Water Effective Interactions

Article pubs.acs.org/JPCB

Double Resolution Model for Studying TMAO/Water Effective Interactions Luca Larini and Joan-Emma Shea* Department of Chemistry and Biochemistry and of Physics, University of California, Santa Barbara, Santa Barbara, California 93106, United States S Supporting Information *

ABSTRACT: The structural properties of water molecules surrounding TMAO molecules are studied using a newly developed atomistic force field for TMAO, combined with a multiscale coarse-graining (MS-CG) force field derived from the atomistic simulations. The all-atom force field is parametrized to work with the OPLS force field and with SPC, TIP3P, and TIP4P water models. The dual-resolution modeling enables a complete study of the dynamical and structural properties of the system, with the CG model providing important new physical insights into which interactions are critical in determining the structure of water around TMAO. TMAO is an osmolyte that stabilizes protein structures under conditions of chemical, thermal, and pressure denaturation. This molecule is excluded from the surface of proteins, and its effect on protein stability is mediated through TMAO−water interactions. We find that TMAO strongly binds two to three water molecules and, surprisingly, that methyl groups repel both the other methyl groups of TMAO and water molecules alike. The latter result is important because it shows that methyl groups are not interacting with each other through the expected hydrophobic effect (which would be attractive and not repulsive) and that the repulsion of water molecules forces a clathrate-like hydrogen bond network around them. We speculate that TMAO is excluded from the vicinity of the protein because the peculiar structure of water around TMAO prevents this molecule from coming in close contact with the protein.

1. INTRODUCTION Trimethylamine N-oxide (TMAO) is an organic osmolyte that has been shown in in vitro experiments to stabilize the native structure of proteins2−4 and nucleic acids.5−7 This molecule inhibits the unfolding of proteins in the presence of chemical denaturants, as well as under conditions of elevated temperatures and pressures. Several marine species, elasmobranchs (sharks and rays) in particular, use TMAO to counteract the elevated concentrations of urea present in their bodily fluids, blocking the denaturation and resulting inactivation of essential proteins.8,9 The plasma concentration of TMAO is known to increase in species that live at great depths in the ocean,10−14 presumably to offset high pressure-induced protein unfolding, leading to loss of enzymatic function and reduced actin polymerization.10,14−16 The effect of TMAO is also observed in bacteria, in which the presence of this osmolyte increases bacterial survival rates at elevated temperatures that would otherwise be lethal to the cell.17 Chemical, heat, and pressure denaturation all affect, in different ways and to varying extents, the interactions between the protein and water.18−22 For instance, at high pressures, the protein’s denatured state, with an expanded, solvent filled hydrophobic core, is favored because hydrophobic solutes prefer to adopt solvent separated conformations under these conditions.23−30 Likewise, when TMAO is now added to the solution, it becomes critical to consider the interactions between water and TMAO to understand how this osmolyte © XXXX American Chemical Society

can stabilize proteins. Indeed, several experiments and simulations have shown that TMAO alters the arrangement of water molecules at a microscopic level, leading to a long− range effect on water structure.31−38 Furthermore, TMAO is repelled by the protein’s backbone, even though a mild attraction to the residue-specific side chain may be present.31,39−41 Because TMAO is generally excluded from the vicinity of the protein, its effect on protein stability must be mediated through its effect on water structure. The molecular origin of TMAO−water interactions, in particular whether they are of entropic or enthalpic nature, remains a matter of debate.41−43 Returning to our example of pressure denaturation, one can rationalize the stabilizing effect of TMAO on proteins at high pressures by TMAO’s effect on water, in particular its ability to retain water around itself. This, in turn, changes the local and long-range hydration properties of water, making the solvation of hydrophobic solutes less favorable.44 Similarly, protein stabilization in the presence of urea and high temperature can also be explained in terms of water−TMAO interactions. At elevated temperatures in the presence of TMAO, the solvent interacts with TMAO rather than the protein, reducing the Special Issue: Peter G. Wolynes Festschrift Received: April 12, 2013 Revised: June 14, 2013

