Direct Osmolyte–Macromolecule Interactions Confer Entropic Stability

Article pubs.acs.org/JPCB

Direct Osmolyte−Macromolecule Interactions Confer Entropic Stability to Folded States Francisco Rodríguez-Ropero and Nico F. A. van der Vegt* Center of Smart Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287, Darmstadt, Germany S Supporting Information *

ABSTRACT: Protective osmolytes are chemical compounds that shift the protein folding/unfolding equilibrium toward the folded state under osmotic stresses. The most widely considered protection mechanism assumes that osmolytes are depleted from the protein’s first solvation shell, leading to entropic stabilization of the folded state. However, recent theoretical and experimental studies suggest that protective osmolytes may directly interact with the macromolecule. As an exemplary and experimentally well-characterized system, we herein discuss poly(N-isopropylacrylamide) (PNiPAM) in water whose folding/unfolding equilibrium shifts toward the folded state in the presence of urea. On the basis of molecular dynamics simulations of this specific system, we propose a new microscopic mechanism that explains how direct osmolyte−macromolecule interactions confer stability to folded states. We show that urea molecules preferentially accumulate in the first solvation shell of PNiPAM driven by attractive van der Waals dispersion forces with the hydrophobic isopropyl groups, leading to the formation of low entropy urea clouds. These clouds provide an entropic driving force for folding, resulting in preferential urea binding to the folded state and a decrease of the lower folding temperature in agreement with experiment. The simulations further indicate that thermodynamic nonideality of the bulk solvent opposes this driving force and may lead to denaturation, as illustrated by simulations of PNiPAM in aqueous solutions with dimethylurea. The proposed mechanism provides a new angle on relations between the properties of protecting and denaturing osmolytes, salting-in or salting-out effects, and solvent nonidealities.

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INTRODUCTION The folding equilibrium of proteins in water is affected by osmolytes, which are small low molecular weight compounds used by cells to protect them against osmotic stresses. A common classification distinguishes between protecting osmolytes and denaturants, typical representatives of which include polyols, sugars, and amino acids (protecting osmolytes) and urea, arginine, and guanidinium chloride (denaturants).1 While protecting osmolytes shift the folding equilibrium in favor of the folded state (F), denaturants shift the folding equilibrium in favor of the unfolded state (U). According to Le Chatelier’s principle, denaturants preferentially bind to U while protecting osmolytes preferentially bind to F. The molecular mechanisms of preferential binding and interactions in relation to protein folding have been the subject of intense scientific debate in the last decades.2−8 To explain denaturant effects, two different mechanisms have been proposed. The first mechanism is the so-called indirect mechanism. It assumes that denaturants alter water structure and favor solvation of hydrophobic groups, leading to protein denaturation.9,10 To our knowledge, there are no experimental studies that convincingly support this mechanism. The second, direct mechanism invokes the idea that denaturants interact with hydrophobic and hydrophilic groups of the protein and is supported by experimental and molecular dynamics (MD) simulation studies.11−13 A direct mechanism implies necessarily a favorable binding interaction between denaturants and proteins. Upon unfolding, the protein © 2014 American Chemical Society

surface increases so that it can interact with a larger number of denaturant molecules, resulting in enthalpic stabilization of the unfolded state.8 Stabilization of folded protein states by protecting osmolytes has been widely explained on the basis of preferential osmolyte exclusion or, equivalently, preferential hydration of the protein.4,14,15 In this scenario, the U- and Fstates are preferentially hydrated and enthalpically favorable protein−osmolyte interactions are absent. The F-state is stabilized through an entropic (depletion) mechanism in which the system minimizes the osmolyte−protein excluded volume, effectively causing preferential binding of the osmolyte to the F-state relative to the U-state. The thermodynamic nature of depletion interactions is however still under debate. As opposed to the above purely entropic mechanism,16 enthalpy becomes a key component in cases where the excluded osmolyte is relatively small.17−20 An indirect mechanism has been proposed as well, where the protecting osmolyte trimethylamine-N-oxide stabilizes folded states due to its effects on water properties.5,21,22 Recent theoretical and experimental studies suggest that osmolyte-induced stabilization of the F-state of polymers may involve a direct mechanism in which the osmolyte molecules interact with the polymer.23,24 Sagle et al.24 reported that urea Received: April 25, 2014 Revised: June 12, 2014 Published: June 13, 2014 7327

