Continuum electrostatic calculations of the pk a of ionizable residues in an ion channel: Dynamic vs. static input structure

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1 Eur. Phys. J. E 31, (010) DOI /epje/i y Regular Article THE EUROPEAN PHYSICAL JOURNAL E Continuum electrostatic calculations of the pk a of ionizable residues in an ion channel: Dynamic vs. static input structure M. Aguilella-Arzo and V.M. Aguilella a Department of Physics, Universitat Jaume I, Av. Sos Baynat s/n, E-1078 Castellón, Spain Received 6 January 010 and Received in final form 18 March 010 Published online: 5 April 010 c EDP Sciences / Società Italiana di Fisica / Springer-Verlag 010 Abstract. We have computed the pk a s of the ionizable residues of a protein ion channel, the Staphylococcus aureus toxin α-hemolysin, by using two types of input structures, namely the crystal structure of the heptameric α-hemolysin and a set of over four hundred snapshots from a 4.38 ns Molecular Dynamics simulation of the protein inserted in a phospholipid planar bilayer. The comparison of the dynamic picture provided by the Molecular Simulation with the static one based on the X-ray crystal structure of the protein embedded in a lipid membrane allows analyzing the influence of the fluctuations in the protein structure on its ionization properties. We find that the use of the dynamic structure provides interesting information about the sensitivity of the computed pk a of a given residue to small changes in the local structure. The calculated pk a are consistent with previous indirect estimations obtained from single-channel conductance and selectivity measurements. 1 Introduction 1.1 Computation of pk a s in proteins A great deal of the biochemical functions performed by cells is regulated by the ph of the adjacent solutions. Through protonation-deprotonation processes the macromolecules change the charge state of their residues and can adopt different conformations, which in turn affect their function. For this reason the titration of proteins has been extensively studied in experiments. In order to get a better description of the protonation-deprotonation equilibrium occurring in ionizable residues, specific theoretical methods have been proposed to compute the pk a of such residues. These methods can be broadly classified in terms of their level of microscopic description of the system [1]. Over the years, great refinements have been made from the early attempts of Tanford and Kirkwood, who treated the protein as a sphere with charges embedded on it []. For instance, the increase in computational power has made it possible to solve the full Poisson-Boltzmann (PB) equation for an arbitrary geometry. This approach and its variations, commonly known as Finite Difference Poisson-Boltzmann (FDPB) methods, are among the most widely used because of their simplicity and reasonable accuracy [3]. The FDPB methods use a static 3D charge distribution as input, usually derived from the crystal structure of the protein resolved by X-ray or NMR techa aguilell@uji.es niques. However, today it is believed that most discrepancies in the computations of pk a have to do with ignoring the local changes in protein conformation following the protonation-deprotonation process [4, 5]. Several methods have been introduced to account for this charge rearrangement, namely the approximate Protein Dipole Langevin Dipole model of Warshel [6], the Multiconformation Continuum Electrostatics (MCCE) approach [7 9] and the combined Finite Difference and Debye-Hückel methods [10,11]. More recently, a method based on the Generalized Born approximation combined with an iterative mobile clustering approach to calculate the equilibria of proton binding to multiple titration sites has been proposed, which seems to be both accurate and fast [1]. Molecular-Mechanics [13] or Molecular Dynamics (MD) [14 0] sampling combined with energy minimization procedures [1] have also been used. Other methods with a higher level of microscopic detail (and also more computing demanding) are the Free Energy Perturbation [], Monte Carlo [3] and the Constant-pH Molecular Dynamics methods [4 6]. Attempts to increase the speed of the method without losing accuracy have been also presented based on a distance- and positiondependent screening of the electrostatic potential, combined with a Monte Carlo algorithm [7]. Finally, there have been attempts to use Quantum Mechanics methods [8 30] to compute pk a of proteins, but these are only applicable to a few isolated residues due to their inherent complexity. For review, see [30 34] and references therein. The effect of the specific environment of protein residues,

