Effective Fragment Potential Study of the Influence ... - ACS Publications

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Effective Fragment Potential Study of the Influence of Hydration on the Vibrational Spectrum of Glucose Christian Vran
cic* and Wolfgang Petrich Kirchhoff Institute for Physics, University of Heidelberg, Heidelberg, Germany ABSTRACT: The standard agent glucose has been the subject of numerous experimental and theoretical studies, especially in the aqueous environments which are present in most biochemical processes. The impact of the solvation process on the vibrational spectra of glucose in the mid-infrared region is investigated in this work. The computational study focused both on the variation of the number of surrounding water molecules from 0 to 229 and on the number of single spectra included in the iterative averaging process. The calculations consisted of a combination of force field methods for the sampling of the configuration space and density functional theory for further geometry optimizations. Effective fragment potentials (EFPs) were employed for the description of the solvent as a compromise between accuracy and computational complexity. A correlation between the experimental data and the number of surrounding water molecules could not be observed for an averaging over a small set of computed single spectra. The inclusion of an additionial polarizable continuum model (PCM) also showed no further impact. However, an increase in the number of underlying single spectra in the averaging process increased the correlation between simulations and the experiment substantially. Especially for 18 explicit EFP water molecules, an inclusion of 80 single spectra delivered a Pearson’s correlation coefficient r ≈ 0.94.

’ INTRODUCTION The monosaccharide glucose is the most important carbohydrate in biochemical and biological processes and has been the object of numerous experimental and computational studies. Various optical approaches have been implemented to monitor glucose in the fluid phase in vitro and ex vivo.1
5 Furthermore, the quantification of glucose and other analytes in dry films of serum has been reported to deliver predictions of appropriate accuracy.6 All these examples make use of the known high absorption of glucose in the mid-infrared (MIR) spectral region at wavelengths around 10 μm which arises from strong vibrations of the glucose molecule. However, in experimental studies the vibrational spectra of glucose molecules embedded in a matrix are investigated, such as a slightly hydrated protein matrix, serum, plasma, or simply water. In the light of molecular modeling of an ideal, isolated glucose molecule, there remains a gap between theory and experiment in terms of this matrix. Water marks the simplest case of such a matrix, and so far, it has remained unclear to a certain extent if and how exactly the vibrational properties of glucose change during the hydration process. In aqueous solution, the molecule exists almost solely in a cyclic form as pyranose. A snapshot of an isolated β-D-glucopyranose molecule is shown in Figure 1. It features two anomeric forms, α and β, depending on the orientation of the C1
O1 bond which can be axial (α) or equatorial (β) to the puckered six-membered ring. Experiments showed a ratio of the concentration of α versus β form at room temperature in solution of about 36:64.7 Another isomerism of the molecule can be found at the O6
C6
C5
O5 torsion r 2011 American Chemical Society

angle, the so-called ω angle, with three stable staggered rotamers for ω = (60
and 180
(gauche
trans [G+], gauche
gauche [G
], and trans
gauche [T]). While the population of the T rotamer in aqueous solution seems negligible, the population of the other two rotamers in solution is approximately equal as shown both experimentally8,9 and by calculations.10,11 The computational study of the hydration process of glucose has been performed by force field methods, ab initio calculations, and density functional theory (DFT) analysis.12
14 These studies often focused on the conformational changes triggered by the solvation process. As the number of atoms of the analyzed system can get very high for a precise prediction, the choice of the underlying descriptive method and the level of theory are always a compromise between accuracy of the calculations and its computational complexity. One way to cope with this circumstance is the reduction of the problem to calculations on water molecules at specific sites of the glucose molecule, e.g., with a maximum number of hydrogen bonds between solvent and solute12 or simply by starting with only a few explicit water molecules. Also, the possibility of describing the solvent as a continuous medium,15 e.g., with the Onsager16 or polarizable continuum model (PCM),17 together with quantum mechanical (QM) modeling methods describing the solute, has been reported.13,14 However, while bulk properties of the surrounding medium are well described by these implicit models, they lack the Received: July 28, 2011 Revised: September 30, 2011 Published: September 30, 2011 12373

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Figure 1. Isolated β-D-glucopyranose molecule with the conventional numbering of non-hydrogen atoms. C, carbon; O, oxygen.

