Dynamical Model for the Counteracting Effects of Trimethylamine N-Oxide on Urea in Aqueous Solutions under Pressure

Abstract

Of cosolutes found in living cells, urea denatures and trimethylamine N-oxide (TMAO) stabilizes proteins; furthermore, these effects cancel at a 2:1 ratio of urea to TMAO. Interestingly, cartilaginous fish use urea and TMAO as osmolytes at similar ratios at the ocean surface but with increasing fractions of TMAO at increasing depths. Here, molecular dynamics simulations of aqueous solutions with different urea:TMAO ratios show that the diffusion coefficients of water in the solutions vary with pressure if the urea:TMAO ratio is constant, but strikingly are almost pressure independent at the ratio found in these fish as a function of depth. This suggests that this ratio may be maintaining a homeostasis of water dynamics. In addition, diffusion is determined by hydrogen-bond lifetimes of the different species in the solution. Based on these observations, a dynamical model in terms of hydrogen-bond lifetimes is developed for the hydrogen bonding propensities of cosolutes and water in an aqueous solution to proteins. This model provides an explanation for both the counteracting effects of TMAO on urea denaturation and the depth-dependent urea:TMAO ratio found in cartilaginous fish.

Graphical Abstract

I. INTRODUCTION

Small organic cosolutes found in living cells have different effects on proteins. For instance, urea strongly denaturizes proteins, which is generally thought to occur by preferential binding to protein^1–6 with little perturbation of bulk water.⁷ In addition, trimethylamine N-oxide (TMAO) strongly stabilizes proteins, although the mechanism is under debate with proposals including preferential exclusion from protein,^8–11 alteration of water structure,¹² or preferential attraction to the protein.^13–14 TMAO has been found to counteract the denaturing effects of urea when added in a 2:1 ratio of urea to TMAO, although the mechanism is also not clear with proposals including direct interactions between TMAO and urea,^15–16 urea-independent preferential exclusion from protein,^{8, 17–18} exclusion of urea from protein,¹⁹ urea-enhanced preferential exclusion from protein with no effect on urea,^20–21 or reversion of urea-induced changes in water structure.¹² In particular, molecular dynamics (MD) simulation studies have implicated that the relative dynamics of TMAO and urea in the hydration shell of staphylococcal nuclease in the urea-enhanced preferential exclusion of TMAO from protein.²¹

Interestingly, some marine organisms appear to take advantage of the counteraction and use a mixture of urea and TMAO as osmolytes to balance the ~0.6 M salt found in seawater. Moreover, chondrichthyans, which are cartilaginous fishes including sharks, batoids (rays and skates), and chimaeras, utilize a 2:1 ratio for shallow water species but the fraction of TMAO increases linearly with depth at which the species is found.²² Since pressure increases by ~1 bar per 10 m depth, TMAO has been suggested as a “piezolyte”²³ that protects proteins against pressure, which appears to be the case for a variety of proteins.²³ However, the mechanism of this effect is not clear either although recent studies indicate that TMAO counteracts the negative effects of pressure by enhancing water structure,^24–26 which may not only protect protein structure but also prevent protein aggregation.^27–28

To clarify the effects of urea and TMAO on proteins, MD simulation studies have recently been performed on aqueous solutions of urea, TMAO, and urea-TMAO mixtures in the absence of protein to understand the changes in behavior between the binary and ternary solutions.^{11, 15, 29–30} Simulations can provide clues to the molecular origins of the thermodynamics of these solutions. For instance, the strong hydrogen bond TMAO and water may play a role in protein stabilization^{12, 31–32} although recent AIMD simulations indicate that the methyl groups of TMAO also contribute.³³ However, analysis by Kirkwood-Buff theory using experimental data indicates that changes in water structure cannot be detected³⁴ and changes in radial distribution functions of water under a range of conditions are relatively small.³⁵ In addition, the results from MD simulations are dependent on the quality of the force field. Several all-atom TMAO models ^{11, 36–39} are frequently used, which appear to give different results especially when urea is present.^{19, 29} Winter, Marx, Kast, Horinek, and their collaborators have spent consider effort in improving the TMAO force field, and a comparison of several recent models shows that the more recent Kast model,³⁹ referred to here as Kast 2016, gives the best representation of thermodynamic, transport, structural, and dielectric properties over a wide concentration range.⁴⁰ This group has also developed methods for improving the accuracy of the force field for TMAO at high pressure^{39, 41} to capture hydration structures as well as thermodynamic properties at high pressures. On the other hand, the force fields for urea generally give more similar results, and unlike TMAO, pressure adaptation of the force field does not appear to be necessary.⁴²

