Water and peptide structure at hydrophobic and hydrophilic surfaces

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by Sandra Roy

B.Sc., Universit´e Laval, 2010

A thesis submitted in Partial Fulfillment of the Requirements for the Degree of

MASTER OF SCIENCE in the Department of Chemistry

c

Sandra Roy, 2012 University of Victoria

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B.Sc., Universit´e Laval, 2010

Supervisory committee

Dr. Dennis K. Hore, Supervisor (Department of Chemistry)

Dr. Fraser Hof, Departmental Member (Department of Chemistry)

Dr. Irina Paci, Departmental Member (Department of Chemistry)

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Supervisory committee

Dr. Dennis K. Hore, Supervisor (Department of Chemistry)

Dr. Fraser Hof, Departmental Member (Department of Chemistry)

Dr. Irina Paci, Departmental Member (Department of Chemistry)

ABSTRACT

In order to better understand the interfacial peptide–water interaction, molecular dynamics simulations were made for both water, and an amphipathic peptide, LKα14, adsorbed at hy-drophobic and hydrophilic surfaces. Structural and orientational analyses were performed on both systems. Vibrational mode frequency and oscillator coupling were analyzed for the interfacial water. When looking at the peptide, DFT (density functional theory) ab initio calculations were performed to obtain the non linear vibrational information of the different side chains conformers. Non linear vibrational spectra derived from these results were simulated for both interfacial water and adsorbed peptide. The sum frequency vibrational spectra obtained were correlated to the orientation analysis results. Comparison with literature results were made for both spectral and orientational analysis. The results obtained of water at hydrophilic surfaces lead us to conclude that the absence of signal in the 3700 cm−1 region is due to a cancellation of strongly opposite oriented water layers rather than the absence of O–H oscillators at this vibrational frequency region. The hydrophobic and water-air simulation resulted in surprisingly strong similarity but with difference in the depth of those features. When analyzing the structure of LKα14,

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at the hydrophilic surface proved that the adsorption process takes longer than for the hydrophobic surface. Due to results of water and peptide adsorption, we propose that the time scale of the adsorption process for peptide interaction with hydrophilic surface is partially due to the multiple, strongly orientated, water layers.

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List of Tables

2.1 Limiting cases for the order parameters defined in Eqns. 2.2 and Eqn. 2.3. . 14 4.1 Overview of Im(χ(2)_kk⊥) signal for the region 2600–3600 cm−1 for LKα

adsorbed on hydrophobic and hydrophilic surfaces. s=strong, m=medium, w=weak, +=positive, -=negative . . . 63 4.2 Leucine tilt angle calculated from our simulation compared to those derived

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List of Figures

1.1 Modelled representation of LKα14. For purpose of easier visualization, most hydrogens have been rendered invisible. Hydrophobic residues (Leu) has been colored blue and the hydrophilic residues (Lys) colored green. . . 6 2.1 Snapshot of the LKα14 adsorbed at the hydrophobic (a) and hydrophilic

(b) surfaces. Leucine residues and lysine residues are represented in blue and green respectively. . . 11 2.2 (a) Sample and beam geometry for SFG experiments at the solid–water

interface. When accessing the solid–water interface, it is customary to use a window or prism. The surface of the prism may be coated or functionalized in order to create the hydrophobic or hydrophilic material of interest. We consider that the positive z axis extends away from the bulk water phase. (b) Definition of the tile angle θ and twist angle ψ relating the molecular (a, b, c) frame to the surface (x, y, z) frame. . . 16 3.1 (a) Water density profile across the water–hydrophobic solid interface. (b)

Order parameters S1θ in red, S2θ in blue, S3θ in green, and Sψ in black. In

both plots, the vertical dashed line indicates the position of the uppermost aliphatic atom, and serves as a reference for the distance scale; positive values of distance tend towards the bulk water phase. The regions labeled A–C were selected for subsequent analysis based on the trends and signs of the order parameters. . . 22

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parameter regions defined in Fig. 3.1. The first column shows the tilt and twist (θ and ψ as defined in Fig. 2.2b) histograms for all water molecules found in this region of the interface. Darker regions indicate lower populations; the white regions indicated the highest population. The second column shows the OH frequency shift with respect to an uncoupled oscillator in the gas phase at 3707 cm−1. This is plotted as a difference in population ∆P with respect to results obtained in the bulk water sample. Data for the low-energy eigenmodes (red), high-energy eigenmodes (blue) are separated; the combination is plotted in black. The plots in the third column are histograms of the water molecule nature, as defined by the difference between h|2c1c2|2i in the region of interest and those values

obtained in the bulk water phase. The results for the low energy modes are plotted in red, high energy modes in blue, and the population-weighted average in black. The final column shows the imaginary component of the nonlinear susceptibility tensor elements: χ(2)_kk⊥ in blue; χ(2)_k⊥k in red, and χ(2)_⊥⊥⊥in black. . . 23 3.3 (a) Water density profile across the vapor–water interface. (b) Order

parameters S1θ in red, S2θ in blue, S3θ in green, and Sψ in black. In both

plots, the vertical dashed line indicates the Gibbs dividing surface, and serves as a reference for the distance scale; positive values of distance tend towards the bulk water phase. The regions labeled A–C were selected for subsequent analysis based on the trends and signs of the order parameters. . 28

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3.4 Cartoon representations of dominant water orientations in various regions of the interface for (a) hydrophobic surfaces (both solid and vapor) and (b) the hydrophilic solid surface. In the case of the hydrophilic surface, only regions A-C are shown. . . 29 3.5 Results of structure, hydrogen bonding, water species analysis, and

nonlin-ear vibrational spectra obtained for the vapor–water interface. The rows are labeled A–C according to the density and order parameter regions defined in Fig. 3.1. The first column shows the tilt and twist (θ and ψ as defined in Fig. 2.2b) histograms for all water molecules found in this region of the interface. Darker regions indicate lower populations; the white regions indicated the highest population. The second column shows the OH frequency shift with respect to an uncoupled oscillator in the gas phase at 3707cm−1. This is plotted as a difference in population ∆P with respect to results obtained in the bulk water sample. Data for the low-energy eigenmodes (red), high-low-energy eigenmodes (blue) are separated; the combination is plotted in black. The plots in the third column are histograms of the water molecule nature, as defined by the difference between h|2c1c2|2i in the region of interest and those values obtained in

the bulk water phase. The results for the low energy modes are plotted in red, high energy modes in blue, and the population-weighted average in black. The final column shows the imaginary component of the nonlinear susceptibility tensor elements: χ(2)_kk⊥in blue; χ(2)_k⊥kin red, and χ(2)_⊥⊥⊥in black. 30

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surface hydroxyl group H atom, and serves as a reference for the distance scale; positive values of distance tend towards the bulk water phase. The regions labeled A–F were selected for subsequent analysis based on the trends and signs of the order parameters and oscillations in the density profile. 34 3.7 Results of structure, hydrogen bonding, water species analysis, and

nonlin-ear vibrational spectra obtained for water adjacent to a solid hydrophilic surface. The rows are labeled A–F according to the density and order parameter regions defined in Fig. 3.6. Data appearing in the four columns are plotted with the same descriptions as appear in the caption to Fig. 3.2. . 35 3.8 A comparison of all systems studied with the vapor–water interface

(com-bined regions A–C) results in red, hydrophobic solid surface (com(com-bined regions A–C) in blue, and hydrophilic solid surface (combined A–F) in green. (a) Difference in the frequency distribution of the interfacial population with respect to that in bulk water. (b) Difference in the overall mode character h|2c1c2|2i between water at the surfaces and bulk water. (c)

Real (dashed lines) and imaginary (solid lines) spectra of χ(2)_kk⊥, (d) χ(2)_k⊥k, and (e) χ(2)_⊥⊥⊥. . . 37 4.1 Snapshot of the LKα14 adsorbed at the hydrophobic (a) and hydrophilic

(b) surfaces. Leucine residues and lysine residues are represented in blue and green respectively. . . 44

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4.2 (a) LKα14 end-to-end distance, dee, (b) distance between the LKα14

center of geometry, dCOG, and the surface, (c) long axis tilt angle, θ.

