D153Q) channels (lacking evident saturation within the tested membrane potential range of ±300 mV, Fig. 3B), the exper-imental data (Fig. 5C, blue diamonds) were normalized to the prediction of the models but were not included in the simulta-neous curvefitting.

A Model of Reciprocal Mechanical Coupling Between S2 and S4 Can Account for Their Activation.A central assumption of the (unsuc-cessful) scheme II (Fig. 5A–E) is that S2 and S4 activate with effective chargeqS2andqS4, respectively, without perturbing each

other’s charge movement during activation. However, the two segments could mechanically interact, or “nudge” each other, during their activation pathway through the membranefield. To Fig. 3. Voltage-sensing charge neutralization impairs the voltage

depend-ence of its segment. (A) Voltage pulses and characteristic evoked K+currents from BKCachannels labeled with TMRM at position 145 (outside S2) with mutation D153Q, to neutralize the voltage-sensing Aspartate of S2 (44). (B) TMRMfluorescence traces recorded during the voltage pulses in A. (C) Normalized K+conductance (G, black circles) andΔF/F (red squares) plotted against membrane potential andfitted with Boltzmann distributions (black and red curves, respectively; seeSI Text). Boltzmann parameters: G-V Vhalf= 285± 15 mV; z = 0.50 ± 0.03 e0. F-V V

half= 3± 0.4 mV; z = 0.16 ± 0.001 e0. n = 4 cells. G-V and F-V curves of the same clone without charge mutation are also included (dashed black and red curves, respectively). (D–F) As in A–C, for channels labeled with TMRM at position 202 (outside S4) with mutation R213G, to neutralize the single voltage-sensing residue of S4 (44). Boltzmann parameters in F are G-V Vhalf= 260± 5.7 mV; z = 0.89 ± 0.077 e0. F-V Vhalf= 80± 2.2 mV; z = 0.24 ± 0.01 e0. n = 7.

Fig. 4. Probing for evidence of S2–S4 interaction in the BKCavoltage sensor. (A) Voltage pulses and characteristic evoked K+currents from BK

Cachannels labeled with TMRM at position 145 (outside S2) with mutation R213G, to neutralize the single voltage-sensing residue of S4 (44). (B) TMRMfluorescence traces recorded during the voltage pulses in A. (C) Normalized K+conductance (G, black circles) andΔF/F (red squares) plotted against membrane potential and fitted with Boltzmann distributions (black and red curves, respectively; seeSI Text). Boltz-mann parameters: G-V Vhalf= 277± 6 mV; z = 0.84 ± 0.01 e0. F-V Vhalf=−28 ± 2 mV; z = 0.24± 0.01 e0. n = 5 cells. G-V and F-V curves of the same clone without charge mutation are also included (dashed black and red curves, respectively). (D–F) As in A–C, for channels labeled with TMRM at position 202 (outside S4) with mutation D153Q, to neutralize the voltage-sensing Aspartate of S2 (44). Boltzmann parameters in F are: G-V Vhalf= 260± 5.6 mV; z = 0.74 ± 0.041 e0. F-V Vhalf=−130 ± 1.8 mV; z = 0.23 ± 0.018 e0. n = 5.

Pantazis et al. PNAS | March 2, 2010 | vol. 107 | no. 9 | 4461

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Fig. 5. Allosteric models of voltage-dependent BKCaactivation. (A) scheme II: Each BKCaVSD (dashed line) is separated into subdomains S2 and S4 with distinct voltage dependence, linked by activation-dependent, intrasubunit interaction H24. The Pore domain can assume the closed (C) or open (O) state, whereas S2 and S4 can be either resting (R) or active (A). S4 activation stabilizes Pore opening via interaction H4P. (B) Normalized K+conductance (G, black circles), S2ΔF/F (blue diamonds), and S4ΔF/F (red squares) from channels without charge neutralization (Fig. 2). scheme II predictions for conductance, S2 and S4 activation are shown as black, blue, and red curves, respectively. (C) As in B for channels with mutation D153Q in S2 (Figs. 3 A–C and 4 D–F). The highly linear S2 ΔF/F data (see Fig. 3B) were renormalized to conform to the model prediction, instead of constraining it. (D) As in B, for channels with mutation R213G in S4 (Figs. 3 D–F and 4 A–C). (E) scheme IIfitted parameters. Parameters of charge-neutralized channels with an asterisk were constrained to be equal to their pseudo-WT channel equivalent. (F) scheme III. This model is similar to II, but predicts that a segment displaces its neighbor during activation, producing a fractional movement of its charge through the membranefield (see Fig. 6A). (G–J) As in B–E, for scheme III. (K) scheme IV is based on scheme II, with the addition of a voltage- and activation-dependent interaction qapp(see Fig. 6B). (L–O) As in B–E, for scheme IV.

