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Comment on 'Hydration and Mobility of Trehalose in Aqueous Solution' Matthias Heyden, Gerhard Schwaab, and Martina Havenith J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp508089t • Publication Date (Web): 20 Aug 2014 Downloaded from http://pubs.acs.org on August 26, 2014
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Comment on ‘Hydration and Mobility of Trehalose in Aqueous Solution’ M. Heyden1,*, G. Schwaab2 and M. Havenith2 1 Max‐Planck‐Institut für Kohlenforschung, Kaiser‐Wilhelm‐Platz 1, 45470 Mülheim an der Ruhr, Germany 2 Lehrstuhl für Physikalische Chemie II, Ruhr‐Universität Bochum, 44780 Bochum, Germany * [email protected]
In this comment, we respond to concerns regarding our interpretation of THz absorption data of carbohydrate solutions (1), raised in the context of a recent nuclear spin relaxation study of Winther et al. (2). Both studies address dynamical properties of water molecules in the hydration shell of solutes and the range of solute‐induced effects using different experimental probes. Winther et al. criticize the use of an effective continuum model, which we employed to describe the solute concentration dependence of experimentally observed THz absorption coefficients. The model (see Ref. (1) for details), describes the evolution of the volume occupied by three absorbing components, the solutes, their hydration shells and the remaining bulk water, as a function of solute concentration. The size of the hydration shell with absorption properties distinct from bulk water, described by its thickness, and its absorption coefficient are the variable fit parameters of the model. By fitting the experimental data, we deduced an increase of the THz absorption in the hydration shell of trehalose by 2% relative to bulk water and a range of this solvent induced effect of approximately 6.5 Å (1). A key feature of the fitted model is the prediction of a nonlinear change in the absorption coefficient with increasing concentration, caused by the onset of overlap between hydration shells and largely determined by their thickness. In their study, Winther et al. replot our data from Ref. (1) and suggest that deviations from a simple linear dependence are not significant. In particular, they suggest omitting the first few data points for concentrations below 0.2 mol/l, resulting in a linear concentration dependence of the remaining data points.
Fig. 1: Schematic representation of the concentration dependent THz absorption of trehalose solutions as described by the 3‐component effective medium model in Ref. (1) (solid red) using the fitted hydration shell thickness of 6.5 Å and a hydration shell absorption coefficient increased by 6% relative to pure water (instead of the measured 2% increase for improved clarity). The schematic
1
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highlights the near‐linear behavior of the model in the high concentration regime (solid black), as well as the ideal linear decrease expected in the absence of a distinguishable hydration shell (dashed black).
In Figure 1, we demonstrate several properties of the effective continuum model introduced in Ref. (3) and employed in Ref (1). The dashed curve describes the ideal linear decrease of the absorption with increasing concentration of less absorbing solutes, when no hydration shells are present. The red solid curve describes the fitted model in Ref. (1) except for an exaggerated increase of the hydration shell absorption coefficient relative to bulk for improved clarity (6% instead of 2% in Ref. (1)). It is evident that this model converges to a linear expression at high concentrations (solid black line), characterized by a y‐axis intercept at zero concentration that corresponds to the hydration shell absorption coefficient. This behavior is reproduced by the linear fit proposed by Winther et al. in Fig. S10 of Ref. (2). The linear fit of the experimental data at concentrations >0.2 mol/l produces a y‐axis intercept at roughly 425 cm‐1. However, the bulk