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The Hydrophobic Effect and the Role of Cosolvents Nico F. A. van der Vegt* and Divya Nayar Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Center of Smart Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany ABSTRACT: Cosolvents modulate aqueous solubility, hydrophobic interactions, and the stability and function of most proteins in the living cell. Our molecularlevel understanding of cosolvent effects is incomplete, not only at the level of complex systems such as proteins, but also at the level of very fundamental interactions that underlie the hydrophobic effect. This Feature Article discusses cosolvent effects on the aqueous solubility of nonpolar solutes, hydrophobic interactions, and hydrophobic self-assembly/collapse of aqueous polymers, recently studied with molecular dynamics simulations. It is shown that direct interactions of cosolvents with nonpolar solutes and aqueous polymers can strengthen hydrophobic interactions and can contribute to stabilizing collapsed globular structures. The molecular-level explanation of these observations requires a better understanding of the entropy associated with fluctuations of attractive solute−solvent interactions and of length-scale dependencies of this quantity.
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INTRODUCTION The hydrophobic effect,1−8 an effective force that acts to minimize the amount of surface that nonpolar molecules expose to their aqueous solvent environment, is of fundamental importance in chemistry and biology. Properties of stimuliresponsive polymer materials,9 as well as many biochemical processes in the living cell,10 are controlled by solvation of nonpolar surfaces and by solvent-mediated interactions between them. Cosolvents can be used to modulate hydrophobic effects. The term “cosolvent” used herein denotes not only a second solvent (e.g., an alcohol) added in small quantities, but also protein denaturants (e.g., guanidinium chloride, urea) and protecting osmolytes (e.g., trimethylamine-N-oxide). Here, we give our view on how cosolvents affect hydrophobic solvation, hydrophobic interactions, and collapse transitions of hydrophobic polymers. Examples discussed include hydrophobes in urea−water mixtures, collapse and unfolding of aqueous polymers in the presence of urea and methanol, and trimethylamine-N-oxide (TMAO) stabilization of proteins. We do not attempt to provide an exhaustive review on all aspects of cosolvent effects, but discuss examples from own research which have provided some new molecular insight into how cosolvents stabilize collapsed hydrophobic structures, mediated through direct cosolvent interactions with the aqueous solute.
molecular interactions. The second approach is based on the Kirkwood−Buff theory.12,13 It establishes relations between the chemical potential of the solute and preferential binding of solvent components, and furthermore provides models for denaturation and osmolyte stabilization which are commonly used in studies of biomolecular (e.g., protein folding) equilibria. Chemical Potential and Solvation Free Energy. The chemical potential drives all chemical transformations. The solute’s excess chemical potential μ★ = μl − μv describes the process of transferring a solute from the ideal vapor phase (v) to the liquid phase (l), where μl and μv are the chemical potentials in the liquid and vapor phases, respectively, at the same concentration of the solute. μ★ quantifies the effects of solvation on the chemical potential and, therefore, on chemical equilibria, provided that the molarity scale is used to express the concentration mentioned above.14 At constant pressure P and temperature T, μ★ = ΔG where ΔG is the experimental Gibbs solvation free energy, which is in turn related to the equilibrium molar solute concentration ratio (cl/cv)eq (partition coefficient) according to ΔG = −RT ln(cl/cv)eq in which R is the gas constant. From a theoretical viewpoint, μ★ corresponds to the reversible work associated with slowly turning on solute− solvent interactions (we shall always assume that the solute concentration is sufficiently small so that solute−solute interactions can be ignored). The potential distribution theorem, here written in inverse form, states11
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THERMODYNAMICS OF FOLDING EQUILIBRIA Solvation and its associated thermodynamic quantities are central to the problem of hydrophobic collapse. In this section, we shall briefly review two complementary thermodynamic approaches. The first approach is based on the potential distribution theorem,11 which establishes relations between the chemical potential of the solute and solute−solvent inter© XXXX American Chemical Society