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dx.doi.org/10.1021/jp403635g | J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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coordinates” in the literature). It has been shown in the literature70 that the “average force” (see Methods section for details) computed by MS-CG is equivalent to computing the actual potential of mean force (PMF) along the generalized coordinates of choice. The advantage of using a CG model is that CG simulations can be readily performed and used to assess which elements (in terms of both model resolution and physical interactions) are required to reproduce the system under investigation. On the other hand, as a consequence of its “average” nature, this CG model is not suitable to evaluate time scales. As a consequence, dynamic properties have been computed through atomistic simulations. Our paper is structured as follows. Following a brief section explaining the simulations protocols, we present the parametrization and validation of the atomistic model and a discussion of the dynamical properties of the TMAO/water mixtures. This is followed by a parametrization and validation of the CG model, and a discussion of the structural properties of TMAO/water and new insights obtained from our dual resolution analysis.

number of solvent−peptide backbone hydrogen bonds, such that denaturation is now more difficult to achieve.45 In this respect, TMAO acts as a chemical chaperone, similar to the heat-shock chaperone proteins used by the cell. The above examples highlight the importance of a molecular understanding of the interaction of water with TMAO for explaining the stabilizing effect of this osmolyte. In this paper, we present a novel approach to study the effect of TMAO on water using a combination of atomistic and coarse-grained (CG) models. We focus on a simple mixture of water and TMAO to clearly identify the structural and dynamical effect that TMAO has on the water molecules. Using both atomistic and coarse-grained models enables us to study the properties of this molecule at two different resolutions, with the dynamics studied at an atomistic level, and the coarse-grained model used to identify the essential interactions between TMAO and water. An atomistic force field, based in part on the parameters by Kast et al.,1 was developed. The Kast model was developed starting from quantum ab initio calculations. Partial charges were evaluated by fitting the electrostatic potential, whereas bonded interaction were determined by normal-mode analysis. These parameters were retained in our current model. However, a new set of Lennard-Jones parameters was developed for three reasons: (1) the model would be extended to work together with the OPLS-AA force field46−52 (a detailed discussion about this point is given in section 3.1); (2) in contrast to the original model, a different set of parameters was developed for different water models (SPC/E,53 TIP3P,54 and TIP4P54); (3) the original model was optimized for a class of compounds (a limitation that was noted by Canchi et al.40,41), whereas our model is specifically optimized to reproduce the behavior of TMAO in water. Although atomistic simulations are the preferred simulation means for evaluating dynamical properties and associated time scales, coarse-grained models can play a complementary role and provide new physical insights into structural aspects. CG modeling helps reduce the complexity of the original model and retains only the most fundamental properties of the system under investigation. To evaluate the effective force between water and TMAO, we have developed the coarse-grained (CG) model shown in Figure 1. This CG model has been constructed using the MS-CG methodology55−70 that computes effective forces from atomistic simulations data.

2. METHODS Details of the simulation protocol are given in this section. Simulations were performed using either the GROMACS (atomistic simulations)71−74 or LAMMPS (coarse-grained simulations)75,76 package. Analysis was performed using the tools available in the VMD software77 or in the packages listed above. In addition, new analysis tools compatible with the GROMACS’s suite have been developed in-house for computing the water structure around each TMAO molecule. 2.1. Molecular Dynamics Simulation with the Atomistic Force Field. Water/TMAO mixtures were simulated at different concentrations and temperatures. For the parametrization of the atomistic force fields, molar ratios for TMAO/water mixtures of 1:5, 1:10, and 1:15 were used. For each concentration, two temperatures were used: 298.15 and 323.15 K. In the literature, different water models are available, each with its own strengths and weaknesses. For this reason we chose to develop a new force field that can work with three of the most popular models: the TIP3P,54 TIP4P,54 and SPC/E53 water models. For all the simulations, the equilibrium volume was computed using the NPT (constant temperature and pressure) ensemble. Once the equilibrium volume was found, NVT (constant temperature and volume) simulations were performed at this volume and later used to develop the coarsegrained model described below. The pressure was kept constant at 1 bar using the Parrinello−Rahman barostat78,79 (time constant τP = 1 ps), and the Nosé−Hoover thermostat80,81 (time constant τT = 0.1 ps) was employed for fixing the temperature. A time step of 1 fs was used for the integration of the equations of motion. All the bonds were kept fixed at their equilibrium values using either SETTLE82 (water) or LINCS83 (TMAO). Periodic boundary conditions were employed as well. The dynamics of the water around the TMAO molecules was evaluated in the NVE (constant volume and energy), which guarantees more accurate dynamics. This analysis was performed with the SPC/E water model, using molar ratios varying between 1:5 and 1:250, in addition to the concentration used for the parametrization. The dynamical properties of the mixture were evaluated at T = 298.15 K.

