Stability of an Ion Channel in Lipid Bilayers: Implicit Solvent Model Calculations with Gramicidin

Sharron Bransburg-Zabary, Amit Kessel, Menachem Gutman and Nir Ben-Tal
Department of Biochemistry, George S. Wise Faculty of Life Sciences, Tel Aviv University, Ramat Aviv 69978, Israel

Correspondence to: Nir Ben-Tal
Tel: (972-3) 640-6709; Fax: (972-3) 640-6834;
e-mail: bental@ashtoret.tau.ac.il; web: http://www.ashtoret.tau.ac.il 

Running title: Stability of gramicidin in membranes

Keywords: Peptide-membrane interactions, solvation, continuum solvent models, Poisson-Boltzmann equation

ABSTRACT
Gramicidin is a helical peptide, 15 residues in length, which dimerizes to form ion-conducting channels in lipid bilayers. Here we report calculations of its free energy of transfer from the aqueous phase into bilayers of different widths. The electrostatic and nonpolar contributions to the desolvation free energy were calculated using implicit solvent models, in which gramicidin was described in atomic detail and the hydrocarbon region of the membrane was described as a slab of hydrophobic medium embedded in water. The free energy penalties from the lipid perturbation and membrane deformation effects, and the entropy loss associated with gramicidin immobilization in the bilayer, were estimated from a statistical thermodynamical model of the bilayer. The calculations were carried out using two classes of experimentally-observed conformations: a head-to-head dimer of two single-stranded (SS) b-helices and a double-stranded (DS) intertwined double helix. The calculations showed that gramicidin is likely to partition into the bilayer in all these conformations. However, the SS conformation was found to be significantly more stable than the DS in the bilayer, in agreement with most of the experimental data. We tested numerous transmembrane and surface orientations of gramicidin in bilayers of various widths. Our calculations indicate that the most favorable orientation is transmembrane, which is to be expected from a channel-forming peptide. The calculations demonstrated that gramicidin insertion into the membrane is likely to involve a significant deformation of the bilayer to match the hydrophobic width of the peptide (22 ֵ), again, in good agreement with experimental data. Interestingly, deformation of the bilayer was induced by all the gramicidin conformations. 
INTRODUCTION
The linear gramicidins are a family of small antibiotic peptides that form membrane-spanning ion channels in lipid bilayers (Andersen, 1984). They are the best-characterized ion channels and serve as common models for studying ion conduction through membranes and peptide-membrane interactions (reviewed in Killian, 1992; Roux and Karplus, 1994; Wallace, 2000). The sequence of the gramicidin A (GA) channel, which was used in this study is (Sarges and Witkop, 1965):
Formyl-L-Val-Gly-L-Ala-D-Leu-L-Ala-D-Val-L-Val-D-Val-L-Trp-D-Leu-L-Trp-D-Leu-L-Trp-D-Leu-L-Trp-ethanolamine.

The structure of gramicidin A was determined at different conditions (Wallace, 2000). It has been found that the peptide is very sensitive to the environment and can adapt a variety of conformations. Due to the alternating sequence of L and D amino acid residues, the peptide forms b-type of helices with a hydrogen-bonding pattern of the backbone similar to that in b-sheets (Urry, 1971; Urry, 1972; Veatch et al., 1974). In these b-helices the residues point outwards and the carbonyl moieties alternately point upwards and downwards in the interior of the helix, providing the helices with a hydrophilic pore. The helices may be right or left-handed; they can differ in the number of residues per turn, and hence in their dimensions and in the orientation of their chains (Urry, 1971; Urry et al., 1971; Veatch et al., 1974). Individual molecules can fold into single-stranded helices, which may form head-to-head dimers (Urry et al., 1971; Urry, 1972; Ramachandran and Chandrasekaran, 1972). Also, double-stranded helices can be formed in which the two strands run either parallel or antiparallel and which involve intermolecular hydrogen-bonding only (Veatch et al., 1974). 
 
	Over the years, based on accumulative evidence, a consensus has been developed that the predominant channel form is a head-to-head dimer of two single-stranded (SS) b-helices (Arsen'ev et al., 1985; Nicholson and Cross, 1989; Koeppe et al., 1992; Busath, 1993; Ketchem et al., 1996). Recently, however, with the appearance of a new double-stranded (DS) intertwined structure, this consensus was challenged (Burkhart et al., 1998) and there appears to be a controversy as to whether the ion conducting form is a SS or DS structure (Editorial. 1998. Love that b-sheet. Nature Struct. Biol. 5: 749-750; Andersen et al., 1999; Cross et al., 1999; Burkhart and Duax, 1999). To clarify this issue further we present calculations of the stability of gramicidin in both SS and DS structures in model lipid bilayers.

