J Mol Model (2014) 20:2229 DOI 10.1007/s00894-014-2229-1

ORIGINAL PAPER

Deducing the molecular properties of zwitterionic, protonated, deprotonated, and double-deprotonated forms of L-cysteine from vibrational spectroscopy (IR, Raman, VCD) and quantum chemical calculations María Mar Quesada-Moreno & Juan Ramón Avilés-Moreno & A. A. Márquez-García & Juan Jesús López-González

Received: 29 December 2013 / Accepted: 2 April 2014 # Springer-Verlag Berlin Heidelberg 2014

Abstract The behavior of L-cysteine (C3H7NO2S, (2R)-2amino-3-sulfanylpropanoic acid) in water at different pH values was analyzed both experimentally and theoretically. The behavior was studied at pH values of 5.21 (at this pH, L-cysteine is a zwitterionic species), 1.00 (protonated species), 8.84 (monodeprotonated species), and 13.00 (dideprotonated species). We carried out a vibrational study using nonchiroptical (IR–Raman) and chiroptical (VCD) techniques complemented by quantum chemical calculations. We adopted a dual strategy, as follows. (i) The hybrid density functionals B3LYP and M062X and the ab initio MP2 method were employed, with the same 6-311++G (d,p) basis set, in order to characterize the relative energies and structures of an extensive set of conformers of L-cysteine. The presence of water was included by utilizing the IEF-PCM implicit solvation model. (ii) The vibrational analysis was made using a

chirality-sensitive using a chirality-sensitive technique (VCD) and chirality-insensitive techniques (IR, including MIR and FIR, and Raman), especially in aqueous solution. The results obtained theoretically and experimentally were compared in order to deduce the most stable structures at each pH. Moreover, for the first time, the monodeprotonated anion of Lcysteine was detected in aqueous solution by means of IR, Raman and vibrational circular dichroism (VCD). Finally, analysis of the low-frequency region using the IR and Raman techniques was shown to be a very important way to understanding the conformational preference of the zwitterionic species. Keywords L-Cys . Vibrational spectroscopy . Quantum chemical calculations . DFT calculations . Ab initio calculations . Conformational preference . Vibrational circular dichroism . Hydrogen bond

This paper belongs to Topical Collection QUITEL 2013 Electronic supplementary material The online version of this article (doi:10.1007/s00894-014-2229-1) contains supplementary material, which is available to authorized users. M. M. Quesada-Moreno : A. A. Márquez-García : J. J. López-González Department of Physical and Analytical Chemistry, University of Jaén, Campus Las Lagunillas, 23071 Jaén, Spain J. R. Avilés-Moreno Laboratoire de Physique des Lasers, Atomes et Molécules, UMR 8523 C.N.R.S., Université de Lille 1, Bât. P5, 59655 Villeneuve d’Ascq Cedex, France Present Address: J. J. López-González (*) Grupo de Química Física Teórica y Experimental FQM173, Edificio B3. Campus Las Lagunillas, Facultad de Ciencias Experimentales, Universidad de Jaén, 23071 Jaén, Spain e-mail: [email protected]

Introduction and motivations The structures of aliphatic amino acids, the building blocks of proteins, have become an increasingly interesting topic to researchers in recent years [1]. They have been analyzed using many different techniques in order to obtain useful information about their structures and biological functions. Studies of their behavior in water are of major interest, because water is the natural medium for biological molecules [2, 3]. The dissociation equilibria of amino acids depend on the pH of the medium in which they are found. In the case of cysteine, the experimental dissociation constants (i.e., the pKa values) for the dissociation of the carboxyl, thiol, and protonated amino groups are 10.70, 8.37, and 1.92, respectively [4]. Thus, dideprotonated anions will be found at pH 13.00,

