Article pubs.acs.org/JPCB
Impact of Ions on Individual Water Entropy Debasis Saha and Arnab Mukherjee* Department of Chemistry, Indian Institute of Science Education and Research, Pune, 411008 Maharashtra India S Supporting Information *
ABSTRACT: Solutes determine the properties of a solution. In this study, we probe ionic solutions through the entropy of individual water molecules in the solvation shells around different cations and anions. Using a method recently developed by our group, we show the solvation shell entropy stemming from the individual contributions correlates extremely well with experimental values for both polarizable and nonpolarizable force fields. The behavior of water entropy as a function of distance reveals significant (∼20%) contributions from the second solvation shell even for the low concentration considered here. While for the cations, contributions from both translational and rotational entropy loss are similar in different solvation shells, water around anions loses much more rotational entropy due to their ability to accept hydrogen bonds. Most importantly, while charge density of cations or anions correlates with the translational entropy loss, anions with similar charge density as that of cations has a much stronger and long-range effect on water. We also show how the modulation of water entropy by ions is correlated to the structural modifications of hydration shell. This study thus provides a step toward understanding the entropic behavior of water in molecular recognition processes between proteins and drug molecules.
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decomposition,23 energetic decomposition using potential distribution theorem,24,25 etc. employ different statistical mechanical approaches. Despite these developments, the systematic use of these methods has been hampered due to limited accuracy in some cases; the reasons for this have been discussed by Velez-Vega et al.26 Moreover, most of these methods are not designed to probe the water molecule at single particle level at a particular distance from the solute. Here we apply the method for calculating individual water entropy, previously reported by our group27 on the hydration shell of ions. Although we showed in the previous study27 that our method captures the right trend in the hydrophobic crossover and a quantitative similarity with solvation entropy around methane, we did not perform an exhaustive comparison with experiments on other systems. We chose ionic solutions because of their variability in terms of size, charge, and interaction, while being simple enough to be tractable computationally. In addition, several aspects of ionic solutions are believed to originate from how the solvation shell water is modulated by ions. The structure maker tag for highly charged ions has been given to those which cause strong electrostatic ordering of nearby water molecules, reducing H-bonds among water molecules.28 The extent to which these structural modifications happen in the solvation shell has inspired several studies,29−32 none, however, with the entropic aspects of water.
INTRODUCTION Water in the environment is rarely found in the absolutely pure form. The presence of different solutes affects the structure and properties of water in its vicinity differently.1 For example, the presence of various ions makes the seawater participate in corrosion processes,2 whereas the ions in cellular water affect the stability of nucleic acids3 and proteins.4 Naturally, the hydration shell of ions has been subjected to numerous experimental and theoretical studies, especially due to the unique properties exhibited by various ions. The structure maker and breaker properties of ions5 have been manifested in the viscosity of different ionic solutions.6 Different ions also have been found to have different propensity to precipitate proteins in aqueous solutions leading to the Hofmeister’s empirical classification.3,4 These various properties are often considered to originate from the manner in which ions modulate the thermodynamics of its hydration water. Here we focus our study on the entropy of solvation shell water around ions, one at a time. The entropy of water has been shown to be important in biologically relevant processes such as molecular recognition7,8 and hydrophobic interactions.9,10 Therefore, several methods have been proposed for evaluating the entropic contribution of water from solvation dynamics. Some of the tools used for evaluating thermodynamic properties of hydration water, such as WaterMap,11,12 STOW,13 and GIST,14,15 implement inhomogeneous solvation theory (IST),16−19 where solute− water pair correlation is used to estimate solvation entropy. Other methods such as 3D-RISM,20 SZMAP,21 GCT,22 2PT © XXXX American Chemical Society
Received: April 22, 2016 Revised: July 12, 2016
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DOI: 10.1021/acs.jpcb.6b04033 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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Figure 1. Deviation in translational entropy (top panel) and rotational entropy (bottom panel) from bulk value for monovalent cations (a and d), divalent cations (b and e), and anions (c and f). Entropy change is multiplied by the temperature 298 K. The color code used in top and bottom panel represents same ions. Note that scales of abscissa are the same between top and bottom panels for each figure while ordinates are different in different figures.
