How Does a Hydrophobic Macromolecule Respond to a Mixed

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How Does a Hydrophobic Macromolecule Respond to Mixed Osmolyte Environment? Indrajit Tah, and Jagannath Mondal J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b08378 • Publication Date (Web): 04 Oct 2016 Downloaded from http://pubs.acs.org on October 7, 2016

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The Journal of Physical Chemistry

How Does a Hydrophobic Macromolecule Respond to Mixed Osmolyte Environment? Indrajit Tah and Jagannath Mondal∗ Tata Institute of Fundamental Research, Center for Interdisciplinary sciences, 21 Brundavan Colony, Narsingi, Hyderabad, India E-mail: [email protected],+914024195021 Abstract The role of the protecting osmolyte Trimethyl N-oxide (TMAO) in counteracting the denaturing effect of urea on a protein is quite well established. However, the mechanistic role of osmolytes on the hydrophobic interaction underlying protein folding is a topic of contention and is emerging as a key area of biophysical interest. Although recent experiment and computer simulation have established that individual aqueous solution of TMAO and urea respectively stabilizes and destabilizes the collapsed conformation of a hydrophobic polymer, it remains to be explored how a mixed aqueous solution of protecting and denaturing osmolytes influences the conformations of the polymer. In order to bridge the gap, we have simulated the conformational behavior of both a model hydrophobic polymer and a synthetic polymer polystyrene in an aqueous mixture of TMAO and urea. Intriguingly, our free energy based simulations on both the systems show that even though a pure aqueous solution of TMAO stabilizes the collapsed or globular conformation of the hydrophobic polymer, addition of TMAO to an aqueous solution of urea further destabilizes the collapsed conformation of the hydrophobic polymer. We also observe that the extent of destabilization in a mixed osmolyte solution is relatively higher than that in pure aqueous urea solution.

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The reinforcement of the denaturation effect of the hydrophobic macromolecule in a mixed osmolyte solution is in stark contrast to the well-known counteracting role of TMAO in proteins under denaturing condition of urea. In both model and realistic systems, our results show that in a mixed aqueous solution, greater number of cosolutes preferentially bind to the extended conformation of the polymer relative to that in the collapsed conformation, thereby complying with Tanford-Wyman preferential solvation theory disfavoring the collapsed conformation. The results are robust across a range of osmolyte concentrations and multiple cosolute forcefields. Our findings unequivocally imply that the action of mixed osmolyte solution on hydrophobic polymer is significantly distinct from that of proteins.


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Introduction Various organisms utilize a class of small aqueous cosolutes known as osmolytes 1–8 to cope up with the osmotic stress. Trimethyl N-oxide (TMAO) 9 is one of the natural osmolytes found in various marine animals. As a protecting osmolyte, TMAO is known to stabilize the conformational structure of proteins by counteracting the action of a denaturing osmolyte, such as urea. 1,10–13 However, the role of osmolytes on the hydrophobic interaction, the major driving force underlying protein conformation, have only started to garner significant attention recently. Initial works on action of osmolytes on hydrophobic interaction have focussed on understanding, via simulation and experiments, the effect of an aqueous osmolyte solution of a hydrophobic macromolecule. 14–18 The prevalent findings suggest that, the globular or so-called collapsed conformation of the macromolecule is stabilized at a low 19 TMAO concentration and destabilized at high urea concentration. However, the question remains how an aqueous mixture of protecting and denaturing osmolyte can influence the collapse behavior of a hydrophobic polymer. Here we show, using extensive free-energy-based computer simulation of a model polymer and a synthetic polymer polystyrene, that while the individual solution of TMAO and urea respectively stabilize and destabilize the collapsed conformation of a polymer, a mixed environment of both the osmolytes further destabilizes the collapsed conformation, even compared to that in an individual aqueous solution of urea. These observations are in line with the seminal theories of preferential binding by Tanford and Wyman and imply that the action of mixed osmolytes on hydrophobic macromolecules are distinctly different from that of a protein. Over the years, numerous experimental 20–29 and theoretical studies 14–16,30–32 have focussed majorly on proteins and sparingly on other macromolecules in single or mixedcomponent osmolyte solutions involving TMAO as a protecting osmolyte and urea as a denaturing osmolyte, resulting in hypothesis of different direct/indirect mechanisms and contradictory conclusions. In case of proteins, it is now established that TMAO counteracts the denaturing effect of urea towards protein but the mechanistic details have differed 3 ACS Paragon Plus Environment


