Signature of Hydrophobic Hydration in a Single Polymer

Signature of hydrophobic hydration SEE COMMENTARY in a single polymer

Isaac T. S. Li and Gilbert C. Walker1

Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, Canada M5S 3H6

Edited by Robert Baldwin, Stanford University, Stanford, CA, and approved August 4, 2011 (received for review April 12, 2011)

Hydrophobicity underpins self-assembly in many natural and syn- thetic molecular and nanoscale systems. A signature of hydrophobicity is its temperature dependence. The first experimental evaluation of the temperature and size dependence of hydration free energy in a single hydrophobic polymer is reported, which tests key assumptions in models of hydrophobic interactions in protein folding. Herein, the hydration free energy required to ex- tend three hydrophobic polymers with differently sized aromatic side chains was directly measured by single molecule force spectroscopy. The results are threefold. First, the hydration free energy per monomer is found to be strongly dependent on temperature and does not follow interfacial thermodynamics. Second, the temperature dependence profiles are distinct among the three hydrophobic polymers as a result of a hydrophobic size effect at the subnanometer scale. Third, the hydration free energy of a monomer on a macromolecule is different from a free monomer;

corrections for the reduced hydration free energy due to hydro- CHEMISTRY phobic interaction from neighboring units are required.

ydrophobic hydration involves the minimization of the free Henergies of water molecules near nonpolar surfaces. Hydro- phobic hydration of macromolecules is central to understanding Fig. 1. The role of hydrophobic collapse in the folding of three polymers protein folding (1–6) and advancing materials science and bio- with decreasing hydrophobicities: hydrophobic homopolymer, copolymer, technologies (7–9). A detailed methodology has been developed and protein (from top to bottom), plotting global free energy vs. radius of to study hydrophobic hydration by the mechanical unfolding of a gyration. Starting from an extended conformation in water, both protein collapsed single hydrophobic polymer (10). Typically, the hydra- and polymer chains are entropically reduced to random coils with reduced tion free energy (ΔGhyd) is assumed to scale with the solvent radii of gyration (red). When a random coil is compacted such that the accessible surface area (SASA) of molecules according to macro- chain can make frequent contact with itself, hydrophobic collapse (yellow) occurs to further reduce the global free energy and the radius of gyration. scopic interfacial thermodynamics, which is supported by the lin- If the hydrophobic units are sparser on the chain, hydrophobic collapse ear correlation between the SASA and the free energy to transfer occurs later during entropic coiling. For proteins, specific interactions (blue) hydrocarbons from a hydrophobic solvent (such as hexadecane) such as hydrogen bonds and salt bridges bring the protein to an energy to water (11). Despite a strong correlation, the experimentally minimum with the most compact structure. Hydrophobic polymers do not measured small hydrocarbon ΔGhyd is smaller than that predicted have such specific interactions and remain as compact random coils. by the calculated SASA (12), showing the breakdown of macroscopic interfacial thermodynamics at the microscopic scale and Theoretical studies of hydrophobic hydration relied on experi- suggesting that the origin of the correlation goes beyond SASA. mental measurements of small molecule solubilities in water and In addition, the temperature dependence of ΔGhyd (the signature their transfer free energies from organic solvents to water. It is of hydrophobic hydration) varies according to the size of the usually assumed that these small molecule ΔGhyd can be directly solute; such temperature dependence cannot be explained simply applied to hydrophobic side chains in polymers and proteins. How- by the macroscopic interfacial free energy. In an earlier attempt ever, this assumption has not been experimentally tested due to the to address these issues, Tolman (13) developed a thermodynamic lack of a suitable experimental model system and the difficulty of treatment that lowers the surface tension of water at the solute- studying hydrophobic macromolecules insoluble in water. Hydro- water interface by taking into account the cavity curvature. Later phobic homopolymers provide simple models of the hydrophobic developments included temperature dependence of the Tolman hydration and collapse of proteins and other linear biological length using simulations to address the temperature dependence molecules (Fig. 1). Preceding hydrophobic collapse, an initially ex- of ΔGhyd (14, 15). However, it was argued that the correction to the effective surface tension to maintain the correlation between tended hydrophobic polymer in water undergoes entropic coiling ΔGhyd and SASA at small length scales lacked a clear physical meaning (16). Instead of depending on a scaling relation with Author