Mg2+, Cl−, I−) with Amber99 force field38,39 solvated by TIP4P40 water model. Simulation Details. All the simulations were carried out using GROMACS41 software package. The ion−water systems were taken in a cubic box. Energy minimizations were performed using steepest descent method42 followed by heating up to 298 K using Berendsen thermostat43 with a coupling constant of 0.2 ps. The final equilibration was carried out for 2 ns at a constant temperature of 298 K and constant pressure of 1 bar using Nose-Hoover thermostat44,45 and Parrinello− Rahman barostat,46 respectively, with a coupling constant of 0.2 ps for each. Electrostatic interactions were treated using PME electrostatics47 with 10 Å cutoff. van der Waals cutoff was set to 10 Å. Choosing the average volume from the NPT equilibration mentioned above, a final molecular dynamics run under NVT condition for 50 ns was carried out for all the ion−water systems with all other parameters similar to the equilibration step. Distance restraint between the cation and anion was maintained throughout all the steps. Method for Single Water Entropy Calculation. The diffusive nature of water does not allow the use of standard quasi-harmonic entropy calculations as employed for a biomolecular system. Hence, we employ a method by Grubmüller and co-workers, known as permutation reduction (PR),48,49 to identify water molecules based on a particular site, and not by their original identity. The permuted water molecule moves only in a localized space for the duration of the simulation. A rigid model of water molecule has two forms of entropytranslational and rotational. For the calculation of the individual translational entropy, quasi-harmonic method has been applied. For rotational entropy calculations, the angular distribution of the individual permuted water molecule has been used. Complete detail of the method is available in ref 27 Method for H-Bond Calculation. We have used the permuted water molecules to study the structural properties by means of measuring average H-bonds per water. Using the widely accepted convention50 for H-bonding, two water molecules are considered to be forming H-bond if the distance between donor and acceptor is less than 3.5 Å and the donorhydrogen-acceptor angle is less than 30°. For the H-bonding
Dynamical aspects of water around ions also generated huge interest. Stirnemann et al.33 showed and subsequently explained using an extended jump model that while some ions tend to slow down the water near it, some other ions accelerate water next to it. The above studies thus provoke the question of how different ions modulate the entropic behavior of water at the single particle level. Another objective is to test the reliability of our method to calculate hydration entropy of ions from entropy contributions of the individual water molecule. In this study, we have calculated the translational and rotational entropy of individual water molecules as a function of distance from different monovalent and divalent cations and anions. The accumulated change in the total entropy of water around an ion has been compared with the experiment to establish the reliability of the method for both polarizable and nonpolarizable force fields. We also measure the entropy change contributions from different solvation shells. Our study reveals the distinct manner in which cations and anions modulate water entropy. The entropic behavior has been compared with structural properties of water around ions to establish the extent of impact the ions have on properties of water.
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METHOD System Setup. For the calculation of entropy and hydrogen bonding behavior, we have used infinitely dilute ion concentration where one cation and one anion were solvated by 2000 water molecules. A distance restraint was put on the cation and anion so that ion pairs cannot form allowing us to calculate the water entropy in the solvation shell of individual ions independently. For cations, we have taken Li+, Na+, K+, Rb+, Cs+, Mg2+, Ca2+, and Zn2+ with keeping the anion as Cl− for all the systems. For anions, we have taken F−, Cl−, Br−, I−, ClO4−, and SO42− with the cation as Na+ for all these systems. We have used polarizable models based on classical Drude oscillators for ions reported by Yu et al.34 except for ClO4− and SO42− whose parameters were obtained from refs. 35 and 36, respectively. Polarizable SWM4-NDP water model37 was used for better depiction of the overall systems. We have compared the result with nonpolarizable models of a few ions (Na+, Cs+, B
DOI: 10.1021/acs.jpcb.6b04033 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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Before we go to further discussion, we need to show how reliable our estimations are. The entropy loss of individual water molecules around a particular ion is currently beyond the reach of experimental methods. Hence, we have estimated the total change in the water entropy from the translational and rotational entropy contributions of individual water molecules around each ion. Figure 2 shows the comparison between the
behavior around cations, only water−water H-bonding has been considered and for anions, we have considered the interaction of ions with the hydrogen atoms of water molecules in addition to the water−water H-bonding.
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RESULTS AND DISCUSSION We begin our discussion with the translational and rotational entropy of individual water molecules in the solvation shell of ions. We will come back to the discussion of different solvation shells on the effect of entropy and water structure, thereafter. Entropy Variation with Distance from the Ions. The translational (TΔStrans) and rotational entropy (TΔSrot) of individual water molecules around various ions are shown in Figure 1 as a function of its distance from the respective ion. The 50 ns simulation employed here provides converged entropy values as shown in Figure S1 in the Supporting Information (SI) for few water molecules around Cl− as a representative ion. Entropy variation around water as a solute in a pure water system is also shown in Figure S2 of the SI for comparison. All the water molecules beyond 4 Å from the central water molecule are found, as expected, to be very similar. The average entropy for all these water molecules is taken to be the bulk water entropy. For the polarizable model, translational bulk entropy value is found to be 5.67 ± 0.03 kcal/ mol, while rotational bulk entropy is estimated to be −0.035 ± 0.004 kcal/mol. The standard deviations in the average values of bulk translational and rotational entropy were calculated from the entropy of several water molecules that are far away from the solute (Figure S2 of the SI). Entropy estimates presented here are multiplied by 298 K to get the unit of free energy. The bulk entropy is subtracted from all the absolute entropy obtained for all other systems shown in Figure 1. Error estimation in entropy calculation is computationally expensive and an extensive detail of the estimate was presented in our earlier study.27 Here, we have calculated the error for a few representative water molecules by taking them from different configurations (Table S2 and S3 in the SI). The error estimates turn out to be small. For all systems, the entropy of the water closest to the ion is the lowest. With increasing distance, entropy increases. Beyond a certain distance, entropy deviation from bulk value reaches zero, as expected. This result allows us not only to predict quantitatively the range within which ions impact water entropy; it shows the strength of the impact and number of water molecules that gets affected, as well. Figure 1a compares the entropy variation for monovalent cations of different sizes, while Figure 1b and 1c do the same for divalent cations and anions, respectively. Water molecules around the smallest cation Li+ have the lowest entropy, followed by an increase in entropy for Na+, K+, Rb+, and Cs+, respectively, according to the increase in size. For Cs+, which has a large hydrophobic surface affinity,51 a slight increase compared to bulk entropy is observed before the entropy reaches the bulk value. Closest set of water molecules around divalent cations loses more entropy than that around the monovalent cations. The increase in entropy with distance is steeper for divalent cations than that of the monovalent ones. Translational entropy behaves similarly for monovalent cations and anions. It is interesting to observe that anions decrease more rotational entropy than cations (compare F− and Li+). The divalent anions studied here are much bigger in size and induce a similar decrease in translational and rotational entropy as monovalent cations.