Results for the peptide in bulk solution (when not adsorbed on any surface) are indicated in black. In the case of bulk solution, dCOG is calculated

with respect to an arbitrary point in the simulation cell. Results of the hydrophobic surface are shown in blue; hydrophilic surface in red (t < 50 ns in solid lines, 2.5 < t < 3 µs in dashed lines). . . 46 4.3 Ramachandran plots illustrating ψ vs ϕ backbone torsional angles of

LKα14 in bulk solvent. Higher populations appear darker (black). The boundaries of the right- and left-handed α-helical, β sheet, and ε regions are according to Morris et al. [2]. Core right-handed α-helical regions are labelled A, allowed regions a, generous regions -a. Core left-handed α-helical regions are labelled L, allowed regions l, generous regions -l. Core β-sheet regions are labelled B, allowed regions b, generous regions -b. . . . 48 4.4 Ramachandran plots illustrating ψ vs ϕ backbone torsional angles of

LKα14 adsorbed at a hydrophobic surface. Higher populations appear darker (black). The boundaries of the right- and left-handed α-helical, β sheet, and ε regions are according to Morris et al. [2]. Core right-handed α-helical regions are labelled A, allowed regions a, generous regions -a. Core left-handed α-helical regions are labelled L, allowed regions l, generous regions -l. Core β-sheet regions are labelled B, allowed regions b, generous regions -b. . . 49

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left-handed α-helical, β sheet, and ε regions are according to Morris et al.[2]. Core right-handed α-helical regions are labelled A, allowed regions a, generous regions -a. Core left-handed α-helical regions are labelled L, allowed regions l, generous regions -l. Core β-sheet regions are labelled B, allowed regions b, generous regions -b. . . 50 4.6 Ramachandran plots illustrating ψ vs ϕ backbone torsional angles of

LKα14 adsorbed at a hydrophilic surface for long times (greater than 2.5 µs). Higher populations appear darker (black). The boundaries of the right- and left-handed α-helical, β sheet, and ε regions are according to Morris et al. [2]. Core right-handed α-helical regions are labelled A, allowed regions a, generous regions -a. Core left-handed α-helical regions are labelled L, allowed regions l, generous regions -l. Core β-sheet regions are labelled B, allowed regions b, generous regions -b. . . 51 4.7 Ramachandran plots illustrating ψ vs ϕ backbone torsional angles of

LKα14 in bulk solvent. They are numbered from the N terminus (a) to the C terminus (m). Higher populations appear darker. . . 53 4.8 Ramachandran plots illustrating ψ vs ϕ backbone torsional angles of

LKα14 adsorbed at a hydrophobic surface. They are numbered from the N terminus (a) to the C terminus (m). Higher populations appear darker. . . . 54 4.9 Ramachandran plots illustrating ψ vs ϕ backbone torsional angles of

LKα14 at an hydrophilic surface for short times (up to 50 ns). They are numbered from the N terminus (a) to the C terminus (m). Higher populations appear darker. . . 55

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4.10 Ramachandran plots illustrating ψ vs ϕ backbone torsional angles of LKα14 at a hydrophilic surface for long times (greater than 2.5 µs). They are numbered from the N terminus (a) to the C terminus (m). Higher populations appear darker. . . 56 4.11 Side chain orientations determined by the tilt of the longest axis that

connects the main chain to the side chain. Residues are labelled starting at the N terminus. Results obtained when LKα14 is adsorbed on the hydrophobic surface are shown in blue; on the hydrophilic surface in red (t < 50 ns in solid lines, 2.5 < t < 3 µs in dashed lines). . . 57 4.12 Side chain orientations determined by the tilt of the chain end vectors.

In the case of Leu residues, the vector the vector starts at the isopropyl methyne carbon and bisects the methyl groups. For Lys, we have chosen the NH+₃ 3-fold symmetry axis. Residues are labelled starting at the N terminus. Results obtained when LKα14 is adsorbed on the hydrophobic surface are shown in blue; on the hydrophilic surface in red (t < 50 ns in solid lines, 2.5 < t < 3 µs in dashed lines). . . 59 4.13 Distribution of side chain dihedrals angles K1–K5 of Lysine residues and

L1–L2 of the Leucine residues. Correlation between the identified dihedral populations and a table explaining these populations. . . 61 4.14 Newman projection of the (a) trans conformation (dihedral = 180/-180) and

(b) gauche conformation (dihedral = 60/-60). . . 62 4.15 Generated SFG spectra of LKα14 showing real (a, d, g) and imaginary (b,

e, h) χ(2), and SFG magnitude (c, f, i). Results obtained when LKα14 is adsorbed on the hydrophobic surface are shown in blue; on the hydrophilic surface in red (t < 50 ns in solid lines, 2.5 < t < 3 µs in dashed lines) . . . 62

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α polarizability Cm2V−1

α(2) _{hyperpolarizability} _Cm3_V−2

λ wavelength m

χ electric susceptibility a.u.

χ(2) second order nonlinear susceptibility a.u.

ω angular frequency rad s−1

t time s

µ electric dipole moment C · m

Γ spectral linewi cm−1

DFT density function theory SFG sum frequency generation MD molecular dynamics R direction cosine matrix

θ, φ, ψ Euler angles for tilt, azimuth and twist deg or rad xyz laboratory coordinate system unit vector

ijk place holders for any of the x, y or z coordinates abc molecular coordinate system unit vectors

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ACKNOWLEDGEMENTS

I would like to thank:

Dennis Hore, for everything. From all the great group dinners with amazing food, to all the support when I was facing challenges of all sorts. I could have not done it without you.

My mom, dad and sister, Linda, Marcel and Samanta, for all the support through all my years in school. You were always there for me, even on the other side of the country, you could always make me feel like you were right beside me, supporting through every decision, every battle. This is dedicated to you, as a proud accomplishment of your unconditional love.

Andrew Schildroth and Veronica Sabelnykova, for having the proof-reading skills that I do not.

Kuo-Kai Hung , for programs allowing us to read the Gromacs binary file format. Also a big thanks for the automation of the calculations for the dipole moment and polarizability derivatives.

Tatiana Popa, Paul Covert, Tsuki Naka and Kuo-Kai Hung, for making life in the basement more interesting.

NSERC and UVic, for financial support.

Compute Canada, for the use of the Westgrid clusters.

Belaid Moa, for all the help in porting some of my code to the Compute Canada clusters.

“La physique est une science qui devient chimie lorsqu’on la chauffe a l’air libre” Jean-Louis Marcel-Charles

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The desire to understand physical properties of substances and solutions, such as boil-ing/freezing point, energy of dissolution and adsorption, have led people to study interactions of matter on a molecular level. Water is vital to life, covers 71% of our planet, composes 50–65% of our body, and is the most common solvent used. Therefore, it is logical that the study of water and its interaction with different environments has been intensively studied. A large body of research has been focused on the molecular structure of water implicated in such interaction and how it affects other processes. The structure of water adjacent to solid surfaces is of fundamental importance to a wide range of fields as diverse as catalysis [3, 4], chemical separations [5–7] and biocompatibility of implant materials [8–11]. In each of these applications, surface-adsorbed water plays a central role in selectively sequestering some molecules to the surface, while inhibiting the adsorption of others. Once molecules in solution have adsorbed to the solid surface, interfacial water plays a further role in governing the conformation and orientation of the adsorbed state. Large molecules such as proteins might tend to be more affected by the water, as a big molecule will not as easily displace water molecules to adsorb on the surface. Depending on the nature of the protein, a different solvation shell will be present around the protein, which can further inhibit or help its adsorption on different surfaces. The protein adsorption process is thus affected by how water molecules are oriented at surfaces [12–14] but also by the relative affinity for the surface of the molecules in play [15].