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reduces the coil-to-globule transition temperature TUF of PNiPAM (Scheme 1) below 32 °C measured in neat water;25

partial atomic charges were obtained from HF/6-31G(d,p) quantum-chemical calculations by using the restrained electrostatic potential (RESP) method (see the Supporting Information).31 Simulations in 1,3-dimethylurea aqueous solution were run at 300 K and ∼2.8 M dimethylurea concentration using simulation boxes containing 12 919 water molecules and 800 dimethylurea molecules. The simulations were performed using the GROMACS 4.5.1 simulation package.32 A simulation time step of 2 fs was chosen to simulate all systems. All simulations were performed in the isothermal−isobaric ensemble (NpT). The pressure (1 atm) and the temperature were kept constant by using the Parrinello−Rahman barostat33,34 (τP = 1.0 ps) in combination with the Nosé−Hoover thermostat35,36 (τT = 0.5 ps). Atomic coordinates were saved every 1 ps for subsequent analysis. van der Waals interactions were treated using a 12−6 LennardJones potential applying a cutoff at 1.40 nm. The electrostatic interactions have been calculated using the particle-mesh Ewald method37 with a real space cutoff of 1.40 nm. Bond lengths were kept at their equilibrium distances using the LINCS algorithm.38,39 Cubic boxes were used for the simulations. The equilibrated average volume of these boxes was ∼230.0 nm3 for those simulations of the polymeric (40 monomer) PNiPAM chain in 5.8 M urea aqueous solution, ∼507.5 nm3 for the systems at 2.8 M 1,3-dimethylurea concentration, and ∼115.0 nm3 for the smaller box containing 8 monomers in urea aqueous solution. The 200 ns long replica exchange molecular dynamics (REMD) simulations40 were performed at temperature intervals between 280 and 361.44 K. In total, 24 replicas separated by 3.21 K have been considered. The temperature difference between consecutive replicas has been estimated according to the temperature predictor by Patriksson and van der Spoel.41 The pressure (1 atm) and the temperature were kept constant in the same way as in all the reported MD simulations in this work. Replica exchanges were performed every 10 000 simulation steps. The local/bulk partition coefficient42

Scheme 1

i.e., urea shifts the equilibrium U ⇄ F in favor of F. We note that in this system TUF corresponds to a lower folding temperature. At urea concentrations higher than 5 M, TUF decreases linearly.7,24 On the basis of FTIR experiments, the authors propose that stabilization of F is owed to direct electrostatic interactions involving urea molecules that bridge PNiPAM carbonyl groups by a bivalent hydrogen bonding mechanism. PNiPAM has been widely studied, for example, as a mimic for the cold denaturation of proteins,26 and osmolyte effects on TUF have been experimentally well-characterized.27 PNiPAM, which is an isomer of poly(isoleucine), thus serves as a good model system to better understand the role of direct protective osmolyte/macromolecule interactions on the stability of protein folded states. On the basis of MD simulations of the PNiPAM folding equilibrium, we propose in this article a new physical mechanism for osmolyte-induced stabilization of folded states through direct osmolyte−polymer interactions. We find that urea molecules preferentially bind the hydrophobic groups in the PNiPAM chain by means of van der Waals (VdW) dispersion interactions. Accumulation of urea in the first solvation shell (FSS) of the polymer leads to the formation of low entropy urea clouds. “Dissolution” of these clouds provides an entropic driving force for collapse, balancing the unfavorable enthalpy at a lower coil−globule transition temperature as compared to hydrophobic collapse in water. We moreover find that this entropic stabilization mechanism vanishes in thermodynamically nonideal dimethylurea/water mixtures, where cosolvent (dimethylurea) aggregation occurs in, both, cosolvent clouds and the distant bulk. The mechanism proposed in this article thus provides further insight in the emergent indirect role of bulk thermodynamic properties of the binary solvent on folding equilibria.

