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Langmuir 2008, 24, 10358-10364
Molecular Simulation Studies of Protein Interactions with Zwitterionic Phosphorylcholine Self-Assembled Monolayers in the Presence of Water Yi He, Jason Hower, Shengfu Chen, Matthew T. Bernards, Yung Chang, and Shaoyi Jiang* Department of Chemical Engineering, UniVersity of Washington, Seattle, Washington 98195 ReceiVed April 26, 2008. ReVised Manuscript ReceiVed June 29, 2008 Molecular simulations were performed to study the interactions between a protein (lysozyme, LYZ) and phosphorylcholine-terminated self-assembled monolayers (PC-SAMs) in the presence of explicit water molecules and ions. The results show that the water molecules above the PC-SAM surface create a strong repulsive force on the protein as it approaches the surface. The structural and dynamic properties of the water molecules above the PC-SAM surface were analyzed to provide information regarding the role of hydration in surface resistance to protein adsorption. It can be seen from residence time dynamics that the water molecules immediately above the PC-SAM surface are significantly slowed down as compared to bulk water, suggesting that the PC-SAM surface generates a tightly bound, structured water layer around its head groups. Moreover, the orientational distribution and reorientational dynamics of the interfacial water molecules near the PC-SAM surface were found to have the ionic solvation nature of the PC head groups. These properties were also compared to those obtained previously for an oligo(ethylene glycol) (OEG) SAM system and bulk water.
Introduction Zwitterionic phosphorylcholine (PC) and hydrophilic/neutral poly(ethylene glycol) (PEG) are two major classes of nonfouling materials that resist nonspecific protein adsorption and cell adhesion.1-3 They have been used widely for many applications, including drug delivery, disease diagnostics, and medical coatings.2,4 Significant efforts have been directed toward developing a fundamental understanding of their molecular-level nonfouling mechanisms.5,6 Both experimental and theoretical studies of PEG7-10 suggest that the water molecules around the terminal groups of the PEG chains play a key role in the resistance to protein adsorption, beyond that attributed to the steric repulsion11 from the PEG chains. From previous molecular simulation studies of oligo(ethylene glycol) (OEG),9,12 it has been shown that there are a large number of tightly bound water molecules around the terminal groups of the OEG chains which are responsible for the strong repulsive force that acts on a protein as it approaches the OEGSAM surface.13 Therefore, the water barrier theory is often used * To whom correspondence should be addressed. E-mail: sjiang@ u.washington.edu. (1) Ratner, B. D.; Hoffman, A. D.; Schoen, F. D.; Lemons, J. E. Biomaterials Science, an Introduction to Materials in Medicine, 2nd ed.; Elsevier: Amsterdam, 2004. (2) Harris, J. M. Poly(ethylene glycol) Chemistry: Biotechnical and Biomedical Applications; Plennum Press: New York, 1992. (3) Ratner, B. D.; Bryant, S. J. Annu. ReV. Biomed. Eng. 2004, 6, 41–75. (4) Iwasaki, Y.; Ishihara, K. Anal. Bioanal. Chem. 2005, 381(3), 534–546. (5) Ishihara, K.; Nomura, H.; Mihara, T.; Kurita, K.; Iwasaki, Y.; Nakabayashi, N. J. Biomed. Mater. Res. 1998, 39(2), 323–330. (6) Vermette, P.; Meagher, L. Colloids Surf., B 2003, 28(2-3), 153–198. (7) Li, L. Y.; Chen, S. F.; Zheng, J.; Ratner, B. D.; Jiang, S. Y. J. Phys. Chem. B 2005, 109(7), 2934–2941. (8) Ostuni, E.; Chapman, R. G.; Holmlin, R. E.; Takayama, S.; Whitesides, G. M. Langmuir 2001, 17(18), 5605–5620. (9) Pertsin, A. J.; Grunze, M. Langmuir 2000, 16(23), 8829–8841. (10) McPherson, T.; Kidane, A.; Szleifer, I.; Park, K. Langmuir 1998, 14(1), 176–186. (11) Jeon, S. I.; Lee, J. H.; Andrade, J. D.; Degennes, P. G. J. Colloid Interface Sci. 1991, 142(1), 149–158. (12) Zheng, J.; Li, L. Y.; Chen, S. F.; Jiang, S. Y. Langmuir 2004, 20(20), 8931–8938. (13) Zheng, J.; Li, L. Y.; Tsao, H. K.; Sheng, Y. J.; Chen, S. F.; Jiang, S. Y. Biophys. J. 2005, 89(1), 158–166.