Our work on aqueous solutions of urea and TMAO³⁰ has focused on the dynamics of these solutions in MD simulations. Our studies show that diffusion coefficients of water (D_w) and of the cosolute i (D_i) have the same dependence on the cosolute concentration over a wide range of concentrations, indicating that the diffusional behavior of the cosolutes and water are both controlled by the viscosity of the solution. Additionally, D_w in the solutions is an exponential function of the cosolute concentrations and D_i is inversely proportional to the cosolute-water hydrogen bond lifetime τ_i^β where β = ~2. Other work has shown that hydrogen bond lifetimes in pure water are affected by the diffusion of water.⁴³ Our work also shows how cosolute-water hydrogen bond lifetimes and thus the diffusion of cosolute influence and are influenced by water-water hydrogen bond lifetimes and thus the diffusion of water. Specifically, the diffusion of TMAO and water in TMAO solutions are much slower than the diffusion of urea and water in urea solutions, which is in good agreement with NMR measurements of diffusion^44–45 and consistent with Fourier transfer infrared (FTIR) spectroscopy studies of changes in water structure⁴⁶ and viscosity measurements. This is because TMAO-water hydrogen bonds have much longer lifetimes than water-water or urea-water hydrogen bonds. In addition, in the ternary solutions with the same total cosolute concentration, the diffusion of urea and water are slower than in the urea binary solutions because TMAO slows bulk water more than urea, while the diffusion of TMAO and water are faster than in the TMAO binary solutions because urea slows bulk water less than TMAO. Thus, the lifetimes of cosolute-water hydrogen bonds influence how much a cosolute slows the diffusion of water but are also not intrinsic to the cosolute-water pair since the diffusion of bulk water also affects cosolute-water lifetimes.

Additionally, a general problem is found with the dynamics in most simulation studies for solutes in water and specifically for TMAO and urea in water.^{30, 38, 40} While agreement of simulation with experiment is generally assessed for diffusion coefficients of the solutes relative to the diffusion coefficient of water, the diffusion coefficients of most standardly used water models are too fast^47–48 and consequently, the absolute values of the solute diffusion coefficients are too fast compared to experiment. However, there have been many recent improvements in water models, including the TIP4P-FB model, which gives good properties including diffusion coefficients for pure water over a wide range of temperatures and pressures.⁴⁹

Here, a consistent explanation is sought for the counteracting effects at the 2:1 urea:TMAO ratio at 1 bar and the depth-dependent urea:TMAO ratio of chondrichthyans. MD simulations are performed of urea and TMAO binary aqueous solutions and urea-TMAO ternary aqueous solutions at pressures between 1 bar and 300 bar, corresponding to the range of depths where chondrichthyans have been found, from the surface to 3000 m. The “skate ratio” ternary solutions have concentrations of urea and TMAO at each pressure based on a linear fit of concentration versus sampling depth for arctic skates.⁵⁰ For the other solutions, the total molal cosolute concentrations are kept at the total urea plus TMAO concentration found in the arctic skates at that pressure, and the “surface ratio” ternary solutions have the urea:TMAO ratio found for surface-dwelling arctic skates at all pressures. Although the surface ratio for skates (~2.7:1) has somewhat less TMAO than thought to be needed for counteracting urea denaturation, urea and TMAO at the surface account for only 0.5 M of the 0.6 M needed to balance the salt in seawater and the other osmolytes may have similar effects as TMAO.⁵¹ Diffusion coefficients and hydrogen bond properties are calculated from the simulations. Based on these results, a dynamical model for the hydrogen bonding propensities of the cosolute and of water in the aqueous solutions relative to pure water is developed, which can explain both the counteracting effects of TMAO on denaturation of proteins by urea and the depth-dependent urea:TMAO ratio found in cartilaginous fish.

