J. Phys. Chem. B 2008, 112, 15417–15425
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Structure of Aqueous Sodium Perchlorate Solutions Ignacio J. General,* Eliana K. Asciutto, and Jeffry D. Madura Department of Chemistry and Biochemistry, Center for Computational Sciences, Duquesne UniVersity, Pittsburgh, PennsylVania 15282, USA ReceiVed: July 15, 2008; ReVised Manuscript ReceiVed: September 29, 2008
Salt solutions have been the object of study of many scientists through history, but one of the most important findings came along when the Hofmeister series were discovered. Their importance arises from the fact that they influence the relative solubility of proteins, and solubility is directly related to one of today’s holy grails: protein folding. In this work we characterize one of the more-destabilizing salts in the series, sodium perchlorate, by studying it as an aqueous solution at various concentrations ranging from 0.08 to 1.60 mol/L. Molecular dynamics simulations at room temperature permitted a detailed study of the organization of solvent and cosolvent, in terms of its radial distribution functions, along with the study of the structure of hydrogen bonds in the ions’ solvation shells. We found that the distribution functions have some variations in their shape as concentration changes, but the position of their peaks is mostly unaffected. Regarding water, the most salient fact is the noticeable (although small) change in the second hydration shell and even beyond, especially for gOw•••Ow, showing that the locality of salt effects should not be restricted to considerations of only the first solvation shell. The perturbation of the second shell also appears in the study of the HB network, where the difference between the number of HBs around a water molecule and around the Na+ cation gets much smaller as one goes from the first to the second solvation shell, yet the difference is not negligible. Nevertheless, the effect of the ions past their first hydration shell is not enough to make a noticeable change in the global HB network. The Kirkwood-Buff theory of liquids was applied to our system, in order to calculate the activity derivative of the cosolvent. This coefficient, along with a previously calculated preferential binding, allowed us to establish that if a folded AP peptide is immersed in the studied solution, becoming the solute, then increasing the salt concentration will make the helix more stable. 1. Introduction At the end of the 19th century, Franz Hofmeister discovered that salts in a solution have different effects on the solubility of proteins; some salts increase their solubility (salting-in), and some decrease it (salting-out).1 The so-called “Hofmeister series” ranks ions in order of their salting-in/out tendency for proteins. It was later found that this series is also related to the stability of the protein and its tendency to fold/unfold. The atomic scale mechanisms governing the stabilizing/ destabilizing effect of the ions in the series are not yet completely understood. They have been attributed to a diverse kind of phenomena such as anion binding to proteins,2,3 change of the hydrogen bond network in water,4,5 etc. In particular, the latter has been the explanation of choice by most scientists during the last century, but this idea has been lately overturned, as several studies showed that ions only perturb their first solvation shell, with no appreciable effects further away.6-8 Hence, the presence of ions does not lead to an enhancement or a breakdown of the hydrogen-bond network in liquid water. So, instead of trying to understand the Hofmeister series on the basis of “global” changes in solvent structure induced by ionic cosolvents, it seems far more logical to consider the effects that these ions have on the local hydration of protein residues. Perchlorate, ClO4-, one of the more-destabilizing anions in the Hofmeister series, has been characterized as the strongest inductor of changes to the water spectra, showing the biggest increase in water O-H frequency. Despite the continuous use * To whom correspondence should be addressed. E-mail: ijgeneral@ gmail.com.
and theoretical importance of perchlorate solutions, in particular sodium perchlorate, there are only a few studies about them and their effects on the properties of water.9 In this paper, we do a thorough analysis of NaClO4 solutions with the intention of contributing to the elucidation of how different concentrations of the salt affect the structure of water, both globally and locally, and how this relates to the stability of proteins immersed in the solution. This paper is organized as follows: In subsection 2.1, we describe the methods and parameters used in the molecular simulations performed for this study. In the next subsection, we analyze the ion-ion, ion-water, and water-water radial distribution functions, corresponding to the simulations, followed by a discussion of the solution’s hydrogen bond structure, with a particular emphasis in the details of the first two solvation shells. Kirkwood-Buff theory of solutions is applied in subsection 2.4, where we also discuss the changes in the activity of water as the concentration of cosolvent varies. Finally, in the last section, a summary and conclusions are presented. 2. Molecular Dynamics Simulation 2.1. Methods. Several solutions of sodium perchlorate, NaClO4, in TIP3P water10 were prepared with concentrations in the interval M ) (0, 1) mol/L, with an average box volume around 611 000 Å3. This was achieved by placing 15, 40, 100, 150, 200, 249, and 297 molecules of cosolvent in about 20 000 water molecules. The simulations were performed using the AMBER 9 molecular dynamics package,11 and they were run simultaneously using a small grid computing system of about 30 computers, based on the BOINC12 infrastructure. A cutoff
10.1021/jp806269w CCC: $40.75 2008 American Chemical Society Published on Web 11/08/2008
15418 J. Phys. Chem. B, Vol. 112, No. 48, 2008
Figure 1. Cl · · · Cl radial distribution function M1 ) 0.109, M2 ) 0.272, and M3 ) 0.802 mol/L.
