Comparison of Different TMAO Force Fields and Their Impact on the

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Comparison of Different TMAO Force Fields and Their Impact on the Folding Equilibrium of a Hydrophobic Polymer Francisco Rodriguez-Ropero, Philipp Rötzscher, and Nico F. A. van der Vegt J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b04100 • Publication Date (Web): 02 Aug 2016 Downloaded from http://pubs.acs.org on August 10, 2016

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The Journal of Physical Chemistry

Comparison of Different TMAO Force Fields and Their Impact on the Folding Equilibrium of a Hydrophobic Polymer Francisco Rodríguez-Ropero, Philipp Rötzscher, and Nico F. A. van der Vegt∗ Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Center of Smart Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287, Darmstadt, Germany E-mail: [email protected]

Abstract Trimethylamine N-oxide (TMAO) is a protective osmolyte able to preserve protein folded states in the presence of denaturants like urea and under extreme thermodynamic conditions of high pressure and temperature. The current understanding posits that TMAO exerts its stabilizing effect on proteins by preferential exclusion from the macromolecular hydration shell. Additionally, TMAO is also known to favor the folding of hydrophobic polymers. In this latter case, theoretical and experimental studies support a scenario in which TMAO directly interacts with the macromolecule. While atomistic simulations may potentially elucidate the precise TMAO-induced stabilization mechanism, the comparative accuracy of the different TMAO force field models available in the literature remains elusive. Herein, we compare four different TMAO models, study their structural hydration properties, and validate the models

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against experimental osmotic coefficients and air-water surface tension data over a broad range of TMAO concentrations. The models were furthermore applied to study the effect of TMAO on the folding equilibrium of a generic hydrophobic polymer in aqueous solution. Interestingly, we find that TMAO increasingly stabilizes the compact globular state of the polymer up to approximately 1 M TMAO, while in turn destabilizing it with further increase in TMAO concentration. Hence, TMAO acts as a stabilizing osmolyte or as a denaturant depending on the TMAO concentration of the solution. TMAO-induced stabilization up to 1 M is accompanied by positive preferential TMAO binding and with an increase in the chain configurational entropy, which is reduced at concentrations higher than 1 M. These results are qualitatively independent of the TMAO force field.

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Introduction Trimethylamine N-oxide (TMAO) (Fig. 1) is a well known protective osmolyte able to counteract not only the denaturant action of urea on proteins 1 and nucleic acids 2 but also able to preserve the native state of biomacromolecule in a wide range of hydrostatic pressures and temperatures. 3 TMAO has been found in a great variety of deep-sea fishes. Indeed the role of TMAO as an extrinsic piezolyte capable of inhibiting pressure denaturation is confirmed by the fact that TMAO content in the muscles of deep-sea fishes linearly increases in species captured down to 7199 m. 4,5 Even though it is commonly accepted that unfavorable interactions of TMAO with the protein backbone causes proteins to retain their active folded state 6–10 a precise molecular understanding to explain the stabilization effect of TMAO is still lacking. A plethora of mechanisms have been proposed in the last years, some of them leading to antithetical conclusions. 11 Wei et al. 12 attribute the stabilizing effect of TMAO invoking an indirect mechanism in which addition of the osmolyte weakens the hydration of the amide group resulting in stronger intramolecular protein hydrogen bonds. On the other hand Kokubo et al. 13 explain the preferential exclusion of TMAO from proteins on the basis of unfavorable electrostatic interactions. Cho et al. 14 proposed an entropic mechanism based on the preferential exclusion of TMAO from long polypeptides in which the osmolyte acts as a crowding agent. This entropic effect might be accompanied by an enthalpic contribution arising from the reduced hydrogen bonding ability of water in the presence of TMAO, as recently proposed based on two-dimensional infrared spectroscopy and site-specific infrared probe measurements. 15 Recently it has been proposed that TMAO stabilizes protein structures in the presence of urea denaturant by removing urea from protein surface. 16,17 Atomistic computer simulations may help providing a better understanding of the TMAO induced stabilization mechanism. Most of the theoretical studies reported in the literature 11 rely on simulations where TMAO molecules are represented using the atomistic force field developed by Kast et al. 18 This atomistic force field was derived from 3



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Figure 1: Trimethylamine N-oxide (TMAO) chemical structure. ab initio quantum mechanics calculations and has been refined by several groups of authors in order to better reproduce other experimental target quantities such as osmotic coefficients, 19 activity data 20 or experimental densities. 21 Here we present a comparative study of four different TMAO force fields 18–21 and their ability to reproduce key experimental data. We have focused our attention on the hydration structure, surface tension, osmotic coefficients and ability to reproduce transfer free energy of a model hydrophobe (neopentane) from water to 1 M TMAO aqueous solutions. In the second part of the article we evaluate how different TMAO force fields affect the folding equilibrium of a generic Lennard-Jones hydrophobic polymer. The different force field models all predict TMAO-induced stabilization of the compact hydrophobic state up to 1 M TMAO. With further increase of the TMAO concentration the unfolding free energy is found to decrease (the m-value changes sign), however the magnitude of this effect is found to be model dependent.

Methods and simulation details TMAO force fields All the force fields considered in this work share the same set of intramolecular force field parameters, which were derived by Kast et al. 18 from ab initio quantum mechanics calculations and uses the following model potential defined over consecutive atoms i, j, k 4


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and l:

X k ij X k ijk ik r θ 0 2 0 2 kr 0 2 Ubonded = + − rij − rij + θijk − θijk rik − rik 2 2 2 bonds angles X X ijkl h i 0 kφ,n 1 + cos(nφ ijkl − φ ijkl )

(1)

torsions n

Bond streteching between two consecutive connected atoms i and j are described with ij

harmonic potentials, which are defined by the force constant kr and the equilibrium bond distance rij0 (first summatory in Eq.1). Angular bending between three consecutive interconnected atoms i, j and k are described with harmonic potentials and Urey-Bradley ijk

1-3 terms, which require of two force constants kθ and krik , equilibrium angle between 0 and the equilibrium distance between the non-connected the three involved atoms θijk 0 (second summatory in Eq.1). Dihedrals between four consecutive interatoms i and k rik

connected atoms i, j, k and l are represented using a cosinus potential, which is defined ijkl

0 and the multiplicity n (third summatory with a force constant kφ,n , a phase angle φ ijkl

in Eq.1). All the bonded force field parameters are summarized in Table 1. Non-bonded parameters differ in each of the four TMAO force fields we have considered in this work and are summarized in Table 2.