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test this condition, we constructed scheme III (Fig. 5F–J), whereby activation of S2 causes a fractional charge movement in S4, while itself experiencing a reactionary force that limits the full extent of charge movement in its own segment. Thus, the charge moved by S2 activation is (1− β)qS2+αqS4, whereαqS4andβqS2are

frac-tional charges of S4 and S2, respectively. Similarly, S4 activation displaces charge (1− α)qS4+βqS2. According to the bestfitting

(Fig. 5J), the fraction of S4 charge movement during S2 activation (α) is 0.21, whereas the equivalent value for S2 (β) is 0.45. S4 activation in the WT effectively moves 0.39e0, in S2-neutralized

channels (D135Q) 0.24 e0, and in S4-neutralized channels

(R213G) 0.16e0. S2 activation in the WT effectively moves 0.26e0,

in S2-neutralized channels 0.06e0, and in S4 neutralized channels

0.19e0. As in scheme I, the total charge moved by S2 and S4

activation isqS2+qS4. However, this model allows for the apparent

reduction of charge in a segment when its neighbor is neutralized, so it can predict the data satisfactorily (Fig. 5G–I), making a reciprocal mechanical perturbation during S2/S4 activation a plausible explanation.

An Alternative Model Involving a Voltage-Dependent Mode of Cooperativity.A different mechanism (Fig. 5K, scheme IV) can account for the experimentalfindings, in which additional charge is moved in the S2/S4 doubly activated state (qapp), resulting in a de

facto voltage-dependent cooperative interaction. This model predicts a steeper voltage dependence experienced by S2 or S4 upon activation of the other sensor (Fig. 5L–N) and is consistent with a dynamicfield focusing interpretation discussed further on. The voltage-independent termH24is of considerable magnitude

(−61 meV, equivalent to 2.4 kT or coupling factor 11) and is little affected by charge neutralization. Conversely, charge neutraliza-tion in a segment not only decreases its own charge but also reducesqappfrom 0.21e0to almost zero, resulting in the reduced

voltage dependence of the neighboring, intact segment (Fig. 5M andN), as observed experimentally (Fig. 4). When direct com-parison of parameters can be made, thefitting of scheme IV is in congruence with thefindings of a previous model of BKCa

acti-vation (44). Specifically, the Pore Domain voltage dependence (L0

equivalent toVhalf= 818 mV at 25 °C,zL= 0.49e0; scheme IV:Vhalf

= 820 mV,q = 0.49 e0) and the VSD-Pore interaction (factorD equivalent to−80 meV at 25 °C; scheme IV H4P:−100 meV).

Becauseqapplowers the free energy of the doubly activated VSD, it

is a cooperative element. Discussion

We used voltage-clampfluorometry to optically track the acti-vation of gating-charge-bearing transmembrane domains S2 and S4 in the human BKCaVSD. These experiments showed that S2

and S4 possess distinct voltage dependence but also revealed that charge neutralization in one voltage-sensing segment recip-rocally reduced the voltage dependence of its neighbor. This clearly indicated that S2 and S4 are functionally coupled, influ-encing each other’s voltage-sensing ability. The possibility that activation of S2 could somewhat influence the fluorescence sig-nal of S4 and vice versa (a condition referred to as sigsig-nal cross-talk) has been investigated extensively both at the macroscopic domain and the microscopic level. The results of this analysis show that signal cross-talk cannot account for the experimental findings and, if cross-talk does occur, it does not significantly affect on our results and conclusions. The analysis can be found inSI Text,“Investigating signal cross-talk,” andFigs. S2–S4.

To understand the nature of the intrasubunit interactions between S2 and S4, we formulated and tested statistical-mechanical models of voltage-dependent BKCaactivation based on different

premises. Models assuming that the BKCaVSD operates as a single

unit with uniform voltage dependence (Fig. S1A–E, scheme I) or on the basis of an energetic S2–S4 interaction alone (Fig. 5 A–E, scheme II) could not account for the data. One model that

pro-duced a satisfactory fit (Fig. 5 F–J, scheme III) was similar to scheme II, with the additional condition that S2 and S4 mechan-ically perturb each other during activation (Fig. 6A), such that when one segment is neutralized, the charge moved when its intact partner activates is reduced. A similar mechanism has been pro-posed to account for the weak voltage dependence of pore opening transitions in BKCa, whereby activating pore structures could

displace VSD segments (4).

