the potassium channel: structure, selectivity and...

JOURNAL OF CHEMICAL PHYSICS VOLUME 112, NUMBER 18 8 MAY 2000

The potassium channel: Structure, selectivity and diffusionT. W. Allena)

Protein Dynamics Unit, Department of Chemistry, Australian National University,Canberra, Australian Capital Territory 0200, Australia

A. Bliznyuk and A. P. RendellSupercomputing Facility, Australian National University, Canberra,Australian Capital Territory 0200, Australia

S. KuyucakDepartment of Theoretical Physics, Research School of Physical Sciences, Australian National University,Canberra, Australian Capital Territory 0200, Australia

S.-H. ChungProtein Dynamics Unit, Department of Chemistry, Australian National University, Canberra,Australian Capital Territory 0200, Australia

~Received 14 December 1999; accepted 8 February 2000!

We employ the entire experimentally determined protein structure for the KcsA potassium channelfrom Streptomyces lividansin molecular dynamics calculations to observe hydrated channel proteinstructure, ion solvation, selectivity, multiple ion configurations, and diffusion. Free energyperturbation calculations display a significant ion discrimination of;9 kT in favor of the larger K1

ion. The protein forming the channel is very flexible yet is unable to fully solvate the Na1 ionbecause of its smaller size and large solvation energy. There is evidence that acidic and basicsidechains may dissociate in the presence of multiple K1 ions to explain experimental ion densitymaps. K1 diffusion is found to vary from approximately 10%–90% of bulk, supporting the highchannel currents observed experimentally. ©2000 American Institute of Physics.@S0021-9606~00!50617-5#

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I. INTRODUCTION

In this article we examine the structure, thermodynaics, and diffusion of ions within the KcsA potassium chanel. We employ coordinates obtained by 3.2 Å resolutx-ray diffraction studies of the potassium channel froStreptomyces lividans1 in molecular dynamics~MD! calcula-tions. The aim is to further our understanding of ion permation and selectivity within this complex biological ion chanel. Understanding the mechanisms behind the operatiothis channel is important because of the channel’s roleneuronal signaling, and its existence in all biological orgaisms.

The potassium channel has received considerable exmental attention recently, especially since the publicationthe KcsA potassium channel structure.1 Studies of gatingmechanisms, involving structural rearrangements,2,3 pHdependence,4 and experiments with similar potassiuchannels5–7 help us understand channel permeation andlectivity. While much about the potassium channel is berevealed, MD simulation of the hydrated channel protseems the only way to unveil microscopic details suchintrapore ion–ion interactions, ion solvation environmeand energy, and localized ion diffusion coefficients. Mstudies of model cylindrical channels,8–10 small bacterialpores such as gramicidin A11 and complex proteins like sodium and nAChR channels12,13 and the large OmpF porin14

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exist. However, to date, MD investigation into the potassiuchannel is limited to a simplified model channel,15 whereonly a small fraction representing the selectivity filter of tprotein is treated explicitly. This simplified model has shsome light on ion permeation and selectivity mechaniswith a minimal computational effort. However, a MD studinvolving the entire channel protein is the only way to etract important microscopic details with minimal model dpendence. The simulations reported here involve a combtotal of 63 ns requiring over 2 CPU years on a SilicGraphics Power Challenge R10000.

The aim of this MD study is to provide an improvechannel description that reproduces and reinforces expmental findings in the KcsA potassium channel. The mimportant property of the potassium channel is its abilityselectively conduct K1 ions with a high throughput~10pA16! while suppressing that of Na1 by at least a factor of104. Thus there must be a free energy barrier for the Na1 ionrelative to the K1 ion that explains this selectivity marginyet the energy profile, lateral ion positions, and levelsdiffusion coefficient should be such that a high K1 ion cur-rent is still possible. Ion positions within the outer channare suggested by ion difference maps,1 and multiple ion con-figurations from MD simulation should approximately reprduce these regions of high ion density. Water positions hnot been resolved experimentally, therefore, MD coordinaprovide a useful means for determining the ability of wato penetrate regions of the pore.

We first detail our model and then describe the struct

1 © 2000 American Institute of Physics

ct to AIP copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

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8192 J. Chem. Phys., Vol. 112, No. 18, 8 May 2000 Allen et al.

of the equilibrated solvated protein and the influence ofplied restraining potentials. Next we report protein potencalculations that are used to analyze the effect of charamino acid residues. We then describe ion coordination,tential energy profiles, and provide a free energy perturbaprofile to give some measure of the extent of ion discrimition within the model channel. Finally, we discuss waproperties, multiple ion configurations, and give estimatesthe ion diffusion coefficient within the channel. This comprehensive set of results should aid our understanding ofmicroscopic properties and conduction mechanisms undeing this important biological channel.

II. MODEL SYSTEM

Figure 1~A! illustrates the model KcsA potassium chanel protein structure, where two subunits of the tetramepeptide chains which form the channel are shown. Each sunit consists of 158 signature amino acid residues, of wh97 have been determined by x-ray diffraction.1 The entireexperimentally determined protein structure is employsuch that in total the model system consists of 396 residincluding terminal groups.17 Initial coordinates, described bDoyle et al.,1 are taken from the Protein Data Bank1bl8 set.The amino acid sequence is divided into segments of intein Table I.

The channel radius profile~accounting for atomic size!for the initial protein coordinates, in the absence of any wter, is shown in Fig. 1~B!. The channel extends from approxmately225 to 25 Å. The selectivity filter region adjacent

FIG. 1. ~A! Initial potassium channel protein structure and reservoir defitions. The outer helices and turrets~light gray ribbons!, pore helices~darkgray ribbons!, selectivity filter ~narrow black ribbons!, and inner helices~white ribbons! for two subunits of the tetramer are drawn.~B! The initialpore radius~accounting for van der Waals radii! is shown. Indicated are theselectivity filter, hydrophobic chamber, hydrophobic pore, and the intralular and extracellular reservoirs.


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the extracellular space extends fromz58 to 22 Å with amean radius of;1.4 Å. This region is lined with carbonyand hydroxyl oxygen atoms making it hydrophilic in naturThere is a large hydrophobic chamber region on the intrellular side of the selectivity filter extending fromz522 to8 Å with an average radius of;6 Å. The field of the porehelix dipole,18 in combination with the –COOH termina~threonine T74 residue! and the abundance of water in thcavity, is thought to stabilize ions and overcome the dieltric barrier within this hydrophobic segment.19

The long thin hydrophobic pore formed by the inner hlices leading to the intracellular space extends from220 to22 Å with a minimum radius of 1.5 Å. Spin labeling anelectron paramagnetic resonance experiments suggestthis conformation may correspond to a closed state2,3 andthat the conducting pore may be much wider. However, sithe dimensions of the hydrophobic pore are not likelyinfluence ion selectivity, and the pore may be made atrarily large by applying forces to the inner helicies, we cosider only the experimentally determined configuration. Tchannel entrances (225,z,220 and 22,z,25 Å! andthe reservoirs (25,uzu,35 Å! provide bulklike environ-ments and useful reference points. Reservoirs are formea harmonic bounding cylinder of radius 8 Å20 acting only onwater oxygen atoms and ions. Periodic boundaries areplied atuzu535 Å, enforced by a single image placed at eaend of the 70-Å-long segment in the axial direction.