Figure 1. Atomistic (left) and coarse-grained (right) representation of TMAO and water. The names used in the main text for the coarsegrained sites are shown.

In this work, we use the CG modeling in an unconventional way, as an analysis tool rather than as a means to achieve sampling on longer time and length scales. Indeed, the system under investigation is simple enough that fully atomistic simulations can be easily performed. However, introducing a CG model allows us to remove “nonessential” degrees of freedom and thereby identify the relevant interactions in the system (usually referred to as “generalized” or “collective B



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Initial parameters were taken from the work by Kast et al.1 and only the value for σii and εii used by the Lennard-Jones potential have been modified (Table 1), mainly because of the

All the simulations were equilibrated for 10 ns, and data were collected over the next 10 ns. All the radial distribution functions were computed in the NVT ensemble using VMD.77 Dynamic properties (such as residency time and diffusion coefficient) have been evaluated in the NVE ensemble using tools available in the GROMACS’ package.84−86 2.2. Molecular Dynamics Simulations of the CoarseGrained Force Field. The CG simulations were performed in the NVT ensemble, employing the Nosé−Hoover thermostat (τT = 0.1 ps) and periodic boundary conditions. All the simulations were equilibrated for 1 ns and data collected for the following 10 ns. The equations of motion were integrated using a time step of 1 fs.

Table 1. Atomistic Force Field Parameters atom C O N H C O N H

3. RESULTS AND DISCUSSION 3.1. Development and Validation of the Atomistic Force Field. The force field developed in this section is meant to be used in conjunction with the OPLS-AA force field. However, as new atom types are developed, it can in principle be used with other force fields as well, provided that the necessary potential functions and combination rules are implemented. The chemical bonds are kept fixed at their equilibrium values using the LINCS algorithm. The valence angle has the form 1 θ kijk(θijk − θijk0 )2 2

where kθijk is the force constant of the angle θijk formed by the particle i, j, and k and θ0ijk is its equilibrium value. Dihedral angles have been included as well according to (2)

where kϕijkl is the force constant, ϕijkl is the dihedral angle among particles i, j, k, l, and ϕ0ijkl is its shift. Electrostatic energy is computed using the standard Coulomb potential: 1 qiqj

4πε0 rij

(3)

where ε0 is the electric constant, rij is the distance between particles i and j, and qi and qij are their charges, respectively. For an efficient computation of the electrostatic interactions, we took advantage of the particle mesh Ewald method (PME)87 implemented in GROMACS. Dispersion forces use the Lennard-Jones potential with a cutoff of 12 Å: ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ σij σij 4εij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ r ⎝ rij ⎠ ⎦ ⎣⎝ ij ⎠

rij < 12 Å (4)

The parameters εij and σij are computed according to εij =

εiiεjj

σij =

σiiσjj

SPC/E 0.3385 0.3109 0.3205 0.2319 TIP3P, TIP4P 0.32705 0.3258 0.311 0.21375

ε (kJ/mol) 0.280 0.604 0.743 0.066 0.28 0.57 0.77405 0.07

different way combination rules are applied in the CHARMM (εij = (εiiεjj)1/2; σij = (σii + σjj)/2) and OPLS-AA force field (eq 5). The quality of the force field was tested against its ability to properly reproduce the correct values for the density at different concentrations and temperatures. These values are reported in Table 2 and show excellent agreement with experimental values. We have used different water models and found that SPC/E water required a slightly different force field than the one used for TIP3P and TIP4P to achieve optimal results. 3.2. Iterative Method for Parameter Optimization. In all the cases mentioned above, we have found the correct set of parameters using a “bisection method”. We started using two sets of parameters and computing the resulting density. The first set employed the parameters by Kast et al.,1 whereas the second set used atom types taken from the standard OPLS force field. The first set gave too high a density and the second too low with respect to the experimental values. At this point a third set was built where both σ and ε were the average of the first two sets. This process was repeated by taking care of using as the initial guess the two sets whose density was closer to experimental but slightly bigger (first set) or slightly smaller (second set). It should be pointed out that these two sets could be chosen from a previous iteration. After three to four iterations, the values reported in Table 1 were chosen as the closest to the experimental values. To better approximate the densities reported in Table 2, each iteration involved checking two simulations. One simulation was performed at 323.15 K and molar ratio 1:15 (lowest experimental density), whereas the other was performed at 298.15 K and molar ratio 1:5 (highest experimental density). 3.3. Dynamical Properties of Water from Atomistic MD. Although the CG models that will be presented in the next section are extremely powerful tools for studying complex materials, it is extremely difficult to build CG models that can correctly reproduce the time scales involved in the system under investigation. As a consequence, for a system as simple as the one that we are studying here, MD simulations with a fully atomistic model are still the preferred means to study the dynamical properties of the system. One of the main results from the dynamics analysis that we have performed is a decrease of the diffusion coefficient D of water with increasing concentrations of TMAO (Table 3). This is consistent with the experimental observation that even at low

