6760
J. Phys. Chem. 1996, 100, 6760-6763
Are There Water-Bridge-Induced Hydrophilic Interactions? Yaxiong Sun† and Peter Kollman* Department of Pharmaceutical Chemistry, UniVersity of California, San Francisco, California 94143-0446 ReceiVed: March 23, 1995; In Final Form: August 7, 1995X
Inspired by experimental studies of the transfer free energies of phenol derivatives with hydroxylmethyl substitutions at ortho, meta, and para positions, Ben-Naim has proposed that water-bridge-induced “hydrophilic interactions” are stabilizing by about 3 kcal/mol, much larger than corresponding hydrophobic interactions. We have used theoretical free energy perturbation calculations to assess this proposal. By use of two sets of partial charge models derived by fitting to ab initio quantum mechanical electrostatic potentials, free energy calculations have shown that the solvation free energy differences between these substituted phenols are small. These results are inconsistent with the aforementioned “water-bridge” hypothesis. Interestingly, these calculated free energies for gas phase f water are quite consistent with the experimental values for octanol f water free energies of transfer but not with the experimental values for toluene f water free energies of transfer, which were used by Ben-Naim to develop his hypothesis. The positional dependence of the free energies of transfer from toluene to water could be complicated by the differential interactions of solutes with liquid toluene, and this was not accounted for in the development of the “water-bridge” hypothesis.
Introduction Solvation plays a critical role in chemistry and biochemistry. Many studies have been made over the years to understand the effects of solvation on molecular conformation and chemical reactions. Both numerical models and conceptual approaches have been applied to study the solvation process. Specifically, water bridges, i.e., water interacting with two solute atoms simultaneously by forming a bridge between them, have often been used to explain many solvation phenomena. A series of studies reported recently by Ben-Naim attempted to theorize and quantify the solvent-induced interactions between two functional groups.1,2 One of Ben-Naim’s hypotheses is that the hydrophilic interaction, i.e., a water-induced interaction between two hydrophilic groups, has a strength of about -3 kcal/mol, much stronger than the corresponding hydrophobic interaction, which has traditionally been considered as the predominant driving force for many biomolecular association phenomena including protein folding.3 On the basis of his hypothesis about the strength of solvent-induced hydrophilic interactions, BenNaim has suggested that hydrophilic interactions, rather than hydrophobic interactions, are responsible for many biomolecular phenomena.4 The most important experimental evidence used by Ben-Naim to support his hypothesis is an experimental study reported by Haberfield on the transfer free energies of substituted phenols (Figure 1 and Table 1).5 From those results, supported by a Monte Carlo molecular simulation study, which will be commented on below, Ben-Naim has suggested that a water-bridgeinduced hydrophilic interaction has a strength of about -3 kcal/ mol. His analysis of the data in Table 1 is as follows. The free energies of transfer from toluene to water provide a good approximation for the relative solvation free energies in water (from the gas phase). Table 1 shows that the strength of free energy of solvation of (hydroxymethyl)phenol depends on the position of the substitution. Ben-Naim proposes that the dramatic differences among the free energies of solvation in † X
Graduate Group in Biophysics. Abstract published in AdVance ACS Abstracts, March 15, 1996.
0022-3654/96/20100-6760$12.00/0
Figure 1. Substituted (hydroxymethyl)phenols (HMP).
TABLE 1: Experimental Free Energy of Transfer (kcal/mol)a phenols
∆G(tol f wat)
∆∆G(tol f wat)b
∆G(oct f wat)
∆∆G(oct f wat)b
o-HMP m-HMP p-HMP
-1.20 -2.80 0.35
1.60 0.00 3.15
0.76 0.69 0.34
0.07 0.00 -0.35
a From ref 5. b Free energy changes relative to the m-HMP transfer free energies.
Table 1 are due to the “interference” of solvation of the two hydroxyl groups in these phenols. Specifically, the solvation free energy of m-(hydroxymethyl)phenol (m-HMP) is much larger than the solvation free energy of both the ortho isomer (o-HMP) and the para isomer (p-HMP), in spite of the fact that the distance of two hydroxyl groups in m-HMP is between the distances in o-HMP and p-HMP. The reason for this, as proposed by Ben-Naim, is that the two hydroxyl groups in m-HMP can form simultaneous hydrogen bonds (H-bonds) with solvent water molecules and not disrupt the water structure. In m-HMP the distance between two hydroxyl groups is about 4.9 Å, which is close to the ideal distance at which the oxygens could form a “H-bond chain” through a water molecule as a bridge. Given the importance of these (hydroxymethyl)phenols in supporting the theory of water-bridged hydrophilic interactions, the purpose of our present study is to test the existence of this water-bridge-induced interaction, especially strong interference of hydrophilic solvation, through molecular dynamics free energy perturbation (FEP) simulations. © 1996 American Chemical Society
Hydrophilic Interactions?