to interpret the nonfouling behavior of OEG. Similar to PEG or OEG, zwitterionic phospholipids have also been shown to have a strong influence on interfacial water molecules.14,15 Ishihara et al. studied the hydration of 2-methacryloyloxyethyl phosphorylcholine (MPC) polymers as well as other hydrophilic polymers, including poly[2-hydroxyethyl methacrylate (HEMA)] and poly[n-butyl methacrylate (BMA)].5 They found that the polymers containing PC moieties have a stronger ability to hold water molecules than the other groups. In one recent study,16 it was shown that fibrinogen (Fg) and bovine serum albumin (BSA) adsorption on PC-SAMs was 1% and 0.7% of a protein monolayer, respectively. In another study,17 it was shown that Fg adsorption on oligo(PC)-SAMs was further reduced to 0.1% of a protein monolayer. Feng et al. reported18 that the adsorption of both Fg and lysozyme (LYZ) on poly(MPC)-grafted surfaces is reduced as the length of the poly(MPC) chains is increased. It should be pointed out that hydrophilic and neutral PEG chains can only form a hydration layer via hydrogen bonds while zwitterionic chains (e.g., PC-SAMs) form a hydration layer via ionic solvation in addition to hydrogen bonding. Thus, it is expected that the structural and dynamic properties of the water molecules near PC and PEG chains should show significant differences.13,19 However, the molecular-level nonfouling mechanisms for PC molecules are still poorly understood. All-atom molecular simulations, including a protein, a surface, water molecules, and ions with explicit molecular models, can provide detailed information regarding the role of the interfacial water molecules near the molecular chains in a surface’s resistance to protein adsorption. In this work, we performed molecular simulations to study the interactions between a protein (LYZ) (14) Bhide, S. Y.; Berkowitz, M. L. J. Chem. Phys. 2005, 123(22), 224702. (15) Lopez, C. F.; Nielsen, S. O.; Klein, M. L.; Moore, P. B. J. Phys. Chem. B 2004, 108(21), 6603–6610. (16) Chen, S. F.; Zheng, J.; Li, L. Y.; Jiang, S. Y. J. Am. Chem. Soc. 2005, 127(41), 14473–14478. (17) Chen, S. F.; Liu, L. Y.; Jiang, S. Y. Langmuir 2006, 22(6), 2418–2421. (18) Feng, W.; Zhu, S. P.; Ishihara, K.; Brash, J. L. Langmuir 2005, 21(13), 5980–5987. (19) Yaseen, M.; Lu, J. R.; Webster, J. R. P.; Penfold, J. Langmuir 2006, 22(13), 5825–5832.
10.1021/la8013046 CCC: $40.75 2008 American Chemical Society Published on Web 08/09/2008
Protein Interactions with Zwitterionic PC-SAMs
and a PC-SAM in the presence of explicit water molecules and ions. The force exerted onto the protein was calculated as a function of its distance above the self-assembled monolayer (SAM) surface. The structural and dynamic properties of the water molecules around the PC-SAM surface were then analyzed. These properties were compared to those obtained previously for an OEG-SAM system and bulk water.
