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Simulations of ion channels – watching ions and water move
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Simulations of ion channels – watching ions and water move Mark S.P. Sansom, Indira H. Shrivastava, Kishani M. Ranatunga and Graham R. Smith Ion channels mediate electrical excitability in neurons and muscle. Threedimensional structures for model peptide channels and for a potassium (K1) channel have been combined with computer simulations to permit rigorous exploration of structure–function relations of channels. Water molecules and ions within transbilayer pores tend to diffuse more slowly than in bulk solutions. In the narrow selectivity filter of the bacterial K1 channel (i.e. the region of the channel that discriminates between different species of ions) a column of water molecules and K1 ions moves in a concerted fashion. By combining atomistic simulations (in which all atoms of the channel molecule, water and ions are treated explicitly) with continuum methods (in which the description of the channel system is considerably simplified) it is possible to simulate some of the physiological properties of channels. ION CHANNELS ARE transmembrane (TM) proteins that enable rapid (~107 ions sec21 channel21) passive movement of selected ions across cell membranes1. They regulate cell functions in both electrically excitable and nonexcitable cells. A number of diseases (‘channelopathies’)2 are associated with dysfunction of ion channels. Several human neurological and muscular disorders result from defects in voltage-gated and ligand-gated ion channels. Ion channels enable us to address a key problem of structural biology, namely how to relate atomic-resolution structure to biological function. In particular, we wish to exploit our experimental and theoretical understanding of ion channels to describe their key physiological properties, such as ion permeation and selectivity, in terms of underlying physical processes. This attempt to integrate structure and function is possible for ion channels because of recent progress in their molecular M.S.P. Sansom, I.H. Shrivastava and G.R. Smith are at the Laboratory of Molecular Biophysics, The Rex Richards Building, Dept of Biochemistry, University of Oxford, South Parks Road, Oxford, UK OX1 3QU; and K.M. Ranatunga is at the Biophysics Section, Blackett Laboratory, Imperial College of Science, Technology and Medicine, Prince Consort Road, London, UK SW7 2BZ. Email: [email protected]
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physiology and structural biology. Several structures of ion channels have emerged, ranging in complexity from a simple model channel, gramicidin (GA)3, to a bacterial K1 channel, KcsA (Ref. 4), and a mechanosensitive channel, MscL (Ref. 5). X-ray structures of other membrane proteins include those of several porins, which can function as ionselective channels. Thus, ion channels are rare in allowing us to examine structure–function relationships at the level of a single protein molecule. The outcome of such studies might provide a paradigm for understanding the physiology of other transport proteins (e.g. aquaporin) at atomic resolution.
Simulation approaches There have been considerable advances in computer simulations of membranes6–8, and much pioneering work has focussed on pure lipid bilayers. This has been extended to membrane-embedded peptides and proteins, allowing their dynamics to be examined on a ns (1029 s) timescale. Simulations enable us to explore dynamic aspects of membranes that cannot be addressed directly by structural biology. They also help us to design novel experiments. For example, X-ray diffraction provides a time- and space-averaged structure (i.e. that has been averaged over the duration of the experiment and between the
different molecules in the crystal) of a membrane protein in a specific environment (e.g. a detergent), whereas simulations enable us to explore the structural dynamics of a single-channel protein molecule embedded in a solvated lipid bilayer, in the presence of ions and water molecules (Fig. 1). Of course, simulations are a complement, not an alternative, to experiment. It is important to consider the timescales that might be addressed by different simulation methods. Atomistic simulations (i.e. simulations in which all atoms of a protein molecule, plus lipid molecules, water and ions are treated explicitly) of membrane proteins generally employ molecular dynamics (MD; see Box 1). The upper limit of MD simulations of membrane systems is currently ~10 ns. Continuing advances in computer power and the widespread use of PC (‘Beowulf’) clusters might extend this by a further order of magnitude over the next few years. By contrast, a mean time of ~100 ns is required for a single ion to move completely through a channel. Of course, analysis of a single-ion passage does not provide a statistically significant sample. Therefore, if computer simulations are to reproduce the physiological properties of single channels, one must either run many long MD simulations or devise a hierarchy of theoretical or computational descriptions that address multiple timescales. One way to address longer timescale events is to describe the channel protein, bilayer and water molecules in a less detailed fashion, and to use continuum electrostatics calculations and Brownian dynamics (BD; see Box 1), for example, to simulate the interactions of ions with this system9.
Short-timescale motions of water and ions Mobility of water molecules and ions. MD simulations can be used to determine whether ions and water molecules diffuse in pores of molecular dimensions at the same rates as in bulk solution. This is important if one is to use continuum models to describe the overall net diffusion of ions through channels, as such models require ionic diffusion coefficients as input parameters. Water and ion diffusion rates have been investigated extensively via simulations of simple model channels. Two such models are channels formed by self-assembling peptides, GA and alamethicin (Alm). GA is a hydrophobic pentadecapeptide that dimerizes to form cation-selective channels. The GA channel is a head-to-head
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TIBS 25 – AUGUST 2000 dimer of b helices of alternating L- and D-amino acids (Fig. 2a,b)3. Alm is a 20residue peptide that forms an a helix ‘kinked’ by a central proline. Alm channels are formed from bundles containing ~6–12 parallel helices10. Larger assemblies correspond to higher single-channel conductances (Fig. 2c,d). GA is a good model for narrow, low-conductance channels (such as the selectivity filter region of K1 channels), whereas Alm is a model for wider channels such as the nicotinic acetylcholine receptor. GA and Alm form structurally different pathways for ions; that is, a GA pore is lined by backbone carbonyl groups, whereas that of Alm is lined by a number of polar side chains. These structural differences are anticipated to lead to differences in the mechanisms of selectivity and/or permeation. Both GA (Ref. 11) and Alm (Ref. 12) channels have been the subject of long (.ns) MD simulations in extended lipid bilayers. The GA study provides a test of the accuracy of such simulations. From the simulated motion of water molecules within the channel and the resistance to entry and exit of water molecules to and from the channel, it was possible to calculate the permeability of water through GA (Ref. 11). This computational estimate agreed well with experimental measurements, thus encouraging a degree of confidence in the results of channel simulations. For both GA and Alm, the motion of water molecules within the pore is restricted relative to that of bulk water. For GA, the waters are restrained to form a single file, and their rotational motion is highly restricted. The mobility of the single-file water ‘chain’ as a whole is sensitive to the degree of internal mobility of the peptide13. The magnitude of peptide motions will, in part, be determined by correct simulation of the bilayer and water environment. Thus, to understand movement of water and ions within a channel it might be critical to model correctly the fluid bilayer environment surrounding the peptide or protein molecule. Although Alm channels are wider than GA channels (radius ~0.25 nm for a hexameric Alm bundle versus ~0.13 nm for GA), they still clearly perturb the motion of water molecules within them. The diffusion coefficients of water molecules along the pore (see z axis; Fig. 3a) within an Alm channel are reduced (by up to an order of magnitude) relative to those of waters in the bulk region. In addition to the slower diffusion of water
Figure 1 An ion channel in a membrane. A model of the pore-forming domain of a mammalian K1 channel (Kir6.2; red)27 is shown embedded in a palmitoyloleoyl phosphatidylcholine bilayer (green; phosphorus atoms of headgroups in purple) with K1 ions (light blue) on either face of the membrane. The size of the simulation box (i.e. the repeating unit that forms the basis of the simulations) is ~8.5 3 8.5 3 8.5 nm3, and it also contains ~12 000 water molecules (not shown). The effective K1 concentration is ~40 mM. EC, extracellular; IC, intracellular. Diagram was prepared using MOLSCRIPT (Ref. 48) and Raster3D (Ref. 49).