inclusion of important directed electronic interactions on a molecular level between solvent and solute. They therefore might be not be sufficient to describe the actual behavior of the system which could be important for a vibrational analysis. The conformation of glucose has been studied by force field methods in vacuo18,19 as well as dynamically in solution.20 DFT has proven to deliver good results, e.g., regarding molecular dynamics11,21
24 or in the conformational analysis of glucose.25 Further DFT studies analyzed the geometry of glucose in an environment of five water molecules.26 Spectral analysis has been pursued by means of computation of 1H and 13C NMR spectra.27 IR spectra of glucose have been computed by vibrational selfconsistent field (VSCF) methods28 and on a DFT level of theory, both as isolated molecules29 and with a small number of water molecules at distinct sites.12 A promising approach for the analysis of solvation processes is the theory of effective fragment potentials (EFPs).30
32 Here, solvent molecules are treated as rigid bodies and considered as decoupled from the solute with additional contributions to the total energy of the system. In this way EFPs may substantially reduce the complexity of the problem. This approach was applied, for instance, to the analysis of cluster formation in aqueous solutions33 or the analysis of the equilibrium of glycine in solution.34 Further, conformational and energetic analysis of alanine combined with different QM methods has delivered good results compared to experimental data.35,36 Also, electronic spectra of coumarin in solution37 have been calculated with EFPs as well as structural and vibrational properties of beryllium aqua and hydroxo complexes.38 The work presented here has the goal of elucidating the potential of EFPs as a tool to compute vibrational spectra of glucose in water. The number of EFP water molecules was taken as a parameter to obtain stable spectra. Moreover, the variance related to a glucose
water configuration with an identical number of water molecules was analyzed. A detailed knowledge of the solvation process might help in understanding various impacts, for instance that of residual moisture in dry films on the vibrational spectrum, and might lead to an improvement in optical sensing techniques. The simulations were based on a sampling of stable energy minima in the configuration space by means of force field methods. Further geometric optimizations and calculations of vibrational spectra were computed on the basis of DFT with the help of EFPs to model the solution and its interactions with the solute on a molecular level. Computed vibrational spectra were compared to experimental data obtained from Fourier transform infrared (FTIR) spectroscopy employing a flow-through cuvette for the analysis of aqueous solutions.

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’ METHODS Starting geometries for the G+ and G
rotamers of α- and β-D-glucose were obtained from crystal structures,39,40 incorporating four glucose conformers in the simulations. For each glucose conformer
water complex, random initial geometry configurations were created with the software package Packmol (version 1.1).41 Afterward, a rigid body optimization was performed with the molecular modeling software package TINKER (version 5.1)42 where the internal geometries of glucose and water molecules remained untouched. In this optimization step, an expanded OPLS all-atom force field for carbohydrates43 was incorporated. A total of 10 000 randomly generated geometries were energetically analyzed for each glucose conformer and distinct number of water molecules. The five configurations with the lowest energies were then selected for the DFT calculations, resulting in 20 geometries per glucose
N water molecule complex (N = 2, 4, 8, 12, 18, 24, 32, 40, 52, 100, 151 and 229). For reasons which will become clear in the Results section, an additional analysis was performed in the case of N = 18: in this extended analysis the 20 lowest energies per conformer configuration were selected, which led to 80 spectra in total. Note that, for isolated glucose molecules without any solvent molecules, the force field optimization steps were skipped and the DFT optimization was applied directly. These rigidly optimized glucose
water configurations were then further optimized by using DFT with the hybrid B3LYP (Becke three-term correlation44,45 and Lee
Yang
Parr exchange46) functional. Following a first geometry optimization with the 6-31+G(d) basis set, the final optimized geometry was obtained using the 6-311++G(d,p) basis set. After this optimization step, the internal structure of the solute and the arrangement of the solvent molecules were fully optimized. Vibrational frequencies were then calculated in the double harmonic approximation. This approximation, along with others applied in the QM calculations, necessitated scaling of the wavenumber after calculation of the spectra. The variation of these scaling factors has been studied extensively.47
49 In this study, they are used as fitting parameters for the comparison with the experiment. The weighted average spectrum was then calculated with a ratio of α and β forms of 36:64 while equally weighting both investigated rotamers. In either case, all spectra were convolved with a Gaussian function with a full width at half-maximum (FWHM) of 10 cm
1. The optimization and calculation process was repeated with identical starting geometries incorporating the polarizable continuum model (PCM) for configurations with 2, 4, 8, 12, and 18 water molecules. In the DFT-based optimization steps and in the calculation of the vibrational frequencies, all water molecules were treated with frozen internal coordinates using effective fragment potentials.32,50 EFPs were originally introduced for the treatment of cluster formation of water (EFP1) and the quantum-mechanical treatment of solutes. The solvent was initially based on a formulation using Hartree
Fock theory (EFP1/HF) which was later extended to DFT-based EFPs (EFP1/DFT).51 Finally, a general implemention of the EFP method (EFP2) has been introduced for the treatment of any solvent.32 In the theory of EFPs, the total Hamiltonian Htotal is split into a QM part HQM and a potential V: Htotal ¼ HQM þ V In this study, the QM part includes the glucose molecule described by the level of theory mentioned above and the water molecules are described as fragment potentials V with one-electron 12374