(a)
J. Phys. Chem., Vol. 100, No. 16, 1996 6761 water molecules in a cubic box of length 25 Å. The simulations were carried out at 300 K and at constant pressure of 1 atm; periodic boundary conditions were applied. The coupling constants to an external heat and pressure bath were 0.4 ps. The SHAKE procedure was employed to constrain all the bonds containing at least one hydrogen atom.11 The dynamics were run with a time step of 1.5 fs and a nonbonded cutoff of 8 Å. Statistical mechanical free energy perturbation theory12 allows for the calculation of free energy differences between two states of a system, A and B. The two states A and B are linked together with a coupling constant of λ. That is, the system is represented by a potential function H(λ), such that H(λ ) 0) ) HA and H(λ ) 1) ) HB, where HA and HB are the Hamiltonians of states A and B. The free energy difference between the states at λ and λ + ∆λ is
〈 (
∆Gλ ) -RT ln exp -
(b)
)〉
Hλ+∆λ - Hλ RT
λ
where R is the gas constant, T is the absolute temperature, and 〈 〉λ denotes the ensemble average at state λ. The total free energy change between A and B is thus λ)1
∆G ) ∑∆Gλ λ)0
Figure 2. Partial charges used in the simulations: (a) RESP charges; (b) equivalenced charges.
Computation Methods All simulations described in this paper were performed using the molecular mechanical simulation package AMBER4.1.6 The Weiner et al. force field was used.7 Ab initio 6-31G* calculations were done for all three phenols in Figure 1. The structures used all have the hydrogen atom of the phenol hydroxyl group pointing away from the substituted group and the oxygen of the substituted group perpendicular to the aromatic ring. All structures were minimized using AMBER/MINMD prior to quantum mechanical calculations. Partial charges in Figure 2a were obtained by fitting to the electrostatic potentials from ab initio calculations using the RESP (restrained electrostatic potential) fitting protocol with the two-stage procedure as described by Bayly and Cornell et al.8,9 To separate electronic effects from solvation effects, another set of charges were calculated by equivalencing all the corresponding functional groups in three substituted molecules, i.e., forcing the corresponding atoms to have the same charges during the fitting (Figure 2b). The solvation properties of this equivalenced charge model should reveal any possible interference phenomena in hydrophilic solvation while eliminating possible complications caused by any specific electronic properties of these phenol derivatives. The phenols were solvated with approximately 500 TIP3P10
Prior to carrying out perturbations, all systems were equilibrated for at least 30 ps. The “window” method of AMBER/ GIBBS6,13 was used for all the free energy calculations. Each window contained 1000 steps of equilibration and 1000 steps of data collection for a total of 300 ps per simulation. All the simulations were run in both the forward (λ ) 1 f 0) and the backward (λ ) 0 f 1) directions to provide an estimate of statistical errors. The calculations presented here do not include intramolecular energies in the free energy calculations, making the assumption that these are identical in the gas phase and in aqueous solution. We (P. Cieplak, D. Veenstra, Y. Sun, and P. A. Kollman) have shown this to be a valid approximation in the calculations of the relative solvation free energies of methanol to ethane, dimethyl ether to propane, and methane to ethane. In addition, many free energy calculations that have been carried out by Monte Carlo calculations using the OPLS model make a similar assumption and have been shown to be usually in excellent agreement with experimental results.14,15 Results and Discussion Table 2 contains the FEP simulation results. With RESP charges, the solvation free energy relative to m-HMP is about 0.5 kcal/mol for o-HMP and -0.4 kcal/mol for p-HMP compared with the experimental toluene to water transfer free energy differences of 1.60 and 3.15 kcal/mol, respectively. When equivalenced charges were used, the relative free energies of the three hydroxylmethyl phenols are even smaller. The solvation free energy differences among the isomers are only about 0.3 kcal/mol. The discussion of these results as related to two separate issues is presented below. 1. RESP Charges. The reason for the fairly large differences between experimental free energies of transfer from toluene to water and the calculated relative solvation free energy differences from gas phase to water using RESP charges is not clear. Although the RESP charge model has been shown to be able to reproduce the solvation free energies of small molecules within 1 kcal/mol,9 there is always a possibility that the charge fitting may not work well for a specific molecule with certain
6762 J. Phys. Chem., Vol. 100, No. 16, 1996
Sun and Kollman
TABLE 2: Free Energy Perturbation Results (kcal/mol) of Substituted Phenol to Unsubstituted Phenol solvation free energies a
∆G o-HMP m-HMP p-HMP
(a) RESP Charges -6.6 -7.1 -7.5
∆∆Gb 0.5 0.0 -0.4
solvation free energies a
∆G o-HMP m-HMP p-HMP
(b) Equivalenced Charges -4.4 -4.4 -4.7
∆∆Gb 0.0 0.0 -0.3
a ∆G is the solvation free energy difference between a substituted phenol and a phenol. b ∆∆G is the solvation free energy of a substituted phenol relative to that of m-HMP. The estimated error is 0.2 kcal/ mol, based on forward and reverse simulations.