The water in the reservoirs is sampled from equilibrabulk water in the rangeuzu.25 Å with radius less than 8 Åsuch that the mean water density is approximately 1 g/c3.The water within the channel (uzu<25 Å! is taken fromequilibrated coordinates with a simplified model of the ptassium channel.15 This simplified model employs aLennard-Jones~LJ! 5-3 potential at the pore lining throughout, except for the narrow hydrophilic selectivity filter regiowhere protein is treated explicitly. Any water molecule wian oxygen atom center closer than 2 Å to a protein atomcenter is moved away or into a reservoir. Water coordinainside and outside the channel are then combined. The nber of water molecules remaining after this procedure is 2

III. MOLECULAR DYNAMICS AND POTENTIALMODELS

MD simulations are performed using theCHARMM v.25code.21 A time step of 1 fs is used in the simulations with thVerlet algorithm. Velocity rescaling at 1 ps intervals leads

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TABLE I. KcsA signature amino acid sequence. The residues within esubunit of the experimentally determined potassium channel protein sture are divided into segments.

Segment Residues

N-terminal 22 CH3– CO–Outer helix 23–61 ALHWRAAGAATVLLVIVLL-

AGSYLAVLAERGAPGAQLITPore helix 62–74 YPRALWWSVETATSelectivity filter 75–79 TVGYGInner helix 80–119 DLYPVTLWGRCVAVVVMVA-

GITSFGLVTAALATWFVGREQC terminal 120 CH3– NH–


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8193J. Chem. Phys., Vol. 112, No. 18, 8 May 2000 The potassium channel

temperatures 29861 K. Coordinates are saved each 0.1for trajectory analysis. A switched force cutoff for electrstatic interactions and a switched potential cutoff for LJ 12interactions are applied to atoms at 12 Å, slowly turnedfrom 8 Å.22 The use of a 12 Å cutoff should prevent detmental effects on diffusion.23,24 Nonbonded interaction listsare recorded out to 13 Å and are updated at 5–10 fs interv

The extended simple point charge~SPC/E! watermodel25 is used in all simulations because of its abilityaccurately reproduce bulk water and ionic properties. SPLJ 12-6 parameters provided by Berendsen, Grigera,Straatsma25 are combined with ion–water parameters26,27

and ion–ion parameters.28 Ion–protein LJ 12-6 interactionare determined byCHARMM with standard combination rules

The united atom ~CHARMM19!29 and all hydrogen~CHARMM22!30 parameter sets are compared to see if expsimulation of hydrogen atoms have any effect on chanprotein and water structure. For example, CH3– is repre-sented by four atoms inCHARMM22, while CHARMM19 re-quires just one atom. After adding the necessary hydroatoms using appropriate bond lengths and angles, thenumber of protein atoms increases from 3504 to 59Equilibrated structures in the presence of water are founbe very similar with the SPC/E water molecules hydratthe pore equally well in both cases. Thus the inclusion ofhydrogen atoms does not appear to be necessary forpotassium channel study, and the additional computatiocost can be avoided.

The TIP3P model31 and its flexible version is found to bunable to solvate the hydrophilic interior of the selectivfilter region, even in the presence of a K1 ion. This wouldresult in energy barriers for a K1 ion attempting to traversethe channel. We note that the failure of the TIP3P wamodel to hydrate the selectivity filter is observed with bounited and all hydrogen parameter sets, despite the factthe all hydrogenCHARMM22 parameters are designed particlarly for use with the TIP3P model. The TIP3P and SPCwater models possess very similar atomic partial chargdipole moments, and Lennard-Jones forces, but havetrasting geometrical parameters. We conjecture thatlarger HOH angle of 109.47° for SPC/E water~in compari-son to 104.52° for TIP3P!, and the increased OH bond lengof 1 Å ~in comparison to 0.957 Å for TIP3P! aid the bridgingof carbonyl groups across the narrow selectivity filter poStable hydrogen bond networks seem to be unattainablethe TIP3P model.

IV. SHAPE OF THE HYDRATED CHANNEL

The structure of the potassium channel protein and wafter 150 ps of equilibration with a weak set of constraint32

is displayed in Fig. 2~A!. It is clear from this figure that thewater is solvating the entire pore of this channel, includthe narrow hydrophobic region toward the intracelluspace. Figure 2~B! displays the time averaged minimum efective pore radius calculated from the last 100 ps of dynaics. The pore radius in the hydrophobic region of the chanis highlighted in Fig. 2~C!. There has been little widening othe long hydrophobic region of the channel compared tooriginal coordinates, despite the reduced constraint stren


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Carbonyl and hydroxyl oxygen atoms reside at least 1from the pore lining in the region225<z<8 Å. Thus thisregion has maintained its hydrophobic nature after equilibtion.

V. CONSTRAINTS

In the present study, the lipid bilayer is not explicitsimulated, instead protein–lipid interactions are represenby some restraining potentials. We summarize results frour survey of restraining potential strengths here. A sinK1 or Na1 ion is placed at key positions within the hydratechannel, and at a reference point (z530 Å! in the extracel-lular reservoir. The ion is held at eachz value with a har-monic force constant of 20 kT/Å2, but is free to move in thexy plane. To ensure thorough equilibration, simulation peods of 250–650 ps are used. Simulations are perform

FIG. 2. ~A! Hydrated potassium channel structure after 150 ps of dynamThe intracellular half of one inner helix has been replaced by thin strandreveal the water positions within the long hydrophobic pore region.~B! Thetime averaged pore radius~accounting for van der Waals radii! is shown.~C!Comparison of equilibrated~solid line! and initial ~dotted line! pore radii inthe hydrophobic regions.


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with various strength restraining potentials applied toprotein to observe their influence on ion discrimination. Hmonic potentials, applied toa-carbon atoms on inner anouter helices, range from 0 to 20 kT/Å2.

Total system energies cannot be compared betwsimulations because of large variations, even after loequilibration periods due to motions of sidechains away frthe pore. For example, a tryptophan sidechain on the inhelix nearz5220 Å has been observed moving 6 Å in 3 ps~200 m/s! resulting in a;200 kT reduction in the total system energy. The effect of this on the pore radius is less t0.1 Å outwards motion restricted to the region223<z<219 Å. Thus, although such a large drop in system enecould suggest lack of equilibration, the change has littlefluence on important channel properties, and most importno influence on the ion energy margins within the selectivfilter.

Table II lists K1 and Na1 ion potential energies at positions near the center (z516.0 Å! and extracellular end (z520.4 Å! of the selectivity filter for various constrainstrengths. With the exception of 5 kT/Å2 where the differ-ence is within the error range, a significant energy marbetween the Na1 and K1 ions exists atz516.0 Å, irrespec-tive of the strength of applied constraints. We note that lamargins are also seen when constraints are only appliethe inner or outer helices. In fact, a large difference existthe absence of any applied constraints. Large potentialergy differences are also seen atz520.4 Å, where only forconstraint strengths 0 and 10 kT/Å2 are the differenceswithin the error range.

Free energy perturbations (K1→Na1) with respect tothe extracellular reservoir, described in Sec. IX, are also pvided forz516.0 Å in Table II. The free energy perturbatiocalculations also reveal a preference for the K1 ion overNa1. High perturbation values of 6–8 kT emerge for anonzero constraints. The lower value obtained in the abseof any constraints is not significant since it is difficultmaintain the protein geometry under such conditions for losimulation periods~800 ps!.