contributions: I.T.S.L. and G.C.W. designed research; I.T.S.L. performed research; SASA, theories and simulations were developed predicting that G.C.W. contributed new reagents/analytic tools; I.T.S.L. and G.C.W. analyzed data; and ΔGhyd has nontrivial size dependence: Below approximately 1 nm I.T.S.L. and G.C.W. wrote the paper. radius, ΔGhyd of a spherical solute scales roughly with the solute The authors declare no conflict of interest. volume; whereas above this value, ΔGhyd scales with SASA and This article is a PNAS Direct Submission. asymptotically approaches the behavior described by macroscopic See Commentary on page 16491. interfacial thermodynamics (6, 17–28). These treatments cor- 1To whom correspondence should be addressed. E-mail: [email protected]. ΔGhyd rectly predict the trend for the temperature dependence of This article contains supporting information online at www.pnas.org/lookup/suppl/ for small molecules. doi:10.1073/pnas.1105450108/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1105450108 PNAS ∣ October 4, 2011 ∣ vol. 108 ∣ no. 40 ∣ 16527–16532 Downloaded by guest on September 29, 2021 that reduces the tension along the chain to a point where the coil- that free monomer ΔGhyd cannot be directly applied to calculate globule transition can occur. The onset of this transition depends the hydration free energy of a hydrophobic macromolecule. on the overall hydrophobicity of the polymer such that the transition begins at higher tension and radius of gyration for a hydro- Results phobic homopolymer than for a mixed hydrophobic/hydrophilic Single Polymer Force Plateau Marks Hydrophobic Hydration. Using polymer such as a protein (Fig. 1). Similar to a protein, a hydro- AFM, a single polymer chain can be pulled from a naturally phobic homopolymer collapses in an aqueous environment into a collapsed state to a hydrated, extended state as illustrated in compact globule that is largely disordered. This collapse captures Fig. 2A. It has been predicted theoretically and shown in simula- the essential physics governing the hydrophobic hydration of a tions that forced hydration of a collapsed hydrophobic polymer protein and is illustrated in Fig. 1. Ensemble studies of hydropho- produces a constant force-distance profile. (29–31) Force-exten- bic polymers are not viable because of their insolubility in water sion curves of single hydrophobic polymers such as polystyrene and limited experimental access to different conformational states (PS), poly(4-tert-butylstyrene) (PtBS), and poly(4-vinylbiphenyl) (e.g., extended and collapsed). However, by way of single molecule (PVBP) show characteristic constant force plateaus correspond- force spectroscopy using atomic force microscopy (AFM), the ing to single-chain hydration (10, 32–34), followed by entropic conformation of a single hydrophobic polymer can be changed elastic stretching before the chain detaches from the AFM can- from collapsed globule to extended coil (Fig. 2A)andΔGhyd in this B B tilever or the Si substrate (Fig. 2 ). Statistical analysis of the force process can be estimated (Fig. 2 ). A previous study provides a plateau magnitudes from thousands of independent molecular detailed description of the control experiments undertaken here pulling events at a given temperature for a given polymer shows for the mechanical unfolding of a collapsed single hydrophobic a quantized distribution (Fig. S1), which suggests that the lowest polymer in aqueous solvents (10). This report presents the effect of temperature on hydrophobic hydration of several polymers and force plateau results from hydration of a single polymer chain. Furthermore, when normalized to the same contour length, the how the size of side chains affects their temperature dependence. A The result shows that a phenomenological model using SASA and force curves can be superimposed on top of one another (Fig. 3 ), macroscopic interfacial thermodynamics cannot account for the showing that the polymer chains have the same persistence length observed temperature dependence of macromolecular hydropho- and that the physics behind the forced hydration is length inde- bic hydration. The observed temperature dependence shows the pendent within the range of polymer sizes accessible to our ex- turnover behavior typically seen in the hydration of small hydro- periment (hundreds of nanometers) The constant force profile phobic molecules. Moreover, individual monomers along the chain is an indication that the hydration free energy for each monomer cannot simply be viewed as independent units threaded together, on the chain is identical within experimental accuracy; and its and analysis of the magnitude of ΔGhyd shows that there are contribution to the total hydration free energy of the extended significant hydrophobic interactions between adjacent units that chain is additive (10). Surface topography scans of all three poly- make the energetic cost to hydrate the chain much smaller than the mers samples confirm that they form compact globules on the Si sum of energies of individual monomers. Therefore, it suggests surface (Fig. S2).