water absorption coefficient has been determined to be 420 cm‐1 with very high precision. Thus, this linear fit deduces an increased absorption of approximately 1% in the hydration shell, which exceeds the experimental uncertainty. The experimental setup used to obtain the reported data was designed to specifically measure precise differences in absorption between the sample solution and the bulk water reference, independent of the absolute values (1) that were obtained previously (3). Hence, the linear fit by Winther et al. confirms the presence of a hydration shell with an increased absorption coefficient. The discrepancy to our result in Ref. (1) (2%) is caused by the ambiguous choice of the 0.2 mol/l concentration cutoff. Another critique raised by Winther et al. relies on the small relative change of the THz absorption in the hydration shell relative to bulk water according to our model of 2%, which they consider to be insignificant. We would like to compare this to the well‐known shifts of the infrared OH stretch frequency in different hydrogen bonding environments. Relative to the total vibrational frequency, these shifts also correspond only to a few % of change, however, no one would doubt that shifts in the OH stretch frequency of 60 cm‐1 (corresponding to a 2% change) are a clear indication of hydrogen bonding. As described previously, the transition between the nonlinear low‐concentration and the linear high‐concentration regime of the concentration dependent THz absorption is determined by the hydration shell thickness. For visual inspection of this nonlinear behavior, it is advantageous to subtract the dominant linear variation of the absorption coefficient with increasing concentration (covering a change in absorption of about 100 cm−1), which can be described by the ideal curve (dashed line in Fig. 1). This linear term is determined by the molar volume of trehalose (208.4 cm3/mol) and the absorption coefficients of pure trehalose and bulk water of 53 cm‐1 and 420 cm‐1, respectively (1). This is shown in Figure 2 for the experimental data from Ref. (1). This representation reduces the apparent signal‐to‐noise ratio, however, the nonlinear behavior can be clearly observed. Figure 2A also shows the fitted model reported in Ref. (1) with a hydration shell thickness and absorption coefficient of 2
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6.5 Å and 429 cm‐1, respectively. The shaded area visualizes the variability of the model within the reported error bars of the fit parameters (±0.9 Å and ±0.7 cm‐1, respectively; the probability distribution of the fit parameters is displayed in Fig. 2B). To quantify the quality of the fit based on the data representation in Fig. 2, we computed the coefficient of determination, adjusted for the model complexity (the number of fit parameters), which yields R2=0.61. The deviation from 1 is caused by the signal‐to‐noise ratio. However, we note that alternative representations of the data, e.g. by a naïve linear fit, result in R2=0.29. Similarly, fitting the data with our continuum model, using a fixed hydration shell thickness of 3 Å (one hydration layer), as suggested by the analysis of nuclear spin relaxation data by Winther et al. (2), yields R2=0.21. This confirms our previous analysis within the employed model.
Fig. 2: A) Deviation of the experimentally observed THz absorption of trehalose solutions (black triangles) from the expected ideal decrease with solute concentration in the absence of distinguishable hydration shells. The fitted 3‐component effective medium model with the fit parameters from Ref. (1) (solid red) is shown in the same representation with the shaded area indicating its variability due to the given error bars of the fit parameters. B) Probability distribution of the two fit parameters of the 3‐component effective medium model, the difference between the hydration shell and bulk water absorption coefficients, Δα, and the thickness of the hydration shell. Contours indicate 10% steps of increasing probability (as shown in Ref. 1).