TABLE II. Effect of restraining potentials on ion energies. Ion potentenergies with respect to the reservoir (DE), and free energy perturbatiomeasurements for the transformation K1→Na1 with respect to the reservoi(DDA) are given for a range of restraining potentials. Values are provifor two test positions:z516.0 Å andz520.4 Å. The energies are listeagainst the strength of constraints (K) on inner and outer helixa-carbonatoms. Errors are61 standard error of means in potential energies, andtaken from hysteresis values for the free energy perturbations.

z K DEK1 DENa1 DDAK1→Na1

~Å! (kT/Å2) ~kT! ~kT! ~kT!

16.0 0 219.165.5 20.364.9 3.260.55 28.163.1 25.264.1 8.061.1

10 216.063.1 26.264.9 5.962.815 216.662.8 2.764.5 6.061.920 228.063.8 211.464.1 6.460.7

20.4 0 212.464.8 28.767.7 •••5 210.962.8 20.564.5 •••

10 29.163.1 29.163.3 •••15 211.363.1 22.264.5 •••20 213.463.8 2.965.9 •••


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As further evidence of the lack of involvement of aplied restraining potentials on ion discrimination we examthe constraint energy contributions to the total systemergy. The total constraint energy~excluding ion constraint!in the presence of a Na1 ion atz516.0 Å with respect to thatfor a K1 ion at the same position for constraints 5, 10, 1and 20 kT/Å2 is 21.861.2, 3.362.2, 0.262.4, and 2.062.7 kT, respectively. Since there is no consistent positcontribution of the constraint energy to the system enewhen a K1 is replaced by a Na1 ion, there should be littlecontribution to ion discrimination. This information permius to choose any strength of constraint within the tesrange. We choose 20 kT/Å2 to maintain stability of the entirestructure over long simulation periods. Similar strengthstraining potentials have been used in model nACstudies.33

VI. EFFECT OF CHARGED AMINO ACIDS

We examine the effect of charged residues by compaprotein potential profiles obtained from MD trajectories wineutral and charged amino acids. In charged protein simtions all glutamic and aspartic acid residues carry a unegative charge (2e) while the basic arginine residues havunit positive charge (1e). Atomic partial charges for neutraacidic and basic residues have been taken from LazaridisKarplus.34 Equilibrated positions of charged residues in tfirst subunit of the protein are listed in Table III. Near thextracellular entrance and selectivity filter region therethree pairs of oppositely charged residues, while nearintracellular entrance there is one pair that is likely to stalize cations in the pore. In the narrow hydrophobic poregion there exists one unpaired positive charge per subthat could destabilize cations.

Figure 3 compares electrostatic potential profilesneutral and charged proteins along the channel axis. Theues plotted are contributions from protein atoms only withlong-range potential truncation. Water contributions arecluded because of the considerable noise introduced by watoms approaching close to profile grid points. Rather thassign an arbitrary dielectric constant to the channel wawe plot the potential for a relative permittivity of 1, acknowedging that channel water will attenuate these electrostpotentials. The influence of positively charged arginine redues, not accompanied by any acidic residues, neaz5214 Å is to raise the potential in the narrow hydrophobpore region by;1.9 V ~or approximately 74 kT for a unitcharge!, despite their distance from the pore. Although mu

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TABLE III. Positions of charged amino acids from equilibrated sampcoordinates. Mean positions of carboxyl oxygens on glutamic acid~E! as-partic acid~D! residues, and of the guanidine carbon on arginine~R! resi-dues are listed. These are centers of high excess charge concentrationdues have been collected into likely pairs.

( r , z) ~Å!

E512 ~16.7, 22.9!, R52

1 ~23.4, 25.5!D80

2 ~9.2, 21.2!, R641 ~10.7, 25.2!

E712 ~6.1, 16.6!, R89

1 ~11.2, 19.5!R27

1 ~19.4,213.9!E118

2 ~3.6, 222.3!, R1171 ~11.9,222.2!


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of this potential may be shielded by water, it is fairly certathat the14e charge in this region would prevent condution. Near the intracellular entrance region we observe amatic fall in protein potential contributions~by approxi-mately 4.2 V or 162 kT! when residues become charged.the selectivity filter and extracellular entrance regionspotential falls by as much as 4.8 V~187 kT!. The generationof a deep second potential well nearz517 Å within the filterregion could have considerable influence on multipleconfigurations and permeation mechanisms.

In all remaining simulations only the neutral proteinconsidered. We comment later on the possible effectcharged residues on ion energies and multiple ion configtions. In MD simulations an integrated switched force cutis applied to electrostatic interactions. Figure 3 also shothe potential profile for the neutral protein with this cutoapplied. The effect of the truncation is negligible except nthe intracellular entrance, where a;0.7 V drop in potentialis observed.

VII. ION POTENTIAL ENERGY PROFILES

A single K1 or Na1 ion is placed at one of 19 differenpositions along the channel axis and simulation is carriedfor 150 ps. Ion potential energies,35 and separate water anprotein contributions, are plotted in Fig. 4 for K1 ~A! andNa1 ~B! ions. These profiles clearly depict the remarkaability of the protein to provide a stabilizing potential awater molecules are stripped away from each ion in thelectivity filter. For the K1 ion the protein accounts for nearlall of the ion’s solvation energy within the range 10<z<16 Å. As a result of the strong protein involvement, tK1 ion experiences low potential energies throughoutselectivity filter.

Potential energy differences with respect to the reserare plotted in Fig. 5 for both ion types. The K1 ion potentialenergy is as low as239.162.7 kT with respect to reservoirThe potential energy margin between Na1 and K1 ions is as

FIG. 3. Protein potential profile: Time averaged electrostatic potentialto the protein along thez axis is shown. The solid curve represents tsimulations with neutral amino acids while the dashed curve representsimulation with charged arginine, glutamic acid, and aspartic acid residThe dotted curve shows the potential profile for the neutral protein calated with a switched force long-range cutoff. The left-hand vertical adisplays the potential inV while the right-hand axis provides energy unicorresponding to a unit chargee.


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high as 2864.6 kT in the selectivity filter. We note that iopotential energies do not include all of the components nessary to describe channel permeation. Changes in thetein energy in response to the introduction of an ion coalso play a significant role. For example, the small positrelative potential energy for Na1 nearz520 Å would not besufficient to explain the inability of Na1 ions to enter the

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FIG. 4. Ion interaction energies of K1 ~A! and Na1 ~B! ions: Total inter-action energies with surroundings are drawn as solid curves~closed circles!,interaction energies with water as dashed curves~open squares!, and theinteraction energy with the protein as dotted curves~open circles!. Errorbars are61 standard error of means and are only shown if larger thanpoint symbol.

FIG. 5. Total ion potential energies with respect to the reservoir valuesdrawn for K1 ~solid curve, closed circles! and Na1 ~dashed curve, opencircles!. Error bars are61 standard error of means.