★
eμ
/ RT
= ⟨eϕ / RT ⟩
(1)
Received: June 30, 2017 Revised: September 4, 2017 Published: September 18, 2017 A
DOI: 10.1021/acs.jpcb.7b06453 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B in which ϕ denotes the potential energy of all interactions between the solute and the solvent and the averaging ⟨...⟩ is performed over equilibrium configurations of the solution (including the solute). Equation 1 can also be written as μ★ = ⟨ϕ⟩ + RT ln⟨e δϕ / RT ⟩
strictly be thought of as an entropy, its above definition is useful because it describes the role of fluctuations in the thermodynamic driving force (ΔG). From the Gibbs− Bogoliubov inequality, which states that ΔG ≥ ⟨ϕ⟩,29,30 it follows that Suv ≤ 0. The negative sign corresponds to the reduction in entropy associated with reorganizing the solvent molecules such that they are all in the equilibrium positions and orientations to host all chemical moieties of the solute. This includes the above-mentioned effects of molecular-sized cavity fluctuations and fluctuations of attractive solute−solvent interactions. The relation of these quantities to the thermodynamic enthalpy (ΔH) and entropy (ΔS) is
(2)
in which δϕ ≡ ϕ − ⟨ϕ⟩. The first term on the right-hand side of eq 2 denotes the average potential energy of interaction of the solute with the solution, while the second term, determined by fluctuations of ϕ, is entropic. The reversible work of introducing solute−solvent interactions ϕ can be formally broken down into two steps using ϕ = ϕR + ϕA.13 In the first step, the repulsive part, ϕR, of this interaction is turned on (“cavity contribution”), followed by the attractive part, ϕA, turned on in the second step. This leads to the following exact expression μ★ = ⟨ϕA ⟩ + μc + RT ln⟨e δϕA / RT ⟩
ΔH = Euv + ΔEvv ΔS = Suv + ΔSvv
(5)
where ΔEvv is the solvent reorganization energy, here defined as the change in solvent−solvent interaction energy due to solute insertion at constant P and constant T. The corresponding solvent reorganization entropy is here denoted ΔSvv. In eq 5, we have ignored a pressure−volume term PΔV, which is negligible at 1 atm ambient pressure. Because the solvation free energy (eq 4) does not depend on ΔEvv and ΔSvv, these two quantities must necessarily be equivalent (ΔEvv = TΔSvv) so that they cancel out in the thermodynamic relation ΔG = ΔH − TΔS. This compensation applies to any solvation process. The solvent reorganization energy and entropy of hydrophobic solvation vary strongly in the presence of cosolvent, as was demonstrated in early experiments31 and computer simulation studies.21,23,24 Thermodynamics of Hydrophobic Collapse. The above analysis of the chemical potential can be applied to protein folding and first-order hydrophobic polymer collapse equilibria, which we consider here. We consider an equilibrium between extended, uncollapsed coil conformations (E) and globular, collapsed conformations (C) of the (bio)polymer
(3)
in which μc is a cavity (solvent-excluded volume) contribution, which is entirely entropic and is determined by microscopic density fluctuations of the solvent that lead to the formation of molecular-sized cavities large enough to host the solute. Hydrophobic solvation of small solutes is dominated by these cavity fluctuations.8 In the last term on the right-hand side of eq 3, δϕA ≡ ϕA − ⟨ϕA⟩. This term accounts for the effect of fluctuating attractive interactions with the preformed solute cavity and is a fundamental player in modulating the hydrophobic effect as we shall see below. These fluctuating attractive interactions lead to a further biasing of the configuration space of the solvent, schematically shown in Figure 1, and to a corresponding reduction of solvent entropy.
E⇄C
(6)
For flexible polymers, neither of these two conformations corresponds to a unique structure. E and C rather represent structurally degenerate yet distinguishable states that can be observed in the distribution of an appropriate metric (e.g., the polymer radius of gyration).32−34 The relative number of Cchains and E-chains at equilibrium is determined by the equilibrium constant K, which is related to the free energy difference
Figure 1. Sampling configuration space x of a solvent molecule (yellow) is biased by the external field ϕA of a fixed solute. For strong attractions, the biasing is stronger, and the corresponding solute− solvent entropy reduction is larger than for weak attractions. The solute−solvent entropy reduction is calculated by monitoring energy fluctuations: Strong attractions cause large energy fluctuations δϕA and a correspondingly large and negative solute−solvent entropy. Weak attractions cause small energy fluctuations and a correspondingly small and negative solute−solvent entropy.