KP =

(nU /nW )local (nU /nW )bulk

(1)

where nU and nW are the number of urea and water molecules in the indicated domains, was calculated as KP =

(⟨nU⟩/⟨nW ⟩)local tot (nUtot /nW )

(2)

where ⟨nX⟩ is the average number of molecules of type X bound to the polymer and ntot X is the total number of molecules of type X in the system (X = U stands for urea, X = W stands for water). KP was calculated as a function of the distance from the polymer by examing the explicit distance dependence of nU(r) and nW(r). The distance was defined as the shortest distance between the center of mass of the urea or water molecule and any atom of the polymer.

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METHODS Our model system consists of a PNiPAM chain with 40 NiPAM units solvated in a simulation box containing 6156 water molecules. The OPLS-AA force field28 has been used to describe the PNiPAM chain, while water was represented with the SPC/E potential.29 This force field combination reproduces the coil−globule transition temperature TUF in pure water in good agreement with experiments.44 800 urea molecules were added to reach an ∼5.8 M urea concentration. Urea molecules were described using a Kirkwood−Buff-derived force field,30 which, combined with the SPC/E water model, describes satisfactorily the urea activity derivatives and the solution structure. Bonded and Lennard-Jones parameters for 1,3dimethylurea were taken from the OPLS-UA force field, while

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RESULTS Force Field Validation. We performed MD simulations at constant atmospheric pressure and temperature (NpT ensemble) starting from a stretched 40-mer PNiPAM chain in pure water at temperatures between 280 and 360 K. Initially, we ran the simulations for 100 ns, but we observed that in some of the systems the PNiPAM radius of gyration (Rg) did not 7328

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been proposed as the driving force that lowers TUF in urea solution relative to water.24 Preferential solvation of nonpolar molecules by urea, driven by attractive VdW interactions, has however been observed as well.47−49 Favorable VdW dispersion interactions between urea and hydrophobic groups give rise to solvent-mediated attractive forces, which provide a driving force for hydrophobic aggregation and stabilize urea separated nonpolar contacts50−52 at a wide range of temperatures.53 It has been suggested that these urea separated contacts play a role in urea denaturation of proteins,50 which could be confirmed in later, large-scale MD simulations.13,54 It however remains elusive what mechanism is operative in driving PNiPAM collapse, i.e., hydrogen bonding (an electrostatic driven mechanism) or a urea mediated VdW mechanism. In the first mechanism, urea should mostly interact with the hydrophilic CO and NH groups, while in the second mechanism urea is expected to preferentially interact with the hydrophobic isopropyl group and the backbone. To investigate the preferential interaction of the urea and water molecules with the NiPAM units, we have performed three sets of simulations at 280 K (TUF) of systems containing 8 NiPAM molecules in a solvent box containing 2187 water molecules and 550 urea molecules. Analysis of Kirkwood−Buff integrals55,56 (see the Supporting Information) shows that NiPAM molecules are preferentially solvated by urea. Figure 2B shows the number density maps of

relax to the expected value, indicating sluggish equilibration. We extended the simulation time up to 400 ns in some of these systems and observed large fluctuations of Rg on 0.1 μs time scales (Figure 1A), especially remarkable at temperatures ±10

Figure 1. Radius of gyration (Rg) for a 40-mer PNiPAM chain: (A) in pure water versus time at 300 K; (B) average value in pure water versus temperature obtained from replica exchange MD simulations; (C) in 5.8 M urea aqueous solution versus time as obtained from a MD simulation trajectory in which a temperature ramp (black line) has been applied; (D) average value versus temperature in 5.8 M urea aqueous solution obtained from the last 50 ns from 200 ns MD simulations.

