Free-Energy Analysis of Peptide Binding in Lipid ... - ACS Publications

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Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX

Free-Energy Analysis of Peptide Binding in Lipid Membrane Using All-Atom Molecular Dynamics Simulation Combined with Theory of Solutions Tomoko Mizuguchi†,‡ and Nobuyuki Matubayasi*,§,∥ †

Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan Institute for the Promotion of University Strategy, Kyoto Institute of Technology, Kyoto 606-8585, Japan § Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan ∥ Elements Strategy Initiative for Catalysts and Batteries, Kyoto University, Katsura, Kyoto 615-8520, Japan ‡

S Supporting Information *

ABSTRACT: All-atom molecular dynamics (MD) simulations are performed to examine the stabilities of a variety of binding configurations of alamethicin, a 20-amino-acid amphipathic peptide, in the bilayers of 1-palmitoyl-2-oleoyl phosphatidylcholine (POPC) and 1,2-dimyristoyl-sn-glycero-3phosphatidylcholine (DMPC). The binding free energy of alamethicin is calculated through a combination of MD simulation and the energy-representation theory of solutions, and it is seen that the transmembrane configuration is stable in both membranes. A surface-bound state is also found to be stable due to the balance between the attractive and repulsive interactions of the peptide with lipid and water, and the key role of water is pointed out for the stability in the interfacial region. A difference between the POPC and DMPC systems is noted when the polar C-terminal domain is buried in the hydrophobic region of the membrane. In POPC, the peptide is unfavorably located with that configuration due to the loss of electrostatic interaction between the peptide and lipid.

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INTRODUCTION The configuration of protein in lipid membrane plays important roles in functions of biorelated membranes and in elaboration of drug-delivery systems.1−3 It is governed sensitively by the cooperation and/or competition of the intra- and intermolecular interactions among the protein, lipids, and surrounding media such as water and ions. For example, the binding orientation of a small peptide, alamethicin, is observed to vary as functions of hydration and lipid composition.4,5 Even a protein with four or five transmembrane helices in Escherichia coli can change its orientation only by addition of a single, positively charged residue.6 To investigate a variety of protein configurations in membrane is thus of great importance in identifying the key factor determining the binding mode of protein and in understanding the mechanism of large-scale motion. In this work, we conduct the free-energy analysis of peptide−membrane interactions with all-atom molecular dynamics (MD) simulations in connection to large-scale changes in the peptide orientation within lipid membrane. The time required to explore a wide range of peptide configurations in the lipid−membrane system exceeds the time scale achieved by atomistic simulations. A variety of implicit solvent models have thus been implemented for describing the peptide−membrane interaction. The continuum dielectric © XXXX American Chemical Society

method with the Poisson−Boltzmann equation was combined with a surface-area approach and was applied to alamethicin− membrane interaction.7,8 An effective solvation model was developed by incorporating the distance-dependent dielectrics, and the voltage effect on the alamethicin orientation was examined.9 At present, the increase of computer power enables the theoretical/computational studies of functional molecules in a lipid membrane at the molecular level. For cholesterol, phospholipid, diacylglycerol, and ceramide, their large-scale motions in membrane were studied from thermodynamic and kinetic viewpoints by coarse-grained and all-atom MD simulations.10−20 Lipid−membrane systems with peptides and their oligomers are also simulated with explicit solvent,21−36 and indeed the peptide−membrane interaction is desirably studied at atomic resolution to faithfully take into account the effects of a variety of specific interactions. In the present work, we investigate the free energy of peptide binding in lipid membrane at a variety of configurations. We Special Issue: Benjamin Widom Festschrift Received: August 18, 2017 Revised: December 14, 2017

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DOI: 10.1021/acs.jpcb.7b08241 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

Figure 1. Four orientational configurations of alamethicin in the bilayer of 1-palmitoyl-2-oleoyl phosphatidylcholine (POPC): (A) vertical, (B) tilted-C-anchored, (C) tilted-N-anchored, and (D) horizontal configurations. The backbone of the peptide is represented as the yellow ribbon. Water is shown in red and white, and the headgroup and tail of the lipid are in cyan and green, respectively.