II. METHODS

The molecular dynamics simulations were performed using the molecular mechanics packages CHARMM version 41a2⁵² and OpenMM version 7.3.1⁵³ compiled with CUDA version 9.2. The following force fields were used: the CGenFF/CHARMM36 all-atom force field⁵⁴ for urea, the Kast 2016 model³⁹ for TMAO, and the TIP4P-FB model⁴⁹ for water. The method to improve the TMAO force field at high pressure^{39, 41} is not used here because the pressure ranges from 1 to 300 bar, and the consequent changes in the partial charges are at most 0.02 e (less than 4%) and should not have substantial impact. Comparisons of simulation against experiment for the density and diffusion as a function of concentration for the TMAO and urea binary solutions using these force fields are excellent (Figs. S1 and S2 in the Supporting Information) and are improvements over using force fields from the previous study.³⁰

The initial structures of TMAO and urea were generated from their internal coordinates. TMAO and urea molecules were placed and rotated randomly in an equilibrated cubic box of water with side length ~40 Å; numbers of each type of molecule are given in Table S1 in the Supporting Information. The general strategy is heating and pressurization in the NPT ensemble and then a production run in the NVT ensemble using OpenMM with a target volume that is the average volume in preliminary 5-ns NPT simulations performed in CHARMM to take advantage of its barostat (see Supporting Information for simulation procedure). The simulations in OpenMM are described briefly here noting changes from default settings. The calculations were in “mixed precision”, in which forces and integration are calculated in single and double precision, respectively. Nonbonded interactions had a cutoff of 12 Å. The Lennard-Jones interactions were turned off using the OpenMM switching function from 10 to 12 Å with no long-range corrections. The PME method, with an Ewald error tolerance of 1×10⁻⁵, was used for the electrostatics. The SHAKE⁵⁵ algorithm was used to fix the covalent bond lengths for hydrogen atoms. Each system was minimized with 500 iterations of the L-BFGS algorithm.⁵⁶ Initial stages of the simulations were performed using a leapfrog Verlet integrator with a 1-fs time step and were maintained in the NPT ensemble using an Andersen thermostat⁵⁷ updated every 1000 steps and a Monte Carlo (MC) barostat⁵⁸ updated every 25 steps. Each system was heated from an initial temperature of 0 K to the final temperature 298 K in 5 K intervals of 5 ps each, followed by pressurization from 1 bar to the final pressure in 20 bar intervals of 20 ps each. Next, the system was equilibrated for 5 ns in the NPT ensemble. The simulations were continued until the volume of the system differed less than 0.05% from the target volume from the 5-ns NPT CHARMM simulations. Starting from this point, the production run was generated utilizing a velocity Verlet integrator with a 1-fs time step maintained in the NVT ensemble using a Nosé-Hoover chain thermostat^59–60 for another 5 ns followed by 50 ns of production run.

Diffusion coefficients and hydrogen properties were calculated from the production runs from coordinates saved every 1 ps. The mean values were calculated from the entire trajectory, and the standard deviations were obtained via a batch-means procedure by dividing each 50-ns simulation into five 10-ns segments of trajectory.⁶¹ The diffusion coefficients D_α for the diffusing species α were calculated from a linear regression of the mean-square displacement as a function of Δt using the Einstein relation.⁶² For the average, the maximum Δt was 100 ps, while for the standard deviation, the maximum Δt was 20 ps. A correction for the simulation box size dependence of the diffusion coefficient⁶³ was included, where the experimental viscosities^{32, 64} were used for the binary solutions and a multiplication of the experimental viscosities at the concentration for each cosolute for the ternary solutions. Hydrogen bond lifetimes τ_DA between a donor D and an acceptor A were also calculated; specifically, D is ‘u’ or ‘w’ for a urea nitrogen or a water oxygen, respectively, and A is ‘u’, ‘t’, or ‘w’ for a urea oxygen, TMAO oxygen, or water oxygen, respectively. The criteria for a hydrogen bond was a distance cutoff of 2.4 Å between the hydrogen atom and an acceptor, and an angle cutoff of 135°.⁶⁵ The lifetime of a continuously formed hydrogen bond was calculated using an auto-correlation method.⁶⁶ Linear fits to diffusion coefficients and hydrogen bond lifetimes, which are used in the Discussion, were weighted by inverse errors; parameters from linear fits are given in Tables S2 and S3 in the Supplementary Information. The number of potential sites that a molecule can hydrogen bond to a protein is assumed to be n_uw = 4 and n_wu = 2 for urea, n_wt = 2 for TMAO, and n_ww = 4 for water.

