Can trimethylamine-N-oxide act to influence the self-aggregation of tert-butyl alcohol?

ABSTRACT We report classical molecular dynamics simulation studies of aqueous solution consisting of water, tert-butyl alcohol (TBA) and trimethylamine-N-oxide (TMAO). In spite of the fact that both TBA and TMAO molecules have very similar geometry with hydrophobic and hydrophilic groups, they behave very differently in aqueous solutions. Our aim is to see the role of TMAO on the self-aggregation (or association) of TBA molecules. We observe that, TMAO acts to postpone the aggregation of TBA molecules (takes place via the hydrophobic ends) to some extent. Addition of 0.10 mole fraction of TMAO shifts the aggregation concentration of TBA from xtba = 0.025 to xtba = 0.06. From the excess coordination number, calculation it is noticed that up to xtba = 0.06, TBA molecules are favourably solvated by TMAO by replacing water molecules from TBA solvation shell but above this concentration, TBA–TMAO interaction decreases. This is further confirmed by water–TMAO interactions which shows a shift above xtba = 0.06 indicating more preferred interactions between them. We also observe a noticeable increase in the water–water hydrogen bond life time in presence of TBA molecules indicating more structuring of water molecules.

The differences in their behaviour in aqueous solution are due to the fact that TBA has a weaker hydration shell, which, above that threshold concentration, does not compensate for the thermodynamic force that leads to the TBA-TBA aggregation. It has also been observed that the qualitative nature of water-protein and alcoholprotein interactions are greatly changed above this concentration [28]. The favourable interactions between the hydrophobic methyl groups of TBA molecules leading to formation of TBA clusters that interact more strongly with the non-polar part of the protein molecules compared to a single alcohol molecule. As a result of this, the solvation of the protein is greatly enhanced. So, it is believed that the clustering effects of TBA molecules at and above this threshold concentration (i. e. x tba ∼ 0.025) is an important factor for enhancing the effects of alcohols on proteins and nucleic acid molecules. Moreover, NMR study as well as recent molecular dynamics simulation study of the effect of urea on the hydrophobic self-association of TBA shows that concentrated urea solution destabilises hydrophobic interactions between TBA molecules [29,30]. It has, further, been argued that the mechanism of this destabilisation closely resembles to that of urea induced protein denaturation provided a native protein structure is essentially determined by the hydrophobic interaction of the side chains. On the other hand, the hydrogen bond interactions between water and TMAO in aqueous TMAO solution is robust and TMAO prefers to solvate water (and co-solute) molecules [31]. This leads to the reduction in the number of hydrogen bond partners available to the protein backbone. Furthermore, the rigid water network make hydrogen bonds between water and protein back bone entropically less favourable, which in turn promotes the formation of intramolecular hydrogen bonds in protein and thus stabilises its native state [32]. TMAO-induced protein (folded state) stabilisation was also explained by enhancement of water-water hydrogen bond life time in presence of it. It has been reported that, 1 M aqueous TMAO solution increases the water-water hydrogen bond life time by a factor of approximately 3.8 compared to that of pure water [22]. TMAO-induced reduction of hydrophobic attraction between the neopentane molecules has also been observed [33][34][35].
As we see that the stability of a protein depends on two factors, namely, alterations of hydrophobic interactions (between the nonpolar moieties) and change in water structure in presence of cosolutes TBA and TMAO. The above findings encourage us to investigate three facts: (1) How the hydrophobic interactions (which causes the self-aggregation) between the methyl groups of TBA molecules are changed in presence of TMAO? (2) Change in the water-water hydrogen bond properties and dynamics in water-TBA-TMAO ternary solution; and (3) The influence of TMAO molecules, if any, on the dynamical properties of TBA molecules. This study aims to shed some lights on to these.
The outline of the present article is as follows. A brief description of models and simulation details are mentioned in Section 2. We present results followed by . . +. discussions in Section 3, and we summarise our conclusions in Section 4.