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1.1 Interfacial water structure

Despite the recognized importance of water at the solid–aqueous interface, these water molecules have received little attention compared with water and solutes in the bulk solution phase. A large part of this disparity is a result of the difficulty in probing interfacial water species with sufficient specificity. For example, grazing incidence techniques have penetration depths on the order of micrometers. Absorption-based techniques employing evanescent waves (such as ATR-IR spectroscopy [16, 17]) probe a depth of hundreds of nanometers to a few microns, depending on the wavelength of the probe light. These length-scales are orders of magnitude larger than the depth of the interface as determined by molecular simulations. Prior to the last two decades, computer simulation was one of the only methods that could comment on structural aspects of adsorbed water layers in the presence of bulk water. Recently, however, nonlinear optical spectroscopy has made significant progress in this field. Under the electric dipole approximation, techniques based on even orders of the susceptibility χ(n)will not generate a response from molecules that are arranged in centrosymmetric environments. As an example, second harmonic generation (SHG) relies on χ(2) _{6= 0, and therefore only those molecules with a net polarity to their}

orientation can participate in the SHG process [18–20]. The non-degenerate version of this experiment, sum-frequency generation (SFG) spectroscopy, is particularly attractive for studying interfacial water species as it enables one of the pump lasers to be in the mid-IR, and tuned over the O–H stretching frequencies from 2800–3800 cm−1 [21, 22]. This permits interfacial water molecules to be further classified according to their hydrogen bonding environment, as increasing coordination produces a greater red shift in the spectra. There have been many SFG studies of neat water at solid surfaces, including those of water adjacent to mineral [23–31], metal [32, 33], self-assembled monolayer [34, 35] and polymer [36–39] surfaces. Some of this work has been summarized in review articles [8, 40–43]. Recently, phase-resolved SFG experiments have been able to produce real and imaginary spectra of χ(2) over IR energies of interest [44–51]. Details of the complex

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imaginary χ(2) _{spectrum, non-resonant background-free imaginary χ}(2)_{, and more clearly}

discerning features in the otherwise broad O–H stretching frequency region. Another advantage of a phase-resolved SFG experiment is that the real and imaginary components of a particular element of χ(2) is related to the absolute orientation of the water molecules, thereby revealing whether the water oxygen atom or hydrogen atoms are directed towards the interface.

Despite recent advancements in the field of SFG, it remains challenging to relate the experimental observables to structural features of the interfacial molecules. Vibrational SFG spectroscopy offers a unique combination of sensitivity and specificity in this regard, but it is difficult to gain structural insight from the spectra alone. For this reason, significant attention has been paid to interfacial water over the past several decades, by DFT ab initio techniques [57, 58], molecular dynamics [59–68] and Monte Carlo simulations [69–74]. As techniques for modelling interfacial water continue to develop, it becomes especially interesting to compare the results to those of SFG spectroscopy. For example, the degree of hydrogen bonding as calculated from the simulation snapshots may be compared with the experimental frequency distribution of O–H vibrations. The order parameters calculated from the Cartesian coordinates may be compared with the intensity of the experimental spectral features.

Over the last decade, it has become possible to generate model SFG spectra from the simulations, thereby providing a direct link between structure and experimental observables. The first such technique was described in 2000 by Morita and Hynes [75], and has since been applied to a variety of vapor and liquid phases adjacent to water [76–81]. In the ‘energy representation’ of the SFG spectrum, the instantaneous forces on each atom were used as an indicator of the condensed-phase O–H frequency red shift from

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the vacuum value and also as a measure of the perturbation of the molecule’s transition dipole moment. In 2002, Morita and Hynes introduced a different procedure for calculating the SFG spectrum, one based on a time-domain treatment [82]. In analogy with bulk IR absorption spectra calculated from the Fourier transformation of the dipole autocorrelation, here the SFG spectrum arises from the transform of the polarizability–dipole moment correlation. This method is generally favored for two reasons. First, it does not require a priori knowledge of the vibrational dephasing time (reciprocal of the homogeneous linewidth in a Lorentzian representation of an O–H oscillator). Secondly, anharmonic contributions may readily be included by modification of the force field. This development has been improved by Morita and others in recent years [83–89]. Skinner’s group has used molecular simulations to assign spectral features based on the hydrogen-bonding character of individual water molecules [55, 90]. All of these methods for generating SFG spectra have been rigorously compared to experimental spectra of the vapor–water interface [82, 83, 85], including isotopic dilution experiments [52, 79, 91]. In this research, we decided to use the ‘frequency domain’ approach to gain more insight in the coupling information of the O–H oscillators.

1.2 Peptides adsorbed on surfaces

Natural or synthetic proteins are frequently the subject of a significant amount of research. Natural proteins are the main components of most body tissues, and are also involved in most biological processes, making their understanding of great importance to understand and cure diseases by example. Synthetic proteins are also important in different research areas, such as drug development and cosmetics. Protein adsorption at surfaces is widely studied because of its impact on cellular activities [12, 92–94]. Upon adsorption, some proteins get denatured [95], and lose their original biological activity [96–98]. Protein adsorption thus requires greater study to understand precisely the nature of these interactions and to be able to predict and control the outcome of systems of

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Proteins are composed of a chain of different amino acids forming a complex form with secondary and tertiary structures. The secondary structure of a protein is defined as the 3D form of the protein segments. Two main protein secondary structures are known: α helix and β sheet. Both structures can be present in the same protein in different places along the protein. The secondary structure of a protein sequence is driven by the nature of the amino acids contained in that sequence. Amino acids side chains can have different properties; neutral, positive or negatively charged. Amino acids are also either hydrophobic or hydrophilic. These side chains properties will affect the intramolecular interaction and, with the right amino acid sequence, will drive the molecule to form a secondary structure to optimize these interactions. These secondary structures are often present in protein as they are more stable.

Since many properties of proteins can be extrapolated from the properties of its amino acid components, a significant amount research has been done on the interaction and structure of individual amino acids on surfaces and interfaces. Methods to analyze amino acid adsorption to surfaces include chromatography [99–101], electron X-ray diffraction [102], spectrophotometry [103], electron microscopy [104], SFG spectroscopy [105–110] and computer simulation [111–115].

Amino acid adsorption can be related to protein adsorption at interfaces, but protein composition and its secondary structure are important factors to consider in the surface interaction and orientation preferences. With previous knowledge of amino acid interaction and growing computational capacity, researchers have started to study specific peptides adsorbed at surfaces by experimental methods [36,116–118] and by simulations [119–123]. Selected research has been focusing on a specific type of secondary structure. Amphi-pathic sequences, and its interaction with surface. AmphiAmphi-pathic molecules are described

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Figure 1.1: Modelled representation of LKα14. For purpose of easier visualization, most hydrogens have been rendered invisible. Hydrophobic residues (Leu) has been colored blue and the hydrophilic residues (Lys) colored green.

as both having a hydrophobic region and a hydrophilic region. This is often present in secondary structure as molecules will try to minimize the interaction between the hydrophobic and hydrophilic components. These molecules have specific properties that makes them interesting in different research areas, such as drug delivery systems [124], gene delivery [125] and antimicrobial peptides [126, 127].

