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Amino Acids at Water-Vapor Interfaces: Surface Activity and Orientational Ordering Esteban Vo¨hringer-Martinez* and Alejandro Toro-Labbe´ Laboratorio de Quı´mica Teo´rica Computacional (QTC), Facultad de Quı´mica, Pontificia UniVersidad Cato´lica, Santiago, Chile ReceiVed: July 7, 2010; ReVised Manuscript ReceiVed: August 20, 2010
The surface activity and orientational ordering of amino acids at water-vapor interfaces were studied with molecular dynamics simulations in combination with thermodynamic integration and umbrella sampling. Asparagine, representing amino acids with polar side chains, displays no surface activity. Tryptophan, in contrast, with its hydrophobic indole ring as side chain unveils a free energy minimum at the water-vapor interface, which lies 6 kJ/mol under the hydration free energy. To study the orientational ordering of tryptophan along the interface, the order parameter was calculated. At the free energy minimum and at the Gibbs dividing surface, the order parameter reveals a parallel alignment of the indole ring with the water surface exposing the π-system to electrophiles in the hydrophobic phase and indicating polarization dependent spectroscopy. In the vicinity of this position a perpendicular orientation is obtained. The surface excess, calculated from the potential of mean force along the interface, is in excellent agreement with experimental measurements. Introduction Amino acids form the building blocks of proteins. Their properties impose the structure of proteins, which is the key to their function in several biological processes. In order to understand these processes, a detailed physicochemical knowledge of these amino acids is crucial. In aqueous solution amino acids behave differently depending on their side chain. Polar side chains render hydrophilic amino acids, whereas aliphatic and aromatic side chains are assigned to hydrophobic ones. Extensive research was focused on their properties in solution, proteins, or lipids, but little is known about their behavior at interfaces. This, however, is crucial since most biological and chemical environments are characterized through various interfaces: membrane-water, protein-water, protein-membrane, or protein-protein interfaces. The most “hydrophobic” interface with respect to water is represented by the water-vacuum interface. Studies on the behavior of amino acids at this interface is the first step to more complex, dynamic interfaces as rendered by proteins. Furthermore, amino acid properties at air-water interfaces have a direct application in drug design related to the respiratory system, where uptake through the alveoli could be improved by molecular engineering. The first experimental studies of amino acids at water-air interfaces measured the surface tension for varying solute concentration providing the basis for a hydrophobicity scale.1 Further experiments by Matubayasi et al. focused on the surface tension as a function of temperature and concentration to obtain the surface entropy and concentration at the air-water interface.2-4 Only recently, also computational studies centered on this topic. The aggregation behavior of up to 15 amino acids at the air-water interface was studied in a quantum chemical analysis of model amino acids with varying aliphatic side chain lengths.5 Shaytan et al. calculated free energy profiles along the vacuum-water interface for side chain analogues from molecular dynamics (MD) simulations.6 However, to our knowledge * To whom correspondence should be addressed. E-mail: evohringer@ uc.cl.