We conclude, that the concentration dependence of the THz absorption coefficients of trehalose solutions reported in Ref. (1) exhibits a pronounced nonlinear behavior, which can be accurately described by our model. We want to point out, that the data point at zero concentration, e. g. the pure water absorption, has the highest experimental certainty due to the employed experimental setup in Ref. (1), which measures specifically the difference in absorption between the sample and a pure water reference cell. Therefore, ignoring this part of the data set is not justified and we confirm our initial hypothesis of extended solute‐induced effects on hydration water reaching beyond the first hydration shell. The analysis relies on the validity of the underlying model to describe the absorption of the solution. Its limitations and the underlying approximations have been discussed before and are described in more detail below. The model employed for the fit of the experimental data is designed for simplicity to keep the number of variable fit parameters low, while including information on the dominating parameters that determine the observed concentration dependent absorption of the solution. The leading term, the linear decrease of the absorption due to the replacement of strongly absorbing water by the weakly absorbing solutes is included as described above with fixed parameters for the absorption coefficients obtained from the pure substances (for an amorphous dry powder of trehalose the absorption coefficient of 53cm‐1 has been obtained in our laboratory1). This reduces 3
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the number of fit parameters and increases their statistical accuracy. The remaining nonlinearities are then attributed to non‐bulk water properties in a fixed size hydration shell around the solute. We define the hydration shell by a step function with respect to the distance to the solute. While this definition may seem unphysical, as a gradual convergence from perturbed water molecules in direct contact to the solute and bulk water is expected, the fixed hydration shell thickness determines the average distance over which a solute induced effect on the hydration water THz absorption can be detected with a minimal number of parameters. Other descriptions, e.g. an exponential decay from hydration shell properties to bulk water properties with increasing distance have been tested. However, while the expressions for the partial volumes of bulk and hydration shell volume become significantly more complex, the effects on the results were found to be minor. 1, 3 In addition, it may be argued that the properties of hydration water depend on solute concentration, in particular that the properties of hydration water in the overlap volume of hydration shells are distinct from non‐overlapping hydration shells. However, a nonlinear concentration dependence of the THz absorption will be dominated by the size of the hydration shell. Adding complexity to the model by introducing concentration dependent hydration water properties and additional parameters is not justified by the fittable features in the experimental data. Another component of the employed model is the distribution of the solutes in the solution. We employ a hard sphere approximation, therefore the solutes cannot penetrate each other. Attractive terms, and consequently a tendency for aggregation are not included. While this again is a simplistic approach, a test of the effect of attractive terms, e.g. a square well potential with a 1 kBT well depth and 1Å range, in the Monte Carlo simulations used to obtain the volume fractions covered by the hydration shells and bulk water in the fitted model, results in a fit with identical absorption coefficients in the hydration shell, but an even larger hydration shell thickness (7.0Å). This can be understood by the reduced coverage of the solution with hydration shells in an aggregating system, which requires a larger hydration shell size to describe the observed transition from the dilute regime (no overlap between hydration shells, large bulk volume fraction) to the high concentration regime (bulk water has been replaced by hydration water). Another crucial assumption in the fitted model is the separation of the total absorption into contributions from three individual components, the solutes, hydration shells and bulk water. The absorption spectrum (apart from a weak dependence of the index of refraction in the far‐infrared) is proportional to the fluctuations the total dipole moment of the system, which can be accessed via the total dipole moment auto‐correlation function4.
CM t M 0 M t n 2 eit CM t dt
(1)
While the dipole moment M can be separated into the sum of individual component dipoles µi (here the components are: the solute, hydration shell and bulk water), the correlation function in Eq. 1 consists of separable contributions from dipole auto 4
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correlations of the individual components and additional cross correlations between them: 3
CM t i 0 i t Ccross t i 3
3
i
ji
Ccross t i 0 j t
(2)
We followed the previously described simulation protocol1 for an isolated trehalose solute solvated by 7062 water molecules to obtain a 200ps microcanonical trajectory after previous equilibration in the isothermal‐isobaric ensemble at 300K and 1bar. The results are shown in Figure 3: The contributions of the cross terms are small compared to the direct contributions of the hydration shell and bulk water, while the contribution of the trehalose solute is close to zero in the applied simulation model. The main contribution of the cross terms results from correlated dipole fluctuations of the hydration shell and bulk water, while contributions from dipole correlations between the solute and its environment are small and tend to compensate each other. The 3‐component model does not account for cross correlations, however, this will not impact the results as long they remain constant and/or are small(as is the case here).
Fig. 3: Contribution to the total THz absorption of individual components and cross terms from an MD simulation of a solvated trehalose molecule. A) Contributions to the THz absorption obtained from dipole auto correlation functions for the trehalose molecule, water molecules within a 6.5Å hydration shell, and bulk water defined by a distances to the trehalose solute between 6.5Å and 12.0Å. The sum of contributions obtained from dipole cross correlations between the components and the total absorption is shown for comparison. B) Separate contributions to the total cross term from dipole cross‐correlation functions between the individual components.