Box 1. Key computational techniques Molecular dynamics. Simulation of the atomic motions of a biomolecule, based on a classical (i.e. non-quantum) potential energy function and numerical (computer) integration of Newton’s laws of motion. Timescale ~1 ns (10–9 s). All atoms (protein, water, lipid, ions) are free to move. Continuum electrostatics. Calculation of the electrostatic field surrounding a biomolecule via numerical solution of the Poisson–Boltzmann equation. A protein is treated as a low dielectric region plus discrete charges representing polar atoms; the surrounding solvent is treated as a high dielectric region, with a Debye–Hückel term to model bulk ionic solutions. Brownian dynamics. Simulation of the diffusion of an ion (or ions) in the electrostatic field generated by a protein. Solvent–ion interactions are treated via a random force related to the diffusion coefficient. Timescale ~1 ms (10–6 s). Only ions are free to move.
molecules with an Alm pore, they are nonrandomly oriented. The dipoles of the water molecules within the pore orient antiparallel to the surrounding helix dipoles (Fig. 3b). This reduces the effective dielectric constant of water within the pore14, thus increasing the strength of electrostatic interactions. Similar effects on water dynamics and orientations have been seen in simulations of other channels formed by bundles of parallel a helices, such as those formed by designed LS peptides (containing only leucine and serine residues)15, and
in simulations of porins16. Furthermore, even simulations of rather idealized systems (e.g. water within channel-sized hydrophobic cavities17) show that the motion of water molecules is restricted. Thus, one can assume that this is a general property of water in channels, which should be taken into account in any continuum model of ion permeation. The motion of ions within pores seems also, in general, to be restricted relative to their motion in bulk solution. This has been shown for idealized systems18 and for GA (Refs 19,20), and
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Dz (10−9 m2 s−1)
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Figure 2 Model ion channels. (a,b) Structure of the channel-forming dimer of gramicidin A (Ref. 3). The broken red line in (a) indicates the monomer–monomer interface. (c,d) Model of the structure of a channel formed by a hexameric assembly of alamethicin helices12. In (a,c) the view is perpendicular to the bilayer normal, with the molecules shown in ‘bonds’ format and the broken grey lines indicating the approximate extent of the bilayer. In (b,d) the view is down the bilayer normal, with the molecules shown in ‘spacefilling’ format. Diagram was prepared using MOLSCRIPT (Ref. 48) and Raster3D (Ref. 49).
has since been extended to a wide range of channel models21,22. In general, it appears that reduction of ion diffusion coefficients within a pore relative to in bulk solution is somewhat less than the corresponding reduction of water diffusion coefficients (e.g. an approximately threefold reduction for K1 ions versus an ~12-fold reduction for water for a hexameric Alm helix-bundle channel). Comparing different channel models21, it was suggested that the reduction in diffusion rate of Na1 ions within a pore might be proportional to pore radius; that is, the narrower the pore the slower the diffusion. Furthermore, for several channel models, the diffusion coefficients of K1 and Cl2 were both reduced to the same extent, suggesting that diffusion rates alone are unlikely to be the source of ion selectivity in channels. Ions and water in K1 channel simulations. The X-ray structure of a bacterial K1 channel provides channel simulation studies with the challenge of developing a detailed physical description of ion permeation and selectivity [KcsA is
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substantially more permeable to K1 than to Na1 (Ref. 23)]. Simulation studies of KcsA have focussed on events at the extracellular mouth and within the narrow selectivity filter adjacent to this (Fig. 4). There have also been preliminary studies of the energetics of ion flow through KcsA, although these are somewhat hindered as the X-ray structure seems to be that of the closed state of the channel. The structure of KcsA is that of a truncated cone, with a central pore running down the centre. The cone is made up of the M1 and M2 helices, which span the bilayer. The wider end of the cone corresponds to the extracellular mouth of the channel. This envelops the pore (P) region, made up of the P-helices, plus a selectivity filter that is formed by a TVGYG sequence motif characteristic of K1 channels. In the X-ray structure this motif adopts an extended conformation. Beneath the selectivity filter is a central water-filled cavity, which, according to the X-ray structure, also appears to contain a loosely bound cation. Finally, the
Figure 3 Perturbed properties of water within an ion channel, illustrated for alamethicin channels. (a) Water diffusion coefficients (Dz) as a function of position along the pore (z) axes. The horizontal broken line indicates the diffusion coefficient of ‘bulk’ water in the simulation. (b) Projection of water dipole moments onto the pore axes. The horizontal broken line near the top of the graph indicates the value of the z-component of the water dipole moments that would be achieved if all the water dipoles were aligned exactly antiparallel to the a helix dipoles of the Alm bundle. These results are for the hexameric Alm channel assembly, but similar results are obtained for other stoichiometries. The extent of the bilayer is shown by the light-blue band, with the approximate locations of the N and C termini of the Alm helices indicated.
pore-lining M2 helices constrict the intracellular mouth to form a putative gate region where the pore radius falls to ~0.11 nm (i.e. less than the Pauling radius of a K1 ion, which is 0.13 nm). From sequence comparisons it appears that the structure of this pore domain is conserved between diverse K1 channels, and so the KcsA structure provides a framework for the understanding of K1 selectivity and permeation. Simulations of a KcsA molecule embedded in a ‘slab’ of octane molecules (providing a simple mimic of a bilayer environment) with water on either side focussed on entry of ions from the extracellular mouth of the channel into the selectivity filter24. As ions entered the channel, they were partially stripped of their hydration shell. This process was aided by electrostatic interactions with nearby charged side chains and interactions
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based on a channel-shaped hywith the backbone carbonyls of drophobic pore onto which a the selectivity filter. The simulations indicated differences in the model of the KcsA filter is grafted. extent of dehydration of Na1 and Their results broadly support the K1 ions, which could be related to ‘rigid-filter’ model of K1-channel the ion-selectivity mechanism of selectivity. However, until similar KcsA. An important implication of calculations are performed for a this study is that the more distant complete model of the channel, acidic side chains (especially and the sensitivity of the results to Glu71 and Asp80) play a role in initial assumptions of ionization aiding entry and exit of cations to state and rigidity are evaluated, it and from the channel. Thus, paris unclear whether simulations ticular attention must be paid to based on a radically simplified their ionization state. model are appropriate. Indeed, in a The X-ray structure of KcsA subsequent paper29 using a com1 reveals that there are two K ions plete model of the protein (but within the selectivity filter (probomitting the surrounding bilayer) ably with a water molecule in the free-energy differences bebetween them), as well as a third tween K1 and Na1 were approxi1 K ion in the central cavity. This mately half of those obtained with agrees with physiological measthe simplified model. In this conurements which indicated that K1 text, a simulation study based on a channels are multi-ion pores1. mammalian K1-channel model deSeveral simulations have adveloped before the KcsA structure dressed the motion of multiple K1 was determined is interesting30. ions plus water molecules within This study suggested that relaKcsA, focussing on events in the tively small changes in the model selectivity filter. Shrivastava and resulted in significant changes Sansom25 ran simulations of KcsA in the predicted single-channel Figure 4 A bacterial K1 channel, KcsA, in a lipid bilayer. (a) in a fully solvated phospholipid conductance. This implies that Starting configuration for a simulation of KcsA in a bibilayer environment. Comparison simulation results are sensitive to layer25. Two subunits of KcsA are shown in ‘ribbons’ of simulations with and without K1 structural details, and so one format, with the M1 helix in red, the P-region in green ions indicates that absence of ions should proceed carefully before 1 and the M2 helix in blue. Three K ions (cyan) and destabilized the structure of the discarding seemingly unimportant some of the bilayer lipid molecules (grey/purple) are selectivity filter, such that it disaspects of a structure. shown in space-filling format. Water molecules are torted its crystallographic conforA novel approach to underomitted for clarity. Key regions of the channel are labelled as follows: C, central water-filled cavity; EC, mation. This could be related to standing permeation through the extracellular mouth; F, selectivity filter; G, (putative) the observed loss of channel activKcsA filter is to calculate the relagate; IC, intracellular mouth. (b) The selectivity