of 8 Å was used for the nonbonded interactions and Particle Mesh Ewald summation was employed for the electrostatic interactions. The time step for the simulations was chosen to be 2 fs. ClO4- ions were described using the force field parameters developed by Baaden et al.13 (atomic partial charges: Cl: 0.580, O1,2,3,4: -0.395, and distance Cl-Oi: 1.43 Å). Na+ ions were added as counter-ions described by the parm99 AMBER force field. Initial coordinates were constructed starting from an equilibrated box of water molecules and randomly replacing some of them by perchlorate and Na+ ions. Following the usual procedure, the system was first minimized for 5000 steepest descent and 5000 conjugate gradient steps. This was followed by a 20 ps heating to 300 K using Langevin dynamics with constant volume. Bonds involving hydrogen were constrained using the SHAKE algorithm. As a third step, the system was driven to a pressure of 1 atm, regulated by a relaxation time of 2 ps, during a 40 ps simulation. Finally, with the system equilibrated at 300 K and 1 atm, a molecular dynamics (MD) run in the (N, p, T) ensemble was performed for 1 ns, and data was recorded every 1 ps. Periodic boundary conditions were used during the entirety of this procedure. The MD simulation time was considered enough based on two facts: (1) during the nanosecond simulation, all measured quantities had a small, stable fluctuation around a central value, which was independent of time. The maximum difference between the values, along the whole simulation, was always (nHB)Ow,1. For perchlorate oxygen the
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General et al.
Figure 8. (a) Cl · · · Ow radial distribution function. (b) Cl · · · Hw radial distribution function. (c) Na+ · · · Ow radial distribution function. (d) Na+ · · · Hw radial distribution function. (e) Op · · · Ow radial distribution function. (f) Op · · · Hw radial distribution function.
situation is more complicated since water molecules do not have the full 4π stereoradians around each of the Op available for establishing HBs, because they are part of a larger molecule, ClO4-. This results in a lower counting of HBs than what one would ideally get if the oxygen was alone. To account for this deficiency, one may consider the four oxygens together, obtaining ∼2.5 in the first shell and, thus, (nHB)Op,1 > (nHB)Ow,1, as expected for a negatively charged atom. One can also readily see that, as expected, the difference between the number of HBs around a water molecule and around the ions, (∆nHB)ion,shell, gets much smaller as one goes from the first to the second solvation shell; for example, for the Na+ case, (∆nHB)Na,1 is ∼97% of (nHB)Ow,1, whereas (∆nHB)Na,2 is ∼14% of (nHB)Ow,2. The same, although not so markedly, happens when considering the perchlorate oxygens (chloride cannot be compared since there’s no information for its second shell). This
indicates that, at least from the hydrogen bonding point of view, the influence of the ions decreases rapidly with distance, in coincidence with the results from Guardia et al.16 Nevertheless, it should be noted that the effects in the second shell are still noticeable. Table 1 also gives a trend for the evolution of nHB with respect to the cosolvent concentration. In the first solvation shell of the three atoms considered, there appears to be a slight increase in the number of hydrogen bonds as the concentration increases, although this change is very small (the maximum change is less than 0.1 HBs in the range studied). On the contrary, the change observed in the second solvation shells, where nHB decreases with increasing concentration is significant, almost a change of 1 HB for the oxygen case, when going from M1 to M3. The explanation for this effect, in the case of the sodium cation, is the following:
Structure of Aqueous Sodium Perchlorate Solutions
J. Phys. Chem. B, Vol. 112, No. 48, 2008 15421
Figure 9. Water-water radial distribution functions in pure TIP3P water (solid line) and in NaClO4 solution (dashed lines), at two different concentrations M1 and M3. Panel 1: Hw · · · Hw RDF. Panel 2: Hw · · · Ow RDF. Panel 3: Ow · · · Ow RDF.
TABLE 1: Number of Hydrogen Bonds in First and (First + Second) Solvation Shells, Per Co-solvent Iona Na+
Cl
shell
1
2
1
M1 M2 M3
0.0 0.1 0.1
8.5 8.5 8.0
3.7 3.7 3.8
*Op 2
Ow
1
2
1
2
0.6 0.6 0.7
5.0 4.9 4.2
1.9
9.6
a Co-solvent molarities Mc (M1 ) 0.109, M2 ) 0.272, and M3 ) 0.802 mol/L) are shown (Cl doesn’t have a defined 2nd shell, see Figure 8). Statistical error Gsw. This will determine whether the cosolvent stabilizes the solute in its native state or destabilizes it into a denatured configuration. In particular, Asciutto et al.19 calculated νsc for a folded AP peptide in a 0.2 mol/L aqueous sodium perchlorate solution, finding its value to be positive. This implies, through the above formulas, that the folded state of the peptide becomes more stable (lower µex s ) with higher concentrations of the salt. The activity of the cosolvent, ac, can be calculated from eq 1 once acc is known. The function that fits this quantity as a function of molarity, as shown in Figure 12, is
acc ) 0.17Mc + 0.93
(5)
Integrating eq 1, taking acc as a linear function (acc ) RcMc + βc) as above, and working in terms of Mc rather than Fc (Fc ) γMc, γ ) 6.022 × 10-4), yields
acc ≡
∂(ln ac) ∂(ln γMc)
|
p,T
= RcMc + βc ⇒ ac ) K(p, T)(γMc)βc exp(RcMc) (6)
where K(p,T) is a constant of integration, function of pressure and temperature, that may be fixed by comparing to an experimental value of the activity of a cosolvent.