Generally it is not surprising, that the estimated size of hydration shells depend on the fact whether single particle motions or collective motions are probed experimentally. As is clearly shown in previous simulation studies5, the vibrational modes of the water hydrogen bond network in the far‐infrared are intrinsically collective and involve correlated motion of water molecules separated by several hydrogen bonds. When probing solute‐solvent interactions via collective vibrations in the THz frequency range6, we therefore expect changes on length scales exceeding the first hydration layer. Our observations, which yielded an influence of 6‐7 Ȧ on the collective motions in the THz range from trehalose solutes has been recently confirmed by an independent measurement by Nernsting and co‐workers7. 5 ACS Paragon Plus Environment
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In agreement with our related work on protein solutions8, a long ranged (15‐20 Å) influence of protein solutes on collective hydration water picosecond dynamics has been reported recently in 2D‐IR spectroscopy experiments on crowded lysozyme solutions and in accompanying molecular dynamics simulations9. In contrast, single molecule dynamics such as rotational relaxation are observed to be effected only in the direct vicinity of the solute. This has been found by experiments as reported by Winther et al.2, and has been also predicted by simulations10. Solute‐induced effects on hydration water properties, and the assignment of hydration shells therefore depend on the employed observable, e.g. static and dynamic properties, as well as on the fact whether single molecule or collective properties are probed. Acknowledgement: This work is supported by the Cluster of Excellence RESOLV (EXC 1069) funded by the Deutsche Forschungsgemeinschaft (DFG). References (1) Heyden, M.; Bründermann, E.; Heugen, U.; Niehues, G.; Leitner, D. M.; Havenith, M. Long‐range influence of carbohydrates on the solvation dynamics of water‐ answers from terahertz absorption measurements and molecular modeling simulations. J. Am. Chem. Soc. 2008, 130, 5773‐5779. (2) Winther, L. R.; Qvist, J.; Halle, B. Hydration and mobility of trehalose in aqueous solution. J. Phys. Chem. B 2012, 116, 9196‐9207. (3) Heugen, U.; Schwaab, G.; Bründermann, E.; Heyden, M.; Yu, X.; Leitner, D. M.; Havenith, M. Solute‐induced retardation of water dynamics probed directly by terahertz spectroscopy. Proc. Natl. Acad. Sci. U. S. A. 2006, 103, 12301‐12306. (4) Ramirez, R.; Lopez‐Ciudad, T.; Kumar, P.; Marx, D. Quantum corrections to classical time‐correlation functions: Hydrogen bonding and anharmonic floppy modes. J. Chem. Phys. 2004, 121, 3973‐3983. (5) Heyden, M.; Sun, J.; Funkner, S.; Mathias, G.; Forbert, H.; Havenith, M.; Marx, D. Dissecting the THz spectrum of liquid water from first principles via correlations in time and space. Proc. Natl. Acad. Sci. U. S. A. 2010, 107, 12068‐ 12073. (6) Heyden, M.; Tobias, D. J. Spatial dependence of protein‐water collective hydrogen‐bond dynamics. Phys. Rev. Lett. 2013, 111, 218101. (7) Sajadi, M.; Berndt, F.; Richter, C.; Gerecke, M.; Mahrwald, R.; Ernsting, N. P. Observing the hydration layer of trehalose with a linked molecular terahertz probe. J. Phys. Chem. Lett. 2014, 5, 1845‐1849. (8) Ebbinghaus, S.; Kim, S. J.; Heyden, M.; Yu, X.; Heugen, U.; Gruebele, M.; Leitner, D. M.; Havenith, M. An extended dynamical hydration shell around proteins. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 20749‐20752. (9) King, J. T.; Arthur, E. J.; Brooks, C. L.; Kubarych, K. J. Crowding Induced Collective hydration of biological macromolecules over extended distances. J. Am. Chem. Soc. 2014, 136, 188‐194.
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(10) Bizzarri, A. R.; Cannistraro, S. Molecular dynamics of water at the protein‐ solvent interface. J. Phys. Chem. B 2002, 106, 6617‐6633.