filter of 1 ity when K channels are exposed tive free energies of different conKcsA at 100 ps and 850 ps of the simulation in (a), to solutions that lack K1 ions. figurations of pairs of ions within showing the concerted motion of ions and water. At Simulations that included K1 ions the filter31. The most stable con100 ps there are a water molecule (red/white) just 1 revealed concerted single-file mofiguration is that with K1 ions at extracellular to the filter (top of diagram), K ions (cyan) tions of a column of water molsites S2 and S4, the configuration at sites S1 and S3, and water molecules at site S2 and just below site S4. At 850 ps there are water molecules and two K1 ions within the with ions at S1 and S3 being the ecules at sites S1 and S3 and just below site S4, and selectivity filter of the channel to next most stable. This suggests a K1 ions at sites S2 and S4. The peptide backbone of occur on a several-hundred ps permeation mechanism in which the filter and the T75 side chains are shown (for two (10212) timescale (Fig. 4b). Such the channel cycles between these subunits only, for clarity). Diagram was prepared using concerted motions of ions and two configurations. This result is MOLSCRIPT (Ref. 48) and Raster3D (Ref. 49). water through the filter might be a in agreement with the simulations general property of K1 channels or of (unrestrained) ions in the filter, K1-channel simulations, as they have used for GA to estimate the free-energy which reveal transitions between these also been observed in simulations of profile experienced by a single ion as it two states (Fig. 4b). KcsA performed by Roux and col- moves along a channel20. Extension of Although ions and water molecules leagues26 and in simulations of a model this to more complex channel geom- move through the filter region of KcsA, of a mammalian inward-rectifier K1 etries and to motion of multiple ions is the protein does not appear to remain channel (see below and Ref. 27). The not trivial. Furthermore, as suggested completely rigid. As can be seen in fact that different simulations give the by simulations on GA (Refs 11,13), a cor- Fig. 4b, for example, small changes in same result is encouraging; however, it rect treatment of the flexibility of the the positions of the carbonyl oxygens should be noted that none of these channel protein (which, in turn, is cou- occur as the K1 ions move. This has imsimulations included a transbilayer pled to the deformability of its bilayer portant implications in terms of the electrochemical potential difference. environment) is necessary. Chung and mechanism of ion selectivity. It has been Energetics. What about the energetics colleagues28 have calculated free-energy argued that selectivity occurs via the filof ion movement through the KcsA se- profiles for K1 and Na1 ions in a some- ter providing an exact fit to a K1 ion, lectivity filter? MD simulations can be what simplified model of a K1 channel, whereas the carbonyl oxygens are too
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approximate approaches to this, distantly spaced for optimal interbased on continuum electrostatics actions with a smaller Na1 ion4. Atomistic − molecular dynamics and on BD, before discussing a This mechanism implies that the Input: more rigorous approach based on filter is relatively rigid. However, a atomic coordinates and free-energy profiles. Of course, all significant degree of flexibility in partial charges; potential energy function such approaches to KcsA will rethe selectivity filter is seen in simuOutput: quire a plausible model of the lations25,26 coupled to the moveDION and εWATER in pore; open conformation of the channel. ment of K1 ions and water FION versus z molecules. This suggests that the Electrostatics approaches to model filter might also be able to undergo channels. Continuum electrostatics z minor changes in conformation to calculations have been used with 1 solvate Na ions optimally, implysome success to predict singleing that a ‘rigid-filter’ model of K1channel current-voltage relationCoarse-grained − continuum channel selectivity might be an ships for channels formed by Input: oversimplification. Free-energy calsimple peptides36–39. For example, DION and ε WATER; FION versus z 29,31 1 culations in which K ions are one can compute electrostaticOutput: computationally ‘transformed’ into potential energy (F) profiles along single channel I/V curves Na1 ions, while within the channel, a pore axis (z) via numerical soluTi BS support the proposal that Na1 ions tion of the Poisson–Boltzmann interact with the filter more weakly equation. In such calculations, the than K1 ions do. However, it is protein is treated as a continuum Figure 5 A hierarchy of approaches to describing ion permepossible that such simulations do of low dielectric (e.g. with a dielecation. Atomistic (i.e. molecular dynamics) simulations not allow the filter and ions to tric constant of e 5 4) in which (green box) provide information on ion and water dyrelax fully to their new configuraatomic partial charges are embednamics and energetics within a pore. Coarse-grained tion. Indeed, unrestrained simuladed. The solvent is treated as (i.e. continuum) calculations (blue box) employ the retions (I.H. Shrivastava et al., unhaving a high dielectric (e 5 78) sults of atomistic simulations to predict physiologipublished) of Na1 ions within the continuum, although, in the light cally observable properties such as single-channel filter suggest that they might bind of the discussion above, it might current-voltage curves. DION, diffusion coefficient of ion; eWATER, dielectric constant of water (in a pore); FION tightly to slightly different sites be appropriate to treat the solvent versus z, free energy profile along the pore axis; I/V, from those occupied by K1, thus within the pore as a region of single-channel current versus voltage relationship. helping to explain the physiologiintermediate dielectric (e ~30). cally observed ‘block’ of KcsA Counterion screening is reprechannels by intracellular Na1 ions23. It simulation25. In one simulation with sented in terms of a Debye–Hückel paseems likely that further simulations three K1 ions, exit of the ion within the rameter derived from the ionic strength will be required to understand fully how central cavity from the channel via its at which the calculation is performed. selectivity is determined by a delicate intracellular mouth was enabled by a Although such calculations embody a balance of ion–protein, ion–water and transient increase in the radius of the number of approximations, they might protein-deformation energies. Another intracellular mouth. It is suggested that provide insights into the electrostatic aspect that cannot be neglected is the such ‘breathing’ motions might form the environment within a model pore. The importance of ion–ion interactions molecular basis of channel opening. electrostatic-potential energy profile within the pore28,32. In general, it is evi- Indeed, simulations of isolated TM represents the potential energy (in dent that presence of multiple K1 ions helices from K1 channels suggest a degree kcal/mol) of a univalent cation in the within the KcsA channel plays an impor- of ‘hinge-bending’ flexibility that might channel, apart from the relatively small tant role in maintaining a high perme- underlie channel-opening motions34. effect of the interaction of the cation ation rate. Hinge-bending of the channel-lining with its own polarization charge (which One aspect of KcsA that has not been helices of a voltage-gated K1 channel will be about the same as the interaction fully addressed by simulation studies is has also been suggested by recent with a single unit of charge on the chanthat the crystal structure appears to be experiments35 in which the ability of nel wall, with the same sign as the perthat of the ‘closed’ form of the channel. channel-blocking compounds to prevent meant ion). Of course, the exact height This is reasonable as the closed state of chemical modification of cysteine resi- or depth of the barriers or wells the channel is favoured at neutral pH, at dues introduced into various sites in the depends on the parameters employed which the crystal structure was solved. pore-lining S6 helix was used to map the in the Poisson–Boltzmann calculations e within the pore and the Examination of the channel structure re- helix conformation around the intra- (e.g. Debye–Hückel parameter within the veals that the ‘gate’ might lie close to cellular mouth of the channel. pore). the intracellular mouth of the channel, From such a profile the one-dimenwhere the pore radius drops to less than Towards longer timescales So far, we have been concerned with sional Nernst–Planck equation1 can be that of a desolvated K1 ion. Electronic paramagnetic resonance (EPR) spectro- timescales shorter than those required used to calculate single-channel currentscopic studies of KcsA (Ref. 33) suggest to describe physiologically meaningful voltage curves. The equation is effecthat channel opening is associated with fluxes of ions. To bridge this temporal tively the electrochemical-diffusion changes in packing of the transmem- gap one must simplify the description of equation for charged particles. It brane helices, so as to widen the pore at a channel system, while retaining the describes the mean flux along the chanits intracellular mouth. A glimpse of this essential properties revealed by MD nel-pore axis as a function of concenprocess might have been obtained by simulations (Fig. 5). We will briefly review tration and electrostatic-potential energy
