How Different Are the Characteristics of Aqueous Solutions of tert

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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution

How Different are the Characteristics of Aqueous Solutions of Tert-Butyl Alcohol and TrimethylamineN-Oxide? A Molecular Dynamics Simulation Study Dibyendu Bandyopadhyay, Yash Laxman Kamble, and Niharendu Choudhury J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b02411 • Publication Date (Web): 13 Aug 2018 Downloaded from http://pubs.acs.org on August 14, 2018

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The Journal of Physical Chemistry

How Different are the Characteristics of Aqueous Solutions of tertButyl Alcohol and Trimethylamine-N-oxide? A Molecular Dynamics Simulation Study

Dibyendu Bandyopadhyay,1 Yash Kamble,2,$ Niharendu Choudhury2,#,* 1

2

Heavy Water Division,

Theoretical Chemistry Section,

Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India #

$

Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India

Present address: Department of Chemical Engineering, Institute of Chemical Technology, Mumbai 400019

*Corresponding author: Email: [email protected], [email protected], [email protected]

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Atomistic molecular dynamics simulations have been used to investigate differences in the characteristics of the aqueous solutions of two structurally similar, biologically important molecules, namely, tert-butyl alcohol (TBA) and trimethylamine-N-oxide (TMAO). By analyzing radial distribution functions, preferential solvation factors and number of nearest neighbors, structural characteristics of the two aqueous solutions are found to be dramatically different. Examining the distribution of nearest neighbor solute and solvent molecules in these two solutions, it is found that the aqueous solution of TMAO is homogeneous, whereas that of TBA is not. Further scrutiny of TBA-TBA radial distribution function at a high concentration by splitting the surrounding TBA molecules into two hemispheres demonstrates that the TBA aggregation occurs not only from the side of methyl moieties of TBA as expected in hydrophobicity induced aggregation, but also occurs from the side of the polar C-OH group. In order to analyze the effect of concentration of the two solute molecules (TBA and TMAO) on the local structure of water, tetrahedral order parameter, distributions of tetrahedral angles and hydrogen bonding angles have been calculated for both the solutions. It is surprising to see that at high concentrations, the local water structure in the TMAO solution is more disrupted as compared to the same in the TBA solution. Finally, the action of these two solutes on the folding-unfolding behavior of Trp-cage miniprotein has been analyzed and their contrasting activities towards the protein stability are correlated to the strikingly different behavior of their aqueous solutions.


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1. Introduction The two organic molecules tert-butyl-alcohol (TBA) and trimethylamine-N-oxide (TMAO) are structurally very similar and amphiphilic in nature, consisting of both hydrophobic and hydrophilic groups. These two molecules differ from each other only because the polar part of TBA is constituted of C-OH group, whereas the same for TMAO is formed by N=O group. However, their action towards protein structure and stability and their behavior in aqueous solutions are markedly different. It is well known through experiments and simulations that TBA forms aggregates in its aqueous solution at a very moderate concentration, whereas TMAO does not.1-49 It is also known50 that addition of TBA into water causes the density of the solution to decrease, whereas on addition of TMAO, density of the solution increases. Most likely, as a consequence51 of these disparate behaviors, TBA acts as a denaturant favoring unfolded structure of a protein whereas TMAO stabilizes native structure of a protein and effectively counteracts denaturation arising from chemical denaturant or elevated pressure/temperature.

The structure and dynamics of the TBA-water solutions have been probed by different experimental techniques such as light scattering,1-6 neutron diffraction,7 small angle neutron scattering (SANS),8-9 and x-ray scattering (SAXS)10-12 experiments. Although some of the earlier studies2,3 suggest clathrate-like hydration structure of TBA, recent SANS experiments7-12 have provided evidence in favor of aggregation of the TBA molecules and they posit it to be hydrophobicity induced.

Information about the formation of TBA aggregates and structure of

the TBA-water solution can also be deduced from the knowledge of dynamical characteristics of the hydration water of TBA. Dynamics of water surrounding a solute molecule has a direct link to the structure of water around the solute. Thus, analyzing the dynamics of hydration water and



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comparing it with the same of bulk water can lead indirectly to gain insight into the solvation structure and the aggregation behavior of the solute molecules. Recently, various state-of-the-art experimental techniques have been employed13-26 to understand dynamics of the hydration water and hence deduce solvation structure of the TBA-water systems. Although these studies have reported slowdown or retardation of the hydration water dynamics, extent of the retardation and the cause of it are still not ascertained. Femtosecond infrared spectroscopy13 of TBA-water system suggested almost four times slowing down of the dynamics of the hydration water molecules as compared to that of the bulk. Similar results based on TMAO and other hydrophobic solute-water systems have also been obtained from the femtosecond twodimensional infrared spectroscopy13 and dielectric spectroscopy.15 The rotational slowing down of the hydration water as reported in these studies is also seen in many classical MD simulations,17,20 but the extent of slowing down is rather small. The results are further supported by the measurements of rotational correlation times using NMR.21−24

The TMAO molecule, although structurally very similar to TBA, behaves completely differently in its aqueous solution. Very recent terahertz/far-infrared (THz/FIR) and Raman spectroscopy measurements25 suggested existence of TMAO-water aggregate at lower TMAO concentrations and subsequent decrease in the number of water molecules in the aggregate with increasing TMAO concentration. Probing the aqueous solution of TMAO using ultrafast optical Kerr effect spectroscopy in the far-infrared region, Mazur et al.26 concluded that the effect of TMAO on the water structure is not significant. Studies based on infrared and Raman spectroscopic measurements26-30 did not find any aggregation in the TMAO solution. On the contrary, concentration-dependent

Raman

spectroscopy

measurements


and

electronic

structure

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calculations of small TMAO-water aggregates however supported31 the idea of TMAO−water (not TMAO-TMAO) aggregate formation. They observed31 it is also found that at least three water molecules form strong hydrogen bonds with the hydrophilic N=O sites of the TMAO molecule and that the water molecules are not directly interacting with the methyl part of the TMAO. Hydration structure of TMAO has also been probed by using soft X-ray emission spectroscopy and chemometric analysis,32 which estimated on an average nine water molecules interacting with a TMAO molecule.