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Table 1: TMAO bonded force field parameters. Atoms are defined according to Figure 1. bonds i j O N N C C H angles i j k O N C N C H C N C H C H dihedrals i j k l O N C H C N C H

ij

rij0 (nm) 0.1407 0.1506 0.1082

ijk

0 θijk (deg) 109.99 108.07 108.16 108.25

krik [kJ/(mol nm2 )] 30133.168 65814.320 40597.352 5493.592

φ 0.0 0.0

n 3 3

kr [kJ/(mol nm2 )] 143335.472 107181.528 247257.664 kθ [kJ/(mol rad2 )] 254.97296 208.94896 576.13680 229.57608 ijkl

kφ,n (kJ/mol) 1.12968 1.12968

0 rik (nm) 0.2330 0.2101 0.2414 0.1768

Table 2: TMAO non-bonded parameters for different force fields. Atoms are defined according to Figure 1. Intra-molecular nonbonded interactions are included between 1-4 and 1-5 neighbours

Force Field Atom q (e− ) σ (nm) Kast 18 O -0.650 0.3266 N 0.440 0.2926 C -0.260 0.3041 H 0.110 0.1775 19 Osmotic O -0.780 0.3266 N 0.528 0.2926 C -0.312 0.3041 H 0.132 0.1775 20 Dipole O -0.910 0.3266 N 0.700 0.2926 C -0.260 0.3600 H 0.110 0.2101 21 Density O -0.650 0.3109 N 0.440 0.3205 C -0.260 0.3385 H 0.110 0.2319

ǫ (kJ/mol) 0.6379 0.8360 0.2826 0.0773 0.6379 0.8360 0.2826 0.0773 0.6379 0.8360 0.2826 0.0773 0.6040 0.7430 0.2800 0.0660

The earliest and most widely used TMAO force field was derived by Kast et al. 18 based on ab initio quantum mechanics calculations. This force field has been normally 6


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referred to as the Kast model. Lorentz-Berthelot combination rules are used to derive intermolecular potential parameters between two non-bonded dissimilar atoms i and j, √ that is σij = (σi + σj )/2 and ǫij = ǫi ǫj . This force field was originally derived to be used in conjunction with the TIP3P water model. 22,23 Even though this force field combination has been extensively used, 13,14,19,24–28 the Kast model has been widely used combined with the SPC/E water model 29 by several groups of authors. 12,30–41 The SPC water model 42 has been considered in a lesser extent. 43,44 The impact of the water model on the hydration properties of TMAO was studied by Kuffel and Zielkiewicz. 44 These authors studied the hydrogen bond network in the TMAO hydration shell using the SPC rigid model and the polarizable POL3 45 water model. Both water models showed similar structural results. Ganguly et al. 16 found that the protein stabilizing effect of TMAO in urea rich solutions by removal of urea molecules from the protein first solvation shell is independent of whether SPC/E or TIP3P water models were used. Recently Mondal et al. 46 found the stabilization of folded states of hydrophobic polymers in the presence of TMAO to be independent of the water model they used, i.e. SPC/E or TIP3P. Canchi et al. 19 refined the Kast model with the goal of reproducing experimentally measured osmotic coefficients of TMAO aqueous solutions in a wide range of concentrations. They showed that the Kast model understimates the osmotic coefficients, especially at increasing TMAO concentrations. Using the Kast model as initial guess, the authors scaled up the original charges with a factor of 1.2 in order to increase the repulsion between TMAO molecules and ultimately increase the osmotic pressure of the resulting systems. In parallel all the ǫij for TMAO-TMAO interactions were downscaled with a √ factor of 0.75 (ǫij = 0.75 ǫi ǫj ), which results in less favorable dispersion interactions between TMAO molecules. The resulting force field was called Osmotic model. Schneck et al. 20 reparameterized the non-bonded parameters of the Kast model to obtain a force field able to reproduce experimental activity data as well as polyglycine transfer free energy. To that end, the authors systematically scaled up the partial charges

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of the oxygen and nitrogen atoms. Additionally, the hydrophobicity of the methyl groups was increased by scaling up σC and σH (see Table 2). In total the authors considered 16 different parameters sets in their study (including the Kast model) and compared their ability to reproduce the target experimental activity data and polyglycine transfer free energy. The optimal force field parameters led to an increased TMAO-TMAO repulsion, which is mostly due to strong TMAO-water interactions. This force field effectively increases the TMAO dipole moment. Because of this we will refer to this force field as Dipole model. In contrast to the previous two models, this model was parametrized using the SPC/E water model. The last force field we have considered was developed by Larini and Shea 21 with the aim of reproducing the experimental density of TMAO aqueous solutions in a wide range of temperatures and concentrations. Since this model was developed to be used together with the OPLS-AA force field, they decided to use geometrical average to derive inter√ √ molecular potential parameters (σij = σi σj and ǫij = ǫi ǫj ). While charges from the Kast model were not modified the authors developed two new sets of Lennard-Jones interaction parameters, that is a set to be used with SPC/E water model and a second set to be used together with TIP3P or TIP4P 47 water models. We will refer to this model as the Density model. Only non-bonded parameters developed to be used together with the SPC/E water model are reported in Table 2.

