Article pubs.acs.org/Langmuir
Binding, Structure, and Dynamics of Hydrophobic Polymers near Patterned Self-Assembled Monolayer Surfaces Lijuan Li and Shekhar Garde* The Howard P. Isermann Department of Chemical and Biological Engineering and The Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, Troy, New York 12180, United States ABSTRACT: We use molecular dynamics simulations to study the binding, conformations, and dynamics of a flexible 25-mer hydrophobic polymer near well-defined patterned selfassembled monolayers containing a hydrophobic strip (with −CH3 head-groups) having different widths in a hydrophilic (−OH) background. We show that the polymer binds favorably to hydrophobic strips of all widths, including the subnanometer ones comprising 3, 2, or even 1 row of −CH3 head-groups, with the binding strength varying from about 107 to 25 kJ/mol for the widest to the narrowest strip. Near wide hydrophobic patches containing 5 or more −CH3 rows, pancakelike conformations are dominant, whereas hairpinlike structures become preferred ones near the narrower strips. In the vicinity of the narrowest 1-row strip, the polymer folds into semiglobular conformations, thus maintaining sufficient contact with the strip while sequestering its hydrophobic groups away from water. We also show that the confinement makes the translational dynamics of the polymer anisotropic as well as conformational dependent. Our results may help to understand and manipulate the selfassembly and dynamics of soft matter, such as polymers, peptides, and proteins, at inhomogeneous patterned surfaces.
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INTRODUCTION Solid−water interfaces are ubiquitous in bio- and nanotechnologies.1−9 Much progress has been made toward designing and synthesizing surfaces with nanoscale chemical or topographical patterns,10−13 especially using self-assembled monolayers (SAMs).14−18 The ability to create such surfaces offers new opportunities for manipulating binding, conformational equilibria, and dynamics of flexible molecules. For example, Suttipong et al.19 recently employed dissipative particle dynamics simulations to study how chemically patterned flat surfaces with single or double stripes of various widths affects the self-assembly of surfactants in their vicinity. They observed rich behavior from monolayer coverage for wide stripes to hemicylindrical or globular aggregates near increasingly thinner stripes. Concomitantly, experimental technology is also developing rapidly to track assembly as well as single molecule trajectories, for proteins, DNA, or surfactants, near chemically heterogeneous surfaces.20−22 Binding of polymers to patterned surfaces, their structure in the bound state, and the various thermodynamic factors affecting binding have been studied in the past.23−26 A phase diagram for adsorption and pattern recognition of polymers at striped surfaces using coarse-grained models in Monte Carlo simulations has been reported recently.27 Other systems of interest, such as polyelectrolytes near oppositely charged flat and curved surfaces, including those of Janus particles, have also been studied.28,29 Given the nanoscopic nature of these systems and the types of molecules involved, we expect that fundamental understanding in this area will impact bionanotechnology applications, biosensors, and other applications where single molecule recognition and manipulation is central. © 2014 American Chemical Society
Here we study how surfaces with well-defined chemical patterns affect the behavior of flexible hydrophobic homopolymers in their vicinity using molecular dynamics (MD) simulations. Specifically, we study the behavior of a flexible hydrophobic 25-mer polymer at SAM surfaces presenting a hydrophobic strip spanning a range of widths in a hydrophilic background. Both the 25-mer polymer and the striped patterned system are of interest for a variety of reasons. We have shown that the 25-mer studied here forms folded globular structures in bulk water and displays proteinlike folding− unfolding thermodynamics over a range of temperatures.39 Studies of salt, pressure, and osmolyte dependence of conformations of this and similar polymers have also highlighted the parallels with effects of these solutes on protein structure and interactions. The behavior of 25-mer polymer near homogeneous SAM surfaces with a range of hydrophobicities has been studied in detail by Jamadagni et al.,30 and serves as an excellent reference for the present study. In particular, Jamadagni et al.30 showed that the hydrophobic 25mer polymer binds to a variety of homogeneous SAMs with the strength of binding decreasing with increasing surface hydrophilicity. The polymer forms flat pancakelike structures near the hydrophobic (−CH3) SAM surface, and gradually beads up into globular structures with increasing surface hydrophilicity, eventually detaching from the most hydrophilic −OH SAM. A SAM surface with a hydrophobic strip comprising −CH3 head-groups in the −OH background represents an excellent Received: September 4, 2014 Revised: October 21, 2014 Published: October 22, 2014 14204
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Figure 1. Snapshots of the MD simulation system and patterned surfaces. (A) Side view of a part of the 5-row system shows the hydrophobic polymer (gray), water (red and white wire frame), and SAM chains with −CH3 (cyan and white) and −OH (red and white) head-groups, where hydrogen atoms are shown in white. (B−I) Top views of the patterned surfaces showing hydrophobic (−CH3) strips of widths varying from 16 rows (homogeneous) to 1 row, in the −OH background. Panels (B)−(E) show starting configurations, which are well ordered. Panels (F)−(I) show typical instantaneous configurations of surfaces, which highlight the slight disorder induced by thermal fluctuations.
