Structure of Leucine Adsorbed on Polystyrene from Nonlinear

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Structure of Leucine Adsorbed on Polystyrene from Nonlinear Vibrational Spectroscopy Measurements, Molecular Dynamics Simulations, and Electronic Structure Calculations Shaun A. Hall, Kailash C. Jena, Travis G. Trudeau, and Dennis K. Hore* Department of Chemistry, University of Victoria, Victoria, British Columbia, V8W 3V6, Canada ABSTRACT: We have used a combination of sum-frequency generation spectroscopy, molecular dynamics simulations, and electronic structure calculations to arrive at a statistical picture of the orientation and conformation of a hydrophobic amino acid on a hydrophobic polymer surface. Vibrational sum frequency spectra of leucine adsorbed at the polystyrene
solution interface appear simple in that only a few vibrational bands are evident. However, electronic structure calculations reveal 10 normal modes in the C
H stretching region between 2800
3000 cm
1. Many of these modes are highly coupled and close in energy. Further, molecular dynamics simulations reveal that leucine adopts five conformations when adsorbed onto the surface, and has two primary preferences for the adsorbed orientation of each conformer. We have combined these results to provide a unified picture of the distribution of adsorbed molecular structures. This general approach is broadly applicable to systems where a simple correspondence between the spectral features and the vibrational normal modes is complicated due to spectral congestion, thereby providing a route for the analysis of larger molecules.

1. INTRODUCTION The broad interest in the study of protein adsorption to polymeric surfaces is fuelled by application to a wide variety of scientific and technical fields. The process of protein adsorption itself is known to be one of the most important events in many biological processes, resulting in the initiation of many cellular activities.1 In terms of chemical applicability, the understanding of this process is vitally important to the fields of chromatography,2
8 where it is used to develop methodologies and separation technologies for the effective removal of proteins from solutions, to the development of biosensors9
11 and drug delivery systems.12
14 It is understood that the interaction of a protein with a polymeric surface can induce a change in secondary and tertiary structure.15 This change can be drastic, even irreversible, in the case of protein denaturation upon adsorption.16,17 As such, there is also a great deal of research on biocompatible polymeric coatings for medical implants, where it is known that the initial response of an implant is the formation of a protein layer at its surface.18 In this case, there is a vested interest in the development of hemocompatible and bacterial-adhesion resistant polymers,19
21 for which a basic understanding of the processes involved in the formation of the protein film would be a great asset. Adsorption of proteins to surfaces has been studied for the better part of the last century by a variety of processes. The methods of choice have included in situ procedures such as fluorescent- and radio-labeling,22 confocal fluorescence microscopy,23 total internal reflection fluorescence,24 attenuated total reflection infrared spectroscopy,25
27 and Raman spectroscopy.28
31 A variety of r 2011 American Chemical Society

ex situ methods have also been employed, specifically atomic force microscopy,32
34 electron microscopy,35,36 neutron scattering,37 and X-ray photoelectron spectroscopy or electron spectroscopy.38
41 The challenge has been in achieving sufficient specificity for the interfacial region, thereby excluding the contribution of bulk molecules to the acquired signals. Over the past decade, second-order nonlinear optical techniques such as second-harmonic generation and sum-frequency generation (SFG) have received increasing attention due to their exquisite selectivity for interfacial molecules. Under the electric dipole approximation, the secondorder susceptibility tensor χ(2) contains nonzero elements only when molecules are immobilized in a polar manner, such as when adsorbed to surfaces. Vibrationally resonant SFG experiments are particularly attractive since specific regions of molecules may be targeted for analysis without the need for chemical labeling. This method has been applied to the study of amino acids,42
44 model peptides,45
48 and proteins.49
52 One of the most useful characteristics of SFG spectroscopy for such molecules is that the spectra are feature-rich, and appear to be sensitive to fine surface structural rearrangements that accompany a change in hydrophobicity, charge, or solution properties such as concentration, ionic strength, or pH. However it remains, even for relatively small molecules, a challenge to relate the observed spectra features to structural characteristics of the molecules at the interface. Part of the problem is a lack of Received: March 17, 2011 Revised: April 25, 2011 Published: May 16, 2011 11216