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TIBS 25 – AUGUST 2000 profile. This method has been applied to several model channels, including Alm (Ref. 37) and the designed Leu–Ser (LS) peptide channel36,39. Both studies correctly predicted the non-linear shape (‘rectification’) of the respective experimental single-channel current-voltage curves. However, it is more difficult to obtain accurate predictions of absolute values of single-channel conductances, as these are rather sensitive to assumptions concerning the cross-sectional area of the channel and the diffusion coefficients of ions within the channel. Of course, the latter properties might be estimated by appropriate MD simulations40. A more deep-seated theoretical problem is that of the correct treatment of ion–ion interactions38. Electrostatics and K1 channels. There have been a number of electrostatics studies of K1 channels, especially KcsA. Carloni and colleagues24 emphasized the importance of the electrostatic field generated by the remainder of the channel in guiding cations into the channel mouth. Roux and MacKinnon41 have shown how the electrostatic field generated by dipoles of the four inwardly pointing P-region a helices of KcsA help to stabilize a K1 ion within the small water-filled cavity in the centre of KcsA, thus helping to solve the fundamental problem of how to transport an ion through the low dielectric barrier presented by a lipid bilayer. Simple electrostatics calculations might also be used to estimate the most likely ionization state of acidic and basic side chains at the mouths of the KcsA channel. This approach was applied to a simple model of the pore domain of a voltage-gated K1 channel (developed before the KcsA structure was solved)42. The results indicated that acidic side chains forming rings at the mouth of the channel were not all ionized, and that the assumed ionization state had a significant influence on the electrostaticpotential energy profile of an ion moved along the channel axis. A similar effect is seen if these calculations are applied to KcsA (K.M. Ranatunga and M.S.P. Sansom, unpublished). Thus, it might be necessary to feed back the results of electrostatics calculations on residue ionization states into MD simulations in order to obtain a correct picture of channel–ion–water interactions. Ideally, one would like to be able to run MD simulations in which the ionization states of side chains were dynamically updated. Brownian dynamics and beyond… Some of the limitations of a Nernst–Planck
approach to predicting physiological channel properties are the result of replacing the discrete ions by an implicitly time-averaged ‘concentration’. It is possible instead to retain discrete ions but make them move in the electrostatic field created by the protein with a random component mimicking the effect of the water. Their motion is described, in this case, by the equations of Langevin dynamics or, if the inertia of the ions is negligible, BD. Such an approach has been outlined in a general fashion43 and shown to be capable of capturing the essence of the physiological permeation behaviour. More recently, BD simulations have been applied to a simplified model of KcsA (Ref. 9) and to atomistic models of porins44,45. In both cases, the BD simulations yielded good predictions of the experimental single-channel conductances, and for the porins ion selectivity (for anions versus cations) was well modelled. This approach has considerable potential for providing a physically meaningful description of ion permeation on a physiologically meaningful timescale. However, several refinements are needed. For example, in the light of MD simulation results for KcsA it seems unlikely that a simple electrostatic potential profile calculated from a rigid channel-model will adequately capture the energetics of channel–ion interactions in the filter region. Moreover, ion–ion interactions in the channel are strongly influenced by the presence of the protein. Furthermore, careful simulation studies will be needed to investigate the appropriate value of the diffusion coefficient to assign to an ion as it moves through different regions of the channel. Finally, there remains the question of the dielectric behaviour of the solvent (which, in turn, influences the strength of channel–ion electrostatic interactions) in different regions of the pore. There are alternatives to BD for linking MD simulations with physiological measurements. For example, it might be possible to split the treatment of the energetics of ion permeation into an atomistic component (namely a free-energy profile from MD simulations) and a continuum component (based on continuum electrostatics and including the transbilayer voltage difference)46. KcsA will remain an important test system for this and related approaches.
The future Simulations have already provided us with a number of insights into how ion
channels work. For example, they have revealed some of the complexities of protein flexibility coupled to ion movement through a narrow pore and are suggestive of the way in which such flexibility might be influenced by the bilayer and solvent environment surrounding the channel protein. However, several challenges remain if simulations are to mirror physical reality more accurately. In particular, it will be necessary to include a representation of a transbilayer electrochemical difference (i.e. difference in ionic concentrations and voltage), and to consider different conformational states (i.e. closed versus open) of a channel. In addition to these computational challenges, one would also like simulations to encompass some of the complexities of mammalian K1 channels. The X-ray structure of KcsA can be used as a starting point for generating models of mammalian K1 channels, and such models can be further explored by simulations. For example, this approach has been applied to the pore-forming domain of an inward-rectifier K1 channel27. In the longer term, it will be important that simulations embrace more complex ion-channel structures, taking into account, for example, possible multiple pathways for permeating ions and changes in channel structure, which occur in response to changes in transbilayer voltage47. The future is promising for simulation studies of ion channels. A computational approach will allow us to determine the origin of numerous physiological properties of ion channels, thus providing a detailed physico-chemical ‘annotation’ of X-ray structures. For example, simulation studies are already yielding insights into mechanisms of ion selectivity in KcsA. By combining accurate models (and, hopefully, experimental structures) of diverse channels with simulations, it should be possible to explain, at a fundamental level, how different channels select between different ions, and how ions, drugs and toxins can selectively block certain channels. In the longer term, it might even be possible to describe the dynamic structural changes underlying channel gating.
Acknowledgements Our thanks to all of our colleagues for their interest in this work, especially Phil Biggin, Declan Doyle and Peter Tieleman. Work in M.S.P.S.’s laboratory is supported by grants from the Wellcome Trust.
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REVIEWS References 1 Hille, B. (1992) Ionic Channels of Excitable Membranes, Sinauer Associates Inc., Sunderland, Massachusetts 2 Ashcroft, F.M. (2000) Ion Channels and Disease, Academic Press, San Diego 3 Ketchem, R.R. et al. (1993) High-resolution conformation of gramicidin A in a lipid bilayer by solid-state NMR. Science 261, 1457–1460 4 Doyle, D.A. et al. (1998) The structure of the potassium channel: molecular basis of K1 conduction and selectivity. Science 280, 69–77 5 Chang, G. et al. (1998) Structure of the MscL homolog from Mycobacterium tuberculosis: a gated mechanosensitive ion channel. Science 282, 2220–2226 6 Jakobsson, E. (1997) Computer simulation studies of biological membranes: progress, promise and pitfalls. Trends Biochem. Sci. 22, 339–344 7 Tieleman, D.P. et al. (1997) A computer perspective of membranes: molecular dynamics studies of lipid bilayer systems. Biochim. Biophys. Acta 1331, 235–270 8 Forrest, L.R. and Sansom, M.S.P. (2000) Membrane simulations: bigger and better? Curr. Opin. Struct. Biol. 10, 174–181 9 Chung, S.H. et al. (1999) Permeation of ions across the potassium channel: Brownian dynamics studies. Biophys. J. 77, 2517–2533 10 Sansom, M.S.P. (1993) Structure and function of channelforming peptaibols. Q. Rev. Biophys. 26, 365–421 11 Chiu, S.W. et al. (1999) Simulation study of a gramicidin/lipid bilayer system in excess water and lipid. II. Rates and mechanisms of water transport. Biophys. J. 76, 1939–1950 12 Tieleman, D.P. et al. (1999) An alamethicin channel in a lipid bilayer: molecular dynamics simulations. Biophys. J. 76, 1757–1769 13 Chiu, S.W. et al. (1991) Time-correlation analysis of simulated water motion in flexible and rigid gramicidin channels. Biophys. J. 60, 273–285 14 Sansom, M.S.P. et al. (1997) The dielectric properties of water within model transbilayer pores. Biophys. J. 73, 2404–2415 15 Randa, H.S. et al. (1999) Molecular dynamics of synthetic leucine-serine ion channels in a phospholipid membrane. Biophys. J. 77, 2400–2410 16 Tieleman, D.P. and Berendsen, H.J.C. (1998) A molecular dynamics study of the pores formed by Escherichia coli OmpF porin in a fully hydrated palmitoyloleoylphosphatidylcholine bilayer. Biophys. J. 74, 2786–2801