Simulation Models In this study, a PC-SAM with 77 R19° lattice structure20 was used to study the interactions between a protein and the surface. The initial configuration of a single chain was obtained from a previous study20 on the packing of PC-SAMs. The single chain was then replicated into an 8 × 8 surface of PC chains on Au(111), forming a lattice structure with a sulfur-sulfur distance of 0.763 nm. This lattice packing density corresponds to a surface area of 50.4 Å2/ molecule, close to that of natural phospholipids.21,22 The SAM surface has the dimensions of 61 Å × 53 Å in the xy-plane. The head groups of the PC chains are aligned parallel to each other on the surface to minimize their dipole components. After the surface was minimized in a continuous medium, with a distance-dependent dielectric constant (ε ) ε0r)23 of water, the SAM chains tilted ∼68° from the z-axis perpendicular to the surface. The energy of the system was then minimized using the conjugate gradient algorithm in an implicit solvent. In molecular mechanics (MM) simulations, a large vacuum gap (larger than the Coulombic cutoff length of 12.0 Å) was introduced on the top of the simulation box in the z-direction to mimic the quasi two-dimensional system. The switch cutoff method was used to calculate nonbonded interactions. The switch cutoff was set to on at 10.0 Å and off at 12.0 Å. All of the sulfur atoms were fixed during simulations. LYZ is often used as a model protein for studies of protein adsorption, since its structure, dynamics, and folding have been extensively discussed.24 The X-ray crystal structure of LYZ, comprising 129 amino acids, was taken from the Protein Data Bank (entry code 7LYZ). Polar and aromatic hydrogen atoms were explicitly added to the protein. All of the amino acids were protonated with the exception of glutamic acid (GLU) and aspartic acid (ASP), which were taken as deprotonated. Four disulfide bonds were added, and the N terminus (NH3+) and the C terminus (COO-) were assigned charges of +1e and -1e, respectively. These assignments create a net charge of +8e on the protein at pH 7. Similar to previous work,12,25 LYZ is used to probe the PC-SAM surface for its ability to adsorb protein. Results from this work are compared with those for OEG-SAMs from previous studies.7,12,13 The all-atom CHARMM27 force field,26 consisting of bond, Urey-Bradley, angle, dihedral, and improper terms as well as nonbonded van der Waals (VDW) and Coulombic interactions, was used to describe the interactions for the protein, PC-SAMs, water, and ions. The VDW interactions are described with a 12-6 Lennard-Jones (LJ) potential where εij is the LJ well depth and Rmin is the separation distance at the LJ minimum. All cross LJ terms were calculated using the geometric combination rule of εij ) (εiεj)1/2 and the arithmetic combination rule for Rminij ) (Rmini + Rminj)/2. The (20) Zheng, J.; He, Y.; Chen, S. F.; Li, L. Y.; Bernards, M. T.; Jiang, S. Y. J. Chem. Phys. 2006, 125(17), 174714. (21) Hauser, H.; Pascher, I.; Pearson, R. H.; Sundell, S. Biochim. Biophys. Acta 1981, 650(1), 21–51. (22) Sheng, Q.; Schulten, K.; Pidgeon, C. J. Phys. Chem. 1995, 99(27), 11018– 11027. (23) Ravichandran, S.; Madura, J. D.; Talbot, J. J. Phys. Chem. B 2001, 105(17), 3610–3613. (24) Smith, L. J.; Mark, A. E.; Dobson, C. M.; Vangunsteren, W. F. Biochemistry 1995, 34(34), 10918–10931. (25) Hower, J. C.; He, Y.; Bernards, M. T.; Jiang, S. J. Chem. Phys. 2006, 125(21), 214704. (26) MacKerell, A. D.; Bashford, D.; Bellott, M.; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; Joseph-McCarthy, D.; Kuchnir, L.; Kuczera, K.; Lau, F. T. K.; Mattos, C.; Michnick, S.; Ngo, T.; Nguyen, D. T.; Prodhom, B.; Reiher, W. E.; Roux, B.; Schlenkrich, M.; Smith, J. C.; Stote, R.; Straub, J.; Watanabe, M.; Wiorkiewicz-Kuczera, J.; Yin, D.; Karplus, M. J. Phys. Chem. B 1998, 102(18), 3586–3616.