	The length of the hydrophobic core of the gramicidin channel is about 22 ֵ (Killian, 1992; Fig. 1), which is significantly shorter than the width of the hydrocarbon region of biological membranes- about 30 ֵ (White and Wimley, 1999). Ample experimental evidence suggests that partitioning of the channel into the bilayer involves local membrane thinning (Bamberg and Benz, 1976; Kolb and Bamberg, 1977; Elliott et al., 1983; O’Connell et al., 1990; Killian, 1992; Durkin et al., 1993; Harroun et al., 1999a). This local membrane deformation enables the hydrophobic regions on the channel and the membrane to match. Thus, the free energy penalty associated with the transfer of the polar channel ends from water into a nonpolar medium can be avoided. 

This argument has been exploited in theoretical models used to provide quantitative interpretation of the experimental data (e.g., Ring, 1996; Lundbaek and Andersen, 1999; Harroun et al., 1999b; Huang, 1999; May, 2000). These theoretical models involved detailed (albeit mean field) treatment of the lipid chains. In contrast, the penalty due to desolvation, which is the driving force for the deformation, was estimated empirically. Despite the crude models used in the studies, they reproduced the experimental data very well; they showed that a free energy minimum is obtained when the hydrophobic region of the membrane assumes a width of 22 ֵ. In contrast, molecular dynamics simulations, which were carried out recently, suggested that the width of the hydrocarbon region adjacent to the gramicidin channel was more than 22 ֵ (Chiu et al., 1999a). Clearly this issue needs further investigation.    

A major theoretical and computational effort was devoted to understanding the role of gramicidin as an ion-conducting channel (e.g., Chiu et al, 1999b; Roux, 1999; Cardenas et al., 2000; reviewed in: Roux and Karplus, 1994; Jakobsson, 1998; Sansom et al., 2000). Moreover, gramicidin is by far the most exhaustively used model in theoretical and computational studies of peptide-membrane interactions (Ring, 1996; Woolf and Roux, 1996; Chiu et al., 1999a; Harroun et al., 1999b; Huang 1999; May, 2000). Yet, the free energy determinants of its partitioning between aqueous solutions and lipid bilayers were never investigated. In this study, we present detailed continuum solvent calculations of the contribution due to desolvation to the free energy of transfer of gramicidin from the aqueous phase into the membrane. These calculations were used to estimate the free energy of transfer of gramicidin from the aqueous phase into the membrane.

METHODS 
The total free energy difference between gramicidin in the membrane and in the aqueous phase (DGtot) can be comprised of the sum of the differences in solvation free energy (DGsol), peptide conformation (DGcon), immobilization effects (DGimm), membrane perturbation (DGlip) and deformation effects (Gdef) (Engelman and Steitz, 1981; Jähnig, 1983; Jacobs and White, 1989; Milik and Skolnick, 1993; Fattal and Ben-Shaul, 1993; Ben-Tal et al., 1996; reviewed in White and Wimley, 1999; Kessel and Ben-Tal, 2002):
DGtot = DGsol + DGcon + DGimm + DGlip + DGdef 				(1)

We present here atomic-detailed calculations of the electrostatic (DGelc) and nonpolar (DGnp) contributions to DGsol. 
DGsol = DGelc + DGnp                                                                                           (2)
DGsol is the free energy of transfer of gramicidin from water to a bulk hydrocarbon phase. It accounts for electrostatic contributions resulting from changes in the solvent dielectric constant, as well as for van der Waals and solvent structure effects, which are grouped in the nonpolar term and together define the classical hydrophobic effect. We calculated DGsol using the continuum solvent model (Gilson, 1995; Honig and Nicholls, 1995; Nakamura, 1996; Warshel and Papazyan, 1998). The method has been described in detail in our earlier studies of the membrane association of helices (Ben-Tal et al., 1996; Kessel et al., 2000a, 2000b; Bechor and Ben-Tal, 2001), monensin-cation complexes (Ben-Tal et al., 2000) and small molecules (Kessel et al., 2001a, 2001b). In the following subsections we present a brief outline, with emphasis on the adaptation of the methodology to the gramicidin-membrane system. 

Electrostatic contributions
The calculations were based on a continuum solvent model in which electrostatic contributions were obtained from finite difference solutions to the Poisson-Boltzmann equation (the FDPB method) (Honig et al., 1993). Gramicidin was represented in atomic detail, with atomic radii and partial charges defined at the coordinates of each nucleus. The charges and radii were taken from PARSE, a parameter set that was parameterized to reproduce gas phase-to-water (Sitkoff et al., 1994) and alkane-to-water (Sitkoff et al., 1996) solvation free energies of small organic molecules. 

In the FDPB calculations reported here, the boundary between gramicidin and the solvents (water or membrane) was set at the contact surface between the van der Waals surface of the gramicidin molecule and a solvent probe (defined here as having a 1.4 ֵ radius (Sharp et al., 1991)). Gramicidin and the lipid bilayer were assigned a dielectric constant of 2, and bulk water was assigned a dielectric constant of 80. As for the pore dielectric constant, we tested values between 2-80 and concluded that the exact value has very little effect on the free energy of transfer of gramicidin into the bilayer (see the Error Estimate below). 