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The Journal of Physical Chemistry C sufficient information regarding the molecular properties, the vibrational hyperpolarizabilities for each mode of interest. For very small molecules, or uncoupled vibrations of larger molecules, local symmetry may be used to arrive at analytical expressions for hyperpolarizability elements from bond-additivity models for the dipole and polarizability response.53
55 When this is not possible, quantum mechanical calculations may be used.56
61 Another challenge concerns uniquely identifying functional groups that appear resonantly enhanced in the SFG spectra. As in the case of bulk IR absorption and Raman experiments, isotopic substitution has greatly assisted in this endeavor for small molecules. For large molecules such as peptides or proteins, there is no escaping the reality that hundreds or thousands of C
H stretching modes will be present in the 2800
3100 cm
1 window. Finally, if the above two concerns are addressed, one is left with the treatment of the orientation distribution of the molecules or functional groups. For weakly physiosorbed molecules, one would expect the distributions of tilt and twist angles to be broad. One approach would be to model the experimental spectra using a Gaussian distribution of the relevant Euler angles, thereby using the experimental data to solve for the mean tilt and twist angles, and the width of each distribution. Another, more general, approach is to consider all families of possible Gaussian distributions that would be consistent with the experimental observations.61 In all of these cases, the difficulty lies in that there are a limited number of experimental observables and a large number of parameters in a realistic orientation distribution function. An alternate approach is to sample the orientation distribution from molecular dynamics trajectories and then project the molecular properties into the lab-frame ensemble average for comparison with experimental spectra.57,62
65 In this work, we have simultaneously addressed these three issues by combining electronic structure calculations to obtain vibrational hyperpolarizabilities, and molecular dynamics trajectories to sample orientation distribution functions. We consider what may appear to be a fairly simply case of the amino acid leucine on a polymer surface. However, we demonstrate that, even such a small molecule possesses an SFG spectrum that is congested with highly coupled and overlapping C
H stretching modes. Furthermore, we have used our simulations to identify five conformations of the molecule when adsorbed to the surface, in addition to its preference for orientation. We provide a framework for combining the results of these steps in order to account for the structure of the molecules revealed by the experimental SFG spectra.

2. MATERIALS AND METHODS 2.1. Experimental Details. The preparation of the polymercoated prism begins with the submersion of the prism in 0.1% v/v nitric acid in concentrated sulfuric acid. This is followed by rinsing for at least 5 min with deionized water with a resistivity of at least 18 MΩ 3 cm (Nanopure, Barnstead Thermo). Next, a two stage polishing process is undertaken. Initially, the three faces of interest present on the dove-cut prism are polished with 3 μm polycrystalline diamond suspension (Buehler Metadi Supreme), followed by a 1 min rinse in deionized water. The second step involves polishing the three faces of interest again with a 0.05 μm silica suspension (Buehler Masterprep) and a final rinse with deionized water. The polymer film is produced by dissolving d8polystyrene with a molecular weight of 270 500 g/mol and a

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polydispersity index of 1.25 (Polymer Source) in CDCl3 to produce a solution of 3% w/w. This solution was then spin coated (Model F3
8 Specialty Coating Systems, IN) on the back face of the prism, accelerated over 1 s to 1500 rpm, spun for 90 s, and decelerated over 1 s. The prism was then dried overnight at room temperature beneath a protective covering. The experimental cell itself is constructed by forming a water tight seal between the polymer-coated side of the prism and the Teflon sample cell through a fluoropolymer O-ring (Marco Rubber, NH). An initial scan of the sample with pure D2O (Cambridge Isotope Laboratories) in the sample cell between 2800
3000 cm
1 was performed to ensure the cleanliness of the system provided no C
H stretching modes were observed. The D2O was then removed and replaced with a 16 mg/mL solution of L-leucine (Aldrich) in D2O. This concentration was chosen since no evidence of leucine adsorption was observed at lower concentrations, as verified by quartz crystal microbalance studies.1 The SFG spectroscopy setup used for these experiments utilizes a 10 Hz, 30 ps Nd:YAG laser (Ekspla PL2241A). One of the pump beams is in the visible at 532 nm focused to a diameter of 1 mm at the sample with an energy of 110 μJ per pulse. A tunable infrared beam is focused to 0.5 mm at the sample with energies in the neighborhood of 200 μJ per pulse. The latter is produced in an optical parametric generator via difference frequency mixing in AgGaS2 (Ekspla PG501). In order to couple these two beams to the buried polystyrene
D2O surface, they enter a dove-cut CaF2 prism (Del Mar Photonics). The visible radiation is incident at 66
while the infrared contacts the interface at 64
. SFG spectra were obtained by varying the infrared beam energy between 2800
3000 cm
1 with a step size of 2 cm
1. At each infrared energy, the SFG intensity was calculated as an average of 100 pulses. Three separate combinations of the perpendicular polarization states (s- and p-) of the three beams present in the experiment, SFG, visible and infrared, were used: ssp, sps, and ppp. 2.2. Molecular Dynamics Simulations. All simulations of leucine adsorption were performed using the GROMACS package66 with 3840 SPC/E water molecules67 and one leucine molecule present in the zwitterionic state. These molecules were placed between two surfaces forming a three-dimensional box of 42  42  70 Å3. Cutoffs were placed upon the van der Waals interactions between atoms at a distance of 9 Å. The surfaces themselves were defined by Steele 10
4 potentials68,69 installed at the planes z = 0 Å and z = 70 Å. Thus, the potential energy of the surfaces was defined by Lennard
Jones interactions integrated over x and y dimensions resulting in the z-dependent potential, "