Langmuir, Vol. 24, No. 18, 2008 10359 electrostatic interactions are described with a Coulombic potential where q is the partial atomic charge and rij is the distance between atoms i and j. The water molecules were described with a modified three-site point charge model (TIP3P) where VDW interaction sites are located on both the hydrogen and oxygen atoms.26
Simulation Protocol Molecular simulations were performed in two steps. First, a series of Metropolis Monte Carlo (MC) simulations were conducted in the NVT canonical ensemble at T ) 300 K to determine the orientation of LYZ above the PC-SAM surface. The system included the protein and the surface and used a continuum distance-dependent dielectric medium. The lowest-energy configuration was then used as the starting point for molecular dynamics (MD) simulations in an explicit water solvent. In the MC phase, LYZ was initially placed at various separation distances (10-50 Å) above the surface with a random orientation. During simulations, LYZ was moved by either uniform random displacement or rotation around an arbitrary axis with an acceptance rate of roughly 50% based on Metropolis criteria. In all of the MC simulations, the SAM surface was fixed in the xy-plane, water was treated as an implicit solvent continuum model, and the protein was modeled as a rigid molecule. Simulations were run for 50 000 MC steps, and only the nonbonded VDW and Coulombic interactions between the SAM and the protein were considered. The final protein orientation with the lowest energy was taken as the initial state for future MD simulations. After the optimal LYZ orientation was determined, three systems were formed with LYZ placed above a PC-SAM surface at separation distances of 2, 5, and 10 Å. These lengths were defined by the minimum distance between any atom of the protein and any atom of the SAM. The systems, including the SAM terminal groups, were solvated with pre-equilibrated TIP3P water molecules. Counterions, one sodium and nine chlorines, were added to neutralize the total charge of the system. Any water molecule within 3.0 Å of the protein or SAM was removed. The whole system, including the protein, water, ions, and SAM were initially energy minimized for 10 000 steps using the conjugate gradient algorithm to remove abnormally close contacts between molecules. Following the minimization, the system was heated to 300 K using a short MD run of 10 000 1.0 fs steps and 50 K increments; the center of mass of the protein was harmonically constrained to its initial position. The heating process allows for the initial relaxation of the SAM surface as well as starting the hydration of both the protein and the SAM chains. After heating, an additional 3000 1.0 fs MD steps were run to allow further isothermal equilibration of water molecules around the protein and the SAM surface. All initial construction, heating, and equilibration were conducted with the CHARMM program. The final frame of the equilibrium steps was used as the initial configuration for 2.0 ns of MD simulation. Figure 1 shows a representative image for all three cases. In the MD phase, the sulfur atom of each SAM chain was fixed in the xy-plane during all simulations. The center of mass of the protein molecule was harmonically constrained. All of the atoms in the protein were allowed to move during MD simulations. Each system utilized periodic boundary conditions, and the minimum image convention was applied only in the x- and y-directions. Two hard walls were set at both the top and the bottom of the simulation box, and reflective boundary conditions were applied. All bonds involving hydrogen atoms were kept rigid using the RATTLE method with a geometric tolerance of 0.0001. The velocity Verlet method was used to integrate Newton’s equations. An NVT ensemble was used with a time step of 2.0 fs. The system temperature was kept constant at 300 K using the Berendsen thermostat with a time constant of 0.1 ps. The switch function was used to calculate VDW interactions between 0.8 and 1.0 nm. The force-shifting function was used for long-range electrostatic interactions with a cutoff distance of 1.2 nm. The atom-based force-shifting function technique27 was selected, (27) Schlick, T. Molecular Modeling and Simulation: An Interdisciplinary Guide; Springer: New York, 2002.
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Figure 1. Representative configuration of the simulation system. LYZ is placed above the PC-SAM surface, and the system is solvated with explicit water molecules and ions. Red, orange, gray, white, blue, and yellow represent oxygen, phosphorus, carbon, hydrogen, nitrogen, and sulfur atoms, respectively. The water molecules are shown as a green wire frame.