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monodeprotonated ones at around pH 8.33, zwitterions at pH 5.02, and cations (completely protonated species) at pH 1.00. Cysteine has traditionally been considered a hydrophilic amino acid due to the belief that the thiol group interacts well with water. Yet, the side chain of this amino acid takes part in the hydrophobic bonding system of the micelle [5, 6]. Moreover, cysteine is involved in the formation of stable disulfide (S–S) bonds, which is an important factor in the structural stability of peptides and proteins [7–9]. Because of its high reactivity, the thiol group of cysteine has many biological functions [10]. A modified form of cysteine (i.e., N-acetyl-L-cysteine) is considered an important thiol-containing amino acid with antioxidant properties; it is involved in the elimination of the free radicals implicated in cancer [11]. In 1989, Zuk et al. examined the CH-stretching vibrational circular dichroism (VCD) spectra of several amino acids (LCys among them) as a function of pH [12]. Moreover, an investigation of the interaction energies of selected conformers of L-cysteine and their (1:1) complexes with water at the B3LYP/aug-cc-pVDZ level was carried out by Sadlej et al. [1]. From among more than 40 calculated 1:1 complexes, three groups of complexes were singled out and examined by calculating their vibrational circular dichroism (VCD) spectra at the B3LYP/aug-cc-pVDZ level of theory. Later, in 2011, Chandra et al. theoretically and experimentally (via FT-IR and Raman spectroscopies) analyzed nonionized L-cysteine (monomer and dimer). The molecular geometry, harmonic and anharmonic vibrational frequencies, and bonding features of L-Cys in the ground state were calculated using the density functional method (B3LYP) with 6-311G (d,p) as the basis set [13]. Recently, the conformational distributions of N-acetyl-Lcysteine (NALC) in aqueous solutions at several representative pH values were investigated using vibrational absorption (VA) and vibrational circular dichroism (VCD) spectroscopies, together with DFT and molecular dynamics (MD) simulations, by Poopari et al. [14]. Moreover, the conformational distributions of neutral L-cysteine in aqueous solutions

were investigated using vibrational absorption (VA), vibrational circular dichroism (VCD), and Raman optical activity (ROA) spectroscopies, together with DFT and molecular dynamics (MD) simulations [15]. In addition, the molecular structures of neutral and dideprotonated L-cysteine in aqueous solutions were investigated using vibrational absorption (VA) and Raman spectroscopies, together with DFT calculations [16]. In the work reported in the present paper, a vibrational spectroscopic technique that is sensitive to chirality (VCD) was coupled to chirality-insensitive methods (far-IR, IR, and Raman) as well as quantum chemical calculations in order to analyze L-Cys in aqueous solutions at four representative pH values (see Fig. 1 for atom numbering): 5.21 (at which L-Cys is a zwitterionic species, “CysZW”), 1.00 (at which it is a protonated species, “CysCAT (+1)”), 8.84 (monodeprotonated species, “CysAN (−1)”), and 13.00 (dideprotonated species, “CysDAN (−2)”). Our strategy involved testing the influence of two different DFT functionals, B3LYP and M062X, on the prediction of the most stable conformers at different pH values. Appropriate selection of the functional is also an important factor in obtaining a reasonable set of the most stable conformers. Solvent (water) effects were taken into account using the IEF-PCM formalism as implemented in Gaussian 09. MP2 calculations were also performed to compare the ab initio relative energies with the DFT results. This work represents the first time that a comparison of the structures and vibrational spectra of L-cysteine calculated with these two DFT functionals and the MP2 method has been performed and an analysis of L-cysteine at different pH values in aqueous solutions has been carried out; it is also worth noting that the monodeprotonated anionic structure has been detected. Finally, we would like to point out that the results obtained in our work using the implicit model (with the M062X functional and MP2 calculations) to predict the far-IR–IR–Raman–VCD spectra were very reasonable. Additionally, the structures obtained in this work are very close—in terms of the orientations of the amino acid groups—to those obtained

Fig. 1 Molecular structures and atom numbering scheme adopted in this study for L-Cys in its zwitterionic, protonated, monodeprotonated, and dideprotonated forms

L-Cys

pH

1.0

Cation (+1)

5.2 Zwitterion

8.8 Anion (-1)

13.0 Anion (-2)

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in [15, 16] with the explicit model, which is an outstanding result. This is the reason, in our opinion, for the good agreement between our theoretical and experimental data; i.e., the most stable sets of conformers obtained with the M062X and MP2 methods at the three studied pH values are similar to those obtained with the explicit model in [15, 16].