(1)

0 ϕ kijkl [1 + cos(nϕijkl − ϕijkl )]

σ (nm)

(5)

Dispersion forces and electrostatics are computed only for atoms further apart than three bonds. For atoms that are connected by three bonds (such as the one involved in dihedral potentials), both electrostatic and dispersion forces are scaled according to the OPLS-AA force field, namely by a factor of 0.5. C



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Table 2. Mixture Densities (g/cm3) molar ratio 1:5 exptl1 TIP3P TIP4P SPC/E

molar ratio 1:10

molar ratio 1:15

298.15 K

323.15 K

298.15 K

323.15 K

298.15 K

323.15 K

1.031 1.035 1.045 1.034

1.021 1.011 1.023 1.015

1.014 1.014 1.024 1.020

1.007 0.991 1.004 1.002

1.008 1.007 1.015 1.013

1.001 0.983 0.996 0.996

Table 3. Physical Properties of the Atomistic System SPC/E, 298.15 K molarity (mol/L) molality (mol/kg) water diffusion coefficient (10−5 cm2/s) D/Dw bound water molecules residency time, OT (ps) residency time, CH (ps)

molar ratio 1:5

molar ratio 1:10

molar ratio 1:15

molar ratio 1:20

molar ratio 1:25

molar ratio 1:50

molar ratio 1:70

molar ratio 1:105

molar ratio 1:210

6.26 11.1 0.4

3.99 5.55 0.93

2.93 3.7 1.26

2.32 2.77 1.54

1.92 2.22 1.71

1.03 1.11 2.08

0.75 0.79 2.22

0.51 0.53 2.37

0.26 0.26 2.46

0.16 2.4 28.7 4.2

0.37 2.7 17.7 3.4

0.49 2.8 15.1 3.1

0.6 2.8 14.2 3

0.67 2.9 13.4 2.9

0.82 2.9 12.1 2.7

0.87 2.9 11.8 2.7

0.93 2.9 11.6 2.6

0.97 3.0 11.2 2.6

concentration,88 TMAO reduces the diffusion coefficient of water by ∼30%. To better compare to experiments, we report the ratio D/Dw as well in Table 3. Dw is the diffusion coefficient for bulk water, which has a value of 2.54 × 10−5 cm2/s in our simulations (the experimental value being comparable at 2.3 × 10−5 cm2/s89). Our model reproduces the correct trend, but water moves generally faster than under experimental conditions. For example, at 1 M the ratio D/Dw is expected to be ∼0.7, whereas our model predicts ∼0.8. This is related to known behavior of bulk SCP and TIP models, which are “faster” than real water. The slowdown of water diffusion can be attributed to TMAO’s ability to strongly bind water molecules.90−92 To further probe this slowdown, we turn to a study of the probability that a water molecule (represented by its oxygen atom), found in proximity of TMAO at a time t0, diffuses away from TMAO in a time t. A proximal water molecule is defined as a water molecule whose oxygen is within 3.4 Å from the oxygen or 4.5 Å from the methyl group. These distances correspond to the first hydration shell around each group. We find that the water molecules are strongly bound to the oxygen of TMAO (Table 3, Figure 2). As a consequence, we can conclude that TMAO should not be considered as a single molecule in solution, but that it actually forms a stable complex with two to three water molecules. This observation is interesting, because it agrees with experimental data from dielectric relaxation91,93 density and activity data.90 Furthermore, a comparison to the dynamics of the proximal water around the methyl groups shows that the water slowdown measured by the diffusion coefficient is mainly associated with binding to the TMAO’s oxygen, in agreement with 2D IR photon echo spectra.94 In fact, Table 3 shows that the residency time of water around a methyl group is still ∼5 times faster than the water bound to OT. Another aspect worth noticing is that the residency time starts increasing for concentrations above 4 M (5.55 mol/kg). This is consistent with dielectric relaxation experiments, which suggest that this regime take place between 4 and 6 mol/kg,93 and 2D IR photon echo spectra,94 which shows a substantial slowdown at 8 M. This effect is a consequence of the competition among TMAO molecules for the few water molecules left in solution at those concentrations.