The system was mapped onto a lattice of 1293 grid points, with a resolution of 3 points per ֵ, and the Poisson equation was numerically solved for the electrostatic potential. The electrostatic free energy was calculated by integration over the potential multiplied by the charge distribution in space.

The dielectric constant of the pore 
In all previous implementations (Ben-Tal et al., 1996, 2000; Kessel et al., 2000a, 2000b, 2001a, 2001b; Bechor and Ben-Tal, 2001), the Poisson equation was solved with two dielectric regions; a high value for water, and a low one for the solute (the peptide or protein) and the membrane. We introduced here a third dielectric region (epore), corresponding to the channel pore. To this end, a cylinder, corresponding approximately to the pore, was defined. The diameter of the cylinder was chosen so that it would be larger than the widest region in the pore, and yet smaller than the external region of gramicidin. The height of the cylinder was set to be equal to the hydrophobic length of gramicidin, e.g., 22 ֵ for the 1GRM structure of Lomize et al. (1993). Beyond this region, the channel flares out and the inside water is less confined. Thus, the value of the solvent was assigned. The free space within the cylinder, that is, space that was unoccupied by gramicidin atoms, was considered to be the intra-channel matrix, and was assigned the dielectric constant epore.

Nonpolar contributions
The nonpolar contribution to the solvation free energy, Gnp, was assumed to be proportional to the water-accessible surface area of gramicidin, ASA, as appears in the expression
Gnp = gASA + b                                                                               (3)
The pore region was excluded from these calculations since it is occupied with water molecules, both when gramicidin is in the aqueous phase and in the lipid bilayer. We used the parameters g=0.0278 kcal/(mol ֵ2) and b=-1.71 kcal/mol that have been derived from the partitioning of alkanes between liquid alkanes and water (Sitkoff et al., 1996), and have been successfully used in our previous studies. The total area of gramicidin accessible to lipids in a particular configuration was calculated with a modified Shrake-Rupley (1973) algorithm.

Gramicidin structures
Three NMR and one X-ray crystal PDB entries of gramicidin were tested; 1GRM (Lomize et al., 1993; 5 NMR conformations), 1MAG (Ketchem et al., 1996; one NMR conformation), 1MIC (Chen et al., 1996; 20 NMR conformations) and 1AV2 (Burkhart et al., 1998; an X-ray structure). In the first two entries, gramicidin is a head-to-head dimer of two single-stranded (SS) b-helices (e.g., Figs. 1 and 2), and in the last two it is a double stranded (DS) intertwined dimer. In contrast to the other three entries, the 1MIC structure is closed, i.e., it does not form a pore and therefore does not represent an ion-conducting channel. 

We added hydrogen atoms to the structures where they were missing, and energy-minimized the new structure (100 steps of steepest descent) using the DISCOVER module of the Insight-II program (MSI, San Diego, CA).

Conformation effects on the transfer free energy
Gramicidin is very sensitive to the external medium and may change its conformation in the transfer between different milieus. The stability of short polyalanine-like -helices in aqueous solutions has been the subject of theoretical and experimental studies (e.g., Zimm and Bragg, 1959; Lifson and Roig, 1961; Scholtz and Baldwin, 1992; Chakrabartty and Baldwin, 1995). These studies indicate that a complete helix-to-coil transition of a polyalanine helix of about 15 residues involves a close to zero free energy value. By extrapolation, the free energy change resulting from conformational changes during the membrane association of gramicidin (DGcon in Eq. 1) should be insignificant, and was thus neglected. This issue will be considered in the Error Estimate below.

Gramicidin immobilization
Each gramicidin molecule has six external degrees of freedom; three translational and three rotational, and is free to translate and rotate when it is in bulk solution. Upon insertion into the membrane, the molecule can move only conjunct to the membrane, thus retaining only two free translational and one free rotational degrees of freedom. The other external degrees of freedom are partially lost and give rise to the free energy penalty of immobilization, DGimm. An upper-bound estimate for the total immobilization free energy loss involved in the membrane insertion of polyalanine a-helices has been calculated as ≈3.7 kcal/mol (Ben-Shaul et al., 1996). This estimate was also used for gramicidin because of the similarity between the two systems. The value of DGimm weakly depends on the contact area between the peptide and the bilayer, and the above estimate is for a bilayer of native width. Our calculations show that gramicidin insertion into the bilayer involves local thinning of the membrane (see Results below); hence a decrease in the contact area between gramicidin and the membrane. Thus, the actual value of DGimm is probably a little smaller.