ΔG E → C = μC★ − μE★
(7)
according to
K = e−ΔG
E→C
/ RT
(8)
Equation 7 shows that ΔG is determined by the solvation ★ free energies μ★ E and μC of E- and C-chains, respectively. Using eq 4, ΔGE→C can be related to solute−solvent energy and entropy terms according to E→C
Studies on solvation of small molecules have frequently used the subscript notation uv to denote solute−solvent interactions and the subscript notation vv to denote solvent−solvent interactions.15−28 With this notation, the solvation free energy can be written as ΔG = Euv − TSuv
E→C E→C ΔG E → C = ΔEuv − T ΔSuv
(4)
(9)
At the collapse temperature TEC, the free energy difference between E-chains and C-chains vanishes. Hence
δϕ/RT
in which Euv ≡ ⟨ϕ⟩ and Suv ≡ − R ln⟨e ⟩. The quantities Euv and Suv are referred to as the solute−solvent energy and solute−solvent fluctuation entropy, respectively. Although Suv is not the temperature derivative of ΔG, and, in that sense, cannot
TEC = B
E→C ΔEuv E→C ΔSuv
=
ΔH E → C ΔS E → C
(10) DOI: 10.1021/acs.jpcb.7b06453 J. Phys. Chem. B XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry B
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COSOLVENT EFFECTS ON SOLVATION AND HYDROPHOBIC INTERACTIONS BETWEEN SMALL MOLECULES Cosolvent Effects on Hydrophobic Solvation. Molecular simulations of small nonpolar molecule solvation in mixtures of water with cosolvents or cosolutes provide several interesting insights into the physical chemistry of solvation relevant for folding equilibria. Significantly, nonpolar solutes are entropically salted in, or salted out, as schematically summarized for selected water−cosolvent systems in Figure 2.18 The energy (ΔEuv) and entropy (TΔSuv) of transferring a
Equations 9 and 10 provide a route to analyze folding equilibria in terms of solute−solvent interactions. At the lower folding temperature of a protein solution (cold denaturation), the entropy (ΔSE→C) and enthalpy (ΔHE→C) changes are both positive.35 Several aqueous polymers exhibit a similar type of transition with positive values of ΔSE→C and ΔHE→C near room temperature. A depression of TEC induced by osmolytes or cosolvents corresponds to polymer collapse (or protein stabilization provided that the lower folding temperature is studied). This effect may be caused by changes in the entropy E→C component (ΔΔSE→C uv ), the energy component (ΔΔEuv ), or changes in both components with the addition of the cosolvent. Preferential Binding. A complementary description of cosolvent effects on folding equilibria is provided by Kirkwood−Buff theory,12 or, equivalently, by Wyman−Tanford theory.36,37 We refer the reader to the review of Pierce et al. for an extensive discussion on this subject.38 Here, we introduce a few quantities that will be used in the discussion below. The molar concentrations of solute and solvent components will be expressed using the notation ci, where the index i = 1 stands for water, i = 2 for the (bio)polymer, and i = 3 for the cosolvent. The dependence of the protein folding or polymer collapse equilibrium on the cosolvent activity a3 is given by ⎛ ∂ln K ⎞ E→C ⎜ ⎟ = ΔΓ 23 ⎝ ∂ln a3 ⎠ P , T
Feature Article
(11)
C E E C Here, ΔΓE→C 23 = Γ23 − Γ23 where Γ23 and Γ23 are the preferential binding coefficients for the E- and C-states, defined as
Γ23 = c3(G23 − G21)
Figure 2. Energy−entropy compensation/reinforcement in smallmolecule transfer thermodynamics between water and water− cosolvent systems.18 NaCl suppresses molecular cavity fluctuations, leading to a negative solute−solvent transfer entropy and salting out. The solute−solvent transfer entropy is also negative in systems (urea, DMSO) where the cosolvent accumulates in the solute solvation shell driven by attractive solute−solvent van der Waals interactions. In these, nearly ideal, water−cosolvent systems, introducing the attractive field (ϕA) in the presence of a solute cavity causes enhanced concentration fluctuations in the solute solvation shell with corresponding fluctuations in solute−solvent energy. Acetone and tert-butanol form nonideal mixtures with water and are microscopically heterogeneous. In these systems, solute cavities are formed in domains with a local excess cosolvent concentration while the attractive field does not cause further fluctuations. This leads to energy−entropy reinforcement and strong salting in.
