Driving Force for the Association of Amphiphilic Molecules - American

LETTER pubs.acs.org/JPCL

Driving Force for the Association of Amphiphilic Molecules Jagannath Mondal and Arun Yethiraj* Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States ABSTRACT: The classical view of the hydrophobic effect is that the association of hydrophobic molecules is entropy-driven and caused by the increase in the entropy of water. In this work, we investigate the thermodynamics of association of amphiphilic molecules that consist of a hydrophobic block and a hydrophilic block. Using atomistic simulations, we calculate the potential of mean force between molecules and obtain the entropic and energetic contributions from calculations at two temperatures. For purely hydrophobic molecules, the association is entropy driven, but for the block copolymers the thermodynamic driving force is sensitive to the conditions: The association between block copolymers is energy-driven in pure water and methanol but is entropy-driven in aqueous solutions with high concentrations of added salt. These results demonstrate that the driving force for association in amphiphilic molecules is sensitive to conditions, and the classical view of the hydrophobic effect is not universal. SECTION: Statistical Mechanics, Thermodynamics, Medium Effects

he hydrophobic effect1,2 causes nonpolar solutes to aggregate in water. For small solutes, this effect is believed to be entropic in origin. A solute molecule disrupts the hydrogen bonding network in water. The water molecules rearrange around this solute with a corresponding loss in entropy. This loss in entropy is reduced by an aggregation of the solute molecules. A molecular level understanding that supports this picture has emerged from a number of computational studies.3
8 The driving force for the aggregation of larger molecules is also thought to be of entropic origin. For example, potential of mean forces studies have shown that the association of rigid polyalanine helices is entropy-driven,9 and the aggregation of Aβ(10
35) peptides is driven by the favorable desolvation of hydrophobic residues at the dimer interface.10 Arguments based on the hydrophobic effect are also used to understand the collapse and aggregation of molecules, such as proteins, that contain both hydrophobic and hydrophilic moieties. The thermodynamic driving force for aggregation can be length-scale-dependent. Preserving the hydrogen-bonding network by the rearrangement of water molecules is not possible at a surface (or sufficiently large solute).11,12 It has been suggested that this could cause a drying transition and thus an enthalpic driving force for aggregation.13
19 The drying of the surface results in an expulsion of water molecules between two surfaces in proximity, resulting in a strong attraction between them. A dewetting of the surfaces is not necessary for aggregation. The association between small graphene plates is driven by an increase in solvent entropy,20
22 but the association between large graphene plates is dominated by the energetic interaction between graphene plates22 and is not accompanied by a drying or dewetting transition. A number of studies have questioned the classical view of the hydrophobic effect. For example, Seeling and Ganz23 have shown, using titration calorimetry, that the transfer of amphiphilic

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molecules from aqueous phase to lipid membrane can be either entropy-driven (for the positively charged local anesthetic dibucaine) or enthalpy-driven (for 2-(p-toluidinyl)napthalene6-sulfonate, tetraphenylborate, and amlodipine). Gorfe et al.24 found that the partitioning of an amphiphilic licopeptide ANCH to a membrane was enthalpy-driven. In this work, we investigate the thermodynamic driving force for the assembly of amphiphilic molecules. As a test case, we consider diblock copolymers of β-amino acids, where the hydrophobic block is composed of β-valine residues and the hydrophilic block is composed of positively charged 2-aminomethyl3,3-dimethyl β-amino acid residues. (See Figure 1.) Using atomistic simulations we calculate the potential of mean force (PMF) between molecules. By performing calculations at two temperatures, we obtain the entropic and energetic contributions to the PMF. We choose β-peptide oligomers because of the stability of the helices (in the hydrophobic block) but find similar results for natural peptides diblock oligomers as well. Most of our calculations are for a 10 residue hydrophobic block and a 10 residue hydrophilic block, and we refer to this molecule as a 10-b10 copolymer. We find that the driving force for association is sensitive to the length of the hydrophilic block and solvent conditions, suggesting that the classical hydrophobic effect is not applicable to amphiphilic molecules. The free energy of association of two (hydrophobic) poly β-valine oligomers in water is entropically driven, but that between 10-b-10 copolymers is energetically driven. Figure 2a depicts the PMF between two 10-residue β-valine oligomers (helical and hydrophobic) in water at temperatures of 285 and 300 K. The total PMF between β valine oligomers has an Received: August 1, 2011 Accepted: September 1, 2011 Published: September 02, 2011 2391

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The Journal of Physical Chemistry Letters attractive minimum at a distance of ∼1 nm, and the strength of the attraction decreases as the temperature is decreased. This is a signature of an entropic attraction. The entropic (
TΔS) and energetic (ΔU) contributions are depicted in Figure 2b and show that there is a large positive energetic penalty to association (∼50 kCal/mol), which is compensated for by a large gain in entropy. This favorable entropy change due to association of β-valine oligomers is typical of the “hydrophobic effect” and is seen for the association of graphene plates21 and rigid poly

Figure 1. Representative snapshot of the block copolymer used in the study where the hydrophobic (H) block is red and the hydrophilic (P) block is green/blue. Also shown are the chemical formulas of the residues that make up each block.

