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Electrostatics of the Intracellular Vestibule of K C Channels

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Electrostatics of the Intracellular Vestibule of K C Channels
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  Electrostatics of the Intracellular Vestibuleof K C Channels Vishwanath Jogini and Benoı ˆ t Roux * Department of Physiology &Biophysics, Weill MedicalCollege of Cornell University1300 York Avenue, New YorkNY 10021, USA Previous calculations using continuum electrostatic calculations showedthat a fully hydrated monovalent cation is electrostatically stabilized at thecenter of the cavity of the KcsA potassium channel. Further analysisdemonstrated that this cavity stabilization was controlled by a balance between the unfavorable reaction field due to the finite size of the cavityand the favorable electrostatic field arising from the pore helices. In thepresent study, continuum electrostatic calculations are used to investigatehow the stability of an ion in the intracellular vestibular cavity common toknown potassium channels is affected as the inner channel gate opens andthe cavity becomes larger and contiguous with the intracellular solution.The X-ray structure of the calcium-activated potassium channel MthK,which was crystallized in the open state, is used to construct models of theKcsA channel in the open state. It is found that, as the channel opens, the barrier at the helix bundle crossing decreases to z 0 kcal/mol, but that theion in the cavity is also significantly destabilized. The results are comparedand contrasted with additional calculations performed on the KvAP(voltage-activated) and KirBac1.1 (inward rectifier) channels, as well asmodels of the pore domain of Shaker in the open and closed state. Inconclusion, electrostatic factors give rise to energetic constraints on ionpermeation that have important functional consequences on the variousK C channels, and partly explain the presence or absence of chargedresidues near the inner vestibular entry. q 2005 Elsevier Ltd. All rights reserved. Keywords:  KcsA; MthK; KirBac1.1; KvAP; Shaker *Corresponding author Introduction Potassium channels are tetrameric membrane-spanningproteinsthatservetofacilitateandcontrolthe passage of K ions across the lipid membrane. 1 The determination of the structure of the KcsA K C channel by X-ray crystallography provided the firstatomic-resolution view of these proteins. 2 The mostimportant functional feature of the channel struc-ture, shown in Figure 1, is the 12 A ˚long narrowpore located along the tetrameric symmetry axisnear the extracellular side. Lined exclusively bymain-chain carbonyl oxygen atoms from theresidues corresponding to the signature sequenceTTVGYG common to all K C channel, 3 this region of the protein acts as a “selectivity filter” by allowingonly the passage of nearly dehydrated K ions. Short a -helices from each of the four subunits, referred toas the pore helices, surround the selectivity filterwith their COOH termini pointing toward thecenter of a wide aqueous cavity, about 15 A˚indiameter and able to contain 25 to 30 watermolecules. It has been suggested that this aqueouscavity, located at the center of the membrane, helpsovercome the electrostatic barrier to ion transloca-tion that is opposed by the low dielectric membranelipid. 2 Common monovalent cations have indeed been observed occupying the cavity in the crystallo-graphic structure, 4 and continuum electrostaticcalculations have shown that the static and reactionfields in the channel are tuned to exclusivelystabilize a monovalent cation at the center of thecavity of the KcsA channel, thus revealing that thechannel has the ability to exert a crude form of valence selectivity while keeping incoming cations 0022-2836/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. Abbreviations used: MD, molecular dynamics; ESR,electron spin resonance; PB, Poisson–Boltzmann; ABNR,adopted basis Newton–Raphson; RMSD, root-mean-square-deviation.E-mail address of the corresponding author: benoit.roux@med.cornell.edu doi:10.1016/j.jmb.2005.09.031  J. Mol. Biol.  (2005)  354 , 272–288  fully hydrated. 5 The free energy of a monovalentcation in the cavity was found to result from a balance of two opposing effects: an unfavorablereaction field due to the finite-size of the water-filled high dielectric cavity, and a favorableelectrostatic field arising from the charge distri- bution of the pore helices. Similar  a -helices,“interrupted” mid-way through the membrane,are also observed in the case of aquaporins 6 and bacterial ClC homologs, 7,8 and appear to be arecurrent structural motif of membrane channelswith an important functional role.ThestructureoftheKcsAchannel,asitappearsinthe crystal structure, corresponds most likely to aclosed state. On the intracellular side, the innerhelices from the four subunits cross into a tight bundle of hydrophobic residues, leaving only anarrow entryway of about 4 A˚radius to the centralcavity. Molecular dynamics (MD) simulations of KcsA in a lipid bilayer indicated that the packing of the inner helices at the bundle crossing is verystable. 