(12)
In eq 12, the quantities G23 and G21 are the polymer−cosolvent and polymer−water Kirkwood−Buff integrals (KBI), respectively, defined as Gij = 4π
∫0
∞
[gij(r ) − 1]r 2 dr
(13)
where gij(r) is the pair correlation function for i,j pairs. Using13 ⎛ ∂ln a3 ⎞ 1 ⎜ ⎟ = 1 + c3(G33 − G31) ⎝ ∂ln c3 ⎠ P , T
(14)
to account for solvent nonideality, eq 11 can be written as E→C ⎛ ∂ln K ⎞ ΔΓ 23 ⎜ ⎟ = 1 + c3(G33 − G31) ⎝ ∂ln c3 ⎠ P , T
nonpolar solute from water to a cosolvent−water mixture provides a data point on the map in Figure 2 which is divided into a salting in (ΔΔG < 0) and a salting out (ΔΔG > 0) region separated by a dashed line with unit slope. Sodium chloride binds water molecules tightly and suppresses cavity fluctuations, leading to strengthening of the hydrophobic effect (Δμc > 0 and TΔSuv < 0) and salting out.17 Interestingly, urea and dimethyl sulfoxide (DMSO) salt in small nonpolar solutes, driven by favorable solute−solvent van der Waals interactions (ΔEuv < 0), but opposed by changes in solute−solvent entropy (ΔSuv < 0) (energy−entropy compensation).17,18,21 In these systems, the unfavorable solute−solvent entropy not only reflects reduced density fluctuations (Δμc > 0), but also reflects fluctuating attractive solute−solvent van der Waals interactions that reduce the entropy further (Figure 1).21 This effect, quantitatively related to the last term on the right-hand side of eq 3, qualitatively reflects that attractive solute−solvent
(15)
In eq 15, the denominator is positive.13 The quantities G33 and G31 are the cosolvent−cosolvent and cosolvent−water KBIs, respectively. In ideal cosolvent−water mixtures, G33 − G31 = 0. If ΔΓE→C < 0, the cosolvent preferentially binds to the E-state. 23 This causes the conformational equilibrium to shift in favor of that state with increasing cosolvent activity. The opposite applies when ΔΓE→C > 0. 23 The application of eq 15 in computer simulations permits researchers to make predictions of cosolvent effects on collapse/folding equilibria from an analysis of preferential binding coefficients.39−41 This provides a transfer free energy ΔΔGE→C corresponding to transferring the equilibrium E ⇄ C from pure water to the cosolvent−water solution.42 C
DOI: 10.1021/acs.jpcb.7b06453 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B interactions bias the partitioning of solvent components between the first solvation shell and the bulk. For small nonpolar solutes as studied by van der Vegt et al., this leads to an overall solute-solvent entropy change which is negative.18 The sign of the solute−solvent entropy change ΔSuv may however depend on the solvent-exposed nonpolar surface area. Such length-scale dependencies43 in systems with cosolvents are not fully understood. Cosolvent interaction with small hydrophobes does not generally lead to a loss in solvent entropy (ΔSuv < 0). Solute transfer from water to, e.g., acetone−water mixtures occurs with a favorable energy change (ΔEuv < 0) and a favorable entropy change (ΔSuv > 0). Hence, we observe energy−entropy reinforcement and strong salting in.17 This reinforcement effect occurs because hydrophobes are solvated in cosolvent-rich domains, which, in contrast to urea−water mixtures, are present in acetone−water and other nonideal cosolvent−water mixtures. As a result, solvent reorganization effects are significantly smaller in acetone−water than in urea−water mixtures. Miscible yet nonideal systems of organic cosolvents and water typically show the above type of concentration fluctuations with transient microscopic clusters of cosolvent molecules.44 Cosolvent Effects on Hydrophobic Interactions. The effects described above have implications for hydrophobic interactions between small solutes. This interaction can be quantified with a pair potential of mean force (PMF), which, for two identical solutes, can be written as
Figure 3. Solvent-mediated hydrophobic interactions are modulated by osmolytes. (a) Depletion stabilization:45 folding causes a release of excluded volume. (b) Osmolyte clouding: folding causes a decrease in osmolyte accumulation.
★ ★ PMF(r ) = u(r ) + μ(2) (r ) − μ(2) (r → ∞ ) ★ = u(r ) + μ(2) (r ) − 2μ★
(16)
in which μ★ (2)(r) is the Gibbs solvation energy of the two combined solutes, fixed at a center-to-center distance r, and u(r) is the solute−solute pair potential. The PMF has a minimum at solute contact which we use here as a measure of the hydrophobic interaction. We note that there are no agreed conclusions in the literature on whether, in pure water, the ★ solvent-mediated part of this interaction (i.e., μ★ (2)(r) − 2 μ ) is 2,28 attractive or repulsive. The hydrophobic interaction may be strengthened by depleting (nonadsorbing) osmolytes driven by their entropy which is larger when the two nonpolar solutes are in contact (Figure 3a).45 This situation corresponds to preferential hydration of the contact state.46,47 Below, we show that interacting (adsorbing) osmolytes may also strengthen the hydrophobic interaction, also driven by the entropy of the osmolyte which is larger when the two nonpolar solutes are in contact (Figure 3b). While the hydrophobic interaction in Figure 3a is driven by steric effects (and therefore by the contribution of μc(r) to μ★ (2)(r)), the hydrophobic interaction in Figure 3b is driven by fluctuating attractive solute−solvent interactions (and therefore by the contribution of RT ln⟨eδϕA(r)/RT⟩ to μ★ (2)(r)) which are related to concentration fluctuations of the combined solutes’ solvation shell. The depletion mechanism (Figure 3a) leads to a depression of the lower collapse temperature (eq 10) only through the effect on ΔSE→C uv . The mechanism in Figure 3b also leads to a depression of the lower collapse temperature, provided that changes in polymer−solvent energy ΔEE→C are insignificant. uv Figure 4 shows a specific system corresponding to the mechanism of Figure 3b.20,48 The PMFs between two
Figure 4. Hydrophobic pair interaction between neopentane molecules in water (0 M urea) and in 6.9 M urea solution. The top left panel shows the neopentane−neopentane potential of mean force (PMF) at 298 K and 1 atm pressure obtained with classical MD simulations using the SPC/E water potential50 and the KBFF51 urea potential.48 Urea strengthens the hydrophobic interaction. The top right panel shows local urea concentrations (green, 6.9 M; red, 14 M; blue, 0 M) for contact-pair and solvent-separated arrangements of the two neopentane molecules. The lower panel shows the entropy contributions to the PMFs in water (0 M urea) (left) and in 6.9 M urea (right).20 Adapted with permission from refs 20 and 48. Copyright 2006 American Chemical Society.