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The normalized root-mean-square deviation (NRMSD) can then be derived as NRMSDðSref , ~SÞ ¼

RMSDðSref , ~SÞ smax
smin

where smax and smin are the maximum and minimum values in the reference spectrum.

Figure 2. Snapshot of an optimized geometry of glucose with 52 EFP1 water molecules (created with the GAMESS visualization software MacMolPlt).54

contributions to Htotal. These include electrostatic interactions and polarization or induction of solvent molecules with both each other and the QM part of the system and, furthermore, a remaining term that incorporates exchange repulsion, charge transfer, and short-range correlation contributions. All DFT and vibrational frequency calculations were performed using the GAMESS (US)52,53 electronic structure code. The IR spectra in aqueous phase were recorded with an FTIR spectrometer (TENSOR 27, Bruker Optik GmbH, Ettlingen, Germany) equipped with a DLaTGS detector. This unit was combined with a CaF2 transmission cell (AquaSpec, Bruker Optik GmbH) offering an optical path length of approximately 7 μm. The solution was prepared by adding glucose (Merck KGaA, Darmstadt, Germany) to deionized water at a concentration of 500 mg/dL. All spectra were recorded in the wavenumber range 985
1200 cm
1 and averaged over 100 scans with a resolution of 4 cm
1. Blackman-Harris three-term apodization was used as well as a zero-filling factor of 2. The Pearson product-moment correlation coefficient r between two spectra ~S(v) and ^S(v) can be calculated as follows:

∑~Si^Si
nð∑~Si Þð∑^Si Þ 1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ¼ s  ffi 1 1 2 2 ~Si
ð∑~Si Þ2 ^Si
ð∑^Si Þ2 n n

∑

∑

where the sums denote the summing of all wavenumber intervals from i = 1 to i = n with n being the total number of 107 intervals obtained experimentally. The root-mean-square deviation (RMSD) between a reference spectrum Sref(v) and a second spectrum ~S(v) consisting of n data points each is defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ~ 2 ðSref i
Si Þ RMSDðSref , ~SÞ ¼ n

∑

with Si being the ith data point in the spectrum.