Simulations of TMAO at water/air interfaces A set of ∼ (4 nm)3 cubic boxes containing different number of water (NW ) and TMAO (NT MAO ) molecules were prepared in order to reach different target TMAO concentrations (Table 3). TMAO molecules were represented using the four aforementioned force fields (Table 2) while water was represented with the SPC/E potential. 29 1-4 LennardJones contributions were included for the TMAO molecules. We have used the GROMACS 4.6.2. simulation package 48 to run all our Molecular Dynamics simulations. Initially sys8


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tems were equilibrated for 5 ns in the NpT ensemble, in which temperature and pressure were kept constant at 298 K and 1 bar by using respectively the velocity-rescaling thermostat 49 (τT = 0.1 ps) and the Berendsen (τP = 0.5 ps) barostat. 50 Isothermal compressibility was set to 4.5x10−5 bar−1 , which is the corresponding value for water. Systems were further run for 5 ns with an integration timestep of 2 fs in the NpT ensemble generated by using the Parrinello-Rahman barostat 51,52 to maintain a constant pressure of 1 bar (τP = 1.0 ps) and the Nosé-Hoover thermostat 53,54 (τT = 0.5 ps) to keep the temperature constant at 298 K. Bond lengths were constrained using the LINCS algorithm 55,56 (in TMAO, only C-H bonds were constrained while are remaining intra-molecular degrees of freedom are flexible). Electrostatic interactions were treated using particle-mesh Ewald (PME) summation 57 with a real space cutoff of 1.40 nm. Long-range corrections to energy and pressure due to the truncation of Lennard-Jones potential were accounted for. Atom pair distance cut-offs were applied at 1.40 nm. Equilibrated boxes were placed in the center of a rectangular box 84.0 nm long on the z direction, while x and y dimensions were kept equal to the size of the corresponding equilibrated cubic box (Table 3). Each system, which contains two vapor-liquid interfaces, has been simulated for 30 ns in the canonical ensemble. The last 25 ns were used in our subsequent analyses.

Table 3: Description of the water/air systems considered in this work. molality 0.0 0.5 1.0 1.5 2.0 2.5 aL

z

Nw NT MAO 2000 0 1847 17 1956 35 1859 50 1799 65 1737 76

Lx,y (nm)a 3.90529 3.85876 3.98055 3.96810 3.95953 3.95668

is equal to 84.0 nm in all the systems

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Calculation of the osmotic coefficients Osmosis is the spontaneous diffusion of solvent molecules from a pure solvent reservoir to another reservoir containing a solution through a semipermeable membrane, which exclusively allows solvent molecules to pass through it. The osmotic pressure is the necessary pressure to stop the influx of the solvent. The osmotic pressure Π can be calculated with the van’t Hoff equation Π = cB RT , where cB is the molar concentration of the solute, R is the gas constant and T is the temperature. The van’t Hoff equation is only valid for ideal and very dilute solutions. Deviations from ideality are accounted through the osmotic coefficient φ via φ = Π real /Π ideal . Osmotic coefficients were calculated for five different molalities from 0.5 to 2.5 m. To that end we followed the approach proposed by Luo and Roux. 58 An equilibrated TMAO-water box (see previous section) was placed in the center of a rectangular box with twice the corresponding length in z-direction. Semipermeable walls were placed at two opposite faces of the original TMAO-water box with their surface normals pointing in the z-direction. The empty part of the resulting box was filled with water molecules and equilibrated for 1 ns in the canonical ensemble. The production run was performed with pressure coupling (1 bar) only in the z-direction using the Parrinello-Rahman barostat and Langevin thermostat for 15 ns. The semipermeable walls were modelled by applying a harmonic potential Vwall (z) acting on the TMAO molecules, thereby confining them inside the original volume:

Vwall (z) = κ (zi − zwall )2

(2)

where κ is the force constant of the potential and zi is the z-component of the position of the TMAO molecule. This potential acts when the z-position of a given TMAO molecule exceeds the wall position |zwall |, i.e. |zi | > |zwall |. As the water molecules are not affected by the wall potential, and hence freely pass through the walls, the chem-

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ical potential of the water is equilibrated throughout the system. A force constant of κ = 2090 kJ mol−1 nm−2 was used in the wall potentials. The Plumed 1.3.0. patch 59 together with Gromacs 4.6.2. was used to run these calculations. The last 10 ns of the simulations were used for analysis. Osmotic coefficients were obtained by averaging the forces exerted by the TMAO molecules on each of the two walls over blocks of 1 ns.

Transfer free energy of neopentane from water to 1M TMAO aqueous solution Transfer free energies ∆Gt from water to 1M TMAO aqueous solutions were defined as ∆Gt = ∆G1MT MAO − ∆Gwater . Neopentane was described using the OPLS-UA force field 60

while the SPC/E model 29 was used for the water. TMAO was described using the four different force fields considered in this work. Solvation free energies in pure water and 1M TMAO aqueous solution were estimated using the Themodynamic Integration (TI) method. 61 Simulation details and system size were taken from the previous work by Ganguly et al. 16 In detail, we have used 26 λ points (∆λ = 0.04). For each point cubic boxes with an initial box length of 5.5 nm were used. Each box contained 1 neopentane molecule solvated with 100 TMAO molecules and 5150 water molecules. A soft core potential was used with the same parameters as in the work by Hajari and van der Vegt. 62 Newton’s equations of motion were integrated using leap-frog stochastic dynamics integrator. 63 Each λ point was firstly equilibrated for 1 ns. The last configuration was used as starting point for 5 ns simulations used for data analyses.