LETTER

alanine peptides in water.9 Also shown in Figure 2a is the free energy of association of two hydrophilic oligomers of positively charged 2-aminomethyl-3,3-dimethyl β-amino acid residues. The PMF between these hydrophilic residues is always repulsive, as expected, because of the positive energy of association. When the hydrophobic and hydrophilic peptides are connected to make a 10-b-10 copolymer, the PMF is strongly attractive and of energetic origin. Figure 3a depicts the PMF at T = 285 and 300 K and shows that the PMF is attractive at similar distances as in the case of the hydrophobic peptides and of similar depth. However, the attraction is weaker at the higher temperature, unlike in the hydrophobic peptides. Figure 3b shows that the PMF consists of a strongly attractive (on the order of
100 kcal/mol) energetic contribution that is balanced by a high entropic cost. The driving force for association depends on the length of the hydrophilic block, with a delicate balance between entropic and energetic effects. Figure 4a,b depicts the PMF for 10-b-1 ad 10-b5 copolymers at two temperatures. For the 10-b-1, the attractive minimum in the PMF is weaker at the lower temperature, implying an entropy-driven process similar to the hydrophobic molecules. For the 10-b-5 copolymers, the depth of the minimum in the PMF is relatively insensitive to temperature, marking the crossover from entropy-driven to energy-driven association.

Figure 2. PMF between poly-β-valine 10-mers (solid lines) and hydrophilic 10-mers (broken lines) in water: (a) total PMF at T = 285 and 300 K and (b) entropic and energetic contributions to the PMF. (For hydrophilic 10-mers, the entropic contribution is negligibly small and hence not shown.)

Figure 3. PMF between 10-b-10 copolymers in water: (a) total PMF at T = 285 and 300 K and (b) entropic and enthalpic contributions to the PMF. 2392

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Figure 4. Total PMF at T = 285 and 300 K for (a) 10-b-1 and (b) 10-b-5 copolymers.

Figure 5. Contributions to the energetic part of the PMF between 10-b10 copolymers.

The dominant contribution to the energy of association comes from the interaction between the solvent molecules. Figure 5 depicts contributions from the peptide-solvent and solvent
solvent energies compared with the total ΔU in Figure 3b. Interestingly, the peptide
solvent contribution to the PMF is repulsive (the hydrophilic part of the peptide is negatively charged), but the solvent
solvent contribution is strongly attractive. The driving force for association is sensitive to the salt concentration. As the salt concentration is increased, the association between 10-b-10 copolymers becomes entropy driven. Figure 6 depicts the entropic and energetic contributions of the PMF for two 10-b-10 copolymers as a function of added (NaCl) salt. Contrary to the case for low salt, for high salt concentrations, the entropic contribution to the PMF dominates. The position of the minimum in the PMF is essentially independent of salt concentration, but the depth of the minimum increases as the salt concentration is increased. This is because the entropic effect becomes stronger in the presence of added salt. These observations are consistent with the Hofmeister effect, where polymers, for example, poly(N-isopropylacrylamide) (PNIPAM), are salted out in the presence of high concentrations of sodium chloride.25 In summary, we find that the association of amphiphilic (block copolymer) molecules can be either entropy-driven or energydriven depending on the nature of the molecules. In pure water,

for purely hydrophobic molecules or when the hydrophilic block is very small, the free energy of association is entropy-driven, and when the hydrophilic block is large, the association is energy driven. The dominant contribution to the attractive PMF in all cases comes from the contribution of the solvent. The effect depends on the polarity of the solvent. Similar results are seen when the solvent is methanol, although the energy-driven association is less prominent, and for oligomers of natural α peptides. In the presence of high concentrations of added salt, however, the free energy of association is entropy-driven. We can only speculate on the physical origin of this behavior. One can think of a “release” of water molecules due to the aggregation of the hydrophobic blocks. In the presence of the hydrophilic blocks, this could result in an increase in the number of water molecules coordinated with the hydrophilic moieties, resulting in a higher density of water near these blocks and therefore a higher solvent
solvent attraction. This coordination diminishes with the addition of excess salt. As a caveat, these calculations are all performed with classical (although atomistic) models of ions and water, where hydrogen bonding occurs solely through electrostatic interactions. It is possible that the conclusions are sensitive to the nature of hydrogen bonding interactions, of course, but the models used here are quite typical of biophysical simulations and are believed to represent these systems quite faithfully. We therefore conclude that the classical view of the hydrophobic effect does not hold for amphiphilic molecules where the association can depend on the nature of the molecules and the solvent conditions. We believe that the simulation approach described in this Letter may have a potential in the understanding of the association of amphiphilic block copolymers of the type PEG-b-PNIPAM, where PNIPAM is a very temperature-sensitive polymer.