Figure 2. Comparison of experimental52 and calculated entropy values for different ions at 298 K. R is the Pearson’s correlation coefficient. Calculated entropy values come from the summations of all the translational and rotational entropy change for individual water molecules around a particular solute.
total entropy change calculated as mentioned above with experimentally reported values.52 We see that our calculated values correlate extremely well (correlation coefficient 0.97) with the experimental values. We also find our calculated values to be very similar to the entropic contribution to the hydration free energy of different ions calculated by Floriánet et al.53 using Langevin dipole model. While the comparison validates our method and result, it also indicates that the origin of the total entropy change is due to varying contributions of water molecules lying at different separations from the ions. To build further confidence to our results, we have estimated the entropy change of water around five ions using a nonpolarizable force field as mentioned before. The comparison has been shown in Figure S3 in the SI. This nonpolarizable model also shows excellent correlation (correlation coefficient 0.98) with experimental results, thus bolstering confidence to the methods adopted and asserting the applicability of the method for various models and force fields. The excellent correlation with experiment implies that we can now obtain experimental values of the individual water entropy with just a constant difference from the theoretically calculated values. The method provides us with a powerful tool to have access of thermodynamics at the molecular level and as a function of distance from a solute. Water Entropy in Different Solvation Shells. Since we have established the accuracy of our method, we can now discuss the entropy changes in different solvation shells of various ions. For this, we have calculated the radial distribution function (RDF) of water oxygen atoms around different ions and have shown the entropy change for individual water in Figure 3 along with the total (translational + rotational) entropy change for all systems. Conventionally, RDF defines the regions of the solvation shells (the first peak corresponding to the first solvation shell, C
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Figure 3. (Upper panel) Radial distribution function (RDF) plots between (a) monovalent cations−water oxygen, (b) divalent cations−water oxygen, and (c) anions−water oxygen. (Lower panel) Single water entropy values for (d) monovalent cations, (e) divalent cations, and (e) anions as a function of distance from the ion. Rest of the detail is the same as Figure 1.
the second peak for the second solvation shell, etc.). The present approach, however, allows us to identify average positions of each molecule belonging within and even between the solvation shells. The same has been shown for nonpolarizable ions in Figure S4 in the SI. Note that for highly charged ions there is a distinction between the first solvation shell and the second as can be seen from Figure 3e where we see a gap between the closest six water and the rest. On the other hand, for ions larger than K+ and anions in general, the solvation shells are more diffused due to their lower charge densities, and we see a continuous presence of water with increasing entropy value. The pronounced second solvation shell was also observed around smaller singly charged and all doubly charged cations from the AIMD simulation study of Ding et al.54 The entropy reduction of the first solvation shell water molecules near monovalent cations is almost half compared to that around divalent cations. Therefore, both the size and the charge affect the entropy, indicating charge density (see Table S1 in the SI) to be a relevant parameter to compare the entropy reduction of water. However, charge density alone cannot explain the difference in the effect on water by cations and anions. Water molecules in the first solvation shell of F− loose more entropy compared to Na+ or even Li+ that have higher charge density than F−. The reason may lie in the capacity of the anions to form H-bond with water and thus have a greater effect in the rotational entropy as mentioned above. The entropy of individual water near halide ions correlates with the dynamical pattern of halide-water hydrogen bonds. H-bond is found to be strongest between water and F− followed by Cl−, Br−, and I− with all of them having a slower H-bond dynamics compared to the water− water H-bond.55 Our calculations also show lower entropy values around these halides ions compared to that around bulk water. Since the RDF gives the knowledge of different solvation shells, we can now probe the contribution of various solvation shells toward the total entropy change of water around a particular solute. Hence, the number of water in different solvation shells and their contributions toward the total entropy change in the first two solvation shells are shown in Table 1. From the table, we see that the major contribution to the total entropy reduction around a solute comes from the water in the
Table 1. Number of Water Molecules in Different Solvation Shells and Their Contributions to the Total Entropy Change for Different Ionsa contributionFHS (%) ion +
Li Na+ K+ Rb+ Cs+ Mg2+ Ca2+ Zn2+ F− Cl− Br− I− SO42− ClO4−
contributionSHS (%)
numberFHS
TΔStrans
TΔSrot
numberSHS
TΔStrans
TΔSrot
5 6 7 8 9 6 6 6 6 6 7 7 12 14
39.1 40.3 36.6 40.7 41.2 38.1 33.8 39.6 18.2 11.4 14.8 14.0 33.8 50.3
39.5 39.2 38.8 34.2 40.8 36.4 38.3 37.7 57.3 61.4 55.7 57.3 46.2 33.3
16 16 19 20 21 14 14 13 19 24 23 26 55 57
10.8 10.6 10.8 11.6 3.5 10.6 10.6 8.6 8.5 8.4 8.4 12.3 4.8 0.4
7.1 7.0 12.2 13.0 14.1 10.7 9.9 10.0 16.0 18.8 21.1 16.4 15.2 14.6
a
FHS: Number of water molecule and contribution to the total entropy change for the first hydration shell; SHS: number of water molecule and contribution to the total entropy change for the second hydration shell. TΔStrans and TΔSrot denotes percentage contribution of translational and rotational entropy to the total entropy loss.