Lipid perturbation effects
The insertion of hydrophobic intrusion into the bilayer interferes with it and gives rise to the lipid perturbation effect. The entropic nature of the effect implies that the lipid perturbation free energy, DGlip, is proportional to the contact area between the peptide and the lipid molecules. Statistical thermodynamical calculations, based on a molecular model of the lipid chains, have provided an upper-bound estimate of DGlip = 2.3 kcal/mol for the insertion of polyalanine a-helices of hydrophobic length of approximately 30 ֵ (Ben-Shaul et al., 1996; Fattal and Ben-Shaul, 1993). The hydrophobic length of gramicidin is approximately 22 ֵ (Fig. 1), so the contact area of gramicidin with the lipid membrane should be smaller than for polyalanine a-helices and DGlip is expected to be smaller than 2.3 kcal/mol. Nevertheless, we used the same upper-bound estimate in the calculations.

Membrane deformation
Figure 1 shows that the hydrophobic core of gramicidin is a cylinder of approximate length 22 ֵ (see (Killian, 1992)), which is shorter than the 30 ֵ width of the hydrocarbon region of a native lipid bilayer. Thus, the insertion of gramicidin into a lipid bilayer may result in a deformation of the lipid bilayer to match the hydrophobic length of the peptide, following the "mattress model" (Mouritsen and Bloom, 1984). The deformation involves an energy penalty, Gdef, resulting from the compression of the lipid chains. Gdef has been calculated by several research groups using different methods and the values are similar (e.g., Mouritsen and Bloom, 1984; Helfrich and Jakobsson, 1990; Fattal and Ben-Shaul, 1993; Ben-Shaul et al., 1996; Nielsen et al., 1998; Dan and Safran, 1998; May and Ben-Shaul, 1999). We rely on the calculations of Fattal and Ben-Shaul (1993) that are based on a statistical-thermodynamic molecular model of the lipid chains. A polynomial fit to these calculations gives: 
Gdef  = 0.0327 dL2 - 1.9342 dL + 28.581                                                               (4)
where Gdef  is measured in kcal/mol and dL is the width of the hydrocarbon region of the lipid bilayer, measured in Angstrom. 

RESULTS
A substantial amount of experimental data, referred to in the Discussion below, suggests that assembly of the gramicidin channel begins with monomer insertion at opposite sides, followed by subsequent dimerization. Yet, in this study we considered the insertion of gramicidin dimers into the lipid bilayer along two hypothetical paths: a vertical path, with the gramicidin principal axis perpendicular to the membrane surface (Fig. 2A) and a horizontal one, with the gramicidin principal axis parallel to the membrane surface (Fig. 2B). The first NMR structure from 1GRM, referred to as 1GRM_1, was used for most of the calculations, because it exhibits the most negative free energy of transfer from the aqueous phase into the bilayer (see below). 

Vertical insertion
Electrostatic, non-polar and solvation contributions to the free energy of transfer of gramicidin from water into a model lipid bilayer of hydrocarbon width of 22 ֵ as a function of the distance, h, between the geometrical center of gramicidin and the membrane midplane, are shown in Figure 3. The figure is roughly symmetrical around h=0, where gramicidin is fully inserted into the membrane with its geometrical center in the bilayer midplane. 

The insertion process may start either at h = -26 ֵ or at h = +26 ֵ, where one of gramicidin’s C-termini is just in contact with the membrane surface. The non-polar interactions derive the process. Their contribution is proportional to the surface area of gramicidin that is buried in the membrane, so it changes in a roughly linear way with h, between h = -26 ֵ and h = -4 ֵ and between h = +4 ֵ and h = +26 ֵ. The interactions are saturated for h = -4 ֵ to h = +4 ֵ, before gramicidin begins to protrude again into the water at the other face of the membrane. 

The electrostatic contribution depends on the polarity of the inserted part and thus increases sharply upon insertion of the polar indole side chains of the four tryptophan residues at the C-terminal half of the peptide (Fig. 2) into the membrane (h=-26 ֵ to h=-20 ֵ, and h=+26 ֵ to h= +20 ֵ). The steepness of the electrostatic free energy curve becomes moderate once the C-terminal region is fully buried in the bilayer, at h = -20 ֵ and h = +20 ֵ. At h = -4 ֵ and h = 4 ֵ, where the other polar C-terminal region protrudes into the aqueous phase from the opposite side of the membrane, there is a sharp decrease in the electrostatic free energy penalty. The minimal electrostatic free energy penalty was obtained at h = 0, where the C-terminal regions protrude evenly from both ends of the membrane.

The solvation free energy is a sum of the electrostatic penalty and nonpolar contributions (Eq. 2). Figure 3 shows that it is highly negative at the optimal location of h=0, implying that gramicidin is likely to partition into the lipid bilayer. However, membrane association involves crossing a barrier of about 35 kcal/mol, due to the electrostatic penalty of removing the polar C-terminal region of one gramicidin monomer from the aqueous phase into the hydrocarbon region of the bilayer. It is obvious from the barrier height that gramicidin-insertion into the bilayer cannot proceed along the path of Fig. 3. This issue is discussed below. 

