Collapse of a Hydrophobic Polymer in a Mixture of Denaturants

How osmolytes influence hydrophobic polymer conformations: A unified view from experiment and theory. Jagannath Mondal , Duncan Halverson , Isaac T. S...
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Collapse of a Hydrophobic Polymer in a Mixture of Denaturants Payel Das,*,† Zhen Xia,†,‡ and Ruhong Zhou*,†,§ †

Computational Biology Center, IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, United States Department of Biomedical Engineering, University of Texas at Austin, Austin, Texas 78712, United States § Department of Chemistry, Columbia University, New York, New York 10027, United States ‡

S Supporting Information *

ABSTRACT: The solvent quality of an aqueous mixture of two good solvents, urea and guanidinium chloride (GdmCl), for a hydrophobic polymer was investigated using atomistic molecular dynamics simulations. A counterintuitive collapse of the polymer was found, suggesting that mixing the two denaturants reduces the solvent quality. This cononsolvency of the polymer in the urea + GdmCl mixture is found to be caused by the preferential adsorption of urea on the polymer. The polymer collapses as a result of indirect long-range interactions between monomers resulting from the presence of urea clouds surrounding them. Surprisingly, urea behaves as the better solvent in the mixture not because there exists a stronger affinity of the polymer for urea. Instead, attractive interactions between two unlike denaturant molecules combined with the direct dispersion interactions of the polymer with both denaturants determine the solvent quality of the mixture.

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INTRODUCTION Solvent-quality-induced changes in the polymer chain dimension1−3 have long been a subject of active research. In particular, the coil-to-globule transition behavior of a hydrophobic polymer in water is central to understanding protein folding (refs 4 and 5 and references therein). Water is a poor solvent for proteins, leading to chain compaction due to hydrophobic interactions. In contrast, denaturants6−8 such as urea and guanidinium chloride (GdmCl) act as good solvents in which proteins behave as extended random-coil-like polymers. Understanding the molecular mechanism by which proteins and simple hydrophobic polymers undergo the solvent-qualityinduced coil-to-globule transition has recently received much attention.9−16 For example, recent molecular dynamics simulations underscore the importance of direct van der Waals (vdW) interactions between hydrophobic groups and denaturant (urea/GdmCl) molecules in the unfolding mechanism of a polymer or a protein.17−20 However, the behavior of the polymer/protein chain in an aqueous mixture of two good solvents (i.e., denaturants) remains largely unexplored. An even more rich conformational behavior is expected when a protein/ polymer is immersed in such a mixture. Understanding the solvent quality of mixtures has practical implications in both biology21,22 and materials science (ref 23 and references therein). The aim of this study is to investigate the solvent quality of a mixture of urea and GdmCl in molecular detail. To avoid the complexities arising from the chemical heterogeneities of a real protein, we use a simple proteinlike hydrophobic homopolymer that undergoes a coil-to-globule transition in pure water and unfolds in either of the single denaturants. Does mixing urea © 2013 American Chemical Society

with guanidinium have no net effect on the solvent quality or make the resulting solvent even better? The solvent quality of a mixture of two good solvents with slightly different solvent quality can also become poorer, which is known as cononsolvency.24−27 Given that guanidinium and urea have distinct chemical natures and slightly different affinities for hydrophobic moieties,28,29 the competition between urea and Gdm+ for monomer sites combined with the interactions between two unlike denaturant molecules may lead to unexpected changes in the solvent quality upon mixing. To investigate to what extent, if any, and how the urea− GdmCl mixture affects the conformational landscape of a hydrophobic polymer, we performed unconstrained atomistic molecular dynamics simulations of the polymer immersed in aqueous mixtures of urea and GdmCl. Counterintuitive chain compaction was found in the mixture. Further analysis reveals that this cononsolvency is induced by the preferential adsorption of urea on the polymer. The resulting collapsed conformations in the mixture show urea binding to more monomer sites, suggesting the formation of effective long-range attractive interactions between monomers as a result of the presence of urea clouds surrounding them. To our surprise, urea behaves as the better solvent in the mixture not because there exits a stronger affinity of the polymer for urea. Instead, the attractive electrostatic interactions between urea and Gdm+ combined with the locally enhanced Gdm population near the polymer (resulting from the polymer−Gdm direct binding) act Received: November 20, 2012 Revised: March 11, 2013 Published: March 21, 2013 4877