Scheme IV also provides a plausible mechanism for the S2–S4 interaction while successfully predicting the data (Fig. 5K–O). In this model, activation of S2 or S4 when the other segment has activated produces more charge movement than transitions to a single-activated state. This“non-additivity” of charge movement during activation is consistent with the dynamic (activation-dependent) electricfield focusing illustrated in Fig. 6B, inspired by previous postulation inShaker K+channels (43, 47): Activa-tion of a voltage-sensing segment could modify aqueous crevices, focusing the field over a shorter dielectric distance. A charged, neighboring segment would then traverse a larger portion of the voltage drop across the membrane, so an observer would measure increased charge movement. Likewise, failure of a segment to focus thefield results in loss of effective charge by its neighbor. Consequently, aqueous crevices could be a dynamic, activation-dependent element of the BKCaVSD, rather than a passive

mor-phological feature. Wefind this interpretation more conceptually satisfying, because it is based on significant evidence supporting the existence of VSD crevices (37–43), including in BKCa(54).

Schemes II–IV assume that pore opening is facilitated by S4 activation via energetic interaction H4P. Including a similar

interaction between S2 and the pore (H2P) mainly decreased the

magnitude ofH4Pwithout significantly affecting the rest of the

parameters or the goodness of thefits(Fig. S1 F–J). A recent model of BKCaincludes S2 as the most distal segment to pore

structures (55), although investigations on KvAP channels sug-gest otherwise (42). Because we cannot distinguish between these alternative models, we can neither ascertain nor refute direct S2-dependent gating in BKCa.

We have demonstrated that transmembrane domains S2 and S4 in the human BKCaVSD possess distinct voltage dependence but

also interact during activation. An interestingfinding is that charge Fig. 6. The mechanical coupling and dynamicfield focusing theories. S2 (green helix) and S4 (red helix) of a wild-type BKCaVSD undergo hypothetical motions during activation. Only segments from one subunit are shown for clarity, possessing voltage-sensing residues: D153 (S2, red), R167 (S2, blue) and R213 (S4, blue) (44). The membrane voltage drop is illustrated by equipotential lines (in black, except the portion traversed by R213 in S4, in red lines). (A) According to the mechanical coupling theory (Fig. 5 F–J, scheme III), segment activation causes the displacement, or nudging, of its neighbor, producing a fractional movement of its charge through the membranefield. (B) According to the dynamicfield focusing theory, segment activation causes aqueous crevices to form, focusing thefield. As a result, in the S2/S4 doubly activated state, these segments have traversed a large portion of the membrane potential, giving rise to qapp,fitted in scheme IV (Fig. 5 K–O).

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movement in one segment is perturbed by charge neutralization in its neighbor. We propose two interpretations to account for the apparent S2–S4 interaction, which are not mutually exclusive: mechanical coupling (Fig. 6A) and dynamic field focusing (Fig. 6B). The VSD of human BKCachannels has been an ideal system to

study such interactions because of its“decentralized” distribution of voltage-sensing residues throughout the VSD (Fig. 1B andS5) (44). Nevertheless, the charged residues neutralized in this inves-tigation and VSD topology are highly conserved (Fig. S5), so it would be of prime interest to pursue the demonstration of similar interactions in other members of the voltage-activated protein superfamily.

Materials and Methods

All experiments were performed on human BKCachannelα subunit clones (hSlo1) (11) with these background mutations: (i) all native extracellular Cys-teines were substituted to Serines (C14S, C141S, C277S); (ii) W203V, which increases the amplitude of voltage-dependent TMRMΔF/F from position 202 outside S4 (51); and (iii) R207Q, to increase POat low intracellular [Ca2+] (3, 51,

52) without influencing gating charge movement (44). Site-directed muta-genesis was performed with QuikChange (Stratagene) and confirmed by sequence analysis. The clones were transcribed in vitro (T7 mMessage mMa-chine; Ambion) for oocyte injection. Xenopus laevis (NASCO) oocytes (stage V– VI) were prepared, injected, and labeled with TMRM as described (51).

Ionic currents were recorded from oocytes under voltage clamp by using the COVG technique (45) in a set-up modified to allow epifluorescence measurements (49). External solution: 120 mM NaMES, 10 mM KMES, 2 mM Ca(MES)2, and 10 mM HEPES. Internal solution: 110 mM K-Glutamate and 10 mM K-HEPES. Intracellular micropipette solution: 2.7 M NaMES and 10 mM NaCl. The holding Vmwas−90 mV.

Please seeSI Textfor data analysis methods, the model construction and fitting routine.