there are no studies focused on the surface properties of single amino acids as the surface activity or the surface orientation. To analyze the energetics at the interface compared to the bulk, free energy calculations in combination with molecular dynamics simulations have emerged as a powerful computational method. During the last years hydration free energies of side chain analogues have been computed with statistical uncertainties on the order of 0.2 kJ/mol.7 Deviations from experimental values were on the order of 4 kJ/mol depending slightly on the employed force field, whereas marginal dependence on the water model was encountered.8 Experimental hydration free energies for amino acids, however, are very difficult to obtain. The neutral form of the amino acids prevails in the gas phase, whereas the zwitterion is the most stable form in solution, such that hydration involves as the first step the proton transfer between the carboxyl and amino group. But the determination of the hydration free energy is not the aim of this study. Moreover, the goal is to provide physicochemical properties of amino acids at the vacuum-water interface, especially their orientation and density at the surface. At the interface and under physiological conditions, the carboxyl and the amino group of the amino acid are expected to be solvated by the surrounding water molecules rendering the zwitterionic the predominant form. Therefore, the free energy profile across a water slab in vacuum was compared between the zwitterionic form of two representative amino acids: asparagine with its polar side chain and tryptophan possessing a hydrophobic indole ring. At physiological conditions both side chains are neutral due to their respective pKb values (pKb(indole) = 17; pKb(amide) = 14). Methods Computational Methods. The simulations were performed with the Gromacs 4.0.5 program package.9 Parameters for the tryptophan and asparagine zwitterion were taken from the OPLS-AA force field,10 since this force field revealed the best performance for the hydration free energy of side chain analogues in comparison to experimental values.7 Two main aspects were considered for the selection of the water model:
10.1021/jp106276z 2010 American Chemical Society Published on Web 09/22/2010
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the model should be compatible with the OPLS-AA force field, and it should reproduce properties of bulk water and the vapor-liquid interface accurately. Recently, the TIP4P/2005 model was proposed by Vega et al.11 This model differs slightly in the Lennard-Jones parameters, the charge of the hydrogen, and the distance from the dummy charge to the oxygen atom from the original TIP4P model from Jorgensen et al.12 It proved to perform better than other models in bulk properties like the density at 1 atm and 298 K, the heat of vaporization, the compressibility, or the diffusion constant. In addition, properties of the vapor-liquid interface, such as the surface tension13 and the vapor-liquid equilibria from the triple to the critical point,14 were significantly improved with respect to other models. The good performance of this model and the close relationship to the TIP4P model, which was used to parametrize the OPLS-AA force field, made this model the best choice. Although polarizable water models may be more accurate at the vapor-liquid interface, they are not compatible with the OPLS-AA force field parameters used for the amino acids. Langevin dynamics were employed with a friction term ξi ) mi/τi for each atom, τi being 2 ps and mi its respective mass. Integration was performed with a time step of 2 fs and a leapfrog algorithm of third order accuracy. This is equivalent to run molecular dynamics with a stochastic temperature coupling and creates the correct NVT ensemble. The particle-mesh-Ewald method (PME) was employed for the electrostatics with a cutoff of 8.5 Å, a PME order of 4, and a fourier spacing of 1 Å. Lennard-Jones (LJ) interactions were computed until a cutoff of 9 Å. A long-range correction was added to the energy and the pressure to eliminate the effect of the finite range LJ cutoff. The neighbor list was updated every step with a radius of 8.5 Å. All bonds of the amino acids were constrained with the LINCS algorithm15 (order of 4), and the SETTLE algorithm16 was used for water. Hydration Free Energy. The hydration free energy of asparagine and tryptophan was obtained employing the thermodynamic integration method with a coupling parameter λ. The electrostatic and dispersion interactions of the respective amino acid with the solvent were reduced in simulations using various constant values for λ, and in a second step they were turned back on in vacuo in the same manner. The hydration free energy was obtained through numerical integration of the derivative of the potential energy with λ(dV/dλ) applying the Simpson rule for different fixed λ values. For each λ value the simulation system consisting of the amino acid in the middle of a cubic box of water with side length of 5 nm and periodic boundary conditions was minimized, equilibrated for 10 ps at constant volume and temperature and in a second simulation of equal length at constant pressure. The production runs at constant volume had a length of 3 ns, resulting in a total simulation time of 372 ns. To avoid singularities, the implemented soft-core potential was employed for the electrostatic and dispersion interactions with σ ) 0.3 nm and R ) 0.5, and the power of λ was set to 1. The same simulation parameters as mentioned above were used, except for the Lennard-Jones interactions, where a shifting function was used, which switches the forces to 0 between 0.8 and 0.9 nm. The PME order was increased to 6, and the hydrogen bonds were constraint with the LINCS algorithm15 using an order of 12. The basic spacing for the λ points was 0.1, except for the electrostatic interactions, where due to large changes in the