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Figure 1. Collapse of a hydrophobic polymer in 6 M aqueous mixtures of urea and GdmCl. (a) Comparison of the probability distribution of the radius of gyration of polymer in pure water, single denaturant solutions, and mixtures of urea and GdmCl. Snapshots of collapsed (Rg = 4.3 Å), semicompact (Rg = 6.5 Å), and extended (Rg = 10.7 Å) polymer conformations are shown. (b) Radial distribution functions between polymer beads and carbon atom of urea−Gdm molecules in pure denaturant solutions and in an equimolar mixture of urea and GdmCl. (c, d) Solvent reorganization in the first solvation shell of polymer during a typical collapse event in the equimolar mixture. The dashed line shows an unfolded conformation (Rg = 10.2 Å) and the corresponding number of bound urea (black) and Gdm+ (red) in the FSS. The snapshot of the corresponding polymer is also shown. Bound urea molecules are shown in red, and Gdm+ cations are shown in green. atm with a Berendsen thermostat and barostat). All simulations were performed using the NAMD2 molecular dynamics program32 with the IBM Blue Gene supercomputer. The CHARMM force field (c32b1 parameter set)33 is used in the current study for the urea and GdmCl denaturants. For the Gdm cation, parameters corresponding to the arginine side chain from the c32b1 parameter set were used. A modified TIP3P water model was used for water with its bond lengths constrained with SHAKE/RATTLE. The uncharged homopolymer interacts with the solvent through the typical Lennard-Jones 12−6 potential with the same combining rules as implemented in the CHARMM force field. The long-range electrostatic interactions were treated with the particle mesh Ewald method (updated for every time step), and a typical 12 Å cutoff was used for the vdW interactions. The time step for all production runs was 2 fs. The minimum of the first peak in the gP‑CX(r) radial distribution function (RDF) plots is used to define the FSS of the polymer for both denaturants, which is 6.5 Å.

as the driving forces underlying the preferential adsorption of urea onto the polymer, leading to its collapse.

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MODEL AND METHODS

The hydrophobic polymer studied here is composed of a linear chain of 32 uncharged monomers in which each monomer is presented with a single bead with a mass equal to that of carbon. Each bead is covalently bonded to its nearest neighbor by a harmonic potential, Vb = Kb(r − r0)2, with a force constant Kb = 400 kcal/Å2/mol and an equilibrium bond length r0 = 1.53 Å (similar to the CH2−CH2 bond length). Nonbonded pairwise interactions between a bead and its first and second nearest neighbors were excluded. No bond angle and no dihedral interactions were included to make the polymer more flexible. Turning off the bond angle and dihedral potential provides higher conformational flexibility to the polymer. Similar polymer models in water and in mixed solutions (including binary cosolvent−water mixture) have been employed in previous simulation studies.17,30,31 The size of an individual monomer is set to 4 Å, and the pairwise monomer−monomer interaction strength, εmm, is equal to 0.24 kcal/ mol. Thus, the resulting model polymer represents a flexibly jointed 32-mer chain composed of monomers sized between methane and ethane. The polymer was immersed in a ∼40 Å × 40 Å × 40 Å box containing either pure water (∼1650 water molecules) or single aqueous denaturant solutions of 6 M urea or 6 M GdmCl (183 denaturant and ∼1200 water molecules). The polymer was also immersed in a box containing a mixture of aqueous denaturant solutions with varying relative concentrations of urea and GdmCl. A total of three different mixed urea−GdmCl denaturant solutions were studied: (1) 4 M urea + 2 M GdmCl, (2) 3 M urea + 3 M GdmCl, and (3) 2 M urea + 4 M GdmCl. The initial state of the polymer in all denaturant solutions was taken to be the folded compact state, which was the most populated structure in pure water. For each system, we generated at least five independent trajectories, with each being about a 100−400-ns-long simulation in the NPT ensemble (at 300 K and 1