K around the experimental TUF. It should be noticed that simulation times only up to 100 ns were considered in previous works, so these fluctuations were not observed.43−46 To determine TUF, we performed replica exchange molecular dynamics simulations40 using 24 replicas within the temperature range 280−361.4 K for 200 ns. TUF was then observed at ∼306 K (Figure 1B), which compares satisfactorily with the experimental data.25 Interestingly, fluctuations of Rg were significantly suppressed in the 200 ns MD simulations at 5.8 M urea concentration and different temperatures. We found the coil−globule collapse transition at ∼295 K, which was also corroborated by one extra 600 ns simulation in which a temperature ramp was used (Figure 1C and D), again in good agreement with experiment24 and confirming the suitability of the model. Apart from providing a driving force that stabilizes the globular conformation at 298 K ambient temperature, we found indications that urea affects the kinetics of chain collapse (see Figure S1 in the Supporting Information). While in urea solution the chain collapses immediately within the first 10 ns of simulation, in water, the fluctuations in coil dimension are bigger and the collapse occurs only after a dwell time (50−100 ns depending on initial conditions) indicative of the presence of larger (free) energy barriers. Polymer Is Preferentially Solvated by Urea due to Favorable Dispersion Interactions. On the basis of Fourier transform infrared spectroscopy measurements, direct hydrogen bonding of the urea molecules with the CO groups has

Figure 2. (A) Snapshot of a fully solvated PNiPAM chain at temperatures of T < 295 K and T > 295 K in 5.8 M aqueous urea solution (urea molecules are shown using a van der Waals representation, water molecules are not shown). Urea clouds surround the macromolecule at both temperatures. (B) 3D density maps for urea (left) and water (right) around a NiPAM molecule. Red indicates average bulk density, green twice bulk density, and blue 3 times bulk density.

urea and water molecules around NiPAM. Water presents two peaks close to the hydrophilic CO and NH groups, while urea presents two peaks in contact with the hydrophobic isopropyl group and the backbone. This feature seems to support a VdW mechanism, which will be discussed in greater detail below. We calculated the average number of urea and water molecules forming hydrogen bonds with two hydrophilic groups belonging to different NiPAM units within the 40-mer PNiPAM chain (Table 1) to further examine the validity of the 7329

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Table 1. Average Number of Water (W) and Urea (U) Mediated Bridges between Hydrophilic NH and/or CO Groups Belonging to Different Monomers in a PNiPAM Chain Containing 40 NiPAM Unitsa aqueous solution

8 M urea solution

temperature (K)

280

320

280

295 (coil)

295 (globule)

320

CO···W···OC CO···W···HN NH···W···HN CO···U···OC CO···U···HN NH···OC CO···W NH···W CO···U NH···U

1.2 3.8 0.1

2.1 3.5 0.4

7.8 42.7 12.8

10.5 34.4 9.3

0.3 2.4 0.1 0.2 0.8 4.8 31.8 9.5 5.6 3.6

0.2 2.8 0.1 0.2 0.7 7.6 30.5 10.0 5.2 3.2

0.9 3.6 0.0 0.2 0.5 9.3 27.0 8.8 4.0 2.5

0.8 2.3 0.4 1.2 1.3 5.0 28.1 10.2 4.8 4.8

a Direct NH···OC, NH···W, CO···W, NH···U, and CO···U hydrogen bonds are also reported. For comparison, we also report the results from simulations in pure aqueous solutions. Hydrogen bonds have been assigned when the distance between donor and acceptor is lower than 2.5 Å and the angle is bigger than 150°.

Figure 3. Probability distribution functions of van der Waals and electrostatic energies for urea (A and C) and water (B and D) in the FSS (continuous line) and in the bulk solution (dotted line) at 280 K (blue), 295 K in the coil (green) and globular (orange) states, and 320 K (red).