4 # 10 2 σ σ
ð1Þ UðzÞ ¼ 2πσ 2 ε 5 z z where σ defines the distance from the surface at which the potential energy will be zero, while ε defines the depth of the potential well. For this work, the value of σ was maintained at 3 Å, while the value of ε was varied to produce surfaces of varying hydrophobicity.70,71 Contact angle measurements for the neat water
hydrophobic surfaces varied from 156
(superhydrophobic) to 84
(semiwetting) as determined by droplet shape analysis.71 There were two reasons for studying leucine adsorption at these different surfaces. First, the specific conformations and orientations of leucine adopted at the surface may be more prevalent at a certain hydrophobicity. This enables us to 11217

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agreement with an experimental SFG study of leucine at the air
water interface.76 In order to approximate all required elements of the R(2) tensor we have employed the harmonic approximation ð2Þ Rlmn ðωIR Þ

¼

ð2Þ RNR , lmn

þ

∑ν

ð1Þ

dRν, lm dμν, n 1 dQν dQν ων
ωIR
iΓν ð2Þ

where dR(1)/dQ is the linear polarizability derivative and dμ/dQ is the dipole moment derivative with respect to the normal mode coordinate Q. The detailed procedure for obtaining these derivatives has been described previously.61

3. RESULTS

Figure 1. Normalized vibrationally resonant SFG spectra of Leu adsorbed at the D2O
PS-d8 surface in the (a) ssp, (b) sps, and (c) ppp polarization schemes.

more robustly sample populations that may be under-represented at a particular surface due to a finite trajectory. Second, the heterogeneity of a real polystyrene surface would result in variation in hydrophobicity on a molecular length scale. By studying these different surfaces, we therefore access the largest possible number of leucine conformers adsorbed at these surfaces. The intramolecular interactions for leucine and between the leucine and surrounding water molecules were based on the OPLS-AA/L force field.72 Each configuration was initially minimized three times via a steepest descent method, using step sizes of 0.01 Å, 0.05 Å, and finally 0.1 Å to ensure the system was not trapped in an unstable starting configuration. The next step involved an equilibration for 200 ps. Each simulation had its own initial set of starting velocities for each atom, generated randomly while ensuring an average temperature of 300 K and at a pressure of 1 atm using the Berendsen thermostat and barostat.73 The pressure was maintained by allowing variation in the x and y directions while maintaining a constant z dimension. This pressure coupling resulted in, at maximum, a 1% variation in the x and y dimensions of the system, which equilibrated after the first 10 ps. Each simulation provided 10 ns of data, with a snapshot of the configuration being saved every 50 fs, resulting in 90 ns of data for each system integrated with a 1 fs step size. In order to ensure the two surfaces were identical, all molecules above the midpoint in the z direction of the box in the simulations were transformed by a 180
rotation about the y-axis prior to analysis. 2.3. Electronic Structure Calculations. All calculations were done using the GAMESS quantum chemistry package74 at the B3LYP/6-31G(d,p) level of theory, as it is noted that this basis set is capable of reproducing infrared spectra of gas phase amino acids.75 A polarizable continuum model (PCM) was used to provide an approximation of an aqueous solution. In the analysis of the normal modes, a frequency scaling factor between 0.94
0.97 provided

3.1. Nonlinear Vibrational Spectroscopy. The vibrationally resonant sum-frequency generation spectra collected for 16 mg/mL Leu adsorbed at the D2O
PS-d8 surface are shown in Figure 1 for (a) ssp, (b) sps, and (c) ppp schemes, where the polarization of the SFG, visible, and IR beams is specified. In each case, ISFG has been normalized with respect to the peak displaying the largest intensity, and the input visible Ivis and infrared IIR pump beam intensities. Considering ð2Þ

ISFG  jχeff j2 Ivis IIR

ð3Þ

the spectra displayed in Figure 1 are therefore proportional to the 2 effective second-order susceptibility |χ(2) eff | , irrespective of any variation in the pump beam fluences during the IR energy scan from ωIR = 2800
3800 cm
1. The objective will be to arrive at a distribution of leucine molecules that can account for the shape (2) of these three spectra. The effective susceptibilities χ(2) ssp , χsps , (2) (2) and χppp may be related to the actual susceptibilities χxxz = χ(2) yyz, (2) (2) (2) (2) χ(2) = χ = χ = χ , and χ by the considering the xzx zxx yzy zyy zzz contribution of the local field corrections Lii and unit polarization vector elements ei, where i refers to any of the lab frame x, y, or z coordinates. ð2Þ χð2Þ ssp ¼ ðey Lyy Þχyyz ðey Lyy Þðez Lzz Þ

ð4aÞ

ð2Þ χð2Þ sps ¼ ðey Lyy Þχyzy ðez Lzz Þðey Lyy Þ

ð4bÞ

ð2Þ ð2Þ χð2Þ ppp ¼ ðez Lzz Þχzxx ðex Lxx Þðex Lxx Þ þ ðex Lxx Þχxzx ðez Lzz Þðex Lxx Þ ð2Þ þ ðex Lxx Þχð2Þ xxz ðex Lxx Þðez Lzz Þ þ ðez Lzz Þχzzz ðez Lzz Þðez Lzz Þ