molecules are flexible with significant intramolecular motions, furthermore, and it is necessary to employ a solution theory that is suitable for treating an inhomogeneous system containing flexible species. The method of energy representation meets this necessity.41−45 In the energy-representation method, the solute−solvent pair interaction energy is adopted for the one-dimensional coordinate of the distribution functions and an approximate functional for free energy is constructed from the energy distribution functions in the solution and reference solvent systems. Molecular simulation is then to be conducted only for the solution and reference solvent systems of interest. No calculation is necessary for a set of intermediate states connecting the solution and reference solvent, leading to the reduction of the computational load. Among a variety of approximate free-energy methods,46−60 the method of energy representation is unique in compromising the accuracy, efficiency, and range of applicability42−44,61−68 and was applied to micellar and membrane systems and to protein with a few hundred residues.62,63,69−77 The drawback of the method is the use of an approximate functional for the solvation free energy, though it was observed for amino-acid analogues in water with OPLS-AA and Amber99sb that the error from the functional is not larger than the error due to the force field.65,67,68 In this work, we apply the energy-representation method to an inhomogeneous membrane system containing a flexible peptide and calculate the solvation free energies over a variety of peptide−membrane configurations. It is to be noted that within the framework of the free-energy functional in the energyrepresentation method, the decomposition is readily possible for the binding free energy into the lipid and water contributions. The effects of the attractive and repulsive interactions of peptide can be discussed, too, and the availability of the free-energy decomposition is a useful feature of the energy-representation method employed in the present work.

use alamethicin, an antibiotic peptide of 20 amino acid residues, and employ all-atom MD simulations with explicit solvent. The purpose of this work is to elucidate the controlling factor for the configuration of peptide in membrane at atomic resolution. We analyze the attractive and repulsive interactions of the peptide with lipid and water and highlight the role of water. It is actually considered that the membrane surface is a stable location for alamethicin at low concentrations without transmembrane voltage,4,8,9,21 along with similar binding modes proposed for other peptide molecules.22,30,32,33,36−38 In our analysis, the binding free energy and its components are examined as functions of the binding configuration to assess the interaction component that is responsible for stable binding. Figure 1 illustrates the four orientations of the peptide− membrane system examined in the present work. In the first one called vertical configuration, the peptide stays in the direction normal to the membrane surface. In the second configuration, the peptide is tilted at 45°, with its C-terminus anchored to the bilayer−water interface. We call this “tilted-Canchored configuration”. In the third one called tilted-Nanchored configuration, the peptide is tilted at 45°, with the Nterminus anchored to the bilayer−water interface. The fourth is called the horizontal configuration, in which the peptide stays in the direction parallel to the membrane surface. We investigate the stabilities of these four configurations at a variety of depths of the peptide in membrane; the tilted-Canchored and titled-N-anchored configurations are examined to connect the vertical and horizontal configurations.8,9 The free energy determines the stability of each peptide− membrane configuration, and its exact calculation is possible by such standard methods as free-energy perturbation and thermodynamic integration.39,40 These methods are computationally demanding, however, because a number of intermediate states needs to be implemented. In the present work, we investigate the stability of alamethicin in lipid membrane by combining MD simulation with a statistical-mechanical theory of solutions. We view the lipid and water as a mixed solvent and the peptide as a solute. The “solvation” then refers to the change of the state from the “reference solvent” consisting only of lipid and water to the “solution” system of interest containing the peptide, lipid, and water, and the (relative) stability of each binding configuration can be assessed by calculating the free energy of solvation conditioned by the binding configuration. Note that the solvation in the present context is an extension of the conventional one in homogeneous fluid such as bulk water. Indeed, the membrane system is inhomogeneous at nanoscale and the binding condition restricts the configuration of the peptide solute in the mixed solvent of lipid and water. The peptide and lipid

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METHODS We performed all-atom MD simulations for alamethicin in two phospholipid bilayer systems. One of the phospholipids is 1palmitoyl-2-oleoyl phosphatidylcholine (POPC), and the other is 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine (DMPC). Each lipid bilayer was set to be planar and was generated with CHARMM-GUI Membrane Builder.78,79 In the MD unit cell, 1 peptide and 242 lipid molecules (121 lipids in each leaflet) with 10 000 water molecules were located. Alamethicin has two main isoforms that differ only in the residue at the 18th position. The structure retrieved from the Protein Data Bank (PDB) has a glutamate at its 18th position, with a bend located at the 14th position with Pro (PDB code: 1AMT).80 This structure was modified by replacing the OH group in the Glu18 B