III. RESULTS

The diffusion coefficient of water D_w in the simulations depends on the type and concentration of cosolute and the pressure (Fig. 1a). D_w in all of the solutions at 1 bar are slower than in pure water, as in previous results.³⁰ As a function of pressure, D_w of pure water demonstrates the anomalous increase in D_w as pressure increases up to a few kbar seen in experiment,⁶⁷ and D_w in the binary solutions and the surface ratio ternary solutions also increase with pressure. However, D_w in the skate ratio ternary solutions are strikingly almost independent of pressure and even decrease slightly, which suggests that the urea:TMAO ratio found in skates may be a strategy to maintain homeostasis of water dynamics at the depth at which they are found. Finally, the water-water hydrogen bond lifetimes τ_ww as a function of pressure have inverse trend to D_w (Fig. 1b).

Figure 1.

Average (a) diffusion coefficients of water and (b) lifetimes of water-water hydrogen bonds from simulations of aqueous solutions with different concentrations of urea and TMAO as functions of pressure. Symbols with error bars are from simulations, solid lines connect simulation data, and dashed lines are experimental data for pure water⁵² scaled to D_w of TIP4P-Ew at 1 bar in (a) and linear fits to simulation data in (b). The water molecules are in urea binary (blue), TMAO binary (red), surface ratio ternary (green), and skate ratio ternary (black) solutions as well as in pure water in the simulation (aqua).

The diffusion coefficients of the cosolutes D_α in the simulations are also dependent on the type and concentration of cosolute (Fig. 2a). At 1 bar, the D_α are faster for urea than TMAO in the binary solutions and urea is slowed and TMAO is speeded up in the ternary solutions, similar to previous results.³⁰ The solute diffusion in the TMAO binary solutions is especially slow apparently because τ_wt is four times longer than τ_ww (Fig. 2b), while in the urea binary solutions, τ_wu is similar to τ_ww (Fig. 2c) and τ_uw is less than half of τ_ww (Fig. 2d). Also, in the ternary solutions, τ_uw increases while τ_wt decreases, indicating that both cosolutes affect the diffusion of water so that it is faster than in the TMAO binary solution but slower than in the urea binary solution, which in turn affects the diffusion of the other cosolute. However, unlike the diffusion of water, the dependence of D_α for the cosolutes on pressure is slight (Fig. 2a). Pressure dependence is seen in hydrogen bond lifetimes since in the binary solutions and the surface ratio ternary solutions, they decrease with pressure while in the skate ratio ternary solutions, the decrease is much smaller, and the very short τ_uw actually increases with pressure (Fig. 2b–d). This indicates the pressure effects are on the water-water hydrogen bonds and changes in cosolute-water hydrogen bonds are a consequence of the changes in water diffusion that do not greatly affect the diffusion of the cosolute.

Figure 2.

Average (a) diffusion coefficients of cosolutes and hydrogen bond lifetimes of (b) water-TMAO, (c) water-urea oxygen, and (d) urea nitrogen-water. Symbols with error bars are from simulations and dashed lines are linear fits to simulation data. The cosolutes are TMAO () or urea nitrogen () in urea binary (blue), TMAO binary (red), surface ratio ternary (green), and skate ratio ternary (black) solutions.

III. DISCUSSION

Considering the potential deleterious effects of urea on proteins in fish, the concentrations are well below what usually is needed to completely denature proteins. However, studies of enzymes with different concentrations of urea and TMAO⁶⁸ indicate that enzyme activity is affected even at 0.5 M urea. Thus, at concentrations needed for osmolytic activity, the perturbation by urea involve many factors such as binding to the protein, micro-unfolding of loops, and shifting equilibrium of different active conformations, rather than complete denaturation. However, given that these can be considered initial steps on the way to unfolding, the effects will be described as stabilizing versus destabilizing.

