Article pubs.acs.org/Langmuir
Structure and Dynamics of Single Hydrophobic/Ionic Heteropolymers at the Vapor−Liquid Interface of Water Srivathsan Vembanur, Vasudevan Venkateshwaran, 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 focus on the conformational stability, structure, and dynamics of hydrophobic/charged homopolymers and heteropolymers at the vapor−liquid interface of water using extensive molecular dynamics simulations. Hydrophobic polymers collapse into globular structures in bulk water but unfold and sample a broad range of conformations at the vapor−liquid interface of water. We show that adding a pair of charges to a hydrophobic polymer at the interface can dramatically change its conformations, stabilizing hairpinlike structures, with molecular details depending on the location of the charged pair in the sequence. The translational dynamics of homopolymers and heteropolymers are also different, whereas the homopolymers skate on the interface with low drag, the tendency of charged groups to remain hydrated pulls the heteropolymers toward the liquid side of the interface, thus pinning them, increasing drag, and slowing the translational dynamics. The conformational dynamics of heteropolymers are also slower than that of the homopolymer and depend on the location of the charged groups in the sequence. Conformational dynamics are most restricted for the end-charged heteropolymer and speed up as the charge pair is moved toward the center of the sequence. We rationalize these trends using the fundamental understanding of the effects of the interface on primitive pair-level interactions between two hydrophobic groups and between oppositely charged ions in its vicinity.
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INTRODUCTION Aqueous interfaces present an ideal platform for studies of structure, dynamics, and assembly of conformationally flexible molecules. Understanding how interfaces affect single-molecule behavior as well as self-assembly in their vicinity is an active area of research.1−11 Recent work has shown that even the most primitive water-mediated interactions between small hydrophobic solutes12−14 or between simple monovalent ions15 are significantly different near hydrophobic surfaces compared to those in bulk water. For example, the desolvation barrier in the free energy of association of two hydrophobic solutes is reduced (or even absent) near hydrophobic interfaces, suggesting faster kinetics of hydrophobic contact formation/ breakage.13,14 The driving force for assembly of many hydrophobic solutes is also predicted to be weaker near an extended hydrophobic surface relative to that in bulk water.13 In contrast, water-mediated interactions between oppositely charged ions are significantly stronger near the vapor−liquid interface of water compared to that in bulk water.15 Molecular origins of the effects of interfacial environments on hydrophobic and ionic interactions have been discussed recently.13−15 The effects of hydrophobic interfaces on primitive hydrophobic phenomena (e.g., the reduction of the driving force and the desolvation barrier height in hydrophobic solute assembly) are also apparent in the behavior of hydrophobic homopolymers at interfaces. In bulk water, a hydrophobic homopolymer (e.g., a freely jointed 25-mer of hydrophobic beads) folds into stable globular structures, whereas the same polymer samples a © 2014 American Chemical Society
range of conformations from collapsed to extended near the vapor−liquid interface of water.5,16 The conformational dynamics of hydrophobic polymers are also orders of magnitude faster at the vapor−liquid interface of water than in bulk water.5 Because hydrophobic and ionic interactions are affected to different extents by the vapor−liquid interface of water, we are interested in exploring the behavior of conformationally flexible heteropolymers at such an interface. For example, how does the introduction of a charge pair in an otherwise hydrophobic polymer change its conformational preferences and dynamics near an interface? A related question of how introducing a charge pair affects the folding and dynamics of a hydrophobic polymer in bulk water has been studied by Jamadagni et al.17 in the context of heteropolymer design. They showed that heteropolymers containing one or two pairs of opposite charges adopt partially globular, or hairpin, or rolled hairpinlike structures in bulk water depending on the number and locations of charged pairs in the polymer sequence. To our knowledge, a systematic study of how a vapor−liquid interface of water affects the behavior of such heteropolymers has not been presented. Here we report the results from molecular dynamics (MD) simulations of hydrophobic polymers containing zero or one oppositely charged ion pair in their sequence in bulk water and Received: January 22, 2014 Revised: March 27, 2014 Published: April 1, 2014 4654
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at the water vapor−liquid interface. We show that the different effects of the interface on hydrophobic and electrostatic interactions lead to different structure and dynamics of polymers there relative to that in bulk water. Specifically, a pair of charges placed at the ends of the polymer affects its structure and dynamics in bulk water negligibly, whereas the effects are remarkable at the vapor−liquid interface. Although the homopolymer unfolds and samples a wide variety of conformations at the interface, the introduction of a single charge pair leads to the formation of stable hairpinlike structures and an order of magnitude slower conformational and translational dynamics. To explore the relative importance of hydrophobic versus electrostatic interactions, we study polymers of two different lengths. We find that at the interface a single pair of charges is sufficient to stabilize compact states of both the polymers. Our results highlight how the differences in the modulation of hydrophobic and electrostatic interactions by interfaces can influence the homopolymer and heteropolymer structure and dynamics. Our results may be useful in understanding the various factors that influence the structure, dynamics, and assembly of biomolecules at interfaces.
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METHODS
Systems. Our systems included two componentswater and a single polymer molecule. To study the behavior of the polymer in bulk water and at the vapor−liquid interface, we performed two different types of simulations. The “bulk” system used a 3D periodic box with one polymer molecule surrounded by water molecules (filling the periodic box), simulated in the constant temperature and pressure (NPT) ensemble. For the interfacial system, as is the practice,18 a slab of water was placed in a 3D periodic simulation box of constant volume with one dimension being significantly longer than the other two, creating two liquid−vapor interfaces of water (Figure 1). All polymers studied in this work are interfacially active and migrate to one of the interfaces. Force Field. Water molecules were represented explicitly using the extended simple point charge (SPC/E) model.19 The model used to describe the polymers is similar to that used by Jamadagni et al.17 Specifically, they are freely joined chains of Lennard-Jones solutes with harmonic bond potentials [σ = 0.44 nm, ε = 0.85 kJ/mol, Ubond = 1/ 2Kb(l − lo)2, with lo = 0.25 nm and Kb = 60 702 kJ/(mol nm2)]. To create heteropolymers, we introduced a charge pair into the polymer sequence by placing a charge of +1.2e on site i and −1.2e on site j of the polymer. The charge value of 1.2e gives a charge density on the monomer that is similar to that of a chloride ion. To study the effect of increasing hydrophobicity (and length) of the polymer, we simulated a 12-mer (C12) and a 24-mer (C24) version of the polymer in both uncharged (homopolymer) and charged (heteropolymer with one charged pair) states. We refer to an n-mer with charged sites i and j as
Figure 1. Snapshot from the MD simulation of a C12 polymer (cyan) at the vapor−liquid interface of water (red, oxygen; white, hydrogen). The box dimensions are approximately 5 × 5 × 8 nm3, with the thickness of the water slab being ∼4 nm. Berthelot mixing rules.25 All simulations were equilibrated for 0.5 ns, followed by production runs of 40 ns for 24-mers and 25 ns for 12mers. Configurations were saved every 0.5 ps to analyze the structure and dynamics of the polymer in bulk and at the vapor−liquid interface. Umbrella Sampling. The potential of mean force (PMF) between the ends of a given polymer was calculated using the umbrella sampling method. For the C24 polymers, we used 17 equally spaced windows spanning the end-to-end distance of r = 0.50 to 4.50 nm. We also used an additional window at r = 0.35 nm to sample end-to-end contact configurations. For the C12 polymers, we sampled the shortrange part of the end-to-end PMF using 6 equally spaced windows spanning r = 0.35 to 0.60 nm. Beyond r = 0.60 nm, we used 18 equally spaced windows to compute the end-to-end PMF up to a distance of 2.4 nm. A harmonic umbrella potential, 0.5K(r − r0)2, was employed in all windows with K = 500 kJ/mol/nm2 for the C24 polymers and K = 2000 kJ/mol/nm2 for the C12 polymers. Each window was equilibrated for 1 ns, followed by a 10-ns-long production run. Data from these windows were combined using the WHAM26 method to obtain the PMF profiles. A similar procedure was used to calculate the PMFs between neutral and charged monomers.