ACKNOWLEDGMENTS. We thank Michela Ottolia and members of the R.O. laboratory for constructive discussion on the manuscript. The hSlo1 clone was a kind gift from Ligia Toro. This work was supported by research grants from National Institutes of Health/National Institute of General Medical Sciences R01GM082289 and the Laubisch Foundation (R.O.), and an American Heart Association Postdoctoral Fellowship (Western States Affiliate) (to A.P.).

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Supporting Information

Pantazis et al. 10.1073/pnas.0911959107

SI Materials and Methods

Data Analysis.Data were analyzed with a customized program developed in our Division. Membrane K+conductance (G) was calculated with the formulaG = I/(Vm−EK), whereI is

steady-state recorded K+current,Vmthe clamped membrane potential

andEKthe equilibrium potential of K+with the solutions used

(-62 mV). G-V and F-V curves werefitted to a Boltzmann dis-tribution of the form: G-V=Gmax/(1+exp(z(Vhalf–Vm)(F/RT))

and F-V= ((Fmax−Fmin)/(1+exp(z(Vhalf–Vm)(F/RT)))−Fminwhere

GmaxandFmaxare the maximum G and F, respectively;Fminis the

minimum F;z is the effective valence; Vhalfis the half-activating

membrane potential;Vmis the clamped membrane potential; F, R

andT are the usual thermodynamic values. F-V curves were nor-malized between minimum and maximumfluorescence levels. All errors are±1 SEM.

SI Model Description and Methodology. As in the actual BKCa

channel, the model consists of four subunits, each of which contains two regulatory domains (S2 and S4) whose occupancies of resting (R) versus active (A) states depend on the activation energiesH2 =q2(V − V2) andH4=q4(V − V4), where Hn =

Hn(A) − Hn(R), and qn and Vn are gating charge and

half-activation voltages, respectively. A single pore unit also possesses independent voltage dependent activation withHP=qP(V − VP).

Cooperativity arising from combined activation of two regulatory domains is described by interaction energies such asH4P, and

W24. The opening of the pore is accompanied by a change in the

global energy ofjH4P, wherej (value: 0–4) is equal to the number

of activated S4 domains. For most models,H2Pwas set to zero

(Discussion). Combined activation of S2 and S4 domains results in the addition of an interaction energyH24if the two domains

reside on the same subunit.W24is unusual in that it is a

voltage-dependent interaction term, a consequence of the excess gating chargeqappthat arises through the proposal that mutual

tran-sition of S2 and S4 charges generates a shift in equipotential lines. Thus,W24=qapp(V − V24), whereV24 =−H24/qapp, and

H24is a voltage-independent interaction.qappwas set to zero for

fittings of scheme II (Fig. 5 A–J andFig. S1F–O).

In a single subunit, the four possible configurations of S2 and S4 are as follows: RR = {R2,R4}, AR = {A2,R4}, RA = {R2,A4},

and AA = {A2,A4}. The total number of states possible in a

closed-pore channel with four subunits is 30, which can be ob-tained by considering how many ways one can distribute four objects (subunits) among four slots (subunit configurations). For example, the state C1102describes the closed state in which one

subunit is in configuration RR, one is in AR, zero are in RA, and two are in AA. An additional 35 open state channels are sim-ilarly described, leading to a total number of 70 states. We em-ploy the configurational notation Cabcdand Oabcd, where C and

O are closed and open states, respectively,a is the number of subunits in configuration RR, b is the number of subunits in configuration AR, c is the number of subunits in configuration RA,d is the number of subunits in configuration AA. A valid state configuration must satisfy: a + b + c + d = 4.

The energies of these states are tabulated as follows:Hpabcd=

pHP+ b(H2) + c(H4+pH4P) +d(H2+ H4 +pH4P+ H24),

where the pore indexp is 0 or 1 depending on whether the pore is closed or open. The partition functionZ of the channel is given by the following expression:

Z ¼ ∑ pabcd Ωabcdexp  − Hpabcd kT  ;

where the state degeneracyΩabcd = 4!/a!b!c!d! and kT has its usual thermodynamic significance.

Computing isotherms requires evaluating the expectation value of the observable in question as a function of voltage using the following expression:

hXðVÞi ¼ Z− 1 pabcd

XpabcdΩabcdexp − H

pabcd kT

 :

The state values for normalized conductance andfluorescence change were assumed to be the following:Gp=p; F2bd= (b +

d)/4; and F4cd= (c + d)/4. Inserting these expressions for Xpabcd

in the preceding equation yields normalized isotherms that range from 0 to 1 on the voltage axis.