neopentane molecules in pure water (0 M urea) and in 6.9 M urea solution are compared. Although urea increases the aqueous solubility of neopentane,49 and acts as a protein denaturant at this concentration, it strengthens the hydrophobic association of the two neopentane molecules.20,48 The lower panel of Figure 4 shows that the contribution of cavity fluctuations (μc) to the PMF is comparable in water (0 M urea) D
DOI: 10.1021/acs.jpcb.7b06453 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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binding” or “preferential interaction” is a thermodynamic quantity (eq 11). Therefore, Γ23 > 0 does not necessarily imply that the intermolecular interactions (hydrogen bonding, van der Waals) of cosolvent molecules with the polymer are stronger (more favorable) than the interactions of water molecules with the polymer in either of the states. Two examples, discussed below, illustrate this: urea at low concentration, and methanol at low concentration, in aqueous PNIPAM solution. Urea Ambivalence: Collapse or Unfolding? PNIPAM in aqueous urea solutions has been studied with MD simulations55,70 to gain better insight into the nature of the positive preferential urea interaction with PNIPAM suggested by experiments.52,53 These simulations showed urea-induced collapse of the chains and showed accumulation of urea in the first solvation shell of the collapsed and uncollapsed polymers; i.e., Γ23 is positive for E-chains and C-chains. Similar observations were made in earlier work on model hydrophobic chains by Mondal et al.33 With simulations of conformationally restrained collapsed and uncollapsed polymers, no evidence could be found in the polymer−solvent energies that indicated stronger urea interactions with the collapsed polymer than with the uncollapsed polymer, e.g., through hydrogen-bonding interactions. Instead, the entropy, as measured by the third term on the right-hand side of eq 3, was found to penalize the chemical potential of the restrained extended chain over the chemical potential of the restrained collapsed chain.70 This finding suggests that the mechanism shown in Figure 3b explains the urea-induced depression of the LCST. ́ The simulations of Rodriguez-Ropero and van der Vegt were performed with 40-mer PNIPAM chains, which are long enough to show very distinct reversible transitions between collapsed and uncollapsed conformations.55 While these MD simulation studies clearly demonstrate that the role of the solute−solvent entropy cannot be discarded, a complete picture could not be obtained because the sampling was limited to a small number of independent collapsed and uncollapsed polymer conformations.55,70 This sampling issue in fact holds for all atomistic simulations of aqueous PNIPAM solutions reported to date in which, typically, a single PNIPAM chain is simulated with MD on time scales up to several hundreds of nanoseconds,54,56,68,71−76 or even up to microseconds with a long chain.77 Although these time scales are long, PNIPAM coil−globule transitions at 300 K occur on similar time scales of typically 100 ns (for short chains with 40 monomers);55 hence, only very few transitions between uncollapsed and collapsed conformations are normally observed during the course of a long MD simulation. To understand how van der Waals and Hbonding interactions of urea and water with the chain affect the thermodynamic driving forces for collapse, suitable averages over many uncollapsed and collapsed chain conformations are required. It is interesting to ask which computational approach is most suitable for tackling this problem. The challenge exists in sampling a vast space of flexible chain conformations which couple to the local solvent environment around the chain. Advanced sampling techniques (e.g., replica exchange methods) are very efficient in studying hydrophobic association in systems where sampling chain conformations is less important than equilibrating the solvent. For example, the hydrophobic interaction between two α-helices can be completely characterized with replica exchange MD,78 providing not only the free energy of association but also the enthalpic and
and in 6.9 M urea. The decisive difference arises from the fluctuating attractive solute−solvent interactions, which contribute to a larger increase of the entropy (TSuv) in 6.9 M urea solution when the hydrophobes are in contact. Due to energy−entropy compensation effects, this mechanism is weaker than depletion stabilization of hydrophobic contacts (e.g., in the presence of NaCl). Recent work, discussed in greater detail in the next section, has however shown that it leads to unexpected urea effects in hydrophobic folding equilibria.