+ −
Cin ,j . Simulation Details. Simulations were performed using the molecular dynamics package GROMACS.20 The Leapfrog algorithm with a time step of 2 fs was used to integrate the equations of motion. Simulations of bulk systems were carried out in the isothermal− isobaric ensemble (NPT), and the interfacial simulations were carried out in the canonical ensemble (NVT). The temperature and pressure were maintained using the stochastic velocity rescaling thermostat of Bussi et. al21 and Berendsen barostat.22 Electrostatic interactions were calculated using the particle mesh Ewald (PME) algorithm23 with a grid spacing of 0.12 nm and a real-space cutoff of 1.3 nm. The Lennard-Jones interactions were also truncated at 1.3 nm. All of the systems studied here contained 4100 water molecules. The bulk water system had a 3D periodic box with dimensions of ∼5 × 5 × 5 nm3. The interfacial system had x and y dimensions of 5 × 5 nm2 and a z dimension of 8 nm with the 4-nm-thick water slab. The LINCS24 algorithm was used to constrain the bonds in water molecules. Parameters for cross interactions were calculated using the Lorentz−
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RESULTS AND DISCUSSION Homopolymers in Bulk and at the Interface. Our goal is to study how aqueous interfaces affect the conformational preferences and dynamics of hydrophobic/ionic heteropolymers. To this end, hydrophobic homopolymers, previously well characterized in bulk water and at the vapor−liquid interface,5,6,27 serve as a reference. Figure 2 shows the probability distributions of the radius of gyration, P(Rg), and sample configurations of two homopolymers, C12 (a 12-mer) and C24 (a 24-mer), in bulk water and at the interface. The monomers of these polymers have attractive interactions with themselves and with water, as described in the Methods section. 4655
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Figure 2. Typical structures adopted by (A) C12 and (B) C24 hydrophobic polymers in bulk water and at the vapor−liquid interface. Panels C and D show the probability distributions of the radius of gyration, P(Rg), for C12 and C24, respectively, in bulk water and at the interface.
In bulk water, the C12 homopolymer shows a bimodal P(Rg) distribution consistent with the results of previous simulation studies.28 The most favorable conformation is the folded state, as seen by the peak at Rg ≈ 0.45 nm (Figure 2A shows some representative configurations). However, the polymer also samples extended states as shown by the peak at Rg ≈ 0.65 nm, with a relatively small barrier (∼kBT) separating the two peaks. The hydrophobic nature of the polymer makes it interfacially active, and the polymer samples a range of Rg values from those of folded to extended configurations, as suggested by the P(Rg) distribution at the interface.5,29 The differences between the bulk and interfacial behavior are dramatic for the longer homopolymer (C24). In bulk water, C24 shows characteristics of a hydrophobic collapse and folds into compact globular conformations, as indicated by the peak at Rg ≈ 0.55 nm. Like C12, C24 is interfacially active and samples a wide range of conformations (Rg = 0.60−1.30 nm), with a weak minimum at Rg ≈ 0.75 nm. In addition to structure, the dynamics of the polymer are also different at the interface compared to that in bulk water, as discussed in more detail later in this article. To summarize, hydrophobic homopolymers either show a bimodal distribution of conformations or prefer compact globular states in bulk water depending on the length of the polymer (i.e., the strength of hydrophobic interactions), whereas at the interface they unfold and sample a wide variety of conformations from compact to extended states. Heteropolymers in the Bulk and at the Interface. Figure 3 summarizes the effect of charging the ends of C12 and C24 polymers on their structural preferences in bulk water and at the vapor−liquid interface of water. Typical configurations of + − + − the charged C112,12 and C124,24 polymers in bulk water are shown in Figure 3A. In bulk water, the P(Rg) distribution for the + − shorter C112,12 polymer remains bimodal but shows an increased preference for the extended/unfolded states relative to that + − observed for the C12 polymer. The longer C124,24 heteropolymer, for which the hydrophobic driving force for collapse is stronger, shows a preference for globular structures. These
Figure 3. Typical structures adopted by end-charged heteropolymers +
−
+
−
C112,12 and C124,24 in (A) bulk water and (B) at the interface, respectively. Panels C and E highlight changes in P(Rg) distributions upon charging the ends of the polymers, C12 and C24, respectively, in bulk water. Panels D and F show the same at the interface.
structures are more open relative to those of the C 24 homopolymer in water, as indicated by the lifting of the tail of the P(Rg) distribution for Rg > 0.6 nm (Figure 3E). These observations are qualitatively consistent with the simulations of Jamadagni et al., 17 who have dissected the different contributions to the heteropolymer conformational equilibrium in bulk water. They showed that the conformational stability of a heteropolymer is governed by the balance of hydrophobic interactions (which drive collapse), hydration and interactions of charge groups (which may prefer being fully separated and solvated or form a sticky pair depending on their strength), and water-mediated charged−hydrophobic monomer repulsions. Although the charging of the polymer ends leads to a preference for open or unfolded structures in bulk water depending on the length of the polymer, interestingly, at the interface, it leads to a stronger preference for folded or compact 1 + ,12 − configurations (Figure 3B,D,F). For example, the C12 polymer folds into compact hairpinlike structures, as indicated by the peak in P(Rg) at Rg ≈ 0.45 nm. A similar preference, + − although perhaps a less pronounced one, is observed for C124,24 . The effects of charging the polymer ends are more clearly observed in the potential of mean force, Wend−end(r), along the separation between the ends, as shown in Figure 4 for the C12, 4656
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Figure 5. (A) PMF between the two neutral monomers in bulk water and at the interface. (B) PMF between positively and negatively charged monomers in bulk water and at the interface. The charge on the monomers is ±1.2e. To account for the preferred location of charges, the PMF is calculated in an x − y plane that is located 0.25 nm away from the interface on the liquid side.