system to study the behavior of conformationally flexible molecules at patterned surfaces. Based on the results of Jamadagni et al.,30 we expect the hydrophobic polymer to bind to a sufficiently wide hydrophobic strip. However, in light of the recent work on context dependence of hydrophobicity, it is unclear if the polymer will recognize and bind to narrow hydrophobic strips. Using a density fluctuations perspective, Acharya et al.31 showed that a patch containing a single −CH3 group is only weakly hydrophobic when presenting in the −OH background. It is only when the diameter of the patch approaches 1 nm (seven −CH3 head-groups in a hexagonal close packing pattern) that it becomes sufficiently hydrophobic. The hydrophobicity of patches on protein surfaces is also known to be context dependent.31,32 These ideas when translated to our system raise the questions: how does the presence of −OH head-groups in the vicinity affect the hydrophobicity of −CH3 strips? Do hydrophobic polymers bind to narrow strips with subnanometer widths? Further, are chemical patterns in an otherwise flat surface sufficient to confine the bound polymer to the strip? How does the confinement affect the conformation of the bound polymer? What are the implications of these results on the dynamics of the polymer near the surface? Here we show that the polymer recognizes hydrophobic strips of all widths, including the narrowest single row of −CH3 head-groups. The strength of binding of the polymer to the surface decreases with decreasing the width of the strip, but is sufficient in all cases to confine the polymer along the strip. The polymer changes its conformation in response to the context and confinement provided by the strip. Correspondingly, the translational dynamics of the polymer become anisotropic and conformational dependent. Our results may help understand the behavior of polymers, peptides, and proteins at patterned surfaces for applications in biosensors33−35 or molecular separations.36,37 The effects of chemical and topographical patterns are also integral in receptor−ligand binding,38 and our results may shed light on the mechanisms of binding in those systems.