ð4cÞ The terms Lii and ei are evaluated by considering the incident and refracted angles of the sum-frequency, visible, and infrared beams, and the refractive indices of D2O and polystyrene. Note that Lii are complex-valued since the beams approach the D2O
PS interface above the critical angle. In order to evaluate eq 4 and thereby model the spectra in Figure 1, we need to determine the actual susceptibility tensor elements according to the following: ð2Þ

χijk ¼ 11218

N ð2Þ ÆR æ ε0 ijk

ð5Þ

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Figure 2. (a) The local coordinate system used to define the methylene plane, and (b) the resulting orientation distribution for standing (blue) and laying (red) Leu molecules. (c) The definition of the 3-carbon plane of the methyl groups and (d) the resulting orientation distribution of this plane for standing (blue) and laying (red) molecules.

with ð2Þ

ÆRijk æ ¼

Z Ω

f

∑ijk lmn ∑ lli lmj lnkRð2Þ lmn dΩ

ð6Þ

where Ω represents the three Euler angles that project the molecular frame of each Leu onto the lab frame, l, m, n represent each of the molecular frame Cartesian coordinates (a, b, c), lli(Ω) is an element of the direction cosine matrix, R(2) lmn is an element of the vibrational hyperpolarizability in the molecular frame, and f(Ω) is the molecular orientation distribution. In the following sections, we will illustrate how we use molecular dynamics simulations to identify contributing Leu conformers at the PS surface, and arrive at suitable f(Ω) for each species. For each conformer, we then use electronic structure calculations to arrive at R(2) lmn for all vibrationally resonant alkyl stretching modes in the region 2800
3000 cm
1. 3.2. Molecular Dynamics Simulations. In a previous molecular dynamics study of leucine adsorption at flat (nonatomistic) surfaces of varying hydrophobicity,77 we have used the orientation of the amino acid’s long axis to determine that it alternates between standing and laying conformations when adsorbed to the surface. We now illustrate the orientation distribution of the methyl and methylene plane when the molecule’s center of geometry is less than 7.5 Å from the surface, and its long axis (pointing from the midpoint between the two methyl carbon atoms toward the midpoint between the amine nitrogen and the carboxylate carbon) makes an angle either less than 20
(or greater than 160
) from the surface normal (standing), or between 80
100
(laying). Figure 2a illustrates the plane of the methylene group defined by the CH2 carbon and two hydrogens. The tilt and twist orientation distribution of this plane is plotted in Figure 2b for molecules found adsorbed in a standing (blue) and laying (red) orientation. Figure 2c illustrates the methyl plane defined by the two CH3 carbon atoms and the isobutyl carbon atom. The orientation distribution showing the

tilt and twist of this plane appears in Figure 2d for standing (blue) and laying (red) leucine molecules at the surface. These maps were constructed by considering adsorption on all six types of surfaces, with water contact angles ranging from 84
156
. We next seek to identify which conformations of leucine are prevalent at the surface. Of the six possible dihedral angles in the leucine molecule, only two of them are relevant in effecting a significant conformational change. We define these as ξ1 between the methylene and isobutyl carbon atoms, and ξ2 between the methylene carbon and the amino acid’s R carbon atom as illustrated in Figure 3a. Using the same adsorption criteria and summing over all types of surfaces, we characterize all adsorbed leucine molecules in terms of their (ξ1,ξ2) angles. This conformation distribution is plotted in Figure 3a for adsorbed leucine found to be standing, and in Figure 3b for laying molecules at the surface. Examining standing and laying maps together, there appear to be five distinct populations of conformers, labeled according to a representative (ξ1,ξ2) set (as shown in Figure 3a) and illustrated in Figure 4. In order to arrive at the relative populations of these conformers in their standing and laying orientations, separated according to the hydrophobicity of the model surface, we first define masks as shown in Figure 3c. We use the boundaries of these regions to again process the individual molecular dynamics trajectories, now separating the bins according to the various surfaces. The results are shown in Figure 5 where the conformers are stacked in no particular order, colored alternately in white or yellow for contrast. Fractions standing appear below the broken line; fractions laying are above the broken line. Figure 5 illustrates that, at the 84
contact angle surface, the (
165, þ83) conformer represents roughly 40% (combined standing and laying) of the total population; the (
78, þ167) conformer represents ∼30% of the total population; the remaining three conformers represent approximately 10% each. Within the (
165, þ83) population, approximately one-quarter of the molecules prefer to adsorb in a standing orientation (with three-quarters laying on the surface) at this least hydrophobic surface. One third of the (
78, þ167) species are standing. For the other three conformers, the left-most side of Figure 5 illustrates that the laying conformation is preferred. As the hydrophobicity of the surface increases, the leucine molecules adopt a primarily standing orientation in their adsorbed state. For the 156
contact angle surface (right-most edge of Figure 5) nearly all of the molecules are found to be standing, roughly 40% each (
165, þ83) and (
78, þ167), with the remaining 20% divided among the other three standing conformers. 3.3. Vibrational Hyperpolarizability Calculations. The use of electronic structure calculations for a harmonic approximation of R(2) lmn (where l, m, n are the molecular-frame a, b, c Cartesian coordinates) has been previously demonstrated.56
61 Typically, the local a, b, c axes are chosen so as to describe the moiety of interest (as illustrated for the CH2 plane in Figure 2a). In the case of leucine, however, the 10 normal modes in the 2800
3000 cm
1 window are highly delocalized and so it is not possible to uniquely describe a reference plane containing the atoms of interest. We therefore take a different approach, calculating the vibrational hyperpolarizability tensor elements in an arbitrary molecular plane. So long as we can identify the coordinate transformation between these molecular a, b, c axes and the laboratory x, y, z frame we can carry out the projection in eq 6 to arrive at the SFG intensities for the resonant modes. We have considered the centroid positions of the (ξ1,ξ2) dihedral angles to arrive at starting structures for the electronic structure calculations. The most populated spot was considered 11219