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in many studies. Both indirect osmolyte-water induced mechanism 33–36 and direct proteinosmolyte induced interaction 14,30–32,37–39 have been hypothesized by experiments and theory. One of the most prevalent hypotheses in the counteraction role of TMAO has been the preferential exclusion of TMAO from the surface of the protein 37,38,40 and the preferential binding of urea on the surface of protein. Overall, majority of the aforementioned works on proteins in a mixed solvent environment have suggested that the two opposing osmolytes’ actions are independent of each other and counter-active in nature. However, on the contrary, Ganguly et al 32 has shown that urea and TMAO are mutually excluded from protein surfaces, accompanied with an increase of osmolyte-osmolyte aggregation, which points to a non-additive, mixed-osmolyte effect. Proteins are generally comprised of heterogenous amino acids and hence isolating individual contributions to a solvent induced change in stability is a difficult task. Towards this end, homopolymers are better suited, which gives an incentive for exploring the action of osmolytes on hydrophobic interaction, one of the central driving forces for protein folding. Initial works on action of osmolytes on hydrophobic interaction had focussed on simulating an aqueous osmolyte solution of homopolymeric chain whose hydrophobicity can be controlled by tuning the dispersion interactions. 14–18 Recently, one of us 30 have systematically explored the collapse behavior of a model Lennard-Jones homopolymers with a controllable dispersion interaction in aqueous solutions of TMAO and urea. The work by Mondal et al 30 had shown that, at a high polymer dispersion interaction and low TMAO concentration, 19 aqueous TMAO acts to stabilize and aqueous urea acts to destabilize the globular structure of the model polymers, as observed in proteins. However, it was found that both urea and TMAO strongly bind to the polymer surface, in contrast to TMAO’s so-called exclusion mechanism from the protein surface. In compliance with the classic theories of Tanford and Wyman, 2,3 Mondal et al’s 30 study highlighted that it is actually the relative difference in preferential binding of osmolytes between collapsed and extended state, rather than the absolute magnitude of preferential binding in either state, which needs to be considered in


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a proper treatment of osmolyte mediated polymer collapse. This work later stimulated a collaboration 31 of single molecule force spectroscopy experiment by Walker group and MD simulation by Berne group to investigate the effect of TMAO and urea on a synthetic hydrophobic polymer polystyrene, which lent credence to the predictions made by the Mondal et al 30 for the model polymer. However, most of the reported works investigating the role of osmolytes on hydrophobic macromolecules have either studied the action of pure aqueous solution of TMAO or pure aqueous solution of urea on the hydrophobic polymer. But, how would a hydrophobic macromolecule conformationally behave in a mixed aqueous solution of TMAO and urea? To bridge this gap, in the present work, we computationally investigate the behavior of a single hydrophobic polymer chain in a mixed aqueous solution of TMAO and urea. Specifically, we have simulated the conformational behavior of both the model hydrophobic polymer and synthetic hydrophobic polymer polystyrene,, 30,31 in a mixed aqueous environment of TMAO and urea and compared the results with that in an aqueous media of pure TMAO or pure urea. Our results are consistent with Wyman-Tanford theory 2,3 of preferential binding of cosolute over solvent towards macromolecules. The robustness of the results has been validated across multiple combination of osmolyte-mixtures of varying concentration, variable polymer-dispersion interactions and the variation of TMAO forcefield. The remainder of the manuscript is organized as follows: The methods section describes the details of molecular models and computational methodology in two independent subsections. The results section is divided into three subsections. The first subsection of results describes our simulated result on action of mixtures of osmolytes on a model polymer and tests the robustness of the result at multiple different combinations of the osmolyte mixtures and the polymer dispersion interactions. The second subsection provides a molecular-level mechanistic interpretation of the observed result using the theory of preferential solvation. The third subsection validates the underlying principle using a synthetic polymer namely polystyrene in a mixed solvent media. Finally, the conclusions and outlook section provides



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an overview of our conclusions and possible biophysical implications.