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0.25 nm). As discussed by Athawale et al.,39 this polymer may be thought of as a coarse-grained version of a 50-mer alkane molecule. As in the previous studies,30,40,41 the SAM is constructed using 10 carbon long alkyl chains with one end harmonically attached to a sulfur atom and the other end presenting the −OH head-groups. We attached two alkane chains in positive and negative z-directions, respectively, creating two SAM−water interfaces. A total of 224 sulfur atoms were position restrained based on gold 111 lattice geometry with separation of 0.5 nm, creating SAM layers with the x−y crosssectional area of 6.92 × 7.00 nm2. By replacing rows of −OH headgroups with −CH3 head-groups, we generated hydrophobic strips of various widths, as shown in Figure 1. The strips are parallel to the xaxis, and the width of a single −CH3 row is about 0.43 nm along the ydirection. Panels (B)−(E) in Figure 1 show top views of well-ordered homogeneous (i.e., 16-row), 11-, 7-, and 5-row −CH3 strips, respectively, in the −OH background at the beginning of the simulations. Thermal fluctuations during the course of the simulation disturb the patterns somewhat, yet the underlying strip structure is maintained, as is clear for 4-, 3-, 2-, and 1-row systems in panels (F)− (I), respectively. The force field parameters of the SAM chains are adopted from Jamadagni et al.30 Water molecules were represented using the extended simple point charge model (SPC/E).42 The SAM and the CG-25 polymer are solvated with approximately 9000 water molecules, leading to a relatively large system with the xyz dimensions of 6.92 × 7.00 × 8.50 nm3, periodic in all the three directions. As done previously,30,40,41 all the simulations were performed in the isothermal−isobaric (N,P,T) ensemble using the molecular dynamics package GROMACS.43 The V-rescale thermostat44 and an anisotropic Berendsen barostat45 were used to maintain the system temperature (300 K) and pressure (1 atm). Electrostatic interactions were calculated using the particle mesh Ewald (PME) algorithm,46 and the LINCS47 algorithm was used to constrain bonds in water molecules. Parameters for cross interactions were calculated using the standard Lorentz−Berthelot mixing rules.48 Configurations were stored every 0.5 ps for analysis.
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RESULTS AND DISCUSSION Polymer Binding and Conformations at Patterned Surfaces. Based on the work of Jamadagni et al.,30 who studied the binding of a CG-25 polymer to homogeneous SAM surfaces with a range of surface chemistries from hydrophobic to hydrophilic, we expect the polymer to bind to the homogeneous (16-row) −CH3 surface. Here we are interested in characterizing the binding as the width of the hydrophobic region is reduced. To this end, for each pattern presented in Figure 1, we performed five independent simulations in which the CG-25 polymer with a different initial conformation was placed in water about 1 nm away from the surface at the beginning of each simulation. For the 1-row system, we also
METHODS
Our system includes three components: a hydrophobic polymer, a patterned SAM surface, and water. The hydrophobic polymer, called CG-25, is the same as the one studied extensively by our group previously30,39 and comprises 25 freely jointed Lennard−Jones monomers (σ = 0.44 nm and ϵ = 0.85 kJ/mol) with harmonic bond potentials (U = 0.5Kb(l − l0)2, where Kb = 60 702 kJ/mol/nm2 and l0 = 14205
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used a larger SAM with 14 × 14 nm2 cross section, which provides a long enough 1-row hydrophobic strip if a straight chain conformation of CG-25 were to bind to the pattern. We found that the CG-25 polymer adsorbs on the hydrophobic strip for all of the surfaces, including the narrowest 1-row pattern. As a typical example, Figure 2 summarizes the results
Figure 2. Binding of the CG-25 polymer to a 3-row patterned surface. (A) Five trajectories (red, green, blue, cyan, and magenta) showing the z center of mass of CG-25 as a function of time. (B) Side views of CG25 at three time points (0, 0.5, and 1.0 ns) indicated by dots in the red trajectory in panel (A).
Figure 3. Polymer density profiles on patterned surfaces. (A) Number density profiles of CG-25 monomers in the z-direction near 3-row (black), 2-row (green), and 1-row (blue) SAM surfaces. The density profile of SAM heavy atoms is shown by a dashed black line. The CG25 density profiles near surfaces with greater than 3-rows (not shown) are similar to that of 3-row pattern. (B) Number density profiles of SAM chains [−CH3 (cyan), −OH (red) head-groups] and of CG-25 monomers (black) in the y-direction. (C) Schematic illustrating the relative arrangement of CG-25 monomers and SAM head-groups in the y-direction for the 3-row pattern.