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HYDROPHOBIC POLYMER COLLAPSE TRANSITIONS Responsive polymers in aqueous solution have received attention in recent years in both experimental and simulation communities. In particular, polyacrylamide-based systems,52−57 but also elastin-like polypeptides (ELPs),52,53,58−60 have been investigated. These aqueous (bio)polymers have a lower critical solution temperature (LCST) close to room temperature. The LCST shifts when Hofmeister salts,53,56,58,59,61,62 osmolytes (TMAO, glycine, betaine),60 urea,52 methylated urea,53 or alcohols63−66 are added to the solution. While strongly hydrated salts, but also glycine and betaine, shift the LCST of these (bio)polymer solutions downward (salting out) due to their depletion from the polymer−water interface, several other salts, urea, TMAO, and alcohols also shift the LCST downward, but instead due to direct interactions with the (bio)polymer. This observation is counterintuitive; if direct interactions occur, the LCST is expected to increase, rather than to decrease, with a corresponding stretching/unfolding of the chain leading to an increase of its solvent-accessible-surface area (SASA). To explain the LCST decrease, it has frequently been assumed that direct interactions with the collapsed polymer are more favorable than those with the uncollapsed polymer. Direct Interactions in the Collapsed State. The work of Sagle et al. has shown that urea causes a downshift of the LCST of poly(N-isopropylacrylamide) (PNIPAM) in aqueous solution; i.e., urea collapses the PNIPAM chain at temperatures below the LCST of PNIPAM in water (305 K) leading to clouding of the polymer solution.52 The authors have explained this rather unexpected result with a bivalent urea hydrogenbonding mechanism in which urea molecules bridge NIPAM monomers on the same collapsed chain (or on different chains) causing stabilization of collapsed chain conformations and clouding of the solution. In later work, Heyda et al. showed that with a weakly hydrated salt (GndSCN) a similar bridging-type ELP polymer collapse is observed due to partitioning of, both, cations and anions in the polymer hydration shell.58 This type of partitioning does not occur with GndCl, which instead increases the aqueous polymer solubility due to favorable interactions of the Gnd+ cation with the extended macromolecular surface.58 Theoretical models based on group additivity cannot describe these nonadditive phenomena. Hence, the use of experimental data obtained from thermodynamic studies on cosolvent interactions with model compounds,67 or preferential interaction data obtained from MD simulations of free monomers in cosolvent−water mixtures,68,69 cannot provide an unambigious description of coil−globule collapse transitions if bridging-type interactions play a role. As described by eq 15, cosolvents shift the coil−globule equilibrium in the direction of the species (C or E) to which they preferentially bind. We emphasize that “preferential E
DOI: 10.1021/acs.jpcb.7b06453 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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Figure 5. Solvation thermodynamics of conformational equilibria of PNIPAM and PDEA in aqueous urea solutions at 300 K and 1 atm.81 The preferential binding coefficients (Γ23) of the collapsed (C) and extended (E) states of PNIPAM and PDEA in 2.7 M urea solution are shown in parts a and b, respectively. For both polymers, ΓC23 > 0 and ΓE23 > 0. Opposite urea effects on conformational equilibria are illustrated by ΓC23 > ΓE23 for PNIPAM and ΓE23 > ΓC23 for PDEA. This can be related to a decrease in the free energy change of polymer collapse relative to collapse in water (ΔΔGE→C < 0) for PNIPAM (c) and an increase in the free energy change (ΔΔGE→C > 0) for PDEA (d) as a function of urea concentration. The > 0. The blue region in part c corresponds to the urea-concentration window where PNIPAM collapse is dominated by the entropy change ΔΔSE→C uv yellow region with larger negative slope of the data corresponds to the urea-concentration window where PNIPAM collapse is dominated by the < 0 associated with urea bridging interactions. The transition of entropy dominance to energy dominance can be related to energy change ΔΔEE→C uv the small and sharp decrease observed in the experimental LCST of PNIPAM below and above 4 M urea concentration, respectively.52 The insets in parts c and d, respectively, show the chemical formulas of PNIPAM and PDEA. Adapted from ref 81 with permission from the PCCP Owner Societies. Copyright 2017.