electrostatic based mechanism. As it can be seen, the average number of urea mediated bridges is very low independent of the temperature and the chain conformation. The molecular interactions responsible for the preferential solvation of PNiPAM by urea were next examined on the basis of a local binding energy analysis. We computed the VdW interaction energy between each urea or water molecule located either in the FSS or in the bulk with the rest of the system. A given urea or water molecule is considered to be in the FSS if its center of mass is within a cutoff distance of 5 Å from the nearest PNiPAM atom. On the other hand, a water or urea molecule is considered to be in the bulk phase if its center of mass is at least 8 Å away from any PNiPAM atom. A spherical cutoff of 14 Å has been used to calculate the energy contributions. The probability distribution of urea VdW energies (Figure 3A) within the FSS presents a peak at lower energy compared to the bulk independent of the temperature. The VdW energy difference is ∼5.0 kJ/mol. The same analysis for water (Figure 3B) reveals minor energy differences between water molecules located in the FSS and those located in the bulk. The probability distribution of electrostatic energies was also calculated (Figure 3C,D) using a reaction field approach (εr = 72). The electrostatic energy is slightly lower in the bulk than in the FSS (the difference is ∼3.9 kJ/mol) for, both, water and urea. Thus, favorable VdW interactions are responsible for the preferential accumulation of urea molecules around PNiPAM. Indeed, the water/urea ratio drops from ∼8.15 in the bulk phase to ∼5.15 in the FSS independent of the temperature, indicating the presence of urea clouds surrounding the PNiPAM chain in solution (Figure 2A). To identify the chemical groups of the polymer responsible for the gain in urea VdW energy, we have performed a detailed energetic analysis of the systems at 295 K, which corresponds to the calculated TUF. We performed the analyses on the basis of a 0.7 μs MD trajectory (see the Supporting Information) in which both coil and globular states are sampled with equal probability. Since conformational fluctuations occur on a time scale of ∼100 ns, our analyses are based on 50 ns long portions of the parent 0.7 μs MD trajectory. We have considered the

intervals 275−325 ns for the coil state (Rg = 1.61 ± 0.21 nm) and 550−600 ns for the globular state (Rg = 1.05 ± 0.01 nm). As it can be seen in Figure 4A and B, the major component of the VdW energy between the PNiPAM chain and urea is due to the urea−isopropyl interactions independent of the chain conformation. Similar results have been obtained at different temperatures (see the Supporting Information). Parts C and D

Figure 4. Probability distribution functions of the VdW energy (in units of kJ/mol of PNiPAM) of PNiPAM with urea molecules located in the FSS in coil (A) and globule (B) conformations sampled at TUF (295 K). Contributions of each chemical group (defined according to Scheme 1) to the total VdW energy distribution are shown (A and B). Probability distribution of the VdW energy (in units of kJ/mol of urea) for urea in the FSS with PNiPAM (C) and with the isopropyl group (D) for both coil and globule conformations at 295 K. 7330