Experimental procedure A commercial L-cysteine sample (99 %) was purchased from Sigma–Aldrich (St. Louis, MO, USA). Mid-IR, Raman, and far-IR spectra of L-cysteine were recorded for the solid samples without performing any purification step beforehand. Likewise, the IR and Raman spectra were recorded in aqueous solutions at room temperature and at different pH: 5.21 (neutral media), 1.00 (acidic media), and 8.84 and 13.00 (basic media). Zwitterionic, protonated (cation), monodeprotonated (SH deprotonation), and dideprotonated (SH and NH3+ deprotonation) species are present at these four representative pH values. We also recorded the vibrational circular dichroism (VCD) spectra for the film samples. Doubly distilled water was used for the solution spectra. To obtain solutions at different pH values, a 4 M solution of HCl or NaOH (Sigma–Aldrich) was added to fresh solutions of L-cysteine (1.50 M, pH5.21). A Crison (Barcelona, Spain) GPL 21 pH meter was used to measure the pH values of the different solutions. The accuracy of the device was 0.01 and its detection range was pH 1–13. All data obtained were corrected to 25 °C (298 K). A FT-IR 4100 JASCO (Tokyo, Japan) spectrometer equipped with a Globar source, a DGTS detector, and KBr optics was used to record the mid-IR spectrum with the ATR accessory for the solid and liquid samples at different pH values. The IR spectra were recorded in the 4000–600 cm−1 range, with 200 scans performed and at resolutions of 1 cm−1 and 4 cm−1 for the solid and liquid samples, respectively. To record the film spectra, more dilute solutions were used to access the optimum absorbance range for VCD measurement of the sample. The solvent was evaporated using NaCl Real Crystal IR Sample Cards [17] in order to get very thin films. To perform the baseline correction, the spectrum of water at the same pH as that present when the spectrum of L-Cys was measured was subtracted. The Raman spectrum of L-cysteine was recorded using a Bruker (Ettlingen, Germany) RF100/S FT–Raman spectrometer equipped with an Nd:YAG laser (excitation line at 1064 nm) and a Ge detector cooled to liquid nitrogen temperature. The spectrum of the solid L-cysteyne was measured using a standard solid sample support in the 4000–50 cm−1 range, performing 200 scans and using a resolution of 1 cm−1. The spectra of the solutions were measured in the 4000– 500 cm−1 region, employing 200 scans and applying a resolution of 4 cm−1, using standard liquid cells.

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The far-IR spectrum of the solid L-cysteine was recorded by means of a Bruker Vertex 70 in the 700–30 cm−1 region, utilizing a resolution of 4 cm−1, 200 scans, a platinum ATR (single reflection diamond ATR accessory), and the silicon beamsplitter for the far-IR region. The VCD spectra of L-cysteine in film were recorded using a JASCO FVS-4000 FTIR spectrometer equipped with an MCTV (2000–900 cm−1) detector. For the film spectra, we prepared very low concentration solutions of the sample at different pH values and evaporated the solvent under anhydrous conditions in order to get very thin films of the sample, which were then measured in several positions by rotating the sample around both the beam propagation axis (90° and 180°) and the axis perpendicular to it (180°) in order to get the true VCD peaks and to ensure that artifacts were absent from the VCD spectra [18–22]. The spectral resolution was set to 4– 8 cm−1, and 2000–8000 scans were typically accumulated in blocks of 2000 scans. For the baseline correction, the VCD spectrum of the film support was subtracted from the thin film spectra of the sample [23, 24]. Finally, it was not possible to get a artifact-free VCD spectrum for the cation. For this reason, we will discuss the VCD data for the zwitterionic and two anionic species.