2 430 The European Physical Journal E Fig. 1. Side (left) and front (right) view of the αhl channel inserted in a DPPC membrane. Ions, solvent and small solutes can cross the membrane through the channel, driven by concentration or electric potential gradients, and feel the electrostatic influence of a different charge distribution at each ph. Image created using VMD. Structure taken from the MD trajectory in [49]. e.g. inclusions of water molecules or highly hydrophobic environments, has been also discussed [35]. In addition to taking into account the dynamic nature of the protein on the pk a computation, there is also growing interest on the reliability of the protein crystal structure as input for any structure-based computation. There are some recent examples of protein structures deposited in the Protein Data Bank that were found to be inaccurate or simply wrong [36]. Additional data coming from molecular simulation or experimental measurements are then very useful to validate the crystal structure or to open a debate about the inconsistencies between the structural data and the protein functional properties [37,38]. It becomes clear that none of the above-mentioned models for pk a computation are flawless [39]. In fact, the accuracy of the methods based on microscopic or macroscopic descriptions is often comparable except when dealing with very specific residues as those lying in the active sites of enzymes. The computational cost should be also borne in mind, since it increases rapidly when going down to the microscopic scale. Consequently, a compromise between both ends must be sought, depending on the characteristics of the protein studied. Reported computations of the pk a of membrane proteins using FDPB methods are scarce. The reason can be found partly in the difficulty entailed in crystallizing membrane proteins (actually, just a few structures are known). Some of these studies have focused on bacterial porins [40 43] and also on Bacteriorhodopsin [44]. The membrane was commonly represented by a structureless region of low dielectric constant. To our knowledge, no attempt was made to include the membrane explicitly, as will be done here. 1. The protein channel α-hemolysin Here, we study the integral membrane protein α-hemolysin (αhl), a toxin from Staphylococcus aureus.the crystal structure of αhl, determined from X-ray diffraction with a resolution of 0.19nm, is known since 1996 [45]. Figure 1 shows the αhl heptamer inserted in a dipalmitoylphosphatidylcholine (DPPC) bilayer. The availability of the αhl structure has fostered the development of models seeking to account quantitatively for the channel functional properties. The αhl channel has the advantage that it can be easily reconstituted in planar membranes, so its single-channel conductance and selectivity can be studied under a wide range of experimental conditions. This makes this protein an ideal system to test current electrodiffusion models. There have been attempts to explain theoretically the transport properties of αhl. Misakian and Kasianowicz [46] described qualitatively the nonlinear, rectifying current-voltage relationship by using a simple onedimensional Nernst-Planck model in which the assumed linear electric potential profile was disrupted by barriers and wells, related to selected charged residues that are facing the pore lumen. Later, more elaborated models based on 3D Poisson-Nernst-Planck and Brownian Dynamics methods [47] gave important clues about the residues involved in the selectivity and rectification properties of the channel. Thus, the channel ionic selectivity was ascribed to the small charge separation due to the salt bridge between residues E111 and K147 in the channel constriction [47]. Also Hybrid Molecular Dynamics-Nernst-Planck methods [48] found a highly reduced diffusion coefficient inside the channel and were able to reproduce the currentvoltage curve using a not too expensive computational method. A few years ago, a landmark paper by Aksimentiev and Schulten [49] reported the first successful attempt to derive electrodiffusion properties from an allatom MD simulation, and a further refinement led to a realistic account of translocation of solutes in events in the millisecond range using MD runs of only few nanoseconds [50]. These theoretical studies on αhl assumed a protein charge distribution consistent with the free solution pk a s of the protein ionizable residues, also known as model pk a s. MD simulations have been reported in which the charge distribution defined at the beginning of the simulation has an important effect on the average

3 M. Aguilella-Arzo and V.M. Aguilella: pk a of ionizable residues in an ion channel 431 structural properties [51]. This means that a right choice of the charge state of the protein, based on a previous computation of the pk a s of the ionizable residues, can be crucial. Besides, the interpretation of ph-dependent conductance and selectivity measurements in terms of the protein channel structural properties relies on a proper estimation of the pk a s of the residues involved. Our main goal in this paper is computing the pk a of all the ionizable residues present in the αhl channel. We choose the FDPB method because it is moderately computationally costly and it is capable of yielding pk a values with accuracy comparable to other more complex methods [33]. On the one hand, we calculate the apparent pk a of the channel residues by using as input the 3D structure of the crystallized αhl channel [45] surrounded by a low polarizability structureless medium that simulates the bilayer membrane. On the other hand, we use as input for the pk a computation a long sequence (4.38ns) of structure snapshots obtained from a MD simulation of the αhl channel [49] including also explicitly a number of lipid molecules surrounding the protein. We intend to compare the dynamic picture provided by the Molecular Simulation with the static one based on the X-ray crystal structure of the protein embedded in a lipid membrane and analyze the influence of the fluctuations in the protein structure on its ionization properties. In addition, we want to explore the sensitivity of the pk a computation of a given residue to small changes in the local structure like those found among the seven monomers that assemble to form the channel. This has been already suggested as a convenient assessment of the reliability of the computed pk a [5]. There have been previous studies that used a combination of FDPB and MD methods. However, the validity of a MD simulation to improve the pk a values obtained using a FDPB method is still controversial. Some results support the validity of this method [13 0], but others still put uncertainty in the capability of MD averaging to improve the method [1]. Nevertheless it seems that this failure to increase the accuracy of the FDPB-computed pk a s appear only in calculations of the pk a s of specific active-site groups or the pk a s of residues deeply buried in the protein. In membrane protein channels this question is not solved yet. Furthermore, the functional properties of the αhl channel involve a large number of the protein residues (especially those located near the aqueous pore, i.e. not deeply buried), rather than a few specific ones. Because of this, it is expected that a combination of MD with FDPB will be advantageous. The calculations presented here intend to throw some light on this issue by analyzing one of the few membrane proteins for which a MD run long enough to simulate explicitly ionic conduction is available. Methods The difference in the free energy of protonation (or deprotonation) of a titratable group in a model compound in free solution and in a biomolecule, G, implies a shift in its pk a according to the equation pk a = G/(.303RT). Therefore, the protonation state of a titratable group may differ in diverse molecular environments. For the modeling of multiple titratable sites we follow the approach of Bashford and Karplus [53] as modified by Antosiewicz et al. [54, 55] and consider the ionization process by adding a positive or a negative charge on a single atom in the titratable group. We regard each ensemble of ionization states of the molecule as a set of charges {z i }, where the index i runs on all atoms. For most atoms z i is 0, but it takes the values 0 or ±1 proton charge for the selected atom in each titratable group, according to its protonation state. The free energy of ionization (by taking as reference state the molecule with all ionizable sites uncharged) may be expressed, within the linear approximation for the PB equation, as G = ( 1 ( (qi + z i )(q j + z j )φ N ij) 1 ( 1 ( (qi + z i )(q j + z j )φ M ij + i ) 1 ( qi q j φ N ) ) ij ( qi q j φ M ) ) ij.303rt z i (pk a i,m ph), (1) where lower indices i and j run on all atoms and upper indices M and N refer to a model compound in which the pk a s are known, and to the biomolecule, respectively. q i denotes the charge of atom i, φ ij are the values that Green s function takes on sites i and j, and the ph refers to the solution. The use of the linearized PB equation ensures that the superposition principle is fulfilled. For a discussion about the validity of this approximation, see [56]. The model pk a s are usually measured on small peptides containing the aminoacid of interest. In order to cancel selfenergy terms, a good model for these small peptide compounds are the isolated (i.e., non-interacting) aminoacids artificially excised from the molecule, assuming that the pk a for these hypothetical compounds would be the same as that measured on small peptides. Under this assumption, eq. (1) further simplifies to G = 1 z ( i φ N ii φ M ) ii i ( N ( M + zi q j φ N ( ij) zi q j φ M ) ) ij + zi z j φ i>j( N ) ( ij +.303RT z i ph i,m ) pka. i () Green s function between atoms belonging to different aminoacids in the model compound is zero (i.e., φ M ij =0if i and j refer to atoms in different residues). The first term in this equation represents the difference in self-energy between placing a charge z i in the titratable site in the protein and in the model compound. The second term is the