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Figure 3. Molecules binned according to their dihedral angles (ξ1,ξ2), separated into (a) standing and (b) laying adsorbed orientations. Light colors (white) indicate that few molecules were found with those dihedral angles; darker regions indicate higher populations. For the purposes of counting, regions of high population were identified and described according to the boundaries shown in (c). The point corresponding to the largest population density in each region is marked with a white circle. The optimized geometries are indicated by the filled circles.

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from the standing (Figure 3a) and laying maps (Figure 3b). These points are marked with white circles in Figure 3. The geometry was then optimized with an effective solvent model (PCM) with atoms in the vicinity of these ξ1 and ξ2 angles constrained. Since the subsequent Hessian calculation requires structures that are at a local minimum on the potential energy surface, the geometry was then further optimized with all degrees of freedom unconstrained. The final optimized geometries are shown with filled circles in Figure 3, connected with lines to their initial starting structures. Throughout this work, we have used the dihedral angles (ξ1,ξ2) of the final optimized structures to label the five conformers of interest. Finally, the Hessian matrix was calculated for each of the five conformers using the same basis set and method, also with a PCM solvent model. The normal-mode frequencies (Hessian eigenvalues) together with a visualization of the corresponding atomic displacements (Hessian eigenvectors) were used to identify 10 IR resonant modes in the 2800
3000 cm
1 region for each conformer. For each vibrational mode, polarizability derivatives dR(1) lm /dQ and dipole moment derivatives dμn/dQ were determined by a 7-point finite difference method as outlined in ref 61. The product of these two quantities was then used to estimate R(2) lmn in the molecular frame. 3.4. Fitting the Experimental Spectra. Our ultimate goal is to describe the SFG spectra in Figure 1 in terms of the relative population of the five conformers in their standing and laying orientations at the surface. Now that we have all elements of R(2) for all C
H stretching modes of each conformer in the molecular l, m, n frame, we use eq 6 to project them into the laboratory i, j, k frame, with a discrete form of the orientation distribution f(Ω) coming from the molecular dynamics trajectory. In this way, after projection, we have the (relative) χ(2) ijk values for the 10 resonant modes of each conformer. We then transform these into effective susceptibility tensor elements for the ssp, sps, and ppp polarization schemes via eq 4. Since we model only the resonant hyperpolarizability elements in a harmonic approximation, we do not account for the nonresonant contribution to χ(2) or any Fermi resonance. An SFG study of leucine at the air
water interface has identified Fermi resonances at 2889 cm
1 and 2930 cm
1.76 With the relative contributions of the 10 resonant modes fixed, and two Fermi resonances defined to be within a small region about these values, we obtain the nonresonant and Fermi amplitudes by fitting the experimental data. We have previously discussed the challenges in fitting a coherent line shape as observed in SFG spectra.61 As a result, we have used a similar approach where parameters are sampled using a Monte Carlo (MC) algorithm. Briefly, a random population distribution was chosen for the five conformers in both orientations, along with the amplitudes and phases of the Fermi resonances and a slight variation in their positions. The 10 best fit values from 2  107 such MC runs were then subject to a constrained L-BFGS-B optimization78,79 to clean up the results. We have first considered each of the five conformers individually to get an idea of their SFG spectra. These results are displayed in Figure 6, where the points are experimental data, the blue lines represent an all-standing orientation, and red lines indicate an all-laying orientation. The 3 polarization schemes are considered simultaneously in arriving at the Fermi resonance frequencies, adjusting the relative weighting of the residuals to the signal-to-noise ratio of the corresponding experiment. Upon inspection of Figure 6, it is immediately apparent that the individual spectra are drastically different from one another. 11220

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Figure 4. (a
e) The five conformers adjacent to a surface in a typical standing orientation as defined by the criteria used in this study. (f
j) The same conformers in their laying orientation adjacent to a surface. The highlighted structures are those determined to contribute most significantly to the observed spectra.

Figure 5. Relative population of each of the 5 Leu conformers in their standing and laying orientation, as a function of the hydrophobicity of the surface. The total fraction of each species is white or shaded yellow for contrast. Fractions standing appear below the broken line; fractions laying are above the broken line. Regions are labeled according to the set of dihedral angles (ξ1,ξ2) identified in Figure 3a.