Given the dispute over exact molecular characteristics of the TBA-water and the TMAO-water solutions, it is expected that the atomistic computer simulation, which easily explore any system with atomistic resolution, will be able to resolve the problem decisively. In fact, several simulation studies16-20,33-48 have been performed to gain molecular level insight into structure, aggregation behavior and dynamics of these two aqueous solutions. Patey and coworkers45 have tried to figure out the origin of such differences in behavior in these two solutions. According to them it is the interaction of the polar part (O-H and N=O in case of TBA and TMAO respectively) of the two molecules with the surrounding water that makes the difference. Using united atom model of TBA, Bagchi and coworkers48 have studied the aqueous TBA solution in great details. Their study is directed towards two aspects: (1) aggregation of TBA molecules and the onset of percolation transition and (2) the effect of increasing concentration of TBA on the local structure of water. Based on the non-monotonic dependence of the first peak height of the TBA-TBA radial distribution function (gCC(r)) on TBA concentration and cluster size distribution, it has been concluded that the TBA solution undergoes percolation transition at a mole fraction of 0.06. The tetrahedral order parameter calculated by considering four nearest



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“water neighbors” of a central water molecule showed a monotonic decrease with the TBA concentration and it is concluded that the tetrahedral structure of water has been broken at higher TBA concentration. In a series of recent works on urea-water52

and guanidinium (Gdm)

chloride-water53 systems, it is shown that at a concentrated solution, some of the water neighbors of a central water molecule get replaced by the solute molecule (sites of urea or Gdm ion) and therefore for calculating tetrahedral order parameter, correct choice of water neighbors is necessary. It is shown52,53 for urea and GdmCl that if the neighboring water molecules are chosen correctly (taking into consideration that a solute site can also be a neighbor of the central water molecule), tetrahedral order parameter does not show considerable deviation from that of the bulk.52,53 In spite of a large number of investigations, a comprehensive knowledge on the behavior of these solutions has not been achieved. Many intriguing issues about the structure and aggregation behavior of these two aqueous solutions are either not addressed properly or not addressed at all. For example, (1) in an earlier study,48 the anomalous increase of peak height of TBA-TBA radial distribution function (RDF) as a function of TBA mole fraction has been termed as anomalous aggregation. Therefore it is interesting to check whether it is really anomalous. (2) When a solute is dissolved in a solvent, generally, it forms a homogeneous mixture. Since both TBA and TMAO molecules are structurally very similar and amphiphilic in nature, it is expected that both will form either homogeneous or heterogeneous solution. Here we want to check whether these two solutes behave in the same way in terms of the homogeneity/heterogeneity of their aqueous solutions. (3) Given the identical amphiphilic nature of both TBA and TMAO, it is expected that both will be hydrated in the similar fashion. By splitting the solvation shells of both the solutes with respect to their hydrophobic and hydrophilic moieties, we intend to investigate whether water molecules are distributed uniformly around the


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TBA or TMAO molecule. (4) Since both the molecules are isosteric and both form hydrogen bonds with water, their effect on water structure should be similar. Here, we also want to probe what is the effect of the two solutes on tetrahedral and hydrogen bonding structure of water.

It is well known that the behavior of these two solutes on protein stability is contrasting. It will therefore be interesting to link these differences in activity to their respective solution behavior. For this purpose, we have studied the activity of these two solutes on the folding-unfolding behavior of the Trp cage miniprotein.54 In this article, we therefore, not only present a detailed comparative account on the structural and aggregation aspects of these two solutions, but also intend to identify which of these solution properties are linked to their activities towards protein stability and denaturation.

In what follows, in Section 2, we describe the Models and Methods. Results and Discussion on the structural aspects of the TBA and TMAO solutions will be presented in Sec. 3.1.1. In Sec 3.1.2, we consider the effect of concentration of the solute (TBA or TMAO) on the structural changes of water. The effect of these two solute molecules on the structural aspects of the Trp cage miniprotein is presented in Sec. 3.2. Finally, a concluding remark has been offered in Sec. 4.

2. Models and Methods In this investigation, for TBA and TMAO, we have used a flexible model with intramolecular bond, angle, and dihedral terms in addition to the nonbonded Lennard-Jones and Coulomb interactions. The force-fields for the same have been obtained from the work of Fornili and



coworkers35. This model is a widely used model and reproduces the density of the solution as a function of mole-fraction of the solutes quite well (see Figure S1 of the Supporting Information). We have also calculated dipole-moments (DM) of the two solutes from the geometrical structure and partial charges of the constituent atoms of the molecule as given in the force-field and these are found to be 2.19 D and 5.53 D for TBA and TMAO respectively. These values are slightly higher than the reported values obtained from electronic structure calculations.55-56 However, the DM values larger than that reported here are also available57 and it is demonstrated that TBA model with a lower DM value does not reproduce experimental miscibility condition, whereas a modified model with a higher DM value does. For water, we have used SPC/E model. Aqueous solutions with different mole fractions of the solute (TBA or TMAO) have been prepared by considering appropriate numbers of solutes and water molecules in a cubic box of appropriate size. The details of the system compositions have been listed in Table 1. We have also performed MD simulations of Trp-cage miniprotein54 (PDB ID: 1L2Y ) in water. In presence of TBA or TMAO. In this case, we have considered 1 protein molecule in an aqueous solution containing 300 with TBA or TMAO molecules and 2570 water molecules corresponding to 4 (M) solution of TBA or TMAO. For the protein AMBER99 force-field is used. The simulations were performed in isothermal-isobaric (NPT) ensemble58 using molecular dynamics extended system approach of Parrinello and Rahman59 to fix the pressure and Berendsen algorithm60 to fix the temperature. In order to simulate bulk systems, periodic boundary conditions and minimum image conventions were employed in all three directions. The LINCS algorithm61 was used to constrain O-H and H-H (virtual) bonds of water. Particle-mesh Ewald (PME) method62-63 was used to treat the long range interactions. Equations of motions were integrated using velocity Verlet algorithm58 with a time step of 0.5 fs. All the simulations


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were performed at a target pressure of 1 atm and a target temperature of 300 K using GROMACS simulation package.64-66 For all simulations of TBA and TMAO solutions, trajectories for the first 20 ns were discarded for equilibration and the same for the next 20 ns have been stored for future analyses. Various quantities like tetrahedral order parameter q4, corresponding triplet angle, hydrogen bond angle distribution etc. have been calculated using standard criteria.52,53,67 For the Trp-cage miniprotein, total simulation time is around 100ns. Last 25ns of the trajectory has been used for calculating equilibrium structural quantity viz. radial distribution function (RDF).