of polymer binding to a 3-row strip; other cases are qualitatively similar. The polymer diffuses in solution, as indicated by the nonmonotonic variation of the z-coordinate of the polymer center of mass in Figure 2A in various trajectories. In four out of the five trajectories, the polymer binds to the surface within about 2 ns, whereas in one of the trajectories it takes over 16 ns for the polymer to bind to the surface. Figure 2B illustrates the path of the polymer pictorially for one of the trajectories. To study the equilibrium conformations and dynamics of the bound polymer, we extended the simulations by additional 25 ns after binding of the polymer to the surface. The binding is sufficiently strong in all cases, such that, once bound, the polymer does not leave the surface over the duration of the simulation. Later in this Article, we report free energy calculations using umbrella sampling, which quantify the strength of binding of the polymer to each surface. Figure 3 summarizes the polymer density profiles in the zand y-directions near the various patterned surfaces. Note that the hydrophobic strip is along the x axis, parallel to the xy plane. Density profiles in the z-direction suggest that the polymer binds in a flat quasi-two-dimensional (2D) parallel-tosurface conformation to most patterned surfaces, as evident in the sharply defined single peak of CG-25 monomer density separated by a distance of 0.37 nm from the SAM surface density peak, indicating a direct contact between the two. A slight outward movement of the first peak and a slight tail beyond the first peak observed in the CG-25 monomer density profile near the 2-row surface (green curve) suggest small deviations from planar conformations of the polymer. The density profile near the 1-row surface displays a clear second peak as well, suggesting beading up of the polymer into threedimensional (3D) conformations near the single −CH3 row, while still maintaining a clear contact with that narrow hydrophobic strip. We provide more detailed views of these conformations later in this subsection. Number density profiles in the y-direction provide further insights into the location of CG-25 monomers on the
hydrophobic strips. On a homogeneous (16-row) surface, the monomer density profile shows oscillations about the average. The peaks of these oscillations in density are located precisely between the peaks of the SAM density profiles suggesting that the monomers sit in the grooves (or dimples) on the SAM surface, thus maximizing the interactions with the −CH3 headgroups. This feature is observed for all surfaces. In 11-, 7-, 5-, and 4-row systems, the repulsion of the monomers from the hydrophilic (−OH) groups is evident in the lower densities of CG-25 monomers toward the edges and the enhancement of the density near the center. The 3-row is the smallest strip that allows the CG-25 monomers to avoid direct contact with the −OH head-groups, whereas in the 2-row and 1-row systems CG-25 monomers are located in the hydrophobic−hydrophilic grooves. The asymmetry of the SAM heavy atom density profiles (reflected in the small shoulder/peak) of the left of each well-defined peak is a result of a combination of the tilt and alignment of the SAM. To better quantify the different conformations of the CG-25 polymer near various patterned surfaces, we calculated the distribution of the radius of gyration of the polymer, and performed clustering analysis of polymer conformations using a greedy-type algorithm implemented in Gromacs.49 Figure 4A shows the probability distribution of the radius of gyration, P(Rg), of CG-25 near different patterned surfaces. For a range of surfaces from a homogeneous −CH3 SAM to the 5-row pattern, the P(Rg) distribution is similar, with the dominant peak at Rg of about 0.7 nm, and a shoulder or a peak at 0.85 nm. The dominant peak near 0.7 nm corresponds to the most populated flat pancakelike structures (circular as well as ‘S’ shaped ones) shown in Figure 4, which are the most compact 2D structures of the polymer. The shoulder and tail at larger Rg values include hairpinlike and other extended structures. There is a clear change in the P(Rg) profile going from 5-row to 4-row surfaces. The confinement presented by the 4-row pattern reduces the population of pancakelike structures, and hairpinlike structures become the dominant ones. Near the narrow 314206
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mediated interactions, which creates the confining boundary. We performed umbrella sampling with the Weighted Histogram Analysis Method (WHAM)50 to calculate the free energy of moving the polymer center of mass (COM) along the ydirection. We used a series of windows separated by 0.2 nm, and applied a harmonic constraint potential to the yCOM of the bound polymer, equal to k(yCOM − y*)2, where k = 1000 kJ/ mol/nm and y* is the center of the window. We used at least 4 ns long simulations in each window to obtain sufficient sampling of the y space; in the boundary region, we used as long as 8−24 ns long windows to ensure the overlap of data from adjacent windows. Thus, the total simulation time to obtain a single potential of mean force (PMF) curve ranged from 80 ns for the narrowest 1-row strip to over 200 ns for the 11-row strip. Figure 5A shows the free energy of the bound CG-25 polymer along the y-direction. We