Hydrophobic polymer in TMAO aqueous solutions We have considered a hydrophobic polymer consisting in 32 uncharged Lennard-Jones beads (σb = 0.40 nm and ǫb = 1 kJ/mol). Bond stretching and angular potentials were modeled through harmonic potentials with r0 = 0.153 nm and θ0 = 111o , which resemble

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respectively the equilibrium bond length between two consecutive methyl groups and the equilibrium bond angle between three consecutive methyl groups in a polyethylene chain. These force field parameters have been directly taken from previous work by Zangi et al. 64 Following the previous work by Mondal et al., 41 the polymer was placed in a cubic box and solvated with 4092 water molecules. We also considered systems of different TMAO concentrations, that is 0.5 M (3929 water and 31 TMAO molecules), 1 M (3696 water and 79 TMAO molecules), 2 M (3000 water and 127 TMAO molecules), 3 M (2800 water and 195 TMAO molecules) and 4 M (2500 water and 257 TMAO molecules). The Potential of Mean Force (PMF) of the hydrophobic polymer was obtained by performing umbrella sampling simulations. The polymer radius of gyration (Rg ) was chosen as reaction coordinate. Rg values ranged from 0.4 to 1.2 nm with a spacing between neighboring windows of 0.025 nm. A force constant of 20 000 kJ mol−1 nm−2 was used in the umbrella potential to ensure a proper distribution of the Rg around each desired value. The weighted histogram analysis method (WHAM) 65 was used to obtain the unbiased PMF. The systems were first energy minimized and equilibrated for 1 ns at a temperature of 298 K and a pressure of 1 bar. During the equilibration, temperature was controlled using the velocity-rescale thermostat and pressure was controlled using the Berendsen barostat. Production runs were performed for 20 ns. The temperature was controlled using the Nosé-Hover thermostat (τT = 0.5 ps) and pressure was controlled using the Parrinello-Rahman barostat (τP = 1.0 ps) during the production runs.

Results Characterization of the TMAO force fields Di Michele et al. used near-infrared spectroscopy to estimate the hydration number of TMAO for a wide range of concentrations. 66 The number of water molecules belonging to the first hydration shell decreases from ∼ 17 water molecules in very dilute TMAO 12


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solutions (∼ 0.2 m) to ∼ 16 water molecules at high TMAO concentrations (∼ 2.7 m). We have examined the TMAO hydration shell by computing the radial distribution functions (g(r)) of water molecules around TMAO molecules (Figure 2) at 0.5 m and 2.5 m. The results were very similar independently of the TMAO concentration. Radial distribution functions obtained from the Kast and Osmotic models practically overlap and present just two peaks. From the first peak we can estimate a size of the hydration shell consisting of 18.4 and 19.3 water molecules for the Kast and Osmotic models respectively. These values are slightly overestimated compared to the experimentally measured data. On the other hand the same radial distribution functions calculated from the Dipole and Density models display two peaks at short distances (≤ 0.5 nm) and a third peak at the same position as the Kast and Osmotic models (∼ 0.75 nm). For the Density model integration of the radial distribution function accounts for 2.1 and 21.8 water molecules for the first and second peaks respectively. For the Dipole model the first peak accounts for 4.2 water molecules while the second accounts for 23.5 water molecules. The smaller peaks at shorter distances are due to the fact that in these two models water strongly binds to the TMAO oxygen atom. Interestingly, dielectric relaxation experiments 67,68 have shown that TMAO molecules strongly bind 2 - 3 water molecules at all concentrations. Femtosecond midinfrared spectroscopy studies show that water molecules solvating the hydrophobic groups in TMAO exhibit slower orientational dynamics compared to the water molecules in the bulk phase. 69

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Figure 2: Radial distribution functions g(r) of the water molecules around the center of mass of TMAO molecules at 2.5 m considering different TMAO force fields. Cubic boxes were run in the NpT ensemble for 30 ns (5 ns equilibration + 25 ns of production run). Similar results were obtained at 0.5 m (not shown). Experimental studies show that water interacts more strongly with the hydrophilic part of TMAO via hydrogen bonds and results in the formation of stable TMAO·2(H2 O) and/or TMAO·3(H2 O) complexes. 70,71 Recently Imoto et al. 72 have reported on basis of ab initio MD simulations an average value of 3.1 hydrogen bonded water molecules per TMAO molecule at ambient pressure. A given water molecule is hydrogen bonded to a TMAO molecule if the following geometric relation is satisfied: 72

rHW ···OT < −1.71 cos(θOW −HW ···OT ) + 1.37

(3)

where the subscripts W and T denote respectively atoms belonging to water and TMAO molecules and distance r is given in Ångströms. θOW −HW ···O is the angle between the intramolecular OW − HW vector and the intermolecular HW − OT vector. Results obtained for all the TMAO models are summarized in Table 4 and show very modest concentration dependency. The Kast, Osmotic and Density models show a similar average number of hydrogen bonded water molecules, which is in good agreement with experi14


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mental results. 70,71 On the other hand, the Dipole model shows a slightly higher average number of hydrogen bonds, which agrees better with the theoretical value estimated from ab initio MD calculations. 72

Table 4: Average number of water molecules forming a hydrogen bond with a TMAO oxygen atom 0.5 m Kast 2.84 Osmotic 2.84 Dipole 3.23 Density 2.85

2.5 m 2.74 2.77 3.19 2.78

It is known that the surface tension of TMAO aqueous solutions slightly decreases with TMAO concentration, 46,73,74 which suggests a weak propensity of TMAO molecules for hydrophobic interfaces. This propensity to accumulate near hydrophobic surfaces is overcompensated by solvophobic/solvophilic forces in proteins. This leads to the TMAO preferential exclusion from protein surfaces and ultimately to the stabilization of the protein native folded state. 74 On the other hand, a completely different mechanism has been recently postulated to explain the stabilization of folded states in hydrophobic polymers like polystyrene in aqueous TMAO solutions. 46 In this study the authors show that TMAO directly interacts with the hydrophobic styrene monomers and yet this osmolyte exerts a protecting effect on the collapsed conformations. These results corroborate their previously reported theoretical model on the collapse of hydrophobic Lennard Jones polymers. 41 In view of these two distinct protective mechanisms it appears to be of crucial importance that a TMAO force field for atomistic simulations must render the correct surface tension dependency with TMAO concentration. Simulations of TMAO at water/air interfaces have been used to calculate the surface tension (γ) of aqueous TMAO solutions at different concentrations (Fig. 3A). To calculate the surface tension γ for each TMAO model we have used the diagonal components of the pressure tensor (Pxx , Pyy and Pzz ) and 15



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the length of the box in the z direction (Lz = 84 nm) according to: 75 L Pxx + Pyy γ =− z − Pzz 2 2

!