E→C Figure 6. Polymer−solvent energy change (ΔΔEE→C uv ) and polymer−solvent entropy change (TΔΔSuv ) on collapse of PNIPAM and PDEA in aqueous urea solution relative to collapse in pure water at 300 K and 1 atm. The polymer−solvent energy changes have been obtained by averaging over 200 independent MD simulations of collapsed (C) and extended (E) polymer conformations, using blocks of 2 ns for each 50 ns simulation.81 The entropy terms TΔΔSE→C have been computed using eq 9 based on the energies ΔΔEE→C and the free energies ΔΔGE→C (Figure 5). In the blue uv uv E→C > 0 and TΔΔS > 0 indicating that the solute−solvent entropy drives PNIPAM collapse relative concentration regions of graphs a and c, ΔΔEE→C uv uv to PNIPAM collapse in neat water when small amounts of urea are added to the solution. In the yellow concentration regions of graphs a and c, the two quantities change sign, indicating that the solute−solvent energy drives PNIPAM collapse relative to PNIPAM collapse in neat water when large > 0 and TΔΔSE→C > 0, indicating that amounts of urea are added to the solution. Graphs b and d for PDEA show that for [urea] < 0.5 M, ΔΔEE→C uv uv < 0, indicating that the solute−solvent entropy drives PDEA the E-state is energetically favored over the C-state. For [urea] > 0.5 M, TΔΔSE→C uv unfolding.
F
DOI: 10.1021/acs.jpcb.7b06453 J. Phys. Chem. B XXXX, XXX, XXX−XXX
Feature Article
The Journal of Physical Chemistry B
PNIPAM, PDEA collapses in water, and in urea solution, with a significantly larger reduction of the nonpolar SASA.81 There> 0, of hydrophobic collapse fore, the entropy change, ΔSE→C uv in pure water is larger for PDEA than for PNIPAM. Addition of small amounts of urea to water at 298 K leads to screening of the nonpolar−aqueous macromolecular interface due to urea adsorption, and to a concomitant decrease in the water contribution to ΔSE→C in the system with urea. Due to its larger uv SASA, this screening effect is larger for PDEA than for PNIPAM. As a result, polymer collapse in the solution with urea leads to smaller positive values of ΔSE→C as compared with uv collapse in pure water. If we assume that urea configurational contributions (Figure 3b) are small in comparison to those of < 0 and chain unfolding water, urea screening leads to ΔΔSE→C uv as shown in Figure 6d for urea concentrations larger than 0.5 M. With this assumption, screening of the nonpolar polymer− water interface should lead to increasing the aqueous solubility of both polymers (more for PDEA than for PNIPAM because PDEA’s SASA is larger). Urea configurational degrees of freedom can however not be ignored for the PNIPAM system with smaller SASA. According to Figure 3b, this configurational bias provides a positive contribution to the overall entropy change ΔΔSE→C uv . For PNIPAM, the positive urea contribution overcompensates for the negative water contributo ΔΔSE→C uv >0 tion, thus leading to a net positive entropy change ΔΔSE→C uv that favors PNIPAM collapse below 4 M urea (Figure 6c). For overPDEA, the negative water contribution to ΔΔSE→C uv compensates for the positive urea contribution resulting in a net negative entropy change ΔΔSE→C < 0 that favors PDEA uv unfolding (Figure 6d). Role of Solute−Solvent Energy Fluctuations in Hydrophobic Collapse. The above discussion of opposite entropy effects in hydrophobic collapse of PNIPAM and PDEA remains at a qualitative level and leaves several questions unaddressed. It is not well-understood how to relate the opposite effects of urea on ΔΔSE→C to the SASA differences of uv these two polymers and to the chemistry of the side chains. Improved molecular understanding may be achieved by evaluating the entropy contribution in Figure 1 for polymer chains in water and for polymer chains in binary urea−water mixtures. Fluctuations in attractive solute−solvent interactions, δϕA, are proportional to solvent density fluctuations near the macromolecular surface. These density fluctuations are particularly useful in characterizing hydrophobic effects.8,83−102 Significantly, the analysis of small length-scale density fluctuations has provided molecular insight into pressure denaturation of proteins7,103 and entropy convergence of protein unfolding entropies.101,104 By means of similar analyses it has been found that water near hydrophobic surfaces is sensitive to perturbations.100 Dewetting has been observed in molecular simulations of hydrophobic plates in water at nanoscale separation,105,106 an effect which was also shown to be important for hydrophobic collapse of multidomain proteins,107 and hydrophobic polymer collapse.108 Fluctuations in attractive solute−solvent interactions are expected to be large for solutes with extended hydrophobic surfaces. This expectation follows the observation of “fat” lowN tails in the probability distribution of observing N water molecules in large observation volumes near hydrophobic surfaces.87,96 Correspondingly, fluctuations in attractive solute− solvent interactions may be large for solutes such as PDEA with