between monomeric solutes are affected in the vicinity of a vapor−liquid interface is an active area of research.14,15 Figure 5 shows the PMFs between two neutral monomers as well as between two oppositely charged monomers in bulk water and at the vapor−liquid interface. In bulk water, the PMFs (between both neutral and ionic solute pairs) show features typical of water-mediated interactions,30,31 including a contact minimum, a solvent-separated minimum, and a desolvation barrier separating the two. At the interface, the strength of water-mediated interactions between neutral solutes decreases and the desolvation barrier disappears, consistent with the weakening of hydrophobic interactions at extended hydrophobic interfaces reported by previous theoretical and simulation studies.13,14 In contrast, the charged monomers show a stronger association as indicated by a deeper contact minimum at the interface.15 The tendency of hydrophobic homopolymers to unfold and sample a broad range of conformations at the interface is consistent with the observed weakening of pair-level hydrophobic interactions there. Also, the observed strengthening of water-mediated electrostatic interactions is expected to lead to the stabilization of hairpinlike configurations of the end-charged heteropolymers at the interface. Does eq 1 capture this consistency quantitatively? Figure 6 compares Wend−end(r) for the two heteropolymers, + − + − 1 ,12 C12 and C124,24 , at the interface predicted using the simple additive model, eq 1, with that obtained from simulations. The agreement between the two is excellent, almost quantitative. This excellent agreement results from the fact that hydrophobic interactions are weak and lead to a relatively featureless
Figure 4. Potential of mean force (PMF) between the ends of homopolymers and end-charged heteropolymers at the interface. (A) +
−
+
−
C12 and C112,12 . (B) C24 and C124,24 . The dashed arrows show the change in the minimum upon charging the polymer ends. +
−
+
−
C112,12 , and C24, C124,24 polymers at the interface. The C12 and C24 homopolymers sample a broad range of conformations with no clear structural preference at the interface. Correspondingly, Wend−end(r) is essentially featureless over much of the r range. For large r values, the PMF shows entropic springlike behavior, whereas at smaller r values its behavior is governed by LennardJones repulsions. In contrast, for the heteropolymers with charged ends, the Wend−end(r) profile shows a clear minimum at r = 0.40 nm, characterizing the strong end-to-end contacts. The + − + − oscillatory nature of the PMF for C112,12 and C124,24 highlights the importance of solvation, suggesting that the end groups are well hydrated even at the interface. Molecular Origins of Heteropolymer Behavior at the Interface. Can a knowledge of Wend−end (r) for a hydrophobic homopolymer at the interface be combined with an understanding of water-mediated interactions between two monomeric neutral or oppositely charged solutes to predict the W+− end−end (r) profile for a heteropolymer? To achieve this, we divide the end-to-end PMF into two contributions: (i) from water-mediated interactions between the two end-group monomers in isolation (e.g., WLJ 2 (r) for neutral ends and W+− 2 (r) when the ends are charged) and (ii) the remaining many-body term. Because the homopolymers and heteropolymers differ only in the end groups, we explore whether the contribution from the many-body terms is similar in the two cases for polymers at the interface. That is +− +− LJ W end − end(r ) − W 2 (r ) = Wend − end(r ) − W2 (r ) +− LJ +− W end − end(r ) = Wend − end(r ) − W2 (r ) + W 2 (r )
Figure 6. PMFs between the ends of 12-mer and 24-mer homopolymers and end-charged heteropolymers (the same as in Figure 4) at the vapor−liquid interface. The predictions of the PMFs for the end-charged heteropolymers using eq 1 are shown using green circles.
(1)
To predict the behavior of polymers at the interface, all of the PMFs in the above equation need to be evaluated at the interface. Understanding how the water-mediated interactions 4657
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Figure 7. (A, B) P(Rg) distributions for C12 and its three charged heteropolymer versions in bulk water and at the interface, respectively. (C, D) The same is shown for C24. The color scheme is listed on the right. The schematics of the heteropolymers highlighting the relative locations of the charged monomers in the polymer sequence is shown on the left.
+
−
+
−
Figure 8. Probability distributions of the z locations of six monomers, numbered 1, 7, 10, 15, 18, and 24 from heteropolymers (A) C124,24 , (B) C724,18 , +
−
,15 and (C) C10 . The distributions for monomers 1, 7, and 10 are shown with lines, and those for 15, 18, and 24 are shown with symbols. The 24 sigmoidal water density profile (black line) is shown for reference in arbitrary units, and a vertical dotted line marks the Gibbs dividing surface. (D) +
−
Dominant conformations of the heteropolymers at the interface. Polymer C724,18 shows two dominant conformations, as shown. (E) Probability distribution of the z COM location for the polymers. (F) Number of hydration shell water molecules (i.e., within 0.7 nm from the monomer center) +
−
+
−
+
−
,15 polymers. for monomers 1−24 in C24, C124,24 , C724,18 , and C10 24
develop a comprehensive model based on eq 1 for those polymers. Heteropolymer Structure and Location as a Function of Sequence. How does the location of charge groups within the polymer sequence affect its structure? To answer this question, in addition to the end-charged versions, we studied two heteropolymers in which the charge groups are placed
reference landscape, which is then dominated by the highly attractive water-mediated interaction between the oppositely charged ends at the interface. How the end-to-end PMF in a heteropolymer changes when the location of the charged groups is changed would also be of interest. Although we have studied the conformational preferences of such heteropolymers in this work (reported below), we have not attempted to 4658
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+
−
,15 symmetrically near the center of the sequence (C512,8 , C10 ) 24 + − + 3 ,10 7 ,18− and equidistant from the center and the ends (C12 , C24 ). Figure 7 presents P(Rg) distributions of three different versions of C12 and C24 heteropolymers as well as those of the corresponding homopolymers in bulk water and at the + − interface. Although the end-charged version, C112,12 , displays a slight shift from compact to extended states in bulk water, the other two versions show significant unfolding, as indicated by the destabilization of the peak in the P(Rg) distribution near 0.40 nm and the enhancement of the peak near 0.75 nm (Figure 7A). Similarly, the extent of unfolding of C 24 heteropolymers in bulk water depends on the location of the charge groups (Figure 7C). Although the end-charged polymer + − + − ,15 and C724,18 heteropolymers retains its globular structure, C10 24 +
to be well hydrated and that of hydrophobic groups to stay on the vapor side of the interface. Figure 8E shows how the placement of the charged groups in the polymer can affect the center-of-mass location. The average number of water molecules in the hydration shell of the monomers of the polymers shown in Figure 8F is also consistent with the charged monomers being strongly hydrated and present on the liquid side and the uncharged monomers being weakly hydrated and present on the vapor side. Dynamics of Polymers at the Interface. The above results show that the charging of a homopolymer affects both its location and conformation at the interface. How different are translational and conformational dynamics of homopolymers and heteropolymers at the interface? Figure 9A shows the
−
show higher degrees of unfolding. Specifically, for C724,18 , the competition between the tendency of charge groups to remain solvated and the neutral monomers to form intrapolymer hydrophobic contacts leads to the stabilization of hairpinlike structures in water, consistent with the results of Jamadagni et al.17 The P(Rg) distributions for different heteropolymers at the interface are qualitatively similar to each other, consistent with the formation of folded hairpinlike structures (Figure 7B,D). The heteropolymers in which the charged groups are placed + − approximately equidistant from the ends and the center, C512,8 +
−
7 ,18 and C24 , appear to show the most compact P(Rg) distributions at the interface, suggesting some sensitivity of the interfacial structures to the heteropolymer sequence. Figure 8 summarizes further details of heteropolymer conformations at the interface, specifically, its location, structural details, and level of hydration. Because the results are qualitatively similar for C12 and C24 polymers, we show results only for C24 in Figure 8. In all heteropolymers, the charged groups remain in the contact state and are well hydrated, “dipped” into the liquid side, whereas the remaining hydrophobic part of the polymer prefers to stay on the vapor side of the interface. Figure 8A shows the probability density distribution for a pair of monomers at the end (1, 24), center (10, 15), and equidistant from the center and ends (7, 18),
Figure 9. (A) Mean-squared displacement, MSD, of the center of mass +
−
+
−
+
−
COM of C24 and C724,18 at the interface.