(4)

The prefactor 1/2 in Equation 4 accounts for the two vapor-liquid interfaces present in our systems. Most of the water models fail in reproducing experimental water surface tension values (γexp = 71.73 mN/m at 300 K). 76 The Kast and Osmotic models predict a moderate increase of the surface tension at low TMAO concentrations (0.5 m), but it decreases at higher TMAO concentrations. The Density model on the other hand predicts the most remarkable decrease of the surface tension with TMAO concentration. Surface tension calculated with the Dipole model increases upon addition of TMAO osmolyte, which contradicts experimental measurements. 46,73,74 In agreement with these results we can see in Fig. 3C how TMAO tends to accumulate at the water-vapor interface for the three TMAO models that predict a decrease of the surface tension with TMAO content. In those simulations in which the Dipole model is used for TMAO we have observed that TMAO molecules deplete from the water-vapor interface, which aligns with the previously mentioned disagreement between the surface tensions predicted by this model and the experimentally measured ones and the overstimation of its hydration number. We have also calculated the orientation of the TMAO molecules at the water-vapor interface. To that end we have calculated the probability distribution of the angle θ defined −−−→ between the N O in TMAO molecules whose center of masses are located in a 0.5 nm thick slab centered at the Gibbs dividing surface and the z axis perpendicular to the water-vapor interface (Fig. 3D). Both Kast and Osmotic models show the maximum at θ ∼ 75◦ , which is slightly smaller to the one predicted by Fiore et al. 40 using the Kast model. The Dipole model presents its maximum value at θ ∼ 63◦ . These values suggest −−−→ that the N O vector is slightly tilted down towards the water phase. Interestingly, the −−−→ Density model presents a sharp peak at θ = 90◦ ( N O vector perpendicular to the z axis), which shows a strong dipole alignment. A second maximum at θ ∼ 40◦ is observed. A 16


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similar distribution was observed at lower TMAO concentrations (not shown). We have also calculated the osmotic coefficients (φ) at different TMAO concentrations for all the TMAO models and compared with experimental values 19 (Fig. 3B). Osmotic coefficients offer a measure of the strength of osmolyte-osmolyte self-interaction. Positive deviations from the van′ t Hoff equation (φ > 1) are due to repulsive self-interactions between cosolvent molecules. The opposite scenario (φ < 1) applies for co-solvent molecules that have attractive self-interactions. Canchi et al. 11,19 suggested that φ > 1 applies for protective osmolytes, which, owing to repulsive self-interactions, will not easily accumulate in the first solvation shell of a protein in solution, while denaturants like urea, which do accumulate there, exhibit osmotic coefficients φ < 1. All TMAO models render φ > 1, except the Kast and the Dipole models at 0.5 m. At intermediate concentrations (1, 1.5 and 2.0 m) the Density and Osmotic models offer the best match with experimentally measured osmotic coefficients (taken from ref. 19 ) while at higher concentrations (2.0 and 2.5 m) the Osmotic and Dipole models perform the best. The Density model understimates the φ value at the highest considered TMAO concentration, while the Kast model understimates the φ values within the whole range of TMAO concentrations.

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Figure 3: (A) Surface tension (γ) and (B) osmotic coefficient (φ) values calculated for different TMAO force fields. Osmotic coefficients are also compared with experimental values 19 which are presented as purple triangles. (C) Normalized density profiles (ρ(z)/ρbulk ) of TMAO nitrogen atoms at the vapor-liquid interfaces (dotted line) in 2.5 m TMAO aqueous solutions. Normalized water densities are shown in the same graph (continuous line). (D) Probability distribution (P(cos(θ)) of the cosinus of the angle θ defined −−−→ between the TMAO N O vector and the axis perpendicular to the liquid-vapor interfaces (z-axis, pointing towards the water phase) in 2.5 m TMAO aqueous solutions. In (C) and (D) z = 0 nm corresponds to the Gibbs dividing surface, which defines the surface at which water density is half of the water density in the bulk phase. We have further validated the different TMAO force fields by comparing their ability to reproduce transfer free energies ∆Gt of neopentane from water to 1M TMAO aqueous solutions. Neopentane has been widely considered as a model hydrophobe to study hydrophobic association in presence of co-solvents. 77–79 Wang and Bolen have reported

18


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that transfer free energies of nonpolar amino acid side chains from water to 1M TMAO tend to be negative and close to 0. 6 Indeed our calculations show that all models render near-zero negative transfer free energies for neopentane from water to 1M TMAO solutions: -1.16 kJ/mol (Kast), -0.86 kJ/mol (Osmotic), -0.17 kJ/mol (Dipole) and -0.94 kJ/mol (Density). In all cases the error in ∆Gt is below 1 kJ/mol. These results confirm that, independently of the TMAO force field, TMAO does not strongly interact with hydrophobic groups, which is in agreement with the results by Wang and Bolen. 6 It should be noticed that Dipole model was derived to reproduce not only experimental activity coefficients but also polyglycine transfer free energies.

Folding equilibrium of a hydrophobic polymer with different TMAO models In this section we discuss the impact of TMAO on the Globular ⇄ Extended (G ⇄ E) conformational folding equilibrium of a generic hydrophobic polymer. To that end, we have calculated the potentials of mean force (PMF) as function of the radius of gyration (Rg ) of the hydrophobic polymer (see details above) in pure aqueous medium as well as at different TMAO concentrations (Fig. 4 for the Osmotic model, Figure S1 for the other TMAO models). The PMF in pure water presents a global minimum at Rg ∼ 0.47 nm and a local minimum at Rg ∼ 1.07 nm, which correspond respectively to globular and extended conformations. At high TMAO concentrations, we can observe the appearance of a local minimum at Rg ∼ 0.60 nm, which corresponds to a hairpin semicompact configuration. Fig. 4 shows that addition of small amounts of TMAO destabilizes the minimum corresponding to the extended state, which means that the G−state is favored over the E−state in comparison to the system in pure water. This protective effect decreases at TMAO concentrations above 1 M and virtually vanishes when TMAO concentration reaches 4 M for the Osmotic and Kast models.