3. Results and Discussions 3.1. Aqueous solution of TBA or TMAO 3.1.1. Local structure of TBA and TMAO and their aggregation behavior The issue of central importance in the present study is to demonstrate differential solution behavior and its relation to propensity of inter-solute association/aggregation in the aqueous solutions of structurally equivalent TBA and TMAO molecules. The radial distribution function (RDF) is a unique tool to get information about short and medium-range structural orders in a disordered liquid and hence can be used to investigate inter-solute (TBA/TMAO) aggregation. The RDFs of the central C atoms (gCC(r)) of the TBA molecules in the TBA solution and the central N atoms (gNN(r)) of the TMAO molecules in the TMAO solution at different concentrations can give us first hand idea about the local structure formed by other solute molecules around a solute molecule. These RDFs are shown in Figures 1(a) and (b) for TBA and TMAO solutions respectively. The concentration range chosen here is the regime where the solute aggregation, if any, is known (from experiments and other sources) to occur and



anomalous properties, if any, are manifested. The comparison of the RDFs of these two systems (TBA and TMAO) will give us idea about whether the structural features in these two systems are different and how these features are linked to their aggregation behavior. One very distinct difference in these two RDF sets (compare Figures 1(a) and (b)) is the presence of a small peak in gCC(r) at around 4.6 Å (Figure 1(a)) and it is absent in case of TMAO (see Figure 1(b)). This small peak comes from the inter-TBA hydrogen bond (H-bond) formation due to the presence of O-H group in TBA. In case of TMAO, no such possibility of inter-TMAO H-bond formation (as N=O group in TMAO cannot form inter-molecular H-bonds) is possible. The major difference between the two sets of RDFs is in the height of the first (major) peak at around 5.7-5.8 Å. The peak height of the TBA RDF (Figure 1 (a)) is more than that of TMAO RDF (Figure 1(b)). From these observations, it transpires that the density of the TBA molecules surrounding a central TBA molecule is more than the density of the TMAO neighbors surrounding a TMAO molecule. Moreover, in case of TMAO, peak height increases monotonically with concentration, but in case of TBA, it increases up to mole fraction x=0.08 and then decreases. In Figure S2 of the Supplementary Information (SI), we show how the (first) major peak (at 5.8 Å) of the TBA-TBA RDF [gCC(r)] and that (at 5.7 Å) for TMAO-TMAO RDF [gNN(r)] changes with the mole fraction (XTBA/TMAO) of the solute. In case of TBA (red plot in Figure S2(a)) first C-C RDF peak increases initially and beyond XTBA=0.08 it decreases with TBA concentration. The same nonmonotonic feature in case of TBA has also been observed by Banerjee et al.48 In case of TMAO solution, however, no such anomalous change in peak height is observed [Figure S2(b)]. In Figure S2(a), we also observe that the height of the small peak (at 4.6 Å) of the TBA-TBA RDF however increases monotonically with concentration.


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Although height of the first peak is an important measure of the short-range correlation arising from particle distribution surrounding a central particle, medium and large-lengthscale heterogeneity and aggregation in the system will be better understood by analyzing tail of the RDF. Here we find an interesting difference in the nature of the RDF tails in TBA and TMAO solutions (see insets of Figure 1(a) and (b)). In the TMAO solution, no large fluctuations were observed [inset of Figure 1(b)], whereas in TBA solution, as the concentration is increasing the oscillatory fluctuation (both period and intensity of the oscillations) in the tail of the RDF is increasing. Recently this oscillatory tail behavior has been highlighted to be associated with the structural heterogeneity and aggregation.68

The non-monotonic change [See Figure S2] of the (first) major peak height of the TBA-TBA radial distribution function has been termed48 anomalous and is often associated69 with the nonmonotonic change in the number of the nearest neighbor molecules (i.e. coordination number). However, a clearer picture emerges53 if one calculates the coordination number (i.e. number of nearest neighbors). By integrating the RDF [gαβ(r)] within a certain region, one can obtain the number of β neighbors within a spherical shell around a central species α, viz., r2

< N β >= 4πρ β ∫ r 2 gαβ (r ) dr ,

(1)

r1

where, ρβ is the bulk density of the species β and r1 and r2 are the suitable lower and upper limits of integration corresponding to radii of the inner and outer spheres respectively around the central α species. The quantity corresponding to r1 = 0 and r2 taken as the distance of the first minimum of the RDF is the number of neighbors of species β in the solvation shell of the species α. In Figure 2(a) and (b), we show the number of solute (TBA/TMAO) neighbors



corresponding to different regions for TBA and TMAO solutions respectively. Now it is interesting to observe that in cases of both TBA and TMAO, this number does not show any anomalous behavior (i.e. no maximum appears) with respect to concentration of the solute (i.e. TBA or TMAO). The only difference is that in case of TBA, the vs. XTBA, changes slope at around XTBA=0.08 signifying a saturated solvation shell. Now from this observation of neighbor numbers, the maximum observed in case of peak heights (Figure S2(a)) can be easily interpreted by taking into account that the gCC(r) is obtained by dividing the local density by the bulk density. After a certain mole fraction (X=0.08 in case of TBA), when the surrounding layer gets saturated, the number of molecules and hence local density ( ρ peak (r ) ) remain almost unchanged, but the bulk density ( ρ 0 ) increases and thus the fraction ( g peak (r ) = ρ peak ( r ) / ρ 0 ), which defines the RDF peak decreases with increase of mole fraction. However, in case of TMAO, we do not observe any such behavior. Till the mole fraction XTMAO =0.2 shown in the Figure 2(b), number of TMAO neighbors around a TMAO molecule increases almost linearly without showing any saturation behavior. Thus, the above results indicate that the onset of aggregation in the TBA-water solution starts at around XTBA=0.06-0.08 and that the TMAO solution remains homogeneous in the entire concentration range studied here.

A better representation of the preferential solvation can be obtained from the ratio of the local mole fraction (e.g. mole fraction in the solvation shell) to the bulk one, i.e. (XSolu)local/(XSolu)bulk. In the present case, the local region is defined as the spherical region around the solute (TBA or TMAO) with a radius corresponding to first minimum of the corresponding RDF (7.8 Å in the present cases). A value of this ratio more than 1 signifies preferential solvation and hence aggregation. In Figure 3, this quantity is plotted as a function of concentration of the solute (TBA


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or TMAO). It is interesting to observe that for TBA, this value is greater than 1 at all concentrations of TBA and it passes through a maximum, but for TMAO, it is always less than 1 and almost linear with the mole fraction. It clearly demonstrates that in case of the TMAO, there is no preferential solvation and aggregation at least up to XTMAO=0.2, but in case of TBA, preferential solvation and aggregation is pronounced at around XTBA=0.08. The non-monotonic nature of this plot for TBA solution can be explained in the same way as the non-monotonic change in the peak heights with concentration as discussed above.