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Figure 2. Five depths of alamethicin in POPC bilayer at the horizontal orientation. The z-axis corresponds to the direction normal to the membrane surface, and z = 0 refers to the membrane center defined as the center of mass of the nitrogen and phosphorus atoms of the lipid molecules. The distance along the z-axis is expressed in the unit of Å, and the bilayer system is symmetric against the reflection at z = 0. The backbone of the peptide is represented as the yellow ribbon. Water is shown in red and white, the lipid headgroups are in cyan, and the lipid tails are in green.

anchored, horizontal, and tilted-N-anchored configurations depicted in Figure 1, respectively. When the binding depth z defined above is set to 0, the tilted-C-anchored and tilted-Nanchored configurations are equivalent to each other due to the symmetry. At z > 0, the C-terminus is closer to the aqueous region than the N-terminus when the peptide configuration is tilted-C-anchored and the converse holds with the tilted-Nanchored configuration. The RMSD of the peptide was computed over the non-hydrogen atoms and was restrained below 3 Å. The depth and tilt angle of the peptide were allowed to fluctuate within ±2 Å and ±5° from the set values, respectively. In summary, the depth, tilt angle, and RMSD of the peptide were restrained (in the vertical configuration, the restraint was applied only to the RMSD) and the other degrees of freedom including those for lipid and water were left unrestrained. All of the restraints were implemented using the collective variables (colvars) module with the details described in the Supporting Information,90 and five independent runs were conducted at each depth and orientation. The free energy for bringing the peptide from vacuum to a given depth in membrane with a given orientation was calculated using the method of energy representation.41−45 The energy-representation method is based on a theory of solutions and provides the solvation free energy, the free-energy change for turning on the solute−solvent interaction. The solvation free energy is then expressed as a functional of energy distribution functions, which are constructed from the pair interaction between the solute and solvent molecules in the solution and reference solvent systems. In the present context, the peptide is treated as a solute and the lipid and water form a (mixed) solvent system. To obtain the solvation free energy through the energy-representation method, the simulations were conducted for the solution system of interest containing the peptide, lipid, and water, for the reference solvent system

side chain with an NH2 group, followed by minimization. The minimized structure was then used as the reference for the calculation of root mean square deviation (RMSD). The sequence of Gln18-alamethicin is Ac-UPUAUAQUVUGLUPVUUQQF-OH, where Ac is acetyl, U is α-amino isobutyric acid, and F-OH is phenylalaninol. All of the MD simulations were carried out with the Gln18-alamethicin, as done in several experimental and computational studies for alamethicin− membrane systems.8,81−84 The NAMD 2.8 program package was employed in the isothermal−isobaric ensemble at 303 K and 1 atm using the CHARMM22 force field with CMAP corrections for the peptide and the CHARMM36 force field for the lipid molecules,85−88 where the parameters for U and F-OH are provided in the Supporting Information. The TIP3P model was adopted for the water molecules.89 The detailed procedures of MD are described in the Supporting Information. MD simulations were conducted for the four configurations shown in Figure 1. For the vertical configuration, we applied a restraint on the RMSD of the peptide to account for small-scale structural fluctuations. For the other three configurations, the restraints on the depth and tilt angle of the peptide were imposed, in addition to the RMSD restraint, to keep the peptide at the desired position and orientation. For each orientational configuration except for the vertical one, we examined five depths of the peptide of 0, 5, 10, 15, and 20 Å, as illustrated in Figure 2; the depth is defined as the distance along the z-axis of the peptide center of mass from the membrane center, where the membrane center was defined as the center of mass of the nitrogen and phosphorus atoms of the lipid molecules and the z-axis corresponds to the direction normal to the membrane surface. The tilt angle of the peptide was defined as the angle between the z-axis and the vector connecting the centers of mass of the terminal residues. The set values of the tilt angle were 45, 90, and 135°, corresponding to the tilted-CC