Model Fitting Regime.Berkeley Madonna was used to run model simulations and fit them to the data. Three “sub-models” as described above were loaded: one for pseudo-WT, one for S2-neutralized (D153Q), and one for S4-S2-neutralized (R213G) channels. Although each submodel had its own parameter set (all listed in Fig. 5E, J, and O andFig. S1E and J), some were fixed to be the same as the WT parameter values (marked with an asterisk in Fig. 5 andFig. S1). Mean, normalized G-V, S2 F-V, and S4 F-V experimental datasets were loaded for WT and charge-neutralized channels, whereas the fourth-order Runge-Kutta integration algorithm was used to solve the model’s dif-ferential equations and predict G-V and F-V curves according to the parameters. The three submodels were simultaneously fit, each to its respective G-V and F-V experimental dataset by using Berkeley Madonna’s Curve Fitting routine with an error toler-ance of 10−4.

Because of the extremely shallow S2 F-V curve from S2-neutralized (D153Q) channels (lacking evident saturation within the tested membrane potential range of±300 mV, Fig. 3B), the experimental data (Fig. 5 C, H, and M andFig. S1C blue dia-monds) were normalized to the prediction of the models (Fig. 5 C, H, and M andFig. S1C, blue curve) but were not included in the simultaneous curvefitting.

Investigating Signal Cross-Talk

I. S2-S4 Signal Cross-Talk at the Macroscopic Domain.A possibility is that thefluorescence signal reported from S2 received a fractional contribution from S4 motions, and vice versa—a condition we refer to as“signal cross-talk.” A consequence of this could be that neutralization of a segment would affect the TMRM fluo-rescence deflections observed from its intact neighbor and ap-parently impair their voltage dependence, without there being a functional interaction between the two segments. To investigate whether this is applicable to our data, we defined the fluo-rescence from S2 and S4 as the weighted sum of the underlying activation probability of S2 and S4 (PS2andPS4), such that:

S4 signal¼ APS2þ ð1 − AÞPS4 [1]

S2 signal ¼ ð1  BÞPS2þ BPS4; [2]

whereA and B are fractional cross-talk factors between zero and one, whilePS2andPS4are voltage-dependent segment activation

probabilities, expressed as Boltzmann distributions. The free fittings of conditions [1] and [2] to the mean, normalized ΔF/F

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data are shown in Fig. S2, whereas the fitting parameters are shown inTable S1, below:

The bestfit of the WT data demonstrates a low value for A and B (A = 0.066, and B = 0). However, because there is significant overlap between the two curves, visually acceptablefits are pos-sible withA and B values as high as 0.5, so that an upper limit for the cross-talk variables cannot be estimated based on this fit alone. We will use additional methods to attempt to place a limit on these variables, butfirst a critically important point must be made regarding the hypothesis of whether cross-talk alone can explain the data, by evaluating the results for the mutant channels. Tofit the mutant data to Eq. 1 and 2, it was absolutely nec-essary to change the shape of the Boltzmann curvesPS2andPS4,

even when the segment in question had not been neutralized. Therefore, although acceptable fits of the data were obtained from linear combinationsPS2andPS4(seeTable S1), this does

not change the fact that neutralization of charge in one segment necessarily perturbs the voltage dependence of its neighbor (e.g., see Table S1 parameters in bold). Therefore, even with the possibility of cross-talk, the mainfinding of this paper, that there is mutual interaction between S2 and S4, does not change. Note that, at the same time, it does not offer a significantly better fit of the data: The sum of squared errors for single-Boltzmannfittings (which do not benefit from the six additional cross-talk param-eters) is 0.0647 (cross-talkfit: 0.0490).

To reinforce the point that no degree of cross-talk can be used to avoid the conclusion of a real interaction between voltage sensors, we offer the following scenario (Fig. S3), where we constrained the fit to not allow a changes in voltage dependence of the non-neutralized segment (i.e., PS2_WT = PS2_R213G and PS4_WT =

PS4_D153Q). Under this condition, which enforces the absence of

any meaningful interaction between voltage sensors, thefits are extremely poor, both visually and quantitatively (Sum Sq = 0.440), despite the fact that this condition has two additional free parameters compared to the single-Boltzmannfittings (Sum Sq = 0.0647). Thefitting parameters are listed inTable S2below.

Investigating cross-talk at the macroscopic domain demon-strates that signal cross-talk alone (without S2–S4 interaction) cannot account for the observed experimental data. However, thefitting of Boltzmann distributions provides very little mech-anistic information and it oversimplifies the underlying com-plexities of a microscopic model. To better understand whether cross-talk is sufficient to account for the apparent interactions

between S2 and S4, we implemented cross-talk factors in our allosteric model framework, as follows.