Figure 2. Probability that a molecule of water within the first coordination shell of OT or CH drifts away after a time t. The concentration of TMAO decreases as reported in the plot. The plot shows that the water is strongly bound to the oxygen of TMAO. The dotted horizontal line indicates where the residency time reported in Table 3 is evaluated. It corresponds to the point where the probability drops below e−1. This would be the characteristic time associated with a purely exponential decay. However, as the curves do not decay exponentially, this number should be considered an estimate.

Our observation that water diffusion is primarily influenced by water binding to the oxygen of TMAO is surprising, because this appears to conflict with the hydrophobic nature of the methyl groups of TMAO. To gain insight into this issue, we turn to CG models. 3.4. Development and Validation of the CoarseGrained Model. The CG model was developed starting from the equilibrated atomistic simulation in the NVT ensemble. The resolution of the CG model is shown in Figure 1 and the MS-CG methodology55−70 was employed to find the parameters of the force field. Each CH3 group and each water molecule is coarse-grained into one bead located at the center of mass of the group or molecule, respectively. Charges have been removed from the system as well, and the electrostatic interactions among groups are taken into account implicitly in the effective force field. As mentioned above, the parameters employed in the CG force field (Table 4) were derived using the MS-CG methodology. This technique is particularly useful in the context of the present work because it allows us to build a CG D



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molecules. The highest temperature was selected for practical reasons. In fact, we tested multiple functional forms for the CG basis set and found that the highest temperature reduced the equilibration time. In the following discussion we will focus on the SPC/E water model. The quality of the CG model can then be assessed by comparing the radial distribution functions to their atomistic counterpart. These distributions are shown in the Supporting Information. The radial distributions are generally correctly reproduced, except for a slightly greater tendency of the oxygen of TMAO to come in very close contact to each other. This is a consequence of the very specific orientation of the water molecules in close contact with this atom, as we discuss in details in the next section. 3.5. Effective Interactions between Water and TMAO from CG Modeling. Before discussing the CG model in more detail, we highlight the novelty of the way in which we are using CG modeling. CG models are typically developed to overcome the prohibitive computational requirements associated with atomistic simulations. Reduction in computational expenses is achieved by simplifying the description of the model being considered. In most cases, the original system cannot be exhaustively studied using standard MD techniques, and the CG model is the only viable way to gain useful insights. In contrast, the model studied in this paper is simple enough that standard atomistic MD can be used, and we actually do run a MD simulation to evaluate dynamical properties of the system, as shown in the previous section. One might then ask, what purpose can be served by a developing a CG model in this case? The advantage of using a CG model is 3-fold. First, the MS-CG method computes effective forces between groups of atoms (namely, CG interacting sites). In this way, not only is the topology of the system under investigation simplified, but also attraction or repulsions between groups (which can be composed of multiple atoms) become immediately apparent. Second, the effective forces computed in this way can actually be used to run CG simulations. The latter is important, because if the CG model reproduces the structural properties of the original model, it means that the resolution selected and the force computed are accurate enough. We have discussed in one of our previous papers64 how resolution and quality of the force field are correlated and we refer the interested reader to that work for further details. In the present paper, the quality of the force field was evaluated by comparing the radial distribution function of the atomistic and CG force fields, a fundamental quantity for liquid mixtures (see also section 3.4). A third motivation is that the methodology used in this work is systematic. As a consequence, it can be extended in a straightforward way to study more complex systems, such as proteins. The analysis of the CG model shows that two interactions are paramount to describe the TMAO behavior in water. The first is the formation of hydrogen bonds between the oxygen of TMAO (OT) and the surrounding water molecules. In Figure 3 we have plotted the effective force between two CG sites as a function of distance. This figure shows that the strength of the effective force between OT and a water molecule is stronger than the interaction between water molecules, so that TMAO strongly binds water molecules, in agreement with previous experimental studies.90−92 The three-body portion of the effective force field suggests that the tridimensional arrangement of water molecules around OT is very similar to the