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Figure 3. Convergence of the solvation free energy Δμ of alamethicin in (a) POPC and (b) DMPC membranes averaged over five runs of the solution system for the vertical configuration (square in red), the tilted-C-anchored configuration at z = 20 (inverted triangle in violet), the tilted-Nanchored configuration at z = 10 (triangle in blue), and the horizontal configuration at z = 15 (circle in green) plotted against the simulation time. The filled symbols are shown against the lower abscissa and refer to the dependence on the MD length of the solution system at a fixed 10 ns length of the reference solvent MD. The open symbols are plotted against the upper abscissa for the reference solvent at a fixed 20 ns length of the solution MD. A 1 ns MD of the reference solvent corresponds to 106 insertions because it was sampled every 1 ps and the number of insertions was 1000 per solvent configuration sampled, as described in the Supporting Information. The lines are drawn for eye guide.

Figure 4. Solvation free energy Δμ against the binding depth z of the peptide in (a) POPC bilayer system and in (b) DMPC bilayer system. (A)− (D) refer, respectively, to the vertical, tilted-C-anchored, tilted-N-anchored, and horizontal configurations introduced with Figure 1. The vertical configuration is plotted at z = 0, and “bulk” refers to the value in bulk water. The Δμ values are common at z = 0 between configurations (B) and (C) due to the symmetry. The bar for the standard error is smaller than the size of the data symbol when it is not shown, and the lines are drawn for eye guide.

nanoseconds, as described in the Supporting Information, and such a (large-scale) conformational change can be well sampled in (much) longer simulations. Still, the focus of the analyses is alamethicin bound in the membranes. The interaction of an αhelix with lipid−membrane environment is the main subject of the work. It was actually reported experimentally that alamethicin stays in the α-helical form at the membrane surface and in methanol,4,91,92 and our surface calculations are in line with those works. The RMSD restraint is then useful to assess which intermolecular interaction leads to the surface binding. By examining the α-helical configuration as a function of the binding depth, it is possible to elucidate the interaction component that governs the stability of the α-helix at the surface.

consisting only of the lipid and water, and for the isolated solute located in vacuum. The force fields were common among the solution, the reference solvent, and the isolated solute, and the simulation setups were identical between the solution and reference solvent systems except for the simulation lengths. The detailed procedures of free-energy calculation is presented in the Supporting Information. For comparison, we also calculated the solvation free energy in bulk water of alamethicin in its α-helical form. The number of water molecules was 10 000, and the restraint on the peptide RMSD was adopted to keep it below 3 Å. The simulation setups are described in the Supporting Information. The RMSD restraint on the peptide was taken to be the same throughout the present calculations, i.e., in bulk water and for all of the binding configurations in the membranes. This was done to highlight the intermolecular effects on a common conformation of peptide, and the effect of conformational relaxation of the peptide in response to the surrounding environment was not taken into account. The deviation from the α-helical form, however, may be particularly significant in bulk water.21,36 Our MD simulations were done to a few tens of

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RESULTS AND DISCUSSION

In the vertical configuration (A) of Figure 1, the average centerof-mass position of the peptide was around z = 2 and 1 Å in the POPC and DMPC membranes, respectively. The center of mass of the C-terminus was further at z = 14 and 13 Å, respectively, and stayed at the interface between the hydroD


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Figure 5. Lipid and water contributions to the solvation free energy plotted against the binding depth z of the peptide. The total value is the same as the one plotted in Figure 4. The upper and lower panels show the POPC and DMPC membrane systems, respectively. (B)−(D) refer respectively to the tilted-C-anchored, tilted-N-anchored, and horizontal configurations introduced with Figure 1. The Δμ values are common at z = 0 between configurations (B) and (C) due to the symmetry, and “bulk” denotes the value in bulk water. The bar for the standard error is smaller than the size of the data symbol when it is not shown, and the lines are drawn for eye guide.