4 43 The European Physical Journal E so-called background term accounting for the energy difference of the interaction between the charge z i and the other partial charges (when all other ionizable groups are uncharged) in the protein and in the model compound. The third term represents the interaction between titratable sites in the protein, and the fourth term is the free energy of ionization at a given ph for the model compound. The free energy described in eq. () can be used to generate the statistical charge state of each ionizable site at each ph using a Monte Carlo method. The FDPB solver used in all pk a computations was UHBD [57], together with some Bash scripts and C programs for the Monte Carlo part of the computation. All the programs were run in Linux. The salt concentration used in calculations was 1M, in accordance with the MD trajectory simulation. The crystal structure of α-hemolysin was obtained from the Protein Data Bank repository [58] (code 7AHL). We added hydrogen atoms, completed the structure (some residues were missing or incomplete) and energy minimized the hydrogen positions. This structure was surrounded laterally by a low polarizability medium (ε = 0) to mimic the lipid membrane, and immersed in a high dielectric constant environment representing the water solution (ε = 80). Thus, our model considers two regions of different polarizability: the protein-lipid membrane and the water solution. The membrane was simulated by a slab of a structureless medium of dimensions Å, with a space left for the protein in the center within the XY plane (the protein channel was oriented along the Z axis). The starting computational box had dimensions with a length of.5å, and successive focusing around each residue was done using finer grids of 1.Å, 0.75Å and finally 0.5Å. Finally, the pk a for a given residue was assigned the average between the actual values obtained for the same residue in each one of the seven monomers. In addition to the X-ray crystal structure, we used as input structure a set of 439 snapshots from an MD simulation of the αhl channel, including the lipid membrane and the solvent (kindly provided by Dr. A. Aksimentiev). The MD simulation included one copy of the αhl protein, a patch of DPPC lipid bilayer and 1M KCl water solution. The simulation was run using NAMD with the CHARMM and CHARMM7 force fields, periodic boundary conditions and particle-mesh Ewald full electrostatics. We extracted each structure from the trajectory (a 4.38ns simulation with 10ps sampling), together with a number of DPPC lipid molecules to account for the membrane, and used the resulting system as a dynamic input for the FDPB computing method described above. We used ε = 80 for the water solution but we performed pk a calculation for two different values of the dielectric constant in the protein-lipid domain: ε = 4 and ε = 0. The electric permittivity of the protein domain is a key parameter in continuum electrostatic calculations. Given the low polarizability of the protein, ε 4 would seem a realistic value. However, the various approximations made in the FDPB methods are usually subsumed in a greatly increased effective dielectric constant for the protein-lipid region in order to get meaningful effective pk a values [1]. Some comparisons with experimentally measured pk a values for globular proteins suggest using an effective dielectric constant ε 0 in pk a calculations. We decided to check whether the use of a dynamic input structure for pk a calculations has any effect on this phenomenological parameter. Since the overall procedure was computationally expensive, we designed a protocol which broke the trajectory and distributed the pk a computations between several CPU s of the Linux API cluster in University Jaume I. As a result of the calculations based on the MD input structure, we obtained the pk a time evolution for each residue in the αhl protein heptamer. The pk a of a given residue was first averaged over the full trajectory of 439 snapshots and then averaged over the seven monomers. Then, these pk a were compared with the values obtained from the crystal structure (with ε = 0), which are assumed to be the most reliable in the absence of experimental data [56]. Our averaging procedure is similar to that of van Vlijmen [15], which consisted on averaging the titration curves and using the resulting average titration curve to obtain the apparent pk a, and a similar approach had been also used by Bashford et al. [44]. 3 Results and discussion 3.1 pk a s from crystal structure and MD structure snapshots Table 1 shows the pk a s of the 95 ionizable residues of each αhl monomer, computed from the channel crystal structure [45] and the MD trajectory by using for the protein and lipid domain ε = 0 (see discussion later). These results are also shown graphically in fig.. The tabulated values of the calculated pk a and the pk a (This pk a shift is the difference between calculated pk a and the corresponding model pk a ) are averages over the seven monomers and the standard deviation σ is also shown. The standard deviation is generally small (σ 0.7 pk a units on the average), with the exception of a few specific residues like Asp4 or Lys37, where small differences in structure among monomers have a big impact on the calculated pk a value. The difference among the computed pk a s for different monomers could be ascribed to the small structural differences naturally occurring in the protein, but also to the errors present in the X-ray structure at the given resolution. In order to minimize any numerical error arising from small differences in the position of each monomer relative to the grid used in the numerical solution of the PB equation, the grid size has been adjusted, so that the remaining differences are mainly of structural origin. Some general trends are observed: for example, the pk a s of all Asp and Glu acidic residues are lower than their model pk a, both using the crystal and the MD structures. Interestingly, it is found that the pk a shift for Asp residues ( pk acrystal ) is generally greater