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RESULTS AND DISCUSSION Figure 1a shows the normalized distributions of the radius of gyration, Rg, of the polymer in water as well as in different aqueous denaturant solutions (single and mixture). The major populated state of the polymer in water is a compact folded state (Rg = ∼4.4 Å, also see Figure S1). During the course of simulation in water, the polymer infrequently visits the extended conformation with Rg > 8 Å as well as an intermediate semicompact conformation with Rg = ∼6 Å, which resembles a hairpin conformation. Snapshots of folded helical, semicompact hairpinlike, and extended conformations are also displayed in Figure 1a. The initial state of the polymer in all denaturant solutions was taken to be the folded compact state, which was the mostly populated structure in pure water. The probability of visiting the unfolded state (with Rg > 8 Å) becomes significantly 4878

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both denaturants, which is at 6.5 Å. The plots in Figure 1c,d clearly show a major solvent reorganization taking place in the vicinity of the polymer during the collapse: the number of urea molecules noticeably increases while some of the bound Gdm+ is excluded from the FSS of the polymer. Consequently, the ratio of the number of urea to Gdm molecules, ρU/G, in the FSS becomes >3 during the collapse. A typical snapshot of an unfolded polymer configuration prior to the collapse also reveals formation of local urea clouds around the polymer (Figure 1d). This result implies that the polymer collapse is triggered by the preferential adsorption of urea in the mixture. In the following text, we quantify how the preferential adsorption of urea is affected by the presence of Gdm+ in the solution. For this purpose, we estimated the average number of bound denaturant molecules in the FSS of extended polymer conformations as a function of the Gdm mole fraction. Figure 2a shows that the solvent composition inside the polymer coil region is very different (does not follow Henry’s law) from the

greater when the polymer is immersed in either 6 M urea or 6 M GdmCl solutions than in water (Figure 1a and S1). It is noteworthy that the hairpinlike state is more accessible in 6 M urea than in either pure water or 6 M GdmCl. The counterintuitive behavior of the polymer is noticed in all of the mixtures of denaturants, in which the probability of visiting an extended conformation becomes noticeably lower compared to that of single denaturant solutions (Figure 1a and SI). Figure 1a also reveals a clear trend: as the relative concentration of GdmCl increases in the mixture, the unfolded state is less visited. Consistently, the average Rg shows a minimum in the 4 M GdmCl + 2 M urea mixture (Table 1 in SI). (From a rough fitting of the data, it appears that the average Rg is lowest when the Gdm+ mole fraction in the mixture is ∼0.8. However, the absolute composition of the mixture in which the average Rg shows a minimum is not critical, and our main findings do not depend on that.) These results suggest that although both single denaturant solutions are good solvents for the polymer, the mixture of the two denaturants acts as a cononsolvent pair for the hydrophobic polymer. Our results are qualitatively robust against the simulation length, as shown by the longer (∼400 ns) trajectory data (Figure S2). The number of folding−unfolding transitions observed during the simulation (Figure S2) strongly suggests that the simulation length used in this study is likely sufficient for the problem under study. In addition, the typical aggregate simulation time for each of the systems (polymer + different mixture of urea and GdmCl) was 1 μs or longer. Nevertheless, enhanced sampling methods, such as a weighted histogram,34 replica exchange,35 and metadynamics36 can also be used to study similar problems efficiently. Furthermore, the fluxtempered metadynamics method,37 a recently proposed sampling method in which local diffusivity information along the order parameter(s) of interest is combined with typical metadynamics, has been shown to generate accurate and efficient conformational sampling. Below, we present an analysis to understand the underlying mechanism of the cononsolvency of the polymer in mixed denaturants. In this context, we use the concept of preferential adsorption that can be defined as the change in the degree of binding of solvent A by the addition of solvent B to an A + B binary solvent mixture. For simplicity, we focus on the system containing polymer solvated in an equimolar mixture of urea and GdmCl in the following text, unless otherwise explicitly stated. To compare the affinity of urea and guanidinium molecules to the polymer, we plot in Figure 1b the gP‑CU(r) and gP‑CG(r) RDFs computed using the unfolded conformations that respectively show the distributions of carbon atoms of urea and guanidinium molecules around the beads of the unfolded polymer. The figures corresponding to the single denaturant solutions indicate the preferential binding of both denaturants, consistent with earlier studies.17−19 In the mixture of denaturants, the gP‑CU(r) RDF clearly shows a significant height increase of the magnitude of the first peak compared to that in 6 M urea solution, implying the preferential adsorption of urea. The role of preferential absorption of urea in driving polymer collapse is then inspected in the mixed denaturant solution. For this purpose, we estimated the number of bound denaturant molecules in the first solvation shell (FSS) of the polymer during a collapse transition (characterized by a decrease in Rg from >8 Å to 3 during collapse in the equimolar mixture, suggesting that the size of the urea cloud is large enough to induce chain compaction. Next, we investigate the molecular interactions underlying the observed preferential absorption of urea in the mixed denaturant solution. Because the polymer has no charge, the only interaction present between polymer and either denaturant molecule is solely van der Waals in nature. The normalized distributions of interaction energies of denaturant molecules (urea/Gdm) in the FSS with polymer show that Gdm has a slightly stronger interaction energy (peak at ∼−2.9 kcal/mol) with the polymer than does urea (peak at ∼−2.2 kcal/mol) in either mixture or in single denaturants (Figure S3). Clearly, this stronger polymer−Gdm interaction cannot explain the preferential adsorption of urea in the mixture. Thus, the preferential adsorption of urea must originate from the solvent−solvent interactions. We next estimated both vdW and electrostatic interaction energies between urea molecules in the FSS of the polymer and in the bulk (defined as 10 Å away from any monomer bead) with the rest of the system for the pure 6 M solution and the equimolar mixture. A spherical cutoff of 13.0 Å for the vdW potential was used in this calculation, whereas no cutoff was applied for the electrostatic interaction. The vdW interaction energy distributions in the FSS and bulk do not show any significant change (in terms of peak position and magnitude) in the mixture compared to the pure solution