This is reasonable considering that the C
H stretching modes are close in energy and highly coupled. As a result, they are very sensitive to the (ξ1,ξ2) torsional angles. Within a single conformer, the variation is generally less pronounced between standing and laying orientations, but the effect of orientation is still seen to affect the quality of the fit. It is also obvious that the predicted spectra based on the (
138,
53) and (
165, þ83) conformations appear to most closely resemble the experimental SFG data. Finally, we emphasize that these spectra are a good illustration of why a method such as this is necessary in describing the experimental data. Although we have already mentioned that 10 resonances are not apparent in the acquired spectra, one can

see how closely spaced the normal modes are in energy as indicated in the vertical solid gray lines in Figure 6. (The dashed lines indicate the positions of the Fermi resonances.) The blue (red) bars at the base of these lines indicate the relate standing (laying) amplitudes of the modes at these positions, in order to provide a sense of which modes are appreciably contributing to the SFG response. For example, in the case of most sps spectra in Figure 6, only the highest energy modes have appreciable population. In such cases, this would justify an approach where experimental spectra are fit with few peaks. However, we note that even here it is not possible to separate all antisymmetric contributions to the largest peak. In a second attempt to fit for the Fermi resonances and the NR background, we have still kept the conformers separate, but have allowed the standing/laying fraction to be additionally optimized in the fit. These results are indicated with the black lines in Figure 6, and are summarized in two columns of Table 1. Here we observe that in many cases (such as the ppp spectra for the (
165, þ83) conformer shown in Figure 6o), the allowance of a flexible standing/laying ratio significantly improves likeness to the experimental result. However, the (
138,
53) and (
165, þ83) conformers still emerge as having a much closer resemblance to the experimental data than any of the other three species. The remaining question is whether some contribution from standing or laying orientations of the other conformers could further improve the agreement with experiment. We now consider contributions from both standing and laying orientation distributions (sampled from the corresponding MD trajectories) of all five conformers. In a highly parallel Monte Carlo approach, for each trial distribution of the 10 populations, we have fit to provide the best nonresonant and Fermi contributions. The best results from 20 million MC runs are summarized in the “all unbiased” column of Table 1 and are used to construct the spectra shown with dashed lines in Figure 7. One can notice that the inclusion of multiple species has dramatically improved the resemblance of the generated spectra to the experimental data. We emphasize that the resonant amplitudes for each species contain no adjustable parameters (dipole moment and polarizability derivatives are directly from the ab initio calculations), nor do the features of the orientation distribution sampled for each species (directly from the molecular dynamics trajectory). Since these results heavily favored the 11221

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Figure 6. Results of fitting the experimental SFG spectra (points) to resonant peak amplitudes for each of the five conformers (rows 1
5) obtained from electronic structure calculations and orientation distributions obtained from molecular dynamics simulations. The polarization schemes ssp, sps, and ppp are shown in columns 1
3, respectively. The contribution of a nonresonant response and two Fermi resonances are determined by fitting the data. The best fit for an all-standing orientation is shown in blue; and all-laying scenario is shown in red. The black lines indicate results for which the standing/laying fraction is optimized in the fit. Frequencies of the normal modes are listed in the first column (left inset); frequencies of the two Fermi Resonances are listed in the right inset. The relative amplitudes of all peaks are indicated with the bars at the corresponding frequency, standing in blue, laying in red.

(
138,
53) and (
165, þ83) conformers, we have performed another iteration of searching where the standing and laying distributions of these two species are biased with extra weight in the population distribution. This was designed to overcome the sampling problem in our high-dimensional parameter space. The results of this search and concomitant nonresonant and Fermi fit are indicated in the “all biased” column of Table 1. Finally, we have considered that these major conformers comprise the entire population distribution, varying only their relative abundance and standing/laying ratio. The results of this search appear in the “(
138,
53),(
165, þ83)” column of Table 1 and the associated spectra are shown with the solid lines in Figure 7. In the end, the qualitative agreement with the experimental data is rather remarkable, considering that the amplitudes of all 10 resonant modes are determined without any input from the experimental parameters. The quantitative agreement would be improved with slight adjustment of the resonant frequencies and Lorentzian peak widths, but this was outside of our primary objective in accounting for the SFG spectra in terms of the relative population of conformers and their distinct orientation distributions.