Models and simulation method
Classical molecular dynamics (MD) simulations of water-TBA-TMAO ternary mixtures with different TBA concentrations were carried out at 298 K temperature and 1 atm pressure. For TBA, we employ the rigid version of all site model proposed by Kusalik et al. [14], and for TMAO we employ all site model introduced first by Kast et al. [24]. The SPC/E potential [36] was employed for water. All three models are considered as rigid, and the interaction between atomic sites of different molecules is expressed as where r αβ is the distance between atomic sites α and β, and q α is the charge on site α. The Lennard-Jones (LJ) parameters, σ αβ and ϵ αβ , are obtained using the combining rules σ αβ = (σ α + σ β )/2 and αβ = √ α β . The values of the potential parameters q α , σ α and ϵ α for TMAO, TBA and water are summarised in Table 1.
For all the MD simulations, we consider in total 500 molecules (water and solute) in a cubic box of length L. The five systems studied here are briefly summarised in Table 2. It is to be noted here in these systems we used the same of TMAO molecules fixed, and the water  are simply replaced by the same number of TBA molecules. The short range LJ interactions were calculated by using a spherical cut-off at distance L/2. In the simulations, the long-range electrostatic interactions were treated using the three-dimensional (3D) Ewald method [37]. For this, a convergence parameter of α = 6.4/L was used. The quaternion formulation [37,38] of the equations of rotational motion was employed. For the integration over time, the leap-frog algorithm with a time step of 10 −15 s was considered. In the beginning of the simulations, the molecules were placed on a face-centered-cubic lattice with random orientations. The physical pressure was maintained by adjusting the box length L. For each of the systems, NVT MD runs of 10 ns were used for equilibration. During this, the velocities were rescaled to maintain the desired temperature. Following this, each system was subjected to production run for a further 20 ns in NPT ensemble [37], and the results are analysed and reported here. It should be noted that our simulation runs were relatively long. This is because of the fact that though the quantities such as internal energies etc. equilibrate within a few picoseconds, a much longer simulation run is required for the stabilisation of structural and dynamical properties. This phenomenon has already been documented previously for aqueous urea solutions [39,40].

Structural properties
Selected site-site radial distribution functions (rdfs) that demonstrate the influence of TBA concentration on the structural properties of different solutions are shown in Figure 1. Note that, the atoms associated with TBA, TMAO and water are denoted by tb, tm and w, respectively and H tb in those figures represents hydroxyl hydrogen of TBA.
Oxygen-oxygen and oxygen-hydrogen distribution functions involving TBA-water and TMAO-water are shown in Figure 1.
The first peak height in the O tm − H w rdf is considerably higher than that of O tb − H w rdf implying a more favourable hydrogen bond interactions between water and TMAO when compared to that for water and TBA (see below). We note as well that the first peak in the H tb − O w distribution function appears at a larger distance than that of O tb − H w and this is associated with a much smaller peak height of the former. These facts depict that in hydrogen bonding interactions with water molecules, TBA prefers to act as a donor rather than an acceptor. Furthermore, with increasing TBA concentration, both first and second peaks of O tm − O w and O tm − H w distributions become more sharper which indicates that water molecules are more structured around TMAO molecules in concentrated TBA solutions. We also observe a negligible dependence of first peak heights of O tb − O w , H tb − O w and O tb − H w rdfs on TBA concentrations indicating negligible change in water-TBA hydrogen bond properties with change in TBA concentration.
Addition of TBA causes an enhancement in the water structure as is evident from the water-water rdf (see Figure S1 of Supporting Information section) where both second and third peaks become visible at the highest TBA concentration. This is due to the fact that, as the TBA concentration increases, more water molecules are shared by the hydrophilic sites of TBA molecules and this, possibly, brings strain to water-water hydrogen bond network. Structuring is also apparently favoured in the water domain for concentrated TBA solutions as indicated by the enhancement of the first peak of water oxygen-oxygen distribution function. This observation is further supported by the enhancement of measured water-water hydrogen bond energies and its life time values for different solutions (see hydrogen bond analysis addressed below).