Theoretical methodology The vibrational study of L-Cys required an extensive conformational search, which was performed for the CysZW (expected at neutral pH), CysCAT (+1) (expected at acid pH), CysAN (−1) (expected at slightly basic pH), and CysDAN (−2) (expected at very basic pH) forms by means of molecular mechanics with different force fields (MMFF and SYBYL) [25, 26]. When a suitable value of the conformational energy was reached (20 kJ mol−1), the lowest nonredundant conformers were selected for further optimization of the structures and the calculation of their relative energies (with ZPE correction) using two density functional approaches (B3LYP [27–29] and M062X [30, 31] functionals) and the 6-311++G (d,p) basis set. In addition, the M062X functional contains a double amount of nonlocal exchange (2X). It is parametrized for nonmetals and contains a treatment for noncovalent interactions. However, the B3LYP functional does not contain a treatment for noncovalent interactions. Thus, it would be reasonable to assume that the results of the calculations of the relative energies using the M062X functional could be more accurate than those obtained with the B3LYP functional. The M062X functional seems to be a good choice in terms of accuracy/cost [32] for calculating the interaction energies of flexible polar systems such as the amino acid studied here. Similar results have been obtained in the study of the zwitterionic structures of L-Phe, L-Tyr [33], S-(−)-perillyc acid [34], L-Threo [35], and L-Ser [36].

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Finally, a second-order perturbation theory (MP2) calculation [37] with the 6-311++G (d,p) basis set was performed to compare the MP2 relative energies with the DFT results. The results from the two different DFT methods were compared to ensure that the theoretical models and the predicted values were internally consistent. All of the energies presented herein are relative energies corrected for the zero point energy. The harmonic IR, Raman, and VCD spectra of each conformer were obtained for both the B3LYP and M062X functionals and the 6-311++G (d,p) basis set. Comparing the results obtained with different functionals is a difficult task because the results are sometimes not evidently reproducible for other systems. In this way, we tested the results obtained with the B3LYP and M062X approaches against those obtained with the well-known MP2 approach. In addition, the enediol forms of the two most stable CysCAT (+1) conformers were optimized at the B3LYP/6-311++G (d,p) and M062X/6-311++G (d,p) levels of theory. They were found to be much less stable than the corresponding cationic forms containing the carboxylic group (i.e., with relative energies of 42 kcal mol−1). In fact, no spectral feature could be assigned to the existence of enediol forms in the freshly prepared cationic solutions. All of the theoretical calculations were carried out using three software packages: Spartan 08 [38] (for the molecular mechanics conformational search), Gaussian 09 [39] (for

structure re-optimization and calculations of spectra), and the VEDA [40, 41] program (for potential energy distribution (PED) matrix calculations). Implicit solvent (water) effects were taken into account using the IEF-PCM formalism [42] as implemented in Gaussian 09.

Results and discussion Theoretical conformational stability Conformational searches with the MMFF and SYBYL force fields found a total of 8, 52, 3, and 8 conformers for the zwitterionic, cationic (+1), anionic (−1), and anionic (−2) structures of L -Cys, respectively. Table 1 shows the zero point corrected (ZPE) relative energies (ΔE0), the equilibrium relative energies (ΔEe), and the Boltzmann populations (%Pop) obtained for L-Cys at three different theoretical levels: B3LYP, M062X, and MP2, using the same 6-311++G (d,p) basis set. Table S1 of the “Electronic supplementary material” (ESM) shows some relevant molecular structural parameters—especially dihedral angles—of this amino acid, obtained at the same levels of theory specified above. Meanwhile, Fig. 2 shows the structures, relative energies, and intramolecular H-bond distances of the most stable

Table 1 Calculated molecular populations and relative energies (corrected for the ZPE) for the zwitterionic (ZW), protonated (CAT), monodeprotonated (AN), and dideprotonated (DAN) conformers of L-Cys optimized at the B3LYP, M062X, and MP2 levels of theory B3LYP/6-311++G (d,p) Conf. Zwitterion CysZW2 CysZW3 CysZW4 CysZW5 Cation CysCAT1 CysCAT2 CysCAT3 CysCAT4 Anion (−1) CysAN1 CysAN2 Anion (−2) CysDAN1 CysDAN2 CysDAN3

M062X/6-311++G (d,p)

ΔE0 (kJ mol−1)

%Pop.a

Conf.