4. DISCUSSION The main goal of this project has been to obtain a sense of the orientation distribution and population of leucine conformers adsorbed at the polystyrene interface, without the prior knowledge of the vibrational assignments. This provides a route for approaching larger molecules and more complex systems. We first address our result that standing orientations are preferred over laying orientations at the polystyrene
water interface. This may be understood from inspecting the structures shown in Figure 4 together with a sense of the water structure at a hydrophobic surface.71,77 We expect that the water density immediately adjacent to the surface is low, and increases to bulkcomparable values at a distance of 4
5 Å from the surface. The standing leucine orientation promotes a greater separation of the hydrophobic isobutyl group from the hydrophilic charged NHþ 3 and COO
groups. This would allow the alkyl portions to occupy regions of low water density, and the zwitterionic groups to experience a greater solvation. An examination of the laying orientations of the five conformers, as shown in Figure 4f
j, allows similar conclusions to be reached. Again, the (
138,
53) 11222

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Table 1. Relative Populations and Orientations of the Leucine Conformers and the Fitting Parameters for the Amplitude and Phase of the Nonresonant Contribution (NR) and the Two Fermi Resonances (FR1 and FR2)a property lowest error

(
138,
53) only

all unbiased

all biased

(
164, þ83), (
138,
53)

9.857

5.116

5.628

4.697

4.547

0.289 0.711

0.886 0.114

0.670 0.330

0.854 0.146

0.932 0.068

total fraction

standing laying

fraction standing

(þ 59, þ119)

0.000

0.000

0.014

0.007

0.000

(
165, þ83)

0.289

0.000

0.198

0.121

0.201

fraction laying

NR

FR1

FR2

a

(
164, þ83) only

(
148, þ175)

0.000

0.000

0.006

0.021

0.000

(
138,
53)

0.000

0.886

0.445

0.690

0.730

(
78, þ167)

0.000

0.000

0.007

0.014

0.000

(þ 59, þ119)

0.000

0.000

0.025

0.002

0.000

(
165, þ83) (
148, þ175)

0.711 0.000

0.000 0.000

0.043 0.028

0.067 0.004

0.055 0.000

(
138,
53)

0.000

0.114

0.203

0.064

0.013

(
78, þ167)

0.000

0.000

0.031

0.010

0.000

ssp amplitude/10
3 au


0.206


0.156


0.322


0.158


0.258

sps amplitude/10
3 au


5.97


5.95


4.03


5.34


5.71

ppp amplitude/10
3 au

1.32

2.64

1.84

2.06

2.05

ppp phase/rad

0.47


1.59


1.60


1.60


1.57

frequency/cm
1 ssp amplitude/10
3 au

2893
2.27

2886
1.69

2890
1.60

2897 1.09

2891
0.356

sps amplitude/10
3 au


0.929

0.743


1.50


0.414

0.552

ppp amplitude/10
3 au

0.464

1.51

0.891

1.42

0.941

ppp phase/rad

0.37


1.40


1.42


1.62


1.13

frequency/cm
1

2939

2937

2939

2938

2944

ssp amplitude/10
3 au


2.26

1.78


2.19

1.31

0.934

sps amplitude/10
3 au


1.93


1.06


0.273


0.177


1.43

ppp amplitude/10
3 au ppp phase/rad

1.73 1.38

2.25
0.23

209 2.56

0.812 1.14

0.555
0.10

All Lorentzian widths are considered to be 6 cm
1, and amplitudes are in arbitrary units.

species has the best potential for hydrophobic interactions, as is exhibited through its unique structural ability to point two methyl groups down toward the surface. While the two polar regions are nearly coplanar with the surface, they are separated from the likely point of contact, the isobutyl region, allowing for solvation of these groups. For the (þ59, þ119), (
78, þ167), and (
148, þ175) conformers, the molecules adopt orientations that are more flat. These configurations lack the necessary separation between their hydrophobic and polar regions that would allow for effective hydrophobic interactions with the surface and solvation of the ionic moieties. This is the most logical reason for their low determined relative populations. While the (
165, þ83) conformer directs only one methyl group to the surface, it still possesses one of the greatest separations of these regions. We now attempt to rationalize our results indicating a preference for the (
165, þ83) and (
138,
53) conformers at the surface. Since the electronic structure calculations were performed identically for each conformer in a polarizable continuum model to more closely model the dielectric constant associated with being in an aqueous solution, we should be able to compare their relative energies. The (
78, þ167) structure was determined to be the lowest energy conformer, with (
165, þ83) only ∼2 kJ/mol higher in energy. The other three conformers are ∼10 kJ/mol higher in energy, with (
138,
53) being the highest at ∼15 kJ/mol above (
78, þ167). Although the polarizable continuum model may be useful as a rough approximation to an

aqueous solution, it does not account for interactions with the polymer surface when the molecules are adsorbed. However, since we do not anticipate any specific leucine
polystyrene interactions beyond those dictated by the interfacial solvent structure,71,77 it is interesting to consider the relative energies of these molecules in the bulk solution environment. Furthermore, the relative abundance of each conformer on the surface, as illustrated in Figure 5 is strongly determined by these relative energies, with (
165, þ83) and (
78, þ167) dominating the adsorbed states and the other 3 conformers together accounting for less than 30% of the molecules. This reveals that the hydrophobicity of the surface influences the standing/laying ratio more than the adsorbed conformation. Although the (
78, þ167) conformer is also low in energy, in its standing orientation it does not have as distinct a stratification of its methyl groups into the low water density region close to the polymer surface. Similarly, although the (
138,
53) conformer lacks stability in the bulk compared to the other shapes, and was not determined to be a large contributor to adsorbed species in the MD trajectories, it shares a common feature with (
165, þ83) in that, in its standing orientation, both methyl groups are nearly coplanar. This allows the hydrophobic portion of the molecule to exist in the low water density region immediately adjacent to the surface. The majority of the effort in this study has been focused on developing algorithms to perform three distinct steps. In the first stage, we required an efficient mining of relevant conformers from multiple MD trajectories; setting these molecules as starting 11223

dx.doi.org/10.1021/jp2025208 |J. Phys. Chem. C 2011, 115, 11216–11225

The Journal of Physical Chemistry C

ARTICLE

resonant contributions as these were the only quantities that were not calculated. An overarching objective in this work was to develop an approach to carry out these steps in as general a manner as possible, with a sight toward more complex systems involving larger molecules.