mean-squared displacement (MSD) of the center of mass of + − + − + ,15− four different polymers, C24, C124,24 , C724,18 , and C10 , at the 24 interface. The slope of the MSD versus time curve is directly related to the diffusion coefficient of the polymer center of mass (COM). Consistent with the results of Jamadagni et al.,5 we find that the C24 homopolymer essentially skates on the liquid−vapor interface, with its translational dynamics being an order of magnitude faster than in bulk water. Because the homopolymer COM is located about 0.25 nm to the vapor side of the Gibbs dividing surface (Figure 8E), the polymer experiences a much lower drag force from the liquid. In contrast, the charged groups of heteropolymers remain hydrated and pull their COM toward the liquid side. Correspondingly, the MSD of heteropolymer COM is significantly reduced, with diffusivity being comparable to that in bulk water. The slowing down of the translational dynamics resulting from the pinning of a heteropolymer to the interface is clearly visible in the sample 2D x − y trajectories of C24 and + − C724,18 in Figure 9B. Figure 10 summarizes the effects of charging a polymer on its conformational dynamics. Consistent with the results of Jamadagni et al.,5 the C24 homopolymer displays fast conformational dynamics, sampling a broad range of Rg values. Such fast conformational dynamics are expected from the relatively featureless free-energy landscape of this homopolymer at the
+ −
along the z direction for the three Ci24,j heteropolymers. We observe that the charged pair prefers to stay on the liquid side of the Gibbs dividing surface (GDS), defined by the halfdensity plane of water at z = 0. The density distributions of the charged and selected neutral groups shown in Figure 8A−C combined with snapshots of typical conformations of the heteropolymers obtained by the clustering of an ensemble of configurations from MD simulations using the Daura clustering algorithm32 provides insight into the different structures adopted by the polymers at the interface. The end-charged + − polymer, C124,24 , forms hairpinlike structures that lie parallel to the interface, where the hydrophobic parts of the polymer remain on the vapor side yet maintain their attractive +
−
+
,15 of polymers C24, C124,24 , C724,18 , and C10 at the vapor−liquid 24 interface. The MSD for the homopolymer, C24, is also shown in bulk water. MSD curves for heteropolymers in bulk water (not shown) are similar to that of C24. (B) 8-ns-long sample x − y trajectories of the
−
,15 , in which the charged groups interactions with water. C10 24 are closer to the center, also displays similar structures except + − that its ends are frayed. The C724,18 polymer adopts two different types of structures, as shown in Figure 8Da hairpinlike structure and a structure with a helical twist in it. The location of the center of mass of a heteropolymer is determined by the balance of the tendencies of charged groups
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+
−
+
−
+
−
,15 Figure 10. (A) Time dependence of Rg of C24, C124,24 , C724,18 , and C10 at the interface. (B) Autocorrelation function, CRg(t), for polymer Rg at the 24 +
−
+
−
,15 at the interface obtained from sample 100 ps MD interface. (C) Two hundred equally spaced configurations of polymers C124,24 and C10 24 trajectories, shown in a gray wireframe representation. A typical configuration is shown in space-fill, with the charged pair highlighted in red-blue.
interface. Whereas the hydrophobic homopolymers skate on the interface with low drag, the tendency of charged groups to remain hydrated pulls the heteropolymers toward the liquid side of the interface, thus pinning them, increasing drag, and slowing the translational dynamics. The conformational dynamics of heteropolymers are also slower than that of the homopolymer and depend on the location of the charged groups in the polymer sequence. Conformational dynamics are most restricted for the end-charged heteropolymer and speed up as the charge pair is moved toward the center of the sequence. Our results highlight the rich variety of structures and translational and conformational dynamics of simple hydrophobic and charged heteropolymer single molecules at a vapor−liquid interface. Given the ubiquity of aqueous interfaces in biological and nanoscopic systems, understanding the conformational behavior of more complex flexible molecules at interfaces will be an important direction to pursue. Although our work focused on the behavior of model single molecules, how many such molecules interact with each other and assemble will also be of interest in future studies.
vapor−liquid interface. The autocorrelation function, CRg(t), calculated from the time-series data of Rg, is a good measure of the conformational dynamics exhibited by the polymer. CRg(t) for the C24 homopolymer shows fast decay over a time scale of 50 ps (Figure 10B). In contrast, the conformational dynamics of heteropolymers are generally slower and depend on the exact location of charged groups within the polymer sequence. For + − example, in the C124,24 heteropolymer, the charged end groups form a strong contact resulting in a stable loop structure of the polymer. The Rg for this polymer shows occasional excursions to larger values; correspondingly, the autocorrelation function displays the slowest decay (Figure 10B). As the charged pair is moved toward the center, the free ends regain their dynamics, + − + − and the correlation time decrease from C124,24 to C724,18 to +
−
+
−
+
−
,15 C10 . Clusters of configurations of polymers C124,24 and 24 ,15 obtained from a 100 ps piece of sample trajectories C10 24 shown in Figure 10C highlight these ideas.
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CONCLUSIONS
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We presented results from extensive molecular dynamics simulations of hydrophobic/charged homopolymers and heteropolymers in bulk water and at the vapor−liquid interface of water. Our simulations show that charging a pair of monomers in an otherwise hydrophobic polymer can result in significant changes in its structure and dynamics at the interface. In bulk water, hydrophobic polymers fold into compact globular structures driven by hydrophobic interactions. Heteropolymers typically retain such compact structures, balancing the tendency of hydrophobic groups to form a core and charged groups to be solvated by water. At a vapor−liquid interface, hydrophobic polymers sample a broad ensemble of structures from folded to extended, consistent with an essentially flat conformational free-energy landscape. Adding a pair of charges to a hydrophobic polymer at the interface stabilizes hairpinlike structures, with the molecular details depending on the specific location of the charged pair in the polymer sequence. We rationalize these trends using the fundamental understanding of the effects of the vapor−liquid interface on the primitive pair-level interactions between two hydrophobic groups or between oppositely charged ions in its vicinity. The translational and conformational dynamics of homopolymers and heteropolymers are also different at the vapor−liquid
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We gratefully acknowledge financial support from NSF-CBET grants 1159990 and 0967937. We also thank Drs. Hari Acharya and Amish Patel for numerous useful discussions.
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REFERENCES
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(5) Jamadagni, S. N.; Godawat, R.; Dordick, J. S.; Garde, S. How interfaces affect hydrophobically driven polymer folding. J. Phys. Chem. B 2009, 113, 4093−4101. (6) Jamadagni, S. N.; Godawat, R.; Garde, S. How surface wettabitity affects the binding, folding, and dynamics of hydrophobic polymers at interfaces. Langmuir 2009, 25, 13092−13099. (7) Anand, G.; Sharma, S.; Dutta, A. K.; Kumar, S. K.; Belfort, G. Conformational transitions of adsorbed proteins on surfaces of varying polarity. Langmuir 2010, 26, 10803−10811. (8) Shi, L.; Tummala, N. R.; Striolo, A. C12E6 and SDS surfactants simulated at the vacuum−water interface. Langmuir 2010, 26, 5462− 5474. (9) Kastantin, M.; Schwartz, D. K. DNA hairpin stabilization on a hydrophobic surface. Small 2012, 9, 933−941. (10) Bee, J. S.; Schwartz, D. K.; Trabelsi, S.; Freund, E.; Stevenson, J. L.; Carpenter, J. F.; Randolph, T. W. Production of particles of therapeutic proteins at the air-water interface during compression/ dilation cycles. Soft Matter 2012, 8, 10329−10335. (11) Park, B. J.; Choi, C.-H.; Kang, S.-M.; Tettey, K. E.; Lee, C.-S.; Lee, D. Double hydrophilic Janus cylinders at an air−water interface. Langmuir 2013, 29, 1841−1849. (12) Berne, B. J.; Weeks, J. D.; Zhou, R. Dewetting and hydrophobic interaction in physical and biological systems. Annu. Rev. Phys. Chem. 2009, 60, 85−103. (13) Patel, A. J.; Varilly, P.; Jamadagni, S. N.; Acharya, H.; Garde, S.; Chandler, D. Extended surfaces modulate hydrophobic interactions of neighboring solutes. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 17678− 17683. (14) Vembanur, S.; Patel, A. J.; Sarupria, S.; Garde, S. On the thermodynamics and kinetics of hydrophobic interactions at interfaces. J. Phys. Chem. B 2013, 117, 10261−10270. (15) Venkateshwaran, V.; Vembanur, S.; Garde, S. On the enhancement of water-mediated ion-ion interactions at the water vapor-liquid interface. Under review. (16) ten Wolde, P. R.; Chandler, D. Drying-induced hydrophobic polymer collapse. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 6539−6543. (17) Jamadagni, S.; Bosoy, C.; Garde, S. Designing heteropolymers to fold into unique structures via water-mediated interactions. J. Phys. Chem. B 2010, 114, 13282−13288. (18) Alejandre, J.; Tildesley, D. J.; Chapela, G. A. Molecular dynamics simulation of the orthobaric densities and surface tension of water. J. Chem. Phys. 1995, 102, 4574. (19) Berendsen, H.; Grigera, J.; Straatsma, T. The missing term in effective pair potentials. J. Phys. Chem. 1987, 91, 6269−6271. (20) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation. J. Chem. Theory Comput. 2008, 4, 435−447. (21) Bussi, G.; Donadio, D.; Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 2007, 126, 014101−1− 014101−7. (22) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. Molecular dynamics with coupling to an external bath. J. Chem. Phys. 1984, 81, 3684−3690. (23) Darden, T.; York, D.; Pedersen, L. Particle mesh Ewald - an N.LOG(N) method for Ewald sums in large systems. J. Chem. Phys. 1993, 98, 10089−10092. (24) Hess, B.; Bekker, H.; Berendsen, H.; Fraaije, J. LINCS: a linear constraint solver for molecular simulations. J. Comput. Chem. 1997, 18, 1463−1472. (25) Allen, M.; Tildesley, D. Computer Simulation of Liquids; Clarendon Press: New York, 1999. (26) Kumar, S.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A.; Rosenberg, J. M. The weighted histogram analysis method for freeenergy calculations on biomolecules 0.1. the method. J. Comput. Chem. 1992, 13, 1011−1021. (27) Ferguson, A. L.; Debenedetti, P. G.; Panagiotopoulos, A. Z. Solubility and molecular conformations of n-alkane chains in water. J. Phys. Chem. B 2009, 113, 6405−6414.