A BCExtended State

entropic relaxation

-T S

Fdz ext ∫ forced extension - GhydN

Force (pN) Force hydrophobic collapse Collapsed Hydrated 80 State Random Coil aggreg

40 GhydN atio -T S ext n polymerization 0

Dispersed Free 400 80 120 160 Monomers Extension (nm)

Fig. 2. Single molecule pulling experiments are used to obtain the hydration free energy of a hydrophobic polymer as it transitions from a collapsed to an extended state. (A) AFM forces the hydration of a single hydrophobic polymer chain in water by pulling it from a collapsed state. The top magnified inset illustrates that the individual monomers on the subnanometer length scale along the extended chain are hydrated. The bottom magnified inset illustrates that hydration of the collapsed globule follows a surface area controlled hydration process. (B) A single molecule force-extension curve showing a force plateau followed by elastic stretching (red) and a baseline with no polymer attachment (gray). The force plateau corresponds to hydration of a single chain; the entropic elastic stretching occurs when the chain extension force is governed by entropy reduction, which is fit closely by the worm-like chain (WLC) model (blue). The area under the WLC fit (blue shade) contains the entropic contribution to the free energy extending the polymer from a collapsed globule. The area between the force plateau and the WLC fit (red shade) is due to hydration only. (C) Free energy differences between polymers and free monomers in various conformational states. The upper portion shows a single molecule extension experiment that converts the collapsed conformationto the extended conformation through a coil-globule transition. In a thought experiment, relaxing the force while maintaining the extended conformation without inducing any collapsed structure leads to a fully hydrated random coil that maximizes chain entropy. The collapse of this fully hydrated random coil back to the collapsed conformation is the hydrophobic collapse identified in this work, and the free energy is associated with −ΔGhyd. Dispersed free monomers can be converted to the collapsed or random coil state through either aggregation or polymerization, respectively, preventing the free monomer hydration free energy from being used directly in calculations of polymer hydration.

16528 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1105450108 Li and Walker Downloaded by guest on September 29, 2021 1.0 A 6.5 C 75 SEE COMMENTARY 70 0.8 6.0 5.5 65 0.6 5.0 ()n 60 0.4 4.5 PS 55 200 pN Force (nN)

0.2 100 nm M D 75

0.0 6.5 nae

6.0 70 f

0 0.5 1.0 o r

65 c

Normalized % Extension 5.5 ()n e

60 30°C 5.0 p( 55 B 4.5 PtBS )N 40°C 6.5 E 75 Solvation free energy (kJ/mol) 70 60°C 6.0 () 5.5 n 65 5.0 60 80°C 4.5 PVBP 55 Probability (arbitrary unit) 50 10090807060 80706050403020 Force (pN) Temperature (°C)

Fig. 3. Experimental results of size and temperature dependencies on hydrophobic hydration. (A) Contour length normalized force-extension curves are well superimposed, showing that globule-coil transition phenomenon probed here is independent of polymer length in the regime accessible to these experiments. (B) PS plateau force histograms show a steady increase of the mean force value as temperature increases. The temperature dependencies hyd of plateau force (solid gray markers) and ΔG (open colored markers) are shown in C, PS (red circle); D, PtBS (green box); and E, PVBP (blue diamond). CHEMISTRY Parabolic fits to the force (solid line) and ΔGhyd (dashed line) data illustrate their distinct dependencies on temperature. While the profile of ΔGhyd for PS is monotonically increasing, the profiles for PtBS and PVBP peak at 55.1 °C and 47.8 °C, respectively. The vertical error bars reflect the standard deviations of the mean from different sets of measurements.