In the hope of gaining more insight into the interaction of more complex peptides, Degrado and Lear [128] developed simple peptides containing leucine and lysine residues mimicking specific secondary structures. LKα14 is one of these peptides containing 14 residues that forms an amphipatic α helix with lysine residues dominating one side of the helix, and the leucine residues dominating the other side (See Figure 1.1). This property makes this molecule even more interesting to study for its interaction with surfaces of different hydrophilicity since this could drive the peptide to favour the adsorption of

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microbalance (QCM) [116, 129], X-ray photoelectron spectroscopy (XPS) [121], time-of-flight secondary ion mass spectrometry (ToF-SIMS) [121], near edge X-Ray absorption fine structure (NEXAFS) [130, 131] and solid-state NMR [1]. All of these techniques give some insight into the secondary structure, but show only an incomplete story of the orientation of the peptide on the surface. To get a better picture of these orientations, SFG is sometimes used in conjunction with these techniques [1, 116, 129–132]. Some stipulation on the sidechain interaction with the surface were based on absence or presence of orientation preference in the SFG signal [116,130]. Other research correlate this relative orientation based on movement restriction showed by solid state NMR [1]. In our research we hope to show the absolute orientation of LKα14 adsorbed at surfaces and how these results can be correlated to the SFG response observed.

1.3 Objectives

The main objective of this research is to understand and compare the structure of water and a peptide at an hydrophobic and hydrophilic surface. To do this, we decided first to understand the water interaction with the surface before adsorption of the peptide and then understanding the adsorption process of the peptide in presence of the water.

Our first objective is thus to use molecular dynamics simulations to study the structure of water adjacent to a solid hydrophobic and hydrophilic surface, and compare our results to those obtained at the more diffuse water–vapor interface and in the bulk water phase. We will then apply a frequency-domain approach to calculate SFG spectra for the water response at these interfaces. Coupling of the two constituent O–H oscillators will provides an opportunity to comment on the nature of the water molecule through the coupling constants. All of our analyses will be performed as a function of distance from the

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interface, thereby performing a depth-profiling that is not readily achieved in experiments. Comparison of our results obtained at both solid surfaces with those from experimental studies will then be possible.

Our second goal is to use molecular dynamics simulation to asses the orientation and structure of LKα14 in bulk water, and adsorbed to the same hydrophobic and hydrophilic surfaces. Ab initio calculations will be used to calculate LKα14 polarizability and dipole moment derivatives for every vibrational mode of interest. We will use these derivates in conjunction with molecular dynamics results to calculate the χ(2)SFG response of adsorbed LKα14 on the different surfaces studied. The correlation between experimental SFG response and interfacial structure will be assesed from the molecular dynamic simulations. For consistency, similar molecular dynamics parameters will be used for the interfacial water and for the peptide adsorption study. This is important since we will correlate the results from water and peptide adsorption.

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Chapter 2 Methods

We now describe details of the MD simulations, including our method of evaluating the water contact angles, calculation of the order parameters used to assess the degree to which specific regions from the surface are structured, calculation of the second-order susceptibility tensor elements, and their variation with the IR probe frequency in an SFG experiment. We also describe the details of the ab initio calculations, the calculation of the dipole moment and polarizability derivatives, and the simulation of the SFG response.

2.1 Molecular dynamics simulation details

2.1.1 Water

Surfaces with different hydrophilicity and hydrophobicity behaviours have been created. A solid surface was created to mimic organic self-assembled monolayers (SAM). The solid substrate consisted of straight chains of OPLS/AA methylene united atoms assembled in a hexagonal fashion, with lattice constants a = 4.38 ˚A and c = 1.60 ˚A as in Ref. 69. In the case of the hydrophobic surfaces (12 centers spanning 17.6 ˚A), the terminal atom was an OPLS/AA methyl united atom. For the neutral hydrophilic surface, hydroxyl termination was added to the 10-atom chains, resulting in an overall length of 18.2 ˚A. The OH groups were oriented 71.5◦ from the surface normal and with a randomized azimuth about the normal. A previous Monte Carlo study by Janeˇcek et al. [69] investigated the effect of the azimuthal angle of surface OH groups on the hydrophobicity of the surface and determined

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that randomly-distributed frozen OH groups resulted in the same water contact angle as freely rotating OH groups. We have therefore fixed the azimuth of the surface OH groups after their initial randomly-generated orientation.

We have studied three different interfaces for water interaction: water vapor, solid substrate with and without hydroxyl coverage. For the peptide, a simulation in the bulk was also performed. For the water interaction, the simulation box dimension was 39.45 × 37.96 × 100 ˚A3. The substrate was placed in contact with 1980 SPC/E water molecules. These water molecules initially occupied ≈ 40 ˚A along the z axis, so enough void (ca. 40 ˚A) was available at the top of the simulation box to allow a vapor– water interface to equilibrate. This avoided the need for pressure coupling, both at the vapor–water and solid–water interface. This was an important consideration since pressure coupling would affect all water molecules in the system, and may have perturbed the surface water structure that we wish to observe. Considerable attention has been paid to the choice of water model employed for interfacial studies and the subsequent generation of SFG spectra. Detailed investigations may be found in the literature using SPC [82, 133], SPC/E [75], TIP4P [90], POL3 [76], E3B [90], CRK [89], and PD [134] models. Reproducing experimental imaginary χ(2) spectra (more details below) at IR energies below 3250 cm−1 remains a current challenge [135]. We chose SPC/E because it provided reasonable agreement with experimental isotopic dilution studies in the high-frequency region of the Im[χ(2)_{] spectra. D}

2O/HOD/H2O data reveal a strong shoulder on

the red side of the uncoupled O–H vibration [136]. A comparison of spectra generated from SPC/E, TIP4P, and E3B water models shows that SPC/E captures this feature the best [90]. However, as a result of the inability of SPC/E to produce Im[χ(2)] > 0 in the 3000 cm−1 region, we have restricted our discussion to IR energies in the range 3300– 3800 cm−1. More details and comparison with experimental data will be provided in the section 4.3. Temperature was kept at 300 K with the help of Berendsen temperature coupling. Simulations were carried out with a 3D periodic boundary condition and the

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Figure 2.1: Snapshot of the LKα14 adsorbed at the hydrophobic (a) and hydrophilic (b) surfaces. Leucine residues and lysine residues are represented in blue and green respectively.

surface atoms were kept fixed in space. Electrostatic interactions were handled by particle mesh Ewald with a real-space equivalent cutoff of 12 ˚A. Van der Waals interactions were cutoff at 12 ˚A. Minimization was followed by a 1 ns equilibration step. MD simulations were carried out for 10 ns while sampling atomistic forces and positions each 50 fs.

2.1.2 Peptide

The amphiphatic Leu-Lys α-helical peptide LKα14 (Ac-KKLLKLLKKLLKL-COO−) was modelled with an OPLS/AA forcefield. It was inititally modelled as a perfect α helix, with backbone torsional dihedrals of φ = −57◦ and ψ = −47◦, and with an acetylated N terminus and a charged C terminus. The N terminus was acetylated and since we assume a pH≈ 7, lysine side chain endings were modelled as NH+₃. To obtain a neutral-charge system, the charged peptide was solvated together with 5 Cl− ions when in the bulk or in the presence of a neutral surface.

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appropriate water density throughout the simulations where the peptide is present with water and the surface, we had to determine the right number of water molecules that needed to be inserted in the simulation box for each surface studied. To achieve this, we first simulated a surface-water-air system and allowed the water to equilibrate to its normal density in the bulk region, at least 20 ˚Afrom the Gibbs dividing surface. The amount of water molecules were calculated in the interfacial region and extrapolated for our system where two surfaces and some bulk is present. To calculate how many water molecules are displaced by LKα14, a simple simulation of a water box with and without the peptide was performed. The final simulation box of dimension 54.79 ˚A × 53.144 ˚A × 90 ˚A dimension thus consisted of the surface, water, and an energy minimized LKα14 that has been centered in the middle of the box. An initial simulation was made with the peptide fixed in space so that the water could equilibrate first. Figure 2.1 show a snapshot of the peptide adsorbed at the hydrophobic (a) and hydrophilic (b) surfaces. LKα14 is represented with the leucine residues in blue and lysine residues in green. As a result of low ordering after short simulations and no permanent adsorption to the surface, we decided to perform longer trajectories for the hydrophilic surfaces, up to 2.5–3µs.