9 The passage of a cation through this narrowentrance, whichcomprisesexclusively hydrophobicside-chains, is not sterically disallowed but requiresa nearly complete dehydration and is energeticallyprohibitive. 10 According to continuum electrostaticcalculations, increasing the diameter of the innerentrance by only 3 A˚is enough to reduce the largeentry barrier from 20 to about 3–4 kcal/mol,suggesting that small movements of the innerhelices could significantly affect the free energy barrier for ion entrance; effectively closing oropening the channel. 10 This is consistent withavailable experimental information. In bilayerexperiments, the KcsA channel is observed to bemostly closed at neutral pH, and that the proba- bility of channel opening increases up to 5–10% atlow intracellular pH. 11–13 Thus, the fact that theKcsA channel was crystallized at pH 5–5.6 14 makesit even more plausible that the X-ray structurecorresponds to a closed state.The X-ray structure of the calcium-activatedpotassium channel from  Methanobacterium thermo-autotrophicum  (MthK), crystallized presumably inan open state with high calcium concentration,revealed the conformational changes associatedwith channel opening. 15 In the structure of theMthK channel shown in Figure 1, the inner helicesare sharply bent away from the central axis at aconserved glycine residue, leaving a wide openentrance to the pore on the intracellular side.Accordingly, the central cavity, which is closed inthe case of the KcsA channel, is transformed into awide vestibular opening that is contiguous with theintracellular side. Data from electron spin reso-nance (ESR) on KcsA show that the inner helicesfrom the four subunits are moving apart during theconformational change triggered by intracellularpH, 12,16 in a manner that is generally consistentwith the X-ray structure of the MthK channel.Furthermore, site-directed mass tagging experi-ments confirm that the inner helices of KcsA inthe open state are a gating component. 17 Crystallo-graphic structures of additional K C channels,shown in Figure 1, provide complementary infor- mation about the putative open and closed confor-mation of the pore domain and support the generalconclusions drawn from KcsA and MthK. Theconformation of the inwardlyrectifying K C channel(KirBac1.1) from  Burkholderia pseudomallei 18 is verysimilar to that ofthe closed KcsA structure,whereasthe conformation of the pore domain of the voltage-activated K C channel (KvAP) from the thermo-philic archaebacteria  Aeropyrum pernix 19 resemblesthat of the open MthK structure. In the case of theKvAP channel, the extensive distortion in thevoltage sensor 19 casts some doubts on the validityof the conformation of the pore domain, though thestructure is very useful because it provides onemore example of a channel that is possibly in anopen state. Figure 1.  All available K C channels. The extracellularside is at the top, and the intracellular side is at the bottom. The main structural elements are the outer helix,the pore helix, the selectivity filter and the inner helix.There are three K ions, two of them are located at S1andS3 position in selectivity filter and one is at the center of the cavity. The Figures were produced with DINO (www.dino3d.org). Electrostatics in K  C Channels   273  There is also evidence that the main features of the intracellular gate formed by the inner helicescan be found in eukaryotic channels. Based onelectrophysiological experiments on the BK channel(large conductance calcium-activated potassiumchannel), Aldrich  et al. , 20 suggested that theconformation adopted by the inner helix in theopen statedetermines the extent of access resistanceon the ion permeation pathway. They concludedthat large conductance channels such as BK andKcsA might adopt the wide-open conformation.The voltage-gated Shaker channel has a PVP motif in the inner helix, which suggests that its open statemay differ from that of MthK. Based on cysteineaccessibility to chemical modification, Yellen andco-workers 21–23 suggested that the gating in Shakeris accompanied by the movement of inner helices.They concluded that thearchitectureof Shaker initsclosed state is similar to that of KcsA, except for a bend in the inner helix (Figure 1). They could alsostabilize a mutant of Shaker in the open state(V476C) using cadmium-binding experiments by bridging the cysteine at position 476 to the histidineat position 486 in an adjacent subunit; thoughBruhova & Zhorov have suggested that theresulting distance constraint between Cys476 andHis486 may not be interpreted in terms of a uniqueopen channel conformation. 