first hydration shell. This pattern is in agreement with the findings of studies performed using potential distribution theorem24,56 where the majority of the contribution is shown to arise from the first solvation shell. By decomposition of various contributions, Beck argued that the local electrostatic contribution varies with the size of the isoelectronic ions, whereas the far-field electrostatic contributions remain similar. However, we find that the second hydration shell also has approximately 20% contribution across all ions, albeit with a larger number of water molecules. Therefore, while an individual water molecule in the first solvation shell contributes to more than 10% to the total entropy loss, a water molecule in the second solvation shell contributes 1% or less. The table also shows that cations reduce both translational and rotational entropy almost equally across different solvation shells. The mechanism of entropy reduction around anions, on D
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Figure 4. Correlation between the total (a) translational entropy (b) and rotational entropy change with the magnitude of surface charge density values of cations and anions. The error in these values, estimated from the average of the error of a few water molecules, lies between 0.28 to 1.52 kcal/mol for translational entropy and 0.23 to 0.84 kcal/mol for rotational entropy.
Figure 5. Average H-bonds per water molecule vs distance of water plot for (a) monovalent cations, (b) divalent cations, and (c) anions. The dashed lines represent the bulk water value. Note that ordinate range is different for different figures.
H-bonds are shown in Figure S5 of the SI. The large error in Hbond is mainly associated with the permuted water molecule sampling different distances from the solute. Therefore, when calculated against a fixed distance, as shown in Figure S6 of the SI for a few water molecules around Na+, the error in H-bond is negligible. Therefore, H-bond in general is a property that depends on the distance from a particular solute. Except for F−, all the ions considered here show an increase in the average Hbond with distance before reaching bulk value (dashed line) of 3.61, as it should, beyond a certain distance. We find here that the average H-bond and entropy values of individual water molecules show a similar trend like entropy for cations; the water in the first shell has much lower H-bond and the ones in the second shell show a little decrease from bulk. Hbond values reach the bulk value at around the same distance as entropy, indicating that the extent of modulation of thermodynamic and structural properties by cations is similar. The anions, however, show a reverse trend, with F− producing an enhanced H-bonding for the neighboring water molecules despite a high reduction in water entropy. The I− ion with much smaller charge density shows only a tiny reduction in entropy but a significant decrease in H-bonding. There may be two reasons for this reversal in behavior. Both cations and anions can hinder H-bond formation among water molecules by creating electrostatic ordering. While cations cannot compensate this loss in average H-bond by participating in H-bond formation, anions can accept H-bond from water molecules. While, I− compensates this loss partially, F− overcompensates it to have more H-bond than bulk.
the contrary, stems mainly from a much greater reduction (>50% in the first solvation shell) of rotational entropy loss, indicating that charge density of ions may mainly affect the translational entropy more than the rotational entropy. Interestingly, residence time, a measure of translational motion, of water around Li+ is found to be much higher compared to F−.57 Therefore, to establish the relation between charge density and different entropy contributions, we have plotted the translational and rotational entropy change of water in the first solvation shell of various ions against the magnitude of their charge densities. The plots are shown in Figure 4. While translational entropy is highly correlated (correlation coefficient −0.95) with charge density, correlation of the same with rotational entropy is rather poor (correlation coefficient −0.78). Therefore, a clear trend between charge density and translational entropy can be observed from the above plot. However, anions affect rotational entropy more than the translational entropy. We probed into the origin of this behavior through examining water structure in the hydration shells. Water Entropy and Water Structure Correlation. To investigate the source of the entropic behavior, we have looked at the structural aspects of solvation water through its hydrogen bonding (H-bond) property. The average number of H-bond made by particular water at a certain distance was calculated for permuted water molecules. The values have been plotted against the average distance of water molecules from the ions and are shown in Figure 5. The errors in the values of average E
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Figure 6. Distribution of the angle θ (shown in the middle) between the vector connecting the ion and the water oxygen atom with the bisector vector of the water molecule for cations (upper panel) and anions (lower panel). (a) and (e) plot is for first water, (b) and (f) plot is for fifth water, (c) and (g) plot is for seventh water and, (d) and (h) plot is for tenth water next to cations and anions, respectively.