horizontal configuration (D), it is seen in Figure 4 that Δμ is not monotonic with the variation of z and has a minimum at the membrane−water interface. The value of the minimum Δμ in the horizontal configuration is comparable to that in the vertical configuration in both of the POPC and DMPC membrane systems, and the stabilization of the peptide at the interface is more apparent in POPC. It has been indeed considered that alamethicin is bound to the membrane surface at low concentrations in the absence of transmembrane voltage4,8,9,21 and the surface binding has been further proposed for other peptide molecules.22,30,32,33,36−38 The z dependence of the solvation free energy Δμ is not monotonic in Figure 4 also in the tilted-C-anchored configuration (B) and the tilted-N-anchored configuration (C). In the former, the C-terminus is closer to the aqueous region than the N-terminus and the peptide is most stable in the inner part of the membrane. Δμ involves a maximum as a function of z, in contrast, for configuration (C). The presence of the maximum is particularly evident in POPC at z = 10, wherein the polar C-terminal domain of the peptide is buried in the hydrophobic region. In an implicit-membrane calculation, Ben-Tal et al. focused on tilted configurations of alamethicin to address the flip-flop kinetics;8 indeed, the peptide is considered to change its orientation through (A) → (B) → (D) → (C) at flip-flop (if the peptide conformation does not change significantly). It was then suggested, in correspondence to an NMR study on alamethicin in POPC,82 that a free-energy barrier appears at the 45° tilted orientation, with the Cterminus buried in the membrane. The all-atom result in Figure 4 for configuration (C) in POPC is in accord with the implicitmembrane result in the sense that Δμ rises significantly toward the outer part of the hydrophobic region, where the polar Cterminal domain loses the favorable interactions with the headgroup of the lipid and water. We will revisit this point and compare the behaviors in POPC and DMPC later when we analyze the attractive interaction of the peptide with lipid and water. It was observed in fluorescence measurements for 1,2dioleoyl-sn-glycero-3-phosphatidylcholine (DOPC) and DMPC

phobic and hydrophilic regions of the membrane. This is reasonable because two out of the three polar residues of alamethicin are located in the C-terminal domain. Indeed, several theoretical and experimental studies suggest that the Cterminus of alamethicin is anchored to the bilayer−water interface.7,81,93,94 We examine the convergence behavior of the solvation free energy Δμ averaged over the five independent runs of the solution system. Figure 3 illustrates Δμ for several configurations against the computation time. The convergence behavior with respect to the MD length of the solution system is shown at a fixed 10 ns length of the reference solvent MD. For all of the configurations treated in this work, the cumulative averages are stable within 2 kcal/mol after 10 ns. The 20 ns MD for the solution system (with averaging over five runs with independent, initial configurations) is thus enough for the following analysis. Figure 3 also shows the convergence behavior against the MD length of the reference solvent system when the MD length of the solution system is kept at 20 ns. It is seen that the 1 kcal/mol convergence is achieved within a few nanoseconds. In this case, the peptide was inserted as a test particle at a given depth and orientation of the reference solvent system consisting only of lipid and water, as described in the Supporting Information. The lateral location of the peptide was then random at the insertion, and the structural inhomogeneity of the membrane along the lateral directions was averaged out during the procedure of insertion. In other words, the averaging over time is largely replaced by the averaging over space for the sampling of the reference solvent. Figure 4 plots the solvation free energy Δμ of alamethicin in configurations (A)−(D) of Figure 1 against the binding depth z, with the value in bulk water shown for comparison. The free energy is much less favorable (more positive) in water than in membrane, and alamethicin binds favorably to the membrane.83,95 It should be noted that the α-helical form is imposed in the peptide simulation. The free-energy difference is expected to be smaller in magnitude when the effect of the conformational change in water is incorporated.9,21,36 In the E


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Figure 6. Average sum of the solute−solvent interaction energy and the lipid and water contributions against the binding depth z of the peptide. The upper and lower panels show the POPC and DMPC membrane systems, respectively, and (B)−(D) refer, respectively, to the tilted-C-anchored, tilted-N-anchored, and horizontal configurations introduced with Figure 1. The ⟨u⟩ values are common at z = 0 between configurations (B) and (C) due to the symmetry, and “bulk” denotes the value in bulk water. The bar for the standard error is smaller than the size of the data symbol when it is not shown, and the lines are drawn for eye guide.