Vo¨hringer-Martinez and Toro-Labbe´ derivative of the potential energy with λ close to λ ) 0 additionally the following values were employed: 0.005, 0.01, 0.015, 0.02, 0.03, 0.04, 0.05, 0.06, 0.08. The value of dV/dλ was written out every picosecond for further analysis. Potential of Mean Force. To obtain the free energy profile across a water slab, the simulation system consisted of a rectangular box with the dimensions 5 × 5 × 20 nm, where a water slab of (5 nm)3 (4121 molecules) was placed in the middle of the box. Periodic boundary conditions were applied in all directions, rendering two water-vacuum interfaces at each side of the water slab perpendicular to the longest side of the box. The system was first equilibrated at 298 K for 1 ns, before the amino acid was placed at different positions along the z-axis of the box. The potential of mean force was obtained using the umbrella method implemented in the pull code of the Gromacs package.9 The distance between the center of mass of the respective amino acid and the water slab was restraint with a harmonic potential employing a force constant of 400 kJ mol-1nm-2. The amino acid was placed at different positions along the z-axis with a spacing of 0.1 nm, ranging a maximum distance of 6 nm to the left and right of the center of the water slab. In total 120 simulations of 3 ns length were performed for each amino acid, summing up 720 ns of total simulation time. This simulation time was needed to get a symmetric potential of mean force (PMF) for each amino acid. After removal of the first 200 ps for equilibration, histograms of the z-coordinate of the center of mass of the respective amino acid were extracted every 0.1 ps and corrected with the position of the water slab. The potential of mean force along the z-coordinate was obtained from the extracted histograms employing the weighted histogram analysis method (WHAM)17 as implemented in the Gromacs package18 for the two amino acids with 250 bins and imposing the same free energy value for both maximal distances at the ends of the PMF. The statistical error and the mean PMF were calculated with a bootstrap analysis (100 cycles; block size 5). Order Parameter. To study the orientation of tryptophan at the surface, the order parameter was calculated for each umbrella simulation at different positions along the z-axis as
P(z) ) 0.5 · (3〈cos2 θ〉z - 1)
(1)
θ represents the angle between the z-axis and the normal of the surface spanned by three carbon atoms at the corners of the aromatic indole ring. A value of 1 is obtained when the aromatic ring is perpendicular to the z-axis, and -0.5 corresponds to a parallel orientation. An order parameter of 0 is obtained when the angle equals the “magic angle” (54.7°). Surface Excess. The obtained free energy profiles allow a calculation of the surface excess according to Gibbs theory. The Gibbs theory treats the interface as a separate phase of zero thickness, which is located at the Gibbs dividing surface and characterized through a 2D concentration known as surface excess Γ. The location of the Gibbs dividing surface z0 is given as the position where the surface excess of the solvent is zero, i.e., where the water density is at half of its bulk concentration. With the position of the Gibbs dividing surface, the surface excess Γs of the solute is given as
Γs )
∫-∞z [c(z) - cgas]dz + ∫z∞ [c(z) - cbulk]dz 0
0
(2)
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where cgas and cbulk are the respective concentrations of the solute in the gas and the bulk phase. c(z) is the concentration of the solute along the coordinate connecting the gas phase and the bulk. In equilibrium the solute concentration in the gas phase is obtained from the hydration free energy and its bulk concentration:
( )
cgas ) cbulk exp
GHydr. kBT
(3)
The calculated hydration free energies for the amino acids in the zwitterionic form are in the range of hundreds of kilojoules per mole, and hence their concentration in the gas phase can be approximated to be zero. The concentration of the solute along z is calculated from its bulk concentration and the difference between the free energy value at z and the hydration free energy:
(
c(z) ) cbulk exp -
G(z) - GHydr. RT
)
(4)
With eqs 4 and 2, the adsorption affinity Γs/cbulk is obtained from the free energy along z and the hydration free energy through the following expression:
Γs ) cbulk
(
∫-∞z exp 0
)
G(z) - GHydr. dz + RT G(z) - GHydr. ∞ exp - 1 dz (5) z0 RT
∫
[ (
) ]
Experimentally, the surface excess is measured through the dependence of the surface tension γ from the solute concentration cbulk:
Γs ) -
dγ 1 RT d ln cbulk
(6)
In the limit of an infinitely dilute (ideal) solution, the adsorption affinity Γs/cbulk is considered, which results as
Γs 1 dγ ) lim cbulk RT dcbulk cbulkf0
(7)
Results and Discussion Hydration Free Energy. The hydration free energies of tryptophan and asparagine in the zwitterionic form were obtained with the thermodynamic integration method as outlined above. For the electrostatic contribution to the hydration free energy, smaller spacing was employed in vicinity of λ ) 0 to reduce the error during the integration procedure, due to the large change in the derivative of the potential energy with lambda (dV/dλ) in this region. The statistical error for dV/dλ of each simulation was calculated with the block averaging method19 and the statistical error of the hydration free energy through Gaussian error propagation. The hydration free energies obtained are GHydr. ) -257 ( 3 and -244 ( 4 kJ/mol for tryptophan and asparagine, respectively. These values have to be compared with the results of Chang et al.,20 who reported hydration free energies for 15 amino
Figure 1. Free energy of asparagine as a function of its distance to the water slab and the water density (gray dashed line). The underlying blue color displays the error of the free energy as one standard deviation obtained from a bootstrap analysis.