have calculated the angle θ between the vector from water oxygen to the ion and the vector bisecting the water molecule as shown in Figure 6. Distributions of θ for four water molecules (1st, 5th, 7th, and 10th water from the solute) are plotted for several ions. From Table 1, it can be seen that while the 1st and 5th water molecules represent the first solvation shell, and the 10th water molecule is representative of the second solvation shell, the 7th water molecule illustrates the behavior of the intermediate between the two. Errors associated with the distribution of θ are shown in Figure S7 and S8 in the SI for the 1st and 10th water molecules from all the ions. Therefore, orientations of these water molecules represent the characteristics of the solvation environment they belong. Water around smaller cations (higher charge density) shows a peak around 166° for bivalent cations and decreases with decreasing charge density (Figure 6a−d). The high θ value indicates that water hydrogens orient away from the cation, as expected. Water around larger cations has a broader distribution. This distribution is maintained for the first six water molecules, i.e, the first solvation shell water. However, the trend vanishes from the seventh water onward, and no pattern was found for remaining water molecules. For anions (Figure 6e−h), as expected, the peak occurs at a smaller angle of 50° indicating that one of the hydrogen atoms is H-bonded to the anion. For anions too, the highest peak is observed for F− for up to 7th water, after which the orientation do not follow any pattern. Interestingly, for anions, even the 10th water shows a peak at around 50°, indicating a rather longranged effect compared to cations. This long-range effect might cause a greater loss of entropy of water around anions compared to cations of similar or even higher charge density. It also explains the higher rotational entropy loss in the second solvation shell for anions as shown in Table 1. Our previous study27 also showed the entropy reduction for particles with −1 charge is higher compared to particle of the same size with +1 charge. We believe that this behavior of anions has implications toward the dynamics of water near biomolecules. Sterpone et al.64 calculated H-bond dynamics near different amino acids and reported H-bond axis tumbling time (τframe reor ). The study showed that the time scales near donor sites (positively charged residues) are smaller compared to the acceptor sites (negatively charged residues), indicating the water near these sites are held
The reduction of H-bonds reflects the structure maker property of the cations as argued by Hribar et al.28 Since structure maker property and entropy are correlated with each other, a correlation between H-bond and entropy is also expected. Our results are in good agreement with experimental observations of Harsányi et al.58 that showed an increase in LiCl salt concentration breaks the H-bond network of water. The study by Mancinelli et al.30 on NaCl and KCl salt solutions using neutron diffraction/EPSR technique also found these solutions to behave like the water at high pressure, indicating an enhanced ordering of water, especially for Na+ ion compared to K+. The pattern we see for H-bonding and entropy of different ions on its surrounding water also causes several observable phenomena in water. Smaller effects on entropy by larger ions indicate a weaker interaction between these ions and water, as found in the case of Br− and I− by Karmakar et al.59,60 The weaker interaction leads to a higher diffusion for the water near larger ions.61 The lowering of entropy, on the other hand, is a related to stronger H-bonding. Interestingly, the different manifestations of structural (H-bond) and thermodynamic (entropy) properties presented here find a similar correlation in dynamical properties also where F− and I− show different modes of reorientation pathways.62 Thus, our study on individual water molecules accurately represents the previously reported results obtained for overall solvation shell of ions. Different experimental studies provide water perturbation by ions to various extents. While the effects have been considered to prevail only up to the first solvation shell by some studies,29,63 the work by Mancinelli et al.30 claimed the effects to be present even in the second and third solvation shells. Our results so far have shown that the largest impact on entropy and H-bonding behavior for individual water is restricted mainly to the first solvation shell, with some effect in the second shell. It is, therefore, interesting to see how different ions affect the orientations of individual water molecules present at different distances from the ion. It can also shed light on the rotational entropy pattern observed for anions. Ding et al. also looked at the average orientational distribution of water molecules in the first solvation shell of NaCl and CsI using ab initio molecular dynamics simulations.54 The difference is that here we can probe into the orientation of individual water molecules at various distances, not just the average of the solvation shell. We F
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ACKNOWLEDGMENTS Department of Science and Technology (DST-SERB), India (Grant No. SB/S1/PC-39/2012).
more strongly compared to donor sites. The dynamical features mentioned corroborate the thermodynamic findings of the present study where an acceptor group like anions or negatively charge amino acids will have a stronger impact on water than cations or positively charged amino acid that act as a donor.