alamethicin is placed outward in configuration (C), Δμlipid becomes less favorable (more positive) and Δμwater acts oppositely. Because of this, a crossover is observed between the lipid and water contributions in the interfacial region. To elucidate the effects of the attractive and repulsive interactions of peptide with lipid and water, we also examine the average sum of the solute−solvent interaction energy ⟨u⟩ and the excluded-volume component of the solvation free energy Δμexcl. ⟨u⟩ captures the effect of the attractive interaction of the solute (peptide) with the solvent (lipid and water), and Δμexcl is the major part of the repulsive interaction between the solute and solvent. ⟨u⟩ is obtained from the simulation of the solution system (peptide−lipid−water system) and is exact (within the statistical error) under the used set of potential functions. It is further given by the sum of the peptide−lipid interaction ⟨u⟩lipid and the peptide−water interaction ⟨u⟩water.97 The excluded volume is the domain of solute−solvent configuration in which the solute molecule overlaps with the solvent and their interaction energy is prohibitively large. In the energy-representation method, the contribution Δμi from each solvent species is written in the integral form as

vesicles, on the other hand, that alamethicin moves to the vertical configuration with (almost) no activation barrier after it is located on the membrane surface.96 This observation is consistent with the free-energy profiles in Figure 4 which indicate that the translocation of the peptide is not of significant barrier if it does not proceed through the tilted-Nanchored configuration (C). In the present study, lipid and water are treated as a mixed solvent system. It is then natural and often useful to separate the contributions from the two solvent species. It should be noted that the separated contribution from each solvent species is not observable in general and a model of solvation needs to be employed to conduct the separation. In the energyrepresentation method utilized in this work, the total solvation free energy Δμ is formally expressed as a sum of the partial contributions Δμi from the ith solvent species (i denotes either lipid or water).42,43,45,63,97 We thus adopt Δμi in the energyrepresentation formalism to discuss the role of each solvent species in the solvation free energy. In Figure 5, we plot Δμi for lipid and water against the binding depth of the peptide for configurations (B)−(D). In the center of membrane, Δμi is larger in magnitude for lipid than for water. When the peptide is brought toward the outer part of membrane, the variation of Δμi depends on the orientation of alamethicin. In the horizontal configuration (D), the variation of the lipid contribution is relatively mild after the peptide leaves the membrane center, whereas the water contribution grows in magnitude until the peptide reaches the interfacial region. In the tilted-C-anchored configuration (B), Δμlipid is more favorable in the outer part of the hydrophobic region and Δμwater increases toward the water-rich region to make the total Δμ less favorable (more positive). Actually, the variation trend of (the total) Δμ is parallel to that of the water contribution Δμwater for the tilted-C-anchored configuration (B) and the horizontal configuration (D) and the key role of water is thus demonstrated in determining the stable depth of peptide binding at those configurations. The behaviors of Δμi are more complicated for the tilted-N-anchored configuration (C). When

Δμi = ⟨u⟩i −

∫ dϵi f (ϵi) = ∫ dϵi ϵiρi (ϵi) − ∫ dϵi f (ϵi) (1)

where ϵi is the pair interaction energy between the solute and the ith solvent species, ⟨u⟩i is the average sum of the interaction energy between the solute and the ith solvent species in the solution system of interest, ρi(ϵi) is the average distribution (histogram) of the pair energy ϵi in the solution system, and f(ϵi) takes into account the effect of solvent reorganization including the excluded-volume effect. The excluded-volume component in Δμi can be introduced by restricting the integral over ϵi to a high-energy domain ranging from ϵci to infinity, where ϵci is a threshold value for defining the excluded-volume domain. The threshold value is taken to satisfy a requirement that the domain of ϵi > ϵci corresponds to the solute−solvent F


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Figure 7. Excluded-volume component in the solvation free energy and the lipid and water contributions against the binding depth z of the peptide. The upper and lower panels show the POPC and DMPC membrane systems, respectively, and (B)−(D) refer respectively to the tilted-C-anchored, tilted-N-anchored, and horizontal configurations introduced with Figure 1. The Δμexcl values are common at z = 0 between configurations (B) and (C) due to the symmetry, and “bulk” denotes the value in bulk water. The bar for the standard error is smaller than the size of the data symbol, and the lines are drawn for eye guide.