Calculation of Hydration Free Energy from Force Curves. The experi- been observed for small hydrocarbon molecules (36), and has mental procedure extending the polymer from a collapsed to an been reproduced by many theoretical studies (19, 21, 23, 28). This extended state involves hydrating the chain and lowering the en- anomalous increase in the hydration free energy before the tropy of the chain (Fig. 2C). To separate the hydration free energy, turnover point is believed to originate from the lowered entropy the contribution associated with chain entropy must be subtracted of water molecules adjacent to the small hydrophobic molecules, from the total work done to stretch the chain (Fig. 2 B and C): as the degrees of freedom of these water molecules are reduced R by the formation of more ordered, dynamic structures. FðTÞdz þ TΔS ðTÞ To examine whether hydrophobic macromolecules follow a ΔGhydðTÞ¼ plateau ext ; [1] N macroscopic or microscopic temperature dependence, the hydration of a single PS chain in water was studied at temperatures where ΔGhydðTÞ is the temperature-dependent hydration free ranging from 30 °C to 80 °C. Force plateaus from approximately energy per monomer on the chain, FðTÞ is the experimentally mea- two thousand force-extension curves corresponding to indepen- sured pulling force integrated over the plateau region of the force dent single-chain pulling events show Gaussian distributions of ΔS ðTÞ B curve, ext is the difference in entropy of a solvent exposed the plateau force at each given temperature (Fig. 3 ). The mean chain from random coil to elastically extended states, N is the plateau force increases monotonically as a function of tempera- number of monomers in the extended portion of the chain and ture (Fig. 3 B and C). An increase of roughly 7 pN in the mean T is temperature. Therefore, the contribution from hydration free plateau force from 30 °C to 80 °C corresponds to a 10% increase energy is calculated as the area between the force plateau and the in the absolute value of the plateau force. A mean force resolu- entropic elastic response of the chain (Fig. 2B). tion of less than 5 pN, below the thermal noise floor of approximately 20 pN in typical AFM force spectroscopy, was achieved Temperature and Size Dependence of Hydration Free Energy. Large from a large sample population that forms well-defined Gaussian hydrophobic particles (radius much greater than 1 nm) behave distributions. The hydration free energy ΔGhyd is calculated differently from small ones (radius smaller than 1 nm). In the from the work done in the plateau region of the force curve macroscopic limit, the temperature dependence of the ΔGhyd of by subtracting the entropic contribution from a single polystyrene large solutes is well-described by interfacial thermodynamics, chain using a method described previously (10); the value of which implies that the temperature dependence of macroscopic ΔGhyd ranges from 5.6 kJ∕mol at 30 °C to 6.1 kJ∕mol at 80 °C ΔGhyd follows similar decreasing trend of the surface tension of for PS (Fig. 3C). water when temperature rises. The macroscopic phenomenon is To further characterize the nature of the temperature depen- surface area dominated and enthalpy driven as the number of dis- dence of ΔGhyd, the effect of side-chain size was examined. Direct rupted water H-bonds at the interface scales with the surface verification of the size dependence of ΔGhyd is experimentally area. For length scales less than 1 nm, ΔGhyd of a hydrophobic challenging. Theoretical studies often use ideal spherical hydro- solute is predicted to scale with its volume rather than surface phobic particles with well-defined subnanometer radii. Experi- area (22–24, 35). In contrast to the temperature dependence of mentally, even the smallest nanoparticles are several nanometers macroscopic interfacial free energy, ΔGhyd for a hydrophobic in diameter; too large to study the length scale of interest con- solute increases at low temperature, reaches a maximum and cerning microscopic hydrophobic hydration. Differently sized decreases at high temperature. This temperature dependence has hydrophobic molecules fall in the right size range for studying