2.2 Water contact angles

Contact angle simulations have been performed to characterize the degree of hydropho-bicity and hydrophilicity of the solid substrate studied. An 895-molecule droplet of water was put on a 155.6 × 144.24 ˚A2 surface. The same equilibration and MD simulation as described above was performed, but for a period of 1 ns. The change in the droplet shape can be correlated to its contact angle by [137]

ZCOM R0 = 2 −4/3_{(3 + cos θ} c) 2 + cos θc 1 − cos θc 2 + cos θc 1/3 (2.1)

where ZCOM is the corrected center of mass, R0 is the radius of the free droplet and θc

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observed for other solid hydrophobic surfaces [59, 138].

2.3 Water order parameters

Order parameters are useful as a quantifiable means to assess the degree to which water molecules are oriented in specific regions of the interface. We define the molecular frame axes as follows: c is along the dipole moment, a is orthogonal to c in the molecular plane, and b is orthogonal to the molecular plane. The Euler angles θ, ψ and φ, defining the orientation of the water molecule with respect to the surface, are defined as follows. We start with the molecular axes c, a and b aligned with the space axes z, y and x, respectively. We then perform a rotation of the molecule by an angle θ along the x axis, followed by a rotation of ψ around the molecular c axis and, finally, a rotation of φ around the z axis (see Fig. 2.2b).

We define three tilt angle order parameters based on the first three terms of a Legendre polynomial expansion following S0θ = 1

S1θ = hcos θi (2.2a)

S2θ = 1 2h3 cos 2_{θ − 1i} (2.2b) S3θ = 1 2h5 cos 3_{θ − 3 cos θi} (2.2c)

and a single twist order parameter

Sψ =

hsin2_{θ cos ψi}

hsin2_θi . (2.3)

Bounds of these four order parameters in limiting cases, along with their values for isotropic distributions of water molecules (bulk) are shown in Table 2.1. For our discussion to follow, it is instructive to note that S1θ and S3θ are polar order parameters, S(θ = 0◦) 6= S(θ =

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Table 2.1: Limiting cases for the order parameters defined in Eqns. 2.2 and Eqn. 2.3. case S1θ S2θ S3θ Sψ isotropic 0 0 0 0 θ = 0◦ 1 1 1 – θ = 90◦ 0 −0.5 0 – θ = 180◦ −1 1 −1 – ψ = 0◦ – – – 1 ψ = 90◦ – – – 0 ψ = 180◦ – – – −1 ψ = 270◦ – – – 0

180◦), while S2θ is not sensitive to the molecular polarity. Also note that S2θ is capable of

distinguishing perfect alignment at θ = 90◦from an isotropic distribution.

2.4 Simulation of SFG response

The SFG intensity is proportional to the magnitude squared of the effective second-order susceptibility χ(2)_eff, and the incident visible (Ivis) and infrared (IIR) laser beam intensities.

ISFG ∝ |χ (2) eff|

2_I

visIIR (2.4)

The second-order susceptibility tensor χ(2) is responsible for the magnitude and phase of the sum-frequency response through the generation of a second-order polarization P(2)_.

This in turn radiates a field at the sum-frequency, ESF. The i component of the ESFvector

at the point of detection is related to the element χ(2)_ijkand the applied fields Evis,j and EIR,k

through

ESF,i∝ Liiei· χ(2)_ijk· LjjejEvis,j· LkkekEIR,k (2.5)

where L are the local field corrections that account for the differences between the electric field magnitudes and phase in air and those at the aqueous surfaces, and e are the unit polarization vectors. The subscripts i, j, k refer to any of the Cartesian lab frame coordinates x, y, z, where x and y are in the plane of the interface, and z is the surface normal as illustrated in Fig. 2.2a. Eq. 2.5 reveals that χ(2) is a rank-three tensor with 27

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can write the l, m, n element of α(2)_as

α(2)_lmn,ν(ωIR) =

hg| ˆαlm|eihe|ˆµn|gi

ων− ωIR− iΓν

(2.6)

where |gi is the vibrational ground state wavefunction, |ei is the vibrational first excited state wavefunction, ˆα is the transition polarizability operator, ˆµ is the transition dipole moment operator, ων is the normal mode frequency, i =

√

−1, and Γν is the homogeneous

line width. The indices l, m, n represent any of the molecular-frame Cartesian coordinates a, b, c. All 27 elements of α(2) _{are calculated following the scheme we have described}

previously [110, 139–141].

Owing to the isotropy in the azimuthal angle of adsorbed water molecules, and the nonresonant nature of their interaction with Evis, there are only 7 nonzero elements of χ(2).

Of these, 3 are independent, so we take advantage of the improved statistics offered by averaging identical elements.

χ(2)_kk⊥≡ 1 2(χ (2) xxz+ χ (2) yyz) (2.7a) χ(2)_k⊥k≡ χ(2)_⊥kk ≡ 1 4(χ (2) xzx+ χ (2) zxx+ χ (2) yzy + χ (2) zyy) (2.7b) χ(2)_⊥⊥⊥≡ χ(2)_zzz (2.7c)

Here x and y components are designated as those parallel to the surface, and z is perpendicular to the surface as shown in Fig. 2.2a.

In an experiment, the incident IR and visible pump beams are typically prepared in polarization states parallel (p) or perpendicular (s) to the plane of incidence, and either the s or p component of the reflected SF field is selected for detection. In the case where the IR beam is p-polarized, the visible beam is s-polarized, and the s-component of the SF is detected (commonly referred to as the ssp configuration), the elements χ(2)yyx and χ(2)yyz are

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Figure 2.2: (a) Sample and beam geometry for SFG experiments at the solid–water interface. When accessing the solid–water interface, it is customary to use a window or prism. The surface of the prism may be coated or functionalized in order to create the hydrophobic or hydrophilic material of interest. We consider that the positive z axis extends away from the bulk water phase. (b) Definition of the tile angle θ and twist angle ψ relating the molecular (a, b, c) frame to the surface (x, y, z) frame.

probed.

χ(2)_ssp = Lyyey· χ(2)yyx· Lyyey · Lxxex+ Lyyey· χ(2)yyz · Lyyey· Lzzez (2.8)

Since χ(2)yyx= 0 (it does not appear in Eqns. 2.7), such an experiment provides direct access

to a single element of the second-order susceptibility tensor.

χ(2)_ssp = Lyyey · χyyz(2) · Lyyey · Lzzez (2.9)

If the experiment is configured for ppp polarizations, 8 elements of χ(2) are probed, 4 of which are non-zero. In this case, the appearance of the spectra changes drastically with different angles of incidence of the visible and IR beams [142–144] as a result of the geometric contributions to the L and e factors in Eq. 2.5. In this paper, we have generalized the applicability of our results by describing the χ(2) elements directly as they appear in Eqns. 2.7, thereby removing the influence of the experimental geometry.

2.4.1 Calculation of water nonlinear susceptibility tensor elements

Sum-frequency spectra over the O–H stretching region were regenerated according to the procedure developed by Morita and Hynes [75]. Briefly, the net force along the O–H bond vector was used as a measure of the red-shift of the low- (ω1) and high-energy (ω2)

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A =

V1,2 ω2

(2.10) where V1,2 = 49.5 cm−1 is situated between the gas-phase symmetric and anti-symmetric

energies.