(28) Athawale, M.; Dordick, J.; Garde, S. Osmolyte trimethylamineN-oxide does not affect the strength of hydrophobic interactions: origin of osmolyte compatibility. Biophys. J. 2005, 89, 858−866. (29) Ashbaugh, H.; Pethica, B. Alkane adsorption at the water-vapor interface. Langmuir 2003, 19, 7638−7645. (30) Pratt, L. R.; Hummer, G.; García, A. E. Ion pair potentials-ofmean-force in water. Biophys. Chem. 1994, 51, 147−165. (31) Pangali, C.; Rao, M.; Berne, B. A Monte Carlo simulation of the hydrophobic interaction. J. Chem. Phys. 1979, 71, 2975−2981. (32) Daura, X.; van Gunsteren, W. F.; Mark, A. E. Folding-unfolding thermodynamics of a β-heptapeptide from equilibrium simulations. Proteins: Struct. Funct. Bioinf. 1999, 34, 269−280.
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Structure and Dynamics of Single Hydrophobic/Ionic Heteropolymers at the Vapor−Liquid Interface of Water Srivathsan Vembanur, Vasudevan Venkateshwaran, 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 focus on the conformational stability, structure, and dynamics of hydrophobic/charged homopolymers and heteropolymers at the vapor−liquid interface of water using extensive molecular dynamics simulations. Hydrophobic polymers collapse into globular structures in bulk water but unfold and sample a broad range of conformations at the vapor−liquid interface of water. We show that adding a pair of charges to a hydrophobic polymer at the interface can dramatically change its conformations, stabilizing hairpinlike structures, with molecular details depending on the location of the charged pair in the sequence. The translational dynamics of homopolymers and heteropolymers are also different, whereas the homopolymers skate on the interface with low drag, the tendency of charged groups to remain hydrated pulls the heteropolymers toward the liquid side of the interface, thus pinning them, increasing drag, and slowing the translational dynamics. The conformational dynamics of heteropolymers are also slower than that of the homopolymer and depend on the location of the charged groups in the sequence. Conformational dynamics are most restricted for the end-charged heteropolymer and speed up as the charge pair is moved toward the center of the sequence. We rationalize these trends using the fundamental understanding of the effects of the interface on primitive pair-level interactions between two hydrophobic groups and between oppositely charged ions in its vicinity.
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INTRODUCTION Aqueous interfaces present an ideal platform for studies of structure, dynamics, and assembly of conformationally flexible molecules. Understanding how interfaces affect single-molecule behavior as well as self-assembly in their vicinity is an active area of research.1−11 Recent work has shown that even the most primitive water-mediated interactions between small hydrophobic solutes12−14 or between simple monovalent ions15 are significantly different near hydrophobic surfaces compared to those in bulk water. For example, the desolvation barrier in the free energy of association of two hydrophobic solutes is reduced (or even absent) near hydrophobic interfaces, suggesting faster kinetics of hydrophobic contact formation/ breakage.13,14 The driving force for assembly of many hydrophobic solutes is also predicted to be weaker near an extended hydrophobic surface relative to that in bulk water.13 In contrast, water-mediated interactions between oppositely charged ions are significantly stronger near the vapor−liquid interface of water compared to that in bulk water.15 Molecular origins of the effects of interfacial environments on hydrophobic and ionic interactions have been discussed recently.13−15 The effects of hydrophobic interfaces on primitive hydrophobic phenomena (e.g., the reduction of the driving force and the desolvation barrier height in hydrophobic solute assembly) are also apparent in the behavior of hydrophobic homopolymers at interfaces. In bulk water, a hydrophobic homopolymer (e.g., a freely jointed 25-mer of hydrophobic beads) folds into stable globular structures, whereas the same polymer samples a © 2014 American Chemical Society
range of conformations from collapsed to extended near the vapor−liquid interface of water.5,16 The conformational dynamics of hydrophobic polymers are also orders of magnitude faster at the vapor−liquid interface of water than in bulk water.5 Because hydrophobic and ionic interactions are affected to different extents by the vapor−liquid interface of water, we are interested in exploring the behavior of conformationally flexible heteropolymers at such an interface. For example, how does the introduction of a charge pair in an otherwise hydrophobic polymer change its conformational preferences and dynamics near an interface? A related question of how introducing a charge pair affects the folding and dynamics of a hydrophobic polymer in bulk water has been studied by Jamadagni et al.17 in the context of heteropolymer design. They showed that heteropolymers containing one or two pairs of opposite charges adopt partially globular, or hairpin, or rolled hairpinlike structures in bulk water depending on the number and locations of charged pairs in the polymer sequence. To our knowledge, a systematic study of how a vapor−liquid interface of water affects the behavior of such heteropolymers has not been presented. Here we report the results from molecular dynamics (MD) simulations of hydrophobic polymers containing zero or one oppositely charged ion pair in their sequence in bulk water and Received: January 22, 2014 Revised: March 27, 2014 Published: April 1, 2014 4654
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at the water vapor−liquid interface. We show that the different effects of the interface on hydrophobic and electrostatic interactions lead to different structure and dynamics of polymers there relative to that in bulk water. Specifically, a pair of charges placed at the ends of the polymer affects its structure and dynamics in bulk water negligibly, whereas the effects are remarkable at the vapor−liquid interface. Although the homopolymer unfolds and samples a wide variety of conformations at the interface, the introduction of a single charge pair leads to the formation of stable hairpinlike structures and an order of magnitude slower conformational and translational dynamics. To explore the relative importance of hydrophobic versus electrostatic interactions, we study polymers of two different lengths. We find that at the interface a single pair of charges is sufficient to stabilize compact states of both the polymers. Our results highlight how the differences in the modulation of hydrophobic and electrostatic interactions by interfaces can influence the homopolymer and heteropolymer structure and dynamics. Our results may be useful in understanding the various factors that influence the structure, dynamics, and assembly of biomolecules at interfaces.