’ RESULTS An optimized geometry of a glucose molecule surrounded by 52 EFP1 water molecules can be found in Figure 2. Figure 3 shows the development of MIR spectra for N EFP1 water molecules (N = 0, ..., 229) included in the simulation without the inclusion of PCM. The spectrum for N = 0 contains four single spectra (one for each conformer). All other averaged spectra in the diagram consist of 20 single spectra. The spectra in the plot are offset by 1 a.u. (arbitrary unit) in intensity for a better visualization. No further scaling of wavenumber or intensity was applied. The average difference per conformer and water configuration of the total energy of the system amounts to 5.2 kcal/mol. It can be seen that the isolated glucose molecule has intensity maxima for the three strongest vibrations at 1050, 1076, and 1108 cm
1. This changes substantially when adding explicit water molecules to the optimization process. Both a shift of the resonance frequencies and a decrease of the average intensities can be observed. This trend continues throughout the increase of the number of water molecules until strong maxima for N = 229 water molecules in Figure 3 can no longer be adequately identified. An exceptional behavior can be found for N = 151 water molecules, where strong vibrational bands can be seen around 1052 cm
1. Pronounced modes close to this wavenumber are existent in the majority of the underlying single spectra. As mentioned previously, each conformer configuration is fully optimized five times. The correlation within a conformational group of spectra with the same number of water molecules can be estimated by calculating Pearson’s correlation coefficient r for each single spectrum with respect to the four other spectra of the same conformer. These results can then be averaged over all four conformers. This estimated mean correlation coefficient has values between 0.187 and 0.455 with no systematic dependence on the number of water molecules recognizable. A more meaningful criterion for further analysis of a specific glucose
water configuration was established by analyzing the number of hydrogen bonds between solute and solvent. The criteria for the existence of such a bond OD
H 3 3 3 OA, with OD and OA being the donor and acceptor oxygen atoms, respectively, were distances d(OD
H) e 1.5 Å and d(H 3 3 3 OA) e 2.4 Å as well as an angle — (ODHOA) > 120
.21 The number of hydrogen bonds as a function of the included water molecules is shown in Figure 4. While the number of hydrogen bonds increases for small numbers of water molecules, no further increase is observed for 18 or more EFP1 water molecules. Note that the underlying glucose conformer does not seem to impact this behavior. In a further investigation the number M of underlying single spectra was increased from 20 to 80 for a fixed number of water molecules (N = 18). Figure 5 depicts the resulting average spectra as a function of the number of single spectra. The order of selection of the spectra was randomized subject to the 12375

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Figure 4. Number of hydrogen bonds after final optimization for all four analyzed glucose conformers (containing five spectra each) as a function of the number of EFP1 water molecules.

1091, and 1116 cm
1 shift to 1045, 1057, 1072, and 1093 cm
1 for an averaging over M = 80 spectra. The correlation between single spectra of the same conformer remained very small with r = 0.248 ( 0.224 for all M = 80 spectra.

Figure 3. Computed averaged MIR spectra of configurations containing 1 glucose and N EFP1 water molecules (N = 0, ..., 229). For clarity, each spectrum is artificially offset by 1 a.u.

constraint that each addition step must include one spectrum per conformer. Again, a smoothing of the spectra as well as a broadening of the resonant peaks can be observed for large numbers of single spectra. The main maxima for M = 8 single spectra at 1049, 1066,

’ DISCUSSION Effective fragment potentials have been proven to deliver a computational method for the study of MIR spectra of glucose in a hydrated environment. Yet it remains unclear if a high correlation with experimental IR spectra can be established for different optimized starting conditions with an increase of the number of explicitly modeled water molecules only. However, it could be shown that, up to a number of 229 EFP1 water molecules, the average correlation among spectra of the same configuration stays very low. This statement also holds for an increased number of repetitions, i.e., with random geometric and therefore different energetic starting conditions of the optimization process. A comparison with experimental data was obtained by calculating Pearson’s correlation coefficient r within all possible subgroups consisting of four spectra (one for each conformer) out of the pool of 20 spectra per water configuration. A scaling of the wavenumber served as the only fitting parameter, as explained under Methods, with an average value of 0.981 ( 0.006. The results can be found in Figure 6, which also includes the correlation of the runs including PCM. A comparison with an analysis where the coefficients were determined by randomly picking four spectra (whereby each spectrum was included only once) showed no significant difference. The data clearly indicate that the correlation to the experiment does not systematically depend on the number of water molecules involved. The relatively large margin of error can be explained by the small correlation among computational spectra. No impact of the inclusion of PCM into the optimization process is evident. Only the large difference in the correlation for the inclusion of two water molecules with and without a continuous model may be a hint that in this case two molecules do not suffice for an appropriate representation of the solvent. The extended simulations with N = 18 water molecules and an increased number of repetitions were processed in a slightly different manner in order to analyze the impact of comparing a larger number of averaged spectra instead of sets of four spectra. 12376

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Figure 6. Pearson’s correlation coefficient of simulated MIR spectra compared to experimental data as a function of the number of water molecules involved for runs with and without the inclusion of PCM.