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channel from the exterior. In Sec. IX we measure the fenergy margin between K1 and Na1 ions. The inclusion ofentropy components should provide a better measure ofability of the channel to discriminate between these ioNevertheless, Fig. 5 gives an indication of the relative sbilities of the two ions at each position within the channand will help explain multiple ion configurations in Sec. X

Within the narrow hydrophobic segment of the chanthe Na1 ion potential energy is 10.665.1 kT above the ref-erence value, approximately 22 kT less stable than the1

ion. This narrow hydrophobic pore will exclude Na1 ionsfrom the channel, but will not prevent K1 ions from passing.Since Na1 ions are known to enter the intracellular mouththe channel and block K1 ion permeation,36 the presence osuch a barrier suggests that the conducting channel shhave a wider hydrophobic pore, in agreement with expmental gating studies.2,3

Figure 6 shows the separate contributions of segmenthe protein to the potential energy of the K1 ion. The porehelix potential energy contribution reaches a minimum286.561.2 kT at z'10 Å, at the intracellular side of theselectivity filter. Although the dipole of the pore helix remains directed toward the origin, the contribution of the pohelix is a maximum nearz'10 Å because of the stabilizineffect of the T74 carbonyl oxygen atom at the base of tpore helix. Note that the contribution of the selectivity filtprotein to the stabilizing potential in the wide chambergion is just as significant as that of the pore helix.

In the simplified model potassium channel15 the porehelices are represented by electric dipoles with char60.6310219 C, leading to an energy well of;60 kT for aK1 ion within the hydrophobic cavity. This well is seen to babout 40 kT in the present study. This suggests the ussmaller charges of approximately60.5310219 C ~based onthe well depth study of Allen, Kuyucak, and Chung15! for thesimple model dipoles to better represent the pore helices

The inner helix provides a249.462.8 kT stabilizingpotential energy nearz5220 Å, with some influence ovethe entire hydrophobic region. A small positive, destabilizi

FIG. 6. Protein contributions to the K1 ion potential energy: The curvelabeled SF, PH, and IH represent the contributions from the selectivity fi~solid curve, closed circles!, pore helix ~dotted curve, open circles!, andinner helix ~dashed curve, closed squares!, respectively. Error bars are61standard error of means and are not shown if they are too small to vie


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contribution of 112.860.8 kT is made by the inner helixnear the extracellular entrance of the selectivity filter. Tcontribution is evident as a bump in the total K1 ion poten-tial energy in Fig. 5. The contribution of the outer helixvery small throughout the channel, varying from appromately20.4 to 1.5 kT.

VIII. ION COORDINATION

In order to explain how the potential energy margiarise within the channel we first examine bulk solvation. Whave determined that within the reservoir region, the topotential energy of the K1 ion is 2216.662.0 kT, of which2173.161.7 kT comes from the first hydration shell and thremaining243.562.6 kT from outer hydration shells. Thtotal potential energy of the Na1 ion is 2281.362.3 kT andthe first shell contribution is2232.261.0 kT, leaving249.062.5 kT for outer shells to contribute. If both ionwere stripped to first hydration shells only, there would brelative barrier of 5.563.6 kT for the Na1 ion in comparisonto the K1 ion. Thus, the large potential energy margins oserved~Fig. 5! must come from inadequate formation of thfirst solvation shell of Na1. Because the first shell contribution of Na1 is much larger than that of K1 ~by ;60 kT!,small deviations from optimal bulklike first shell solvatiowill have a more drastic effect on Na1 stability. For ex-ample, if one were to artificially shift the bulk first hydratioshells of K1 and Na1 ions outwards by 0.1 Å,37 the contri-bution of the first shell to the ions’ potential energies wourise by 9.962.2 and 16.361.3 kT, respectively, resulting ina 6.462.5 kT energy margin.

Radial distribution functions~RDFs! for K1 and Na1

ions have been calculated at each position within the chapore. Figure 7 shows the positions of the first maxima inion–water oxygen and ion–protein oxygen RDFs for K1 ~A!and Na1 ~B! ions. The bulk first shell RDF properties arlisted in Table IV as a comparison. Both ion types expeence a close-packed first solvation shell throughout the chnel and reservoirs, except at some positions within the setivity filter. Averaging the difference between first ionprotein and bulk ion–water oxygen maxima over the ran8<z<21.7 Å results in a mean gap of 0.0360.02 Å for theK1 ion, and 0.1060.02 Å for the Na1 ion. The gap observedfor Na1 arises because protein oxygens are unable to min toward the ion enough to mimic water oxygens. Withbulk, the first Na1 shell ~density peaking at 2.32 Å! residesapproximately 0.44 Å closer to the ion than does that forK1 ion ~at 2.76 Å!. The protein oxygens may be held awafrom the Na1 ion by internal protein restoring forces whicprohibit large flexible motions, by external electrostatic avan der Waals interactions of the filter protein with the pohelix, by repulsive Coulomb forces acting between carbonon opposite sides of the pore, or may be pushed away fthe small ion by the larger hydrating water molecules eitside of the ion. Because K1 has a Pauling radius 1.33 Åapproximately equal to that of a water molecule (;1.4 Å!,little bending of the protein chain would be required to pemit good solvation. However, a smaller Na1 ion ~with Paul-ing radius 0.95 Å! at the same position would require larginward motions of central oxygens.

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Figure 8 illustrates the ability of the selectivity filter tproperly solvate K1, but not Na1 ions. The left panel of Fig.8~A! shows a side-on view of a sample of the protein awater structure in the presence of a K1 ion held nearz

FIG. 7. Solvation radii of K1 ~A! and Na1 ~B! ions: Positions of the firstmaximum in the RDFs for water oxygen~solid curves, closed circles! andprotein oxygen~dashed curves, open circles! are compared to the position othe first maximum in the bulk ion–water RDF~horizontal dash-dot line!.Errors are60.04 Å for all values.


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517.3 Å. The K1 ion is solvated by two water moleculeand six protein~four glycine and two valine carbonyl! oxy-gen atoms. Two of the four valine carbonyl groups hamoved away from the pore, possibly due to the unfavorainteraction they have with the ion’s hydrating water mo

FIG. 8. ~A! Sample coordinates for a K1 ion held nearz517.3 Å. Theleft-hand panel shows an orthogonal view of the protein and water strucat the end of the simulation. Only the selectivity filter segment of the pro~TVGYG where T5threonine, V5valine, G5glycine, and Y5tyrosine! isshown, and only two of the four subunits of the tetramer are drawn.large gray sphere is the K1 ion, small black spheres represent oxygen atomgray spheres represent carbon and nitrogen atoms, and white spheressent hydrogens. The right-hand panel of~A! shows the ion-glycine carbonyoxygen configuration as viewed from along thez axis. Here the gray sphereis the K1 ion and the white spheres are carbonyl oxygen atoms.~B! Viewsof the structure in the presence of a Na1 ion are shown.

st

waterescentwaterPC/E

is usedwhile

TABLE IV. Bulk ion propertiesr max, r min , n, andD are the first minimum and maximum in the RDF, the firhydration number and the diffusion coefficient, respectively.Dself is the water self-diffusion andt21 is thefirst-order inverse rotational correlation time constant of pure water. Simulations involve 528 SPC/Emolecules in a periodic box of side 25.08 Å at temperature 298 K. After 200 steps of steepest dminimization and 50 ps of heating and equilibration, 100 ps of dynamics is used to determine pureproperties. A single ion is added, removing water molecules within 2.6 Å of the ion center, leaving 525 Smolecules. After 200 minimization steps and 50 ps of heating and equilibration, 500 ps of trajectory datato produce bulk ion diffusion estimates. Errors in hydration results are estimated from distribution dataerrors in diffusion coefficients are61 standard error of means.