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Comment
Comment on 'Hydration and Mobility of Trehalose in Aqueous Solution' Matthias Heyden, Gerhard Schwaab, and Martina Havenith J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp508089t • Publication Date (Web): 20 Aug 2014 Downloaded from http://pubs.acs.org on August 26, 2014
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
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Comment on ‘Hydration and Mobility of Trehalose in Aqueous Solution’ M. Heyden1,*, G. Schwaab2 and M. Havenith2 1 Max‐Planck‐Institut für Kohlenforschung, Kaiser‐Wilhelm‐Platz 1, 45470 Mülheim an der Ruhr, Germany 2 Lehrstuhl für Physikalische Chemie II, Ruhr‐Universität Bochum, 44780 Bochum, Germany * [email protected]
In this comment, we respond to concerns regarding our interpretation of THz absorption data of carbohydrate solutions (1), raised in the context of a recent nuclear spin relaxation study of Winther et al. (2). Both studies address dynamical properties of water molecules in the hydration shell of solutes and the range of solute‐induced effects using different experimental probes. Winther et al. criticize the use of an effective continuum model, which we employed to describe the solute concentration dependence of experimentally observed THz absorption coefficients. The model (see Ref. (1) for details), describes the evolution of the volume occupied by three absorbing components, the solutes, their hydration shells and the remaining bulk water, as a function of solute concentration. The size of the hydration shell with absorption properties distinct from bulk water, described by its thickness, and its absorption coefficient are the variable fit parameters of the model. By fitting the experimental data, we deduced an increase of the THz absorption in the hydration shell of trehalose by 2% relative to bulk water and a range of this solvent induced effect of approximately 6.5 Å (1). A key feature of the fitted model is the prediction of a nonlinear change in the absorption coefficient with increasing concentration, caused by the onset of overlap between hydration shells and largely determined by their thickness. In their study, Winther et al. replot our data from Ref. (1) and suggest that deviations from a simple linear dependence are not significant. In particular, they suggest omitting the first few data points for concentrations below 0.2 mol/l, resulting in a linear concentration dependence of the remaining data points.
Fig. 1: Schematic representation of the concentration dependent THz absorption of trehalose solutions as described by the 3‐component effective medium model in Ref. (1) (solid red) using the fitted hydration shell thickness of 6.5 Å and a hydration shell absorption coefficient increased by 6% relative to pure water (instead of the measured 2% increase for improved clarity). The schematic
1
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highlights the near‐linear behavior of the model in the high concentration regime (solid black), as well as the ideal linear decrease expected in the absence of a distinguishable hydration shell (dashed black).
In Figure 1, we demonstrate several properties of the effective continuum model introduced in Ref. (3) and employed in Ref (1). The dashed curve describes the ideal linear decrease of the absorption with increasing concentration of less absorbing solutes, when no hydration shells are present. The red solid curve describes the fitted model in Ref. (1) except for an exaggerated increase of the hydration shell absorption coefficient relative to bulk for improved clarity (6% instead of 2% in Ref. (1)). It is evident that this model converges to a linear expression at high concentrations (solid black line), characterized by a y‐axis intercept at zero concentration that corresponds to the hydration shell absorption coefficient. This behavior is reproduced by the linear fit proposed by Winther et al. in Fig. S10 of Ref. (2). The linear fit of the experimental data at concentrations >0.2 mol/l produces a y‐axis intercept at roughly 