If l, m, n are considered to be any of the molecular frame Cartesian coordinates a, b, c, then values of the polarizability tensor ∂αlm/∂r and dipole moment vector ∂µn/∂r are

those calculated in Ref. 75, where r is the individual O–H bond vector. For each molecule in the simulation, these properties were first projected into the i, j, k lab frame according to ∂αij ∂r = c1· R(θ1, ϕ1, ψ1) T _· ∂αlm ∂r1 · R(θ1, ϕ1, ψ1) (2.11a) + c2· R(θ2, ϕ2, ψ2)T · ∂αlm ∂r2 · R(θ2, ϕ2, ψ2) ∂µk ∂r = c1· ∂µn ∂r1 · R(θ1, ϕ1, ψ1) + c2· ∂µn ∂r2 · R(θ2, ϕ2, ψ2) (2.11b)

where θ, ϕ, and ψ are the Euler angles that rotate each of the O–H bonds (r1 and r2) into

the lab frame via the transformation operator (direction cosine matrix)

R =   (ˆx · â) (ˆx · ˆb) (ˆx · ˆc) (ˆy · â) (ˆy · ˆb) (ˆy · ˆc) (ˆz · â) (ˆz · ˆb) (ˆz · ˆc)   (2.12)

whose elements are the scalar product of the unit vectors in the molecular l, m, n axes and the lab frame i, j, k axes. In the case of the rank-two tensor ∂α/∂r, the transformation also requires application of the transposed operator RT_{. The coefficients c}

1 and c2 couple the

two O–H oscillators to form the low- and high-energy vibrational eigenmodes, so Eq. 2.11 provides the lab-frame α and µ derivatives for a water molecule. In the gas phase, the low energy eigenmode is the symmetric stretch with c1/c2 = +1; the high energy mode is the

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antisymmetric in the description of the condensed phase since hydrogen bonding greatly affects the nature of the coupling.

Lab frame elements of the frequency-dependent second-order susceptibility were then determined according to χ(2)_ijk(ωIR) ∝ X N (∂αij/∂r · ∂µk/∂r)low ωlow− ωIR− iΓ + (∂αij/∂r · ∂µk/∂r)high ωhigh− ωIR− iΓ (2.13)

where N is the number of molecules considered, ωlowand ωhigh are the frequencies of the

low- and high-energy eigenmodes, and the numerators in the above terms are the solutions to Eq. 2.11 determined separately for both eigenmodes. Note that in the numerator of Eqns. 2.13, the subscript i refers to any of the lab frame Cartesian coordinates x, y, or z; in the denominator i =√−1, resulting in complex values of the χ(2) _{elements. To provide}

the best agreement with the experimental results we have fixed the linewidth Γ = 15 cm−1.

2.4.2 Nonlinear vibrational spectra of LKα14

To compute the visible-infrared sum-frequency spectra for LKα14 adsorbed at the solid surfaces, we consider only the residue side chains contribution to the observed response in the region 2600–3600 cm−1. This covers the C–H and N–H stretching modes monitored in the experimental studies. To take all vibrational mode into consideration, a more general representation of the equations used previously have to be used. Briefly, we make the harmonic approximation α(2)_lmn,ν(ωIR) = 1 2mνων ∂α(1)_lm ∂Q ∂µn ∂Q 1 ων − ωIR− iΓν (2.14)

where mν is the reduced mass of each normal mode and Q is the normal mode coordinate.

These two quantities are determined from a Hessian calculation. Here α(1) is the linear polarizability and µ is the dipole moment; their derivatives with respect to Q are calculated numerically with B3LYP/G-31(d) basis set and PCM solvent as described previous research [110, 139–141]. The complete hyperpolarizability at the IR probe beam frequency ωIR is

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experimental studies to be small. The hyperpolarizability in the surface frame α(2)_ijk is obtained by projection, where i, j, k are any of the laboratory (surface) frame Cartesian x, y, z components. This is accomplished with the direction cosine matrix R as shown in Eqn. 2.12 to write α(2)_ijk= abc X l abc X m abc X n RilRjmRknα (2) lmn. (2.16)

The second-order susceptibility χ(2)_ink is then the straightforward summation of lab-frame hyperpolarizabilities χ(2)_ijk = 1 ε0 X N α(2)_ijk (2.17)

where N is the number of frames over the course of the MD trajectory, with one LKα14 molecule per frame. Only frames when LKα14 is adsorbed were considered in the above summation.

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Chapter 3 Water structure at hydrophobic and

hydrophilic surfaces

3.1 Overview

Water interaction with interfaces have been extensively studied in the past decade for its importance in various processes such as catalysis [3, 4] and chemical separations [5–7]. Sum frequency generation vibrational spectroscopy has been used as an effective method to assess the water orientation at interfaces [8, 40–43]. This method gives great insight into the interfacial structural preferences since it is surface specific, giving signal only in the presence of anisotropy. SFG signal intensity comes from the square of the hyperpolarizability, |χ(2)_|2_{. Although useful, peak overlaps and spectral interference}

makes the SFG signal complicated to analyze. Also, the magnitude of the SFG signal does not contain the structural information about the hyperpolarizability direction on either side of the interface. This information can be found by measuring the phase of the hyperpolarizability and has been successfully used to asses water–vapour interfacial structure [52–55]. Since the resulting spectra is still complicated, progress has been made to asses interfacial water structure by different simulation techniques, specifically ab initio[57, 58], molecular dynamics [57, 58] and Monte Carlo [69–74]. To better correlate specific water orientations with its non-linear response, studies have been made to simulate SFG response of the interfacial water structure from computer simulations [75–81]. We

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We thus used molecular dynamics simulations to study the structure of water molecules adjacent to solid surfaces. The hydrophobic surfaces resemble self-assembled monolayers with methyl termination, while the hydrophilic surfaces are terminated with hydroxyl groups. The resulting water structure is characterized by its density profile, order parameters, and molecular tilt-twist distribution as a function of distance from the surface. In both cases, results are compared to those obtained in bulk water and also to the vapor– water interface. In order to make a deeper connection to experimental studies, we have applied a frequency-domain approach to calculate the nonlinear vibrational spectra of the O–H stretching response. We have observed that, despite the sharp atomic discontinuity imposed by the surface, water next to a hydrophobic surface is similar in structure and spectral response to what is observed for the more diffuse vapor–water interface. At the hydrophilic surface, water ordering persists for a greater distance from the surface, and therefore the spectral response accumulates over a greater depth. In the strongly-hydrogen bonded region of the spectrum, this is seen as an increased nonlinear susceptibility. However, in the energy region of the uncoupled O–H oscillators, we demonstrate that the low experimental signal is in all likelihood due to net cancellation of the microscopic response rather than an absence of those species. This cancellation comes from opposing water molecule orientations over a distance well within the experimental coherence length.

3.2 Results

3.2.1 Water at a solid hydrophobic surface

Density and order parameters for water at the solid hydrophobic surface is presented in Fig. 3.1. The density shows a depletion zone of around 2 ˚A, as has been seen before in the literature [59]. Two distinct orientations can be seen in the order parameter plot, as

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Figure 3.1: (a) Water density profile across the water–hydrophobic solid interface. (b) Order parameters S1θ in red, S2θ in blue, S3θ in green, and Sψ in black. In both plots, the

vertical dashed line indicates the position of the uppermost aliphatic atom, and serves as a reference for the distance scale; positive values of distance tend towards the bulk water phase. The regions labeled A–C were selected for subsequent analysis based on the trends and signs of the order parameters.