since it has been demonstrated to generate stable nanosecond trajectories for double-stranded DNA.28 The cell-based neighbor list with a cutoff range of 14.0 Å was used to reduce the computational time for energy and energy-derivative calculations. The cell-based neighbor list was updated automatically if any atom in the list was moved by more than (14.0 - 12.0)/2 ) 1.0 Å. During simulations, configurations and trajectories were saved approximately every 1.0 ps for 2 ns. Configurations for the final 500 ps were used for the analysis of structural and dynamic properties, including the force exerted on the protein from both the water molecules and SAM chains. The three simulation systems varied in size from about 20 000 to 23 000 atoms. A MD simulation was also performed with bulk water for comparison. The system in this simulation consists of 910 TIP3P water molecules. These water molecules were confined in a box with a size of 30.0 Å × 30.0 Å × 30.0 Å. The MD simulation in the NVT ensemble was run for a period of 1.5 ns at 300 K with coordinates and velocities stored every 1 ps. Furthermore, previous simulation results for an OEG-SAM system with a separation distance of 5 Å were reanalyzed13 to obtain several properties, including the dipole distribution and the residence time dynamics of the interfacial water molecules. All of the MD simulations were performed with an in-house BIOSURF program on a 20-node Intel Dual Core (CPU 2.8 GHz) Linux cluster. The BIO-SURF program was developed as a generalized engine for molecular simulation studies of biomolecular interfaces.12 Standard simulation techniques29-31 are used in the program.
Results and Discussion In this work, LYZ was used as a model protein to probe the interactions of a protein with a PC-SAM surface. The orientation of LYZ above the PC-SAM surface as obtained from MC simulations was similar to that found previously for LYZ above an OEG-SAM surface.13 The force exerted on the protein in a direction normal from the SAM surface can provide a clear distinction between surfaces that resist protein adsorption and (28) Norberg, J.; Nilsson, L. Q. ReV. Biophys. 2003, 36(3), 257–306. (29) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1987. (30) Reference deleted in proof. (31) Leach, A. R. Molecular Modeling: Principles and Applications; Pearson Education Limited: Edinburgh Gate, 2001.
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Figure 2. Interaction force exerted on the protein as it approaches the PC-SAM surface in the presence of explicit water molecules. The force is calculated in the z-direction, normal to the PC-SAM surface. The total force (Ftotal) is the sum of the forces from the PC-SAM surface (FSAM) and water (Fwater).
those that do not. This force should also have a close relationship with the structural and dynamic properties of the water molecules around the PC-SAM surface. Therefore, to investigate the nature of the hydration of the PC-SAM surface, several properties were studied with molecular simulations, including the radial distribution functions of the heavy atoms near the charged sites of the PC head groups, and the orientation distribution, residence time dynamics, and reorientational dynamics of the water molecules near the PC-SAM surface. Interaction Forces between the Protein and the SAM or Water. The results in Figure 2 show that the water molecules above the PC-SAM surface generate a strong repulsive force on LYZ. This interaction force decreases monotonically as the separation distance between the PC-SAM and the LYZ increases. The force was measured between all of the water molecules in the system and all of the atoms in the protein. The separation distance at which a strong repulsive force was observed in the PC-SAM system was shorter than that found in the OEG-SAM system.13 In the OEG-SAM, system a repulsive force was observed at a separation distance of 5 Å from the surface, as compared to the separation distance of 2 Å seen for the PC-SAM in this work. Since the PC- or OEG-SAM surface has strong hydration, as a protein approaches to the surface, this protein will disrupt the surface hydration layer around the PC- or OEGSAM surface, leading to a strong repulsive force. Thus, this repulsive force can be explained by the destruction of the hydration layer of the SAM surface.12-14 The difference between the PCSAM and the OEG-SAM surfaces in their separation distance from the protein that was required for a repulsive force to be generated indicates that the hydration layer around the PC-SAM is restricted to a thinner shell around the surface as compared to the OEG-SAM. In a study of the solvation of ions by Omta and co-workers,32 it was found that ions only affected the water molecules inside the first solvation shell (∼3.6 Å). Zwitterionic PC-SAMs are expected to have a thin solvation shell around the PC head groups similar to that found for the ions. Thus, a strong repulsive force was only found when the LYZ was in close proximity to the surface. However, it appears that the structure of water molecules around the OEG head groups propagates to longer distances from the OEG surface. Similar to what was (32) Omta, A. W.; Kropman, M. F.; Woutersen, S.; Bakker, H. J. J. Chem. Phys. 2003, 119(23), 12457–12461.