peptide treated in the present work and for the small, hydrophobic solutes examined in the previous work63 and that a common mechanism is operative for the solute’s stability toward the outer region of membrane. According to Figure 4, Δμ has an evident maximum as a function of the binding depth z for the tilted-N-anchored configuration (C) in POPC. This is in correspondence to the z dependence of ⟨u⟩ in Figure 6. In the DMPC membrane system, the increase of ⟨u⟩lipid is overwhelmed by the decrease of ⟨u⟩water and thus the total ⟨u⟩ decreases toward the outer region of membrane. In the POPC membrane system, on the other hand, the decrease of ⟨u⟩water is more moderate and the ⟨u⟩lipid increase is only partially compensated by the water contribution ⟨u⟩water with appearance of a maximum for the total ⟨u⟩ at z = 10. As is commonly adopted in molecular simulation, ⟨u⟩ is expressed as a sum of the electrostatic and van der Waals components. When ⟨u⟩ is decomposed into these components, it was observed that (the average value of) the electrostatic component varies with z in the range of −200 to −100 and −210 to −115 kcal/mol in POPC and DMPC, respectively, whereas the van der Waals component stays at −150 to −130 kcal/mol in both membranes. The latter is less sensitive to the depth and orientation of the peptide, and it is the electrostatic component which governs the z dependence of ⟨u⟩. At z = 10 in the tilted-N-anchored configuration (C), the electrostatic component in ⟨u⟩ was −100 and −130 kcal/mol in POPC and DMPC, respectively, and the difference in the electrostatic interaction between the POPC and DMPC systems corresponds with the membrane thicknesses. When the thickness is measured as the average distance (along the direction normal to the membrane surface) between the phosphorus atoms in the two leaflets, it was 39 and 36 Å for POPC and DMPC in our MD without peptide, respectively; the POPC bilayer is thicker by ∼3 Å than DMPC, in agreement with other simulation studies using CHARMM36 force field and X-ray scattering experiment.99−101 At the depth of z = 10 in configuration (C), the polar residues in the C-terminal domain

overlap and is essentially inaccessible in the solution system of interest (ρi(ϵi) = 0 in MD). In the present work, we set ϵci = 25 kcal/mol, whereas the following discussion is valid irrespective of the (reasonable) setting of the ϵci value. The excludedfor each of lipid and water (i is either volume component Δμexcl i lipid or water) is determined by restricting the domain of integration to ϵi > ϵci , and the total effect of the excluded excl volume is given by Δμexcl = Δμexcl lipid + Δμwater. In Figures 6 and 7, we show ⟨u⟩ and Δμexcl, respectively, as functions of the binding depth z. The (total) ⟨u⟩ decreases mostly toward the membrane outside, with the increase of the (total) Δμexcl. These two factors thus compete against each other and result in the nonmonotonic dependencies of Δμ on the binding depth in Figure 4. Figure 6 also plots ⟨u⟩lipid and ⟨u⟩water. It is seen that the lipid contribution ⟨u⟩lipid overwhelms the water contribution ⟨u⟩water in the inner part of the membrane and that the former is comparable to or smaller in magnitude than the latter in the interfacial or outer region of the membrane. Actually, the water contribution ⟨u⟩water grows in magnitude with z and the total ⟨u⟩ becomes more favorable (more negative) toward the membrane outside due to ⟨u⟩water. In Figure 7, Δμexcl is similarly separated into the contributions from lipid and water. The increase of the total Δμexcl is brought by the contribution from water, whereas the lipid contribution is less sensitive to the binding depth. Water plays a key role in determining the repulsive effect for peptide in lipid membrane. In a previous work,63 the solvation free energy was calculated for hydrophobic solutes in DMPC membrane. It was then found that the solute−solvent interaction energy ⟨u⟩ becomes larger in magnitude in the outer region of membrane due to the growth of the water contribution. The variation of ⟨u⟩ with the binding depth z actually competes against the effect of excluded volume Δμexcl, leading to a mild dependence of Δμ on z and the diffuse distribution of a hydrophobic solute from the membrane center to the interfacial region, which is in agreement with experiment.98 This shows that the attractive interaction effect captured by ⟨u⟩ and the repulsive interaction effect represented by Δμexcl act similarly in membrane for the G