acids and their respective side chain analogue in cyclohexane and water. Their values for the hydration free energy of the zwitterionic form of tryptophan and asparagine are -270 and -252 kJ/mol, with simulation uncertainties between 0.8 and 4 kJ/mol for all amino acids depending on their size. Both free energies present a larger absolute value than the results obtained in this study. The difference does not stem from different force fields used for the amino acids, since in both studies the OPLS-AA force field was used. The water models, however, vary from each other slightly. Chang et al. used the TIP4P model, whereas in this study the TIP4P/2005 model was employed, since this model reproduces water properties in different phases and especially at the interface better. The TIP4P/2005 model varies in the charge of the hydrogen, the position of the dummy atom, and the Lennard-Jones parameter from the former. In a recent study, Shirts et al. found only a small water model dependence of the hydration free energies for side chain analogues in combination with the OPLS-AA force field.8 Thus, the water model might not cause the observed difference. Another difference is the spacing of the λ values. To reduce the error during integration, here the spacing was reduced in regions where dV/dλ presented large variations as in the study by Hess et al.21 where very accurate free energies for amino acid side chain analogues were obtained. Chang et al. employed a spacing of 0.2, two times larger than the one in this study, in combination with the Bennett acceptance method to calculate the free energy difference between two λ values. Although this method is known to converge faster, near λ ) 0 a spacing of 0.2 might not be enough. The largest deviation, however, might be produced by the small box size employed by the authors. Three hundred sixty water molecules in a box with a side length of approximately 2.1 nm are not enough to screen the long-range electrostatic interactions of the amino acids through the solvent between the periodic images. Especially in the zwitterionic form the large dipole would interact through the periodic images and increase artificially their electrostatic interaction and, therefore, lead to too large hydration free energies. This would explain the difference between their values and the one obtained in this study. Unfortunately, there are no direct experimental values for hydration free energies with which to compare, since solvation of amino acids is also associated with a proton transfer between the carboxylic and the amino group of the more stable neutral form in the gas phase. Potential of Mean Force. Figure 1 shows the potential of mean force (PMF) of asparagine with respect to its distance to
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Figure 2. Free energy profile of tryptophan as a function of the distance to the water slab and the water density (gray dashed line). The underlying blue color displays the error of the free energy as one standard deviation obtained from a bootstrap analysis.