The number distribution of the solute (TBA or TMAO) molecules around a central solute molecule (i.e. TBA or TMAO) can give insight into the aggregation behavior of the solutes. Therefore, here we analyze the number distribution of TBA or TMAO molecules around the same. The distributions of “solute” neighbors P(NNeighbor) for TBA and TMAO are shown in Figure 4 (a) and (b) respectively. It is important to note the differences in the nature of the curves for TBA and TMAO. The most interesting feature of the distributions is that: in case of TMAO, the distribution is mostly Gaussian, signifying a homogeneous nature of the aqueous solution of TMAO, but in case of TBA, the distribution is non-Gaussian in nature. For TMAO, the Gaussian distribution as a whole and the position of the peak maximum shifts towards right signifying that more and more TMAO neighbors are coming around a TMAO molecule as the mole fraction of TMAO is increased. On the other hand, for TBA, apart from that the peak position of the distribution shifts towards right, a long tail exists at lower values of neighbors. Even for the lowest mole fraction (XTBA=0.04) shown here, there are TBA molecules with a large number of TBA neighbors (see finite value of the distribution in the range NTBA=5-11). But in case of TMAO, the distribution for XTMAO=0.04 ends at around NTMAO=5. Thus, the TBA solution is



heterogeneous even at as low a concentration as XTBA=0.04 and it remains heterogeneous with larger aggregates at higher mole fractions of TBA. At the highest concentration, the peak position in case of TBA is around 10-11, whereas in case of TMAO it is around 6-7. All these facts demonstrate that there is aggregation in TBA solution, but not in TMAO solution. If we look at the distribution (see Figure 5) of number of water molecules around a solute (TBA or TMAO) molecule, a complimentary picture emerges and a clear idea about the nature of the two solutions can be further ascertained. In case of TMAO (Figure 5(b)), the water number distribution around a TMAO molecule follows a perfect Gaussian distribution and the distribution shifts towards lower number of water neighbors as the mole fraction of TMAO increases. In this case even at the highest concentration, there is no TMAO molecule with zero water neighbors. For TBA, however, the distribution is non-Gaussian and complimentary to the TBA number distribution shown in Figure 4(a). It is interesting to observe that at higher TBA mole fractions, there are a large fraction of TBA molecules having either no (see a large finite value of the distribution at or near Nwater=0) or a very few water neighbors and it is not the case for the TMAO solution. Thus the contrasting water distributions around TBA and TMAO molecules also corroborate the conclusion drawn from the number distributions of the solute molecules.

Having established that TBA in its aqueous solution at higher mole fraction forms aggregate, whereas TMAO in the same concentration range does not, it is now important to look further into the TBA solution. As we have seen in Figure 1 that a small peak in the gCC(r), which is not present in case of gNN(r) of TMAO, appears at r=4.6 Å and we posited that it is due to inter-TBA hydrogen bond formation. Now, we would like to verify it further. In order to accomplish it,


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while computing gCC(r), we divide the spherical region around TBA into two hemispheres, one containing the C-O group and the other containing all methyl groups of TBA. See the pictorial representation of these two hemispheres in Figure 6. The RDFs split in the manner stated above for the highest TBA mole fraction is shown in Figure 7. (The splitting of gCC(r) into two halves as done here is shown in the Supporting Information.) If we consider only the hemisphere containing C–O group of TBA, the entire small peak at r=4.6 Å and also a part of the main peak at r=5.8 Å are recovered (see green curve in Figure 7). On the other hand, if we consider the hemisphere containing methyl part of the TBA, we find (see blue curve in Figure 7) that the small peak at r=4.6 Å does not appear at all, but the large first peak (at r=5.8 Å) is partially recovered. Thus it is evident that the small gCC(r) peak (at r=4.6 Å ) results from the TBA accumulated from the C-OH side of the TBA molecule. The C-C distance of 4.6 Å indicates that it is due to inter-TBA H-bond formation. It is also important to mention that the major RDF peak at r=5.8 Å originates from the contributions from both the hemispheres (compare red dotted curve with the blue and green curves at r=5.8 Å in Figure 7). In order to quantify number of neighbors from both the hemispheres and within a radial distance of 5 Å that contains the first small peak and of 7.8 Å that contains both the small and the major peaks of gCC(r), we have integrated the gCC(r) within the specified limit and the numbers are shown in Table 2. A number of important points are to be noted. The region around 5 Å radius of a TBA molecule in which the small peak in gCC(r) appears (see 2nd and 3rd column of Table 2), all the TBA molecules are accumulated in the hemisphere containing C-O bond of TBA. The TBA accumulation from the other hemisphere (containing methyl groups) in this case is negligibly small. However, when the gCC(r) is integrated up to 7.8 Å (see columns 4 and 5) which defines the first neighbor shell, the TBA molecules are distributed on both the hemispheres. Almost 40% of the total TBA neighbors



are from the polar C-OH side. In many earlier studies, it is discussed that aggregation generally happens from hydrophobic methyl side. However, we have found here that around 35-40% of the TBA neighbors are in the polar side of the molecule. In case of TMAO (see columns 6 and 7) also the number of TMAO neighbors is almost the same in both the hemispheres.

In order to see how water molecules are arranged around a TBA or a TMAO molecule, we show in Figure 8 the RDFs between central C (or C2) and water oxygen (OW) in case of TBA solution (Figure 8(a)) and that between central N (or N2) and water oxygen (OW) for TMAO (Figure 8(b)). In both the cases, there are two distinct peaks within a radial distance of 6.7 Å (remember that the radius of TBA-TBA solvation shell is around 7.8 Å). The first small peak (around r=3.6 Å) originates due to accumulation of water in the polar (C-OH or N=O) side of the molecule and this is most probably due to possibility of formation of hydrogen bonds between the polar groups of the solute and water molecules. The second peak arises due to accumulation of water around the hydrophobic methyl moieties. Comparing the plots in Figure 8(a) and (b) at higher concentration (compare green curves in Figure 8(a) and (b)), it is evident that in case of TBA, a large region around a central TBA is depleted of water. Such depletion region is not observed in case of TMAO. This fact will be easily understood if we analyze the number of water molecules around TBA or TMAO corresponding to the regions of the two peaks (troughs of which are at r=4.1 Å and 6.5 Å) of the RDF shown in Figure 8. Now we divide these nearest neighbor water molecules into two hemispheres, one containing the C-O bond (in case of TBA) or N=O bond (in case of TMAO), and the other containing methyl groups (See Figure 6 for definition of the two hemispheres). If we consider spherical region within 4.1 Å of the solute, in both the cases of TBA and TMAO (see columns 2 and 3 of Tables 3 and 4 respectively), majority of water