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Figure 3. (a) Structure of the zwitterionic PC-terminated SAM and radial distribution functions for water around different atoms of the PC head group, including (b) nitrogen and phosphorus; (c) oxygen, O1 and O2; (d) oxygen, O3 and O4; and (e) carbon, C1, C2, and C3.
found before for the OEG-SAM surface,13 it is also interesting to see that the PC-SAM surface itself actually generates a slightly attractive force on the protein due to VDW attractions. This result further supports the conclusion that the repulsive force of the protein-surface interactions is mainly generated by the hydration layer near the surface. Radial Distribution Functions around the PC Chains. The results shown in Figure 2 indicate that the water layer on the PC-SAM surface plays a key role in generating the strong repulsive force. Thus, in this work, the structural and dynamic properties of this water layer were analyzed to obtain a better understanding of the origin of this repulsive force. An OEGSAM system was used for comparison. All of the results presented
below are from the simulations of LYZ at a separation distance of 5 Å above a PC-SAM or OEG-SAM surface. First, the radial distribution functions (RDFs) for the interactions between several atoms around PC chains and water molecules were calculated, and these results are shown in Figure 3. The RDF or g(r) is defined as
gij(r) )
〈Nij(r) ⁄ V(r)〉 Fj,bulk
where Nij(r) is the ensemble averaged number of atoms j in a spherical shell of volume V(r) at a distance r from atom i and Fj,bulk is the bulk density of atom j. It should be pointed out that a spherical shell V(r) may contain water molecules, as well as
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protein and SAM chain atoms. Thus, to obtain a more accurate gij(r) value, the local volume occupied by water molecules was calculated by subtracting the volume occupied by molecules other than water from the total spherical shell volume. Unlike the conventional calculation of g(r), this improvement eliminates the need to manually rescale the tail of g(r) to 1.0 at longer distances. In Figure 3, RDFs are plotted for the nitrogen (N), phosphorus (P), and oxygen atoms (O1, O2, O3, and O4) around the P site, which may form hydrogen bonds with the oxygen atoms of water near the PC-SAM surface. The RDFs for the carbon atoms in the methyl groups (C1, C2, and C3) were also plotted. The results show that the O3 and O4 oxygen atoms have the best solvation among all of these surface atoms. For the O3 and O4 oxygen atoms, a sharp, strong first peak was observed at 0.28 nm, corresponding to the nearest-neighbor distance between the oxygen atoms and the surrounding water molecules. The intensity of this peak is significantly higher than that of bulk water, which indicates that there is a strong interaction between these two atoms and the near-surface water molecules through hydrogen bonding. Similar peak positions have also been observed for the strong hydration of hydrogen-bonded oxygen atoms in other studies.12,25,33 Since the O1 and O2 atoms are embedded in the main chain, the first peak in the g(r) curve for them is significantly smaller than that for the O3 and O4 atoms due to steric effects. N atoms also have a well-defined hydration shell. The first peak position of water is at 0.43 nm, which is larger than that for the O1 and O2 atoms. The methyl groups attached to the N atom are responsible for this difference.15 In Figure 3e, sharp peaks can be observed at ∼0.3 nm for the carbon atoms in the methyl groups. These peaks indicate the strong hydration of the N atoms comes from that of these methyl groups. P atoms were also observed to have a strong hydration shell. In a similar study, Lopez et al. concluded that the phosphate ions are solvated by water molecules, which primarily interact with the oxygen atoms attached to them.15 Orientation Structure of Water on the PC-SAM Surface. The orientation of the water molecules near the SAM surface can be characterized with dipole autocorrelation functions to reflect the different hydration nature of these two surfaces. In this work, the orientation of a water molecule was described by the angle θ between its dipole vector and the surface normal. With this definition, the distribution should be flat for bulk water, since all dipole angles are equally possible. To study the water molecules inside the first solvation layer, we excluded the water molecules that were beyond 4 Å from the surface. Dipole distributions for bulk water and water above an OEG-SAM surface were included as references. Although both PC-SAM and OEG-SAM surfaces are proteinresistant and have strong hydration, the origin of strong hydration is different, leading to different molecular-level nonfouling mechanisms. As shown in Figure 4, they reorient water molecules in significantly different ways. Due to the ionic nature of the PC head groups, the PC-SAM surface provides many possible water orientations in the solvation layer. While the hydration of the OEG-SAM surface is largely due to hydrogen bonding, the dipole of the water molecules above the OEG-SAM surface is directional. Therefore, the water molecules above the PC-SAM surface tend to have a flat dipole distribution, similar to bulk water, whereas the water molecules above the OEG-SAM surface have preferred dipole vectors in specific directions. These results show that the origin of the nonfouling mechanisms of PC-SAM and OEGSAM are very different from each other. PC-SAM achieves the (33) Tasaki, K. Macromolecules 1996, 29(27), 8922–8933.