II. S2–S4 Signal Cross-Talk at the Microscopic Level.InFig. S4A–D, we globallyfit the data with a variant of our allosteric model in which S2 and S4 activation are not linked by energetic, me-chanical, or any other kind of interaction, although S4 is still allosterically linked to the pore domain. The cross-talk mecha-nism was implemented as follows: Activation of a segment pro-duces a change in itsfluorescence, represented by values F2←S2

andF4←S4for S2 and S4 signal, respectively. These values were

fixed to 1. In addition, activation of S2 induces a fractional change in the fluorescence of the S4 signal (value F4←S2).

Likewise, activation of S4 perturbs S2fluorescence signal by the termF2←S4. The cross-talk termsF4←S2andF2←S4werefit freely

for each BKCachannel clone.

These microscopic terms can be roughly related to the mac-roscopic variables (A and B) through the relations: A = F4←S2/

(F4←S2+F4←S4), andB = F2←S4/(F2←S4+F2←S2).

Thefits are visibly poor, demonstrating that cross-talk alone cannot account for the data. This is in agreement with the analogous macroscopic Boltzmannfittings (Fig. S3). As an aside, inclusion of an S2-Pore interaction (H2P) did not improve the

goodness of thefit.

Finally, to estimate a reasonable value for an upper limit of the cross-talk values, we attempted to improve thefits of the dynamic field and mechanical interaction models used in the main paper by addingF2←S4andF4←S2to thefitted variables. The inclusion of

cross-talk in the mechanical interaction model (Fig. 5 F–J, scheme III) is included inFig. S4E–H, whereas the same for the dynamic field focusing model (Fig. 5 K–O, scheme IV) is in-cluded inFig. S4I–L. For an easier comparison between models with and without cross-talk, please seeTables S3andS4below

WhereA and B are defined in terms of the microscopic cross-talk variables as above,α and β are the fractions of S2 and S4 nudged during activation according to the interpretation of scheme III andqappis the apparent additional charge caused by

field focusing (scheme IV). The fitted values of A and B repre-sent a reasonable upper limit of cross-talk in the context of two possible models that explain our data. In no case do they exceed Table S2. Fitted parameters for the constrained Boltzmann

fitting described in Fig. S3 Fig. S3

plots Clone Vhalf_S2, mV zS2, e0 Vhalf_S4, mV zS4, e0 A B

A, D WT −59 0.48 −97 0.67 0.30 0

B, E D153Q −9.3 0.17 −97* 0.67* 0.45 0.014

C, F R213G −59* 0.48* 79 0.21 0 0.45

Parameters of mutant channels marked with an asterisk (*) were con-strained to be equal to their wild-type equivalent.

Table S3. Mechanical interaction or nudging mechanism (Scheme III)

Zero cross-talk

(Fig. 5 F–J) With cross-talk (Fig. S4 E–H)

Parameter: A B α β A B α β

WT channels 0 0 0.21 0.45 0.18 0.0076 0.28 0.46

D153Q (S2 neutralized) 0 0 0.21* 0.45* 0.039 2.1× 10−60.28* 0.46* R213G (S4 neutralized) 0 0 0.21* 0.45* 0 0.16 0.28* 0.46* Parameters of mutant channels marked with an asterisk (*) were con-strained to be equal to their wild-type equivalent.

Table S1. Parameters for thefittings in Fig. S2 Fig. S2

plots Clone Vhalf_S2, mV zS2, e0 Vhalf_S4, mV zS4, e0 A B

A, D WT −57 0.52 −83 0.78 0.066 0

B, E D153Q 50 0.16 −150 0.25 0.13 0.20

C, F R213G −140 0.42 130 0.32 0.22 0.44

Table S4. Dynamicfield focusing mechanism (Scheme IV) Zero cross-talk

(Fig. 5 K–O) With cross-talk (Fig. S4 I–L)

Parameter: A B qapp, e0 A B qapp(e0)

WT channels 0 0 0.21 2.2×10−8 0.0076 0.24 D153Q (S2 neutralized) 0 0 0.0063 0.058 0 1.8× 10−6 R213G (S4 neutralized) 0 0 0.0027 0.0065 1.8× 10−7 0.0058

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20% of the observed signal. It should also be noted thatfits did not improve markedly, and the model-specific parameters (α, β, qapp) did not change substantially—if anything, there appears to

be a slightly greater extent of mechanical interaction or field focusing.

In conclusion, the introduction of cross-talk factors does not relieve the necessity of some type of mutual interaction between S2 and S4 as a means of explaining our data. If cross-talk does occur, it is likely a minor effect, as estimated by only limited improvements in our ability tofit data with reasonable models.