Property K1 Na1

r max ~Å! 2.7660.04 @2.7a# 2.3260.04 @2.4a#r min ~Å! 3.6560.15 3.1060.08n 7.260.4 @5.5b# 5.5660.03 @4–6c#D (Å 2/ps! 0.1460.01 @0.1957d# 0.0960.01 @0.133e#Dself (Å 2/ps! [email protected]#t21 ~ps21! 0.1960.01

aReference 38. dReference 41.bReference 39. eReference 42.cReference 40.


dinneiniis

o

A

yllecto

oe

mreis

t

ath

ut

of

orne

in

in-

rge

he

ir

he

nori-


ecules, lack of space near the ion, or the hydrogen boninteraction offered by the hydroxyl group on the tyrosisidechain. We note the obvious flexibility of the protewhere one of the two subunits shown has been shifted wrespect to the other, helping solvate the ion. This flexibilityin agreement with the experimental findings of Kiss, LTurco, and Korn.5 The right-hand panel of Fig. 8~A! revealsthe close fit with neighboring glycine-carbonyl oxygens.good fit with the two valine-carbonyl groups also occurs.

Figure 8~B! shows the structure with a Na1 ion heldnearz517.3 Å. We note that the flipping of valine-carbongroups increases available volume for those water molecuand is likely to reduce the repulsive electrostatic forces aing between opposite carbonyl groups. The hydrating wamolecules would provide obstacles to the inward motionvaline and tyrosine carbonyl groups, and because of strpotentials maintaining the shape of the valine-glycintyrosine linkage, their presence could be to some degreesponsible for the poor Na1-carbonyl fit. The right-handpanel of Fig. 8~B! displays the Na1-glycine carbonyl oxygenarrangement. In order to achieve the bulk coordination nuber of approximately 6, all four of the glycine oxygens arequired within the first shell of the ion. However, in thsample the mean gap of approximately 0.21 Å would leadan energy barrier. Figure 9 shows the RDFs for K1 ~A! andNa1 ~B! for water and protein oxygens for an ion held nez517.3 Å. This time averaged representation reinforcesview of the poor fitting of the first solvation shell of the Na1

FIG. 9. Radial distribution functions for K1 ~A! and Na1 ~B! ions held nearz517.3 Å. Solid curves show the ion–water oxygen RDF while dascurves show the ion–protein oxygen RDF.


g

th

-

s,t-erf

ng-re-

-

o

re

ion. A similar picture emerges at each position throughothe selectivity filter.

Figure 10 displays the first shell coordination numbersK1 ~A! and Na1 ~B! ions. Throughout the filter region bothions appear to maintain first solvation numbers equal togreater than bulk, with just a small loss of less than ooxygen for the K1 ion atz523 Å. However, both ions showconsistent reductions from bulk of their solvation numbersthe narrow hydrophobic pore. The losses for the K1 ion donot seem to have affected its potential energy adverselythis region, whereas the Na1 ion has developed a large potential energy barrier~see Fig. 5!, illustrating the difficultythe smaller ion faces in attempting to achieve such a lasolvation energy. Since protein contributions to K1 and Na1

ions in this region are identical~to within errors!, they con-tribute nothing to the observed potential energy margin. Tmargin arises from poor first shell solvation of the Na1 ion.The first shell contributions to the K1 and Na1 ions at z5210 Å, for example, are2166.663.2 and2208.264.2kT, or 6.563.6 and 24.064.3 kT greater than the reservovalues.

d

FIG. 10. Solvation numbers of K1 ~A! and Na1 ~B!: First water~dashedcurves, open squares!, protein~dotted curves, open circles!, and total~solidcurves, closed circles! solvation numbers taken from integrated distributiofunctions are plotted. The bulk first hydration numbers are drawn as hzontal dash-dot lines.


ery

eeresf tip

d-inenn

ndin

ois

aritynto

el

inr

nio

io

thre

is

th

d

ath

ra-

fileain

t toout

d,

rt a

ow-theisese-hey-pic

half.m-c-

rgyn-l-

note of

ro-inb-

8.en,

rans-


The angleC a water dipole makes with the ion–watvector within the first hydration shell of the ion is given b

C5cos21F r IH2 2r IO

2 2r OH2

2r IOr OH cosa G , ~1!

wherer IO andr IH are the positions of the first maxima in thion–water oxygen and ion–water hydrogen RDFs, resptively, and r OH51 Å and a554.74° for the SPC/E watemodel. Variations of up to 45° from the reservoir valuhave been observed for both ion types near the center oselectivity filter. Occasionally one water molecule may flfrom its natural orientation~negatively charged oxygen atomdirected towards cation! as a result of strong hydrogen boning of the water with the carbonyl groups of the proteHowever, the protein appears to be able to compensatstabilizing the ion with its polar groups. Thus we can seedirect correlation between hydration water orientations aion potential energy margins within the filter region, aattribute most of the discrimination to the poor fit of proteoxygens within the Na1 solvation shell.

In summary, toward the center and extracellular sidethe filter region where the influence of the pore helix fieldreduced, and water contributions to the ion solvationsmall, both ions rely strongly on coordination by selectivfilter protein oxygen atoms. The close fit of protein oxygein the K1 shell, and the small solvation energy requiredstabilize that ion, result in a deep potential energy wHowever, when water contributions are limited, Na1 re-quires a much larger stabilizing potential from the proteatoms. The carbonyl and hydroxyl groups are unable to pvide this amount of energy, and the Na1 ion experiences aless favorable environment.

IX. FREE ENERGY PERTURBATION

The ability of the channel to discriminate between K1

and Na1 ions is best determined by calculation of free eergy differences. We employ the free energy perturbatmethod43 using thePERT and WHAM facilities of CHARMM.The quantity we calculate

DDAK1→Na1~z!5DAK1→Na1~z!2DAK1→Na1~z0!, ~2!

is the free energy change associated with the creatannihilation transformation of a K1 ion into a Na1 ion withrespect to the reservoir reference value atz0 . EachDA is anaverage of forwards and backwards transformations. IfDDA value is positive it means that more energy is requito transform from K1 to Na1 within the channel than isrequired in a bulklike environment, thus indicating that itless likely for a Na1 ion to exist at that point than a K1 ion.Similar calculations have been carried out in the past forgramicidin channel44 and a simple model potassiumchannel.15 Following equilibration, with an ion constraineat a z coordinate, potential parameters of the K1 ion aretransformed into those of the Na1 ion in six windows of 20ps ~5 ps equilibration and 15 ps ensemble generation!. Re-verse transformations begin after equilibration with a N1

ion. Free energy perturbation values used for examining


c-

he

.byod

f

e

s

l.

o-

-n

n/

ed

e

e

effect of constraints on selectivity~Sec. V! involve longer 50ps windows~30 ps equilibration and 20 ps ensemble genetion!.

Figure 11 shows the free energy perturbation prothroughout the channel. The free energy changes rempositive, or near zero over the entire channel with respecthe extracellular reservoir. The difference is large throughthe selectivity filter, reaching a maximum of 8.660.5 kT atz517.3 Å. This free energy difference would corresponvia a Boltzmann factor, to a selectivity margin of 5.43103,complying with experimental evidence of a;104 margin inion conductances. We note that Fig. 5 appears to suppolarge margin between Na1 and K1 ions in the range 8<z<10.2 Å due to effective solvation of K1 by threonine resi-dues near the chamber entrance of the selectivity filter. Hever, Fig. 11 reveals that only a small margin exists infree energy. Therefore the greatest ion discrimination arwithin the selectivity filter and not within the chamber rgion, as one may be led to believe from Fig. 5. Also, tlarge Na1 – K1 potential energy difference in the narrow hdrophobic pore has not been completely annulled by entrocontributions.