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CONCLUSION In this study, we report the entropy change of individual water molecules in different solvation shells of ions. The sum of contributions of the individual water entropy around a particular ion correlates extremely well with experiment for both the polarizable and nonpolarizable force fields. This study also reveals a fundamental difference in the approach of cations and ions by which they reduce the entropy of the surrounding water molecules. Our quantitative measurements at individual water level provide the exact extent of the perturbations caused by anions on the surrounding water molecules, albeit for a lower concentration of ions. The similarity between entropic and H-bonding behavior shows that the manner in which ions modulates thermodynamics of the surrounding water has consequences toward the structure maker and breaker properties of these ions. The potential distribution theorem of Beck shows that the local electrostatic contribution to the hydration free energy is negative for smaller ions (F− and Na+) and are considered structure makers, while larger ions have positive contribution and thus can be considered structure breakers.24 The study reveals that charge density governs the translational entropy of solvent molecules, whereas the rotational entropy involves the strength of the interaction between ion and water. This manifests in differing roles of cations and anions on the water entropy. The general pattern found across all systems is that ions mostly affect the first solvation shell water. However, significant contribution (20%) to the entropy reduction comes from the second solvation shell. The scenario will be likely to change with an increase in the ion concentration where solvation shells of different ions will overlap. Finally, our method successfully reproduces (within a constant) the experimental solvation entropy while retaining the information at the individual water level. The success of the present method implies that it can be applied to find the entropic behavior of water around proteins and DNA that govern important roles in drug design.11,65
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REFERENCES
(1) Marcus, Y.; Ben-Naim, A. A Study of the Structure of Water and Its Dependence on Solutes, Based on the Isotope Effects on Solvation Thermodynamics in Water. J. Chem. Phys. 1985, 83, 4744−4759. (2) Kritzer, P. Corrosion in High-Temperature and Supercritical Water and Aqueous Solutions: A Review. J. Supercrit. Fluids 2004, 29, 1−29. (3) Record, M. T., Jr; Zhang, W.; Anderson, C. F. Analysis of Effects of Salts and Uncharged Solutes on Protein and Nucleic Acid Equilibria and Processes: A Practical Guide to Recognizing and Interpreting Polyelectrolyte Effects, Hofmeister Effects, and Osmotic Effects of Salts. Adv. Protein Chem. 1998, 51, 281−353. (4) Lo Nostro, P.; Ninham, B. W. Hofmeister Phenomena: An Update on Ion Specificity in Biology. Chem. Rev. 2012, 112, 2286− 2322. (5) Marcus, Y. The Hydration Entropies of Ions and Their Effects on the Structure of Water. J. Chem. Soc., Faraday Trans. 1 1986, 82, 233− 242. (6) Frank, H. S.; Evans, M. W. Free Volume and Entropy in Condensed Systems Iii. Entropy in Binary Liquid Mixtures; Partial Molal Entropy in Dilute Solutions; Structure and Thermodynamics in Aqueous Electrolytes. J. Chem. Phys. 1945, 13, 507−532. (7) Baron, R.; Setny, P.; Andrew McCammon, J. Water in Cavity− Ligand Recognition. J. Am. Chem. Soc. 2010, 132, 12091−12097. (8) Frederick, K. K.; Marlow, M. S.; Valentine, K. G.; Wand, A. J. Conformational Entropy in Molecular Recognition by Proteins. Nature 2007, 448, 325−329. (9) DeLorbe, J. E.; Clements, J. H.; Teresk, M. G.; Benfield, A. P.; Plake, H. R.; Millspaugh, L. E.; Martin, S. F. Thermodynamic and Structural Effects of Conformational Constraints in Protein-Ligand Interactions. Entropic Paradoxy Associated with Ligand Preorganization. J. Am. Chem. Soc. 2009, 131, 16758−16770. (10) Smith, D. E.; Zhang, L.; Haymet, A. D. J. Entropy of Association of Methane in Water - a New Molecular-Dynamics ComputerSimulation. J. Am. Chem. Soc. 1992, 114, 5875−5876. (11) Young, T.; Abel, R.; Kim, B.; Berne, B. J.; Friesner, R. A. Motifs for Molecular Recognition Exploiting Hydrophobic Enclosure in Protein−Ligand Binding. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 808−813. (12) Pearlstein, R. A.; Hu, Q. Y.; Zhou, J.; Yowe, D.; Levell, J.; Dale, B.; Kaushik, V. K.; Daniels, D.; Hanrahan, S.; Sherman, W.; Abel, R. New Hypotheses About the Structure-Function of Proprotein Convertase Subtilisin/Kexin Type 9: Analysis of the Epidermal Growth Factor-Like Repeat a Docking Site Using Water Map. Proteins: Struct., Funct., Bioinf. 