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osmolyte effects on folding equilibria in terms of structural characteristics determined by the distribution of solvent components in the system. Structural and energetical analyses, however, do not provide a picture as to why urea preferentially binds to the state with smaller solvent accessible area for the system studied herein. Because the effect of urea on the folding equilibrium at any given temperature is determined by how the lower folding temperature TUF varies with urea concentration, we decided to study the folding enthalpy and entropy which determine TUF. As will be discussed below, this approach further provides insight in emergent effects of bulk solvent nonidealities on folding. TUF is determined by the folding enthalpy (ΔHUF = HF − HU) and folding entropy (ΔSUF = SF − SU) according to TUF = ΔHUF/ΔSUF. At TUF, the folding entropy exactly balances the folding enthalpy, i.e., ΔHUF = TUFΔSUF, and the pertinent question is how this balance is affected by cosolvents. The contribution of the solvent to ΔSUF contains a cavity contribution (polymer−solvent excluded volume), which always favors F, and a contribution related to energy fluctuations caused by the attractive parts of the intermolecular interactions.51,58 At the lower folding temperature, ΔHUF and ΔSUF are both positive, but in urea solution, both quantities are smaller than in neat water (see the Supporting Information, Table S1). The decisive difference however is that folding in urea solution leads to a shift of the enthalpy/entropy balance to greater entropy dominance as compared to folding in pure water, thus resulting in lowering of TUF; i.e., the folding entropy per unit change in enthalpy is larger in urea solution. We interpret this result as being caused by partial “dissolution” of urea clouds upon folding, following ideas in earlier work where it was demonstrated that release of urea molecules from the FSS upon creating hydrophobic contacts between small molecules leads to entropic stabilization.51 Analysis of the variance in the PNiPAM−solvent attractive energy in the U- and F-states in pure water and in 5.8 M urea solution supports this view: while in urea solution at 295 K the variance decreases with 15.5(±0.4) × 103 (kJ/mol)2 upon folding, and the corresponding decrease in pure water at 306 K amounts to 2.2(±0.3) × 103 (kJ/mol)2. Because reduced energy fluctuations imply larger entropy, we thus find that urea provides an entropic driving force for folding. The energy fluctuations in urea solution result from the difference in the VdW component of the urea binding energy in bulk as compared to the FSS (Figure 3A). This physical picture can be considered general for systems where the macromolecule attracts urea, or other cosolvent species, in its FSS through VdW forces. In the nearly ideal urea−water mixtures studied here, hydrophobic collapse leads to loss of urea aggregation in the PNiPAM solvation shell, releasing urea molecules into a homogeneous bulk with a corresponding positive contribution to the entropy change ΔSUF that stabilizes the folded state. It is interesting to now make a Gedanken experiment and consider the same collapse process in a nonideal cosolvent−water system, i.e., a cosolvent that unlike urea which is homogeneously dispersed at the molecular scale forms molecular clusters in bulk aqueous solution. In this system, hydrophobic collapse may again lead to loss of cosolvent aggregation in the PNiPAM solvation shell, but released cosolvent molecules may now contribute to clustering in the inhomogeneous bulk, resulting in a smaller ΔSUF as compared to an ideal solvent. This effect of solvent nonideality, if present, leads to larger TUF and destabilization of F in comparison to the system with urea.

of Figure 4 show that the urea−PNiPAM and urea−isopropyl VdW energy does not show a significant dependence on the chain conformation. In a similar way, we have performed a detailed analysis of the electrostatic interactions of the PNiPAM chain with both water solvent and urea cosolvent (see the Supporting Information). The results are in accordance with the results presented in Table 1. Strong electrostatic CO/water and NH/water interactions corroborate that these groups are strongly hydrated independent of the temperature. Urea Preferentially Binds to the Folded State of PNiPAM. Osmolytes or cosolvents that shift the equilibrium U ⇄ F in favor of F tend to reduce the lower folding temperature TUF, while osmolytes that shift the equilibrium in favor of U tend to increase TUF relative to water. The lower folding temperature of PNiPAM in water is reduced in the presence of urea, leading to salting-out and stabilization of the folded, globular state. Because urea shifts the equilibrium in favor of the F-state, it preferentially binds to that state.57 Figures S3 and S4 (Supporting Information) show the PNiPAM−urea (GPU) and PNiPAM−water (GPW) Kirkwood−Buff integrals55,56 and the preferential binding parameter ΓPU = ρU(GPU − GPW), where ρU is the urea number density. While the preferential binding parameter is indeed higher in the folded state than in the unfolded state, it should be noted that the number of urea molecules in the FSS decreases upon folding (from 77 to 56 at 295 K for the system studied here, which implies a higher Kirkwood−Buff integral for the U-state compared to the Fstate). These observations are counterintuitive. Despite favorable direct VdW interactions with the macromolecular surface, urea preferentially binds to a state that has smaller solvent accessible area. Figure 5 presents the local/bulk

Figure 5. Local/bulk partition coefficient KP as a function of the distance to the polymer in the F-state (red) and U-state (blue) at 295 K in 5.8 M urea aqueous solution.

partition coefficient KP (see eq 2).42 If the nature of the exposed groups is conformation dependent, differences in urea binding strength to the U- and F-states may occur. Clearly, Figure 5 provides no compelling evidence for this. This is further supported by the fact that the urea and water binding interaction with the FSS is conformation independent (Figure 3). We further note that the internal structures of the collapsed PNiPAM conformations in water and in 5.8 M urea solution are different (see the Supporting Information, Figure S6), showing more pronounced tendency in urea solution to keep the isopropyl groups solvent exposed. Direct Interactions Confer Entropic Stability to Folded States. An analysis of the quantities ΓPU and KP often provides useful information that allows one to interpret 7331