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Figure 4: Potentials of mean force (PMF) as a function of the radius of gyration (Rg ) of the hydrophobic polymer at different TMAO concentrations. TMAO has been described using the Osmotic model. To quantify the TMAO concentration dependent effect on the G ⇄ E conformational equilibrium we have calculated the free energy difference between the G− and E− states (the unfolding free energy ∆GGE ) at different TMAO concentrations. The conformational equilibrium G ⇄ E is characterized by the equilibrium constant K, which relates the number densities of extended (ρE ) and globular (ρG ) chains at equilibrium through K = ρE /ρG . Alternatively K can be expressed as a function of the above mentioned free energy difference ∆GGE resulting in K = exp[−∆GGE /RT ]. Combination of the above definitions of K renders ∆GGE = −RT ln(ρE /ρG ). To decide whether a given configuration is in the E− or G−state we have assigned a cut-off based on the PMF showed in Fig. 4 and Fig. S1. Thus, below Rcut g = 0.70 nm a chain is considered to be in the G−state, otherwise a chain is in the E−state. We are aware that also non-perfectly globular intermediate structures like hairpins meet the criteria Rcut g < 0.70 nm. However we want to keep the discussion in terms of a two-state problem. The unfolding free energy is obtained from 20


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R∞

Rcut g

exp[−∆GGE /RT ] = R cut Rg 0

e −PMF(Rg )/RT dRg e

−PMF(Rg )/RT

(5)

dRg

using the PMF data shown in Fig. 4 and Fig. S1. The unfolding free energy (∆GGE ) (Fig. 5) displays a non-monotonic trend. A linear stabilizing effect at TMAO concentrations up to 1 M is observed (up to 2 M for the Kast model), while beyond this concentration the protective effect of TMAO linearly decreases with osmolyte concentration for all the TMAO force fields except the Density model. ∆GGE at 4 M for the Dipole model is higher that at 3 M. It should be noted that this model displays the higher hydration number as well as the highest average number of hydrogen bonded waters, which lead to poor equilibration due to slower dynamics of the system at high TMAO concentrations and hence inaccurate predicted ∆GGE at high concentrations. The Density model shows a stabilizing and practically concentration-independent action for TMAO concentrations above 1 M. A widespread quantity to classify co-solvent and osmolytes as either denaturants or stabilizers is the so-called m-value. 74,80 Provided that the effect of osmolytes on the unfolding free energy (∆GGE ) follows a linear dependendency with the osmolyte concentration, the m-value (i.e. m = ∂∆GGE /∂cosmolyte ) can be obtained from: (0M)

∆GGE = ∆GGE + mcosmolyte

(6)

(0M)

In Eq. 6, ∆GGE is the unfolding free energy in the absence of osmolyte and cosmolyte is the osmolyte concentration. Resulting from Eq. 6, protective osmolytes are characterized by positive m-values. Denaturants on the other hand are characterized by negative mvalues. From Fig. 5 we can distinguish two different regimes. For TMAO concentrations below 1 M m-value for the hydrophobic polymer is positive, i.e. TMAO acts as a protective osmolyte. Contrarily, for TMAO concentrations above 1 M and contingent on re-defining (1M)

Eq. 6 as ∆GGE = ∆GGE + mcosmolyte the resulting m-value is negative, i.e. TMAO acts as 21



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a denaturant at concentrations higher than 1 M. For the Kast model positive m-value is observed up to 2 M TMAO concentrations.

Figure 5: Free energy difference (∆GGE ) characteristic of the G ⇄ E folding equilibrium as a function of the TMAO concentration for different TMAO models. A given chain is in the G−state if Rg < 0.70 nm, otherwise the chain is in the E−state. Error bars are within the symbol size. Addition of TMAO leads to an increased stabilization of the extended state. Indeed, Figure 5 evidences that the denaturant effect of TMAO at high concentrations is linearly proportional to the TMAO content. At 4 M, both Kast and Osmotic models destabilize the globular conformation in favour of a hairpin conformation with Rg ∼ 0.60 nm. 22


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To understand how the composition of the solvent affects the conformational equilibrium G ⇄ E we make use of the Wyman-Tanford approach: 81,82 ∂lnK = ∆ΓGE ∂lnaT

(7)

In the equation above, ∆ΓGE = ΓE − ΓG where ΓE and ΓG are the preferential binding coefficients 83 for the E− and G− states and aT is the TMAO activity. If ∆ΓGE < 0, TMAO

preferentially binds to the globular state, which causes the conformational equilibrium to shift in favor of globular state upon increase of TMAO content. The opposite applies when ∆ΓGE > 0. We have calculated Γ using the following expression: 84

Γ = nT −

ntot T − nT

ntot W − nW

× nW

(8)

where nT and nW are respectively the number of TMAO and water molecules bound to the hydrophobic polymer within a given distance range. Superscript tot denotes the total number of TMAO or water molecules present in the system. h. . .i stands for thermal averaging. We have calculated Γ for the conformations corresponding to both minima in the PMF’s (Fig. 4) (G− and E− states) at 0.5 M, 1 M and 4 M TMAO concentrations (Fig. 6 for the Osmotic model and Fig. S2 for the other models). Preferential binding coefficients have been calculated for frozen and flexible chains. The comparison provides insights in the role of conformational flexibility on preferential binding and conformational stability. Internal polymer fluctuations were suppressed by applying on each polymer bead a harmonic potential with a force contant of 1000 kJ mol−1 nm−2 (frozen chains), while in the flexible chains we have used an umbrella potential with a force constant of 20 000 kJ mol−1 nm−2 to restrain the mean Rg at the target value.