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TIBS 25 – AUGUST 2000 17 Sansom, M.S.P. et al. (1996) Water in channel-like cavities: structure and dynamics. Biophys. J. 70, 693–702 18 Lynden-Bell, R. and Rasaiah, J.C. (1996) Mobility and solvation of ions in channels. J. Chem. Phys. 105, 9266–9280 19 Chiu, S.W. et al. (1993) The nature of ion and water barrier crossings in a simulated ion channel. Biophys. J. 64, 98–109 20 Roux, B. and Karplus, M. (1994) Molecular dynamics simulations of the gramicidin channel. Annu. Rev. Biophys. Biomol. Struct. 23, 731–761 21 Smith, G.R. and Sansom, M.S.P. (1998) Dynamic properties of Na1 ions in models of ion channels: a molecular dynamics study. Biophys. J. 75, 2767–2782 22 Smith, G.R. and Sansom, M.S.P. (1999) Effective diffusion coefficients of K1 and Cl2 ions in ion channel models. Biophys. Chem. 79, 129–151 23 Heginbotham, L. et al. (1999) Single Streptomyces lividans K1 channels: functional asymmetries and sidedness of proton activation. J. Gen. Physiol. 114, 551–559 24 Guidoni, L. et al. (1999) Potassium and sodium binding in the outer mouth of the K1 channel. Biochemistry 38, 8599–8604 25 Shrivastava, I.H. and Sansom, M.S.P. (2000) Simulations of ion permeation through a potassium channel: molecular dynamics of KcsA in a phospholipid bilayer. Biophys. J. 78, 557–570 26 Bernèche, S. and Roux, B. (2000) Molecular dynamics of the KcsA K1 channel in a bilayer membrane. Biophys. J. 78, 2909–2917 27 Capener, C.E. et al. (2000) Homology modelling and molecular dynamics simulation studies of an inward rectifier potassium channel. Biophys. J. 78, 2929–2942 28 Allen, T.W. et al. (1999) Molecular dynamics study of the KcsA potassium channel. Biophys. J. 77, 2502–2516 29 Allen, T.W. et al. (2000) The potassium channel: structure, selectivity and diffusion. J. Chem. Phys. 112, 8191–8204 30 Hu, J. et al. (2000) Calculation of the conductance and selectivity of an ion-selective potassium channel (IRK1) from simulation of atomic scale models. Mol. Phys. 98, 535–547 31 Åqvist, J. and Luzhkov, V. (2000) Ion permeation mechanism of the potassium channel. Nature 404, 881–884 32 Dorman, V.L. et al. (1999) Ionic interactions in multiply occupied channels. Novartis Foundation Symp. 225, 153–169 33 Perozo, E. et al. (1999) Structural rearrangements underlying K1-channel activation gating. Science 285, 73–78 34 Shrivastava, I.H. et al. (2000) Structure and dynamics of
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K1 channel pore-lining helices: a comparative simulation study. Biophys. J. 78, 79–92 Camino, D.D. et al. (2000) Blocker protection in the pore of a voltage-gated K1 channel and its structural implications. Nature 403, 321–325 Kienker, P.K. et al. (1994) A helical-dipole model describes the single-channel current rectification of an uncharged peptide ion channel. Proc. Natl. Acad. Sci. U. S. A. 91, 4859–4863 Woolley, G.A. et al. (1997) Intrinsic rectification of ion flux in alamethicin channels: studies with an alamethicin dimer. Biophys. J. 73, 770–778 Chen, D. et al. (1997) Permeation through an open channel: Poisson–Nernst–Planck theory of a synthetic ionic channel. Biophys. J. 72, 97–116 Dieckmann, G.R. et al. (1999) Exploration of the structural features defining the conduction properties of a synthetic ion channel. Biophys. J. 76, 618–630 Adcock, C. et al. (2000) The nicotinic acetylcholine receptor: from molecular model to single channel conductance. Eur. Biophys. J. 29, 29–37 Roux, B. and MacKinnon, R. (1999) The cavity and pore helices in the KcsA K1 channel: electrostatic stabilization of monovalent cations. Science 285, 100–102 Ranatunga, K.R. et al. (1998) Protein–water–ion interactions in a model of the pore domain of a potassium channel: a simulation study. Biochim. Biophys. Acta 1370, 1–7 Bek, S. and Jakobsson, E. (1994) Brownian dynamics study of a multiply-occupied cation channel – application to understanding permeation in potassium channels. Biophys. J. 66, 1028–1038 Schirmer, T. and Phale, P.S. (1999) Brownian dynamics simulation of ion flow through porin channels. J. Mol. Biol. 294, 1159–1167 Im, W. et al. Grand canonical Monte Carlo–Brownian dynamics algorithm for simulating ion channels. Biophys. J. (in press) Roux, B. (1999) Statistical mechanical equilibrium theory of selective ion channels. Biophys. J. 77, 139–153 Yellen, G. (1998) The moving parts of voltage-gated ion channels. Q. Rev. Biophys. 31, 239–295 Kraulis, P.J. (1991) MOLSCRIPT: a program to produce both detailed and schematic plots of protein structures. J. Appl. Cryst. 24, 946–950 Merritt, E.A. and Bacon, D.J. (1997) Raster3D: Photorealistic molecular graphics. Meth. Enzymol. 277, 505–524
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Simulations of ion channels – watching ions and water move Mark S.P. Sansom, Indira H. Shrivastava, Kishani M. Ranatunga and Graham R. Smith Ion channels mediate electrical excitability in neurons and muscle. Threedimensional structures for model peptide channels and for a potassium (K1) channel have been combined with computer simulations to permit rigorous exploration of structure–function relations of channels. Water molecules and ions within transbilayer pores tend to diffuse more slowly than in bulk solutions. In the narrow selectivity filter of the bacterial K1 channel (i.e. the region of the channel that discriminates between different species of ions) a column of water molecules and K1 ions moves in a concerted fashion. By combining atomistic simulations (in which all atoms of the channel molecule, water and ions are treated explicitly) with continuum methods (in which the description of the channel system is considerably simplified) it is possible to simulate some of the physiological properties of channels. ION CHANNELS ARE transmembrane (TM) proteins that enable rapid (~107 ions sec21 channel21) passive movement of selected ions across cell membranes1. They regulate cell functions in both electrically excitable and nonexcitable cells. A number of diseases (‘channelopathies’)2 are associated with dysfunction of ion channels. Several human neurological and muscular disorders result from defects in voltage-gated and ligand-gated ion channels. Ion channels enable us to address a key problem of structural biology, namely how to relate atomic-resolution structure to biological function. In particular, we wish to exploit our experimental and theoretical understanding of ion channels to describe their key physiological properties, such as ion permeation and selectivity, in terms of underlying physical processes. This attempt to integrate structure and function is possible for ion channels because of recent progress in their molecular M.S.P. Sansom, I.H. Shrivastava and G.R. Smith are at the Laboratory of Molecular Biophysics, The Rex Richards Building, Dept of Biochemistry, University of Oxford, South Parks Road, Oxford, UK OX1 3QU; and K.M. Ranatunga is at the Biophysics Section, Blackett Laboratory, Imperial College of Science, Technology and Medicine, Prince Consort Road, London, UK SW7 2BZ. Email: [email protected]
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physiology and structural biology. Several structures of ion channels have emerged, ranging in complexity from a simple model channel, gramicidin (GA)3, to a bacterial K1 channel, KcsA (Ref. 4), and a mechanosensitive channel, MscL (Ref. 5). X-ray structures of other membrane proteins include those of several porins, which can function as ionselective channels. Thus, ion channels are rare in allowing us to examine structure–function relationships at the level of a single protein molecule. The outcome of such studies might provide a paradigm for understanding the physiology of other transport proteins (e.g. aquaporin) at atomic resolution.
Simulation approaches There have been considerable advances in computer simulations of membranes6–8, and much pioneering work has focussed on pure lipid bilayers. This has been extended to membrane-embedded peptides and proteins, allowing their dynamics to be examined on a ns (1029 s) timescale. Simulations enable us to explore dynamic aspects of membranes that cannot be addressed directly by structural biology. They also help us to design novel experiments. For example, X-ray diffraction provides a time- and space-averaged structure (i.e. that has been averaged over the duration of the experiment and between the
different molecules in the crystal) of a membrane protein in a specific environment (e.g. a detergent), whereas simulations enable us to explore the structural dynamics of a single-channel protein molecule embedded in a solvated lipid bilayer, in the presence of ions and water molecules (Fig. 1). Of course, simulations are a complement, not an alternative, to experiment. It is important to consider the timescales that might be addressed by different simulation methods. Atomistic simulations (i.e. simulations in which all atoms of a protein molecule, plus lipid molecules, water and ions are treated explicitly) of membrane proteins generally employ molecular dynamics (MD; see Box 1). The upper limit of MD simulations of membrane systems is currently ~10 ns. Continuing advances in computer power and the widespread use of PC (‘Beowulf’) clusters might extend this by a further order of magnitude over the next few years. By contrast, a mean time of ~100 ns is required for a single ion to move completely through a channel. Of course, analysis of a single-ion passage does not provide a statistically significant sample. Therefore, if computer simulations are to reproduce the physiological properties of single channels, one must either run many long MD simulations or devise a hierarchy of theoretical or computational descriptions that address multiple timescales. One way to address longer timescale events is to describe the channel protein, bilayer and water molecules in a less detailed fashion, and to use continuum electrostatics calculations and Brownian dynamics (BD; see Box 1), for example, to simulate the interactions of ions with this system9.