To understand how cosolutes could affect the stability of proteins in these solutions, a dynamical model for the propensity of cosolutes and water in a solution to interact with protein is proposed here. While protein stability is generally considered in terms of thermodynamic properties, here the effects of cosolutes on these processes are considered in terms of diffusion coefficient and hydrogen bond lifetimes, both dynamical properties. However, the thermodynamic free energies involve a considerable entropic contribution due to the large ensembles involved. Thus, hydrogen bond lifetimes in molecular dynamics simulations have been associated with the strength of hydrogen bonds in water⁶⁹ and in proteins⁷⁰ since the activation free energy is the relevant energy that must be found in the dynamics of the environment.

Hydrogen bonds in proteins are in “fluxional equilibrium”.⁷⁰ In protein unfolding, the protein goes from the folded state with intramolecular hydrogen bonds to the unfolded state with its polar groups mostly hydrogen bonded to water. Moreover, proteins are generally only marginally stable even under physiological conditions, on the order of a few kcal/mol,⁷¹ which corresponds to only a few hydrogen bonds.⁷² A hydrogen bond in a protein “P” to “X”, which can be a species within the protein or a water molecule, can form a new hydrogen bond to a water molecule “w” cosolute or a molecule α, if present, that is initially hydrogen bonded to bulk water “W”. Hydrogen bonds are assumed to be a donor and acceptor pair but not distinguished here for simplicity.

$$\text{P}\cdots \text{X}+\text{w}\cdots \text{W}\underset{\propto D_{\text{w}}}{\stackrel{k_{\text{ww}}}{\rightleftharpoons }}\text{P}\cdots \text{w}+\text{W}$$ (1)

$$\text{P}\cdots \text{X}+\alpha \cdots \text{W}\underset{\propto D_{\alpha }}{\stackrel{k_{\alpha \text{w}}\mathrm{or}{k}_{\text{w}\alpha }}{\rightleftharpoons }}\text{P}\cdots \alpha +\text{W}$$ (2)

Assuming that the rate of the forward reaction (i.e., destabilizing if X is in the protein because it is intramolecular) is determined by the rate at which water or cosolute becomes “available” to hydrogen bond to protein. The rate that a molecule becomes “available” is assumed to be the rate of breaking a hydrogen bond with water and the rate of breaking a D-H…A hydrogen bond is assumed to be the inverse of the lifetime of that hydrogen bond; i.e., k_DA = 1/τ_DA, times the number of potential sites n_DA the molecule has to hydrogen bond to the protein. Also, assuming the rate of the reverse reaction (i.e., stabilizing) is determined by the ability of the water or cosolute to move away from the protein and so is proportional to its diffusion coefficient, D_w or D_α, respectively.

The hydrogen bonding propensity to protein of cosolute in the solution at a given pressure, Ω, is defined relative to the same number of water molecules in pure water at 1 bar

$$\mathrm{\Omega }=\frac{{\sum }_{\alpha }{m}_{\alpha }\left\{{\sum }_{i_{\alpha }}{n}_{i_{\alpha }w}{k}_{i_{\alpha }\text{w}}+{\sum }_{j_{\alpha }}{n}_{w{j}_{\alpha }}{k}_{w{j}_{\alpha }}\right\}{D}_{\text{w}}/D_{\alpha }}{m_{\text{S}}{n}_{\text{ww}}k{°}_{\text{ww}}}$$ (3)

where i_α and j_α are the atom types of the donors and acceptors, respectively, in α, m_α is the molality of α, m_S = Σ m_α is the total cosolute molality, and “°” denotes pure water at 1 bar. Thus, Ω > 1 implies that cosolute tends to hydrogen bond to protein, stabilizing the unfolded state and thus favoring denaturation while Ω < 1 implies cosolute tends to remain hydrogen bonded to water. While Ω is similar to Timasheff’s preferential binding parameter,⁸ Ω < 1 does not imply that the protein would be stabilized relative to being in pure water. Also, Ω is the propensity of binding of any cosolute, so, it contains contributions from both TMAO and urea in the ternary solutions.