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METHODS
Systems. Our systems included two componentswater and a single polymer molecule. To study the behavior of the polymer in bulk water and at the vapor−liquid interface, we performed two different types of simulations. The “bulk” system used a 3D periodic box with one polymer molecule surrounded by water molecules (filling the periodic box), simulated in the constant temperature and pressure (NPT) ensemble. For the interfacial system, as is the practice,18 a slab of water was placed in a 3D periodic simulation box of constant volume with one dimension being significantly longer than the other two, creating two liquid−vapor interfaces of water (Figure 1). All polymers studied in this work are interfacially active and migrate to one of the interfaces. Force Field. Water molecules were represented explicitly using the extended simple point charge (SPC/E) model.19 The model used to describe the polymers is similar to that used by Jamadagni et al.17 Specifically, they are freely joined chains of Lennard-Jones solutes with harmonic bond potentials [σ = 0.44 nm, ε = 0.85 kJ/mol, Ubond = 1/ 2Kb(l − lo)2, with lo = 0.25 nm and Kb = 60 702 kJ/(mol nm2)]. To create heteropolymers, we introduced a charge pair into the polymer sequence by placing a charge of +1.2e on site i and −1.2e on site j of the polymer. The charge value of 1.2e gives a charge density on the monomer that is similar to that of a chloride ion. To study the effect of increasing hydrophobicity (and length) of the polymer, we simulated a 12-mer (C12) and a 24-mer (C24) version of the polymer in both uncharged (homopolymer) and charged (heteropolymer with one charged pair) states. We refer to an n-mer with charged sites i and j as
Figure 1. Snapshot from the MD simulation of a C12 polymer (cyan) at the vapor−liquid interface of water (red, oxygen; white, hydrogen). The box dimensions are approximately 5 × 5 × 8 nm3, with the thickness of the water slab being ∼4 nm. Berthelot mixing rules.25 All simulations were equilibrated for 0.5 ns, followed by production runs of 40 ns for 24-mers and 25 ns for 12mers. Configurations were saved every 0.5 ps to analyze the structure and dynamics of the polymer in bulk and at the vapor−liquid interface. Umbrella Sampling. The potential of mean force (PMF) between the ends of a given polymer was calculated using the umbrella sampling method. For the C24 polymers, we used 17 equally spaced windows spanning the end-to-end distance of r = 0.50 to 4.50 nm. We also used an additional window at r = 0.35 nm to sample end-to-end contact configurations. For the C12 polymers, we sampled the shortrange part of the end-to-end PMF using 6 equally spaced windows spanning r = 0.35 to 0.60 nm. Beyond r = 0.60 nm, we used 18 equally spaced windows to compute the end-to-end PMF up to a distance of 2.4 nm. A harmonic umbrella potential, 0.5K(r − r0)2, was employed in all windows with K = 500 kJ/mol/nm2 for the C24 polymers and K = 2000 kJ/mol/nm2 for the C12 polymers. Each window was equilibrated for 1 ns, followed by a 10-ns-long production run. Data from these windows were combined using the WHAM26 method to obtain the PMF profiles. A similar procedure was used to calculate the PMFs between neutral and charged monomers.
+ −
Cin ,j . Simulation Details. Simulations were performed using the molecular dynamics package GROMACS.20 The Leapfrog algorithm with a time step of 2 fs was used to integrate the equations of motion. Simulations of bulk systems were carried out in the isothermal− isobaric ensemble (NPT), and the interfacial simulations were carried out in the canonical ensemble (NVT). The temperature and pressure were maintained using the stochastic velocity rescaling thermostat of Bussi et. al21 and Berendsen barostat.22 Electrostatic interactions were calculated using the particle mesh Ewald (PME) algorithm23 with a grid spacing of 0.12 nm and a real-space cutoff of 1.3 nm. The Lennard-Jones interactions were also truncated at 1.3 nm. All of the systems studied here contained 4100 water molecules. The bulk water system had a 3D periodic box with dimensions of ∼5 × 5 × 5 nm3. The interfacial system had x and y dimensions of 5 × 5 nm2 and a z dimension of 8 nm with the 4-nm-thick water slab. The LINCS24 algorithm was used to constrain the bonds in water molecules. Parameters for cross interactions were calculated using the Lorentz−
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RESULTS AND DISCUSSION Homopolymers in Bulk and at the Interface. Our goal is to study how aqueous interfaces affect the conformational preferences and dynamics of hydrophobic/ionic heteropolymers. To this end, hydrophobic homopolymers, previously well characterized in bulk water and at the vapor−liquid interface,5,6,27 serve as a reference. Figure 2 shows the probability distributions of the radius of gyration, P(Rg), and sample configurations of two homopolymers, C12 (a 12-mer) and C24 (a 24-mer), in bulk water and at the interface. The monomers of these polymers have attractive interactions with themselves and with water, as described in the Methods section. 4655
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Figure 2. Typical structures adopted by (A) C12 and (B) C24 hydrophobic polymers in bulk water and at the vapor−liquid interface. Panels C and D show the probability distributions of the radius of gyration, P(Rg), for C12 and C24, respectively, in bulk water and at the interface.
In bulk water, the C12 homopolymer shows a bimodal P(Rg) distribution consistent with the results of previous simulation studies.28 The most favorable conformation is the folded state, as seen by the peak at Rg ≈ 0.45 nm (Figure 2A shows some representative configurations). However, the polymer also samples extended states as shown by the peak at Rg ≈ 0.65 nm, with a relatively small barrier (∼kBT) separating the two peaks. The hydrophobic nature of the polymer makes it interfacially active, and the polymer samples a range of Rg values from those of folded to extended configurations, as suggested by the P(Rg) distribution at the interface.5,29 The differences between the bulk and interfacial behavior are dramatic for the longer homopolymer (C24). In bulk water, C24 shows characteristics of a hydrophobic collapse and folds into compact globular conformations, as indicated by the peak at Rg ≈ 0.55 nm. Like C12, C24 is interfacially active and samples a wide range of conformations (Rg = 0.60−1.30 nm), with a weak minimum at Rg ≈ 0.75 nm. In addition to structure, the dynamics of the polymer are also different at the interface compared to that in bulk water, as discussed in more detail later in this article. To summarize, hydrophobic homopolymers either show a bimodal distribution of conformations or prefer compact globular states in bulk water depending on the length of the polymer (i.e., the strength of hydrophobic interactions), whereas at the interface they unfold and sample a wide variety of conformations from compact to extended states. Heteropolymers in the Bulk and at the Interface. Figure 3 summarizes the effect of charging the ends of C12 and C24 polymers on their structural preferences in bulk water and at the vapor−liquid interface of water. Typical configurations of + − + − the charged C112,12 and C124,24 polymers in bulk water are shown in Figure 3A. In bulk water, the P(Rg) distribution for the + − shorter C112,12 polymer remains bimodal but shows an increased preference for the extended/unfolded states relative to that + − observed for the C12 polymer. The longer C124,24 heteropolymer, for which the hydrophobic driving force for collapse is stronger, shows a preference for globular structures. These
Figure 3. Typical structures adopted by end-charged heteropolymers +
−
+
−
C112,12 and C124,24 in (A) bulk water and (B) at the interface, respectively. Panels C and E highlight changes in P(Rg) distributions upon charging the ends of the polymers, C12 and C24, respectively, in bulk water. Panels D and F show the same at the interface.