Table 4. Coarse-Grained Force Field Parameters Bond type NT-OT NT-CH type OT-NT-CT CT-NT-CT

krij (kcal mol−1 Å−2)

r0ij (Å)

700 700 Angle

1.407 1.577

kθijk (kcal mol−1 rad−2)

θ0ijk (deg)

50.09 111.26 Three Body

108.65 110.1

type

λijk (kcal/mol)

cos θ0ijk

OT-W-W W-OT-OT W-OT-W W-W-W

18.1 91.9 19.9 16.4

−0.37 −0.28 −0.37 −0.40

force field that reproduces the atomistic forces obtained from atomistic simulations. In this framework, the effective force F⃗I acting on each coarse-grained site I is defined as

FI⃗ =

∑ fi ⃗

(6)

i∈I

where fi⃗ is the force acting on the ith atom belonging to the CG site I. Generally, the exact functional form of F⃗I is too complicated to be used in practical applications, so that it is usually approximated by simpler and more computationally efficient functional forms such as eqs 7−9 above. The MS-CG method approximates the exact force F⃗I though a least meansquare fitting of the parameters used in the CG force field. The bonded interactions are represented by

kijr(rij − rij0)2

(7)

θ kijk (θijk − θijk0 )2

r0ij

(8)

krij

where is the equilibrium bond distance and is the force constant for the bond between the ith and jth particle. The other symbols have the same meaning as in the atomistic case, except for the absence of 1/2 in front of eq 8, as GROMACS and LAMMPS use different definitions for the force constants. The nonbonded interactions were described by both twoand three-body potentials. The two-body interactions were tabulated with bins of 0.01 Å, and a cutoff of 7.5 Å was used. Three-body interactions were instead computed using the form originally proposed by Stillinger and Weber:95,96 ⎛ γij ⎞ ⎛ γik ⎞ ⎟⎟ exp⎜ λijk (cos θijk − cos θijk0 )2 exp⎜⎜ ⎟ ⎝ rik − aik ⎠ ⎝ rij − aij ⎠

(9)

The three-body interactions have a cutoff aik = 3.7 Å, which corresponds roughly to the first solvation shell. γij was fixed at 1.2, a commonly used value in the literature.89 The use of three-body nonbonded interactions for the system under investigation would, in principle, require finding the parameters associated with 40 interactions. However, the MS-CG method helps identify that three-body interactions have to be taken into account only for the interactions involving the water and the oxygen of TMAO (Table 4). In this work the force field was developed using the all-atom MD simulations with a 1:15 TMAO/water ratio at 323.15 K (SPC/E water model). The highest concentration of TMAO guarantees a good sampling of the interactions among TMAO E



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methyl groups do not interact through a hydrophobic effect (which should be attractive), but instead that their polarization is enough to repel each other and keep them in solution. This finding is very important to understand the different behavior of TMAO in water when compared to other small osmolytes.92,97,99−103 For example, tert-butyl alcohol (TBA) consists of a hydrophilic moiety connected to three methyl groups and shares a topology similar to that of TMAO. However, TBA tends to associate in water, because of its essential hydrophobic nature, whereas TMAO does not. Similarly, tetramethylurea (TMU) shares a similar hydrophilic/hydrophobic pattern but is far less soluble. In summary, our CG analysis reveals that the local (not global) water structure is deeply affected by the presence of TMAO in solution. On one hand, the oxygen on the TMAO molecule forms hydrogen bonds with the surrounding water molecules. On the other hand, the methyl groups are kept in solution by the repulsion from the two other methyl groups and the water molecules. The repulsion between water molecules and methyl groups suggests that the water may form a clathrate-like structure around the methyl. We can verify this by turning back to our atomistic simulations, which retain the hydrogen atoms and thus allow us to analyze the structure of hydrogen bond network. The direction of the hydrogen bonds is evaluated through the angle α as defined by Panuszko et al.36 and is shown in Figure 5. The first step in defining the angle α