Figure 7. Best fit ratios of the conformers, showing the (a) ssp, (b) sps, and (c) ppp spectra. Experimental data are indicated with points. The results of the unconstrained search over both populations of five conformers (10 species total) are indicated with broken lines; the results of the search constrained to both populations of the two best conformers (4 species total) are indicated with solid lines.

points for electronic structure calculations; and then arriving at closely related structures for which vibrational hyperpolarizabilities may be computed. It would be interesting to perform a similar analysis with an atomistic polymer surface. However, even such a structurally detailed surface would require proper parametrization in order to describe the physical and chemical properties of polystyrene. In this respect, our MD simulations with surfaces of varying hydrophobicity allow us to sample leucine interactions at a heterogeneous polystyrene surface prior to such parametrization efforts. As future electronic structure calculation capabilities improve, more accurate descriptions of molecules adsorbed at surfaces will be obtained. In addition, we used a polarizable continuum model to approximate a water environment around leucine. This does not take the differences in bulk and interfacial solvation into account. Coupled with ab initio molecular dynamics simulations, interactions with atomistic surfaces and explicit solvent will allow a more complete theoretical description of the surfaces to be accessible. In an intermediate step, each leucine conformer was projected onto an orientation distribution obtained from relevant frames from the same dynamical trajectories. We note that here too, we are working under the assumption that the interactions between leucine, water, and the surfaces are well-parametrized in the classical force field. Our heterogeneous sample technique should overcome some of the sampling error in this case as well, so the orientation distribution is not derived from a single surface. In the final step, Monte Carlo sampling was used to compare spectra generated from trial population distributions with the experimental spectra in three polarization schemes—each MC step required fitting for the optimal nonresonant and Fermi

5. CONCLUSIONS A methodology for the determination of the relative population of amino acid conformers at surfaces was developed. The approach utilized electronic structure calculations, molecular dynamics simulations, and vibrational sum frequency generation experiments. As a demonstration, the method has been applied to a system where the structure of leucine adsorbed to a polystyrene surface was determined. Five molecular conformations were identified at the surface, each with its associated orientation distribution. The predicted SFG spectra that most closely matched those obtained experimentally in three different polarization schemes were dominated by two conformers. It was further determined that molecules that are standing at the surface, with their alkyl groups directed toward the surface and their charged amino and carboxylate groups toward the solvent are highly favored. We rationalize our findings based on maximizing contacts between their alkyl regions and the waterdepleted hydrophobic surface, while maintaining an orientation in which their charged groups point directly into the solvent. The methodology developed in this study illustrates that it possible to obtain structural information from vibrational spectra, even if significant coupling among numerous bands precludes identification or assignment of the spectral features. This should permit extension of this work to larger, more complex molecules adsorbed at interfaces. ’ AUTHOR INFORMATION Corresponding Author

*Phone: 250-721-7168; Fax: 250-721-7147; E-mail: dkhore@ uvic.ca.

’ ACKNOWLEDGMENT We wish to thank the Natural Science and Engineering Research Council of Canada (NSERC) for support of this science with a Discovery Grant. Lasers were purchased with a Canadian Foundation for Innovation Leaders Opportunity Fund and British Columbia Knowledge Development Fund. Computers were purchased with startup funds from the University of Victoria. S.A.H. is grateful to NSERC for an Alexander Graham Bell graduate scholarship. ’ REFERENCES (1) Mermut, O.; York, R. L.; Phillips, D. C.; McCrea, K. R.; Ward, R. S.; Somorjai, G. A. Biointerphases 2006, 1, 5–11. (2) Lu, J. R.; Zhao, X.; Yaseen, M. Curr. Opin. Colloid Interface Sci. 2007, 12, 9–16. (3) Chena, H.; Yuana, L.; Song, W.; Wub, Z.; Lia, D. Prog. Polym. Sci. 2008, 33, 1059–1087. (4) Zhang, L.; Sun, Y. Biochem. Eng. J. 2010, 48, 408–415. (5) Krishnan, S.; Weinman, C. J.; Ober, C. K. J. Mater. Chem. 2008, 18, 3405–3413. (6) Elbert, D. L.; Hubbell, J. A. Annu. Rev. Mater. Sci. 1996, 26, 365–394. (7) Szleifera, I. Biophys. J. 1997, 72, 595–612. 11224

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