the center of mass of the water slab. As a guide the water density along the same axis is presented (averaged over all simulations). The free energy in vacuum is set to zero. The PMF is symmetric with respect to the middle of the water slab, which demonstrates converged sampling. When asparagine starts to interact with the water molecules at the edges of the water slab, the free energy becomes negative. It is in this region where the errors in the PMF are largest. This is due to the fact that the amino acid becomes microsolvated with a small number of water molecules and all possible configurations have to be sampled to obtain the correct free energy change. The extension of the simulation from 1 to 2 and 3 ns did not alter the PMF considerably, such that extensions of at least 1 order of magnitude or more would be needed. The free energy change in hydration of the amino acid, however, was already obtained with the thermodynamic integration method (TI). In the PMF, the hydration free energy corresponds to the average of the free energies at absolute distances smaller than 1.5 nmsthe region which will be referred as the bulk region (see below). Therefore, at the edges of the PMF the free energies smaller than this average were scaled by a factor to reach the hydration free energy obtained with the TI method. The rest of the free energies in the PMF were corrected through addition of the difference (approximately half the value of the hydration free energy), thereby maintaining possible free energy differences between the bulk and the interface. The error in the free energy in the bulk region and at the interface is shown as a blue shade and represents one standard deviationsobtained from a bootstrap analysis. Its values range from 2 to 4 kJ/mol. The profile of the water density along the z-axis, also shown in Figure 1, is 0 until a distance of 3 nm, where it starts increasing. At a distance of 1.5 nm from the center of mass of the water slab, the density reaches a constant value of 973 g/dm3, which is close to the experimental value of bulk liquid water at 298 K and 1 bar (F ) 997 g/dm3). This region will be denoted the bulk region. Half the value of the density, which corresponds to the position of the Gibbs dividing surface, is reached at a distance of 2.5 nm from the center of the water slab. Figure 2 displays the PMF of tryptophan. The free energy in vacuum, i.e., at the left and right side, is set to zero. In accordance with asparagine the PMF is symmetric, with decreasing free energy values in the vicinity of the water slab. Due to the same issues described for asparagine above, also here the free energies were scaled at the edges of the PMF up to the value corresponding to the hydration free energy (|d| J 2.5 nm), whereas only the difference was added to the free energies corresponding to smaller distances (maintaining free
Vo¨hringer-Martinez and Toro-Labbe´ energy differences between bulk and interface). From a distance of 1.5 nm until the center of the water slab, the free energy is constant (bulk region, F ) 981 g/dm3). The error in the free energy ranges between 3 and 4 kJ/mol. The PMF values of tryptophan vary from the one obtained for asparagine by a minimum in the free energy at the water-vacuum interface with respect to the value in the bulk (see Figure 2). These two minima lie clearly outside the error bars (for a more detailed description see Figure 1 of the Supporting Information). The values of the minima at the right and the left side differ by approximately 1 kJ/mol, which lies in the calculated error range. Their average free energy amounts to -263 kJ/mol, and the average distance to the center of the water slab is 2.3 nm. Subtracting this value from the hydration free energy yields an adsorption free energy of 6 kJ/mol, which corresponds to 2.4 × kBT (kB being the Boltzmann constant and T the temperature of 298 K). This adsorption free energy implies a concentration at the interface which is about 11 times larger than in the bulk. Asparagine, in contrast, displays no minimum at the interface and hence no surface activity. The obtained adsorption free energy of tryptophan calculated as the difference between the minimum free energy and the hydration free energy can be compared to the value of -11.6 kJ/mol for the side chain analogue reported by Shaytan et al.6 The authors also reported a minimum in the free energy with respect to the bulk phase for the side chain analogue of asparagine, which is not observed in this study and contradicts the polar character of the amino acid. The difference in the adsorption free energy of tryptophan and the minimum obtained for the asparagine analogue demonstrate that the physicochemical properties of the whole amino acid with its backbone may differ considerably from the properties of the side chain analogue in accordance with the study by Ko¨nig et al.22 Order Parameter. The obtained results show that tryptophan has a propensity to be found at the vacuum-water interface compared to the bulk. The orientation of the molecule at the interface, however, remains unknown. Its orientation with respect to the water-vacuum interface is crucial to understand its reactivity toward reactants in the hydrophobic phase (e.g., gases at the air-liquid interface) or its reactivity on protein surfaces. The order parameter serves as a characteristic indicator for the orientation of molecules in different environments and might be obtained experimentally for proteins via NMR.23 In this study the order parameter as defined in eq 1 was calculated for each umbrella window. Because of the symmetry observed in the PMF, the average value of the left and the right side of the water slab was calculated as a function of the distance to the center of the water slab (see Figure 3). The angle between the normal of the plane spanned by carbon atoms located at three corners of the indole ring and the z-axis was employed for its calculation. Order parameters for the benzene ring only or another set of aromatic carbon atoms yielded the same results, since the indole ring is almost flat during the simulation. In vacuum, which corresponds to a distance between 6 and 4 nm, the order parameter is 0, representing an isotropic distribution of the aromatic ring. In the bulk (d E 1.5 nm) also a value of 0 is expected. As shown in Figure 3, a large fluctuation is observed for this region, whose average and respective error of the mean amount to 0.02 ( 0.03 (blue line). From the bulk phase toward the interface, the order parameter becomes negative and reaches a minimum at a distance of 2 nm. This represents a favored perpendicular orientation with
Amino Acids at Water-Vapor Interfaces
Figure 3. Order parameter P(z) with respect to the z-axis averaged over the left and right side of the box as function of the distance to the center of the water box. The blue line is obtained by smoothing the data points from a distance of 1.5 until 6 nm. From there the average of the bulk phase is displayed.