refer to the polymer as the Figure 4. Conformations of CG-25 at different patterned surfaces. (A) Probability distribution of the radius of gyration, P(Rg), of CG-25. P(Rg) in bulk water (dashed black line) is also shown for reference. (B) Average Rg, as well as Rg(x) and Rg(y) components (i.e., about xand y-axes) are shown as a function of the number of −CH3 rows. Color scheme: 16- (purple), 11- (blue), 7- (cyan), 5- (green), 4(goldenrod), 3- (orange), 2- (dark red), and 1-row (black). (C−F) Top and side views of two most representative conformations of CG25 near 7-, 4-, 3-, and 1-row surfaces obtained by performing clustering analysis of conformations from MD simulations are shown. Figure 5. (A) Potential of mean force of the CG-25 polymer center of mass along the y-direction in the vicinity of the SAM surface. The curves are referenced to zero when the polymer is fully on the −OH surface. The center of the hydrophobic strip is located at y = 0. The −CH3/−OH boundaries for each pattern are shown by vertical dashed lines in different colors. Color Scheme: 11- (blue), 7- (cyan), 5(green), 4- (goldenrod), 3- (orange), 2- (dark red), and 1-row (black). (B) PMFs in the left boundary region, aligned by translating them such that the left −CH3/−OH boundary is at the same location (dashed line) in all the curves. (C) Free energy at the minimum, which is akin to the free energy of polymer binding to the hydrophobic patch, as a function of the patch width.
row and 2-row patterns, pancakelike structures have rather small probability, and the dominant structures are hairpinlike, as indicated by a well-defined peak near Rg of 0.85 nm. There is another clear shift in the P(Rg) distributions between 2- and 1-row patterns. In fact, the P(Rg) profile near the single row pattern is qualitatively different from all of the remaining patterns. While a peak near Rg of 0.8 nm is consistent with 2D hairpinlike conformations, significant population of globular 3-D conformation is also observed. That is, the polymer beads up into a 3D ellipsoidal globule, yet maintains contact with the single −CH3 row. The globule is, however, not entirely bulklike as the most stable globular conformation in bulk water has Rg of about 0.55 nm. Also, we do not observe a straight chain configuration of the polymer in the 1-row 14 × 14 nm2 cross section systems. The above confinement induced conformational changes are captured by the variation of average Rg, Rg(x), and Rg(y) as a function of the width of the hydrophobic strip. Average Rg shows a small decrease as the number of rows is reduced from 16 to 5, consistent with the overall preference for flat compact pancakelike structures. As the width is reduced from 5, 4, 3, to 2, there is a monotonic increase in average Rg, consistent with the dominance of hairpin structures. The variation of Rg(x) (decrease) and Rg(y) (increase) further suggests that the hairpinlike structures are aligned with the strips. Finally, the beading up of the CG-25 polymer into 3D ellipsoids near the 1row pattern leads to the reduction of overall Rg and of Rg(y) and a slight increase in Rg(x). Free Energy of Confinement and Binding. The above results show that, despite the SAM surface being topographically flat, the hydrophobic−hydrophilic boundary between the −CH3 and −OH head-groups appears like a confining wall to the bound polymer. The polymer is driven to the hydrophobic strip by strong hydrophobic interactions, and is repelled from the −OH portion of the SAM by water-
“bound” polymer, because we apply the umbrella potential to the center of mass of the polymer after the polymer is adsorbed onto a hydrophobic strip. No special constraining potential was applied in the z-direction, and the polymer indeed detaches partially and then completely once it crosses over fully to the hydrophilic (−OH) SAM region. The raw PMF data display a small nonsystematic asymmetry that is within the errors of our calculations. To obtain better statistics, we averaged data from left and right directions from the center of the strip, leading to the symmetric PMF profiles. The deepest and the widest PMF profile is observed for the 11-row strip (Figure 5A); note that the 16-row system is homogeneous and does not have any −OH groups on the surface. The free energy of the polymer at the center of the 11row hydrophobic strip is about 107 kJ/mol lower than that on the −OH part of the SAM surface. This strong driving force for the polymer to bind to the hydrophobic region leads to the confinement of the polymer to the hydrophobic strip, even though the SAM surface is essentially flat. The exact locations of the left and right −CH3/−OH boundaries are marked in Figure 5A by dashed lines. The length scale over which the influence of the boundary is felt by the polymer depends on the size of the polymer probe as well as the inherent distance over which the behavior of water (solvent) is perturbed by the 14207
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Figure 6. Top views (top panels) and side views (bottom panels) of the dominant conformations of the CG-25 polymer observed in different umbrella sampling windows near the 5-row patterned surface. The y-coordinate of the center of windows in which such conformations are observed with high probability are listed under each panel. y = 0 corresponds to the center of the hydrophobic strip.