Li and Walker PNAS ∣ October 4, 2011 ∣ vol. 108 ∣ no. 40 ∣ 16529 Downloaded by guest on September 29, 2021 microscopic hydrophobic size dependency, but there is no single The turnover behavior of the extended polymer ΔGhyd has an parameter to describe the size of a molecule considering the dif- important ramification: The hydration entropy diminishes at a ferent molecular geometry (molecules are usually not spheres) critical temperature corresponding to the hydration free energy and interactions with water. These complications make it difficult maximum. The negative hydration entropy below this tempera- to interpret direct comparison of ΔGhyd with molecular size even ture suggests that the overall degree of conformational freedom when good correlation exists, such as in the case of linear alkanes. of water is reduced surrounding the solute. Above the critical However, one can verify the effect of molecular size on hydropho- temperature, the thermal motion overcomes the restrained water bic hydration by examining the effect of size on the temperature molecules’ confining potentials and the hydration entropy be- dependence of ΔGhyd. comes positive. The results indicate that the critical temperature The hydration free energy of small (1–3 Å) nonpolar molecules corresponding to zero hydration entropy decreases as the solute monotonically increases with temperature in the experimentally size increases. Therefore, at a given temperature, different accessible range as in the case of short-chain alkanes and noble mechanisms govern the hydration of hydrophobic side chains de- gases. Larger nonpolar molecules (<10 Å) such as benzene and pending on their sizes. The negative hydration entropy at lower toluene exhibit a different characteristic temperature depen- temperature suggests that water is more structurally organized dence of ΔGhyd, which increases with temperature and reaches around extended hydrophobic polymers. Even though the length a maximum before it decreases as temperature continues to rise. of the polymer extends hundreds of nanometers, the size across Once the particle size is greater than a few nanometers, its the chain is subnanometer, which is small enough to allow water hydration free energy follows macroscopic interfacial thermo- connectivity across the chain. Temperature dependence of ex- ΔGhyd dynamics, which monotonically decreases as temperature rises. tended polymer showed similar size dependence as for ΔGhyd Theories on small particle hydration have shown that as the par- small molecules, whose per surface area decreases from ΔGhyd macroscopic interfacial free energy (when the spherical solute ticle size increases, the temperature at which is maximized ∼1 will shift lower, providing a smooth transition between the tem- radius exceeds nm) to 0 as the solute size shrinks (6, 23, 28). ΔGhyd perature dependence of ΔGhyd from small to large solute (21, 23, This similar size dependence of places the interaction be- 28). To examine this effect, two other hydrophobic polymers with tween extended polymers on the same small molecule length identical backbones but side chains of different sizes were used: scale as their free monomer counterparts. The different nature of small molecule hydration from macroscopic interfacial energy PtBS and PVBP with calculated monomer sizes (backbone + side warrants reexamining the hydrophobic interaction of polymers. chain) of approximately 9.5 Å and approximately 11.4 Å, respec- In particular, the lower-than-SASA-predicted hydration free en- tively. Both polymers’ monomers are larger than that of PS ergy suggests a weaker driving force for the association of hydro- (∼7.2 Å), but not large enough to fall into the macroscopic re- phobic residues in a chain. gime. The single molecule force-extension curves for PtBS and However, free monomer ΔGhyd cannot be directly applied to PVBP have the same features as PS because of the same physical polymer systems. As Fig. 2C illustrates, ΔGhyd can be obtained by phenomena (coil-globule transition and hydrophobic hydration) measuring free monomer solubility or transfer energy from the governing their shape. However, the temperature-dependent equilibrium