425 cm‐1. However, the bulk water absorption coefficient has been determined to be 420 cm‐1 with very high precision. Thus, this linear fit deduces an increased absorption of approximately 1% in the hydration shell, which exceeds the experimental uncertainty. The experimental setup used to obtain the reported data was designed to specifically measure precise differences in absorption between the sample solution and the bulk water reference, independent of the absolute values (1) that were obtained previously (3). Hence, the linear fit by Winther et al. confirms the presence of a hydration shell with an increased absorption coefficient. The discrepancy to our result in Ref. (1) (2%) is caused by the ambiguous choice of the 0.2 mol/l concentration cutoff. Another critique raised by Winther et al. relies on the small relative change of the THz absorption in the hydration shell relative to bulk water according to our model of 2%, which they consider to be insignificant. We would like to compare this to the well‐known shifts of the infrared OH stretch frequency in different hydrogen bonding environments. Relative to the total vibrational frequency, these shifts also correspond only to a few % of change, however, no one would doubt that shifts in the OH stretch frequency of 60 cm‐1 (corresponding to a 2% change) are a clear indication of hydrogen bonding. As described previously, the transition between the nonlinear low‐concentration and the linear high‐concentration regime of the concentration dependent THz absorption is determined by the hydration shell thickness. For visual inspection of this nonlinear behavior, it is advantageous to subtract the dominant linear variation of the absorption coefficient with increasing concentration (covering a change in absorption of about 100 cm−1), which can be described by the ideal curve (dashed line in Fig. 1). This linear term is determined by the molar volume of trehalose (208.4 cm3/mol) and the absorption coefficients of pure trehalose and bulk water of 53 cm‐1 and 420 cm‐1, respectively (1). This is shown in Figure 2 for the experimental data from Ref. (1). This representation reduces the apparent signal‐to‐noise ratio, however, the nonlinear behavior can be clearly observed. Figure 2A also shows the fitted model reported in Ref. (1) with a hydration shell thickness and absorption coefficient of 2
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6.5 Å and 429 cm‐1, respectively. The shaded area visualizes the variability of the model within the reported error bars of the fit parameters (±0.9 Å and ±0.7 cm‐1, respectively; the probability distribution of the fit parameters is displayed in Fig. 2B). To quantify the quality of the fit based on the data representation in Fig. 2, we computed the coefficient of determination, adjusted for the model complexity (the number of fit parameters), which yields R2=0.61. The deviation from 1 is caused by the signal‐to‐noise ratio. However, we note that alternative representations of the data, e.g. by a naïve linear fit, result in R2=0.29. Similarly, fitting the data with our continuum model, using a fixed hydration shell thickness of 3 Å (one hydration layer), as suggested by the analysis of nuclear spin relaxation data by Winther et al. (2), yields R2=0.21. This confirms our previous analysis within the employed model.
Fig. 2: A) Deviation of the experimentally observed THz absorption of trehalose solutions (black triangles) from the expected ideal decrease with solute concentration in the absence of distinguishable hydration shells. The fitted 3‐component effective medium model with the fit parameters from Ref. (1) (solid red) is shown in the same representation with the shaded area indicating its variability due to the given error bars of the fit parameters. B) Probability distribution of the two fit parameters of the 3‐component effective medium model, the difference between the hydration shell and bulk water absorption coefficients, Δα, and the thickness of the hydration shell. Contours indicate 10% steps of increasing probability (as shown in Ref. 1).