To obtain the activity of water, eq 6 may be inserted into the combination of the defining relation of the activity of a component in a multicomponent solution, dµi ) RT d(ln ai), with the Gibbs-Duhem relation at fixed T and p, Σini dµi ) 0 (ni being the number of moles of species i), yielding -
nc
βc
(
aw ) K(p, T)Mc nw exp -
)
nc RM nw c c
(7)
where K is a constant that should be set to 1 to satisfy the requirement aw ) 1 when Mc ) 0. Figure 13 shows a plot of this function. The activity of water is expected to decrease as the concentration of salt increases (and, thus, its effective concentration decreases), but this is not true before the molarity becomes larger than M0 ≈ 0.25 mol/L. At concentrations higher than M0, the average Gibbs energy of the water molecules in the solution is reduced relative to pure water, due to the electrostatic interaction of the ions and the dipoles of some water molecules, leading to a reduction of their activity. 3. Conclusions In this work we have characterized the structure of the aqueous sodium perchlorate solution, in terms of its RDFs, hydrogen bond network, and activity. This was achieved by means of molecular dynamics simulations for various concentrations of the cosolvent (NaClO4), ranging from Mc ) 0.081 to 1.603. We have calculated the RDFs for the ion-ion, ion-water, and water-water cases and have showed that there are some changes in their shape as concentration changes, but the position of the peaks are mostly unaffected. Regarding water, the most salient fact is the noticeable (although small) change in the second hydration shell, especially for the Ow · · · Ow RDF, as salt concentration varies. This ion-induced perturbation past the first solvation shell was already noted by Mancinelli et al.,29 who explained the broadening of the first peak in gOw•••Ow, commented before, as a result of the reduction of the distance to the second solvation shell. Although this reduction is not clearly seen here, it is important to note that the locality of salt effects should not be restricted to considerations of only the first solvation shell, but one should keep in mind the somewhat important variations in the second shell, mostly appreciable between Ow and Ow. This perturbation of the second shell also appears in the study of the HB network, where the difference between the number of HBs around a water molecule and around the Na+ cation gets much smaller as one goes from the first to the second solvation shell (97 f 14%), but this difference is not negligible.
Structure of Aqueous Sodium Perchlorate Solutions The effect of the ions past their first hydration shell is not enough to make a noticeable change in the global HB network, meaning that the total number of HB connections is not significantly affected by the ions. In this regard, one can say that the change in concentration is only a local effect. In the second part of this work, the KB theory of liquids has been applied to the aqueous sodium perchlorate solution in order to calculate the activity derivative of the cosolvent. This coefficient, along with the preferential binding calculated by Asciutto et al.,19 permitted us to establish that if an AP peptide is immersed in the studied solution, becoming the solute, and if it is in a folded state, then increasing the salt concentration will make the helix more stable. This prediction is being tested in a follow-up work.30 Acknowledgment. We thank the BOINC community for their help in the set up of the grid computing system that made this work possible. We are also grateful to Professors Montgomery Pettitt and Paul E. Smith for helpful discussions and suggestions. References and Notes (1) Hofmeister, F. Arch. Exp. Pathol. Pharmakol. 1888, 24, 247–260. (2) Hoshino, M.; Yumoto, N.; Yoshikawa, S.; Goto, Y. Protein Sci. 1997, 6, 1396–1404. (3) Goto, Y.; Aimoto, S. J. Mol. Biol. 1991, 218, 387–396. (4) Cox, W. M.; Wolfenden, J. H. Proc. R. Soc. London Ser. A 1934, 145, 486. (5) Hribar, B.; Southall, N. T.; Vlachy, V.; Dill, K. A. J. Am. Chem. Soc. 2002, 124, 12302. (6) Cappa, C. D.; Smith, J. D.; Wilson, K. R.; Messer, B. M.; Gilles, M. K.; Cohen, R. C.; Saykally, R. J. J. Phys. Chem. B 2005, 109, 7046– 7052. (7) Krekeler, C.; Delle, L. J. Phys.: Condens. Matter 2007, 19, 192101. (8) Omta, A. W.; Kropman, M. F.; Woutersen, S.; Bakker, H. J. Science 2003, 301, 347.
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