The most favorable location of gramicidin in the membrane is obtained at h = 0, where the solvation free energy reaches its most negative value of -32 kcal/mol. In this gramicidin-membrane configuration the two C-terminal regions protrude into the aqueous phase and the electrostatic free energy penalty is minimal. Such a configuration is possible only if the length of the hydrophobic core of gramicidin matches the width of the hydrocarbon region of the bilayer, i.e., if the membrane is locally distorted. 

The membrane width
The native width of the hydrocarbon region of biological membranes is about 30 ֵ, while the hydrophobic core of gramicidin is only 22 ֵ long (Fig. 1; Killian, 1992). Thus, insertion of gramicidin into bilayers of native width involves burial of gramicidin's C-terminal regions inside the bilayer, which results in a large electrostatic free energy penalty (Fig. 3). The alternative involves membrane deformation to match the length of the hydrophobic core of gramicidin. We carried out a series of calculations of the insertion free energy of gramicidin into lipid bilayers of different widths to test this possibility. Table 1 and Figure 4 summarize the results of the calculations and enable the estimation of the most favorable membrane width. The table shows that membrane thinning has an opposing effect on DGsol and DGdef; the former decreases (becomes more negative) while the latter increases with the decrease of the membrane width. This balance determines the most favorable membrane width for gramicidin insertion, which is associated with the most negative value of DGtot, and which was observed at 22 ֵ. This width was found to be the most favorable one for all the conformations in PDB entry 1GRM and for most of the gramicidin structures that were tested (see below). We therefore used it for the remainder of calculations, unless otherwise stated.

The conformation
A total of 27 gramicidin conformations of four different PDB entries were tested. Of the four entries, two are single-stranded (SS) head-to-head dimers (PDB identifiers: 1GRM (5 conformers) and 1MAG (1 conformer)) and two double-stranded (DS) intertwined dimers (PDB identifiers 1MIC (20 conformers) and 1AV2 (one conformer)). We repeated the calculations of Figure 3 for all these conformations. That is, we calculated the free energy of transfer of gramicidin in each of the 27 conformations from the aqueous phase into lipid bilayers of different width at different locations. The results of these calculations are summarized in Table 2. The table presents the most negative value of the transfer free energy obtained for each PDB entry, and the membrane width at which it was obtained. It also presents the free energy breakdown. It is evident from the table that, while gramicidin may partition into the membrane in all the conformations that were tested, the most negative value of the transfer free energy was obtained for the single-stranded head-to-head b-helix dimer of 1GRM_1. This value is significantly more negative than the values obtained for the other conformations, suggesting that 1GRM_1 is the most likely conformation of gramicidin in lipid bilayers. We therefore used it throughout this study. It is noteworthy that, regardless of the conformation, gramicidin insertion into lipid bilayers is likely to involve a significant local thinning of the membrane.  
 
Our calculations also demonstrate that relatively minor structural changes can affect the value of DGsol, and therefore DGtot, significantly; differences as high as 7 kcal/mol were obtained between NMR conformers of the same PDB entry with trace root mean squares deviations (RMSD) of less than 0.7 ֵ. These differences usually reflect variations in the configuration of backbone hydrogen bonds. The dipoles of the N-H and C=O groups neutralizes each other to a large extent in the vicinity of the optimal hydrogen-bonding configuration, such that the free energy of transfer of an optimal backbone hydrogen bond from the aqueous phase into the hydrocarbon region of the bilayer (DGsol) is only about 2 kcal/mol (Ben-Tal et al., 1996). Slight changes in the distance between the hydrogen donor and acceptor or in the inclination angle between the N-H and C=O groups typically disrupt the degree of neutralization and therefore involve an increase in the magnitude of DGsol penalty.

In view of this, the ~5 kcal/mol difference in the DGsol values of the 1GRM_1 and 1MAG structures (Table 2) is not surprising. Even though both are single stranded head-to-head dimmers of the same fold, their trace RMSD is ~1.2 ֵ. In fact, the 1GRM_1 structure is elongated and its hydrophobic region is ~1 ֵ longer than that of 1MAG. Thus, its transfer from the aqueous phase into the membrane involves a reduced membrane thinning compared to that of 1MAG. This obviously leads to a 0.5 kcal/mol decrease in the magnitude of the DGdef penalty of 1GRM_1 compared to 1MAG. Moreover, it leads to an increase of 2.3 kcal/mol in the magnitude of the nonpolar contribution to DGsol in 1GRM_1 compared to 1MAG because of the increase in the area of the gramicidin-membrane interface. The rest of the ~5 kcal/mol difference is mainly due to accumulative effects of slight changes in the electrostatic desolvation penalty associated with the transfer of backbone hydrogen bonds from the aqueous phase into the hydrocarbon region of the bilayer.