We conclude, that the concentration dependence of the THz absorption coefficients of trehalose solutions reported in Ref. (1) exhibits a pronounced nonlinear behavior, which can be accurately described by our model. We want to point out, that the data point at zero concentration, e. g. the pure water absorption, has the highest experimental certainty due to the employed experimental setup in Ref. (1), which measures specifically the difference in absorption between the sample and a pure water reference cell. Therefore, ignoring this part of the data set is not justified and we confirm our initial hypothesis of extended solute‐induced effects on hydration water reaching beyond the first hydration shell. The analysis relies on the validity of the underlying model to describe the absorption of the solution. Its limitations and the underlying approximations have been discussed before and are described in more detail below. The model employed for the fit of the experimental data is designed for simplicity to keep the number of variable fit parameters low, while including information on the dominating parameters that determine the observed concentration dependent absorption of the solution. The leading term, the linear decrease of the absorption due to the replacement of strongly absorbing water by the weakly absorbing solutes is included as described above with fixed parameters for the absorption coefficients obtained from the pure substances (for an amorphous dry powder of trehalose the absorption coefficient of 53cm‐1 has been obtained in our laboratory1). This reduces 3
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the number of fit parameters and increases their statistical accuracy. The remaining nonlinearities are then attributed to non‐bulk water properties in a fixed size hydration shell around the solute. We define the hydration shell by a step function with respect to the distance to the solute. While this definition may seem unphysical, as a gradual convergence from perturbed water molecules in direct contact to the solute and bulk water is expected, the fixed hydration shell thickness determines the average distance over which a solute induced effect on the hydration water THz absorption can be detected with a minimal number of parameters. Other descriptions, e.g. an exponential decay from hydration shell properties to bulk water properties with increasing distance have been tested. However, while the expressions for the partial volumes of bulk and hydration shell volume become significantly more complex, the effects on the results were found to be minor. 1, 3 In addition, it may be argued that the properties of hydration water depend on solute concentration, in particular that the properties of hydration water in the overlap volume of hydration shells are distinct from non‐overlapping hydration shells. However, a nonlinear concentration dependence of the THz absorption will be dominated by the size of the hydration shell. Adding complexity to the model by introducing concentration dependent hydration water properties and additional parameters is not justified by the fittable features in the experimental data. Another component of the employed model is the distribution of the solutes in the solution. We employ a hard sphere approximation, therefore the solutes cannot penetrate each other. Attractive terms, and consequently a tendency for aggregation are not included. While this again is a simplistic approach, a test of the effect of attractive terms, e.g. a square well potential with a 1 kBT well depth and 1Å range, in the Monte Carlo simulations used to obtain the volume fractions covered by the hydration shells and bulk water in the fitted model, results in a fit with identical absorption coefficients in the hydration shell, but an even larger hydration shell thickness (7.0Å). This can be understood by the reduced coverage of the solution with hydration shells in an aggregating system, which requires a larger hydration shell size to describe the observed transition from the dilute regime (no overlap between hydration shells, large bulk volume fraction) to the high concentration regime (bulk water has been replaced by hydration water). Another crucial assumption in the fitted model is the separation of the total absorption into contributions from three individual components, the solutes, hydration shells and bulk water. The absorption spectrum (apart from a weak dependence of the index of refraction in the far‐infrared) is proportional to the fluctuations the total dipole moment of the system, which can be accessed via the total dipole moment auto‐correlation function4.
CM t M 0 M t n 2 eit CM t dt
(1)
While the dipole moment M can be separated into the sum of individual component dipoles µi (here the components are: the solute, hydration shell and bulk water), the correlation function in Eq. 1 consists of separable contributions from dipole auto 4
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correlations of the individual components and additional cross correlations between them: 3
CM t i 0 i t Ccross t i 3
3
i
ji
Ccross t i 0 j t
(2)
We followed the previously described simulation protocol1 for an isolated trehalose solute solvated by 7062 water molecules to obtain a 200ps microcanonical trajectory after previous equilibration in the isothermal‐isobaric ensemble at 300K and 1bar. The results are shown in Figure 3: The contributions of the cross terms are small compared to the direct contributions of the hydration shell and bulk water, while the contribution of the trehalose solute is close to zero in the applied simulation model. The main contribution of the cross terms results from correlated dipole fluctuations of the hydration shell and bulk water, while contributions from dipole correlations between the solute and its environment are small and tend to compensate each other. The 3‐component model does not account for cross correlations, however, this will not impact the results as long they remain constant and/or are small(as is the case here).
Fig. 3: Contribution to the total THz absorption of individual components and cross terms from an MD simulation of a solvated trehalose molecule. A) Contributions to the THz absorption obtained from dipole auto correlation functions for the trehalose molecule, water molecules within a 6.5Å hydration shell, and bulk water defined by a distances to the trehalose solute between 6.5Å and 12.0Å. The sum of contributions obtained from dipole cross correlations between the components and the total absorption is shown for comparison. B) Separate contributions to the total cross term from dipole cross‐correlation functions between the individual components.