The free energy differences observed here are aboutthe values obtained with a simple selectivity filter model15

In that study, only the filter segment of the protein is eployed with harmonic constraints used to mimic all interations with the remaining structure. The larger free enedifference can be attributed to the reduced flexibility icurred by applying constraints directly to the selectivity fiter. Although investigations showed that energies didchange much when constraints were varied, the presenceven quite small constraints applied directly to the filter ptein is sufficient to prevent the large deformations seenthis improved channel model. An example of this is the suunit shifting and flipping of carbonyl groups seen in Fig.Nevertheless, the same mechanisms found in AllKuyucak, and Chung15 hold in this study, and it is only themagnitude of the discrimination that has been reduced.

FIG. 11. Free energy perturbation profile: Free energy changes for the tformation K1→Na1 with respect to the reservoir (z530 Å! value are plot-ted. Errors bars represent the hysteresis in each measurement.


ers

tng

tn

thlath

rAtoio

ona

diaiuexoethhynhe

de

nd

lf-totethth

ly

enre

so afu-

ta-or-an-g

heelf-ta-

e-aseon-

re-ac-fil-m

ehiningtal

00

gyo-ter

e

ber

hea--

theofu-

redef ans

Tthe

bud


X. WATER PROPERTIES

Water self-diffusion coefficients are calculated by avaging the mean square displacements of water moleculeing an overlapped data procedure.45 We consider the range0.5–10 ps after the initial shoulder, which correspondsinertial motion within the hydration cage. Before calculatidiffusion coefficients, the center of mass of the systemsubtracted to remove any net momentum associated withperiodic boundary. We consider only axial diffusion giveby

Dz51

2

d

dt^@z~ t !2z~0!#2&. ~3!

Water rotational correlation is determined by analyzingdecay of the dipole autocorrelation. The dipole autocorretion function is defined as the time and system average ofcosine of the anglex(Dt) a water dipole at timet01Dtmakes with its dipole at timet0 . The sampling procedure fothis calculation is identical to that used for diffusion.mono-exponential decay is justified by analysis of the aucorrelation functions and the inverse rotational correlattime is given by

t2152d

dtln^cosx~Dt !&. ~4!

Table V includes mean water density, rotational correlatiand self-diffusion estimates for the hydrated potassium chnel. Only those waters within the channel pore, having raposition less than the time averaged minimum pore radare included in density and diffusion estimates. Thiscludes molecules embedded in the protein outside the pThroughout the entire channel and reservoirs the water dsity remains approximately the same as bulk. Despitesmall dimensions of the long hydrophobic pore, and thedrophilic nature of the selectivity filter region, self-diffusioremains above 1/4 of bulk self-diffusion throughout tchannel.

We compare our results to those for the simple mochannel of Allen, Kuyucak, and Chung.15 Mean axial self-diffusion in the selectivity filter, hydrophobic chamber, along pore regions of this model channel were;7%, 71%,and 141% of bulk self-diffusion, respectively. The sediffusion in the selectivity filter has risen in comparisonthe simple model because of increased flexibility of the filprotein. It has fallen in the chamber region because ofless spherical shape and the significant involvement of–COOH termini of the pore helices, now treated explicit

TABLE V. Pure water properties: Water density (r), first-order inverserotational correlation time constant (t21), and self-diffusion coefficients(Dz) are given for the three segments of the channel. The percentvalues correspond to the axial self-diffusion where bulk values are listeTable IV. Errors are61 standard error of means.

Segment~Å! r ~g/cm3! t21 ~ps21! Dz ~Å 2/ps! % bulk

8<z<22 Å 1.06 0.02560.009 0.0660.05 26621%22<z<8 Å 1.01 0.06060.007 0.0960.01 3966%

220<z<22 Å 1.01 0.04860.008 0.0660.01 2665%


-us-

o

ishe

e-e

-n

,n-l

s,-re.n-e-

l

ree

.

The self-diffusion in the long hydrophobic pore has besignificantly reduced as a result of narrowing of the pofrom minimum radius 3 to;2 Å in this model, and thepresence of wall structure. Reduced water density was alcontributing factor to the enhanced hydrophobic pore difsion in the simplified model.

It is seen in previous work10,15 that there is a strongrelationship between axial self-diffusion and inverse rotional correlation. Average first-order inverse rotational crelation time constants from the simplified potassium chnel model15 in the selectivity filter, wide chamber, and lonpore are approximately 0.005, 0.06 and 0.12 ps21, respec-tively. The inverse time constants~Table V! have risen in thefilter region and fallen in the hydrophobic segments of tchannel in this work for the same reasons the axial sdiffusion was seen to change. The reduction of inverse rotional correlation in the hydrophobic regions is likely to dcrease the shielding ability of the water and thus increelectrostatic interactions between ions and protein. In ctrast the increase int21 in the selectivity filter is likely tocause some shielding of electrostatic forces within thatgion. We conjecture that this could lead to reduced intertion energies and ion–ion distances within the selectivityter, altering the preferred multiple ion configurations frothose observed by Allen, Kuyucak, and Chung.15

XI. MULTIPLE ION CONFIGURATIONS

To investigate multiple ion configurations, two or threK1 ions are added to the channel at various positions witthe selectivity filter and wide hydrophobic chamber, creatconfigurations similar to those anticipated by experimendata1 and simple model simulations.15 A total of 30 simula-tions, in the absence of any external field, of length 150–2ps are carried out. The optimum position of a single K1 ionwithin the channel would be governed by its free enerprofile. Ignoring entropic contributions, the ion potential prfile in Fig. 5 suggests that an ion inside the selectivity filregion would prefer to reside nearz58 – 10 or 16 Å. Wheninitially two ions are placed within the selectivity filter, thmean coordinates after simulation are$10.0, 16.4% Å, whilewhen one ion is placed in the filter and one in the chamthe mean coordinates are$5.0, 15.0% Å. These two configu-rations are illustrated in Figs. 12~A! and 12~B!, respectively.

The potential energy profile of Fig. 5 indicates that tion nearz55 Å observed, in our second two ion configurtion, would prefer to reside nearz58 – 10 Å due to the presence of a deep well. However, there is evidence, based onfree energy perturbation results of Fig. 11, that the depththis well may be considerably reduced by entropic contribtions. Considering ion–ion repulsion may lead to a preferz55 Å equilibrium position. However, we remark on thpossibility that there is some obstacle to the passage oion from z55 to 10 Å. Analysis of mean ion radial positionsuggests that energy minima for the K1 ion are considerablyoff axis in the hydrophobic chamber region~by as much as2.3 Å!. Examination of sample coordinates where a K1 ionresides near the mean position (z'5 andr'2.3 Å! revealsthat the distances of the ion to carbonyl oxygen atoms on74

and T75 residues are 4.68 and 5.38 Å, respectively, while

lkin


heithnuil

in

th

ap-er,oneage

here-

n

ra-

ty

end

ly-

ourx-arenelar

otri-

or a

theed.

that

a-eri-t byelyeri-sedl-es.e ofenta

nsofg

ofe

h

e

n


distances to hydroxyl oxygens on T74 and T75 are 8.05 and2.76 Å. Thus, as a result of the flexibility of the protein, tion appears to bind to the base of the selectivity filter wstrong interactions from neighboring residues at the termiof the pore helix. While this is the case after extended equbration periods, this binding may be avoided in a conductchannel. Finally we note that a K1 ion placed beyondz'19 Å may be easily ejected from the channel.