where, CC tb and C tb refer to central and methyl carbon atom of TBA, respectively, and are shown in Figure S2 of Supporting Information section. Since it has been found that in aqueous solution above, a threshold TBA concentration (x tba = 0.025) selfaggregation of TBA molecules takes place and in this selfaggregation process the methyl group of TBA participates [11,12,[15][16][17], so there must be some water loss around the hydrophobic methyl groups of TBA in order to facilitate this process. In this context, it is worth noting that the results of previous studies [16,17] also suggest that the dehydration of hydrophobic methyl groups of TBA serves as a sensitive indicator for monitoring TBA selfassociation. This fact is quite apparent in CC tb − O w and C tb − O w distribution plots ( Figure S2 (a) and (b) of Supporting Information section). As TBA concentration is increased, the heights of both peak first and second peak of C tb − O w (second peak in case of CC tb − O w rdf) decrease. A more quantitative estimation of loss of number of water molecules from the first solvation shell of CC tb and C tb of TBA can be estimated by calculating the number of water molecules present in the solvation shell of these atomic sites of TBA. These coordination numbers (CN αβ ) are calculated by using the following equation [35]: Oxygen-oxygen and oxygen-hydrogen radial distribution functions of TBA-water and TMAO-water for different systems considered. The subscripts w, tb and tm refer to water, TBA and TMAO molecules, respectively.
where CN αβ is the the number of atom of type β surrounding atom type α in a shell extending from r 1 to r 2 and ρ β represents the number density of atom type β in the system. For the calculation of first solvation shell coordination number, the typical values of r 1 and r 2 can be considered as zero and the location of the first minimum in the corresponding rdf, respectively. In Figure 2, we show the average number of water molecules in the first solvation shell of a TBA molecule as well as in the first solvation shell of hydrophobic methyl group of TBA for different TBA concentrations in presence of TMAO. In this figure, we further compare these coordination number values with that of the systems containing no TMAO molecules (for this, we have carried out separate simulation run for binary water-TBA solutions). Note that, for calculating the average number of water molecules present in the first solvation shell of a TBA molecule, we calculated these coordination number values for all atomic sites of TBA (using distribution functions involving all the atomic sites of TBA and water oxygen followed by application of Equation (2)) and then summing them up.
Considering the results for binary water-TBA solutions (without TMAO molecules), first we notice a sharp reduction in the number of first shell water molecules for both TBA and its hydrophobic methyl group up to x tba = 0.06. Above this threshold concentration, these coordination number values flatten out and show only a little further change up to x tba = 0.1. Here, it is important to mention that this finding is in accordance with the previously reported results [16,17]. It is also worth mentioning that quite a number of physical properties of water-TBA binary solution undergo rapid change below x tba = 0.06 [11,12,41]. Moreover, what is remarkable is that for a given TBA concentration the number of water molecules lost from the first solvation shell of a TBA molecule is essentially equal to the lost in the number of water molecules from the solvation shell of its methyl group suggesting that in the self-aggregation of TBA molecules, it is the hydrophobic methyl group which dehydrates predominantly (and contributes predominantly in TBA self-association). Now, if we concentrate on the effect of TMAO on these coordination numbers, we can observe that the TBA coordination numbers as well as their concentration dependencies affected significantly in presence of 50 TMAO molecules. At a given TBA concentration, by comparing the coordination number values in absence and in the presence of TMAO molecules, we find that there is a loss of few water molecules from the first solvation of shell of TBA in ternary systems. This is expected as from binary TBA-water systems some of the water molecules are now replaced by TMAO molecules from the solvation shell of TBA. A close examination of change of these coordination number values as TBA concentration is increased further reveals that the rate of loss of water molecules is significantly slowing down in the presence of TMAO molecules up to x tba = 0.06. Above this threshold concentration, the difference between these coordination number increases further. Here, we would like to mention that we did not observe concentrationdependent any such pattern in the change in number of water molecules around TMAO and its methyl group. Rather, the number of water molecules in the first solvation shell of TMAO (and its methyl group) continuously decreases at a much slower rate (data not shown). These findings enforce us for a further investigation of how the number of TMAO molecules in the first solvation shell of a TBA molecule changes with concentration and this is discussed right below.