Fig. S1. Alternative models. (A) Scheme I: the BKCaVSD is a superunit with uniform voltage dependence, so the activations of S2 and S4 are indistinguishable. The Pore domain can assume the closed (C) or open (O) state, whereas each VSD (from eachα subunit) can be either resting (R) or active (A). VSD activation stabilizes Pore opening via interaction H. (B) Normalized K+conductance (G, black circles), S2ΔF/F (blue diamonds) and S4 ΔF/F (red squares) from channels without charge neutralization (Fig. 2). Scheme I predictions for conductance and VSD activation are shown as black and blue/red curves, respectively. (C) As in B for channels with mutation D153Q in S2 (Figs. 3 A–C and 4 D–F). (D) As in B, for channels with mutation R213G in S4 (Figs. 3 D–F and 4 A–C). (E) Scheme I fitted parameters. Parameters of charge-neutralized channels with an asterisk were constrained to be equal to their pseudo-WT channel equivalent. (F) Scheme II (Fig. 5A) with the addition of an S2-Pore interaction H2P. (G–J) As in B–E, for scheme II + H2P. Model predictions of S2 and S4 activations are blue and red curves, respectively. In H, the highly linear S2ΔF/F data (blue diamonds; also see Fig. 3B) were renormalized to conform to the model prediction (blue curve), instead of constraining it.

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Fig. S2. Cross-talk at the macroscopic domain I: Free parameterfitting. (A–C) To investigate the possibility of cross-talk accounting for the experimental data, the normalized, meanΔF/F data from S2 (blue circles) and S4 (red circles) from channels without charge neutralization mutation (A), channels with a neu-tralized voltage-sensing charge in S2 (D153Q, B), and channels with a neuneu-tralized S4 (R213G, C) werefitted with the weighted sums (linear combinations) of two Boltzmann distributions (PS2and PS4), reflecting the underlying voltage dependence of S2 and S4 activation, respectively. The blue and red curves rep-resent these weighted sumsfit to S2 and S4 fluorescence data, respectively. The cumulative sum of squared errors is 0.0490. The fitting parameters are listed in

Table S1and discussed inSI Text,“Investigating Signal Cross-Talk.” (D–F) Fluorescence data are shown as in A–C for the corresponding BKCaclones used. Instead of the weighted sums, the individual constituent Boltzmann distributions (PS2and PS4) are shown as blue and red curves, respectively.

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Fig. S3. Cross-talk at the macroscopic domain II: Cross-talk cannot exclude S2–S4 interactions. The data and curves shown are as inFig. S2. In thesefits, in-teractions between S2 and S4 are excluded, by introducing the constraint that the voltage dependence of segment activation is not perturbed by charge neutralization in the opposite segment. In this case, PS2_WT= PS2_R213Gand PS4_WT= PS4_D153Q. The cumulative sum of squared errors is 0.440. Thefitting parameters are listed inTable S2and discussed inSI Text,“Investigating Signal Cross-Talk,” section I.

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Fig. S4. Investigating cross-talk at the microscopic level. (A–D) Fitting of a statistical-mechanical model (as in Fig. 5 andFig. S1) without any interaction between S2 and S4. Instead, activation of S4 contributes to thefluorescent signal from S2, as expressed by cross-talk term F2←S4. Likewise, S2 activation contributes to S4fluorescence by factor F4←S2. (A) Normalized mean K+conductance (G, black circles), S2ΔF/F (blue diamonds) and S4 ΔF/F (red squares) from channels without charge neutralization (“pseudo-WT”, Fig. 2). Predictions of this model for conductance and S2 and S4 fluorescence signals are shown as black, blue, and red curves, respectively. (B) As in A, for channels with a charge neutralization mutation in S2 (D153Q). (C) As in A, for channels with a charge neutralization mutation in S4 (R213G). (D) Thefitting parameters of the model. Parameters of charge-neutralized channels with an asterisk were constrained to be equal to their pseudo-WT channel equivalent. (E–H) As in A–D. This time, a model similar to scheme III (Fig. 5F) was fit, with the addition of signal cross-talk parameters FS2←S4and FS4←S2. In F, the highly-linear S2ΔF/F data (blue diamonds; also see Fig. 3B) were renormalized to conform to the model prediction (blue curve), instead of constraining it. (I–L) As in E–H. This time, a model similar to scheme IV (Fig. 5K) was fit, including cross-talk parameters FS2←S4and FS4←S2. SeeSI Text,“Investigating Signal Cross-Talk,” section II, for a discussion of the fittings.