pancake at the center, and switches to a hairpin structure as its center of mass is constrained near the boundary on the −CH3 side of the strip. As the polymer is moved further to the −OH side, the hairpin unravels, it maintains partial contact with the hydrophobic strip, but it also lifts from the surface on the −OH side. Finally, when the polymer is pushed over to the −OH side of the surface (about 1 nm from the boundary), it forms a globule and detaches from the surface, consistent with the calculations of Jamadagni et al.30 The conformational behavior of the polymer in the boundary region of most strips, down to the 2-row strip, is qualitatively similar to that discussed here for the 5-row case, leading to the similar PMF profiles in that region. For the 1-row case, the inherent structures of the polymer on the strip are already partially globular, and the nature of the PMF profile in the y-direction is somewhat different from the other cases. Although the PMFs in Figure 5 are along the y-direction, they allow us to make almost quantitative estimates of the free energy of binding of the polymer from bulk water to a hydrophobic strip. Though the exact route for polymer binding to the hydrophobic strip may be complex, the thermodynamics of binding are path-independent. Thus, for convenience, we divide the binding of the polymer to a hydrophobic strip into two sequential steps: in the first step, the polymer is brought from bulk water to the −OH portion of the SAM surface, followed by moving it from the −OH surface to the center of the hydrophobic strip in the second step. In bulk water as well as near the −OH surface, the CG-25 polymer forms globular structures. The free energy change in the first step is small, about 0−5 kJ/mol as reported by Jamadagni et al.30 Thus, the dominant contribution to polymer binding to the hydrophobic strip comes from the second step. Using the minimum of the PMF in Figure 5A as an estimate of the change in free energy in the second step, gives values that vary from about 107 kJ/mol (for the 11-row strip) to 25 kJ/mol (for the 1-row surface). The value of 107 kJ/mol for the 11-row surface is consistent with independent calculations of polymer binding by Jamadagni et al.30 For a polymer constrained in the compact globular state, they report a free energy of binding of CG-25 to a homogeneous −CH3 SAM to be about 90 kJ/mol. The polymer studied here is not constrained to stay in the globular state. The change from globular to pancake conformations near the −CH3 surface adds a further favorable contribution of about 15 kJ/mol,30 leading to an estimate of the binding free energy of about 105 kJ/mol, thus providing an almost quantitative agreement between these two independent calculations.