In Figure 3, we have shown how TBA-TBA and TBA-TMAO coordination number changes with TBA concentration. The TBA-TBA coordination number values are obtained by using CC t − CC t distribution function and the results are shown both in the presence and in the absence of TMAO molecules. For TBA-TMAO coordination numbers for different systems, we followed the method analogous to that adopted above for TBA-water, with the TMAO nitrogen atom used in place of the water oxygen atom. As per the expectation, in both the presence and absence of TMAO, TBA-TBA coordination number increases with increasing TBA concentration. However, for all binary TBA-water systems, the coordination numbers are much larger than that for the respective ternary TBA-TMAO-water systems. Moreover, in the absence of TMAO molecules, the increase in the TBA-TBA coordination is much steeper up to x tba = 0.06 and then there is a distinct change to a smaller slope. On the other hand, in the solutions with TMAO molecules this coordination number value increases at a much slower rate, and a small change in the slope is observed above x tba = 0.06. Concentrating on the effect of TBA concentration on TBA-TMAO coordination values, we find that these values does not vary much up to x tba = 0.06. The net change in these coordination number values between x tba = 0.002 and x tba = 0.06 is approximately −0.5 and the same is −2.5 between x tba = 0.06 and x tba = 0.10. The physical significance, if any, of the small initial enhancement in the TBA-TMAO coordination number (as x tba is increased from 0.002 to 0.02) is unclear to us. These findings act as corroborative evidences that in ternary TBA-TMAO-water system, TBA molecules do not selfaggregate strongly below x tba = 0.06.
Above information encourage us to look in to TBA-TMAO interactions more closely. Note that in TBA-TMAO interactions, the hydrophobic interactions between methyl groups (of them) as well as hydrogen bonding interactions are expected to make significant contributions. A qualitative picture of TBA-TMAO hydrogen bonding interactions can be obtained from the distribution functions of O tm − O tb and O tm − H tb and the same are shown in Figure S3 of Supporting Information section. Here, we present the results for two systems namely system 1 and system 5. A more quantitative picture of these hydrogen bonding interactions are discussed elaborately below. It is apparent that with increasing TBA concentration, there is a sharp enhancement in the first peak of both the rdfs suggesting more stronger association between TBA and TMAO molecules through hydrogen bonding interactions. C tb − C tm distribution function for all the concentrations studied here is presented in Figure S4 of Supporting Information section. Since it has been reported in the literature that TMAO decreases the hydrophobic interactions between two hydrophobic molecules [33,34], our goal is to see if it (TMAO) can influence (or helps to decrease) the hydrophobic interactions between the hydrophobic methyl groups of TBA molecule. We observe that, 50 TMAO molecules can prevent the self-aggregation of TBA molecules up to x tba = 0.06, and this is quite evident from the increased first peak height of C tb − C tm distributions up to this concentration. Above x tba = 0.06, a sharp decrease in the peak height indicates, albeit indirectly, TMAO's inability to protect the self-aggregation of TBA molecules.