24 Very recently, thestructure of the eukaryotic voltage-activated Kv1.2channel has been determined. 25 Comparison withthe pore domain of the bacterial KvAP channelshows that the latter constitutes a good template formodeling the open state of Kv channels.Although the fine details of the molecularprocesses associated with gating are probably notuniversal for all K C channels, it seems clear thatcontrolling the size of the aperture at the helical bundlecrossingon the intracellularside bybendingthe inner helices is an important mechanism.Previous calculations using continuum electrostaticshowed that the electrostatic field from the porehelices contribute significantly to stabilize a mono-valent cation inside the aqueous cavity of the closedKcsA channel. 5 Important questions arise concern-ing the electrostatic stabilization of a cation andhow it is going to be affected when the channelopens up and the geometry of the inner entrance,with allits complexdielectric boundaries, isaltered.The goal of the present study is to characterize theelectrostatic properties of the channel in the openstate and see how they relate to those of the channelin the closed state. The approach that we takeconsists in determining the free energy to transfer acation from the bulk to the channel environmentusing computations based on the finite-diff erencePoisson–Boltzmann (PB) equation. 5,10,26 Theinfluence of the pore architecture and aminoacid sequence on the ion in the intracellularvestibule is analyzed using all the available X-raystructures as well as models of K C channels.The paper is concluded with a discussion of the possible biological implications of the mainfindings. Theory and Methods Decomposition of the electrostatic free energy The electrostatic free energy to transfer an ionfrom the bulk solution to a point  r  in the pore can becalculatedasthedifferencebetweentheelectrostaticfree energy of the ion-channel complex (ic) and, thefree energy of the isolated channel (c) and ion (i) inwater: DD G ð r Þ Z ½ D G ic ð r Þ K D G c K D G i   (1)where  D G ic ( r ) is the electrostatic energy of thechannel with the ion at  r ,  D G c is the electrostaticenergy of the channel in the absence of the ion at  r ,and  D G i is the electrostatic energy of the K ion faraway in bulk water. Each  D G  is calculated as a sumover all the atomic charge  q i  of the protein and ionspresent in the system: D G Z 12 X i q i f ð r i Þ  (2)where  f ( r i ) is the electrostatic potential at theposition of the atomic charge  q i . It is calculated bysolving the PB equation: 27,28 V $ ½ e ð r Þ Vf ð r Þ K  k 2 ð r Þ f ð r Þ Z K 4 pr ð r Þ  (3)where  r ð r Þ Z P i  q i d ð r K r i Þ  is the total atomic chargedistribution in the system,  e ( r ) is the position-dependent dielectric constant, and   k ð r Þ  is theposition-dependent ionic screening constant (it is0 for present calculations). In practice, the r -dependentfunctions r ( r ), e ( r )and   k ð r Þ aremappedonto a cubic discrete grid and the potential  f ( r )is calculated by solving the PB equation with afinite-difference method. 28 The total electrostatic free energy in equation (2)can be formally expressed using the Green’sfunction  M  for the complex (ic), isolated channel(c) and ion (i). 29 For the sake of simplicity, let usassumethat theion isparticle  i Z 1carryinga charge q 1 . The free energy of the complex is then: D G ic Z 12 X ni Z 1 ;  j Z 1 q i  M ic ð i ;  j Þ q  j Z 12  q 1  M ic ð 1 ; 1 Þ q 1 C 12 X n j Z 2 q 1  M ic ð 1 ;  j Þ q  j C 12 X ni Z 2 q i  M ic ð i ; 1 Þ q 1 C 12 X ni Z 2 ;  j Z 2 q i  M ic ð i ;  j Þ q  j Z 12  q 1  M ic ð 1 ; 1 Þ q 1 C X n j Z 2 q 1  M ic ð 1 ;  j Þ q  j C 12 X ni Z 2 ;  j Z 2 q i  M ic ð i ;  j Þ q  j  ð 4 Þ (the symmetry property of the Green’s function 274  Electrostatics in K  C Channels    M ic ( i ,  j ) Z  M ic (  j , i ) has been used). The free energy of the isolated protein can be expressed as: D G c Z 12 X ni Z 2 ;  j Z 2 q i  M c ð i ;  j Þ q  j  (5)and the free energy of the isolated ion in solutioncan be expressed as: D G i Z 12  q 1  M i ð 1 ; 1 Þ q 1  (6)The general solution for the electrostatic freeenergy for transferring the charge  q 1  from the bulkto an inhomogeneous medium with dielectric boundaries having both reaction field and staticfield terms may be expressed as: DD G Z ½ D G ic K D G c K D G i  Z 12  q 1  M ic ð 1 ; 1 Þ q 1 C X n j Z 2 q 1  M ic ð 1 ;  j Þ q  j C 12 X ni Z 2 ;  j Z 2 q i  M ic ð i ;  j Þ q  j K 12  q 1  