Material and Methodology Simulation model: We have simulated two different systems in the current work: A model bead-on-a-spring polymer chain ( 32 beads) ( Figure 1a)) and a synthetic polymer namely 20-mer of polystyrene (Figure 1b)) in different aqueous media of osmolytes. Both of the systems have been previously studied by Mondal et al 30,31 extensively in the context of osmolyte-polymer interaction and the details of the models can be found else-where. 16,30,31 Here we provide a brief overview of the models.

a)

b)

Figure 1: A representative configuration of two systems of hydrophobic macromolecule studied in the manuscript: a) model polymer in extended configuration ( orange colored) and b) 20-mer of polystyrene in an aqueous mixture of TMAO (red colored) and urea (green colored).Water molecules are represented by blue dots. Briefly, the model polymer beads are uncharged and interact with the surrounding particles via dispersion interactions modelled using Lennard-Jones potential. The bead diameter σ is 0.4 nm. The hydrophobic character of the polymer is tuned via varying Lennard Jones interaction energy b . In this work, majority of the simulation has been performed by using b = 1.0 kJ/mol. However, we have also checked for the robustness of our result by using 6 ACS Paragon Plus Environment

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an alternative b = 0.6 kJ/mol. The beads are connected by harmonic bond and harmonic angle, the values of which can be found in the previous works of Mondal et al 30 and Zangi et all 16 . Apart from the bond and the angle restraints, the 1-4 nonbonding interaction is also present among the beads. We have simulated water molecules via SPC/E model, 41 urea via Kirkwood-Buff potential, 42 and TMAO using the forcefield developed by shea and coworkers 32,43 which is considered an improvement over Kast forcefield. 44 We have nevertheless validated our result via repeating the simulation using two other forcefields of TMAO developed by Kast et al 44 and Netz and coworkers. 32,45 The geometric combining rules were used to model the intermediate interactions of both and σ. We have simulated a total of ten different osmolyte compositions by inserting necessary number of TMAO, urea and water molecules in a box consisting of polymer: polymer solvated in a) neat water, b) 0.5 M aqueous TMAO solution, c) 1 M aqueous TMAO, d) 1M aqueous urea solution, e) 4.5 M aqueous urea solution f) 7M aqueous urea solution, g) aqueous mixture of 0.5 M TMAO + 4.5 M urea, h) aqueous mixture of 1 M TMAO + 1 M urea solution i) aqueous mixture of 1M TMAO + 4.5M urea, j) aqueous mixtures of 1M TMAO+7M urea and investigated the polymer conformational behavior in the respective mixtures. The approximate box dimension of the system, after energy minimization and NPT equilibration, ranged from 5.5 nm to 5.8 nm. In the second part of the work, We have also simulated a synthetic hydrophobic polymer namely a 20mer of polystyrene, previously simulated by Mondal et al. 31 To be consistent with previous work , we have used the identical parameter and concentration for polystyrene, TMAO, water and urea, as used previously. In this case, 4 different systems were simulated by inserting necessary number of TMAO, urea and water molecules : 20-mer of polystyrene solvated in a) neat water, b) 1 M aqueous TMAO, c) 7 M aqueous urea and d) aqueous mixture of 1 M TMAO + 7 M urea. The approximate box dimension of the system after energy minimization and NPT equilibration ranged from 6 to 6.5 nm. Simulation Method : The majority of the simulation efforts was invested in obtaining



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free energy landscape of polymer conformation (both model Lennard Jones-polymer and polystyrene) along the radius of gyration of the polymer in each of the aforementioned osmolyte solutions. Towards this end, we have performed umbrella sampling simulations 46 using radius of gyration of the polymer as a collective variable. To generate the representative configurations required for each of the so-called ’umbrella sampling windows’, we first performed independent equilibrium Molecular Dynamics simulations for 100 ns at constant pressure of 1 bar and temperature of 300 K, starting with an extended all-trans configuration of the polymer. To avoid any bias and to supplement any missing configurations for subsequent umbrella sampling simulations, these simulations were also repeated starting with a collapsed configuration of the polymer. For umbrella sampling simulations, the values of the radius of gyration ranged from 0.4 nm to 1.2 nm at a spacing of 0.05 nm for the model Lennard-Jones polymer and 0.700 nm to 1.6 nm at a spacing of 0.05 nm for 20-mer of polystyrene. Each of the umbrella sampling simulations started with configuration corresponding to desired radius of gyration, as obtained from the aforementioned equilibrium simulations. Then each of the configurations were subjected to a harmonic restraint to ensure a gaussian distribution of the radius of gyration around each desired value of the radius of gyration. Each of the umbrella sampling windows were sampled for 20 ns using NPT ensemble. We used Nose-Hoover thermostat 47,48 for maintaining the average temperature of 300 K and the Parrinello-Rahman barostat 49 for maintaining the average pressure of 1 bar. All the water molecules were simulated as rigid molecule using SETTLE algorithm. 50 Finally, Weighted Histogram Analysis Method ( WHAM) 51,52 was used over the last 10 ns of each of the umbrella sampled trajectories to generate unbiased histograms and the corresponding potentials of mean force or free energies. The total simulation length for all umbrella sampling simulations for each osmolyte solution was 340 ns for the model Lennard-Jones polymer ( and hence a total of 3.4 microsecond simulation for 10 different systems) and 380 ns for polystyrene chain. All simulations were performed using Gromacs 5.0.6 53 patched with Plumed 54 plugin to enable umbrella sampling