Preferential solvation
Preferential solvation or preferential interaction is a measure of deviation from the ideal solvation model. Following Ben-Naim [42], it can be defined as where, x αβ (r), the local mole fraction, is defined as the number of α molecules divided by the total number of molecules present in a sphere (of radius r) around a β molecule and x α is the total mole fraction of α molecule. So, δ αβ measures local mole fraction minus total mole fraction. V c is the volume with radius r and G αβ is called Kirkwood-Buff G-factor. G αβ is calculated using rdf, g αβ (r), as [43,44] We estimated excess coordination number,N αβ , from the density-weighted integral as In above Equation (5), 4πρ α r 2 g αβ (r) represents the average number of α molecules around a β molecule in a spherical shell of width dr at radius r and 4πρ α r 2 dr measures (ideal) average number of α molecules in a spherical shell. So, N αβ represents nothing but the excess number of α molecules around a β molecule. Since g αβ (r) goes to unity at large distance, Equation (5) can be written as, where the upper integration limit r c represents the radius of a correlation volume in which the solution structure differs from that in the bulk and thus g αβ (r) deviates from unity. A positive value of N αβ indicates enhancement of molecule α around a β molecule, while a negative value of it indicates its depletion. Note that, in these calculations, r c is sufficiently large so that beyond which the correlations are small giving rise to g αβ (r) 1. Here, we also note that in a recent study, Perera and co-workers reported that the asymptotes of different correlation functions that obtained from computer simulations are greatly affected by the size of the system [45,46]. The preferential solvations between TBA-water, TMAO-water and TBA-TMAO are shown in the N αβ profiles in Figure 4. Note that, we have used central atom-central atom distribution functions, i.e. N tm -O w , CC tb -O w and CC tb -N tm rdfs for calculating N αβ for TMAO-water, TBA-water and TBA-TMAO interactions, respectively. We observe that for all the systems studied here, N αβ is negative for water-TBA interactions except for system S1 where only one TBA molecule present in which the value of N αβ is close to unity. Given that only one TBA molecule is present in that system, no TBA-TBA aggregation is possible and this fact is reflected, albeit indirectly, in the N αβ of TBA-TMAO where a much negative value is observed. Nevertheless, with increasing TBA concentration, the value N αβ for water-TBA interaction decreases (more negative) indicating less and less water preference of TBA molecules. In case of TMAO-water interactions, we see that up to x tba = 0.06, the N αβ values are slightly negative and these values show a much weaker dependence of TBA concentration. But, above this concentration, there is a sharp increase in the N αβ leading to its positive value implying that water-TMAO interactions become more favourable. In Figure 4(c), we show the preferential solvation obtained from TBA-TMAO interactions where we see up to this threshold TBA concentration, there is no change in the values of N αβ and it, actually, oscillates around zero. But, above x tba = 0.06, there is a modest reduction in the N αβ value indicating less interactions between TBA and TMAO.

Hydrogen bond properties and dynamics
Further insights into the nature of interactions between different solution species in TBA-TMAO-water ternary solutions can be obtained by considering the strength and number of the hydrogen bonds between various species. Following earlier works [47][48][49][50][51], we adopt a set of geometric criteria to define hydrogen bonds. Two water molecules were considered to be hydrogen bonded if their inter-oxygen distance is less than 3.41Å and, the hydrogen-oxygen distance is less than 2.38Å and simultaneously, the oxygen-oxygen-hydrogen angle is less than 45 o . These oxygen-oxygen and oxygen-hydrogen cut-off distances were determined from the positions of the first minimum in the corresponding rdfs. In a similar manner, for water-TMAO, water-TBA, TMAO-TBA and TBA-TBA hydrogen bonds, we select the cut-off distances according to the location of the first minimum of the appropriate rdf. An angle of 45 o was also used to define all these hydrogen bonds. Here, we note that we have used non polarisable models for all the molecules (i.e. water, TBA and TMAO). Though, the geometric criteria used in this study to calculate hydrogen bond properties and dynamics serve as great tools, they do not represent 'realistic' hydrogen bonds. Average hydrogen-bond energies together with the average hydrogen bond numbers (given in parentheses) are summarised in Table 3. The changes of these quantities as TBA concentration changes are also shown in Figure S5 of Supporting Information section. The hydrogen bond numbers are expressed per second species mentioned in the column labels, i.e. W-TB represents the average water-TBA hydrogen bond number per TBA molecule, W-TM refers to the average water-TMAO hydrogen bond number per TMAO molecule and so on. In the same table, the hydrogen bond donor and acceptor atoms are denoted as D and A, respectively. It can be seen that W-TM hydrogen bonds are the strongest among all types of hydrogen bonds considered in this study. For system 5, the W-TM hydrogen-bond energy is 9.54 kJ/mol more stabilised than the W-W hydrogen bond and 6.19 kJ/mol more stabilised than that for the TM-TB. We note that the hydrogen-bond energies are not a strong function of TBA concentration. The W-W hydrogen bond energy of system 5 is just 0.63 kJ/mol more negative than that of system 1. The average number of W-W and W-TM hydrogen bonds decrease as TBA is added to the solution and we note that the decrease is nearly proportional to the number of water molecules replaced by TBA. We also observe a slight increase of W-TM hydrogen bond energy values on addition of TBA. In case of W-TB, the hydrogen bonds with water donor is ∼10 kJ/mol more stabilised than that for the case where water molecule acts as an acceptor. It suggests that, water molecule prefers donating its hydrogen atom to TBA rather than accepting hydrogen from it. In the same table, we also present the total number of hydrogen bonds Table . Hydrogen bond energies (kJ/mol of solution) and average hydrogen bond numbers (given in brackets) for the systems considered. In the column headings, W, TB and TM refer to water, TBA and TMAO and the subscripts D and A represent donor and acceptor, respectively. The hydrogen bond numbers are defined with respect to the second species mentioned in the column headings (i.e. per water molecule in column , per TBA molecule in column  etc.). Total TB is the total number of hydrogen bonds formed by a single TBA molecule.