Short-timescale motions of water and ions Mobility of water molecules and ions. MD simulations can be used to determine whether ions and water molecules diffuse in pores of molecular dimensions at the same rates as in bulk solution. This is important if one is to use continuum models to describe the overall net diffusion of ions through channels, as such models require ionic diffusion coefficients as input parameters. Water and ion diffusion rates have been investigated extensively via simulations of simple model channels. Two such models are channels formed by self-assembling peptides, GA and alamethicin (Alm). GA is a hydrophobic pentadecapeptide that dimerizes to form cation-selective channels. The GA channel is a head-to-head
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TIBS 25 – AUGUST 2000 dimer of b helices of alternating L- and D-amino acids (Fig. 2a,b)3. Alm is a 20residue peptide that forms an a helix ‘kinked’ by a central proline. Alm channels are formed from bundles containing ~6–12 parallel helices10. Larger assemblies correspond to higher single-channel conductances (Fig. 2c,d). GA is a good model for narrow, low-conductance channels (such as the selectivity filter region of K1 channels), whereas Alm is a model for wider channels such as the nicotinic acetylcholine receptor. GA and Alm form structurally different pathways for ions; that is, a GA pore is lined by backbone carbonyl groups, whereas that of Alm is lined by a number of polar side chains. These structural differences are anticipated to lead to differences in the mechanisms of selectivity and/or permeation. Both GA (Ref. 11) and Alm (Ref. 12) channels have been the subject of long (.ns) MD simulations in extended lipid bilayers. The GA study provides a test of the accuracy of such simulations. From the simulated motion of water molecules within the channel and the resistance to entry and exit of water molecules to and from the channel, it was possible to calculate the permeability of water through GA (Ref. 11). This computational estimate agreed well with experimental measurements, thus encouraging a degree of confidence in the results of channel simulations. For both GA and Alm, the motion of water molecules within the pore is restricted relative to that of bulk water. For GA, the waters are restrained to form a single file, and their rotational motion is highly restricted. The mobility of the single-file water ‘chain’ as a whole is sensitive to the degree of internal mobility of the peptide13. The magnitude of peptide motions will, in part, be determined by correct simulation of the bilayer and water environment. Thus, to understand movement of water and ions within a channel it might be critical to model correctly the fluid bilayer environment surrounding the peptide or protein molecule. Although Alm channels are wider than GA channels (radius ~0.25 nm for a hexameric Alm bundle versus ~0.13 nm for GA), they still clearly perturb the motion of water molecules within them. The diffusion coefficients of water molecules along the pore (see z axis; Fig. 3a) within an Alm channel are reduced (by up to an order of magnitude) relative to those of waters in the bulk region. In addition to the slower diffusion of water
Figure 1 An ion channel in a membrane. A model of the pore-forming domain of a mammalian K1 channel (Kir6.2; red)27 is shown embedded in a palmitoyloleoyl phosphatidylcholine bilayer (green; phosphorus atoms of headgroups in purple) with K1 ions (light blue) on either face of the membrane. The size of the simulation box (i.e. the repeating unit that forms the basis of the simulations) is ~8.5 3 8.5 3 8.5 nm3, and it also contains ~12 000 water molecules (not shown). The effective K1 concentration is ~40 mM. EC, extracellular; IC, intracellular. Diagram was prepared using MOLSCRIPT (Ref. 48) and Raster3D (Ref. 49).
Box 1. Key computational techniques Molecular dynamics. Simulation of the atomic motions of a biomolecule, based on a classical (i.e. non-quantum) potential energy function and numerical (computer) integration of Newton’s laws of motion. Timescale ~1 ns (10–9 s). All atoms (protein, water, lipid, ions) are free to move. Continuum electrostatics. Calculation of the electrostatic field surrounding a biomolecule via numerical solution of the Poisson–Boltzmann equation. A protein is treated as a low dielectric region plus discrete charges representing polar atoms; the surrounding solvent is treated as a high dielectric region, with a Debye–Hückel term to model bulk ionic solutions. Brownian dynamics. Simulation of the diffusion of an ion (or ions) in the electrostatic field generated by a protein. Solvent–ion interactions are treated via a random force related to the diffusion coefficient. Timescale ~1 ms (10–6 s). Only ions are free to move.
molecules with an Alm pore, they are nonrandomly oriented. The dipoles of the water molecules within the pore orient antiparallel to the surrounding helix dipoles (Fig. 3b). This reduces the effective dielectric constant of water within the pore14, thus increasing the strength of electrostatic interactions. Similar effects on water dynamics and orientations have been seen in simulations of other channels formed by bundles of parallel a helices, such as those formed by designed LS peptides (containing only leucine and serine residues)15, and
in simulations of porins16. Furthermore, even simulations of rather idealized systems (e.g. water within channel-sized hydrophobic cavities17) show that the motion of water molecules is restricted. Thus, one can assume that this is a general property of water in channels, which should be taken into account in any continuum model of ion permeation. The motion of ions within pores seems also, in general, to be restricted relative to their motion in bulk solution. This has been shown for idealized systems18 and for GA (Refs 19,20), and
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Dz (10−9 m2 s−1)
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Figure 2 Model ion channels. (a,b) Structure of the channel-forming dimer of gramicidin A (Ref. 3). The broken red line in (a) indicates the monomer–monomer interface. (c,d) Model of the structure of a channel formed by a hexameric assembly of alamethicin helices12. In (a,c) the view is perpendicular to the bilayer normal, with the molecules shown in ‘bonds’ format and the broken grey lines indicating the approximate extent of the bilayer. In (b,d) the view is down the bilayer normal, with the molecules shown in ‘spacefilling’ format. Diagram was prepared using MOLSCRIPT (Ref. 48) and Raster3D (Ref. 49).
has since been extended to a wide range of channel models21,22. In general, it appears that reduction of ion diffusion coefficients within a pore relative to in bulk solution is somewhat less than the corresponding reduction of water diffusion coefficients (e.g. an approximately threefold reduction for K1 ions versus an ~12-fold reduction for water for a hexameric Alm helix-bundle channel). Comparing different channel models21, it was suggested that the reduction in diffusion rate of Na1 ions within a pore might be proportional to pore radius; that is, the narrower the pore the slower the diffusion. Furthermore, for several channel models, the diffusion coefficients of K1 and Cl2 were both reduced to the same extent, suggesting that diffusion rates alone are unlikely to be the source of ion selectivity in channels. Ions and water in K1 channel simulations. The X-ray structure of a bacterial K1 channel provides channel simulation studies with the challenge of developing a detailed physical description of ion permeation and selectivity [KcsA is
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substantially more permeable to K1 than to Na1 (Ref. 23)]. Simulation studies of KcsA have focussed on events at the extracellular mouth and within the narrow selectivity filter adjacent to this (Fig. 4). There have also been preliminary studies of the energetics of ion flow through KcsA, although these are somewhat hindered as the X-ray structure seems to be that of the closed state of the channel. The structure of KcsA is that of a truncated cone, with a central pore running down the centre. The cone is made up of the M1 and M2 helices, which span the bilayer. The wider end of the cone corresponds to the extracellular mouth of the channel. This envelops the pore (P) region, made up of the P-helices, plus a selectivity filter that is formed by a TVGYG sequence motif characteristic of K1 channels. In the X-ray structure this motif adopts an extended conformation. Beneath the selectivity filter is a central water-filled cavity, which, according to the X-ray structure, also appears to contain a loosely bound cation. Finally, the
Figure 3 Perturbed properties of water within an ion channel, illustrated for alamethicin channels. (a) Water diffusion coefficients (Dz) as a function of position along the pore (z) axes. The horizontal broken line indicates the diffusion coefficient of ‘bulk’ water in the simulation. (b) Projection of water dipole moments onto the pore axes. The horizontal broken line near the top of the graph indicates the value of the z-component of the water dipole moments that would be achieved if all the water dipoles were aligned exactly antiparallel to the a helix dipoles of the Alm bundle. These results are for the hexameric Alm channel assembly, but similar results are obtained for other stoichiometries. The extent of the bilayer is shown by the light-blue band, with the approximate locations of the N and C termini of the Alm helices indicated.