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simulation along the radius of gyration. We employed an experimentally relevant quantity called preferential binding coefficient (Γs ) 2,3 Nstot − ns · nw Γs = ns − tot Nw − nw

(1)

where ns is the number of cosolute ( urea or TMAO) called bound to the polymer and Nstot is the total number of cosolutes in the system. On the other hand, nw is the number of water molecules bound to the polymer and Nwtot is the total number of water molecules in the system. Γs quantifies the excess of cosolute molecules s in the polymer solvation shell as compared to its average concentration in the solution. We calculated the values of Kp and Γ as a function of distance from the polymer. Towards this end, we employed similar protocol as previously implemented by Mondal et al. 30,31 To compare the relative preferential binding of each of the cosolutes, we took the central atom (O for water, N for TMAO and C for Carbon) of the cosolutes, solvent and any polymer bead for which the distance is shortest. Towards this end, we carried out additional simulations which are as follows: To obtain better statistics, we froze the polymer either in the collapsed or in the extended conformation of the polymer and then simulated the systems for 15 ns and repeated for five independent velocity seeds (hence a total of 75 ns for each of the conformation). We have also verified the effect of the magnitude of force used to restrain the polymer in either collapsed or extended conformation by repeating the simulation in the presence of a weak harmonic force along the radius of gyration of polymer. As depicted in figure S1, we have found that the qualitative results hold good irrespective of the magnitude of restraints. The simulations were repeated for 15 ns in each of the collapsed and extended conformation of polymer for each osmolyte solutions. In each cases, Γs was averaged over these ensemble of trajectories, and the standard deviations were obtained via block averaging. The entire protocol was repeated for both the model 32-bead polymer and the 20-mer of polystyrene. We also have validated our result against another relevant quantity called local-bulk



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partition coefficient Kp , which is defined as 7

Kp =

hns i Nwtot · . hnw i Nstot

(2)

Here hnX i is the average number of molecules of type X bound to polymer and NXtot is the total number of molecules of type X in the system (where X = s stands for the cosolvent (urea or TMAO) and X = w stands for water). Kp is intensive and reflects the affinity of the cosolvent for the polymer regardless of the exposed surface area of the polymer.

Results and Discussion Effect of osmolyte mixtures on a model polymer Even though we have used multiple combinations of osmolytes, we first mainly focus on the conformational behavior of the model polymer in an aqueous mixture of 1 M TMAO and 4.5 M urea. Both concentrations are widely used to study the effects of the respective osmolytes in vitro and in silico, majorly based on the fact that a very low concentration of TMAO is known to counteract the action of high concentration of urea in a protein. Nevertheless, we have also explored multiple other concentrations of the osmolytes which are described in Method section and the relevant results will also be discussed in the aforementioned paragraphs. To quantitatively explore the entire conformational degrees of freedom, we simulate the free energy landscape of the polymer conformations by performing a series of umbrella sampling simulations along the radius of gyration of the polymer, in individual solution namely neat water, an aqueous solution of 1M TMAO, aqueous solution of 4.5 M urea and finally a mixed osmolyte solution of 1M TMAO and 4.5 M urea. Figure 2a and 2b compares the free energy landscape and the corresponding probability distributions of the polymer conformations along the radius of gyration in each of the aforementioned solutions.