Generally it is not surprising, that the estimated size of hydration shells depend on the fact whether single particle motions or collective motions are probed experimentally. As is clearly shown in previous simulation studies5, the vibrational modes of the water hydrogen bond network in the far‐infrared are intrinsically collective and involve correlated motion of water molecules separated by several hydrogen bonds. When probing solute‐solvent interactions via collective vibrations in the THz frequency range6, we therefore expect changes on length scales exceeding the first hydration layer. Our observations, which yielded an influence of 6‐7 Ȧ on the collective motions in the THz range from trehalose solutes has been recently confirmed by an independent measurement by Nernsting and co‐workers7. 5 ACS Paragon Plus Environment
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In agreement with our related work on protein solutions8, a long ranged (15‐20 Å) influence of protein solutes on collective hydration water picosecond dynamics has been reported recently in 2D‐IR spectroscopy experiments on crowded lysozyme solutions and in accompanying molecular dynamics simulations9. In contrast, single molecule dynamics such as rotational relaxation are observed to be effected only in the direct vicinity of the solute. This has been found by experiments as reported by Winther et al.2, and has been also predicted by simulations10. Solute‐induced effects on hydration water properties, and the assignment of hydration shells therefore depend on the employed observable, e.g. static and dynamic properties, as well as on the fact whether single molecule or collective properties are probed. Acknowledgement: This work is supported by the Cluster of Excellence RESOLV (EXC 1069) funded by the Deutsche Forschungsgemeinschaft (DFG). References (1) Heyden, M.; Bründermann, E.; Heugen, U.; Niehues, G.; Leitner, D. M.; Havenith, M. Long‐range influence of carbohydrates on the solvation dynamics of water‐ answers from terahertz absorption measurements and molecular modeling simulations. J. Am. Chem. Soc. 2008, 130, 5773‐5779. (2) Winther, L. R.; Qvist, J.; Halle, B. Hydration and mobility of trehalose in aqueous solution. J. Phys. Chem. B 2012, 116, 9196‐9207. (3) Heugen, U.; Schwaab, G.; Bründermann, E.; Heyden, M.; Yu, X.; Leitner, D. M.; Havenith, M. Solute‐induced retardation of water dynamics probed directly by terahertz spectroscopy. Proc. Natl. Acad. Sci. U. S. A. 2006, 103, 12301‐12306. (4) Ramirez, R.; Lopez‐Ciudad, T.; Kumar, P.; Marx, D. Quantum corrections to classical time‐correlation functions: Hydrogen bonding and anharmonic floppy modes. J. Chem. Phys. 2004, 121, 3973‐3983. (5) Heyden, M.; Sun, J.; Funkner, S.; Mathias, G.; Forbert, H.; Havenith, M.; Marx, D. Dissecting the THz spectrum of liquid water from first principles via correlations in time and space. Proc. Natl. Acad. Sci. U. S. A. 2010, 107, 12068‐ 12073. (6) Heyden, M.; Tobias, D. J. Spatial dependence of protein‐water collective hydrogen‐bond dynamics. Phys. Rev. Lett. 2013, 111, 218101. (7) Sajadi, M.; Berndt, F.; Richter, C.; Gerecke, M.; Mahrwald, R.; Ernsting, N. P. Observing the hydration layer of trehalose with a linked molecular terahertz probe. J. Phys. Chem. Lett. 2014, 5, 1845‐1849. (8) Ebbinghaus, S.; Kim, S. J.; Heyden, M.; Yu, X.; Heugen, U.; Gruebele, M.; Leitner, D. M.; Havenith, M. An extended dynamical hydration shell around proteins. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 20749‐20752. (9) King, J. T.; Arthur, E. J.; Brooks, C. L.; Kubarych, K. J. Crowding Induced Collective hydration of biological macromolecules over extended distances. J. Am. Chem. Soc. 2014, 136, 188‐194.
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(10) Bizzarri, A. R.; Cannistraro, S. Molecular dynamics of water at the protein‐ solvent interface. J. Phys. Chem. B 2002, 106, 6617‐6633.
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