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molecules gets accumulated in the hemisphere containing the polar group (i.e. upper hemisphere according to Figure 6). Within a spherical shell up to 6.5 Å around TBA, number of water molecules in the upper hemisphere (containing polar part) is more than that in the lower hemisphere (containing Me groups). But for TMAO, within the same radius, number of water molecules in both the hemispheres is almost the same. In fact at higher mole fractions, the number of water molecules in the lower hemisphere is slightly more than that in the upper hemisphere. Now, looking at the effect of solute (TBA or TMAO) concentration on the hydration water, we observe that in both the cases neighboring water molecules decreases and this decrease is around 54% in TBA and 36% in TMAO for the concentration range shown in the Tables 3 and 4. It is interesting to notice that in the region (containing the first peak) within the radius of 4.1 Å, with increasing solute concentration, number of water molecules sharply decreases around TBA, but it decreases only marginally in case of TMAO (compare Column 2 of Table 3 with that of Table 4). This shows that in case of TMAO the polar part is always (irrespective of concentration) surrounded by water, but for TBA dehydration of the polar part is significant with increasing concentration. Most probably, the TBA-water HBs are replaced by TBA-TBA HBs as the mole fraction of TBA increases. All these facts lead to the conclusion that there is significant TBA accumulation (apart from the non-polar part) from the side of the polar part of the TBA molecule as well. If we consider results at low concentration, where both TBA and TMAO are surrounded mostly by water, it is found (see Table 3, 4) that in case of TMAO, number of water molecules around the hydrophobic and hydrophilic moieties (within 6.5Å) is almost the same i.e. the distribution of water molecules around the TMAO molecule is uniform irrespective of polar and nonpolar moieties present in it. But in case of TBA, hydrophilic part is surrounded by more number of



water molecules as compared to the hydrophobic part. A plausible reason can be found in terms of their DM values. The major contribution to the overall DM of these molecules comes from the hydrophilic moiety (C-OH in case of TBA and N=O in case of TMAO) of the molecule. For example, the DM of the N=O group in TMAO is around 4.83D, which is around 87% of the overall DM (5.57D) and the DM of the C-OH group in TBA is around 2.12D, which is around 97% of the total DM. This fact along with the geometrical volume restriction may be the reason for the observed difference in the water numbers around the hydrophilic and hydrophobic moieties of the two solute molecules.

3.1.2. Effect of solutes on the tetrahedral and hydrogen bonding structures of water. Water is a network forming liquid due to inter molecular hydrogen bond formation. In order to maximize the number of hydrogen bonds, the local arrangement of water is such that the four water neighbors around a central water molecule form a tetrahedron. When solute molecules are present at high concentration, it is expected that the solute molecules also can occupy the solvation shell of a water molecule. If it happens and if the solute site is not in the tetrahedral position, it is likely that the local tetrahedral structure of water will be disrupted. In order to assess the tetrahedrality of water in the TBA and TMAO solution, we calculate tetrahedral order parameter q, and the distribution of tetrahedral angle extended by two neighboring water molecules to a central water molecule. We also gauge the average number of water-water Hbonds (HB), and the distribution of HB angles ( θHB) corresponding to first five nearest (water) neighbors of a central water molecule. In Figure 9(a) and (c), the average tetrahedral order parameter is shown as a function of concentration of TBA and TMAO respectively, and in Figure 9(b) and (d), distributions of the corresponding tetrahedral angles (θTd) are shown. The


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tetrahedral order parameter q is calculated in two different ways. The red lines in Figure 9 (a) and (c) is obtained by considering first four “water” neighbors (without considering whether any solute molecule is present among these “water” neighbors). In a solution, where solute concentration is quite high, there is likelihood that a solute molecule/site may replace a water neighbor from the solvation shell of a water molecule. Now, it is observed (see red lines in Figures 9(a) and (c)) that for both TBA and TMAO solutions, with increasing concentration, tetrahedral order parameter decreases substantially, signifying disruption in tetrahedral network structure. However, considering that a solute molecule may also be a neighbor of a water molecule, we also calculate by choosing only n (≤4) neighboring water molecules that are (distance wise) within the first four neighbors (considering both solute molecule/site and water as neighbors). The blue curves in Figure 9(a) and (c) show the values calculated in this way as a function of mole fraction of TBA and TMAO respectively. Now, it is seen that the decrease in as a function of solute mole fraction is marginal (compare the slopes of blue and red lines). Comparing blue curves in Figures 9 (a) and (c), we see that the decrease in with solute mole fraction in case of TMAO is more than the same in case of TBA. It will be even more evident if we consider the change in the distribution of tetrahedral angle as a function of solute concentration (see Figures 9(b) and (d)). In case of TBA solution (Figure 9(b)) there is almost no change in the distribution, whereas in case of TMAO, the change in the distribution with concentration is clearly visible. The non-tetrahedral peak at around 60° in case of TMAO increases with increasing TMAO mole fraction.

The disruption in the H-bond network of water can be further assessed by comparing average number of hydrogen bonds as a function of concentration in the TBA and TMAO



solutions. The average number of hydrogen bonds for TBA-water, TMAO-water and TBA-TBA are shown in Figure S3(a) of the Supporting Information. For dilute solution, the number of Hbonds per TMAO molecule is around 3, which is consistent with the recent experimental results.30,32 The decrease in the number of TBA-water HBs is more than that of TMAO-water HBs (compare red and blue lines in Figure S3(a)). It is expected because in concentrated TBA solution, due to formation of aggregates, number of contacts of TBA molecules with water has been reduced. The green line (scale in the right axis) in the same figure shows the number of TBA-TBA HBs. Although the number of TBA-TBA HB is very small, it is increasing with concentration. In Figure S3(b) of the SI, the for water-water HBs as a function of solute mole fraction in TBA (red line) and TMAO (blue line) solutions are shown. It is evident that decrease in water-water in the TMAO solution is more than that in the TBA solution. It is not surprising, because in TBA solution, due to large aggregate formation, water molecules are pushed together to get a bulk like environment; whereas in TMAO solution, which behave like a homogeneous solution, individual TMAO molecules are surrounded by water molecules and thus disruption in the HB network of water is more.