5 M. Aguilella-Arzo and V.M. Aguilella: pk a of ionizable residues in an ion channel 433 Table 1. pk a of the 95 ionizable residues per monomer in the αhl channel. pk a is the average over the seven monomers of the αhl channel (between monomers and along the trajectory when applicable). The pk amodel is the pk a of a residue in free solution. σ denotes the standard deviation of the pk a among the seven monomers (ε = 0 is assumed for the protein-membrane region: see details in main text). Crystal structure MD simulation Atom Residue No. pk amodel pk a σ pk a pk aintr pk a σ pk a pk aintr NT Ala CG Asp CG Asp NZ Lys CG Asp NZ Lys CG Asp OH Tyr CG Asp NZ Lys CD Glu ND1 His NZ Lys NZ Lys OH Tyr CG Asp CG Asp NZ Lys ND1 His NZ Lys NZ Lys CZ Arg NZ Lys OH Tyr CZ Arg OH Tyr CD Glu CD Glu NZ Lys NZ Lys CG Asp CD Glu CG Asp OH Tyr OH Tyr CZ Arg CG Asp NZ Lys CD Glu OH Tyr OH Tyr CG Asp CG Asp NZ Lys ND1 His NZ Lys

6 434 The European Physical Journal E Table 1. (Continued). Crystal structure MD simulation Atom Residue No. pk amodel pk a σ pk a pk aintr pk a σ pk a pk aintr OH Tyr CG Asp NZ Lys CD Glu CG Asp NZ Lys NZ Lys NZ Lys OH Tyr CG Asp CZ Arg CG Asp OH Tyr NZ Lys CZ Arg NZ Lys CG Asp CG Asp NZ Lys CG Asp CG Asp CZ Arg NZ Lys NZ Lys CG Asp OH Tyr CD Glu CZ Arg CZ Arg CG Asp CG Asp OH Tyr ND1 His NZ Lys NZ Lys CG Asp NZ Lys CG Asp CZ Arg CD Glu CZ Arg OH Tyr NZ Lys CG Asp CD Glu NZ Lys CD Glu CD Glu CT Asn

7 M. Aguilella-Arzo and V.M. Aguilella: pk a of ionizable residues in an ion channel A 1 10 pka value 8 6 model pka MD pka crystal pka 4 pka B From MD trajectory From crystal structure Residue Number Residue Basic residues Acidic residues Fig.. (Colour on-line) A) Comparison of the pk a values computed using the single-crystal structure (triangles) and the monomer-averaged pk a s from the MD trajectory (circles). Model pk a s are also shown as black squares. B) pk a shifts for residues in α-hemolysin calculated from the crystal structure (yellow) and the MD structure (blue). The standard deviation (between monomers and along the trajectory when applicable) is also shown as error bars. Basic and acidic residues are shown apart. pk a shifts obtained from MD and crystal structures are shown side by side, and ordered by increasing residue number. Most acidic residues with positive shifts correspond to tyrosines. than for the Glu ones ( pk acrystal 1). It is also found than Tyr residues exhibit a large positive pk a shift ( pk acrystal > ), and this effect is greater when the crystal structure is used. The pk a shift of Lys residues is moderate ( pk acrystal 1), but this effect is slightly more pronounced when using the MD structure compared with the crystal structure. Arg residues also exhibit a positive pk a shift, though more pronounced ( pk acrystal ). Finally, the pk a shifts of histidines are also negative, although the shift is smaller when using the MD structures ( pk acrystal 3, pk amd ). All these trends are clearly seen in fig. B: In general basic residues are shifted to higher pk a and acidic residues to lower pk a compared Fig. 3. (Colour on-line) Close view of the neighbors of the residue Asp4 (central side chain) in the seven monomers of the crystal α-hemolysin structure. The backbone in shown in yellow. The seven monomers are RMS fitted to each other using the backbone atoms. As a result, no significant differences appear among the position of the seven structures, as evidenced by the superposition of the side chains. Hydrogen atoms were removed for clarity. Image created using VMD [59]. with their free solution values. Tyrosines are an especial case, with positive shifts. In summary, residues with model pk a higher than 7 exhibit a positive pk a shift and residues with model pk a lower than 7 exhibit a negative pk a shift. The relatively big differences found between the pk a of the same residue in each of the seven monomers could be attributed to the electrostatic interaction with the neighboring residues: For example, if we examine the intrinsic pk a (that is, the pk a computed without taking into account the interaction between neighbor ionizable residues) of Asp4 in each of the seven monomers we find values ranging from 5 to 7, which are spread over a much narrower range than the apparent pk a shown in table 1 (the intrinsic pk a includes interaction energies coming from the changing dielectric environment and the partial charges, but not from the interaction between residues). Let us analyze more closely this example. If we select the residues lying near Asp4 a we find that His48 g and Lys37 a are close enough to strongly interact with it (lower indices a to g make reference to each one of the seven monomers, the order being that of the pdb file). In fact, the distance between the atoms bearing charge in the pk a procedure is 5.45Å (distance from Asp4 a.cg to His48 g.nd1) and 3.85Å (between Asp4 a.cg and Lys37 a.nz) whereas these distances are 5.0Å (between Asp4 f.cg and His48 e.nd1) and 3.76Å (between Asp4 f.cg and Lys37 f.nz), that is, slightly lower in the latter case. This compares well with the pk a values predicted for Asp4 in the corresponding monomers which are 5.6 and -.0. We see that a few tenths of Å, which cause hardly noticeable structural differences between monomers (see fig. 3), yield important pk a deviations, because of the increased electrostatic interaction. Interestingly this example serves to illustrate two opposite effects usually present in pk a computations: On