Horizontal insertion
The ion-conducting state of gramicidin exists when it is vertically inserted into the lipid bilayer (Fig. 3, h = 0). Nevertheless, other membrane-associated orientations may be energetically favorable and may serve as intermediates in the insertion process. We tested several orientations, and Figure 5 presents data obtained for insertion of 1GRM_1 into the membrane along the hypothetical horizontal path of Figure 2B. The solvation free energy curve obtained for horizontal insertion is significantly different from the curve obtained for vertical insertion (Fig. 3, filled circles). It is characterized by a moderate minimum, at h =-20 ֵ, where the hydrophobic side chains are inserted into the bilayer while the polar terminal regions are still in the aqueous phase, and by a high flat maximum, between h = -8 ֵ and h = 10 ֵ, where the terminal regions are fully buried in the bilayer.

Convergence tests
All the calculations were carried out using a grid of 1293 points and a scale of 3 grid points per ֵ. We repeated the calculations (with the 1GRM_1 structure) using a grid size of 1613 and scales of 4 and 5 grid points per ֵ, to test the convergence of the calculations. The results indicate that the calculations converged to less than 0.3 kcal/mol. This high precision is a result of the simple model that we used to characterize the system, e.g. the neglect of the polar head group region of the bilayer, and the conformational freedom of gramicidin. These simplifications of the model may result in higher systematic errors, as discussed below.

ERROR ESTIMATE
The limitations of the continuum solvent model, and in particular the slab representation of the bilayer, for the treatment of peptide-membrane systems, were discussed at length (Milik and Skolnick, 1993; Ben-Tal et al., 1996; 2000; Berneche et al., 1998; La Rocca et al., 1999; Nina et al., 2000; Kessel et al., 2000a; 2000b; Bechor and Ben-Tal, 2001). The main shortcoming of the model is the neglect of the polar head group region. However, accumulative evidence (reviewed in Kessel and Ben-Tal, 2002) suggests that this should not be a major problem for highly hydrophobic peptides such as gramicidin, which interact predominantly with the hydrocarbon region of the bilayer (Killian, 1992). 

	The main uncertainty in continuum solvent treatment of the gramicidin channel is the value assigned to the dielectric constant inside the pore. The choice of this value is crucial in studies of the channel conductivity (e.g., Chiu et al, 1999b; Kurnikova et al., 1999; Roux, 1999; Cardenas et al., 2000). However, our calculations demonstrate that the solvation free energy is, in essence, independent of the value assigned to the dielectric constant inside the pore. We repeated the calculations of Figure 3 using several values of the pore dielectric constant in the range 2 to 80. The calculations showed that the variance between the solvation free energy values was only 0.1 kcal/mol at h = 0, in the most stable gramicidin-bilayer configuration (data not shown).

While the desolvation contributions to the transfer free energy were explicitly calculated, the values assigned to the other terms in Eq. 1 are based on estimates. The main source of error in this study probably derives from these terms. Three of these terms are related to the structure and elasticity of the membrane: the free energy penalties associated with the effects of gramicidin immobilization, lipid perturbation and membrane deformation. All together these estimates give a penalty of about 8-9 kcal/mol, which is an upper-bound to the correct value as indicated in Methods above. It is important to emphasize that these values depend on the contact area between gramicidin and the bilayer. The latter varies very little between the different gramicidin structures used in this study. Thus, differences in the total free energy of transfer of these structures from the aqueous phase into the bilayer (DDG) are probably much more accurate than the transfer free energies of individual structures.

An important concern in this study is the assumption that gramicidin was taken as a rigid body in all sets of calculations. In fact, structure flexibility was taken into account to some extent by carrying out sets of calculations using the 27 experimentally observed structures (as opposed to the use of only one structure). 

The main uncertainty in this study comes from the estimate of DGcon, the free energy difference due to conformational changes in gramicidin’s structure in the transfer from the aqueous phase into the bilayer. It is virtually impossible to measure or calculate this value directly and we had to use an alternative. Our approach was based on a hypothetical path, according to which gramicidin assumes its membrane-associated conformation in the aqueous phase prior to its insertion into the lipid bilayer. The underlying assumption here was that at least one of the 27 experimentally determined structures that we used is close enough to the correct structure of the peptide in the membrane. This assumption is common in most of the continuum solvent model and molecular dynamics studies, but it needs to be experimentally verified. 

Following this approach, the DGcon contribution should be estimated for virtual structural changes that occur at the aqueous phase. The highly hydrophobic nature of gramicidin precludes direct measurement of such changes, and the unique structural features of gramicidin, e.g., the fact that its sequence includes both L and D amino acids and that it forms b-helices, makes it very difficult to calculate the DGcon contribution directly. Thus, we were forced to rely on estimates derived from studies on related systems, and assumed that the value of DGcon should be approximately zero (see Methods above). This assumption is consistent with the fact that gramicidin was experimentally detected in a variety of conformations; had DGcon been significantly larger, only one conformation would have been observed.