between free monomers and their aggregates (similar ΔGhyd profiles of the of both PtBS and PVBP were significantly to the collapsed state of a polymer). The change of hydration free different from the monotonically increasing profile of PS. In the energy due to polymerization from free monomers to a polymer is case of PtBS, the slightly larger side chain shows a maximum in significant, as the magnitude of hydration free energy of free ΔGhyd 55 1 0 9 D at . . °C (Fig. 3 ). For PVBP with even larger side monomers is 3–4 times greater than that assigned to repeated ΔGhyd 47 8 0 9 E chain, maximum shifts lower to . . °C (Fig. 3 ). units on the polymer. The large difference in hydration free en- The turnover behavior is characteristic of solutes whose sizes lie ergy is not surprising when a realistic picture of the polymer is in the crossover regime between hydrophobic hydration of small considered: For PS, the size of each monomer from the backbone hyd (<7 Å) and large (>20 Å) solutes. A parabolic fit to ΔG ðTÞ of to the end of the side chain is approximately 7.2 Å, whereas PS (Fig. 3C) yields an extrapolated hydration maximum at the distance between adjacent monomers is only 2.5 Å (Fig. S3). 92 45 °C. Experiments above 80 °C could not be performed The proximity of neighboring side chains indicates that there are to further verify this trend because of the formation of air bubbles likely significant hydrophobic interactions between them. As a on the AFM cantilever. The different temperature dependencies result, the net free energy required to hydrate each sandwiched of PS, PtBS, and PVBP are direct results of the differing sizes of monomer unit on the chain is reduced compared to the free en- the side chains. ergy required to hydrate a free monomer without neighbors. Therefore, the resulting estimated driving force for hydrophobic Discussion collapse of a chain is actually much lower than if one were to as- C As Fig. 2 illustrates, the forced hydration process changes the sume each monomer on the chain has the same hydration free conformation of the hydrophobic polymer from collapsed to ex- energy as a free monomer. Knowing the hydration free energy of tended state with constant tension. The tension on the extended, free monomers from either transfer or solubility experiments solvent exposed portion of the chain keeps that portion of the may be insufficient to predict the free energy of macromolecules, chain constantly extended at approximately 75% of its contour and the direct measurement of the hydration free energy in the ΔS 0 length, which significantly lowers the entropy ( ext < ) between system of interest by the single molecule technique presented the extended and relaxed conformations, both of which are fully here may be necessary for accurate assessment. hydrated (Fig. 2 B and C). Here, the fully hydrated, relaxed con- The temperature and monomer size dependence of ΔGhyd are formation is not a stable state accessible to our experiment as it consistent with hydrophobic polymer unfolding simulations from would only exist transiently and undergo rapid hydrophobic col- Athawale et al. (27). Their work suggests that the turnover beha- lapse (shown by the reversible force curves in ref. 10). Such a tran- vior of ΔGhyd is present only when a Lennard–Jones attraction sient state was considered to compute the free energy contributed between polymer and water is introduced. However, study from from only hydration as the chain unfolds. A fully hydrated, but Huang and Chandler (28) indicates that attraction between solute extended state, shares the same hydration contribution but also has and water does not significantly alter the turnover temperature of a large free energy contribution from the reduced chain entropy ΔGhyd, as the attraction does not add to the entropic contribution ΔS TΔS ext. The temperature-dependent contribution of ext causes to the free energy. In experimental systems, it would be difficult the turnover temperature of ΔGhyd to be lower than that of FðTÞ, to assess the contribution because of polymer-solvent attraction. as shown in Fig. 3 C, D,andE. Furthermore, it was pointed out that the turnover temperature is