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b)

a)

εb = 1.0 kJ/mol

Figure 2: (a) Potentials of mean force and (b) corresponding probability distribution along radius of gyration for polymer chain with an b = 1.0 kJ/mol. The representative polymer configurations corresponding to collapsed ( Rg ∼ 0.45 nm), hairpin (Rg ∼ 0.60 nm) and extended ( Rg ∼ 1.0 nm) conformations which are the locations of major basins. As evident from figure 2a and 2b, in all aqueous media, the free energetically most favorable conformation of polymer corresponds to a collapsed conformation ( Rg ∼ 0.45 nm), which is representative of a hydrophobic polymer, along with a local basin corresponding to the extended conformation ( Rg ∼ 1.0 nm ) and a local intermediate representing a semicompact hairpin conformation ( Rg ∼ 0.6 nm). However, as gleaned from the computed free energy profiles in figure 2 a, the extent of relative free energy barrier to extended conformation is systematically influenced by different osmolyte solution. Relative to neat water, the extended state gets more destabilized in 1M TMAO solution and gets more stabilized in 4.5 M urea solution, thereby apparently behaving like a protecting and denaturing osmolyte respectively, as is general trend in case of a globular protein. However, in a mixture of these two osmolyte solution ( 1M TMAO + 4.5M urea), the polymer extended state gets further stabilized, even compared to that in pure urea solution. The relative stabilization of the extended state of polymer in a mixed environment of osmolyte, even compared to that in pure urea solution implies that, in a mixed osmolyte solution, TMAO actually promotes the



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denaturation propensity of the polymer. This act of reinforcement of extended or unfolded state of a hydrophobic polymer by TMAO in a mixed osmolyte solution is distinctly different from well-known counteraction mechanism of TMAO and urea prevalent in proteins and thereby indicates a completely different mechanism that underlies a polymer in a mixed osmolyte solution. Our result is robust with respect to the change of osmolyte concentration in the mixture, different hydrophobicity of the polymer and variation of TMAO forcefield. Figure 3a delineates the concentration dependence of free energy profiles of polymer along radius of gyration, obtained using umbrella sampling techniques. As evident from the free energy profiles of the polymer in 0.5 M TMAO and 1 M TMAO in figure 3a, addition of TMAO molecules in neat water monotonically increases the free energy barrier to the extended conformation, thereby systematically destabilizing the polymer’s extended state relative to neat water. However, gradual addition of TMAO in an aqueous media of 4.5 M urea solution (thereby constituting mixed media of 0.5 M TMAO with 4.5 M urea and 1 M TMAO with 4.5 M urea) monotonically stabilizes the polymer’s extended state relative to that in pure urea solution. The overall result points to an interesting observation that addition of TMAO in neat water protects the hydrophobic polymer against unfolding while addition of TMAO in pure urea solution promotes the formation of extended state of the same polymer. The observed trend of further stabilization of the extended conformation in a mixed osmolyte media, relative to pure aqueous media holds qualitatively true with respect to the variation of urea concentration from 1M to 7M. As illustrated in figure S2 a) and b), both an aqueous mixture of 1M TMAO + 7M urea and an aqueous mixture of 1M TMAO + 1M urea stabilize the extended polymer conformation relative to individual aqueous osmolyte solution, thereby acting as a potentially stronger denaturing agent than the pure aqueous urea media. We note that we have not explored the TMAO concentration beyond 1M majorly because it has been recently observed 19 that pure aqueous TMAO itself acts as a denaturant at a higher concentration.


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b)

a)

εb=0.6 kJ/mol

ε =1.0 kJ/mol b

d)

c)

ε b=1.0 kJ/mol

εb=1.0 kJ/mol

Figure 3: (a)Concentration dependence of Potentials of mean force along polymer ( = 1.0 kJ/mol) radius of gyration using Shea et al’s 32,43 forcefield of TMAO . (b) Comparison of Potentials of mean force along the radius of gyration with b = 0.6 kJ/mol. Validation of robustness of trend of Potentials of mean force along polymer radius of gyration c) with Kast forcefield 44 of TMAO and d) with Netz forcefield 32,45 of TMAO with polymer dispersion interaction b = 1.0 kJ/mol. We have also explored the effect of polymer dispersion interaction in the overall trend of the free energy profile. As depicted in figure 3b, decreasing the polymer dispersion interaction from = 1 kJ/mol to 0.6 kJ/mol ( and thereby reducing the polymer-cosolvent interaction via combination rule) makes the extended conformation of the polymer freeenergetically most favorable configuration. However, the qualitative effect of mixed osmolyte media on the polymer free energy landscape remains the same, albeit weaker than that with = 1.0 kJ/mol. The overall trend qualitatively holds true even when repeating the simulation using two independent TMAO forcefields developed by Kast et al 44 of TMAO, ( figure 3c) 13 ACS Paragon Plus Environment


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and Netz and coworkers 32,45 (figure 3d).