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Figure 4. Distribution of the dipole angles for the water molecules near the PC-SAM surface, near the OEG-SAM surface, and in bulk water.
nonfouling capability via strong ionic hydration, while OEGSAM achieves similar capability via strong hydrogen-bonding hydration. Residence Time of Water near the PC-SAM Surface. The residence time of the interfacial water is an important dynamic behavior for correlating the affinity between a surface and the hydration water. A slower decay in the residence time dynamics indicates that a surface has a stronger hydration. The residence time is determined by the fraction of water that remains in a layer of specified thickness over a time interval. It can be evaluated from the survival time correlation function, Cr(t).34 The Cr(t) functional expression is shown as
Cr(t) )
NW 〈PRj(0) PRj(t)〉 1 NW j)1 〈P (0)〉2 Rj
∑
where PRj is a binary function that equals 1 if the jth water molecule resides in a layer of thickness R for time t without leaving the layer, and is evaluated for all water molecules NW that begin in that layer. The broken brackets (〈〉) denote the ensemble average. For all of the dynamic properties, only the water molecules within the first 4 Å from the SAM surfaces were analyzed. Figure 5 shows the survival time correlation functions plotted over time for both PC-SAM and OEG-SAM systems. To measure the residence time dynamics quantitatively, the mean residence time of the water molecules in the hydration layers of the PCSAM and OEG-SAM surfaces was calculated. The mean residence time can be obtained by fitting an exponential decay function to the Cr(t) curve as follows:34-36
( )
Cr(t) ) Ar exp -
t τr
where Ar is the amplitude and τr is the mean residence time.35 For a given analysis in which the layer thickness is constant, the mean residence time is representative of the interaction strength between the water and the hydrated surface. Mean residence (34) Dastidar, S. G.; Mukhopadhyay, C. Phys. ReV. E 2003, 68(2), 021921. (35) Impey, R. W.; Madden, P. A.; Mcdonald, I. R. J. Phys. Chem. 1983, 87(25), 5071–5083. (36) Garcia, A. E.; Stiller, L. J. Comput. Chem. 1993, 14(11), 1396–1406.
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Figure 5. Survival time correlation functions of the water molecules near the PC-SAM and OEG-SAM surfaces.
layer of the OEG-SAM surface. This dynamic exchange is directly related to the affinity between the water and the surface. Therefore, these results indicate that the PC-SAM surface interacts with water more strongly than the OEG-SAM surface. Reorientation of Water near the PC-SAM Surface. The reorientation of water molecules above a surface shows the dynamic change of their dipoles. The strong interactions between the PC-SAM surface and water molecules are attributed to two factors. One is from the hydrogen-bonding interactions between the surface and water and the other is from the ionic solvation of the zwitterionic head groups present on the surface. The latter is the major factor that differentiates the PC-SAM surface from the OEG-SAM surface. To confirm this, we divided the water molecules within 4 Å from the surface into two parts: (1) hydrogen-bonded water molecules (type I water) and (2) the rest of the water molecules that do not form a hydrogen bond with the surface but are within the first 4 Å from the surface (type II water). In this study, the geometric criterion was used to determine hydrogen bonds. A hydrogen bond exists if the donor-acceptor distance is