J. Phys. Chem. B, Vol. 114, No. 40, 2010 13009 energy values in the bulk phase (up to 1.5 nm), and the integrals were evaluated numerically with the Simpson rule (see eq 5). To account for the statistical error, Γs/cbulk was calculated for each profile obtained in the bootstrap analysis resulting in a mean surface excess and its error of the mean. The value obtained from the 100 profiles for tryptophan is (3.6 ( 0.2) × 10-9 m and (-4.8 ( 0.1) × 10-10 m for asparagine. In accordance with the results of the PMF, tryptophan is surface active corresponding to a positive value. For asparagine a negative value is obtained, reflecting the absence of surface activity and no free energy minimum at the interface. These results have to be compared to the experiments by Bull and Bresse,2 who measured the change in surface tension for different amino acid concentrations. The experimental values for the derivative of the surface tension with respect to the solute concentration are (-9.6 ( 0.7) × 10-6 and (1.2 ( 0.1) × 10-6 N m2/mol for tryptophan and asparagine respectively, displaying the surface activity of tryptophan, which reduces the surface tension in contrast to asparagine. These values can be extrapolated to 0 solute concentration (eq 7, T ) 300 K) yielding values for Γ/cbulk of (3.8 ( 0.3) × 10-9 m for tryptophan and (-4.8 ( 0.4) × 10-10 m for asparagine. The results obtained from the simulations in this study are in perfect agreement with the experimental values, validating the method and the parameters. Conclusions
Figure 4. Representative snapshots of the orientation of the aromatic indole ring in tryptophan at different distances from the center of water slab (the z-coordinate is aligned along the image surface). Left side: at a distance corresponding to the minimum of the order parameter located at d ) 2 nm. Right side: at a distance corresponding to the maximum of P(z).
respect to the water surface (i.e., along the z-axis), which would result in a higher reactivity of the exposed carbon atoms of the indole ring toward reactants in the hydrophobic phase. A representative snapshot is shown on the left side of Figure 4. The order parameter increases for larger distances and reaches its maximum at 2.6 nm, close to the position of the Gibbs dividing surface (2.5 nm). At this position and also at the minimum of the free energy, the indole ring tends to be aligned along the water surface (see Figure 4 right side). This has implications for its reactivity and spectroscopy. The exposed π-system of the indole ring would favor reactions of additive character with electrophiles, and absorption coefficients should differ from the polarization of the photons and be larger than the ones in the bulk. Indeed, in the experimental study of Crawford et al., who measured second harmonic generation of a tryptophan solution at the air-water interface, the molecular hyperpolarizability was found to be in-plane with the water surface.24 Surface Excess. To compare the simulation results to experimental observables, the surface excess in the limit of zero solute concentration defined in eq 5 was calculated. For its evaluation the unscaled PMFs were used, since the results do not depend on the absolute value of the hydration free energy and scaling magnified the errors of the free energy when it starts to become negative, leading to huge deviations in the values of the surface excess. Due to the symmetry of the PMFs with respect to the center of the water slab, the average values of the free energy on the right and left sides were calculated. The hydration free energy was obtained as the average of the free
Molecular dynamics simulations in combination with umbrella sampling and the thermodynamic integration method, and a detailed analysis of the structural ordering at the interface, have revealed that amino acids do differ in their surface activity and orientational ordering at water-vapor interfaces depending on the character of their side chain. The calculated hydration free energies obtained with thermodynamic integration improve earlier published results, which suffered from electrostatic interactions of the amino acid zwitterions through the periodic images. Asparagine with a polar side chain presented no minimum in the free energy profile across the interface. This is also reflected in the calculated negative surface excess, which matches the experimental value. Tryptophan with its hydrophobic indole ring, in contrast, displays a minimum in the free energy profile at the interface. This minimum corresponds to an adsorption energy of 6 kJ/mol and is shifted by 2 Å from the Gibbs dividing surface toward the bulk. The calculated surface excess is positive, reflecting its surface activity, and agrees with the experimental value. The surface activity of tryptophan in comparison to asparagine is accompanied with an orientational ordering at the interface. At the free energy minimum and at the Gibbs dividing surface, the indole ring of tryptophan is preferentially aligned along the water surface, whereas positions in the vicinity toward the bulk and the gas phase are characterized through orientations perpendicular to the surface. Isotropic orientation is obtained in the gas phase and in the bulk. This orientational ordering at the interface has implications for its reactivity and spectroscopy at hydrophobic interfaces. Acknowledgment. E.V.-M. thanks the Alexander von Humboldt Foundation and the Bundesministerium fu¨r Bildung und Forschung for financial support, and A.T.-L. is thankful for support provided by Proyecto FONDECYT 1090460. The authors thank Jochen Hub for carefully reading the manuscript.