formed by a single TBA molecule (Total TB ) for different systems. This is important given the fact that in this study our goal is to see the role of TMAO on TBA aggregation and the number of hydrogen bonds each TBA molecule is engaged with can be a signature of TBA self-aggregation. It is noticed that the value of Total TB remains essentially unaltered up to x tba = 0.06 concentration. Above this concentration, we observe a sharp drop of 0.15 of its value, and this reduction is mainly due to the loss of water-TBA hydrogen bonds. We have also considered the dynamics of waterwater hydrogen bonds in water-TBA-TMAO solutions. Hydrogen-bond dynamics were investigated using an approach employed by earlier workers [46][47][48][49][50]. For this, we define two hydrogen-bond population variables h(t) and H(t). h(t) is unity if a particular tagged pair of particles is hydrogen bonded (according to the definition adopted above) at time t and is zero otherwise. H(t) is unity if the tagged pair of particles remains continuously hydrogen bonded from time 0 to time t, and is zero otherwise. We then define the continuous hydrogen-bond time correlation function S HB (t) as [47][48][49][50][51][52] where denotes an average over all hydrogen bonds that are present at t = 0. Clearly, S HB (t) describes the probability that a pair of molecules, which was hydrogen bonded at t = 0, remains continuously hydrogen bonded up to time t. For all systems considered, once past the internal regime (t ࣙ 0.2 ps), S HB (t) exhibits a single exponential decay. The time integral of S HB (t), denoted τ HB , describes the average time that a hydrogen bond survives after it is chosen at t = 0. Since the hydrogen bonds are chosen randomly without imposing any condition on when they were created, τ HB is the average persistence time (life expectancy) of a randomly chosen hydrogen bond [48]. We note that other times characterising different aspects of hydrogen-bond dynamics can also be defined [48].
Results obtained for water-water hydrogen bonds in water-TBA-TMAO solutions are given in Table 4. In Figure S6 of Supporting Information section, the decay of S HB (t) with time (for water-water hydrogen bonds) is also shown for the highest and lowest TBA mole fractions. The effect of TMAO molecules on water-water hydrogen bond dynamics can be obtained by comparing the estimated τ HB values for different water-TBA-TMAO ternary solutions with that of water-TBA solutions (in the absence of TMAO) available in the literature [30]. We find that for system 2 (x tba = 0.02), the presence of 50 TMAO molecules increases the life time for waterwater hydrogen bond from 1.49 to 2.41 ps and this observation is valid for all other systems. We further notice that in water-TBA-TMAO ternary mixture, the addition of TBA enhances τ HB increase from 2.29 ps in system 1 to 2.83 ps in system 5. Note that, for binary mixture of water-TMAO mixture consisting of 450 water molecules and 50 TMAO molecules (having no TBA molecules), the water-water hydrogen bond life time value is 1.77 ps [31]. Addition of one TBA molecule increases waterwater hydrogen bond life time modestly to 2.29 ps. The life time increases further with increasing TBA concentration.