Towards a preferential-solvation based molecular interpretation The aforementioned behavior of the hydrophobic polymer in different osmolyte solutions, although distinct from the precedent notion in protein, is in reasonable agreement with seminal Wyman-Tanford approach of preferential solvation. The Wyman-Tanford approach hypothesizes the preferential binding coefficient Γs (see equation 1) 2,3 as the key quantity to describe the dependence of the polymer conformational equilibria on cosolutes: Γs > 0 if the osmolyte preferentially accumulates next to the polymer and is < 0 if it is excluded from the polymer. Note that Γs is closely related to a frequently used parameter known as Kirkwood Buff integral. 32,42 The effect of preferential binding on a conformational equilibrium between the collapsed and the extended configurations C E (with an equilibrium constant K) is usually interpreted in terms of the thermodynamic analysis put forward by Wyman and Tanford, 2,3 which leads to ∂ ln K = ∆ΓC→E , ∂ ln as

(3)

where as is the activity of the cosolute in the binary solution. According to Eq. 3 and illustration of Figure 4a, an increase in the concentration of the cosolute would lead to the macromolecular unfolding if ∆Γ > 0, and in contrast would favor the folded state over the unfolded one if ∆Γ < 0. Figure 4b-d illustrates and compares the profiles of Γs as a function of distance from the polymer surface, for the collapsed and the extended state of polymer in different osmolyte solution. Irrespective of different osmolyte solution, we find Γs > 0 for both the collapsed and the extended conformation of the polymer at a relevant distance from the polymer close to first solvation shell of the polymer. In the context of the aforementioned approach of theory of preferential binding, Γs > 0 implies that both TMAO and urea preferentially binds to the polymer surface. However, the sign of ∆Γ i.e. the relative preferential binding of cosolutes in


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a)

b) ΔΓ < 0

k1 TMAO

k2 Collapsed (C)

Extended(E)

d)

ΔΓ > 0 (TMAO+Urea)

c) Urea

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ΔΓ > 0 aq media of 1 M TMAO + 4.5 M urea

Figure 4: (a) A schematic representation Wyman-Tanford theory of preferential binding coefficient relating ∆Γ with conformational equilibrium constant. Comparison of Profiles of Preferential binding coefficient of b) TMAO in 1 M TMAO solution, (c) urea in 4.5 M urea solution. (d) TMAO+urea in mixed aqueous solution of 1 M TMAO and 4.5 M urea solution as a function of the distance from the polymer surface ( b = 1.0 kJ/mol) in a collapsed (red) or extended (black) configuration. Vertical dashed lines indicate the positions of the polymer first solvation shell in each case (5.5 ˚ A), and the black arrows in panels b, c and d represent the relative sign of ∆Γ. collapsed versus extended conformation, is distinctly different in different osmolyte solution, which determines the direction of conformational equilibrium. As depicted in figure 4b, in aqueous TMAO solution, ∆Γ < 0, implying relatively higher preferential binding of TMAO in collapsed conformation, which promotes the stabilization of collapsed state of polymer relative to neat water. On the other hand, as reflected in figure 4c and d in both aqueous urea solution and mixed TMAO-Urea solution, ∆Γ > 0, implying relatively lower preferential binding of cosolutes ( only urea in case of aqueous urea solution and all constituent cosolutes ( TMAO and urea) in a mixed solution) in collapsed conformation. Hence, in accordance with Wyman-Tanford approach, collapsed conformation of polymer is