Figure 3. Interaction energy (in kcal/mol) distribution of urea. Probability distributions of (a) vdW energies and (b) electrostatic energies of urea with rest of the system in the FSS (solid line) and in the bulk (dashed line). Black lines correspond to the equimolar mixture, and red lines correspond to the pure 6 M urea solution. (c) Electrostatic interaction energies of urea with Gdm only in FSS (solid line) and in the bulk (dashed line) in the equimolar mixture.

guanidinium (Figure 3b). In the mixture, urea in the bulk has a broader electrostatic energy distribution with a peak at lower energy (peak at ∼−24.5 kcal/mol) compared to the pure solution (peak at ∼−23.5 kcal/mol). In the FSS, the peak of the distribution further shifts to a lower energy value (∼−25.5 kcal/mol), and the same for the single denaturant solution remains unperturbed. In addition, the distribution of FSS in the mixture becomes narrower with a smaller fraction of urea having a higher energy. These findings suggest that each urea molecule in the bulk of the mixture gains ∼1 kcal/mol electrostatic energy on average compared to the 6 M urea solution. Whereas there is no net electrostatic energy gain for urea moving from bulk to FSS in the 6 M urea solution, in the mixture each urea further gains another ∼1 kcal/mol electrostatic energy on average. To confirm the molecular origin of this electrostatic stabilization of urea in mixture, we further estimated the electrostatic interaction energies of urea in the FSS and in bulk with Gdm only. Figure 3c confirms that there exist attractive 4880

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adsorption of the better solvent do not necessarily lie in the preferential affinity. Instead, attractive interactions between two solvent components can be the driving factor.