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Supporting Information Available: Amplified representation of the free energy difference between the bulk and the interface for tryptophan. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Bull, H. B.; Breese, K. Arch. Biochem. Biophys. 1974, 161, 665– 670. (2) Matubayasi, N.; Miyamoto, H.; Namihira, J.; Yano, K.; Tanaka, T. J. Colloid Interface Sci. 2002, 250, 431–7. (3) Matubayasi, N.; Namihira, J.; Yoshida, M. J. Colloid Interface Sci. 2003, 267, 144–50. (4) Matubayasi, N.; Matsuyama, S.; Akizuki, R. J. Colloid Interface Sci. 2005, 288, 402–6. (5) Vysotsky, Y. B.; Fomina, E. S.; Belyaeva, E. A.; Aksenenko, E. V.; Vollhardt, D.; Miller, R. J. Phys. Chem. B 2009, 113, 16557–16567. (6) Shaytan, A. K.; Ivanov, V. A.; Shaitan, K. V.; Khokhlov, A. R. J. Comput. Chem. 2010, 31, 204–16. (7) Shirts, M. R.; Pitera, J. W.; Swope, C.; Pande, V. S. J. Chem. Phys. 2003, 119, 5740. (8) Shirts, M. R.; Pande, V. S. J. Chem. Phys. 2005, 122, 134508. (9) Hess, B.; Kutzner, C.; van der Spoel, D. J. Chem. Theory Comput. 2008, 4, 435–447.
Vo¨hringer-Martinez and Toro-Labbe´ (10) Jorgensen, W.; Maxwell, D.; TiradoRives, J. J. Am. Chem. Soc. 1996, 118, 11225–11236. (11) Abascal, J.; Vega, C. J. Chem. Phys. 2005, 123, 234505. (12) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. J. Chem. Phys. 1983, 79, 926–935. (13) Vega, C.; de Miguel, E. J. Chem. Phys. 2007, 126, 254707. (14) Vega, C.; Abascal, J. L. F.; Nezbeda, I. J. Chem. Phys. 2006, 125, 34503. (15) Hess, B.; Bekker, H.; Berendsen, H.; Fraaije, J. J. Comput. Chem. 1997, 18, 1463–1472. (16) Miyamoto, S.; Kollman, P. J. Comput. Chem. 1992, 13, 952–962. (17) Kumar, S.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A.; Rosenberg, J. M. C. J. Comput. Chem. 1992, 13, 1011–1021. (18) Hub, J.; de Groot, B. L. Proc. Natl. Acad. Sci. U.S.A 2008, 105, 1198–1203. (19) Hess, B. J. Chem. Phys. 2002, 116, 209–217. (20) Chang, J.; Lenhoff, A. M.; Sandler, S. I. J. Phys. Chem. B 2007, 111, 2098–106. (21) Hess, B.; van der Vegt, N. F. A. J. Phys. Chem. B 2006, 110, 17616–17626. (22) Ko¨nig, G.; Boresch, S. J. Phys. Chem. B 2009, 113, 8967–74. (23) Best, R. B.; Clarke, J.; Karplus, M. J. Am. Chem. Soc. 2004, 126, 7734–5. (24) Crawford, M. J.; Haslam, S.; Probert, J. M.; Gruzdkov, Y. A.; Frey, J. G. Laser Tech. Surf. Sci. II 1995, 2547, 142–151.
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