8 436 The European Physical Journal E the one hand we find an increase in the pk a of the acidic residue Asp4 related to Born energy (from a model pk a of 4.0 to an intrinsic pk a 6), because it is more energy costly to deprotonate the acidic residue in a low-dielectricconstant medium than in free solution. On the other hand, the interaction energy of Asp4 with its neighbor residues (positively charged when ionized) has the opposite effect, facilitating the deprotonation and consequently lowering the pk a. Other residues with high pk a standard deviation, i.e., with different pk a in every monomer, can be analogously analyzed. The case of Lys37 a is somewhat similar: the interaction with Asp4 a and especially with Asp100 g would explain the unusual positive pk a shift, and the small changes in distances between them would account for the high standard deviation (σ =.) between monomers a-f. Other residues in table 1 have been highlighted because of their specific position in the protein channel. Residues facing the pore lumen (shown in roman boldface) and residues somewhat buried and lying near the aqueous pore (shown in italic boldface) share a common feature: their pk a shift is small because their environment resembles that of the aminoacid in free solution. They are interesting because of their expected influence on channel electrodiffusion properties. Among them we find Asp17 and Lys131 with important pk a shifts, both located near the pore mouth in the stem region: we may speculate that they interact with each other causing their pk a to deviate from the model pk a, despite their position in the protein-solution interface (the inspection of their intrinsic pk a seems to support also this explanation). In spite of the relatively large pk a shifts found for many residues, an interesting information contained in table 1 (and clearly seen in fig. B), useful for theoretical studies on the αhl channel and for the interpretation of experiments, is that at neutral ph the expected ionization state of every channel residue is the same as that we would obtain using the model pk a (the so-called null model). However, a slight change of the ph in experiments (simply units up or down) would cause significant changes in the charge distribution. This is of importance on many controlled experiment or theoretical models in which the ph is selected at will [46,47]. As for the pk a shift experienced by the residues, in some cases we find extreme deviations compared with the model pk a (for example in Asp100), though mainly for residues deeply buried. Tyrosines are an especial case, with big pk a shift probably because they are buried, or located near the protein-membrane interface. In order to better visualize the general trend of each residue pk a shift according to its position in the protein, we have represented graphically in fig. 4 the axial position for each ionizable residue in a single monomer, versus the radial distance to the pore axis. Two differently colored dot sets are represented, according to the pk a shift of the residue. Acidic and basic residues are shown as triangles and circles, respectively. Residues located near the protein-solution interface (not the aqueous pore) have in most cases a small pk a shift (blue) because of the similarity between their environment and that of the compound in free solution. The similarity in the residue environment Distance to axis (Å) CA and CB positions pka < 1 pka > 1 MEMBRANE AQUEOUS PORE Acid Basic Axial position (Å) Fig. 4. (Colour on-line) Graphical representation of the relative position of the ionizable residues in one of the seven αhl monomers. Vertical axis represents the distance of each residue to the symmetry axis of the heptamer. Note that the relative distances between residues could be misleading because their angular distance is lost in this planar representation. Small pk a shifts (< 1) are in blue and large pk a shifts (> 1) are shown in magenta (calculated using the channel crystal structure). Acidic residues are represented by triangles and basic residues by circles. The light grey area covers approximately the region occupied by the lipid membrane. means that the free energy required to charge-uncharge the residue in this position will be comparable to that in free solution. This will be generally true except when charged residues lie in their neighborhood. In this case, depending on the sign of the neighboring residue, the free energy will increase or decrease compared to that without the specific interaction. The reverse situation is also true: residues which are buried in the protein exhibit large pk a shifts (magenta). In this case it is expected a big contribution coming from the low-polarizability environment inside the protein. Generally this contribution, the Born energy term, will decrease the pk a of the basic and increase the pk a of the acid residues, but the low polarizability of the protein also magnifies greatly the interaction term which has the opposite effect on the average. As a result of these two tendencies the pk a of the buried residues often departs from 7, giving rise to important pk a shifts. 