M i ð 1 ; 1 Þ q 1 K 12 X ni Z 2 ;  j Z 2 q i  M c ð i ;  j Þ q  j (7)and: DD G Z 12  q 1 ½  M ic ð 1 ; 1 Þ K  M i ð 1 ; 1 Þ q 1 C q 1 X n j Z 2  M ic ð 1 ;  j Þ q  j 2435 C 12 X ni Z 2 ;  j Z 2 q i ½  M ic ð i ;  j Þ K  M c ð i ;  j Þ q  j 2435  (8)which can be written as: 5 DD G Z 12  q 21  A C q 1 B C C  (9)where  A  corresponds to the magnitude of thereaction field contribution,  B  to the magnitude of the static field contribution, and  C is a constant termdue to the influence of the dielectric constant of theion on the protein charges. The constant  A  dependson the geometry and the size of the high dielectricaqueous cavity. The constant  B  depends on theelectric field arising from the static charge distri- butiononchannelshieldedbythedielectricregions.In the case of a small ion, the constant  C  is normallynegligible ( x 0.2 kcal/mol) and the free energy of anion in theporecalculatedfromthePBequation istypicallydominatedbythecontributionsfromstaticand reaction field. 5,10,29 (note that  C  is exceptionallyequal to 2.5 kcal/mol in the case of the open statemodel I of KcsA because the presence of the ioninside the cavity creates a region of low dielectricconstant that gives rise to an unfavorable dehy-dration of Thr75).A special procedure was designed to efficientlydissect all the contributions to the total electrostaticfree energy of an ion along the channel axis.According to equation (9), the total free energy isdominated by the reaction field  D G rf  and the staticfield  D G sf  contributions. The reaction field contri- bution is calculated using  D G rf  Z [ D G ic K D G i ]. Thiscan be calculated using a single PB calculation inwhich the protein charge have been turned off tozero followed by a reference PB calculationcorresponding to the isolated ion in the bulk. Thestatic field contribution is a linear sum of the staticfield from each charges of the protein: D G sf  Z X N  j Z 2 q 1  M ic ð 1 ;  j Þ q  j Z q 1 f ic ð r ; q 1 Z 0 ; q 2 ; . ; q N  Þ ð 10 Þ In principle, extracting the static field contri- bution from each residue is possible by solving thePB equation for the field  f ic ( r ; q 1 Z 0, q 2 , . , q N  ), inwhichallproteinchargesareturnedoffexceptthoseof the residue of interest. However, such aprocedure is highly inefficient to obtain a fulldissection of the static field contribution per residue becauseitwouldrequireafullnumericalsolutiontothe PB equation for each specific residue. This can be avoided by exploiting the symmetry of theGreen’s function,  M ic (1,  j ) Z  M ic (  j ,1): D G sf  Z X N  j Z 2 q 1  M ic ð 1 ;  j Þ q  j Z X N  j Z 2 f ic ð r ; q 1 ; q 2 Z 0 ; . ; q N  Z 0 Þ q  j  ð 11 Þ To find the contribution from each specificresidue on the stability of ion in the cavity, theelectrostatic field  f ic ( r ; q 1 , q 2 Z 0, . , q N  Z 0), generated by the ion in the cavity is first calculated with allother charges turned off. Then, the interactionenergy between the static field and any specificresidue is calculated as a simple sum over all theprotein charges  q  j  (with  j Z 2, . , N  ). Using thismethod, the contribution from each individualresidue of the channel to the total static field can be obtained efficiently using a single PB equation. Atomic models In the calculations, all the channel atoms and the bound ions (two in the selectivity filter and one inthe vestibular cavity) are represented explicitly,with associated atomic charges and radii. Thecrystallographic structures of  the KcsA channel(PDB entry 1BL8 and 1K4C), 2,14 the MthK channel(PDB entry 1LNQ), 15 the pore domain of the KvAPchannel (PDB entry 1ORQ), 19 the KirBac1.1 channel Electrostatics in K  C Channels   275  (PDB entry 1P7B) 18 were used. As this studywas completed, the structure of the eukaryoticvoltage-activated Kv1.2 channel (PDB entry 2A79)was reported. 25 Comparison with the two TMhelices of the pore domain S5-S6 of the bacterialKvAP channel shows relatively small differences,with only 2.5 A˚RMS deviation for the C atoms andan intracellular opening of about 12 A˚radius. Thisshows that the pore domain of KvAP constitutes agood template for modeling the pore domain of Kvchannels in the open state. Missing hydrogen atomswere added using HBUILD within the CHARMMpackage. 30 In all these structures, the defaultprotonation state was used forallionizable residuesexcept for Glu71 in KcsA and Glu106 in KirBac1.1(equivalent to Glu71 in KcsA), which are proto-nated. 10,31 An open state model of KcsA was derived fromthe X-ray structure of the MthK channel (KcsAmodel I). To obtain a structural alignment, the backbone atoms of the pore helix and selectivityfilter of the KcsA channel (residues 60–81) weresuperimposed onto the corresponding atoms of theMthK channel using the “COOR ORIENT RMS”command of CHARMM. 