pore-lining M2 helices constrict the intracellular mouth to form a putative gate region where the pore radius falls to ~0.11 nm (i.e. less than the Pauling radius of a K1 ion, which is 0.13 nm). From sequence comparisons it appears that the structure of this pore domain is conserved between diverse K1 channels, and so the KcsA structure provides a framework for the understanding of K1 selectivity and permeation. Simulations of a KcsA molecule embedded in a ‘slab’ of octane molecules (providing a simple mimic of a bilayer environment) with water on either side focussed on entry of ions from the extracellular mouth of the channel into the selectivity filter24. As ions entered the channel, they were partially stripped of their hydration shell. This process was aided by electrostatic interactions with nearby charged side chains and interactions
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based on a channel-shaped hywith the backbone carbonyls of drophobic pore onto which a the selectivity filter. The simulations indicated differences in the model of the KcsA filter is grafted. extent of dehydration of Na1 and Their results broadly support the K1 ions, which could be related to ‘rigid-filter’ model of K1-channel the ion-selectivity mechanism of selectivity. However, until similar KcsA. An important implication of calculations are performed for a this study is that the more distant complete model of the channel, acidic side chains (especially and the sensitivity of the results to Glu71 and Asp80) play a role in initial assumptions of ionization aiding entry and exit of cations to state and rigidity are evaluated, it and from the channel. Thus, paris unclear whether simulations ticular attention must be paid to based on a radically simplified their ionization state. model are appropriate. Indeed, in a The X-ray structure of KcsA subsequent paper29 using a com1 reveals that there are two K ions plete model of the protein (but within the selectivity filter (probomitting the surrounding bilayer) ably with a water molecule in the free-energy differences bebetween them), as well as a third tween K1 and Na1 were approxi1 K ion in the central cavity. This mately half of those obtained with agrees with physiological measthe simplified model. In this conurements which indicated that K1 text, a simulation study based on a channels are multi-ion pores1. mammalian K1-channel model deSeveral simulations have adveloped before the KcsA structure dressed the motion of multiple K1 was determined is interesting30. ions plus water molecules within This study suggested that relaKcsA, focussing on events in the tively small changes in the model selectivity filter. Shrivastava and resulted in significant changes Sansom25 ran simulations of KcsA in the predicted single-channel Figure 4 A bacterial K1 channel, KcsA, in a lipid bilayer. (a) in a fully solvated phospholipid conductance. This implies that Starting configuration for a simulation of KcsA in a bibilayer environment. Comparison simulation results are sensitive to layer25. Two subunits of KcsA are shown in ‘ribbons’ of simulations with and without K1 structural details, and so one format, with the M1 helix in red, the P-region in green ions indicates that absence of ions should proceed carefully before 1 and the M2 helix in blue. Three K ions (cyan) and destabilized the structure of the discarding seemingly unimportant some of the bilayer lipid molecules (grey/purple) are selectivity filter, such that it disaspects of a structure. shown in space-filling format. Water molecules are torted its crystallographic conforA novel approach to underomitted for clarity. Key regions of the channel are labelled as follows: C, central water-filled cavity; EC, mation. This could be related to standing permeation through the extracellular mouth; F, selectivity filter; G, (putative) the observed loss of channel activKcsA filter is to calculate the relagate; IC, intracellular mouth. (b) The selectivity filter of 1 ity when K channels are exposed tive free energies of different conKcsA at 100 ps and 850 ps of the simulation in (a), to solutions that lack K1 ions. figurations of pairs of ions within showing the concerted motion of ions and water. At Simulations that included K1 ions the filter31. The most stable con100 ps there are a water molecule (red/white) just 1 revealed concerted single-file mofiguration is that with K1 ions at extracellular to the filter (top of diagram), K ions (cyan) tions of a column of water molsites S2 and S4, the configuration at sites S1 and S3, and water molecules at site S2 and just below site S4. At 850 ps there are water molecules and two K1 ions within the with ions at S1 and S3 being the ecules at sites S1 and S3 and just below site S4, and selectivity filter of the channel to next most stable. This suggests a K1 ions at sites S2 and S4. The peptide backbone of occur on a several-hundred ps permeation mechanism in which the filter and the T75 side chains are shown (for two (10212) timescale (Fig. 4b). Such the channel cycles between these subunits only, for clarity). Diagram was prepared using concerted motions of ions and two configurations. This result is MOLSCRIPT (Ref. 48) and Raster3D (Ref. 49). water through the filter might be a in agreement with the simulations general property of K1 channels or of (unrestrained) ions in the filter, K1-channel simulations, as they have used for GA to estimate the free-energy which reveal transitions between these also been observed in simulations of profile experienced by a single ion as it two states (Fig. 4b). KcsA performed by Roux and col- moves along a channel20. Extension of Although ions and water molecules leagues26 and in simulations of a model this to more complex channel geom- move through the filter region of KcsA, of a mammalian inward-rectifier K1 etries and to motion of multiple ions is the protein does not appear to remain channel (see below and Ref. 27). The not trivial. Furthermore, as suggested completely rigid. As can be seen in fact that different simulations give the by simulations on GA (Refs 11,13), a cor- Fig. 4b, for example, small changes in same result is encouraging; however, it rect treatment of the flexibility of the the positions of the carbonyl oxygens should be noted that none of these channel protein (which, in turn, is cou- occur as the K1 ions move. This has imsimulations included a transbilayer pled to the deformability of its bilayer portant implications in terms of the electrochemical potential difference. environment) is necessary. Chung and mechanism of ion selectivity. It has been Energetics. What about the energetics colleagues28 have calculated free-energy argued that selectivity occurs via the filof ion movement through the KcsA se- profiles for K1 and Na1 ions in a some- ter providing an exact fit to a K1 ion, lectivity filter? MD simulations can be what simplified model of a K1 channel, whereas the carbonyl oxygens are too
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approximate approaches to this, distantly spaced for optimal interbased on continuum electrostatics actions with a smaller Na1 ion4. Atomistic − molecular dynamics and on BD, before discussing a This mechanism implies that the Input: more rigorous approach based on filter is relatively rigid. However, a atomic coordinates and free-energy profiles. Of course, all significant degree of flexibility in partial charges; potential energy function such approaches to KcsA will rethe selectivity filter is seen in simuOutput: quire a plausible model of the lations25,26 coupled to the moveDION and εWATER in pore; open conformation of the channel. ment of K1 ions and water FION versus z molecules. This suggests that the Electrostatics approaches to model filter might also be able to undergo channels. Continuum electrostatics z minor changes in conformation to calculations have been used with 1 solvate Na ions optimally, implysome success to predict singleing that a ‘rigid-filter’ model of K1channel current-voltage relationCoarse-grained − continuum channel selectivity might be an ships for channels formed by Input: oversimplification. Free-energy calsimple peptides36–39. For example, DION and ε WATER; FION versus z 29,31 1 culations in which K ions are one can compute electrostaticOutput: computationally ‘transformed’ into potential energy (F) profiles along single channel I/V curves Na1 ions, while within the channel, a pore axis (z) via numerical soluTi BS support the proposal that Na1 ions tion of the Poisson–Boltzmann interact with the filter more weakly equation. In such calculations, the than K1 ions do. However, it is protein is treated as a continuum Figure 5 A hierarchy of approaches to describing ion permepossible that such simulations do of low dielectric (e.g. with a dielecation. Atomistic (i.e. molecular dynamics) simulations not allow the filter and ions to tric constant of e 5 4) in which (green box) provide information on ion and water dyrelax fully to their new configuraatomic partial charges are embednamics and energetics within a pore. Coarse-grained tion. Indeed, unrestrained simuladed. The solvent is treated as (i.e. continuum) calculations (blue box) employ the retions (I.H. Shrivastava et al., unhaving a high dielectric (e 5 78) sults of atomistic simulations to predict physiologipublished) of Na1 ions within the continuum, although, in the light cally observable properties such as single-channel filter suggest that they might bind of the discussion above, it might current-voltage curves. DION, diffusion coefficient of ion; eWATER, dielectric constant of water (in a pore); FION tightly to slightly different sites be appropriate to treat the solvent versus z, free energy profile along the pore axis; I/V, from those occupied by K1, thus within the pore as a region of single-channel current versus voltage relationship. helping to explain the physiologiintermediate dielectric (e ~30). cally observed ‘block’ of KcsA Counterion screening is reprechannels by intracellular Na1 ions23. It simulation25. In one simulation with sented in terms of a Debye–Hückel paseems likely that further simulations three K1 ions, exit of the ion within the rameter derived from the ionic strength will be required to understand fully how central cavity from the channel via its at which the calculation is performed. selectivity is determined by a delicate intracellular mouth was enabled by a Although