ΔE0 (kJ mol−1)

%Pop.a

Conf.

ΔEe (kJ mol−1)

%Pop.a

0.0 2.1 5.2 6.8

61.9 26.6 7.6 4.0

CysZW1 CysZW2 CysZW3 CysZW4

0.0 1.0 6.1 6.7

54.6 37.0 4.6 3.7

CysZW2 CysZW3 CysZW4 CysZW5

0.0 5.5 6.9 11.2

84.8 9.1 5.2 1.0

0.0 4.4 4.4 6.0

70.0 12.0 11.9 6.1

CysCAT1 CysCAT2 CysCAT3 CysCAT4

0.0 3.4 8.1 9.2

75.8 19.5 2.9 1.8

CysCAT1 CysCAT2 CysCAT3 CysCAT4

0.0 4.7 7.6 8.9

81.7 12.3 3.7 2.3

0.0 0.2

52.0 48.0

CysAN1 CysAN2

0.0 2.0

69.0 31.0

CysAN1 CysAN2

0.0 1.1

60.6 39.4

0.0

86.2

CysDAN1

0.0

71.8

CysDAN1

0.0

82.6

5.7 7.0

8.6 5.1

CysDAN2 CysDAN3

2.8 6.4

22.8 5.4

CysDAN2 CysDAN3

4.2 9.0

15.3 2.1

ΔE0 zero point corrected (ZPE) relative energy; ΔEe equilibrium relative energy a

MP2/6-311++G (d,p)

Boltzmann population from ΔE0 with T=298.16 K

J Mol Model (2014) 20:2229 Fig. 2 Structures of the most stable zwitterions, protonated (cation (+1)), deprotonated (anion (−1)), and dideprotonated (anion (−2)) species of L-Cys optimized at the M062X/6-311++ G (d,p) level of theory. Relative energies (corrected for the zeropoint energy) in kJ mol−1 are given in parentheses at the M062X/6-311++G (d,p), MP2/6311++G (d,p), and B3LYP/6311++G (d,p) levels of theory, respectively. H-bond lengths are shown in pm

Page 5 of 15, 2229 Cation (+1) 261 pm

ZW

Anion (-1) 202 pm

226 pm

227 pm

195 pm

Anion (-2) 266 pm

225 pm

282 pm CysCAT1 (0.0, 0.0, 0.0) 274 pm

CysZW1(0.0,20.0,19.0)

234 pm

195 pm 261 pm

266 pm CysZW2 (1.0, 0.0, 0.0)

CysCAT2 (3.4, 4.7, 4.4) 262 pm

245 pm

CysCAT3 (8.1, 7.6, 4.4) 260 pm

260 pm

197 pm

CysZW3 (6.1, 5.5, 2.1)

239 pm

266 pm

CysAN1 (0.0, 0.0, 0.0)

CysDAN1 (0.0, 0.0, 0.0)

229 pm

262 pm

206 pm

CysAN2 (2.0, 1.1, 0.2)

232 pm

CysDAN2 (2.8, 4.2, 5.7) 281 pm

234 pm

CysDAN3 (6.4, 9.0, 7.0)