2010, 78, 2571−2586. (13) Li, Z.; Lazaridis, T. Computing the Thermodynamic Contributions of Interfacial Water. Methods Mol. Biol. 2012, 819, 393−404. (14) Nguyen, C. N.; Kurtzman Young, T.; Gilson, M. K. Grid Inhomogeneous Solvation Theory: Hydration Structure and Thermodynamics of the Miniature Receptor Cucurbit[7]Uril. J. Chem. Phys. 2012, 137, 044101. (15) Nguyen, C. N.; Cruz, A.; Gilson, M. K.; Kurtzman, T. Thermodynamics of Water in an Enzyme Active Site: Grid-Based Hydration Analysis of Coagulation Factor Xa. J. Chem. Theory Comput. 2014, 10, 2769−2780. (16) Chang, C. E. A.; McLaughlin, W. A.; Baron, R.; Wang, W.; McCammon, J. A. Entropic Contributions and the Influence of the Hydrophobic Environment in Promiscuous Protein-Protein Association. Proc. Natl. Acad. Sci. U. S. A. 2008, 105, 7456−7461. (17) Wallace, D. C. On the Role of Density-Fluctuations in the Entropy of a Fluid. J. Chem. Phys. 1987, 87, 2282−2284.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b04033. Figure showing convergence of a few water molecules; figure showing entropy around water as a solute; figure showing correlation between experiment and simulation for nonpolarizable model; table of charge densities; and figure showing water entropy and RDF using nonpolarizable mode, error in the translational and rotational entropy values, error in H-bond calculation, and error in θ angle calculation (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]; Telephone: +91 2590 8051; Fax: +91 2589 9790. Notes
The authors declare no competing financial interest. G
DOI: 10.1021/acs.jpcb.6b04033 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B (18) Ashbaugh, H. S.; Paulaitis, M. E. Entropy of Hydrophobic Hydration: Extension to Hydrophobic Chains. J. Phys. Chem. 1996, 100, 1900−1913. (19) Lazaridis, T. Inhomogeneous Fluid Approach to Solvation Thermodynamics. 2. Applications to Simple Fluids. J. Phys. Chem. B 1998, 102, 3542−3550. (20) Sindhikara, D. J.; Hirata, F. Analysis of Biomolecular Solvation Sites by 3d-Rism Theory. J. Phys. Chem. B 2013, 117, 6718−6723. (21) Grant, J. A.; Pickup, B. T.; Nicholls, A. A Smooth Permittivity Function for Poisson-Boltzmann Solvation Methods. J. Comput. Chem. 2001, 22, 608−640. (22) Gerogiokas, G.; Calabro, G.; Henchman, R. H.; Southey, M. W. Y.; Law, R. J.; Michel, J. Prediction of Small Molecule Hydration Thermodynamics with Grid Cell Theory. J. Chem. Theory Comput. 2014, 10, 35−48. (23) Lin, S.-T.; Blanco, M.; Goddard, W. A. The Two-Phase Model for Calculating Thermodynamic Properties of Liquids from Molecular Dynamics: Validation for the Phase Diagram of Lennard-Jones Fluids. J. Chem. Phys. 2003, 119, 11792−11805. (24) Beck, T. L. A Local Entropic Signature of Specific Ion Hydration. J. Phys. Chem. B 2011, 115, 9776−9781. (25) Beck, T. L. The Influence of Water Interfacial Potentials on Ion Hydration in Bulk Water and near Interfaces. Chem. Phys. Lett. 2013, 561, 1−13. (26) Velez-Vega, C.; McKay, D. J. J.; Kurtzman, T.; Aravamuthan, V.; Pearlstein, R. A.; Duca, J. S. Estimation of Solvation Entropy and Enthalpy Via Analysis of Water Oxygen-Hydrogen Correlations. J. Chem. Theory Comput. 2015, 11, 5090−5102. (27) Sasikala, W. D.; Mukherjee, A. Single Water Entropy: Hydrophobic Crossover and Application to Drug Binding. J. Phys. Chem. B 2014, 118, 10553−10564. (28) Hribar, B.; Southall, N. T.; Vlachy, V.; Dill, K. A. How Ions Affect the Structure of Water. J. Am. Chem. Soc. 2002, 124, 12302− 12311. (29) Omta, A. W.; Kropman, M. F.; Woutersen, S.; Bakker, H. J. Negligible Effect of Ions on the Hydrogen-Bond Structure in Liquid Water. Science 2003, 301, 347−349. (30) Mancinelli, R.; Botti, A.; Bruni, F.; Ricci, M. A.; Soper, A. K. Perturbation of Water Structure Due to Monovalent Ions in Solution. Phys. Chem. Chem. Phys. 2007, 9, 2959−2967. (31) Paschek, D.; Ludwig, R. Specific Ion Effects on Water Structure and Dynamics Beyond the First Hydration Shell. Angew. Chem., Int. Ed. 2011, 50, 352−353. (32) Tielrooij, K. J.; Garcia-Araez, N.; Bonn, M.; Bakker, H. J. Cooperativity in Ion Hydration. Science 2010, 328, 1006−1009. (33) Stirnemann, G.; Wernersson, E.; Jungwirth, P.; Laage, D. Mechanisms of Acceleration and Retardation of Water Dynamics by Ions. J. Am. Chem. Soc. 2013, 135, 11824−11831. (34) Yu, H. B.; Whitfield, T. W.; Harder, E.; Lamoureux, G.; Vorobyov, I.; Anisimov, V. M.; MacKerell, A. D.; Roux, B. Simulating Monovalent and Divalent Ions in Aqueous Solution Using a Drude Polarizable Force Field. J. Chem. Theory Comput. 2010, 6, 774−786. (35) Baer, M. D.; Kuo, I. F. W.; Bluhm, H.; Ghosal, S. Interfacial Behavior of Perchlorate Versus Chloride Ions in Aqueous Solutions. J. Phys. Chem. B 2009, 113, 15843−15850. (36) Vila Verde, A.; Lipowsky, R. Cooperative Slowdown of Water Rotation near Densely Charged Ions Is Intense but Short-Ranged. J. Phys. Chem. B 2013, 117, 10556−10566. (37) Lamoureux, G.; Harder, E.; Vorobyov, I. V.; Roux, B.; MacKerell, A. D., Jr A Polarizable Model of Water for Molecular Dynamics Simulations of Biomolecules. Chem. Phys. Lett. 2006, 418, 245−249. (38) Wang, J.; Cieplak, P.; Kollman, P. A. How Well Does a Restrained Electrostatic Potential (Resp) Model Perform in Calculating Conformational Energies of Organic and Biological Molecules? J. Comput. Chem. 2000, 21, 1049−1074. (39) Pérez, A.; Marchán, I.; Svozil, D.; Sponer, J.; Cheatham, T. E.; Laughton, C. A.; Orozco, M. Refinement of the Amber Force Field for