16530 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1105450108 Li and Walker Downloaded by guest on September 29, 2021 much more sensitive to the size of the solute than the attraction water. The temperature dependencies of the hydration free en-

between solute and solvent (28). The length of the polymer used ergy for single-chain PS, PtBS, and PVBP differ from macro- SEE COMMENTARY in the experiment reported here is much greater (hundreds of scopic interfacial thermodynamics specifically due to the small nanometers) than the 25 mer (∼4 nm) used in the simulation length scales of the monomer units along the chain. Furthermore, from Athawale et al. (27). As a result, the experiment does not ΔGhydðTÞ from the three polymers clearly showed the tempera- probe the finite size effect as in the work of Athawale et al. In tures that correspond to ΔGhydðTÞ maxima decrease, for increas- addition, because both area and volume of the extended polymer ing hydrophobic side-chain sizes. This trend provides an apparent are proportional to the extended chain length, the experiment transition from the monotonically increasing profile of ΔGhydðTÞ cannot directly test whether the extended polymer ΔGhyd is area for PS to the monotonically decreasing profile of a macroscopic or volume dependent. hydrophobe. The results of this paper demonstrate that monomer Traditionally, the hydration of linear alkanes has been studied size plays a key role in the origin of hydrophobic interaction en- as a model for hydrophobic hydration and interaction. Similar to ergy in polymer systems from homopolymers to heteropolymers polymers, the lengths of linear alkanes can be increased (from such as proteins. The length scale of amino acid is relevant here; ∼3.5 Å for methane to ∼12.5 Å for decane), whereas the cross- the deviation of the actual hydration free energy from the predic- sectional diameter remains approximately 3.5 Å. As shown below, tion of interfacial thermodynamics is significant to the folding the implications of these results are consistent with the existing and stability of proteins. When only a few hydrophobic residues linear alkane data. Data from transfer free energy experiment at associate, the resulting complex may not reach the length scale 298 K (11) show that hydration free energy linearly correlates where the hydrophobic interaction is driven by the minimization with alkane chain lengths of various hydrocarbons and derivatives of interfacial area; but rather, the energy to form the complex (Fig. S4), suggesting the total hydration free energy is additive for scales according to its volume. Therefore, the resulting hydro- each additional CH2 at a given temperature (37). The additive phobic complex should be rather weak and short-lived until the effect is consistent with the finding that, for a linear macromo- complex reaches a certain critical nucleation size, which may play lecule, the hydration free energy of the extended state is the a key role in the stability of early-stage protein folding. For in- sum of the contributions by individual monomers along the chain. stance, during the early stage of protein folding from a random The additive nature implies that the temperature dependence coil, the path of hydrophobic association among different-sized ΔGhyd of for the whole extended polymer chain is identical to hydrophobic core residues may be significant to the stability of ΔGhyd of a single repeated unit on the chain, independent of particular intermediates. This work highlights the risks of under- the chain length. The temperature dependence of linear alkane estimating how many amino acids are required to form a stable CHEMISTRY hydration energies shows weak length dependence from methane hydrophobic core of a protein. to nonane even though the length spans from the microscopic to the macroscopic thermodynamics regimes. To explain this weak Materials and Methods length dependence, one must distinguish the different molecular Polymer Sample Preparation. The preparation and surface deposition of geometries—the size of a linear molecule such as alkane and PS, PtBS, and PVBP polymers were performed according to the previously polymer cannot be characterized by its length, whereas size de- described procedure (10). pendence in theoretical studies usually refers to the radii of spherical particles. In addition, there are significant hydrophobic Single Molecule Force Spectroscopy. All single molecule experiments in this interactions between adjacent CH2 units on the linear alkane study employed the Asylum Research MFP-3D AFM. The use of stiffer because the transfer free energy of methane from hexadecane 60 pN∕nm Si3N4 AFM tips from Veeco (MLCT-AUNM) minimized the intrinsic to water is 16.6 kJ∕mol, but the additional transfer free energy cantilever bending due to different experiment temperatures, a problem that makes softer cantilevers employed in the previous work (10) unusable. for each additional CH2 is only 4.7 kJ∕mol (Fig. S3). The spring constants of the cantilevers do not change significantly (<1%) This work adds an important piece to the puzzle of hydropho- from 30 °C to 80 °C, as verified by the thermal noise method. The following bic solvation. It is worth noting that in previous work the solvation methods were employed to minimize measurement errors: First, one AFM free energy was shown to correlate with interfacial free energy cantilever was used for every set of temperature-dependent experiments when both monomer size and temperature were kept constant; (30°C to 80 °C), which eliminated the cantilever calibration error (∼5–10%) the only varying parameter being the chemical composition of within each set of temperature-dependent experiments. The final force value the solvent (10, 38). The results of this study show that, in the at each temperature is obtained from averaging five to eight sets of inde- more general case, one should include a temperature T depen- pendent experiments. Second, it was verified that the measured force was dence in both the monomer hydration free energy and the solvent unaffected by any slow-drifting parameters, such as changes in laser intensity quality terms in the simple total solvation free energy expression or formation of air bubbles on the AFM cantilever. This verification was for the extension of the polymer ΔGsolv (10): achieved using different temperature sequences to ensure that there was total no correlation between temperature and time. To avoid finite size effect of the collapsed state, single chains were pulled from a layer of polymer ag- ΔGsolv ðTÞ¼ΔGhydðr;TÞχðTÞN; [2] total gregate such that the change of surface area of the collapsed state can be approximated to 0. Roughly 150,000 force curves were collected per polymer where r is the size of monomers on the chain, ΔGhyd is the sample per experiment to ensure sufficient statistics of the results. Approxi- hydration free energy per monomer on the chain in pure water, mately 75% of the force curves did not exhibit chain pulling events, roughly N is the number of solvent exposed monomers, and χ is the relative 15% percent exhibited rugged profiles characteristic of complex adhesion solvent quality correction factor defined by the ratio between rupture processes and were discarded. The remaining approximately 10% γ of the force curves were selected for further analysis. For each of the selected solvent-polymer and water-polymer interfacial free energies ( sp and γ ): force-extension curves, the last force plateau corresponding to single-chain wp hydration was identified and a force histogram containing the last force χðTÞ¼γ ðTÞ∕γ ðTÞ: plateau and the baseline was collected and fitted to two Gaussian functions. sp wp The peak to peak distance between the two Gaussians gave the plateau force magnitude of each force curve.

Conclusion ACKNOWLEDGMENTS. We acknowledge funding support from the Natural The experimental results presented here provide a fundamental Science and Engineering Research Council of Canada (NSERC), and the Office description of the hydration of a single hydrophobic chain in of Naval Research (ONR).

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