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The Journal of Physical Chemistry B are buried deeply in the hydrophobic region. A favorable interaction of the peptide with the headgroup of lipid and water is less easily attained in POPC because the polar domain of the peptide stays at the membrane center in this case and the polar region of the membrane system is located farther in POPC than in DMPC. Figure 4 further indicates that alamethicin tilts more easily in the DMPC membrane than in POPC. Indeed, the average tilt angle in the vertical configuration was observed to be 13 and 17° in POPC and DMPC, respectively (note that no restraint was applied to the tilt angle in the vertical configuration).28,102 Actually, this observation is in agreement with the concept of hydrophobic mismatch.29,34,35,103−110 The hydrophobic thickness of the lipid membrane can be estimated as the distance (along the normal direction) between the C2 atoms of the acyl chains in the upper and lower layers of membrane,111 and it was 27 and 25 Å for POPC and DMPC, respectively, in our simulations. The hydrophobic length of peptide is often taken as 1.5 Å multiplied by the number of residues with an assumption of an ideal α-helix,106,107,110,112 on the other hand, and its value for the 20-residue alamethicin is 30 Å when the entire peptide is considered to form an α-helix. This length is larger than the hydrophobic thickness of the membranes examined, and DMPC has a shorter thickness than POPC. Accordingly, the peptide is expected to tilt in the membranes and more in DMPC, in agreement with the computed tilt angles noted above.

compensated by the favorable change in the interaction with water.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b08241. Procedures for MD simulation and free-energy calculation; force-field parameters for α-amino isobutyric acid and phenylalaninol (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Nobuyuki Matubayasi: 0000-0001-7176-441X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the Grants-in-Aid for Scientific Research (nos. JP15K13550, 21300111, 23651202, and JP26240045) from the Japan Society for the Promotion of Science and by the Elements Strategy Initiative for Catalysts and Batteries and the Post-K Supercomputing Project from the Ministry of Education, Culture, Sports, Science, and Technology. The simulations were conducted partly using PRIMERGY at Research Center for Computational Science in National Institute of Natural Sciences and the HPCI systems of COMA at University of Tsukuba, TSUBAME2.5 at Tokyo Institute of Technology, CX400 at Nagoya University, and Cray XC30 at Kyoto University through the HPCI System Research Project (project IDs: hp170097 and hp170221), in addition to computational resources from the MEXT Joint Usage/Research Center “Center for Mathematical Modeling and Applications”, Meiji University, Meiji Institute for Advanced Study of Mathematical Sciences. We are also grateful to Prof. Wataru Shinoda of Nagoya University for his help in the initial stage of the present work.

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CONCLUSIONS All-atom MD simulation was performed for a peptide bound in lipid membrane. The energetics was analyzed for alamethicin in POPC and DMPC bilayers over a variety of configurations, and the solution theory in the energy representation was employed in combination with MD to compute the free energy of binding the peptide into membrane. The peptide was stable at the configuration in which its end-to-end vector is vertical to the membrane surface, and the stability was examined as a function of the binding depth for horizontal and tilted configurations. A surface-bound state was also found to be stable in the horizontal configuration, reflecting the balance between the attractive and repulsive interactions of the peptide in lipid membrane. The attractive interaction was then treated in terms of the average sum of the solute−solvent interaction and was more favorable (more negative) toward the outer region of membrane. The repulsive interaction was represented by the excluded-volume component in the solvation free energy, on the other hand, and it was shown to grow toward the aqueous region. Actually, the dependencies of the attractive and repulsive interactions on the binding depth were seen to follow those of the water contributions. This illustrates the importance of water in determining the peptide configuration in lipid membrane. The competitive behavior between the attractive and repulsive interactions was further observed in the tilted configurations, leading to nonmonotonic dependence of the binding free energy on the binding depth. The difference between the POPC and DMPC systems was most appreciable at the tilted orientation with the polar C-terminal domain buried in the membrane. In the POPC bilayer, such configuration was evidently unfavorable in the outer part of the hydrophobic region and this was because the unfavorable change in the interaction of the peptide with lipid upon its outward transfer from the membrane center is only partially

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