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and TUF(dimethylurea) > TUF(urea). This is supported by our simulations which show that, at 300 K, PNiPAM is collapsed in urea solution, while it is fully unfolded in the solution with dimethylurea. This observation, furthermore, is consistent with experiments by Sagle et al., which showed that TUF is larger in aqueous solutions with di- and tetramethylurea as compared with pure water or urea solutions24 and illustrates how solvent nonideality influences the polymer folding equilibrium.

To investigate this hypothesis, we performed MD simulations of PNiPAM in 2.8 M 1,3-dimethylurea solution. We also simulated the binary 2.8 M dimethylurea−water mixture, which behaves nonideal as evidenced by dimethylurea and water clustering in the simulations (see Figure 6). As for the above

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DISCUSSION AND CONCLUSIONS Mechanisms by which small neutral organic molecules (osmolytes) and salts modulate protein stability have been studied for many decades but are still not completely understood. Because proteins are marginally stable at room temperature, small molecular interactions can induce large effects. The mechanism by which denaturants and stabilizing osmolytes affect conformational stability is commonly discussed in terms of their direct interactions with the macromolecule, depletion or crowding effects, and effects on water structure. Herein, complementary aspects are uncovered related to effects of bulk solvent properties on folding equilibria that have thus far remained elusive. The key question addressed in this work has been why urea stabilizes the folded (globular) state of PNiPAM in aqueous solution, as observed in previous experiments and in the simulations reported herein. Analysis of structural data obtained from the molecular simulations cannot satisfactorily answer this question. In both systems, pure water and 5.8 M urea, the PNiPAM coil-to-globule collapse transition results in a swollen globular state where the amide groups maintain most of their hydrogen bonds with water (Table 1). It is therefore unlikely that a direct hydrogen bonding mechanism involving the amide group stabilizes the folded state of PNiPAM in aqueous urea solution. This conclusion is further supported by comparing the electrostatic energy distributions of urea and water molecules in the FSS and in the bulk solvent (Figure 3). Differences in structural polymer characteristics of the U- and F-states in water and in urea solution could be identified. However, these differences have no significant effect on the solvent (urea, water) binding energy for those states at different temperatures above and below TUF (Figure 3). We find that in both states, folded and unfolded, PNiPAM is preferentially solvated by urea driven by favorable urea−PNiPAM VdW dispersion interactions. Preferential urea solvation is particularly pronounced at the isopropyl group and causes a buildup of urea clouds surrounding the PNiPAM chain. Favorable urea interactions with the polymer may naturally lead to the assumption that urea shifts the folding equilibrium to the unfolded state in order to maximize the solvent exposed surface area, but that is contrary to what is observed. Instead, buildup of urea clouds driven by favorable enthalpic urea−PNiPAM interactions leads to an overcompensating unfavorable entropy responsible for shifting the folding equilibrium to the folded state with smaller exposed surface area. Although entropy effects cannot readily be interpreted in terms of single molecule interactions, they provide useful insight into how bulk solvent properties affect the folding/ unfolding equilibrium. To this end, we further considered 1,3dimethylurea, which acts as a denaturant and shifts the PNiPAM folding equilibrium in favor of the unfolded state. Urea-induced stabilization of F and dimethylurea-induced stabilization of U can be explained by analyzing the different roles of the entropy in the systems with these two osmolytes.