entropic components. The folding equilibrium of the Trp-cage miniprotein, in which the native state essentially consists of one structure, has also been studied with replica exchange MD.79,80 With flexible polymer chains, this technique rapidly becomes more expensive. In particular, the sampling of the structurally degenerate collapsed state is very challenging. The work of Nayar et al. therefore assumes a two-state equilibrium (eq 6) and computes the preferential urea binding coefficients in each of the two states in order to obtain the free energy change of polymer collapse in urea solution relative to the free energy change of polymer collapse in pure water (ΔΔGE→C) using the Kirkwood−Buff approach (eq 15).81 To this end, 100 MD simulations of unrestrained collapsed and 100 MD simulations of unrestrained uncollapsed PNIPAM conformations were performed on time scales where reversible transitions between collapsed and uncollapsed conformations occur. With this approach, suitable conformational averaging of the preferential binding coefficients ΓE23 and ΓC23, which depend very sensitively on the conformation of the chains, can be achieved (see data in Figure 5a,b). The thermodynamic driving force for PNIPAM collapse ́ proposed by Rodriguez-Ropero and van der Vegt55,70 has been revisited with this approach, confirming that an entropy-driven collapse occurs below 4 M urea.81 Figure 5c shows ΔΔGE→C of a PNIPAM 40-mer chain in urea−water mixtures. The data show that urea decreases the aqueous solubility of PNIPAM (ΔΔGE→C < 0) in agreement with experiment.52 Together with a direct simulation analysis of the energetic component ΔΔEE→C (the solute−solvent entropic component then follows uv from eq 9) shown in Figure 6, all thermodynamic quantities pertinent to chain collapse could be determined and related to the observed H-bonding and van der Waals interactions of the chain with its local solvent environment.81 It was found that, above 4 M urea, bivalent hydrogen-bonding (enthalpic) interactions dominate ΔΔGE→C. Below 4 M urea, the energy E→C E→C (ΔΔEE→C uv ) and entropy (TΔΔSuv ) contributions to ΔΔG E→C are both positive (cf. Figure 6a,c), indicating that ΔΔSuv (cf. Figure 6c) drives the salting out of PNIPAM (ΔΔGE→C < 0). This confirms the earlier conclusions,55,70 schematically depicted in Figure 3b. Interestingly, the experimental LCST data of Sagle et al.52 show an inflection to a stronger LCST depression above 4 M urea, which, according to these recent MD simulations,81 originates from a transition of an entropydriven collapse (Figure 3b) to an enthalpy-driven (ureabridging) collapse. Contrary to PNIPAM, the aqueous solubility of poly(N,Ndiethyl acrylamide) (PDEA) increases with the addition of urea.82 The simulation analysis of Nayar et al. confirms this (see Figure 5b,d).81 This observation has been attributed by Wang et al.82 to differences in side-chain chemistry: urea bivalent Hbonding occurs with the secondary amide (PNIPAM) but not with the tertiary amide (PDEA). These opposite urea effects on the aqueous solubility of PNIPAM and PDEA however raise an intriguing question: Why do small amounts of urea ( 0) is observed irrespective of its conformational state.114 This agrees with recent work by Mukherji et al. in which it was found that a long (256-mer) PNIPAM chain locally remains in good solvent while it is globally collapsed in a solution with 10% methanol.77 Mukherji et al. assume that global collapse is caused by enthalpic methanol bridging interactions.77 Alternative explanations emphasize competitive H-bonding,113 geometric frustration effects,115 the role of conformational entropy,114 and cosolvent-mediated enhancement of the attractive mean force between nonpolar groups.116 Because positive preferential methanol binding is observed, it indeed seems natural to assume that, in analogy with urea, methanol interacts more strongly with the collapsed chain than with the uncollapsed chain through H-bonding or van der Waals interactions. This assumption however turns out not to be supported by
Figure 7. PNIPAM co-nonsolvency (300 K, 1 atm) in methanol− water mixtures.117 (a) Average number of hydrogen bonds formed by water and methanol with the 40-mer PNIPAM side-chain amide groups. (b) Change in the polymer solute−solvent energy upon polymer collapse (which here includes changes in the internal energy of the chain) as a function of methanol concentration. The number of NH−water H-bonds decreases sharply at low methanol concentrations (