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Figure 3.2: Results of structure, hydrogen bonding, water species analysis, and nonlinear vibrational spectra obtained for water adjacent to a solid hydrophobic surface. The rows are labeled A–C according to the density and order parameter regions defined in Fig. 3.1. The first column shows the tilt and twist (θ and ψ as defined in Fig. 2.2b) histograms for all water molecules found in this region of the interface. Darker regions indicate lower populations; the white regions indicated the highest population. The second column shows the OH frequency shift with respect to an uncoupled oscillator in the gas phase at 3707 cm−1. This is plotted as a difference in population ∆P with respect to results obtained in the bulk water sample. Data for the low-energy eigenmodes (red), high-energy eigenmodes (blue) are separated; the combination is plotted in black. The plots in the third column are histograms of the water molecule nature, as defined by the difference between h|2c1c2|2i in the region

of interest and those values obtained in the bulk water phase. The results for the low energy modes are plotted in red, high energy modes in blue, and the population-weighted average in black. The final column shows the imaginary component of the nonlinear susceptibility tensor elements: χ(2)_kk⊥in blue; χ(2)_k⊥kin red, and χ(2)_⊥⊥⊥in black.

indicated by a generally-positive Sψnear the interface that becomes negative near the bulk.

This is due to a flip in the overall water orientation with respect to the normal. At the point Sψ changes sign, around 3 ˚A, we can see a shoulder in the plot of S1θ and S3θ and also in

the density. This was the deciding factor to limit Region A there; the end of Region B was dictated by the change in sign of the first and third tilt order parameters.

When looking at tilt-twist histograms (first column in Fig. 3.2), two important water structures stand out in the region closest to the interface. The dominant orientation in Region A shows a 120◦ tilt, and 0◦ twist. This corresponds, as has been seen in the

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literature, to having one (uncoupled) hydrogen sacrificing hydrogen-bonding opportunities to the surface, thereby permitting the rest of the water sites to maximize possible hydrogen bonds. [60, 61] Region B is dominated by water molecules nearly parallel to the plane of the interface (θ ≈ ψ ≈ 90◦). Finally, this is the only population that remains visible in Region C, albeit slightly shifted towards θ > 90◦. This geometry may be understood on the basis of hydrogen bonding between the successive layers, as has been observed for diffuse hydrophobic interfaces [145]. The population maxima are much less pronounced in Region C as the interface is rapidly becoming bulk-like. This is consistent with all 4 order parameters approaching zero at ≈ 8 ˚A from the surface (Fig. 3.1b). Cartoons of the various water orientations and intramolecular geometries corresponding to these regions appear in Fig. 3.4a.

The second column in Fig. 3.2 shows the difference in population between water molecules in the bulk compared to those in the surface regions, as a function of the OH frequency shift from the gas phase value of 3707 cm−1. Data for the low energy eigenmodes are plotted in red, high energy modes in blue, and the combined population in black. In all three cases, negative values of ∆P indicate that the population at those frequencies at the surface is less than what is found in the bulk phase; ∆P > 0 indicates an enhanced population at the interface. In the region closest to the surface (region A), the hydrogen that is pointing towards the surface shows a high population in the low frequency shift region, as expected since this OH group is making the fewest number of hydrogen bonds. The other hydrogen of the same molecule has the necessary geometry to participate in more H-bonds, and is seen to contribute more towards red-shifted populations at the surface. The same trend continues, but with diminished population difference when moving towards the bulk water phase (Regions B and C).

The coupling constants c1 and c2, as defined in Eq. 2.11, provide information on

the nature of the vibrational modes and their localization. We have followed the same treatment as outlined by Morita [75] for the vapor–water interface in calculating the degree

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identified, a shortcoming of h2c1c2i is that a value of zero can represent either a mode

that has equal contributions of symmetric and antisymmetric characters, or one that is completely localized (uncoupled OH oscillators). For this reason, it is more useful to plot h|2c1c2|2i. Although the magnitude squared does not preserve the sign of 2c1c2, we

know this information since we calculate the high- and low-energy eigenmodes separately (Fig. 2.13).

In the third column of Fig. 3.2, we plot ∆h|2c1c2|2i, the difference between the

delocalization in the bulk water phase and found that for our defined regions of the interface. Since the water environments are similar, this representation allows the surface features to be more easily identified. Results for low-energy modes are plotted in red, high energy modes in blue, and the population-weighted average in black. The water structure at the surface (Regions A and B) is dominated by uncoupled OH oscillators. One of these OH pairs has a very small frequency shift due to its inability to form H-bonds. This peak in the population (column 2) corresponds to a frequency of approximately 3750 cm−1. However, we do not observe a corresponding feature in the ∆h|2c1c2|2i plot, indicating

that these molecules have roughly the same delocalization as in the bulk. This effect is due to the fact that any water molecule showing this frequency shift in bulk, will also have its stretching vibrations localized on one of the OH groups. The other OH group of the same molecule at the surface is significantly red-shifted, yet localized as a result of the asymmetry in the H-bonding environments on either side of this rather sharp interface. This is why we see a negative deviation from the bulk in the degree of delocalization on the low energy side of the ∆h|2c1c2|2i spectra in Regions A and B. The other water molecule is

parallel to the interface, thus maximizing hydrogen bonding with the oxygen from the first water molecule. We note the small positive peak at 3750 cm−1, resulting from the relative

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paucity of uncoupled oscillators in the bulk. The second orientation with θ ≈ ψ ≈ 90◦, more prominent in Region B, has more equivalent hydrogens and this can be seen as greater delocalization. However, as a result of the water orientation in Region A, the geometry is not ideal to maximize the hydrogen bonds. These broken H-bonds appear around 3550– 3600 cm−1. Approaching the bulk phase in Region C, we observe similar behavior, but with the difference between surface and bulk roughly an order of magnitude less pronounced.

The right-most column in Fig. 3.2 shows the spectra calculated for the Im[χ(2)_kk⊥] in blue, Im[χ(2)_k⊥k] in red, and Im[χ(2)_⊥⊥⊥] in black. Imaginary components were determined according to Eq. 2.13, as they are more descriptive of interfacial structure than |χ(2)| (or |χ(2)_|2_{), and more revealing of the resonances than Re[χ}(2)_{]. To facilitate comparison}

between different regions of the interface, spectra were normalized so that the maximum response in any region was set to unity. We note that the response is not normalized to the number of molecules, as the SFG response should increase with either increased orientation or population of oriented molecules. Starting with the region closest to the surface (A), we note that although there are two distinct populations, it is primarily the out-of-plane molecules that contribute to the SFG response. Moving into Region B, the population of in-plane water molecules is enhanced, and yet we observe a very similar shape in the SFG spectra. In Region C, as the water becomes less ordered (Fig. 3.1b), we expect the SFG response per molecule to decrease. However, this is a very large region of the interface (see the density profile in Fig. 3.1a), and so the collective response is responsible for the majority of the SFG signal. In this region, we note that the zero-crossing of Im[χ(2)_kk⊥] is red-shifted by ≈ 100 cm−1 compared to regions closer to the surface. In addition, the relative amplitudes of the positive and negative features are comparable. This is in contrast to the greater amplitude observed at higher frequencies closer to the surface.

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order parameter profiles obtained for the vapor–water interface are shown in Fig. 3.3. The density displays a monotonic transition from bulk to vapor values. The primary difference between this superhydrophobic vapor interface and the solid surface (see Fig. 3.1) is in the extent of the interface, defined by either the density or order parameters. The vapor– water interface extends over ≈ 8 ˚A, whereas the density and structural variation of water at the solid hydrophobic surface occurs over ≈ 6 ˚A. The results of the tilt-twist histograms, populations, and mode character analysis can mostly be described in the same way as for the solid hydrophobic interface (where two water orientations dominate as observed in Fig. 3.5).

We have also compared the orientation of molecules at the vapor-water interface to that observed in previous studies. In cases where regions more than ≈ 2 ˚Atowards the vapor side of the Gibbs dividing surface have been separated in the analysis, species with tilt angles of 60◦ have been isolated [52, 75, 146, 147]. These water molecules, which direct one of their O-H bonds towards the surface normal, are not observed in our tilt-twist histograms. This is to be expected, as they have been shown to be very low in population compared to the dominant 120◦ structures [75, 89, 133]. It has already been established that the 120◦ structures are the dominant contributors to the SFG response at IR energies above than 3600 cm−1 [75]. In any case, all of the structures throughout all regions of the interface are taken into account when we calculate our SFG response.