In order to further investigate the effect of the solute (TBA or TMAO) on the water-water hydrogen bonding, we choose each of the first five water neighbors (here neighbors are properly chosen by considering the fact that solute site can also be a neighbor of a water molecule) of a central water molecule and calculate the distribution P(θHB) of the hydrogen bonding angle between the chosen neighbor and the central water molecule. The distributions of θHB for the first five neighbors in case of TBA solution are shown in Figure 10(a)-(e). It is important to notice that the distributions for 1st to 4th neighbors are of the same nature featuring two peaks at around


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0° and 106° corresponding to H-bonding angles. However, the nature of distribution changes in case of the 5th neighbor, for which the major peak of the distribution is at 60°. It signifies that each of the first four neighbors that form the first hydration shell is hydrogen bonded to the central water molecule and the 5th neighbor does not form H-bond with the central water molecule. It is also important to note that for all the neighbors, the distribution remains almost unchanged as a function of TBA concentration. Thus if neighbors are correctly chosen it is easily shown that the H-bonding arrangement is not disrupted even at higher concentrations. However, in case of TMAO solution, from the same distributions (see Figure 11(a)-(e)) we observe a significant distortion at higher TMAO concentrations for 4th neighbor onwards. A new peak (see Figure 11(d)) at around 60°, the same as that observed for the 5th neighbor, emerges. It signifies a distortion in the HB network caused due to a population of 4th neighbors that are not H-bonded to the central molecule. This is consistent with the results shown in Figure S3(b) of the SI. The issues of choosing correct water neighbors and the distortion in the HB network of water at higher concentrations in the aqueous solutions of urea and guanidinium chloride have been thoroughly investigated in our earlier works.52,53

3.2. Trp-cage protein in the aqueous solution of TBA or TMAO In order to check conformational state of the protein in presence of TBA or TMAO, in Fig. 12 we have shown the root mean square displacement (RMSD) of the backbone atoms at time t relative to the same of the starting structure of the Trp-cage miniprotein in presence of TBA or TMAO. As the plots clearly suggest, the RMSD of the protein in presence of TBA increases within 10ns and thereafter it remains steady within the equilibrium fluctuations. Beyond 10ns, the RMSD of the protein in TBA solution is more than that in the TMAO solution and it remains



so for entire 100 ns. In case of TMAO, in fact, the protein backbone has become more compact. It suggests that the protein structure is more open in TBA than in TMAO solution. In order to check equilibrium distribution of TBA or TMAO molecules around the backbone of the Trpcage protein, the radial distribution function of the central C atom in TBA or central N atom of TMAO is calculated around the backbone sites. The RDFs of the central C atom of TBA and central N atom of TMAO around the protein backbone are shown in Fig. 13. The TBA RDF shows a peak at around 5 Å whereas the TMAO RDF is slowly varying without any pronounced peak and away from the protein. The less than 1 height of the RDF peak is not surprising, because in a crowded protein environment, approach of TBA/TMAO from all possible angles in a spherical shell around the backbone atoms is restricted. That’s why in most of the cases, where RDF of a species is calculated around a part of the protein, g(r) with peak value less than 1 may be obtained, even though the density of that species in a small accessible volume near the protein is more than the bulk density. It is not an unusual feature for the RDF of water or any solute around the protein and has been reported in the literature.70,71 From Fig. 13 it is clearly evident that (i) the approach of TBA is closer to the protein than that of TMAO and TBA has a clear peak (although height is less than 1) indicating local ordering, (ii) local density of TBA is more than that of TMAO throughout the distance up to 15-20 Å from the backbone. Thus, more number of TBA molecules than TMAO molecules have been accumulated closer to the backbone. The slowly varying monotonic density profile for TMAO shows that these molecules prefer to stay away from the protein backbone. In order to analyze further how TBA or TMAO approach the protein backbone, whether through hydrophobic or the hydrophilic part of it, we have calculated the RDF of the oxygen and hydrogen atoms of TBA -OH group and the oxygen atom of TMAO around the backbone (see Fig. 14 (a)). It is evident from this plot that OH of the


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TBA comes closer to the backbone and both H and O sites of the –OH group of TBA approach closer to the backbone atoms. And it is likely that the OH group is forming H-bonds with the backbone. The oxygen site of the TMAO, however, is away from the backbone. Note that that there is no peak and the density of TMAO starts growing from a larger distance as compared to TBA (compare blue curve in Figure 14(a) with the red or green one). In order to check whether TBA or TMAO can approach the backbone through their respective hydrophobic moiety, the RDFs of the methyl groups of TBA and TMAO around the backbone of the protein has also been calculated and shown in Figure 14(b). It is interesting to observe that the methyl groups of TBA are closer to the backbone as compared to the same from TMAO. Thus TBA approaches the backbone through both its hydrophobic and hydrophilic ends. However, preferential interaction of TBA or TMAO with the backbone of the protein can be better understood, if the molefraction of the solute around the backbone relative to bulk is estimated.72

Therefore, we have calculated the number as well as mole fraction of TBA or TMAO in a region (of radial distance of 9 Å from the backbone sites) around the backbone. We have calculated the mole fraction of the solutes (TBA or TMAO) in the region near the backbone relative to that in the bulk (defined by the ratio (XTBA )Shell / (XTBA)Bulk) and tabulated in Table 5. Now it is clear (from Table 5) that for the TBA-protein solution, mole fraction of TBA near the backbone sites is more than the same in the bulk (see Table 5 that the relative ratio (XTBA )Shell / (XTBA)Bulk is greater than 1). On the contrary, for TMAO-protein solution, the TMAO mole fraction around the backbone sites is close to that of the bulk (the relative ratio (XTMAO )Shell / (XTMAO)Bulk being close to 1). Thus, the TMAO molecules are homogeneously distributed not only in its aqueous solution, but also in presence of the Trp-cage miniprotein.



The difference in behavior of the TBA and TMAO towards Trp-cage miniprotein can be analyzed in the light of the solution properties of the two solutions (as discussed in Sec. 3.1). One of the most important results of the previous section is that the TMAO in its aqueous solution is distributed homogeneously and that the TMAO-water interaction is too strong to allow formation of TMAO-aggregates. Due to these two important properties of the TMAO solution, the TMAO molecules do not get accumulated near the protein, instead they prefer to be distributed homogeneously throughout the solution. Earlier studies73-75 have shown that the interaction between protein backbone and TMAO molecules is un-favorable making the folded states of the protein more stable relative to denatured states in TMAO solutions.