Now consider three unconstrained ions placed within

FIG. 12. Multiple ion configurations. Sample coordinates representativthe two most frequently observed two ion~A and B!, and three ion~C andD! configurations are shown. The large gray spheres are the K1 ions, smallblack spheres represent oxygen atoms, gray spheres represent carbonitrogen atoms, and white spheres represent hydrogens.


si-g

e

selectivity filter and chamber regions in the absence ofplied electric fields. If two ions are placed too close togethespecially with one ion near the extracellular entrance,ion is expelled from the channel. In this case the averpositions of the remaining two ions is$3.3, 15.4% Å, a con-figuration seen in two ion simulations. In no instance is tselectivity filter seen to hold three ions. One ion alwayssides in the wide chamber region with meanz value 2.0 Å,and two ions in the selectivity filter. Two discrete three ioconfigurations arise with mean positions$2.0, 9.6, 15.6% and$2.0, 11.4, 19.3% Å as illustrated in Figs. 12~C! and 12~D!.From two ion simulations the latter of these two configutions is thought to be fairly unstable.

Experimentally, regions of high ion probability densiare seen near the middle of the wide chamber region~z be-tween 0 and 5 Å!, a broad peak toward the intracellular sidof the selectivity filter adjacent to threonine carbonyl ahydroxyl oxygen atoms~betweenz58 and 13 Å!, and to-ward the extracellular side of the filter between central gcine and tyrosine carbonyl rings~betweenz518 and 20 Å!.The occurrence of positions 2.0, 9.6, 11.4 and 19.3 Å inmultiple ion simulations is therefore in agreement with eperimental findings. The configurations observed herealso in agreement with those seen in simplified chanstudies.15 However, the frequent occurrence of an ion nez515– 16 Å in two and three ion configurations is nstrongly supported by experiment. Comparison with expement is made difficult by the low resolution~4.0 Å! of the Rbdifference map of Doyleet al.1 However, it is likely that theneutral protein model used here results in a preference fz515– 16 Å position over az518– 20 Å position. In Fig. 3we see a deep potential energy well in the outer end ofselectivity filter when acidic and basic residues are chargIt is possible that the presence of multiple K1 ions causesdissociation of these residues, leading to an energy wellincreases the propensity for a K1 ion in the outer region ofthe selectivity filter. If this were the case then any combintion of two or three ion states could reproduce the expmentally determined ion positions. It has been pointed ouAllen, Kuyucak, and Chung15 that because of the relativinstability of the three ion configurations, it is more likethat a combination of two ion states is responsible for expmental ion density maps. However, the possible increadielectric response of water within the selectivity filter, aluded to in Sec. X, could help stabilize the three ion statFinally, the idea of having charges created by the presencmultiple ions in the channel is preferable to permancharges since such stabilizing fields could eliminate a N1

energy barrier to conduction in the absence of K1 ions.To observe the effect of external fields on ion positio

in the chamber and filter regions, a total of 25 simulationslength 400 ps with a strong 7 mV/Å applied field pushinions outwards or inwards~intracellular–extracellular orextracellular–intracellular! are carried out. In the presencea strong 7 mV/Å field pushing cations out of the cell, thonly two ion configurations seen have mean coordinates$5.3,12.4% or $5.5, 15.6% Å. With the opposite driving force theonly two ion configurations seen are$9.5, 16.0% and $9.6,19.8% Å. Note that this driving force is not sufficient to pus

of

and


ee

ele

ioe

oed

iomsed

ffigr

si,antr

n.afro

hm

b-coreitssioroy-

ofen

t,thestin

lkre

fu-el

cli-K

erity

an

canlicr

ancy

re-lix

3e

-to

ofr-e

inthe

ncet

-ingideÅ

ratedri-

n


an ion from the energy minimum nearz510 Å into the hy-drophobic chamber within 0.4 ns. With three ions maintainin the channel in the presence of an outwards external fithe mean configuration is$5.1, 12.3, 18.1% Å.

XII. ION DIFFUSION COEFFICIENTS

Table VI lists mean ionic diffusion values in the thresegments of the channel. The results given involve a tota17 simulations of length 200–400 ps with three ions placin the channel in the absence of any applied field. Diffuscoefficients in the presence of a strong external electric fiare found to be similar and are therefore not reported. Cficients are calculated using the same procedure as usewater self-diffusion.

In the selectivity filter region 10% of bulk K1 ion diffu-sion is observed on average. We note that analysis oftrajectories reveals that ion motion is governed by Coulointeractions between ions rather than by diffusive procesAn illustration of this is given by Allen, Kuyucak, anChung.15 Brownian dynamics studies46 have shown that thechannel achieves high conductances with diffusion coecients at this level. We remark that the 12 Å long-rancutoff, although not expected to interfere with ion–ion inteactions within the short selectivity filter region, could posbly prevent ions from traversing the entire channel. Thusone were to further this current investigation to study chnel permeation, alternative treatment of long-range elecstatic forces, such as Ewald summation,47 may be required.

In the wide hydrophobic region the K1 ion exhibitsaround half of its bulk diffusion. In the same region a Na1

ion experiences only approximately 1/6 of bulk diffusioHowever, because multiple ion configurations with the N1

ion have not been attempted, this measurement comesplacing a single Na1 ion in the hydrophobic cavity. Figure 5shows that, in the absence of Coulomb repulsion by otions, this ion may be locked in a local energy minimureducing its mean square displacement.

In a separate set of simulations, a single K1 or Na1 ionis placed at one of several positions in the long hydrophopore region and a series of 163200 ps simulations are performed for each ion so as to compute average diffusionefficients. The operation of the long hydrophobic poformed by the inner helix is likely to be dependent ondimension. If the atoms are rigidly held near the initial potions, ions may be unable to traverse the pore. Therefwhen simulating ions in this long narrow region we empla weaker set of constraints.32 This permits the region to ex

TABLE VI. Ion diffusion results. Estimates of axial ion diffusion are givefor each region of the potassium channel. Errors are61 standard error ofmeans.

Ion Segment~Å! Dz (Å 2/ps! % bulk

K1 8<z<22 0.01460.003 1063%22<z<8 0.07060.008 5069%

220<z<22 0.1260.07 86656%

Na1 22<z<8 0.01560.002 1764%220<z<22 0.0360.01 37616%


dld

ofdnldf-for

nbs.

-e--if-

o-

m

er

ic

-

-e,

pand slightly in the presence of a hydrated ion. Diffusionthe K1 ion varies depending on the position of the ion. Whan ion is placed near the wider pocket atz'215 Å, little iontranslation is observed, whereas an ion placed atz'210 Åwill quickly move toward the wide chamber region. In facdiffusion ranges from near zero up to almost four timesbulk value with an average value of 86% of bulk. The famotion of ions is in agreement with trajectories observedBrownian dynamics simulations.46 As a comparison the Na1

ion shows moderately low diffusion, with around 1/3 of buion diffusion on average throughout the narrow long poregion. Because of the smaller size of the Na1 ion, it doesnot experience such large fluctuations in diffusion.