such calculations embody a balance of ion–protein, ion–water and transient increase in the radius of the number of approximations, they might protein-deformation energies. Another intracellular mouth. It is suggested that provide insights into the electrostatic aspect that cannot be neglected is the such ‘breathing’ motions might form the environment within a model pore. The importance of ion–ion interactions molecular basis of channel opening. electrostatic-potential energy profile within the pore28,32. In general, it is evi- Indeed, simulations of isolated TM represents the potential energy (in dent that presence of multiple K1 ions helices from K1 channels suggest a degree kcal/mol) of a univalent cation in the within the KcsA channel plays an impor- of ‘hinge-bending’ flexibility that might channel, apart from the relatively small tant role in maintaining a high perme- underlie channel-opening motions34. effect of the interaction of the cation ation rate. Hinge-bending of the channel-lining with its own polarization charge (which One aspect of KcsA that has not been helices of a voltage-gated K1 channel will be about the same as the interaction fully addressed by simulation studies is has also been suggested by recent with a single unit of charge on the chanthat the crystal structure appears to be experiments35 in which the ability of nel wall, with the same sign as the perthat of the ‘closed’ form of the channel. channel-blocking compounds to prevent meant ion). Of course, the exact height This is reasonable as the closed state of chemical modification of cysteine resi- or depth of the barriers or wells the channel is favoured at neutral pH, at dues introduced into various sites in the depends on the parameters employed which the crystal structure was solved. pore-lining S6 helix was used to map the in the Poisson–Boltzmann calculations e within the pore and the Examination of the channel structure re- helix conformation around the intra- (e.g. Debye–Hückel parameter within the veals that the ‘gate’ might lie close to cellular mouth of the channel. pore). the intracellular mouth of the channel, From such a profile the one-dimenwhere the pore radius drops to less than Towards longer timescales So far, we have been concerned with sional Nernst–Planck equation1 can be that of a desolvated K1 ion. Electronic paramagnetic resonance (EPR) spectro- timescales shorter than those required used to calculate single-channel currentscopic studies of KcsA (Ref. 33) suggest to describe physiologically meaningful voltage curves. The equation is effecthat channel opening is associated with fluxes of ions. To bridge this temporal tively the electrochemical-diffusion changes in packing of the transmem- gap one must simplify the description of equation for charged particles. It brane helices, so as to widen the pore at a channel system, while retaining the describes the mean flux along the chanits intracellular mouth. A glimpse of this essential properties revealed by MD nel-pore axis as a function of concenprocess might have been obtained by simulations (Fig. 5). We will briefly review tration and electrostatic-potential energy
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TIBS 25 – AUGUST 2000 profile. This method has been applied to several model channels, including Alm (Ref. 37) and the designed Leu–Ser (LS) peptide channel36,39. Both studies correctly predicted the non-linear shape (‘rectification’) of the respective experimental single-channel current-voltage curves. However, it is more difficult to obtain accurate predictions of absolute values of single-channel conductances, as these are rather sensitive to assumptions concerning the cross-sectional area of the channel and the diffusion coefficients of ions within the channel. Of course, the latter properties might be estimated by appropriate MD simulations40. A more deep-seated theoretical problem is that of the correct treatment of ion–ion interactions38. Electrostatics and K1 channels. There have been a number of electrostatics studies of K1 channels, especially KcsA. Carloni and colleagues24 emphasized the importance of the electrostatic field generated by the remainder of the channel in guiding cations into the channel mouth. Roux and MacKinnon41 have shown how the electrostatic field generated by dipoles of the four inwardly pointing P-region a helices of KcsA help to stabilize a K1 ion within the small water-filled cavity in the centre of KcsA, thus helping to solve the fundamental problem of how to transport an ion through the low dielectric barrier presented by a lipid bilayer. Simple electrostatics calculations might also be used to estimate the most likely ionization state of acidic and basic side chains at the mouths of the KcsA channel. This approach was applied to a simple model of the pore domain of a voltage-gated K1 channel (developed before the KcsA structure was solved)42. The results indicated that acidic side chains forming rings at the mouth of the channel were not all ionized, and that the assumed ionization state had a significant influence on the electrostaticpotential energy profile of an ion moved along the channel axis. A similar effect is seen if these calculations are applied to KcsA (K.M. Ranatunga and M.S.P. Sansom, unpublished). Thus, it might be necessary to feed back the results of electrostatics calculations on residue ionization states into MD simulations in order to obtain a correct picture of channel–ion–water interactions. Ideally, one would like to be able to run MD simulations in which the ionization states of side chains were dynamically updated. Brownian dynamics and beyond… Some of the limitations of a Nernst–Planck
approach to predicting physiological channel properties are the result of replacing the discrete ions by an implicitly time-averaged ‘concentration’. It is possible instead to retain discrete ions but make them move in the electrostatic field created by the protein with a random component mimicking the effect of the water. Their motion is described, in this case, by the equations of Langevin dynamics or, if the inertia of the ions is negligible, BD. Such an approach has been outlined in a general fashion43 and shown to be capable of capturing the essence of the physiological permeation behaviour. More recently, BD simulations have been applied to a simplified model of KcsA (Ref. 9) and to atomistic models of porins44,45. In both cases, the BD simulations yielded good predictions of the experimental single-channel conductances, and for the porins ion selectivity (for anions versus cations) was well modelled. This approach has considerable potential for providing a physically meaningful description of ion permeation on a physiologically meaningful timescale. However, several refinements are needed. For example, in the light of MD simulation results for KcsA it seems unlikely that a simple electrostatic potential profile calculated from a rigid channel-model will adequately capture the energetics of channel–ion interactions in the filter region. Moreover, ion–ion interactions in the channel are strongly influenced by the presence of the protein. Furthermore, careful simulation studies will be needed to investigate the appropriate value of the diffusion coefficient to assign to an ion as it moves through different regions of the channel. Finally, there remains the question of the dielectric behaviour of the solvent (which, in turn, influences the strength of channel–ion electrostatic interactions) in different regions of the pore. There are alternatives to BD for linking MD simulations with physiological measurements. For example, it might be possible to split the treatment of the energetics of ion permeation into an atomistic component (namely a free-energy profile from MD simulations) and a continuum component (based on continuum electrostatics and including the transbilayer voltage difference)46. KcsA will remain an important test system for this and related approaches.
The future Simulations have already provided us with a number of insights into how ion
channels work. For example, they have revealed some of the complexities of protein flexibility coupled to ion movement through a narrow pore and are suggestive of the way in which such flexibility might be influenced by the bilayer and solvent environment surrounding the channel protein. However, several challenges remain if simulations are to mirror physical reality more accurately. In particular, it will be necessary to include a representation of a transbilayer electrochemical difference (i.e. difference in ionic concentrations and voltage), and to consider different conformational states (i.e. closed versus open) of a channel. In addition to these computational challenges, one would also like simulations to encompass some of the complexities of mammalian K1 channels. The X-ray structure of KcsA can be used as a starting point for generating models of mammalian K1 channels, and such models can be further explored by simulations. For example, this approach has been applied to the pore-forming domain of an inward-rectifier K1 channel27. In the longer term, it will be important that simulations embrace more complex ion-channel structures, taking into account, for example, possible multiple pathways for permeating ions and changes in channel structure, which occur in response to changes in transbilayer voltage47. The future is promising for simulation studies of ion channels. A computational approach will allow us to determine the origin of numerous physiological properties of ion channels, thus providing a detailed physico-chemical ‘annotation’ of X-ray structures. For example, simulation studies are already yielding insights into mechanisms of ion selectivity in KcsA. By combining accurate models (and, hopefully, experimental structures) of diverse channels with simulations, it should be possible to explain, at a fundamental level, how different channels select between different ions, and how ions, drugs and toxins can selectively block certain channels. In the longer term, it might even be possible to describe the dynamic structural changes underlying channel gating.
Acknowledgements Our thanks to all of our colleagues for their interest in this work, especially Phil Biggin, Declan Doyle and Peter Tieleman. Work in M.S.P.S.’s laboratory is supported by grants from the Wellcome Trust.
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