4. Conclusions In the present investigation, using atomistic MD simulations, we have thoroughly analyzed structural aspects of TBA and TMAO solutions. From the analyses of radial distribution functions and the number of nearest neighbors it is observed that aggregation occurs in TBA solution at around mole fraction of 0.06-0.08. From the analysis of the relative proportion of the solute in the solvation shell to the bulk it is clear that for TBA has a higher density around itself as compared to the bulk. But for TMAO the ratio is always less than 1, suggesting a homogeneous environment. By careful analysis, it is shown that the non-monotonic change of the relative proportion (Figure 3) and of the RDF peak heights (Figure S2(a)) for TBA-water system is not anomalous, but a consequence of the saturation of the nearest neighbor shell of the TBA molecules. From the number distribution of the solute, it transpires that TMAO number distribution at all mole fractions is almost Gaussian, suggesting a homogeneous distribution, whereas TBA number distribution is non-Gaussian in nature and therefore not homogeneous.


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From the number distribution of water around the solute (TBA or TMAO) it is even clearer that in TBA solution there is a large fraction of TBA molecules with almost zero or a few water neighbors. It implies the presence of TBA aggregates in the solution. At higher concentrations, the size of the aggregates as estimated from the peak position of the distribution varies in the size range N=10-12. It is very interesting to observe that the solution of TMAO being homogeneous, the nature of the distribution of number of water molecules surrounding a TMAO molecule is perfectly Gaussian. From the analysis of decomposition of the gCC(C) by dividing the spherical region around TBA into two hemispheres (see Figure 6), it is observed (Figure 7) that the small 1st peak arises solely due to TBA neighbors from the upper hemisphere (containing polar part). It is due to TBA-TBA H-bond formation. Contrary to the general belief that aggregation in TBA solution is due to accumulation of TBA from the methyl side (hydrophobic interaction), we have shown that the TBA molecules approach the central TBA molecule from both the polar C-O side and the nonpolar methyl side. The above observation is consistent with the conclusion that contacts between alcohols in water are random rather than hydrophobic, as made in a recent study.76 Our analyses of various order parameters related to local structure of water indicates that the distortion in tetrahedral (Figure 9) and H-bonding networks (Figure 10, 11 and S3) is more in TMAO solution than in TBA solution. In TBA solution because of the aggregate formation there are regions of water with bulk like environments and thus these water molecules behave like bulk water. On the other hand, in TMAO solution, one or more TMAO molecule/s is/are present in the solvation shell of water and therefore the presence of TMAO in the water solvation shell breaks the tetrahedral and H-bonding structure of water. The fact that TMAO disrupts water structure more than TBA holds even at lower mole fractions. It is known that TMAO forms almost three hydrogen bonds through its oxygen site only, whereas TBA forms around two



hydrogen bonds through its oxygen as well as hydrogen sites. Since TBA has a –OH group similar to water, the nearest water neighbors can occupy tetrahedral position without much disruption of the tetrahedral structure of water. On the other hand, as TMAO forms almost three hydrogen bonds with water through its oxygen site only, it induces more strain and hence more disruption in the tetrahedral arrangement of water. Our observation that TMAO molecules disrupt the H-bonding and tetrahedral network of water considerably is in agreement with the same obtained from the recent femtosecond mid-infrared pump-probe spectroscopy.77 From the simulation of Trp-cage miniprotein in presence of TBA or TMAO aqueous solution, it is demonstrated that the TBA molecules get preferentially accumulated near the backbone of the protein, whereas TMAO molecules tend to be away from the backbone. The close to 1 value of the mole fraction of the TMAO near the backbone relative to bulk (see Table 5) signifies that the homogeneous nature of the TMAO solution is an important aspect that keeps the TMAO molecules away from the protein backbone. The increase in volume (see Figure 1 of SI) on addition of TBA arising due to not so strong TBA-water interaction helps in stabilizing the denatured state, in which increase in solvent excluded volume occurs.51

In summary, although TBA and TMAO molecules are structurally very similar, the local structure and the distributions of the constituent species in their aqueous solutions are amazingly different. It seems that the reason for this disparate behavior of these two structurally similar systems lies in the different charge distribution (electronic density distribution) pattern (see Table 2 of Ref. 35) of these two molecules. Investigation to identify the origin of such differences in properties of these two solutions is in progress. Recent solvation dynamics study78 using femtosecond transient absorption measurements showed considerable differences in the


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dynamical response of these two systems. Although non-monotonic retardation in the solvation dynamics with concentration in both TMAO-water and TBA-water systems is observed, the solvation response time of the former is shown to be faster than that of the later. Our preliminary study on the dynamical behaviors of these two solutions also indicates significant differences in the aqueous solutions of these two structurally similar solutes. Further investigation in this direction is underway. Recent phase-sensitive heterodyne-detected vibrational sum frequency generation spectroscopy measurements have shown79 different orientational preference of TBA and TMAO at the water-vapor interface. Studies in this direction are also in progress.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Method of splitting RDF into two hemispheres, Results on variation of peak height of the RDF and of average number of hydrogen bonds with the concentration of the solute.

Acknowledgements We would like to thank Computer Division, BARC for providing ANUPAM supercomputing facility and support. It is a pleasure to thank Dr. P. D. Naik, Dr. S. Mohan, Dr. T. K. Ghanty and Dr. K. Bhanja of Bhabha Atomic Research Centre, Mumbai, India for their support and encouragement.

The authors declare no conflict of interest.



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FIGURE CAPTIONS Figure 1. (a) Radial distribution functions (RDFs) of the central carbon (C) atoms of the TBA around the same are shown at various concentrations of the TBA-water binary mixture. (b) The radial distribution functions of the central nitrogen (N) atoms of the TMAO around the same are shown at various concentrations of the TMAO-water binary mixture. In the legends various mole fractions of TBA and TMAO are shown. In the insets of both the figures, the tails of the respective RDFs are magnified.

Figure 2. (a) Average number () of TBA neighbors around a central TBA molecule within a specified radial distance from the central molecule as a function of mole fraction of TBA. (b) The same () for TMAO. The legends in the plot mention the radial distance around the central TBA or TMAO molecule up to which integration [cf. Eq. (1)] of the respective RDF is performed.

Figure 3. Ratio of the mole fraction (X1st shell) of the solute (TBA or TMAO) in the solvation shell of the solute molecule to the mole fraction (XBulk) of the same in the bulk.

Figure 4. (a) Number distribution (P(NTBA)TBA) of neighboring TBA molecules within a specified radial distance around a central TBA molecule. (b) The number distribution (P(NTMAO)TMAO) of the neighboring TMAO molecules within a specified radial distance around a central TMAO molecule.



Figure 5. (a) Number distribution (P(NWater)TBA) of neighboring water molecules within a specified radial distance around a central TBA molecule at various TBA mole fractions and (b) the number distribution (P(NWater)TMAO) of the neighboring water molecules within a specified radial distance around a central TMAO molecule at various TMAO mole fractions. The legends in the plot mention the concentration and the radial cutoff distance.