Figure 3. Graph showing that the attractive force between water molecules (W) is weaker than the effective force between the water and oxygen of TMAO (OT). As a consequence, TMAO in solution forms stable complexes with two to three water molecules bound to it.

arrangement around the oxygen of another water molecule. As a consequence, the oxygen in TMAO can bind up to three water molecules (the fourth site being occupied by the rest of the molecule), once more in agreement with the atomistic model and with previous experimental and theoretical studies.36,91,97−99 However, OT can only act as an acceptor of hydrogen bonds, so that it acts as a defect in the hydrogen bond network of water. In fact, if three water molecules are bound to it, all of them must have one of their hydrogens oriented toward the oxygen of TMAO, in contrast to what happens in bulk water. It is worth noticing that our CG model has coarse-grained all the hydrogens in the system. In this way, their presence can only be inferred indirectly through the geometric arrangement of the water molecules, mainly from the three-body potential. As a consequence, it cannot properly model the formation of defects due to distorted hydrogen bonds. Interestingly, the CG model shows greater tendency of the OTs to come in close contact, suggesting that the water structure around this oxygen plays a key role in the solvation of TMAO. A second aspect worth noting is the interaction between water molecules and methyl groups of TMAO. As shown in Figure 4, the methyl groups do not show a clear binding preference between surrounding water molecules or other methyl groups in the solution. This finding suggests that the

Figure 5. Definition of the angle α. α is defined as the angle between the plane containing one water molecules and the surface of the sphere with the molecule of interest in the center and with a radius equal to the distance between the molecules and the water molecule. Distances are generally computed between the centers of mass of the molecules involved, unless otherwise noted.

consists of constructing a sphere with the center located at the center of mass of a TMAO molecule and with a radius equal to the distance between the centers of mass of the TMAO and the water molecule of interest. At the same time, a plane can be defined that contains the water molecule. The angle α is the angle between this plane and the surface of the sphere. A value of 0° or 180° means that this plane is tangent to the sphere, in other words the water molecule cannot form hydrogen bonds with TMAO. In contrast, an angle of 90° means that one of the hydrogens points toward the TMAO molecule; i.e., it forms hydrogen bonds. Figure 6 shows the structure of the hydrogen bond network around a TMAO molecule based on this analysis. This analysis suggests that the hydrogen bond network of the water forms a “bubble” around the TMAO molecule with the hydrogen bonds oriented along the surface of this bubble. The oxygen of the TMAO is located on this surface (as it can form hydrogen bonds), whereas the methyl groups are on the inside of this bubble. This model is in agreement with the structure proposed by Panuszko et al.36 based upon a combination of quantum and MD simulations.

Figure 4. Effective force between methyl groups (CH) and water (W). The CH groups do not show a stronger attraction to the other methyl groups than to water, which is the signature of the hydrophobic effect. As a consequence, CH groups do not show a strong tendency to aggregate but are more likely to remain in solution. The small difference at short distances is connected to excluded volume effects, with the water being smaller than a methyl group. F



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Figure 6. Structure of the water molecules surrounding TMAO. (a) and (c) show the distribution of the angle α as defined in Figure 5, whereas (b) shows a cartoon of the local water structure surrounding a molecule of TMAO. In (a) R is the distance between the center of mass of a water molecule and the oxygen of TMAO (OT), whereas in (c) R is the distance between the center of mass of TMAO and the center of mass of a water molecule excluding the water molecules whose center of mass is closer than 3.4 Å to OT. The probability reported is P(R,α)/4πr2 sin αΔRΔα, where P(R,α) is the probability of finding one water molecules at distance R and angle α. As can be seen, water molecules form hydrogen bonds with OT, whereas they avoid the methyl groups building a clathrate-like cage around them. (c) shows a snapshot from our simulations. All the data are shown for the TMAO/water mixture with ratio 1:20 but are representative for all the other cases.