The hydrogen bonding propensity to protein of water in the solution at a given pressure, Ψ, is defined relative to the same number of water molecules of pure water at 1 bar

$$\text{Ψ}=\frac{k_{\text{ww}}}{k_{\text{ww}}^{°}}$$ (4)

Thus, Ψ > 1 implies water in the solution has weaker structure than in pure water and tends to hydrogen bond to protein, stabilizing the unfolded state and thus favoring denaturation while Ψ < 1 implies water in the solution has stronger structure than in pure water and tends to remain in the bulk, destabilizing the unfolded state and thus favoring the native state. Ψ differs from Timasheff’s preferential hydration parameter, which is simply the negative of the preferential binding parameter,⁸ since it explicitly considers contributions from water in the bulk.

In the dynamical model, the net effect on a hydrogen bond of the protein in the solution at a given pressure relative to that in pure water at 1 bar in terms of the propensities Ω and Ψ is described by K′

$$K=\left(\frac{m_{\text{S}}}{m_{\text{w}}}\mathrm{\Omega }+\mathrm{\Psi }\right)K^{°}=K^{\prime }{K}^{°}$$ (5)

where K is the equilibrium constant for breaking the hydrogen bond in the solution at a given pressure and K° is the equilibrium constant for breaking the hydrogen bond in pure water at 1 bar.

Ω, Ψ, and K′ can be calculated from the lifetimes and diffusion coefficients from molecular dynamics simulations. Here they are calculated from the linear fits to the simulation data given in Fig. 1 and 2; the linear fits are given in Tables S2 and S3 of the Supplementary information.

At 1 bar, Ω (Fig. 3a) predicts effects of urea and TMAO that are consistent with other structural models from simulations.^{18, 73} For the urea binary solution, Ω > 1 because the urea-water lifetimes are short, indicating that urea would hydrogen bond to protein and favor its denaturation. For the TMAO binary solution, Ω ≈ 0 because the TMAO-water lifetimes are long, indicating that TMAO would hydrogen bond more strongly to water than protein although as mentioned above, Ω does not indicate how it would affect protein stability. When both TMAO and urea are present in the ternary solutions, Ω for the surface ratio indicates the total amount of cosolute that could hydrogen bond to protein is reduced from the urea solution but urea itself is only very slightly worsened in its ability to hydrogen bond to protein. Examining hydrogen bonding of urea to the surface of dihydrofolate reductase (DHFR), which has ~160 residues, Ω predicts about eleven urea molecules should hydrogen bond in a surface ratio urea:TMAO solution and about fourteen in a urea binary solution, while preliminary simulations of DHFR in these solutions show 6.5 in a surface ratio urea:TMAO solution and 8 in a urea binary solution. While Ω predicts somewhat more than found in the simulations, the difference in size between urea and water is not taken into account in Ω and urea may be too big to reach parts of the surface that water can. As pressure increases, Ω for the binary and surface ratio ternary solutions have little pressure dependence, reflecting the relative lack of pressure dependence in D_i, while the skate ratio ternary solution shows a sharp decrease with pressure (Fig. 3a). This implies one function of the higher concentration of TMAO with increasing depth may be to replace a destabilizing cosolute with one that does not interact with protein, which may be necessary since pressure may decrease at least some intraprotein hydrogen-bond lifetimes.⁷⁴

Figure 3.

Schematics of interactions of (a) cosolutes with protein different values of Ω and (b) water with protein for different values of Ψ. Urea (), TMAO (), water ()

At 1 bar (Fig. 3b), Ψ appears to be a good measure of the water structure since it is consistent with experiments of the effects of cosolutes on water.^{32, 46, 75} Ψ ≈ 1 for the urea binary solution indicating it is close to pure water while Ψ << 1 for the TMAO binary solution indicating it is strengthened relative to pure water. Ψ predicts that the main effect of TMAO is strengthening hydrogen bonds in bulk water while urea has hydrogen bonds that are similar to pure water, which is consistent with FTIR results.⁴⁶ When both TMAO and urea are present in the ternary solutions, Ψ becomes lower than the urea binary solution because TMAO strengthens bulk water hydrogen bonds. Moreover, the increase in Ψ of pure water with increasing pressure, which leads to Ψ > 1 at pressures above 1 bar (Fig. 3b), indicates water favors denaturation because water-water hydrogen bonds get weaker under pressure. Examining intramolecular hydrogen bonds in DHFR, Ψ predicts DHFR in pure water should have two fewer hydrogen bonds at ~200 bar than at 1 bar while simulations also show two fewer in Escherichia coli DHFR.⁷⁴ The binary and surface ratio ternary solutions show similar increase in Ψ with pressure as pure water. However, the skate ratio ternary solution shows much less of an increase and Ψ < 1 even at higher pressures, indicating that the higher concentration of TMAO at greater depth could counteract the effects of pressure on bulk water hydrogen bonds by strengthening them, thereby stabilizing protein structure.