3. Indirect experimental measurement of pk a Before the channel crystal structure was solved, Kasianowicz and Bezrukov [60, 61] studied the ph-dependent current fluctuations in the αhl channel reconstituted in a planar lipid bilayer. From the spectral analysis of the lowfrequency noise, and using a simple model based on the reversible protonation of a number of identical ionizable residues, they evaluated an effective pk a 5.5 for those unknown residues involved in the ionic current fluctuations. None of the seven residues considered a decade later

9 M. Aguilella-Arzo and V.M. Aguilella: pk a of ionizable residues in an ion channel 437 by Misakian and Kasianowicz [46] as candidates to control ion transport through the channel (because of their position, near the pore lumen) have pk a values close to 5.5. More recently, Aksimentiev and Schulten [49] proposed that His144 could be the specific residue responsible for the observed protonation-deprotonation dynamics, without excluding the influence of other residues. Their conclusion was based on large-scale MD simulation of channel conductance and on the model pk a of histidines, 6.3. By setting neutral the seven histidines near the rim, they simulated the conductance at ph 4.5 and found an increase, in agreement with that observed experimentally [61]. These results are not ruled out completely by our pk a calculations, which suggest a value of 4.1 ± 0.6 for this residue. Anyway, it has to be born in mind that the interplay of multiple and different ionizable sites needs a more subtle interpretation of the current fluctuation in the αhl channel. We have explored alternative possibilities by focusing on the ionizable residues located near the aqueous pore, which are most probably involved in the transport properties of the protein. Some residues are present in pairs of one acidic and one basic residue, and close enough to interact strongly when one of them is charged. This is the case for Lys147 and Glu111, or Lys131 and Asp17. This last couple has the charged groups located very close each other ( 0.3nm) and they might be related to the increase in the channel current noise near ph 5. Though there are no direct experimental measurements of the pk a s of the αhl channel residues, indirect evidence supporting our results can be found in a few studies of this channel. A Poisson-Nernst-Planck simulation of this system [47], proposed the residues located in the end of the stem domain as the main determinants of the asymmetry in conductance of the αhl channel. More specifically they suggested that D18 is the group responsible for the channel rectification. Also, αhl channel current measurements at different ph values [46] showed that the current asymmetry at ph = 4.5 and ph = 7.5 was very similar. In view of these two findings, we can conclude that the pk a for the D18 group must be lower than its model pk a (4.0) in order to explain the small differences. This is consistent with our calculation for this residue (pk acrystal 3.4 ± 0.6 andpk amd 3.5 ± 0.4). 3.3 pk a s from MD: sensitivity to structural relaxation and dielectric properties The results of the pk a calculation performed by using the series of 439 MD snapshots as dynamic input structure (and the same value ε = 0 for the protein-lipid region as in the crystal structure calculations) are shown in table 1 and fig.. As mentioned in the Methods section, the tabulated values are the average over the snapshots and over the seven monomers. There is a general agreement between the two sets of pk a values, the difference being less than 0.9 pk a units on the average. Nevertheless, there are specific groups for which the discrepancy is high. These include Asp4, Tyr68, Asp100, Lys110 and His59 with more than 3 pk a unit differences between pka Model pka Crystal pka MD average ε = 0 ε = Time (ns) Fig. 5. Time evolution of the pk a of residue Glu111 a along a MD trajectory (grey line) calculated using ε = 0 (left panel) and ε = 4 (right panel) for the protein. The solid line shows the average value along the trajectory. The dashed line represents the pk a computed from the crystal structure, by using ε = 0. Model pk a is represented by a dotted-dashed line. both procedures. Interestingly, it is also found that most groups with significant discrepancies between the MD and crystal pk a sets have usually also a great pk a dispersion among monomers (i.e., higher than the average) in the crystal-based calculations, and frequently also in the MDbased calculations. In some cases, as in Asp4, the crystal pk a standard deviation of the group is more than 3 pk a units. There is no clear evidence of an improvement in the pk a calculation from the MD structure. However, in the absence of a good benchmark