structures are more open relative to those of the C 24 homopolymer in water, as indicated by the lifting of the tail of the P(Rg) distribution for Rg > 0.6 nm (Figure 3E). These observations are qualitatively consistent with the simulations of Jamadagni et al., 17 who have dissected the different contributions to the heteropolymer conformational equilibrium in bulk water. They showed that the conformational stability of a heteropolymer is governed by the balance of hydrophobic interactions (which drive collapse), hydration and interactions of charge groups (which may prefer being fully separated and solvated or form a sticky pair depending on their strength), and water-mediated charged−hydrophobic monomer repulsions. Although the charging of the polymer ends leads to a preference for open or unfolded structures in bulk water depending on the length of the polymer, interestingly, at the interface, it leads to a stronger preference for folded or compact 1 + ,12 − configurations (Figure 3B,D,F). For example, the C12 polymer folds into compact hairpinlike structures, as indicated by the peak in P(Rg) at Rg ≈ 0.45 nm. A similar preference, + − although perhaps a less pronounced one, is observed for C124,24 . The effects of charging the polymer ends are more clearly observed in the potential of mean force, Wend−end(r), along the separation between the ends, as shown in Figure 4 for the C12, 4656
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Figure 5. (A) PMF between the two neutral monomers in bulk water and at the interface. (B) PMF between positively and negatively charged monomers in bulk water and at the interface. The charge on the monomers is ±1.2e. To account for the preferred location of charges, the PMF is calculated in an x − y plane that is located 0.25 nm away from the interface on the liquid side.
between monomeric solutes are affected in the vicinity of a vapor−liquid interface is an active area of research.14,15 Figure 5 shows the PMFs between two neutral monomers as well as between two oppositely charged monomers in bulk water and at the vapor−liquid interface. In bulk water, the PMFs (between both neutral and ionic solute pairs) show features typical of water-mediated interactions,30,31 including a contact minimum, a solvent-separated minimum, and a desolvation barrier separating the two. At the interface, the strength of water-mediated interactions between neutral solutes decreases and the desolvation barrier disappears, consistent with the weakening of hydrophobic interactions at extended hydrophobic interfaces reported by previous theoretical and simulation studies.13,14 In contrast, the charged monomers show a stronger association as indicated by a deeper contact minimum at the interface.15 The tendency of hydrophobic homopolymers to unfold and sample a broad range of conformations at the interface is consistent with the observed weakening of pair-level hydrophobic interactions there. Also, the observed strengthening of water-mediated electrostatic interactions is expected to lead to the stabilization of hairpinlike configurations of the end-charged heteropolymers at the interface. Does eq 1 capture this consistency quantitatively? Figure 6 compares Wend−end(r) for the two heteropolymers, + − + − 1 ,12 C12 and C124,24 , at the interface predicted using the simple additive model, eq 1, with that obtained from simulations. The agreement between the two is excellent, almost quantitative. This excellent agreement results from the fact that hydrophobic interactions are weak and lead to a relatively featureless
Figure 4. Potential of mean force (PMF) between the ends of homopolymers and end-charged heteropolymers at the interface. (A) +
−
+
−
C12 and C112,12 . (B) C24 and C124,24 . The dashed arrows show the change in the minimum upon charging the polymer ends. +
−
+
−
C112,12 , and C24, C124,24 polymers at the interface. The C12 and C24 homopolymers sample a broad range of conformations with no clear structural preference at the interface. Correspondingly, Wend−end(r) is essentially featureless over much of the r range. For large r values, the PMF shows entropic springlike behavior, whereas at smaller r values its behavior is governed by LennardJones repulsions. In contrast, for the heteropolymers with charged ends, the Wend−end(r) profile shows a clear minimum at r = 0.40 nm, characterizing the strong end-to-end contacts. The + − + − oscillatory nature of the PMF for C112,12 and C124,24 highlights the importance of solvation, suggesting that the end groups are well hydrated even at the interface. Molecular Origins of Heteropolymer Behavior at the Interface. Can a knowledge of Wend−end (r) for a hydrophobic homopolymer at the interface be combined with an understanding of water-mediated interactions between two monomeric neutral or oppositely charged solutes to predict the W+− end−end (r) profile for a heteropolymer? To achieve this, we divide the end-to-end PMF into two contributions: (i) from water-mediated interactions between the two end-group monomers in isolation (e.g., WLJ 2 (r) for neutral ends and W+− 2 (r) when the ends are charged) and (ii) the remaining many-body term. Because the homopolymers and heteropolymers differ only in the end groups, we explore whether the contribution from the many-body terms is similar in the two cases for polymers at the interface. That is +− +− LJ W end − end(r ) − W 2 (r ) = Wend − end(r ) − W2 (r ) +− LJ +− W end − end(r ) = Wend − end(r ) − W2 (r ) + W 2 (r )
Figure 6. PMFs between the ends of 12-mer and 24-mer homopolymers and end-charged heteropolymers (the same as in Figure 4) at the vapor−liquid interface. The predictions of the PMFs for the end-charged heteropolymers using eq 1 are shown using green circles.
(1)
To predict the behavior of polymers at the interface, all of the PMFs in the above equation need to be evaluated at the interface. Understanding how the water-mediated interactions 4657
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Figure 7. (A, B) P(Rg) distributions for C12 and its three charged heteropolymer versions in bulk water and at the interface, respectively. (C, D) The same is shown for C24. The color scheme is listed on the right. The schematics of the heteropolymers highlighting the relative locations of the charged monomers in the polymer sequence is shown on the left.
+
−
+
−
Figure 8. Probability distributions of the z locations of six monomers, numbered 1, 7, 10, 15, 18, and 24 from heteropolymers (A) C124,24 , (B) C724,18 , +
−
,15 and (C) C10 . The distributions for monomers 1, 7, and 10 are shown with lines, and those for 15, 18, and 24 are shown with symbols. The 24 sigmoidal water density profile (black line) is shown for reference in arbitrary units, and a vertical dotted line marks the Gibbs dividing surface. (D) +
−
Dominant conformations of the heteropolymers at the interface. Polymer C724,18 shows two dominant conformations, as shown. (E) Probability distribution of the z COM location for the polymers. (F) Number of hydration shell water molecules (i.e., within 0.7 nm from the monomer center) +
−
+
−
+
−
,15 polymers. for monomers 1−24 in C24, C124,24 , C724,18 , and C10 24
develop a comprehensive model based on eq 1 for those polymers. Heteropolymer Structure and Location as a Function of Sequence. How does the location of charge groups within the polymer sequence affect its structure? To answer this question, in addition to the end-charged versions, we studied two heteropolymers in which the charge groups are placed
reference landscape, which is then dominated by the highly attractive water-mediated interaction between the oppositely charged ends at the interface. How the end-to-end PMF in a heteropolymer changes when the location of the charged groups is changed would also be of interest. Although we have studied the conformational preferences of such heteropolymers in this work (reported below), we have not attempted to 4658
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+
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,15 symmetrically near the center of the sequence (C512,8 , C10 ) 24 + − + 3 ,10 7 ,18− and equidistant from the center and the ends (C12 , C24 ). Figure 7 presents P(Rg) distributions of three different versions of C12 and C24 heteropolymers as well as those of the corresponding homopolymers in bulk water and at the + − interface. Although the end-charged version, C112,12 , displays a slight shift from compact to extended states in bulk water, the other two versions show significant unfolding, as indicated by the destabilization of the peak in the P(Rg) distribution near 0.40 nm and the enhancement of the peak near 0.75 nm (Figure 7A). Similarly, the extent of unfolding of C 24 heteropolymers in bulk water depends on the location of the charge groups (Figure 7C). Although the end-charged polymer + − + − ,15 and C724,18 heteropolymers retains its globular structure, C10 24 +
to be well hydrated and that of hydrophobic groups to stay on the vapor side of the interface. Figure 8E shows how the placement of the charged groups in the polymer can affect the center-of-mass location. The average number of water molecules in the hydration shell of the monomers of the polymers shown in Figure 8F is also consistent with the charged monomers being strongly hydrated and present on the liquid side and the uncharged monomers being weakly hydrated and present on the vapor side. Dynamics of Polymers at the Interface. The above results show that the charging of a homopolymer affects both its location and conformation at the interface. How different are translational and conformational dynamics of homopolymers and heteropolymers at the interface? Figure 9A shows the
−
show higher degrees of unfolding. Specifically, for C724,18 , the competition between the tendency of charge groups to remain solvated and the neutral monomers to form intrapolymer hydrophobic contacts leads to the stabilization of hairpinlike structures in water, consistent with the results of Jamadagni et al.17 The P(Rg) distributions for different heteropolymers at the interface are qualitatively similar to each other, consistent with the formation of folded hairpinlike structures (Figure 7B,D). The heteropolymers in which the charged groups are placed + − approximately equidistant from the ends and the center, C512,8 +
−
7 ,18 and C24 , appear to show the most compact P(Rg) distributions at the interface, suggesting some sensitivity of the interfacial structures to the heteropolymer sequence. Figure 8 summarizes further details of heteropolymer conformations at the interface, specifically, its location, structural details, and level of hydration. Because the results are qualitatively similar for C12 and C24 polymers, we show results only for C24 in Figure 8. In all heteropolymers, the charged groups remain in the contact state and are well hydrated, “dipped” into the liquid side, whereas the remaining hydrophobic part of the polymer prefers to stay on the vapor side of the interface. Figure 8A shows the probability density distribution for a pair of monomers at the end (1, 24), center (10, 15), and equidistant from the center and ends (7, 18),
Figure 9. (A) Mean-squared displacement, MSD, of the center of mass +
−
+
−
+
−
COM of C24 and C724,18 at the interface.