K′ compares how a solution at a given pressure should affect a given intramolecular hydrogen bond in a protein versus pure water at 1 bar via both cosolute binding (Ω) and water structure (Ψ). At 1 bar (Fig. 4), K′ indicates that the urea binary solution would destabilize the hydrogen bond while the TMAO binary solution would stabilize it; and both would destabilize it as pressure is increased. In addition, a urea-TMAO ternary solution with a constant 2.7:1 urea:TMAO ratio at 1 bar would neither stabilize or destabilize it relative to pure water at 1 bar, but would also destabilize it as pressure is increased. However, the skate ratio urea-TMAO ternary solutions would neither stabilize or destabilize it at any pressure relative to pure water at 1 bar. In addition, since the effects of urea and TMAO are mainly on different parts of the system, i.e., the protein and water, respectively, their effects are likely additive and interactions between urea and TMAO do not need to be invoked. While cancellation of the effects of urea and TMAO in K′ may be fortuitously good, this suggests that the urea:TMAO ratio found in arctic skates is a balance between not too much binding of urea and not too much increase in water structure due to TMAO. Future studies include simulations of proteins in urea and TMAO aqueous solutions to test the predictions of this model.

Figure 4.

(a) Ω and (b) Ψ for simulations at different cosolute concentrations as a function of pressure. The results are for urea binary (blue), TMAO binary (red), surface ratio ternary (green), and skate ratio ternary (black) solutions as well as for pure water (aqua).

Of course, results from simulations and thus values for Ω, Ψ, and K′ are dependent on the quality of the force fields. The dependence can be examined by comparisons to simulation results using the force fields from the previous study³⁰ (Figs. S3 to S6 in the Supporting Information). While the previously used force fields gave somewhat poorer agreement with experiment for density and diffusion coefficients (Fig. S1–S2), the conclusions from Ω, Ψ, and K′ are quite similar. Thus, Ω, Ψ, and K′ presented here appear relatively robust with respect to force fields.

IV. CONCLUSIONS

The molecular dynamics simulations of urea and TMAO aqueous solutions show that urea only slightly slows the diffusion of water while TMAO causes a much more significant slowdown of water. The simulations also indicate that the urea:TMAO ratio maintained by skates from different depths appear to be adjusted so that water diffusion is almost constant with depth whereas the diffusion of pure water increases with depth. This suggests a homeostasis of water diffusion, and since the increased diffusion in pure water appears to be due to shorter lifetime hydrogen bonds, a homeostasis of water-water hydrogen bond lifetimes. The dynamical model proposed here assesses how cosolutes could influence protein stability based on the hydrogen bonding in aqueous solutions of the cosolutes. The model predicts that the main effect of urea is destabilization by hydrogen bonding to protein and that the main effect of TMAO is stabilization by strengthening hydrogen bonds of water in the solution. It also suggests that the long lifetime TMAO-water hydrogen bonds observed in dielectric spectroscopy⁷⁶ and ab initio molecular dynamics simulations^{31, 33, 77–78} are critical to protein stabilization by TMAO. In addition, since the effects of urea and TMAO are mainly on different parts of the system, they appear additive and the model predicts that counteracting effects of urea and TMAO are by reducing the amount of urea used for osmolyte and by stabilizing water structure and thus destabilizing the unfolded state, which is consistent with other results.^{8, 18} Thus, a proposed hydrophobic association between TMAO and urea due to the mismatch between the strengths of TMAO-water and urea-water hydrogen bonds⁷⁸ does not need to be invoked for the counteraction. Moreover, the model predicts that TMAO acts as a piezolyte by strengthening water-water hydrogen bonds that get weaker under pressure, so the water diffusion remains the same at different pressures. Finally, this model provides an alternative interpretation of the accumulation of TMAO around folded conformations;^13–14 namely, the stronger water structure in TMAO solutions may squeeze TMAO out of bulk water so that it tends to associate with folded conformations.