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destabilized in both pure urea and mixed TMAO-Urea solution, relative to neat water. In fact, higher value of ∆Γ in mixed osmolyte solution than that in pure urea solution suggests relatively higher extent of destabilization in mixed osmolyte solution than that in pure urea solution, which is consistent with our free-energy-based results. We note that, in the present work, in the case of mixed osmolyte solution, we have focussed on computing the preferential binding coefficient of the combination of TMAO + Urea. In other words, we have analyzed the cumulative preferential interaction of both TMAO and urea in order to discern their combined interaction on a polymer. We have never attempted to implement the WymanTanford relation to dissect the contribution arising due to only one of the two osmolytes in the mixture . Hence, in a mixture, we are using the Wyman-Tanford relation for effectively a two-component solvent mixtures , constituting of combination of TMAO + Urea as cosolute and water as solvent and hence Wyman-Tanford relation, in its current context, will hold fine. We also note that plausibility of extension of the Wyman-Tanford model to dissect the contribution of each of the cosolutes in a three-component mixture is worth exploring in a future work. We also quantified another relevant quantity local bulk partition coefficient (Kp ) which reflects the affinity of the cosolvent for the polymer regardless of the exposed surface area of the polymer. As shown in figure S3 in SI text, irrespective of osmolyte solution, Kp > 1, suggesting preferential binding of osmolytes on a polymer surface over water, complementing our finding based on Γ. More over, identical to the trend of Γ, relative to extended conformation, the local bulk partition coefficient of osmolyte in 1M TMAO solution is higher in collapsed conformation while lower in both 4.5M Urea and mixed solution of 1M TMAO and 4.5M Urea. Delving into the representative configuration of the collapsed and extended conformations of the polymer in its solvation shell provides us a better underlying picture of osmolyte’s action on polymer in different solution. As depicted in figure 5a, in aqueous TMAO solution, the first solvation shell of collapsed conformation has more TMAO molecules bound than


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that in extended conformation, mainly because of prospect of more hydrophobic contacts between hydrophobic methyl groups of TMAO and collapsed state of polymer chain. a)

c)

b)

d) 1M TMAO

4.5M Urea

1M TMAO + 4.5M Urea

Figure 5: Representative snapshots of respective cosolutes bound first solvation shell of polymer in collapsed and extended conformation: a) TMAO molecules in 1M TMAO b) urea molecules in 4.5M urea, c) TMAO and urea molecules in mixture of 1M TMAO and 4.5M urea. the snapshots corresponding to collapsed configurations are kept larger so as to delineate the solvation shell clearly. d) Comparison of radial distribution function of TMAO and urea in different osmolyte solutions. On the other hand, in aqueous urea solution, as represented by figure 5b, more urea molecules accumulate next to extended conformation than collapsed conformation, mainly due to favorable access to higher surface area. However, in a mixed osmolyte solution, urea preferentially occupies the first solvation shell of the polymer, leaving very less number of sites for TMAO to occupy the polymer-surface. As a result, as shown in figure 5c, in the presence of urea molecules, in a mixture, TMAO molecules have very little rooms for making significant TMAO-polymer hydrophobic contacts in collapsed conformation, unlike that in pure aqueous TMAO solution. On the other hand, presence of higher surface area in extended conformation provides more sites to TMAO molecules in a mixed osmolyte environment. This is also quantified by polymer-cosolute radial distribution function as well ( figure 5d). Consequently, the cumulative number of cosolutes ( i.e. TMAO and urea 17 ACS Paragon Plus Environment


combined) in extended conformation is relatively higher than that in collapsed conformation in a mixed osmolyte solution.

How does a mixed osmolyte solution act towards a real polymer? Our aforementioned finding of effect of osmolyte solutions on model lennard Jones polymer is in reasonable agreement with simulation of a synthetic polymer namely polystyrene (degrees of polymerization= 20) in different osmolyte solution.

a)

ΔΓ < 0

polystyrene in osmolyte solution TMAO

b) polystyrene in aq. TMAO

polystyrene in mixture of TMAO+urea

polystyrene in aq. urea

(TMAO+Urea)

c) Urea

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ΔΓ > 0

d) ΔΓ> 0

Figure 6: (a) Potentials of mean force along the radius of gyration for polystyrene in neat water, individual osmolyte solution and mixed osmolyte solution. Progression of preferential binding coefficient as a function of distance from polymer surface for b) TMAO in TMAO solution, c) urea in urea solution (d) (TMAO+urea) in mixed osmolyte solution. for b-d, both collapsed (red) or extended (black) configuration for polystyrene has been compared. Vertical dashed lines indicate the positions of the polymer first solvation shell in each case (5 ˚ A), and the black arrows in panels b, c and d represent the relevant sign of ∆Γ, thereby connecting the Wyman-Tanford theory with polymer conformational equilibrium.