We compare our results for K1 ions with those found byAllen, Kuyucak, and Chung.15 In that model the K1 diffu-sion remains close to bulk levels (.50%! throughout thehydrophobic pore, and drops to as low as 8% of bulk difsion in the selectivity filter. We again note that the modchannel is as much as 1 Å wider throughout the hydrophobipore, which should enhance diffusion. However, the simpfied model appears to give a reasonable description of1

ion diffusion throughout the channel.Ion diffusion results may also be compared to oth

model channels. A suitable comparison for the selectivfilter region would be gramicidin A where K1 ion diffusionranges between 29% and 49% of experimental bulk.48 Sincethe potassium channel selectivity filter is narrower thgramicidin ~with radius;2 Å!, our estimate of;10% ofbulk diffusion is in reasonable agreement. The resultsalso be compared to those for narrow hydrophicylinders.10 A radius 2.1 Å cylinder with a regular moleculawall has mean Na1 diffusion of around 20% of bulk. Alarger K1 ion in a smaller hydrophilic pore should lead tosmaller diffusion coefficient, and thus there is a consistebetween the models.

We make comparison of wide hydrophobic chambersults with a nAChR model channel created by an M2 hebundle. The pore is as narrow as 6 Å radius and supports 2/of bulk Na1 ion diffusion.49 This result compares well to th50% K1 diffusion observed in the 5 Å hydrophobic chamber. We compare our narrow hydrophobic pore resultsthose within atomic periodic cylinders10 of radius 2.1 Å. Na1

diffusion in this cylindrical channel is approximately 18%bulk diffusion. While this value is lower, it compares favoably to our result of;37% for the hydrophobic pore of thpotassium channel. Results for a 2 Å exponentially repulsivecylindrical pore9 show around 15% of bulk Na1 diffusion,also in fair agreement. Thus our ion diffusion results withall segments of the potassium channel are consistent withexisting estimates from model pores.

Given the high levels of K1 ion diffusion throughout thehydrophobic regions of the potassium channel, and evidethat 10% diffusion within the selectivity filter does nogreatly attenuate conductances,46 we expect a high throughput of ions within this channel. Ions are observed remainclose to the channel axis in all segments except the whydrophobic cavity where a mean radial position of 2.3occurs. However, these mean positions have been genewith a single ion held at the one position for extended pe


ltec

onin

ed

epa

inido

ict oaanaudr

ieFastiauece

ene

teheth

blerybid–itym-

nrk/E

raty

anmrlal

beritthee-onlix.

tois

that

-pe-

lden-

on

e

iesy-tsin

d byo-ibleen-

ane-uts-

er

S.

try

an,

sson,

.


ods. The presence of one or two ions in the selectivity fimay hold the third ion away from the pore helix and seletivity filter –COOH termini~where the ion appears to bind!.In fact, three ion configurations show a preference forz52rather than 5 Å for an ion in the chamber. In this case the iwould reside closer to the axis, primed for its passagethe selectivity filter once a vacancy occurs.

XIII. SUMMARY AND CONCLUSION

Simulations with the entire experimentally determinprotein structure of the KcsA potassium channel fromStrep-tomyces lividanshave been reported. The inclusion of thentire protein has reduced model dependencies in comson to previous simulations with a simplified model.15 Themodel dependencies are limited to the size of constraapplied to the outer regions of the protein to mimic the lipbilayer, the water model, and the extent of dissociationacidic and basic sidechains within the protein, each of whhas been investigated in this study. A survey of the effecrestraining potentials reveals that, within the regime of weharmonic constraints on inner and outer helices, the restring potentials have negligible effect on ion discriminatioSecond, comparison of water models shows that TIP3P,its associated flexible model, are inappropriate for the stof narrow hydrophilic regions such as the selectivity filteThe excellent description of bulk water and ion propertmakes SPC/E the obvious water model for this study.nally, the effect of charged arginine, glutamic acid, andpartic acid residues on protein contributions to the potenprofile has been determined. It is likely that these residwill remain mostly neutral. However there is some evidenof the need for charged sidechains near the extracellulartrance. It is possible that experimentally determined ion dsities may only be achieved if an additional deep energy wnear the extracellular end of the selectivity filter were creaby some of these charged residues. The generation of tcharges by dissociation in the presence of multiple ions ismost likely occurrence as this would maintain the Na1 ionenergy barrier in the absence of K1 ions.

The inclusion of the entire protein leads to consideraflexibility of the selectivity filter, resulting in enhanced watdiffusion and rotation. Large motions of carbonyl and hdroxyl groups on the selectivity filter protein have been oserved. While these large motions are not required to provK1 – Na1 ion discrimination, they do alter the ion–proteinwater arrangements and affect the level of ion selectivThe reduced ion discrimination with this flexible potassiuchannel model leads to;9 kT free energy difference between K1 and Na1 ions ~in comparison to 18 kT with thesimplified model!. The corresponding selectivity margiwould be of the order 104 as seen experimentally. We remathat measurements of selectivity found with the SPCmodel may be underestimated because of the exaggeK1 ion coordination, which reduces relative ion stabiliwithin the channel.

The explicit inclusion of the pore helix has providedabsolute measure of the stabilization within the wide chaber region, whereas this was a free parameter in the easimplified model. The minimum of the pore helix potenti


r-

to

ri-

ts

fhfkin-.ndy

.si--ls

en--lldsee

e

--e

.

ted

-ier

has shifted from near the center of the hydrophobic chamto the bottom of the filter. This is a result of the explictreatment of the –COOH terminus on the pore helix andincreased flexibility of the selectivity filter protein. The slectivity filter protein contributes as much to the stabilizatiof ions in the hydrophobic chamber as does the pore he

The shape of the narrow hydrophobic pore is seenchange little after hydration. Even when the inner helixheld by very weak constraints, it remains narrow~radius;2Å! after extended simulation periods. There is evidencethis may correspond to a closed conduction state.2,3 Despitethe small dimensions of the pore, the K1 ion remains ener-getically stable while the Na1 ion, because of its large solvation energy, is poorly coordinated in this region and exriences destabilization. Thus Na1 ion would be excludedfrom the intracellular pore in this current model, and woutherefore be unable to block the channel as seen experimtally. This supports the notion of a wider open conductistate.

Finally, ion diffusion within the channel is seen to rangfrom ;10% in the selectivity filter to as high as;90% inthe narrow chamber. These results confirm earlier studwith the simplified potassium channel model. Brownian dnamics simulations46 have demonstrated that high currencan be achieved with a reduced ion diffusion coefficientthe filter, because the permeation mechanism is governethe Coulomb repulsion of ions, and not by diffusive prcesses. The fact that ion diffusion is not reduced to negliglevels supports the high throughputs measured experimtally.

ACKNOWLEDGMENTS

This work was supported by grants from the AustraliResearch Council and the National Health & Medical Rsearch Council of Australia. All calculations were carried owith the Silicon Graphics Power Challenge and Alpha Cluter of the ANU Supercomputer Facility. We thank Dr. RogBrown for his help in compilingCHARMM on the Alpha plat-form.

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s ainatye

s

mon

mi

.

.

owio

n-he

ce

s-

hys.


zler, T. Steinkamp, and R. Wagner, EMBO J.14, 5170~1995!.17Because terminal groups are not present in experimental coordinate

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ndll

ic

-

L.

n,

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the potassium channel: structure, selectivity and...

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