30 The backbone coordi-nates of residues 19–31 in the outer helix (TM1) andresidues 68–98 in the inner helix (TM2) of the MthKchannel werecopied to map thepositionof residues28–40 (TM1) and 84–114 (TM2), respectively, in themodel open state of the KcsA channel. The side-chain were then reconstructed in the same rota-meric statesasinthehighresolutionX-raystructureof KcsA (closed state). The model was furtherrelaxed and optimized using adopted basis New-ton–Raphson (ABNR) energy minimization in thepresence of harmonic restraining potentials used tomaintain the secondary structure of the MthKchannel. The final model has the same side-chainrotamers as in the closed state KcsA, but the backbone conformation of MthK for the TM1 andTM2 helices. A model of KcsA in the open state based on the KvAP structure was also constructedaccording to the same procedure (KcsA model II).Additional intermediate models of KcsA werealso generated by interpolating the backbonedihedral angle values between the two end-pointsclosed and open states. The dihedral anglesrequired for generating intermediate structureswerecalculatedasalinearinterpolationfromclosedstatetoopenstate(modelI).Residues23–45inouterhelix (TM1) and residues 95–108 in inner helix(TM2) of closed and the modeled open state havevery different backbone dihedral values. The backbone dihedrals of these residues are changedto get the intermediate states. The side-chainrotamers were unchanged. The intermediate struc-tures were refined using energy minimization,fixing the invariant parts of the protein.Lastly, models of the closed and open state of Shaker were examined to broaden the scope of thepresent study. The model of  the closed state, basedon residue accessibility, 21–23 was kindly provided by Gary Yellen. The model of the open state of Shaker was constructed following the results of Bruhova & Zhorov. 24 It was derived from thestructure of the KvAP channel based on two keyobservations: (1) Cd 2 C locks the mutant V476C inthe open state by bridging the cysteine at position476 to the histidine at position 486 from the adjacenthelix; (2) Cd 2 C  blocks the locked-open doublemutant V474C/V476C by binding to the cysteineat position 474. Both models of Shaker were refined by using SCWRL 2.95 32 followed by energyminimization. PB computations All the channel structures are oriented with theirpore along the  Z -axis relative to the membrane(which extends in the  XY  plan). The negative  Z -axiscorresponds to the intracellular side and thepositive  Z -axis corresponds to the extracellularside. The center of the channel cavity is at  Z Z 0 A˚,located at the center of the membrane spanningfrom 12.5 A˚to  K 12.5 A˚. The aqueous solution(including the water-filled cavity at the center of the channel) is represented as a uniform continuummedia with dielectric constant of 80. The channelwith all explicit atoms is embedded into a lowdielectric planar slab representing the membrane.The hydrocarbon core of the membrane is rep-resented as a uniform sla b of 25 A˚thickness with adielectric constant of 2. 33 Avalue of 2 was assumedfor the dielectric constant of the protein interior. Awater probe of 1.4 A˚radius was used to define themolecular surface corresponding to the dielectric boundary. 29 To insure that the proper dielectricconstant is assigned to the interior of the pore andthe inner vestibule of the channel, a cylinder of radius  r  and  e Z 80 is first cut-out from themembrane slab before the channel structure isoverlaid onto it (the precise value of the radius isunimportant, as long as the edge of the cylindricalcut is covered by the protein structure). A radius of 8 A˚was used for the closed state KcsA and Shaker,8.5 A˚for the KirBac1.1, 15 A˚for the open state KcsAand MthK, 12 A˚for KvAP and the open stateShaker.All the PB calculations were performed in twostepswithacubicgridof130 3 points,startingwithagrid spacing of 1.0 A˚(with periodic boundaryconditions applied in the membrane  XY   plane),followedbyafocusing aroundthemain region witha grid spacing of 0.5 A˚. All the calculations wereperformed using the PBEQ module, 29,34,35 which isimplemented into the biomolecular simulationprogram CHARMM. 30 The atomic charges weretaken from the all-atom PARAM22 force field 36 of the CHARMM program. The atomic radii used todefine the protein–solvent dielectric boundary wereoptimized to reproduce the results of MD freeenergyperturbationcalculations with explicit watermolecules for the 20 standard amino acids. 34 The representation of the protein interior in termsof a dielectric constant is not unique and hasoften been the object of detailed discussion. 27,37,38 276  Electrostatics in K  C Channels 
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