4. CONCLUSIONS In this work we have developed a coarse-grained and an atomistic force field to study the structural and dynamical properties of TMAO/water mixtures. Both resolutions show that TMAO molecules form stable complexes with two to three water molecules, in agreement with experimental90,91,93 and theoretical97,99,104 studies. The CG model shows that the effective interaction between water and the oxygen of TMAO is stronger than between water molecules. Consistently, the atomistic simulations show that the water molecules bound to TMAO take as long as 100 ps to dissociate. Less obvious is the behavior of the methyl groups. In fact, the atomistic simulations show that the diffusion of the water is mainly affected by the presence of the oxygen of TMAO. This behavior is puzzling and is not consistent with the hydrophobic nature of the methyl groups. To understand the origin of this behavior, we turn to the CG model. This model shows a surprising result, which to our knowledge, has never been reported before. We find that the effective force between methyl groups is similar to the effective force between methyl and water molecules. In addition, this effective force is repulsive, whereas a hydrophobic interaction between methyl groups should be attractive. This finding also helps explain why TMAO is more soluble than other molecules that share a similar hydrophobic/hydrophilic pattern. If we put together the two results mentioned above (water bound to oxygen and nonhydrophobic methyl groups), we can suggest a possible mechanism of interaction between TMAO and proteins. The repulsion from the vicinity of the protein can be explained by the combination of two effects: (1) TMAO lacks hydrophobic groups and (2) both oxygen and methyl groups enforce a very specific geometry of the hydrogen bond network around each TMAO molecules. As a consequence, a direct interaction with the protein is unlikely, in agreement with previous experimental and theoretical studies.31,39,40,43 On the basis of the discussion above, we can conclude that the complex TMAO·2H2O or TMAO·3H2O acts as a chemical chaperone.105,106 In this context, the stabilization of the folded state is mainly driven by excluded volume effects, which are entropically driven.105,106 This is in agreement with a recent simulation by Cho et al.43 who studied the effect of TMAO on the structure of short polypeptides and the Alzheimer Aβ16−22

peptide. They showed that TMAO can change the structure of the Aβ16−22 peptide from a random coil to an α-helix upon addition of TMAO, and that the exclusion of TMAO from the polypeptide chains is affected by the length of the peptide. As the polypeptide grows in length, TMAO is excluded from the vicinity of the protein, and the protein adopts a compact conformation. Hu et al.107 have shown that the exclusion of TMAO from the vicinity of the protein is actually a consequence of the distorted hydrogen bond network produced by the presence of this osmolyte. These studies also support a description that involves an entropic stabilization of the native state. In fact, in this picture, the unfolded state (which has high entropy) is destabilized by unfavorable contacts with the solvent. As a consequence, the protein prefers a more compact conformation, generally the native state. At the same time, there is a gain in the translational entropy of the solvent, because of the reduced volume occupied by the protein. An important aspect of this work is the development of a novel analysis technique that involves both MD and CG simulations. The identification of the “nonhydrophobic” nature of the methyl group and the strength of the TMAO−water hydrogen bonding are a clear example of the power of this methodology. The two levels of resolution work hand in hand. The all-atom MD simulations are essential for correctly evaluating time scales, and we used this approach to show that the slowdown of the water dynamics is a consequence of strongly binding TMAO molecules. The CG model complements this information by providing the effective strength of each interaction and by teasing out which are the essential interactions to describe a TMAO/water mixture. In this way, we have found the unexpected result that, in the context of a TMAO/water mixture, methyl groups do not behave as hydrophobic moieties, as suggested by previous experimental studies by Sagle et al. at interfaces108 and Koga et al. in 1propanol mixtures.109 It is clear that this approach can be extended to study other mixtures or more complex systems. In fact, mixtures of osmolites (or crowders) are commonly employed by the cell to regulate protein folding and activity.41,105,110−115 G



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ASSOCIATED CONTENT

S Supporting Information *

Radial distribution functions and topology files with the new set of parameters for both atomistic and coarse-grained models. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (805) 893 5604. Fax: (805) 893 4120. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support from the National Science Foundation (MCB1158577) and the David and Lucile Packard Foundation are gratefully acknowledged. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI1053575. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin and the National Institute for Computational Sciences at Oak Ridge National Laboratory for providing HPC resources through the XSEDE grant number TG-MCA05S027. This research used ShaRCS, UC Shared Research Computing Services Cluster, which is technically supported by multiple UC IT divisions and managed by the University of California, Office of the President. We acknowledge support from the Center for Scientific Computing at the CNSI and MRL: an NSF MRSEC (DMR-1121053) and NSF CNS-0960316.

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Water Effective Interactions

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