Recent experimental and theoretical-computational studies of folding and stability in soluble peptides of up to 30-40 residues that adapt a and b structures indicate that the folding free energy usually does not exceed 5 kcal/mol (Wצjcik et al., 1990; Scholtz and Baldwin, 1992; Boczko and Brooks, 1995; Chakrabartty and Baldwin, 1995; Yang and Honig, 1995; Guerois and Serrano, 2001; Young and Brooks, 1996; Guo et al., 1997; Brooks, 1998; Bursulaya and Brooks, 2000; Ferrara et al., 2000; Levy et al., 2001). This value can be regarded as an upper-bound to the free energy change resulting from conformational changes during the membrane association of gramicidin (DGcon). 

Again, for the current study, differences in the value of the DGcon component between the various gramicidin structures (DDGcon) matter more than the absolute values of DGcon associated with conformational changes of each structure. These differences should be much smaller than 5 kcal/mol, since gramicidin shifts between well-defined conformations rather than undergoing a complete unfolding. In summary, while the DGtot values of Table 2 should be regarded as estimates with about ±5 kcal/mol accuracy, differences between them (DDGtot) should be significantly more accurate with maximum error of ±3 kcal/mol or less. 

DISCUSSION
Gramicidin is very hydrophobic and our calculations showed that it is likely to partition into lipid bilayers in all the conformations that were tested, both as a head-to-head dimer of two single-stranded (SS) helices and as an intertwined double-stranded (DS) helix; both in open (ion-conducting) and closed conformations (Table 2). Interestingly, of the two DS conformations, 1MIC (Chen et al., 1996), which is closed and cannot serve as a channel, was found to be very stable in membranes. In contrast, the 1AV2 (Burkhart et al., 1998) conformation, which has a pore and may be capable of conducting ions, was found to be only marginally stable in the bilayer. One obvious conclusion from the calculations is that the SS conformations (PDB identifiers: 1GRM (Lomize et al., 1993) and 1MAG (Ketchem et al., 1996)) are significantly more stable than the DS conformations (PDB identifiers: 1MIC (Chen et al., 1996) and 1AV2 (Burkhart et al., 1998)) in bilayers (Table 2). This is mainly due to the four Trp residues of gramicidin (Cross et al., 1999; Killian and von Heijne, 2000). Membrane insertion of the DS structures involves burying these residues inside the hydrocarbon region of the bilayer in the DS structures. This leads to a large electrostatic free energy penalty, mainly due to the transfer of the polar N-H groups of the Trp side-chains from the polar phase, where they can form hydrogen bonds with water molecules or the polar head groups, into the hydrocarbon region of the bilayer, which has no hydrogen bonding capabilities. In contrast, in the SS structures, the Trp residues are located close to each other at the C-terminus of each monomer (Fig. 2) and the membrane may deform to avoid this penalty (Fig. 6).

The calculations showed that of the six SS conformations (5 in 1GRM and 1 in 1MAG), 1GRM_1 is associated with the most negative DGtot value, thus supporting the previous view that it is the main conformation of the channel in membranes. The fact that both the SS and DS conformations were found to be stable in the membrane may explain why both were experimentally detected. The calculations showed that while gramicidin may associate with bilayers in a surface orientation (Fig. 5; DGtot ~ -6 kcal/mol), it is much more stable in a transmembrane orientation (Fig. 3; DGtot ~ -24 kcal/mol). This is expected, given its role as a channel, and is in accordance with the experimental data (e.g., Killian, 1992). The DGtot value obtained for the transmembrane orientation is very negative, suggesting that gramicidin will be predominantly in this orientation, and will, in essence, be excluded from the aqueous phase.

	The hydrophobic length of the gramicidin dimer is shorter than the width of the hydrocarbon region of the native bilayer, and the calculations demonstrated that, regardless of the conformation of gramicidin, its membrane insertion is likely to involve a significant local thinning. In particular, membrane insertion of the channel in its most stable conformation, 1GRM_1, is likely to involve local membrane deformation to match the 22 ֵ length of 1GRM_1 (Fig. 6). This is in very good agreement with the available experimental data (Bamberg and Benz, 1976; Kolb and Bamberg, 1977; Elliott et al., 1983; O’Connell et al., 1990; Killian, 1992; Durkin 1993; Harroun et al., 1999a) and the vast majority of theoretical-computational work (e.g., Ring, 1996; Harroun et al., 1999b; Huang, 1999; Lundbaek and Andersen, 1999; May, 2000). However, it is in conflict with recent molecular dynamics (MD) simulations (Chiu et al., 1999a). A possible explanation for the discrepancy between the MD simulations and the rest of the studies (including this one) is that the electrostatic free energy penalty associated with the transfer of the polar C-termini of the gramicidin channel from the aqueous phase into the hydrocarbon region of the bilayer may have not been fully taken into account. Other possibilities are discussed in the original paper.

	Membrane insertion of two antimicrobial peptides, gramicidin and alamethicin (Barranger-Mathys and Cafiso, 1996; Kessel et al., 2000a), involves local membrane deformation. One possible reason that comes to mind is that since both peptides are designed to make the membrane permeable, evolutionary pressure has led to the design of the most economical peptides, which are just long enough to span the membrane, in order to minimize the energetic cost of their synthesis. Thus, alamethicin, which is the less hydrophobic of the two, can only induce a minor deformation of about 2 ֵ, while gramicidin can significantly deform the membrane. 