Nucleic Acids: Improving the Description of A/Γ Conformers. Biophys. J. 2007, 92, 3817−3829. (40) Jorgensen, W. L.; Maxwell, D. S.; TiradoRives, J. Development and Testing of the Opls All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118, 11225−11236. (41) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. Gromacs 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435−447. (42) Schlick, T. Molecular Modelling and Simulation: An Interdisplinary Guide; Springer, 2010. (43) Berendsen, H. J. C.; Postma, J. P. M.; Vangunsteren, W. F.; Dinola, A.; Haak, J. R. Molecular-Dynamics with Coupling to an External Bath. J. Chem. Phys. 1984, 81, 3684−3690. (44) Nose, S. A Molecular-Dynamics Method for Simulations in the Canonical Ensemble. Mol. Phys. 1984, 52, 255−268. (45) Hoover, W. G. Canonical Dynamics - Equilibrium Phase-Space Distributions. Phys. Rev. A: At., Mol., Opt. Phys. 1985, 31, 1695−1697. (46) Parrinello, M.; Rahman, A. Polymorphic Transitions in SingleCrystals - a New Molecular-Dynamics Method. J. Appl. Phys. 1981, 52, 7182−7190. (47) Darden, T.; York, D.; Pedersen, L. Particle Mesh Ewald: An N Log(N) Method for Ewald Sums in Large Systems. J. Chem. Phys. 1993, 98, 10089−10092. (48) Reinhard, F.; Grubmuller, H. Estimation of Absolute Solvent and Solvation Shell Entropies Via Permutation Reduction. J. Chem. Phys. 2007, 126, 014102. (49) Reinhard, F.; Lange, O. F.; Hub, J. S.; Haas, J.; Grubmuller, H. G_Permute: Permutation-Reduced Phase Space Density Compaction. Comput. Phys. Commun. 2009, 180, 455−458. (50) Laage, D.; Hynes, J. T. A Molecular Jump Mechanism of Water Reorientation. Science 2006, 311, 832−835. (51) Schwierz, N.; Horinek, D.; Netz, R. R. Anionic and Cationic Hofmeister Effects on Hydrophobic and Hydrophilic Surfaces. Langmuir 2013, 29, 2602−2614. (52) Marcus, Y. Ion Properties; Marcel Dekker: New York, 1997. (53) Florián, J.; Warshel, A. Calculations of Hydration Entropies of Hydrophobic, Polar, and Ionic Solutes in the Framework of the Langevin Dipoles Solvation Model. J. Phys. Chem. B 1999, 103, 10282−10288. (54) Ding, Y.; Hassanali, A. A.; Parrinello, M. Anomalous Water Diffusion in Salt Solutions. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 3310−3315. (55) Chowdhuri, S.; Chandra, A. Dynamics of Halide Ion−Water Hydrogen Bonds in Aqueous Solutions: Dependence on Ion Size and Temperature. J. Phys. Chem. B 2006, 110, 9674−9680. (56) Merchant, S.; Asthagiri, D. Thermodynamically Dominant Hydration Structures of Aqueous Ions. J. Chem. Phys. 2009, 130, 195102. (57) Lee, S. H.; Rasaiah, J. C. Molecular Dynamics Simulation of Ion Mobility. 2. Alkali Metal and Halide Ions Using the Spc/E Model for Water at 25 °C. J. Phys. Chem. 1996, 100, 1420−1425. (58) Harsányi, I.; Pusztai, L. On the Structure of Aqueous Licl Solutions. J. Chem. Phys. 2005, 122, 124512. (59) Karmakar, A.; Chandra, A. Effects of Dispersion Interaction on Vibrational Spectral Diffusion in Aqueous Nabr Solutions: An Ab Initio Molecular Dynamics Study. Chem. Phys. 2015, 448, 1−8. (60) Karmakar, A.; Chandra, A. Water in Hydration Shell of an Iodide Ion: Structure and Dynamics of Solute-Water Hydrogen Bonds and Vibrational Spectral Diffusion from First-Principles Simulations. J. Phys. Chem. B 2015, 119, 8561−8572. (61) Kim, J. S.; Wu, Z.; Morrow, A. R.; Yethiraj, A.; Yethiraj, A. SelfDiffusion and Viscosity in Electrolyte Solutions. J. Phys. Chem. B 2012, 116, 12007−12013. (62) Boisson, J.; Stirnemann, G.; Laage, D.; Hynes, J. T. Water Reorientation Dynamics in the First Hydration Shells of F- and I. Phys. Chem. Chem. Phys. 2011, 13, 19895−19901. H
DOI: 10.1021/acs.jpcb.6b04033 J. Phys. Chem. B XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry B (63) Omta, A. W.; Kropman, M. F.; Woutersen, S.; Bakker, H. J. Influence of Ions on the Hydrogen-Bond Structure in Liquid Water. J. Chem. Phys. 2003, 119, 12457−12461. (64) Sterpone, F.; Stirnemann, G.; Hynes, J. T.; Laage, D. Water Hydrogen-Bond Dynamics around Amino Acids: The Key Role of Hydrophilic Hydrogen-Bond Acceptor Groups. J. Phys. Chem. B 2010, 114, 2083−2089. (65) Abel, R.; Young, T.; Farid, R.; Berne, B. J.; Friesner, R. A. Role of the Active-Site Solvent in the Thermodynamics of Factor Xa Ligand Binding. J. Am. Chem. Soc. 2008, 130, 2817−2831.
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DOI: 10.1021/acs.jpcb.6b04033 J. Phys. Chem. B XXXX, XXX, XXX−XXX