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Figure 6: Preferential binding coefficient Γ for globular (dotted line) and extended (continuous line) configurations at 0.5 M, 1 M and 4 M TMAO concentrations for frozen (left) and flexible (right) chains. It should be noted that Γ converges in all cases at distances r ∼ 1 nm to positive values, which means that TMAO co-solvent molecules directly interact with the hydrophobic polymer independently of the TMAO concentration, polymer conformation and polymer flexibility. Let us firstly consider the situation in which polymer chains are flexible. For clarity we focus our discussion on the Osmotic model (see Fig. S2 for the other models). Figures 4 and 5 show how addition of TMAO alters the unfolding free energy. We can distinguish three situations depending on the TMAO concentration. At 0.5 M, ∆ΓGE ∼ −0.3, which means that TMAO preferentially binds to the G−state. TMAO therefore stabilizes the G−state at this concentration (see Eq. 7), i.e. addition of TMAO displaces the G ⇄ E equilibrium towards the left in agreement with the previous discussion. At 1 M, ∆ΓGE ∼ 0. The fact that ∆ΓGE vanishes at this TMAO concentration can be interpreted as an inflexion point separating protective and denaturant regimes. As seen in Fig. 5, at 1 M TMAO concentration ∆GGE displays its maximum value. At 4 M TMAO concentration, TMAO preferentially binds to the E−state (∆ΓGE ∼ 1.2), in agreement with the negative m-value at high concentrations. 24


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When the polymer chains are kept frozen ∆ΓGE > 0 within the entire TMAO concentration range. Thus in the absence of polymer chain flexibility, the polymer-solvent interactions shift the G ⇄ E equilibrium in favor of the E−state. Since Γ is always positive, TMAO acts as a denaturant through direct preferential interaction with the configuration with the higher solvent accessible surface area (SASA). To obtain a consistent picture we thus see that polymer flexibility must be taken into account. In a previous study we showed that polymer flexibility – and hence its configurational entropy – is crucial to explain the mechanism of PNiPAM polymer collapse in methanol aqueous solutions. 85 We have calculated the configurational entropy Sconf of the polymer using the Schlitter formula, 86 which yields to an approximate upper value of the absolute entropy S: 87

S < Sconf

"

k Te = 0.5kb ln det I + b 2 Mσ ℏ

#

(9)

where kb is the Boltzmann constant, T is the temperature, e is the Euler’s number, ℏ is the Planck constant, I is the identity matrix, M is the 3N-dimensional diagonal matrix containing the N masses of the polymer beads and σ is the covariance matrix of the fluctuations of polymer bead positions. Figure 7 shows Sconf calculated for fully flexible polymer chains in the G−state (initial Rg = 0.47 nm) at different TMAO concentrations. Addition of TMAO initially leads to an increase and next a decrease of the globule’s configurational entropy with increasing TMAO concentration. Thus, configurational entropy initially contributes to stabilizing the compact globule but contributes to destabilizing it at higher TMAO concentration. This observation is force field independent. We note that this trend correlates with the stability of the globule shown in Figure 5.

We can conclude that TMAO directly interacts with the hydrophobic polymer and yet favors the collapsed conformation over the unfolded state. This observation challenges the commonly accepted stabilization mechanism by preferential exclusion. 13,14,27,88–91 However the protective effect is concentration dependent, reaching a maximum stabi25



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lization at TMAO concentrations ∼ 1 M. In the last years, there have been several studies which evidence that collapse of macromolecules in the presence of co-solvent molecules may be induced by direct interaction of the co-solvent with the macromolecular surface. 41,46,85,92–94 When the interaction between the macromolecule and the co-solvent is highly attractive such stabilization may be due to cross-linking or bridging-like interactions between the co-solvent and the macromolecule. 95 Alternatively, co-solvents that weakly interact with a macromolecule may stabilize collapsed macromolecular states on the basis of entropic forces, as we have recently proposed for poly(N-isopropylacrylamide) (PNiPAM) in urea aqueous solutions 93,94 and in low concentration methanol aqueous solutions. 85 Recently reported stabilization of folded polystyrene chains in presence of TMAO 46 falls in the same category.

Figure 7: Configurational entropy (T Sconf ) calculated according to the the Schlitter formula (Eq. 9) for flexible globules at T = 298K. Ten independent 50 ns long MD simulations have been considered to calculate T Sconf at each TMAO concentration. T Sconf in pure water is depicted as a purple cross. The initial Rg of the polymer chains was 0.47 nm. Polymer chains were fully flexible in the 50 ns MD simulations and remained in their globular G−state at all times.

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Conclusions In the first part of this work we have compared the ability of four different TMAO force fields 18–21 to reproduce key experimental quantities such as hydration properties, surface tensions, osmotic coefficients at different concentrations and transfer free energy of neopentane from water to 1 M TMAO aqueous solutions. The Kast and Osmotic models lead to TMAO hydration numbers in good agreement with experimental data, while the Dipole and Density models lead to oversized hydration shells. All force fields however predict a similar number of TMAO-water hydrogen bonds of ∼3, which is in agreement with experimental measurements. The Dipole model is the only force field that predicts an increase of the surface tension with TMAO concentration, which is in disagreement with experimental data. Congruent with this, all the force fields except the Dipole model show accumulation of TMAO molecules at the liquid-vapor interface. We have also calculated the osmotic coefficient at different TMAO concentrations. Compared to experimental results, the Osmotic model performs the best within the whole concentration range, while the Density model understimates the osmotic coefficient at high concentrations. All the force fields predict, in good agreement with experimental data, near zero and negative transfer free energies for neopentane from water to 1 M TMAO aqueous solutions. This agreement is especially good for the Dipole model. In the second part of this work we have studied the impact of TMAO on the G ⇄ E conformational equilibrium of a generic hydrophobic polymer. We have calculated the PMFs at different TMAO concentrations using the polymer Rg as reaction coordinate. Within the TMAO concentration range considered in this work, in comparison to the pure water system addition of TMAO leads to a stabilization of the compact state. However the impact of TMAO on the conformational equilibrium displays a strong concentration dependency. At concentrations below 1 M, the TMAO stabilizing effect is linearly additive for all the force fields under study. This trend is however inverted at concentrations above 1 M (2 M for the Kast model), in which the stabilizing effect linearly decreases. 27