chemical differences at the boundary. The physical left-to-right boundary width of the 11-row region is about 4.8 nm. Only over the central 1.8 nm region is the polymer PMF flat, suggesting that the influence of the boundary is felt by the polymer 1.5 nm inward from each −CH3/−OH chemical boundary. The distribution of polymer radius of gyration in Figure 4A and its average in Figure 4B suggest that the radius of the polymer disk is 0.7−0.8 nm, which accounts for about half of the above distance of boundary influence. The remaining 0.7−0.8 nm represents the range over which the boundary region influences the behavior of water in the vicinity. We note that the boundary between −CH3 and −OH group also has small thermal fluctuations (see Figure 1F−I). The range of about 0.7−0.8 nm estimated here for the length scale of the influence of the boundary on the behavior of water is consistent with that obtained by Acharya et al. using a water density fluctuations perspective.31 As the width of the hydrophobic strip is reduced to about 3 nm (7 rows), the influence of the two boundaries reaches the center of the strip, as is evident from Figure5A. The polymer PMF across the 7-row hydrophobic strip contains a negligible flat region at the center. As the width of the hydrophobic region is further reduced, the confining well becomes gradually shallower. However, even for the 1-row −CH3 strip, the PMF at the center is sufficiently deep (about 25 kJ/mol) for the polymer to bind to the surface. Another interesting feature of the PMFs reported in Figure 5 is their similarity near the boundary. Figure 5B shows the PMFs translated along the y-direction, such that the location of the left −CH3/−OH boundary is the same for all the curves. Except for the 1-row case, the PMFs in the boundary region overlap with each other within the errors of our calculations. The origin of this similarity comes primarily from the similarity of the chemical and hydration environment of the polymer on the −OH side of the boundary, as well as the similarity of the polymer conformations in the close vicinity of the −CH3 side of the boundary. To understand this point better, in Figure 6, we show the characteristic conformations of the CG-25 polymer when its center of mass is located at different y locations: at the center of the −CH3 strip, near the edge on the −CH3 and on the −OH sides, and on top of the −OH portion of the surface. These conformations represent the most populated cluster in that window as obtained by the greedytype algorithm.49 The conformational preferences at the center of the −CH3 strip are already well described above (Figure 4). For the 5-row case illustrated in Figure 6, the polymer forms a 14208
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Figure 7. Translational dynamics of CG-25 at different patterned surfaces. (A−C) Overall mean square displacement, MSD, of the center of mass of CG-25 and its x, y components. (D) y-MSD over a longer period of 2 ns. (E) 2D diffusivity and its x, y components. (F) Footprint of the COM of CG-25 during a 3 ns simulation trajectory on these surfaces. Color scheme: 16-rows (purple), 11-rows (blue), 7-rows (cyan), 5-rows (green), 4rows(goldenrod), 3-rows (orange), 2-rows (dark red), and 1-row (black).
Dynamics. The above analysis of polymer free energies near various patterned surfaces shows that the bound polymer is confined to the hydrophobic strip, with the nature of confinement changing from quasi-2D (near wider strips) to essentially 1D (near the narrow sub-nanometer strips). Such confinement is expected to affect the dynamics of the polymer on the surface. Jamadagni et al.30 showed that the translational dynamics of the polymer on a homogeneous −CH3 surface are actually faster than that in bulk water, which they ascribed to the sliding of the polymer pancake on the featureless greasy −CH3 surface aided by the somewhat faster translational dynamics of water near the hydrophobic surface. Figure 7 summarizes the variation of polymer dynamics at different patterned surfaces. Near the homogeneous −CH3 surface, which serves as a reference, the overall 2D diffusivity of the polymer is roughly 8.2 ×10−6 cm2/s, consistent with the value reported by Jamadagni et al.30 As the width of the hydrophobic strip is decreased, the overall diffusivity also decreases monotonically, and importantly, the nature of the MSD versus t curve suggests a subdiffusive motion of the polymer. The resolution of the dynamics in the x- and ydirections provides insights into this subdiffusive behavior. As the width of the strip decreases, the confinement in the ydirection limits the movement of the polymer center of mass to the width of the strip, and correspondingly, the MSD in the ydirection saturates with time near all strips. For 1-, 2-, and 3row systems (with sub-nanometer widths), the confinement in the y-direction essentially eliminates the movement in that direction, with apparent diffusivity in that direction to be essentially zero. The dynamics in the x-direction are surprisingly insensitive to the width of the hydrophobic strip almost down to the 3-row system. Subtle changes are, however, visible for 5-row, 4-row, and 3-row systems. For example, the diffusivity in the xdirection increases slightly going from the 5- to 4-row system, and drops back down for the 3-row system. We hypothesize that these subtle changes originate from the corresponding changes in the preferred conformation of the polymer and the drag induced by water near the hydrophilic −OH head-groups. Moving from the 5-row to 4-row system, the CG-25 polymer
shows a clear shift from pancakelike to hairpinlike structures, with their long axis aligned with the x-axis. The cross-sectional area of a hairpin that is relevant to the movement along the xdirection is smaller than that of a pancake, leading to the somewhat faster dynamics near the 4-row strip. To further probe conformation dependent anisotropic dynamics of the CG-25 polymer, we calculated the time dependence of MSD of the polymer when the polymer is constrained to be in the pancake conformation as well as separately when the polymer is constrained to be in a hairpin conformation near the 7-row hydrophobic strip. Figure 8 shows that the dynamics of
Figure 8. Translational dynamics of CG-25 constrained to be in pancake (lines) and hairpin (open circles with lines) conformations along (A) x- and (B) y-directions near the 7-row hydrophobic strip.