for the pk a values, the advantage of the MD-based calculation is that it yields a slightly smaller standard deviation in the pk a values between monomers ( σ crystal =0.73, whereas σ MD =0.59). Therefore, to a certain extent, the conformational relaxation of the protein minimizes the limitations of the resolution of the protein crystal structure [5]. One of the drawbacks of continuum electrostatic calculations is the representation of the dielectric properties of the protein. This is done usually by employing values of the dielectric constant for the protein, the lipid and the water phase that are justified a posteriori by comparison with experiments whenever they are available. There are several studies about this issue in globular proteins but little or almost anything has been done in membrane protein channels. It has been discussed whether the use of a static input structure or several dynamic structures has influence on the choice of the dielectric constant in calculations [0]. For the protein domain, ε = 4 is the most widely accepted value, based on measurements of dry proteins and peptide powders [1], whereas in continuum pk a calculations on globular proteins ε = 0 yield more accurate results [1, 54]. According to some authors, ε 4 would be the recommended value for pk a calculations based on conformational ensembles. Motivated by this, we performed pk a calculations using the MD trajectory and a low dielectric constant (ε = 4). Results differ considerably from those based on the static X-ray struc-

10 438 The European Physical Journal E ture. Figure 5 shows a example: Glu111 a. The computed pk a for the different structures strongly fluctuates along the trajectory (fig. 5, right panel), but in each snapshot the value is consistently far from the value obtained using the crystal structure with ε = 0 (crystal pk a in the figure). However, the MD-computed pk a by using ε =0(fig.5, left panel) shows a time evolution with much smaller fluctuations and with an average value closer to the crystal pk a. The averaging procedure over the whole trajectory does not improve the pk a estimate (see the solid line on the right panel) but yields a very different value to that obtained using the crystal structure with ε = 0 (dashed line). The above results imply that the use of a dynamic protein structure does not allow employing low permittivity values for the protein-membrane region in continuum pk a calculations. However, it provides a way of testing the stability of the set of computed pk a s against small changes in the local conformation of the residues. This can be accomplished through the additional statistical information present in the averaging procedure, while just a set of single pk a values are obtained from the static X-ray crystal structure. 4 Summary and conclusions The pk a values of the ionizable residues of the αhl channel have been computed by using a FDPB method with two types of input structures, namely the crystal structure of the heptameric α-hemolysin (Protein Data Bank code 7AHL) and a set of 439 snapshots from a 4.38ns Molecular Dynamics simulation of the protein inserted in a phospholipid planar bilayer. When the static input structure is used, the calculated pk a values of the 95 ionizable residues are the result of the average over the seven monomers. When the dynamic structure is taken as input, double averaging is made: first over the set of snapshots and then over the monomers. This procedure intends to minimize the errors in the input structure. The main findings can be summarized as follows: ThepK a values obtained by averaging over the MD trajectory compare very well with those coming from the single-crystal structure provided the same value of the protein dielectric constant is used. Discrepancies arise only in those residues which exhibit differences between monomers in the pk a values computed from the crystal structure. The calculated pk a for residues facing or near the pore lumen are consistent with previously reported indirect pk a measurements. Generally, the pk a values obtained by averaging over the MD trajectory have lower standard deviation than those obtained averaging over the monomers of the structure. This can be interpreted in the sense that the relaxation involved in the MD simulation is beneficial for the pk a calculation and gives, in principle, more reliable results than those obtained using a single static structure. The use of a low dielectric constant (ε = 4) and the averaging over the MD trajectory yields very different pk a s from those obtained with the crystal structure. This means that, at least for this protein channel, the use of conformational ensembles does not imply necessarily employing low dielectric constants to obtain reliable pk a results. Support from the Spanish Ministry of Science and Innovation, (MICINN Project No. FIS ) and Fundació Caixa Castelló-Bancaixa (Project No. P1-1A009-13) is acknowledged. M.A. thanks the valuable advice and fruitful discussions with Bertrand Garcia-Moreno and Carolyn Fitch during his stay in the Dept. of Biophysics of Johns Hopkins University (Baltimore, MD, USA). 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