	Figure 3 shows that membrane insertion of 1GRM_1, the most stable form of gramicidin in the bilayer, involves crossing a free energy barrier of about 35 kcal/mol. Similar calculations, carried out using the other structures showed that their membrane insertion also involves crossing large free energy barriers; the smallest barriers (about 23 kcal/mol) were obtained for the 1MAG and 1MIC structures (data not shown). Thus, the insertion path of Fig. 3 is evidently unrealistic. There is no data on the path taken for gramicidin insertion into membranes in vivo. However, all the available in vitro kinetic measurements support the notion that the monomers are first inserted at opposite ends and subsequently, due to fluctuations in the thickness of the membrane, dimerize to form a conducting channel (Kolb et al., 1977; Elliot et al., 1983; O’Connell et al., 1990; Durkin et al., 1993; Sandblom et al., 2001; reviewed in Killian, 1992).

ACKNOWLEDGEMENTS
This work was supported by the Israel Science Foundation (grant 683/97-1) and Fellowships from the Wolfson and Alon Foundations to N.B-T.

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Figure Legends
Fig. 1. Surface electrostatic potential of gramicidin. Gramicidin is in its homo-dimeric form (the first entry in PDB entry 1GRM (Lomize et al., 1993), denoted as 1GRM_1). The electrostatic potential () was color-coded and displayed on the molecular surface of the dimer using GRASP (Nicholls et al., 1991). Negative potentials (–10 kT/e <  < 0) are red, positive potentials (0    10 kT/e) are blue, and neutral potentials are white. The hydrophobic core of the gramicidin dimer, of ≈ 22 ֵ length, (marked by the arrow) is flanked by the polar C-termini of each monomer. The calculations below show that in the energetically optimal location, gramicidin is in a transmembrane orientation in the bilayer with the hydrophobic region buried in the hydrocarbon region of the bilayer and the termini protruding into the polar media.

Fig. 2. Modes of gramicidin insertion. A schematic diagram showing two hypothetical insertion processes of gramicidin into a lipid bilayer: (A) vertical insertion, in which the principal axis of gramicidin is perpendicular to the membrane surface; (B) horizontal insertion, in which the principal axis is parallel to the membrane surface. The distance h is measured between the geometrical center of gramicidin and the bilayer midplane. The gramicidin structure (1GRM_1) is shown as a space-filling model in its homo-dimeric form and the hydrocarbon region of the bilayer is depicted by the shaded rectangle. Each gramicidin monomer is a b-helix of disk-like shape, and the monomers are non-covalently bound to each other via their N-termini, while their C-termini are solvent exposed. Oxygen atoms are red, carbon atoms gray, nitrogen atoms blue and hydrogen atoms white.

Fig. 3. Vertical insertion. Insertion of gramicidin into a bilayer along the hypothetical path of Fig. 2A. (A) DGnp (open circles), DGelc, (crosses) and DGsol (full circles) as a function of the distance, h, between the geometrical center of gramicidin and the membrane midplane. The head-to-head homo-dimer 1GRM_1 structure was used, and the width of the hydrocarbon region of the membrane was set to 22 ֵ. The zero energy of the system was set to a configuration at which gramicidin is entirely in the aqueous phase (i.e., infinite gramicidin-membrane distance), and the calculations were carried out using a grid size of 1293, a scale of 3 grid points per ֵ, and a pore dielectric constant of 10.

Fig. 4. DGtot-dependence on the (local) width of the hydrocarbon region of the bilayer. The values were taken from Table 1. The most negative value of DGtot was obtained at membrane width of 22 ֵ. 

Fig. 5. Horizontal insertion of gramicidin into the bilayer along the hypothetical path of Fig. 2B. DGsol as a function of the distance, h, between the geometrical center of gramicidin and the membrane midplane. The 1GRM_1 structure was used and the width of the hydrocarbon region of the membrane was set to its native value of 30 ֵ.  The zero free energy of the system was set to a configuration at which gramicidin is entirely in the aqueous phase (i.e., infinite gramicidin-membrane distance), and the calculations were carried out using a grid size of 1293, a scale of 3 grid points per ֵ and a pore dielectric constant of 10. The solvation free energy minimum of about -6 kcal/mol can be seen in the figure at h=-20 ֵ, where gramicidin is horizontally adsorbed on the surface of the bilayer.

Fig. 6. A schematic representation of gramicidin in the locally-deformed lipid bilayer. The space-filling model of the peptide (1GRM_1) was displayed with INSIGHT-II (MSI, San Diego, CA). Oxygen atoms are red, carbon atoms green, nitrogen atoms blue and hydrogen atoms white. The two white lines represent the boundaries of the hydrocarbon region of the lipid bilayer.