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:138 :253 :189 :174 :304 :248 :199 :335 :278 :227 :385 :313 109: 223: 159: 144: 274: 217: 175: 205: 248: 200: 358: 286:

S1

S2

S3

S4

T L T G R V L V V L V F A L S I G A L V I Y F I D - S S N P I S S Q A R V V A I I S V F V I L L S I V I F C L E T L P E F K S G P A R I I A I V S V M V I L I S I V S F C L E T L P I F R T I L H Y S P F K A V W D W L I L L L V I Y T A V F T P Y S A T L T G R V L V V L V F A L S I G A L V I Y F I D - S S N P I S S Q A R V V A I I S V F V I L L S I V I F C L E T L P E F K S G P A R I I A I V S V M V I L I S I V S F C L E T L P I F R T I L H Y S P F K A V W D W L I L L L V I Y T A V F T P Y S A F Y K D F T L Q IDM A F N V F F L L Y F G LRF I A A N D K D I T D P F F L I E T L C I I W F T FEL T V R F L A C P N K S F T D P F F I V E T L C I I W F S F E F L V R F F A C P S K Y A C Q P L A V V D L I V D I M F I V D I L I N F R T T Y V N F Y K D F T L Q IDM A F N V F F L L Y F G LRF I A A N D K D I T D P F F L I E T L C I I W F T FEL T V R F L A C P N K S F T D P F F I V E T L C I I W F S F E F L V R F F A C P S K Y A C Q P L A V V D L I V D I M F I V D I L I N F R T T Y V N L W F W L E V N S V VDF F T V P P V F V S V Y L -L N F C R D V M N V I D I I A I I P Y F I T -L A T V V A E E E A G F F T N I M N I I D I V A I I P Y Y V T I F L T E S N K S A V H Y F K G W F L I D M V A A I P F D L L I F G S G S E E -L W F W -L E V N S V VDF F T V P P V F V S V Y L -L N F C R D V M N V I D I I A I I P Y F I T -L A T V V A E E E A G F F T N I M N I I D I V A I I P Y Y V T I F L T E S N K S A V H Y F K G W F L I D M V A A I P F D L L I F G S G S E E -N R S W L G L R F L R A LRL - I Q F S E I L Q F L N I L L A I LRV IRL VRV FRI F K L - S R H S K G L Q I L R R V V Q I F R I M R I L R I F K L - S R H S K G L Q I L - - L I G L LKT ARL LRL V R V - A R K L D R Y S E Y N R S W L G L R F L R A LRL - I Q F S E I L Q F L N I L L A I LRV IRL VRV FRI F K L - S R H S K G L Q I L R R V V Q I F R I M R I L R I F K L - S R H S K G L Q I L - - L I G L LKT ARL LRL V R V - A R K L D R Y S E Y 399: 447: 490: 520: :429 :477 :519 :545 hSlo1 Shaker KV1.2-2.1 hERG1 hSlo1 Shaker KV1.2-2.1 hERG1 hSlo1 Shaker KV1.2-2.1 hERG1 hSlo1 Shaker KV1.2-2.1 hERG1

Fig. S5. Voltage sensor domain homology. Alignment of the VSDs of hSlo1, encoding the human BKCaa subunit; Shaker, encoding a Drosophila voltage-gated K+channel; the human Ether-à-go-go related gene, encoding HERG; and the K

V1.2-2.1 chimera, used to produce the most recent crystal structure of a VSD to date (1). Positions of the transmembrane domains S1-S4 are shown (colored bars) as resolved from KV1.2-2.1. Conserved charged residues are boxed. Voltage-sensing residues in BKCa(2), Shaker (3,4) and HERG (5) channels are in red type. BKCaresidues substituted to cysteine for TMRM labeling are highlighted in orange; neutralized voltage-sensing residues in blue.

1. Long SB, Tao X, Campbell EB, MacKinnon R (2007) Atomic structure of a voltagedependent K+ channel in a lipid membrane-like environment. Nature 450:376–382. 2. Ma Z, Lou XJ, Horrigan FT (2006) Role of charged residues in the S1-S4 voltage sensor of BK channels. J Gen Physiol 127:309–328.

3. Seoh SA, Sigg D, Papazian DM, Bezanilla F (1996) Voltage-sensing residues in the S2 and S4 segments of the Shaker K+ channel. Neuron 16:1159–1167. 4. Aggarwal SK, MacKinnon R (1996) Contribution of the S4 segment to gating charge in the Shaker K+ channel. Neuron 16:1169–1177.

5. Zhang M, Liu J, Tseng GN (2004) Gating charges in the activation and inactivation processes of the HERG channel. J Gen Physiol 124:703–718.

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References

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