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The exception is the Density model, whose stabilizing effect is practically independent of the TMAO concentration. Hence, the sign of the m-value depends on the TMAO concentration range and at high TMAO concentrations (> 1 M) any further increase in TMAO concentration destabilizes the G−state in favor of the E−state de facto acting as a denaturant agent. It is worth noting that reported m-values to evaluate the effect of osmolytes and co-solvents over the conformational equilibrium of a given protein are normally calculated considering the unfolding free energy (∆GGE ) in pure water and at one specific concentration and assuming a linear concentration dependency of (∆GGE ) with co-solvent concentration. 74 TMAO co-solvent accumulates on the polymer first solvation shell and yet may act as either protective osmolyte or denaturant. Since the model hydrophobic polymer is uncharged, accumulation of TMAO on the polymer first solvation shell must be driven by weak non-directional van der Waals forces. Results shown in this article may guide future work on force field development and force field refinement for co-solvents that act either as protective osmolytes or denaturant agents.

Acknowledgement This research was supported by the German Research Foundation (DFG) within the Collaborative Research Center "Multiscale Simulation Methods for Soft Matter Systems" (SFBTRR146). We thank David Rosenberger and Timir Hajari for their help in setting up the procedure to calculate the osmotic coefficients. We thank Pritam Ganguly for providing the files to calculate the transfer free energies from water to 1 M TMAO solutions for neopentane. We express our gratitude to the Hochschulrechenzentrum at the TUDarmstadt for the computational time provided.

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Supporting Information Available Potentials of Mean Force (PMF’s) and Preferential binding coefficients (Γ) for the Kast, Dipole and Density models interacting with the hydrophobic generic polymer are included in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org/.

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(7) Courtenay, E. S.; Capp, M. W.; Anderson, C. F.; RecordJr., M. T. Vapor Pressure Osmometry Studies of Osmolyte-Protein Interactions. Implications for the Action of Osmoprotectants in Vivo and for the Interpretation of "Osmotic Stress" Experiments in Vitro. Biochemistry 2000, 39, 4455–4471. (8) Auton, M.; ; Bolen, D. W. Additive Transfer Free Energies of the Peptide Backbone Unit That Are Independent of the Model Compound and the Choice of Concentration Scale. Biochemistry 2004, 43, 1329–1342. (9) Street, T. O.; Bolen, D. W.; Rose, G. D. A Molecular Mechanism for OsmolyteInduced Protein Stability. Proc. Natl. Acad. Sci. USA 2006, 103, 13997–14002. (10) Rose, G. D.; Fleming, P. J.; Banavar, J. R.; Maritan, A. A Backbone-Based Theory of Protein Folding. Proc. Natl. Acad. Sci. USA 2006, 103, 16623–16633. (11) Canchi, D. R.; García, A. E. Cosolvent Effects on Protein Stability. Annu. Rev. Phys. Chem. 2013, 64, 273–293. (12) Wei, H.; Fan, Y.; Gao, Y. Q. Effects of Urea, Tetramethyl Urea, and Trimethylamine NOxide on Aqueous Solution Structure and Solvation of Protein Backbones: A Molecular Dynamics Simulation Study. J. Phys. Chem. B 2010, 114, 557–568. (13) Kokubo, H.; Hu, C. Y.; Pettitt, B. M. Peptide Conformational Preferences in Osmolyte Solutions: Transfer Free Energies of Decaalanine. J. Am. Chem. Soc. 2011, 133, 1849– 1858. (14) Cho, S. S.; Reddy, G.; Straub, J. E.; Thirumalai, D. Entropic Stabilization of Proteins by TMAO. J. Phys. Chem. B 2011, 115, 13401–13407. (15) Ma, J.; Pazos, I. M.; Gai, F. Microscopic Insights Into the Protein-Stabilizing Effect of Trimethylamine N-oxide (TMAO). Proc. Natl. Acad. Sci. USA 2014, 111, 8476–8481.

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(16) Ganguly, P.; Hajari, T.; Shea, J.-E.; van der Vegt, N. F. A. Mutual Exclusion of Urea and Trimethylamine N-Oxide from Amino Acids in Mixed Solvent Environment. J. Phys. Chem. Lett. 2015, 6, 581–585. (17) Borgohain, G.; Paul, S. Model Dependency of TMAO’s Counteracting Effect Against Action of Urea: Kast Model versus Osmotic Model of TMAO. J. Phys. Chem. B 2016, 120, 2352–2361. (18) Kast, K. M.; Brickmann, J.; Kast, S. M.; Berry, R. S. Binary Phases of Aliphatic NOxides and Water: Force Field Development and Molecular Dynamics Simulation. J. Phys. Chem. A 2003, 107, 5342–5351. (19) Canchi, D. R.; Jayasimha, P.; Rau, D. C.; Makhatadze, G. I.; García, A. E. Molecular Mechanism for the Preferential Exclusion of TMAO from Protein Surfaces. J. Phys. Chem. B 2012, 116, 12095–12104. (20) Schneck, E.; Horinek, D.; Netz, R. R. Insight into the Molecular Mechanisms of Protein Stabilizing Osmolytes from Global Force-Field Variations. J. Phys. Chem. B 2013, 117, 8310–8321. (21) Larini, L.; Shea, J.-E. Double Resolution Model for Studying TMAO/Water Effective Interactions. J. Phys. Chem. B 2013, 117, 13268–13277. (22) Jorgensen, W. L. Quantum and Statistical Mechanical Studies of Liquids. 10. Transferable Intermolecular Potential Functions for Water, Alcohols, and Ethers. Application to Liquid Water. J. Am. Chem. Soc. 1981, 103, 335–340. (23) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of Simple Potential Functions for Simulating Liquid Water. J. Chem. Phys. 1983, 79, 926–935.

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Comparison of Different TMAO Force Fields and Their Impact on the

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