mean-squared displacement (MSD) of the center of mass of + − + − + ,15− four different polymers, C24, C124,24 , C724,18 , and C10 , at the 24 interface. The slope of the MSD versus time curve is directly related to the diffusion coefficient of the polymer center of mass (COM). Consistent with the results of Jamadagni et al.,5 we find that the C24 homopolymer essentially skates on the liquid−vapor interface, with its translational dynamics being an order of magnitude faster than in bulk water. Because the homopolymer COM is located about 0.25 nm to the vapor side of the Gibbs dividing surface (Figure 8E), the polymer experiences a much lower drag force from the liquid. In contrast, the charged groups of heteropolymers remain hydrated and pull their COM toward the liquid side. Correspondingly, the MSD of heteropolymer COM is significantly reduced, with diffusivity being comparable to that in bulk water. The slowing down of the translational dynamics resulting from the pinning of a heteropolymer to the interface is clearly visible in the sample 2D x − y trajectories of C24 and + − C724,18 in Figure 9B. Figure 10 summarizes the effects of charging a polymer on its conformational dynamics. Consistent with the results of Jamadagni et al.,5 the C24 homopolymer displays fast conformational dynamics, sampling a broad range of Rg values. Such fast conformational dynamics are expected from the relatively featureless free-energy landscape of this homopolymer at the
+ −
along the z direction for the three Ci24,j heteropolymers. We observe that the charged pair prefers to stay on the liquid side of the Gibbs dividing surface (GDS), defined by the halfdensity plane of water at z = 0. The density distributions of the charged and selected neutral groups shown in Figure 8A−C combined with snapshots of typical conformations of the heteropolymers obtained by the clustering of an ensemble of configurations from MD simulations using the Daura clustering algorithm32 provides insight into the different structures adopted by the polymers at the interface. The end-charged + − polymer, C124,24 , forms hairpinlike structures that lie parallel to the interface, where the hydrophobic parts of the polymer remain on the vapor side yet maintain their attractive +
−
+
,15 of polymers C24, C124,24 , C724,18 , and C10 at the vapor−liquid 24 interface. The MSD for the homopolymer, C24, is also shown in bulk water. MSD curves for heteropolymers in bulk water (not shown) are similar to that of C24. (B) 8-ns-long sample x − y trajectories of the
−
,15 , in which the charged groups interactions with water. C10 24 are closer to the center, also displays similar structures except + − that its ends are frayed. The C724,18 polymer adopts two different types of structures, as shown in Figure 8Da hairpinlike structure and a structure with a helical twist in it. The location of the center of mass of a heteropolymer is determined by the balance of the tendencies of charged groups
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+
−
+
−
+
−
,15 Figure 10. (A) Time dependence of Rg of C24, C124,24 , C724,18 , and C10 at the interface. (B) Autocorrelation function, CRg(t), for polymer Rg at the 24 +
−
+
−
,15 at the interface obtained from sample 100 ps MD interface. (C) Two hundred equally spaced configurations of polymers C124,24 and C10 24 trajectories, shown in a gray wireframe representation. A typical configuration is shown in space-fill, with the charged pair highlighted in red-blue.
interface. Whereas the hydrophobic homopolymers skate on the interface with low drag, the tendency of charged groups to remain hydrated pulls the heteropolymers toward the liquid side of the interface, thus pinning them, increasing drag, and slowing the translational dynamics. The conformational dynamics of heteropolymers are also slower than that of the homopolymer and depend on the location of the charged groups in the polymer sequence. Conformational dynamics are most restricted for the end-charged heteropolymer and speed up as the charge pair is moved toward the center of the sequence. Our results highlight the rich variety of structures and translational and conformational dynamics of simple hydrophobic and charged heteropolymer single molecules at a vapor−liquid interface. Given the ubiquity of aqueous interfaces in biological and nanoscopic systems, understanding the conformational behavior of more complex flexible molecules at interfaces will be an important direction to pursue. Although our work focused on the behavior of model single molecules, how many such molecules interact with each other and assemble will also be of interest in future studies.
vapor−liquid interface. The autocorrelation function, CRg(t), calculated from the time-series data of Rg, is a good measure of the conformational dynamics exhibited by the polymer. CRg(t) for the C24 homopolymer shows fast decay over a time scale of 50 ps (Figure 10B). In contrast, the conformational dynamics of heteropolymers are generally slower and depend on the exact location of charged groups within the polymer sequence. For + − example, in the C124,24 heteropolymer, the charged end groups form a strong contact resulting in a stable loop structure of the polymer. The Rg for this polymer shows occasional excursions to larger values; correspondingly, the autocorrelation function displays the slowest decay (Figure 10B). As the charged pair is moved toward the center, the free ends regain their dynamics, + − + − and the correlation time decrease from C124,24 to C724,18 to +
−
+
−
+
−
,15 C10 . Clusters of configurations of polymers C124,24 and 24 ,15 obtained from a 100 ps piece of sample trajectories C10 24 shown in Figure 10C highlight these ideas.
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CONCLUSIONS
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We presented results from extensive molecular dynamics simulations of hydrophobic/charged homopolymers and heteropolymers in bulk water and at the vapor−liquid interface of water. Our simulations show that charging a pair of monomers in an otherwise hydrophobic polymer can result in significant changes in its structure and dynamics at the interface. In bulk water, hydrophobic polymers fold into compact globular structures driven by hydrophobic interactions. Heteropolymers typically retain such compact structures, balancing the tendency of hydrophobic groups to form a core and charged groups to be solvated by water. At a vapor−liquid interface, hydrophobic polymers sample a broad ensemble of structures from folded to extended, consistent with an essentially flat conformational free-energy landscape. Adding a pair of charges to a hydrophobic polymer at the interface stabilizes hairpinlike structures, with the molecular details depending on the specific location of the charged pair in the polymer sequence. We rationalize these trends using the fundamental understanding of the effects of the vapor−liquid interface on the primitive pair-level interactions between two hydrophobic groups or between oppositely charged ions in its vicinity. The translational and conformational dynamics of homopolymers and heteropolymers are also different at the vapor−liquid
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We gratefully acknowledge financial support from NSF-CBET grants 1159990 and 0967937. We also thank Drs. Hari Acharya and Amish Patel for numerous useful discussions.
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REFERENCES
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