As we have followed Morita’s frequency-domain treatment to arrive at the coupling constants and SFG spectra using the same (SPC/E) water model, we verified that we have reproduced their results for the vapor–water interface. The only difference here is that the results we display for the coupling constants in Fig. 3.5 are the differences, ∆h|2c1c2|2i

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Figure 3.3: (a) Water density profile across the vapor–water interface. (b) Order parameters S1θ in red, S2θ in blue, S3θ in green, and Sψ in black. In both plots, the vertical dashed

line indicates the Gibbs dividing surface, and serves as a reference for the distance scale; positive values of distance tend towards the bulk water phase. The regions labeled A–C were selected for subsequent analysis based on the trends and signs of the order parameters.

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Figure 3.4: Cartoon representations of dominant water orientations in various regions of the interface for (a) hydrophobic surfaces (both solid and vapor) and (b) the hydrophilic solid surface. In the case of the hydrophilic surface, only regions A-C are shown.

calculated by Morita, and are also remarkably similar to what we observe at our solid hydrophobic surface. Comparison with homodyne (non-phase resolved) SFG experiments is difficult as the appearance of the spectra is extremely sensitive to the nonresonant contribution to |χ(2)_|2_{. Since the nonresonant contribution is real, the imaginary spectra are}

more readily compared. This has been the subject of many recent discussions. [42,135] All of the heterodyne experimental SFG data [52] agree with Im[χ(2)] > 0 for the uncoupled O–H oscillator near 3700 cm−1, Im[χ(2)] crossing zero near 3600 cm−1to take on negative values as the hydrogen-bonding environment is observed to be increasingly red-shifted. A second zero-crossing occurs near 3150 cm−1; O–H oscillators that are more red-shifted than 3150 cm−1 are observed with Im[χ(2)_{] > 0. Early attempts to simulate the vapor–}

water SFG spectra were unable to reproduce Im[χ(2)_{] > 0 in the 3000 cm}−1_{region. Recent}

attempts have been able to predict the correct sign of Im[χ(2)_{] for the most}

hydrogen-bonded region, but with varying magnitudes compared to the SFG amplitude in other regions of the spectrum.

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Figure 3.5: Results of structure, hydrogen bonding, water species analysis, and nonlinear vibrational spectra obtained for the vapor–water interface. The rows are labeled A–C according to the density and order parameter regions defined in Fig. 3.1. The first column shows the tilt and twist (θ and ψ as defined in Fig. 2.2b) histograms for all water molecules found in this region of the interface. Darker regions indicate lower populations; the white regions indicated the highest population. The second column shows the OH frequency shift with respect to an uncoupled oscillator in the gas phase at 3707cm−1. This is plotted as a difference in population ∆P with respect to results obtained in the bulk water sample. Data for the low-energy eigenmodes (red), high-energy eigenmodes (blue) are separated; the combination is plotted in black. The plots in the third column are histograms of the water molecule nature, as defined by the difference between h|2c1c2|2i in the region of

interest and those values obtained in the bulk water phase. The results for the low energy modes are plotted in red, high energy modes in blue, and the population-weighted average in black. The final column shows the imaginary component of the nonlinear susceptibility tensor elements: χ(2)_kk⊥in blue; χ(2)_k⊥kin red, and χ(2)_⊥⊥⊥in black.

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begin, simply inspecting the density and order parameters in Fig. 3.6, evidence of many different structures can be realized. The density shows high and low regions with almost no depletion zone, as is typical for hydrophilic surfaces [65]. As a result of this complexity, we have chosen six regions for analysis. The end of region A was decided according to the change of sign of the tilt and twist order parameters. All order parameters show strong ordering in that first interfacial region. Region B was chosen by identifying the maximum in the density profile, but still includes two distinct orientations since Sψ has a positive

and negative feature there. This change of sign is accompanied by a kink in the S3θ plot.

Since the delimitation of those two structures is not clear, they were placed in the same region. The third region (C) analyzes the shoulder present in the density plot near 2 ˚A. This region show a fairly high degree of orientation for both Sψ and S1θ. This corresponds to a

low average degree of twist degree and a high degree of tilt orientation. In the same way, Regions D, E and F were chosen according to order parameter signs, density peaks, and overall trend.

The results of all the regions are shown in Fig. 3.7. The first region (A) has a low density but strongly oriented water molecules. The orientation of 120◦ tilt and 90◦ twist corresponds to both hydrogens pointing towards the bulk at an angle. This is likely to promote some hydrogen bonding from the water oxygen to the surface hydrogen atoms. This orientation would be the most favorable in certain regions of the surface where two surface OH groups from the substrate are directed towards to each other to H-bond with oxygen lone pairs. This would explain why the density of this water orientation is relatively low, as shown in Region A of Fig. 3.6a. Since the degree of H-bonding is high, we can see a positive deviation of the overall population at higher frequency shift. Both high and low energy OH modes have a higher population at high frequency shift, illustrating that both

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modes contribute. Since both OH groups are in the same environment and it is mostly the oxygen lone pairs that contribute to the hydrogen bonding, the modes are highly coupled, and thus we see a higher-than-bulk delocalization of the modes around 3200 cm−1. The resultant χ(2) _{response is expected to show a slight negative contribution in kk⊥ (ssp)}

because water hydrogens are pointing towards the bulk. However, the other orientation present in this and the adjacent region has a stronger positive contribution. Cartoons illustrating intramolecular water geometries and orientations with respect to the surface are shown in Fig. 3.4b.

The second region (B) has a high population of water occupying multiple orientations. These include water oriented with both hydrogens directed towards the surface, and another with hydrogens directed towards bulk. Perhaps the most interesting is the ‘curved’ tilt-twist population. This orientation changes from 60◦ to 90◦ tilt and from 0◦ to 60◦ twist. This feature is interesting because the commonality between those orientations is actually the orientation of one of the hydrogens at an angle toward the surface. (This is also present in Region A.) That implies that the OH bonds here orient themselves to hydrogen bond with the oxygen of the surface, while the rest of the molecule optimizes its orientation with respect to the surrounding molecules while maintaining this constraint. The frequency shift supports this interpretation by again having an overall higher population than bulk in the higher frequency region. This will have a large positive contribution in the χ(2) _response

in the hydrogen bonded region. The OH group not interacting with the surface will show a lower frequency shift and will probably be more localized. One main feature that stands out in the degree of delocalization graph in the first two regions (Fig. 3.7A–B, third column), is that the OH oscillators are more localized than bulk. This agrees with the fact that the first layer of water orientation depends mostly on the interaction with surface hydroxyl, making the OH modes more localized. One OH interacting with the surface hydroxyl will exhibit greater H-bonding and have lower energy, while the other OH oscillator will have a lesser redshift but still display a localized feature. It is this orientation that causes the overall

Water and peptide structure at hydrophobic and hydrophilic surfaces

Contents

List of Tables

List of Figures

1.1

Interfacial water structure

1.2

Peptides adsorbed on surfaces

1.3

Objectives

Chapter 2

Methods

2.1

Molecular dynamics simulation details

2.1.1

Water

2.1.2

Peptide

2.2

Water contact angles

2.3

Water order parameters

2.4

Simulation of SFG response

2.4.1

Calculation of water nonlinear susceptibility tensor elements

2.4.2

Nonlinear vibrational spectra of LKα14

Chapter 3

Water structure at hydrophobic and

hydrophilic surfaces

3.1

Overview

3.2

Results

3.2.1

Water at a solid hydrophobic surface