electrostatic interactions between urea and Gdm in the bulk (distribution peak at ∼−4.3 kcal/mol). In fact, the osmotic coefficient behavior of aqueous mixtures containing urea and GdmCl suggests the existence of such a favorable interaction between those two denaturants.39 In the FSS of the polymer in the mixture, the electrostatic stabilization of urea is even more pronounced as suggested by the shift in peak location and magnitude. Consistently, the average electrostatic interaction energy of urea with guanidinium in the FSS is ∼−5.0 kcal/mol compared to ∼−2.9 kcal/mol in the bulk. Such additional stabilization of urea in the vicinity of the polymer is likely due to the enhanced local concentration of Gdm molecules, which is a consequence of the polymer−Gdm direct dispersion interaction (Figure S3). Thus, our results suggest a novel mechanism for the preferential adsorption of urea on hydrophobic polymer in the mixture, which is not solely driven by the stronger polymer−urea binding (the polymer still binds Gdm+ more strongly). Instead, the enhanced population of urea in the FSS is a combined consequence of its attractive electrostatic interactions with Gdm and the direct dispersion interaction of the polymer with both denaturants. The higher concentration of Gdm as a result of its direct dispersion interaction with polymer attracts more urea molecules (in addition to those directly bound with polymer already) in the FSS, resulting in the unexpected preferential adsorption of urea on the polymer in the mixture. Consequently, the polymer collapses as a result of the indirect long-range interactions between monomers as a result of the presence of urea clouds surrounding them. More importantly, burying a urea molecule inside the hydrophobic core contacting multiple sites of the polymer chain is favorable (similar to the urea dry globules for proteins in urea19), but burying a charged Gdm is not. Thus, the preferential adsorption of urea near the polymer is still a result of direct interactions of polymer with both Gdm and urea. If this is an indirect mechanism, we should observe a clustered urea near Gdm in pure solution, which is not the caseurea and Gdm mix very well. Preferential-adsorption-induced polymer collapse23,40 was first predicted by Shultz−Flory41 and Brochard−de Gennes38 theories. The collapse of a polymer chain in a critical mixture of two good solvents was first considered by Brochard and de Gennes,38 whereas Shultz−Flory theory41 predicts that such chain compaction can also occur in a mixture of two good solvents far from the critical temperature. These effects were later observed in the Monte Carlo lattice simulations by Magda et al.42 According to the Shultz−Flory theory,41 the effective polymer (P)−solvent interaction parameter χ for an equimolar A + B mixture depends on polymer−solvent affinities as well as interactions between solvents themselves because χ can be expressed as χ = 0.5(χAP + χBP) − 0.25χAB + (((χAP − χBP)2)/ (4.0(2.0 − χAB))). Interactions between polymer and solvent and solvent molecules themselves result in the redistribution of solvent molecules and shift the solvent composition near the polymer compared to that in the bulk. Such microscopic changes in the solvent may not be explained in terms of the changes in bulk properties. However, in the literature the cononsolvency due to preferential adsorption has been primarily attributed to the preferential affinity of polymer for one solvent over the other.23 Recently, we have also proposed using large-scale molecular simulations in which proteins may undergo non-native collapse in urea + GdmCl mixtures because of their preferential affinity for Gdm+.43 On the contrary, this study suggests that the molecular forces for the preferential

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CONCLUSIONS Using molecular dynamics simulations, we characterize the solvent quality of the mixture of two protein denaturants, urea and GdmCl, for a hydrophobic 32-mer homopolymer. The counterintuitive noncosolvency of the polymer in the mixture is revealed, which is induced by the preferential adsorption of urea on the polymer. Consistent with earlier theories and lattice simulations, our simulations provide a realistic picture of the polymer collapse in the mixture. The polymer collapses, resulting from the effective long-range interaction between monomers mediated by urea clouds. Further analysis reveals a novel mechanism for the preferential adsorption of urea, which is not directly determined by the polymer−urea interactions. Instead, a complex interplay of polymer−solvent affinities and solvent−solvent interactions appears to be the driving force. The preferential adsorption of urea occurs because of the combined effect of two factors: (i) direct dispersion interactions of urea and Gdm+ with polymer and (ii) attractive electrostatic interactions between urea and Gdm+. Consequently, the higher concentration of Gdm+ near the polymer attracts more urea molecules (in addition to those directly bound to polymer already) near the polymer. These findings underline the importance of interactions between two solvent components in determining the solvent quality of the mixture. We believe that these results have implications in the conformational preferences of proteins as well as polymers in the mixture of two good solvents.

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ASSOCIATED CONTENT

S Supporting Information *

Collapse of a hydrophobic polymer in mixtures of denaturants. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Eugene Shakhnovich and Bruce Berne for useful discussions. This work is supported by the IBM Blue Gene Science program.

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REFERENCES

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