Diffusion coefficients
Itis evident from some experimental studies of aqueous alcohol solutions including TBA that the measurements of translational diffusion coefficients may provide information about the structure and self-association of alcohol molecules in these solutions [29,53]. Thus, it is important to estimate the self-diffusion coefficients of different solution species and in particular, how the self-diffusion coefficients of TBA molecules in different solutions are getting affected in presence of TMAO molecules. Towards this, for all systems considered here, we have calculated the translational diffusion coefficients of water (D w ), TBA (D tba ), and TMAO (D tmao ) molecules by integrating the velocity-velocity autocorrelation function [37]. Figure 5 presents the calculated values of D w , D tba and D tmao as a function of mole fraction of TBA molecules. Here, it is to be noted that, the diffusion coefficients of pure SPC/E water is found to be 2.65 × 10 −5 cm 2 s −1 (not shown). As can be seen that with increasing TBA mole fraction, the diffusion coefficients of all solution species are decreased and the lowest diffusion coefficient values are obtained for the highest TBA mole fraction considered here. Since the main goal is to see how the diffusion coefficient values of TBA is changed with changing TBA concentrations, it is instructive to focus on the D tba values for different systems. It is apparent that the value of D tba decreases sharply up to x tba = 0.06, after which it decreases at a much slower rate. This observation acts as a corroborative evidence to what we observed in coordination number analysis (discussed above) and implies, albeit indirectly, that in presence of TMAO the threshold concentration for TBA self-aggregation appears at x = 0.06.

Summary and Conclusions
In this paper, we discuss results of classical MD simulation for different aqueous solutions of TBA-TMAO mixtures in which we keep the number of TMAO molecules fixed for all the systems and we increase the TBA concentration from very low to moderately high by replacing water molecules with the same number of TBA molecules. From the calculations of site-site rdfs, it is found that the addition of TBA molecules enhances both first and second peak heights of O tm − O w and O tm − H w distributions indicating that water molecules are more structured around TMAO molecules. The loss of water molecules around TBA molecules were also observed from C tb − O w distribution plot followed by the corresponding first shell coordination number calculations. The sharp increase in the peak height and increase in the number of TBA molecules in the first shell was apparent from C tb − C tb rdf plot giving some hints about the possible aggregation of TBA molecules at higher concentration. Our preferential solvation studies reveal that water molecules prefer to interact with TMAO molecules over TBA molecules. The increase in the water-TMAO interactions and decrease in TBA-TMAO interactions above x tba = 0.06 has also been observed. The C tm − C tb distribution function shows a increase in peak height up to x tba = 0.06 and above this concentration, the peak height decreases. So up to this concentration, TMAO reduces the hydrophobic interactions between the hydrophobic ends of TBA molecules and thereby preventing TBA association which occurs through the hydrophobic ends.
We have also estimated hydrogen properties of different types of hydrogen bonds as well as average life time of water-water hydrogen bond. On addition of TBA molecules, modest increase in water-water hydrogen bond life time and hydrogen bond strength has been observed. TMAO-water hydrogen bond is the strongest one followed by TBA-TMAO hydrogen bond. In case of water-TBA hydrogen bond, the hydrogen bond with water donor is relatively more stronger than when water acts as acceptor. Interestingly, the average number of hydrogen bonds formed by a TBA molecule with the solution species remains essentially unaffected up to x tba = 0.06 concentration. But, above this concentration, a sharp drop in its value is observed and this reduction in its value is due to loss of some water-TBA hydrogen bonds. Furthermore, the calculated self-diffusion coefficient values of TBA for different systems reveals that the threshold concentration for TBA self-aggregation process is moved to x tba = 0.06. These observation act as corroborative evidences that TMAO acts to prevent the self-aggregation of TBA to some extent when compared to binary water-TBA mixture. Since our findings demonstrate TMAO's ability to counteract the aggregation of TBA molecules (which is responsible protein denaturation) up to a certain concentration, one may expect that TMAO can counteract the deleterious effect of TBA on protein conformational change to certain extent. We hope to address this problem in near future.

Disclosure statement
No potential conflict of interest was reported by the author.