hairpinlike configurations are indeed faster in the x-direction relative to those of pancakes, and vice versa. Near the 3-row strip, although the conformations are predominantly hairpinlike, the polymer now also makes direct contact with the −OH boundary and its hydration water, presumably leading to a higher hydrodynamic drag, and the corresponding slowing down of the dynamics in the x-direction relative to that for the 4-row system. For the 2-row and 1-row systems, direct interactions with the −OH boundary and the corresponding drag force dominate, leading to the significant slowing down of the dynamics in the x-direction.
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CONCLUDING REMARKS We studied how surfaces with simple and well-defined chemical patterns affect the binding, conformations, and dynamics of 14209
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flexible hydrophobic homopolymers in their vicinity using extensive molecular dynamics simulations. Our results show that the polymer binds to hydrophobic strips of all widths with sufficient binding strength, including to the narrowest strip with only single hydrophobic row. Umbrella sampling calculations show that the free energy of confinement of the polymer over the hydrophobic strip varies from 25 kJ/mol near the narrowest strip to 107 kJ/mol near the widest. This largest value is consistent with the free energy of binding of the polymer from water to a flat hydrophobic surface. In its bound state, the polymer changes its preferred conformations in response to the context and confinement provided by the strip. The pancakelike conformations are most populated near wide hydrophobic strips containing 5 or more −CH3 rows, while hairpinlike structures become dominant near narrower strips. In the vicinity of the narrowest 1-row strip, the polymer beads up into a 3D ellipsoidal globule, yet maintains sufficient contact with the single −CH3 row. We also showed that the confinement makes the translational dynamics of the polymer anisotropic as well as conformational dependent. Our results may help to better understand and manipulate the conformations, self-assembly, aggregation, and dynamics of soft matter, such as polymers, surfactants, peptides, and proteins, in the vicinity of heterogeneous solid and aqueous interfaces. Recent simulations of surfactants near surfaces presenting two narrow hydrophobic stripes separated by a narrow hydrophilic stripe by the Striolo group showed exotic structure formation in their vicinity.19 How the hydrophobic polymer studied here responds to such patterns will be of interest in the future. Further, it may be possible to create 2D mazes, sinusoidal or other patterns using a combination of hydrophobic and hydrophilic chemistries. A polymer that either diffuses or is driven along such underlying patterns may be able to respond to those patterns, thereby allowing temporal and/or spatial control over polymer conformation or dynamics over patterned surfaces. Such systems may open up applications in molecular separations, sensing, or materials development.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
We thank Hari Acharya, Vasudevan Venkateshwaran, and Srivathsan Vembanur for helpful discussions and comments on this manuscript. We thank Center for Computational Innovations at Rensselaer for computational resources. This work was partially supported by the National Science Foundation (Grant Number CBET-1159990).
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