electronic structures and conformational isomers. On the other hand, the calculated free energies for gas phase to water are quite consistent with the experimental values for octanol to water free energies of transfer. Since toluene is a more apolar solvent than octanol, one would expect that the theoretical calculations would lead to free energies closer to the toluene to water than the octanol to water free energies of transfer. If the experimental free energies of transfer from toluene to water are indeed valid, the differences among these substituted phenol isomers likely arise from interactions with toluene, possibly involving some specific properties of liquid toluene that interact with these phenols differently. 2. Equivalenced Charges. The simulation results with equivalenced charges are designed for testing the existence of water-bridge-induced hydrophilic interactions, independent of any differences in solute charge distributions. Very small differences in the solvation free energies were calculated for the three different substitution positions with different separations between the polar groups. These pseudo “substituted phenols” with the equivalenced electrostatic charges as in Figure 2b should be able to reproduce the effect of hydrophilic solvation interference, if there is such an effect. We would now like to comment on the Monte Carlo simulation study by Mezei and Ben-Naim.16 In that work they calculated the potential of mean force (PMF) between two water molecules in aqueous solution, with fixed orientations for both water molecules of the dimer. It was found from the PMF calculations of three different orientations of the dimer that there are free energy barriers to separation ranging from 1.7 to 6.0 kcal/mol, averaging about 3 kcal/mol. It is thus concluded by the authors, in support of the interpretations of the experimental transfer free energies of the phenols discussed above, that the magnitude of the “hydrophilic interaction” is approximately 3 kcal/mol. It is important to note that the direct interaction between the two waters in the dimer was not included in the PMF, so the PMF calculations included the solvation free energy only. By use of a macroscopic model, the solvation free energy of two interacting dipoles can be expressed as follows:17
Gsolvation ) G(sol) - G(vac) ) G(vac)/ - G(vac) )
(
-G(vac) 1 -
1
)
proportional to the direct interaction energy. The more negative solvation free energy at small distances observed in the waterdimer PMF is simply due to the stronger repulsion between the dimer waters. It is unclear to us how these results could be related to water-bridge-induced, extra strong solvation at a specific separation distance. It is interesting to note that in the three configurations studied in ref 3, the dipole-dipole interactions between dimer waters are all repulsive. One orientation that has the two water monomers pointing in opposite directions has the largest repulsion; therefore, it has the largest barrier observed in the solvation free energy PMF. In short, these water-dimer solvation free energy PMF’s do not seem to be able to justify the existence of specific “water bridges” and the enhancement of solvation interference due to these “water bridges” at specific separations. Finally, we wish to emphasize that the simulation results presented here do not suggest in any way that “the experiment is wrong,” since we did not simulate the same experimental condition (from water to toluene) because of technical difficulties. One the other hand, these results do provide the only direct test of the aforementioned “water bridge” hypothesis regarding hydrophilic interactions in water. This is especially important when one considers that in the development of that hypothesis, toluene to water free energies of transfer were used to “approximate” gas phase to water free energies of transfer. Conclusions The FEP results show that the calculated solvation free energy differences are small (