Figure 6. Pictorial representation of the TBA and TMAO molecules in which the spherical region around the molecule has been divided into two hemespheres, one containing the polar (COH for TBA and N=O for TMAO) part and the other containing the nonpolar (all methyl groups) part of the molecule.

Figure 7. The C-C (TBA-TBA) radial distribution functions calculated by considering the spherical region around a TBA molecule divided into two hemespheres as shown in Figure 6. The mole fraction of TBA considered is 0.2, the highest concentration considered in the present study.

Figure 8. The (a) TBA-water and (b) TMAO-water radial distribution functions. The RDF is calculated between the central C2 atom and oxygen (OW) of water in case of TBA and the central N2 atom and the oxygen (OW) of water in case of TMAO.


Page 42 of 63

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Figure 9. (a) Average tetrahedral order parameter ⟨q⟩ as a function of mole fraction of TBA. The results represented by the red lines with squares (in Figure 9(a) and (c)) are obtained by choosing the first four “water” neighbors of a central water molecule. The results represented by the blue lines with filled circles (in Figure 9(a) and (c)) are obtained by first choosing four nearest neighbors irrespective of whether it is solute (TBA or TMAO) or water and then calculating with n (n ≤ 4) water molecules that are within the first four (distance-wise) chosen neighbors. Details of the method and normalization are described in Ref. 49. (b) Distributions P(θTd) of the tetrahedral angles ((θTd) for various mole fractions of TBA. (c) Same as in (a) but for the TMAO solution. (d) Same as in (b), but for the TMAO solution.

Figure 10. Hydrogen bond angle distributions P(θHB) at various TBA mole fractions. The angle formed between a reference water molecule and one of its water neighbors. The hydrogen bonding angle θHB is the angle formed by the line joining the two oxygen atoms and the OH bond vector of the donor water. Distributions for five nearest water neighbors are shown in panels (a)−(e).

Figure 11. Same as in Figure 10, but for TMAO solution.

Figure 12. Root mean square deviation (RMSD) of the backbone of the Trp-cage miniprotein with respect to initial PDB structure as a function of time in aqueous solutions of TBA (red lines) and TMAO (blue lines).



Figure 13. Radial distribution functions (RDF) of the central C atoms of TBA (red line) and the central N atoms of TMAO (blue line) around the backbone sites of the Trp-cage miniprotein.

Figure 14. (a) Radial distribution functions of the hydrophilic O atoms (red line) and H atoms (green line) of the OH group of TBA, and the hydrophilic O atoms (blue line) of the N=O group of TMAO around the backbone sites of the Trp-cage miniprotein. (b) Radial distribution functions of the hydrophobic C atoms of the methyl groups of TBA (red line) and the same of TMAO (blue line) around the backbone sites of the Trp-cage miniprotein.


Page 44 of 63

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Table 1. Number of solute (TBA or TMAO) and water molecules considered for different systems. Mole

Number of

Number of

Total number of

fraction

TBA/TMAO

water molecules

molecules

molecules 0.01

20

2016

2036

0.02

41

2016

2057

0.04

84

2016

2100

0.08

175

2016

2191

0.125

288

2016

2304

0.16

384

2016

2400

0.20

504

2016

2520



Page 46 of 63

Table 2. Average number of TBA/TMAO molecules within a specified region around a TBA/TMAO molecule. Mole Fraction

No. of TBA within 5.0 Å Hemisphere

No. of TBA within 7.8 Å

No. of TMAO within 7.5 Å

Hemisphere Hemisphere Hemisphere Hemisphere

Hemisphere

containing C-

containing

containing

containing

containing

containing

O bond

Me groups

C-O bond

Me groups

N-O bond

Me groups

0.04

0.15

0.019

1.46

2.40

0.88

0.77

0.08

0.26

0.013

2.46

3.92

1.72

1.54

0.12

0.30

0.014

3.04

4.58

2.56

2.32

0.16

0.55

0.017

3.54

5.07

3.12

2.82

0.20

0.58

0.016

3.73

5.20

3.71

3.41


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Table 3. Average number of water molecules within a specified region around a TBA molecule. Mole fraction

No. of water within 4.1 Å


Hemisphere

Hemisphere

Hemisphere

Hemisphere

containing C-OH

containing Me

containing C-OH

containing Me

bond

groups

bond

groups

0.04

2.33

0.153

13.85

10.54

0.08

2.01

0.082

11.15

6.46

0.12

1.82

0.056

9.54

4.74

0.16

1.65

0.047

8.27

3.77

0.20

1.45

0.038

7.76

3.27

Table 4. Average number of water molecules within a specified region around a TMAO molecule. Mole fraction



Hemisphere

Hemisphere

Hemisphere

Hemisphere

containing N=O

containing Me

containing N=O

containing Me

bond

groups

bond

groups

0.04

2.84

0.38

15.92

15.28

0.08

2.74

0.39

14.21

13.84

0.12

2.61

0.38

12.47

12.35

0.16

2.49

0.37

11.15

11.30

0.20

2.35

0.36

9.75

10.05



Page 48 of 63

Table 5. Average number and normalized mole fraction of the osmolyte (TBA or TMAO) molecules within a specified region (9 Å) around the backbone sites of the Trp-cage protein. Protein-TBA-Water solution [(XTBA)Bulk = 0.105] No. of water

33.69

Different sites of TBA No. of sites of TBA Shell

(XTBA )

Bulk

/ (XTBA)

C

Me

O

5.04

15.49

5.10

1.30

1.20

1.30

Protein-TMAO-Water solution [(XTMAO)Bulk = 0.105] No. of water Different sites of TMAO

41.03 N

Me

O

No. of sites of TMAO

4.43

13.27

4.42

(XTMAO )Shell / (XTMAO)Bulk

1.0

0.96

1.0


Page 49 of 63

4

XTBA=

1.05

(a)

0.01 0.02 0.04 0.08 0.12 0.16 0.20

g (r) CC

1.00

3

0.95 0.90

2

Fig. 1

18

20

22

24

1 0

(b)

2.0

XTMAO=

1.05

0.01 0.02 0.04 0.08 0.12 0.16 0.20

1.00 0.95

g (r) NN

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.5

0.90

1.0

18

20

22

24

0.5 0.0

0

5

10 o 15 r (A)


20


(a) TBA-TBA

TMAO

>

TBA

9

How Different Are the Characteristics of Aqueous Solutions of tert

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