’ COMPUTATIONAL METHOD Simulations are performed in the NVT ensemble using the GROMACS 4.0.5 package.26 For the β-peptides, we use the atomistic force field developed in our group27
29 that is compatible with the CHARMM22 forcefield30 that we use for other components including (TIP3P) water, methanol, sodium and chloride ions, and natural amino acids. The initial configurations are generated as follows. The simulation cell is a cube with side length 6.5 nm for the case of 10-b-10 block copolymers and 4.5 nm for the case of 10-mer of 2393

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Figure 6. (a) Energetic and (b) entropic contributions to the PMF between 10-b-10 copolymers for various salt concentrations.

β-valine. For windows corresponding to distance beyond 1.4 nm between a pair of objects, the two block copolymers are kept in a side-by-side parallel fashion at the position of each of the windows. For windows ranging from 0.4 to 1.4 nm, to avoid bad contacts, we use the configuration corresponding to adjacent window (higher distance), and the molecules are pulled to the desired position. This initial configuration is subjected to energy-minimization using the steepest-descent technique. The configurations of molecules is then solvated with solvent with some solvent molecules replaced with chloride ions to ensure electroneutrality. The overall system is then subjected to energy minimization in the presence of umbrella potential. The system is evolved using molecular dynamics in the NVT ensemble with temperature maintained using a Nose
Hoover thermostat.31,32 All bonds involving hydrogen are fixed at their equilibrium distance using LINCS constraint algorithm.33 The SETTLE34 algorithm is used to keep the water molecules rigid. The system is evolved using a leapfrog algorithm with a time step of 2 fs. Lennard-Jones (LJ) interactions are switched smoothly to zero at 1.0 nm, and particle-mesh Ewald (PME) summation35,36 is used for the long-range electrostatic interactions. The PME parameters are as follows: real space cutoff distance of 1.4 nm and interpolation order of 6, with a maximum fast Fourier transform grid spacing of 0.12 nm. We use umbrella-sampling to compute the PMF between molecules. The reaction coordinate (ξ) is the distance between the fifth residue of the hydrophobic segment of the two molecules. We employ 23 windows ranging from 0.4 to 2.6 nm at a separation of 0.1 nm. The force constant for the umbrella sampling is 3000 KJ/(mol 3 nm2). The weighted histogram analysis method (WHAM)37,38 is used to unbias the histogram. The entropy is calculated from the finite difference temperature derivative of the PMF or ΔA(ξ) at each intersolute separation ξ, that is
ΔSðξÞ ¼

ΔAðξ, T þ ΔTÞ
ΔAðξ, TÞ ΔT

ð1Þ

where A is the Helmholtz free energy, ξ is the reaction coordinate, T is the temperature, and ΔT is the temperature difference between two simulations. We perform simulations for T = 285 and 300 K and ΔT = 15 K. The energetic contribution is obtained from ΔU(ξ) = ΔA(ξ) + TΔS(ξ). Following work of Choudhury et al.,21 to elucidate the contribution from solvent molecules to the PMF, we evaluate

the solvent contribution ΔWSOL to the PMF ΔA(ξ) by subtracting the direct potential between two solutes, UPEP
PEP from the PMF, that is ΔWSOL ðξÞ ¼ ΔAðξÞ
UPEP
PEP

ð2Þ

Because most of the entropic contribution comes from solvent, we can calculate the solvent-induced enthalpy of association (ΔUSOL) as ΔUSOL ðξÞ ¼ ΔWSOL ðξÞ þ TΔSðξÞ

ð3Þ

To clarify the role of the reorganization of water molecules around the solutes, further analysis of ΔUSOL is necessary. The solvent contribution to the enthalpy of association can be split further into two terms, namely, a solute
solvent direct interaction, ΔUPEP
SOL, and solvent
solvent enthalpy change (ΔUSOL
SOL). Now, ΔUPEP
SOL represents the potential energy of interaction of a pair of the solutes separated by a distance ξ with the surrounding water molecules relative to its value at infinite distance. Hence, the solvent
solvent enthalpy change (ΔUSOL
SOL) can be calculated by subtracting ΔUPEP
SOL from ΔHSOL, that is ΔUSOL
SOL ðξÞ ¼ ΔUSOL ðξÞ
ΔUPEP
SOL ðξÞ

ð4Þ

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We thank Professor Qiang Cui for useful discussions and a critical reading of the manuscript. This research was supported by the National Science foundation through the UW-Madison Nanoscale Science and Engineering Center (NSEC) (NSF grant DMR-0832760) and grant no. CHE-1111835. We are grateful for computational support from Abe machine in National Center for Supercomputing Application (NCSA), queen bee machine in LONI supercomputers, and Trestles machine in SDSC supercomputer under grant number TG-CHE090065 and the UW Madison Centre for High Throughput Computing (CHTC) Condor supercomputing facility. This research was supported in part by National Science Foundation Grant CHE-0840494. 2394

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