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As depicted from the series of free energy profiles as a function of radius of gyration in figure 6a, the free energetically most stable conformation of the polystyrene chain corresponds to radius of gyration ∼ 0.750-0.800 nm, the so-called collapsed state of the polymer. However, the extent of stabilization of collapsed state of polystyrene relative to that of extended conformation is strongly dependent on the osmolyte composition of the solution. In commensurate with the aforementioned result of model polymer, the collapsed state of the polystyrene is relatively more stabilized in aqueous media of TMAO and less stabilized in aqueous solution of urea, relative to neat water. However, in a more striking agreement with the model polymer, addition of TMAO molecules to an aqueous solution of urea further destabilizes the collapsed state of the polystyrene, relative to aqueous media. Most importantly, the trend of preferential binding results in polystyrene are also in line with the Wyman-Tanford theory of preferential binding. As shown in figure 6b-d, the difference between the preferential binding coefficient of extended and collapsed configuration i.e. ∆Γ is negative in aqueous TMAO and positive in both aqueous urea and mixed solution of TMAO and urea, implying that, relative to neat water, collapsed conformation will be more stabilized in aqueous TMAO solution and more destabilized in aqueous urea and mixed solution of TMAO and urea solution.

Conclusions To conclude, our simulation results shed light on a unique role of mixed osmolyte solution on hydrophobic polymer, which is distinct from that in protein. The effect of osmolyte on macromolecule is usually investigated in protein and hence it is natural to compare the qualitative trend of our polymer-based result with the prevalent result of protein. In accordance with what is observed in protein, collapsed conformation of polymer is respectively stabilized and destabilized in aqueous solution of TMAO and aqueous solution of urea. However, the role of mixed solution of TMAO and urea is distinctly different in a hydrophobic polymer



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compared to that of protein : while TMAO is known to counteract the effect of urea in a protein, our simulation result with a hydrophobic polymer suggests that TMAO, in a mixed environment, will reinforce the effect of urea by further destabilizing the collapsed conformation of polymer. The Wyman-Tanford theory of preferential binding coefficient sheds light on the key difference in the molecular mechanism of osmolyte-polymer interaction compared to that of osmolyte-protein interaction. For protein, preferential binding coefficient Γ is found to be < 0 for TMAO while > 0 for urea, implying that TMAO preferentially excludes from the surface of protein while urea prefers to bind to the surface of protein. However, for a hydrophobic polymer, the preferential binding coefficient Γ is > 0 for both TMAO and urea, which suggests that both TMAO and urea would bind to polymer surface. We believe that the preferential binding of TMAO to a hydrophobic polymer in contrast to preferential exclusion of the same from a protein surface has key implication in the end result of the polymer conformational behavior in a mixture of TMAO and urea, compared to that of protein. We find that urea preferentially coats the polymer surface in a mixed osmolyte solution, which provides very little prospect for TMAO to make hydrophobic contacts in collapsed state, relative to that in extended conformation, which can accommodate more TMAO molecules due to the larger surface area. Hence, cumulative number of cosolute molecules close to the polymer surface is higher in extended conformation of polymer than that in collapsed conformation, giving rise to positive ∆Γ and hence destabilization of collapsed conformation relative to aqueous media of urea solution. We hope that our current work on conformational behavior of hydrophobic polymer in a mixed osmolyte solution will stimulate novel experiments and theoretical efforts to dissect and understand the osmolyte-macromolecule interaction in the context of hydrophobic interaction. We also note that in a similar context, the mutually enhancing effect of TMAO and urea on denaturation` u has also recently been observed by Ganguly et al 39 where it is shown that TMAO at high concentration reduces hydrophobic aggregation and while a mixed osmolyte solution of TMAO and urea reduces the aggregation further. Moreover, recently polymer conformational behavior at


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higher TMAO concentrations have been explored reporting intriguing observation. 19 Future direction will involve the effect of wide range of osmolyte concentrations 55 and other intrinsic properties of polymer namely charge and degree of polymerization and cononsolvency 56 on the hydrophobic interaction.

Acknowledgments This work was supported by computing resources obtained from shared facility of TIFR Center for Interdisciplinary Sciences, India. JM would like to acknowledge intramural research grants obtained from TIFR, India and Ramanujan Fellowship of DST, India. Part of the work was carried out in San diego supercomputing resources provided by XSEDE ( TG-CHE150024). JM would like to thank Dr. Isaac Li and Dr. Kalyaneswar Mandal for a critical reading of the manuscript and Dr. Guillaume Stirnemann for useful discussions.

Supporting Information Available Illustration of effect of restraining forces on preferential binding, free energy profiles at different combination of TMAO and urea concentrations, local-bulk partition coefficient(Kp ) for different osmolyte solution This material is available free of charge via the Internet at http://pubs.acs.org/.

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Collapsed (C)

Extended(E)


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How Does a Hydrophobic Macromolecule Respond to a Mixed

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