Figure 7. Averaged Pearson’s correlation coefficient as a function of the number of single spectra included. The inset shows the Pearson correlation coefficients of subsets of all 80 spectra for an averaging over M = 4, ..., 24 spectra. Figure 5. Computed averaged MIR spectra of configurations consisting of 1 glucose and 18 EFP1 water molecules as a function of the number of single spectra included (M = 8, ..., 80). Each averaged spectrum contains an artificial relative intensity offset of 0.75 a.u. for better graphic representation.

Figure 7 shows the averaged Pearson’s correlation coefficient as a function of the number of single spectra included in the averaging process. If this number was smaller than 40, the full set was randomly divided into subsets and r was computed for each subset and averaged afterward. In the inset of Figure 7 the single coefficients of these subsets can be found. An increase of the average Pearson’s correlation coefficient can be observed which levels off (for M g 40) to a value of r ≈ 0.94. In turn, the correlation between averaged spectra and the experiment increases with an increasing number of spectra included in the preliminary averaging process for M < 40. The comparison between the experiment and the averaged spectra with the largest set of underlying single spectra can be found in Figure 8.

Both the scaling of the wavenumber and an intensity offset were set as parameters while minimizing the NRMSD between experimental and simulated spectra. It is of note that both criteria, Pearson’s correlation coefficient and the NRMSD, delivered identical results for the wavenumber scaling factor as a free parameter with a value of 0.987 for the data illustrated in Figure 8. A correlation factor of 0.941 and an NRMSD of 9.5% reflect a very good agreement between experiment and simulation. The presented results suggest that a larger number of reruns, with alternating starting conditions, seems more favorable than an increase of the number of water molecules. This finding also implies a very high spectral variation among glucose
water configurations for different optimization starting conditions. Future research of the impact of solvation processes, both on other molecules and with alternative solvents or matrix molecules, on vibrational spectra should confirm the results. Studies of other physical effects such as electronic excitations might also be helpful for a validation. Further, it would be interesting to 12377

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Figure 8. Comparison of an experimental MIR spectrum of aqueous glucose solution in a flow-through cuvette versus a simulated spectrum of 1 glucose and N = 18 EFP1 water molecules consisting of M = 80 single spectra.

investigate a tolerable compromise between the number of solvent molecules involved and the correlation with the experiment because the number of hydrogen bonds might not indicate the best possible ratio for the formation of stable spectra.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The authors thank Stefan B€ottger and Udo Kebschull for their help and computational time at their group’s cluster. We further thank Annemarie Pucci and her research group for supporting the experimental work as well as Peter Comba and Bodo Martin for their recommendations. This work was supported in part by bwGRiD,55 where a substantial part of the calculation was performed. In addition to his affiliation with the Kirchhoff Institute for Physics, W.P. is an employee of Roche Diagnostics GmbH, Mannheim, Germany. ’ REFERENCES (1) Handbook of Optical Sensing of Glucose in Biological Fluids and Tissues; Tuchin, V. V., Ed.; Taylor & Francis, Inc.: Boca Raton, FL, 2008. (2) Vrancic, C.; Fomichova, A.; Gretz, N.; Herrmann, C.; Neudecker, S.; Pucci, A.; Petrich, W. Analyst 2011, 136, 1192–1198. (3) K€olhed, M.; Haberkorn, M.; Pustogov, V.; Mizaikoff, B.; Frank, J.; Karlberg, B.; Lendl, B. Vib. Spectrosc. 2002, 29, 283–289. (4) Heise, H. M.; Bittner, A.; Koschinsky, T.; Gries, F. A. Fresenius' J. Anal. Chem. 1997, 359, 83–87. (5) Fabian, H.; Lasch, P.; Naumann, D. J. Biomed. Opt. 2005, 10, 031103. (6) Rohleder, D.; Kocherscheidt, G.; Gerber, K.; Kiefer, W.; K€ ohler, W.; M€ocks, J.; Petrich, W. J. Biomed. Opt. 2005, 10, 031108. (7) Angyal, S. J. Angew. Chem. 1969, 81, 172–182. (8) Abraham, R. J.; Chambers, E. J.; Thomas, W. A. Magn. Reson. Chem. 1992, 30, S60–S65. (9) Nishida, Y.; Ohrui, H.; Meguro, H. Tetrahedron Lett. 1984, 25, 1575–1578. (10) Schnupf, U.; Willett, J.; Momany, F. A. Carbohydr. Res. 2010, 345, 503–511.

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