Figure 6. (A) Snapshot of a fully solvated PNiPAM chain at 300 K in 2.8 M 1,3-dimethylurea aqueous solution. Dimethylurea molecules belonging to the PNiPAM FSS are shown using a van der Waals representation, while water molecules are not shown for clarity. (B) Zoom in into the nonideal bulk phase showing clustering of 1,3dimethylurea molecules (water molecules are not shown). Clustering leads to larger solvent potential energy fluctuations in the bulk as compared with the FSS. (C and D) Probability distribution functions of van der Waals and electrostatic energies for 1,3-dimethylurea in the FSS (blue line) and in the bulk solution (red line) at 300 K.

systems with urea, the simulation of PNiPAM in dimethylurea− water solution shows evidence for preferential PNiPAM solvation by the cosolvent species, driven by favorable cosolvent−PNiPAM VdW dispersion interactions. From the energetic analysis presented in Figure 6C and D, it can be inferred that transfer of a dimethylurea molecule from the bulk into the FSS provides a net favorable enthalpic interaction of 1.5 kJ/mol dimethylurea. This number compares to 1.1 kJ/mol in the system with urea. Hence, both systems are very similar in view of the enthalpic cosolvent−PNiPAM interactions. Interestingly, the dimethylurea VdW and electrostatic energy distributions are broader in the bulk as compared to the FSS, which is probably due to the large concentration fluctuations in the bulk solvent (see Figure 6B). Comparison of the variances of the total urea or water binding energy (VdW plus electrostatic) in the bulk versus FSS shows an interesting trend (see the Supporting Information, Table S2). While in the PNiPAM/pure water system, the water binding energy fluctuations in the FSS are larger than in the bulk, only small differences between binding energy fluctuations of water (and urea) molecules in the FSS or in the bulk are observed in urea solution. While the urea binding energy fluctuations in the FSS and in the bulk are approximately equal, dimethylurea binding energy fluctuations in turn are significantly larger in the bulk. These observations suggest that the folding entropy in dimethylurea solution will be smaller than that in urea solution, 7332

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Urea molecules are homogeneously dispersed in the bulk solvent and tend to accumulate in the FSS of the polymer. The resulting urea cloud entropically penalizes the U-state and shifts the folding/unfolding equilibrium in favor of F, as described above. Dimethylurea molecules tend to accumulate in the FSS of the polymer driven by VdW dispersion forces, too, but moreover form cosolvent clusters in the bulk solvent phase. While folding reduces cosolvent accumulation in the polymer’s FSS, it in turn increases nonlocal cosolvent clustering in the bulk, which leads to unfavorable folding entropy that shifts the folding/unfolding equilibrium in favor of U. This latter, denaturant effect, caused by a nonlocal (or indirect) phenomenon related to thermodynamic nonideality of the bulk solvent, is likely to be applicable to different cosolvents. The emergent role of solvent entropy described here provides new insights into the effects of solvent nonidealities on folding equilibria. The folding/unfolding equilibrium of the PNiPAM model system discussed in this work is dominated by hydrophobic effects (the amide groups remain hydrated before and after folding) and van der Waals dispersion interactions with the osmolyte molecules. The osmolyte mechanism discussed here hence does not include hydrophilic effects, which play an additional role in protein folding/unfolding equilibria. These hydrophilic effects may include direct osmolyte interactions with polar groups and osmolyte effects on protein−water hydrogen bonding. We finally point out that analogies may be drawn between the nonideal solvent effects discussed herein and nonadditive (e.g., ion pairing) effects of anions and their counter cations on folding equilibria of biomacromolecules.59

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ASSOCIATED CONTENT

* Supporting Information Figures showing Rg vs time in water and 5.8 M urea, running Kirkwood−Buff integrals at different temperatures (monomer and polymer), running preferential urea binding parameter (polymer), Rg vs time in 5.8 M urea at 295 K, radial distribution function of isopropyl groups relative to the PNiPAM center of mass in the globular state, PNiPAM/solvent energy distributions, and force field parameters for 1,3-dimethylurea; tables showing folding enthalpy and entropy; and Kirkwood−Buff analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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ACKNOWLEDGMENTS

This research was supported by the German Research Foundation (DFG) within the Cluster of Excellence 259 “Smart Interfaces - Understanding and Designing Fluid Boundaries”. The authors would like to express their gratitude to the Hochschulrechenzentrum at the TU-Darmstadt for the computational time provided. We thank Pritam Ganguly for useful discussion. 7333

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