195 pm

263 pm

CysCAT4 (9.2, 8.9, 6.0)

zwitterions and protonated (cation (+1)), monodeprotonated (anion (−1)), and dideprotonated (anion (−2)) forms of L-Cys optimized at these three theoretical levels. The conformational preferences indicated by the DFT and MP2 results suggest that the most populated structures are two conformers for CysZW (92 % of the total population), two conformers for CysCAT (+1) (95 %), two conformers for CysAN (−1) (100 %), and two conformers for CysDAN (−2) (95 %). The changes in conformational distribution seen for CysZW and CysDAN (−2) when DFT and MP2 are used with the same basis set are also worthy of comment. For instance, the M062X method predicts that CysZW1 conformer is the most stable, comprising around 55 % of the total population. However, this conformer was not among the most stable set obtained from B3LYP and MP2 calculations, which predict that the CysZW2 conformer is the most stable in terms of energy, comprising around 62 % and 85 % of the total population for B3LYP and MP2, respectively. The CysZW2 conformer is the second most stable in energy when M062X is used (37 % of the total population). The CysZW3 and CysZW4 conformers are the second and the third most stable, respectively, when B3LYP (27 % and 8 %) and MP2 (9 % and 5 %) are applied. CysZW3 and CysZW4 are predicted to be the third and the fourth most stable upon the use of M062X. Focusing our attention on the B3LYP or MP2 results, we can conclude that three H-bonds are present in the most stable conformer (CysZW2) of the zwitterionic form and two H-

CysZW4 (6.7, 6.9, 5.2)

bonds in the second most stable zwitterionic form (CysZW3). In this way, and as expected, the most stable CysZW conformer has more H-bonds than that less stable one of this form of the cysteine. For CysDAN (−2), the CysDAN8 conformer is found at the B3LYP level to be the second most stable in terms of energy, comprising around 8 % of the population, but this was not found with the M062X and MP2 calculations. Anyway, the presence of this conformer is not relevant because it contributes a population of only 8 % to the weighted calculated spectra. Aside from this example, there are clear similarities among the relative energies obtained using the three levels of theory for the remaining conformers. Two H-bonds are present in the two most stable conformers of the dideprotonated form, i.e., CysDAN1 and CysDAN2, which comprise around 80 % and 15 % of the population, respectively, according to the three methods. Table 1 offers further details on the conformational landscapes of CysAN (−1) and CysCAT (+1). For each of the two most stable CysAN (−1) conformers, two H-bonds are again present. CysAN1 represents around 60 % of the population and CysAN2 around 39 % according to the methods used. Finally, three H-bonds are present in the most stable CysCAT (+1) conformer and there are two H-bonds in the second most stable. Once again, with all the methods used, the fractions of the total population are around 76 % and 15 %, respectively. The CysCAT1 conformer has more H-bonds than CysCAT2, which is less stable than CysCAT1, as expected, in the same way as for the CysZW form.

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These results are important because the calculated IR, Raman, and VCD spectra differ depending on the predicted relative energies and, consequently, populations. The preferred conformation changes according to the theoretical model used. Because the same basis set was used in all three cases, the energy differences found arise through the use of different treatments for electron density, i.e., the B3LYP and M062X functionals. Table S1 of the ESM shows some relevant molecular structural parameters of L-Cys (ZW, CAT, AN, and DAN), with special attention paid to some characteristic dihedral angles, as obtained from DFT (B3LYP and M062X functionals) and MP2 calculations (see Fig. 1 for atom numbering). The variations in the compared dihedral angles are smaller than 14° when we compare the results obtained with B3LYP, M062X, and MP2 calculations performed with the 6-311++G (d,p) basis set. This fact confirms that the optimized structures are the same in the three cases. The best conformational set in terms of structure is generated by the MP2 calculation, but this method is also the most computationally demanding. It seems that a good choice in terms of balancing accuracy (structure, energy, and harmonic spectra) against computational cost could be the M062X functional, which is more computationally demanding than the B3LYP functional but much less so than second-order perturbative (MP2) calculations. In the CysZW1 and CysZW3 conformers of L-Cys, an intramolecular hydrogen bond is formed between N1–H14 and O6=C3. However, in CysZW2 and CysZW4, the –NH3+ group rotates and the intramolecular hydrogen bond is formed between N1–H5 and O6=C3. The most important difference between these conformers is the rotation of the –CH2–SH– group, which changes the values of some torsion angles, i.e., dihedral angles τ3(C3C2C9S10) and τ4(H11S10C9C2). All of the dihedral angles for the CysCAT (+1) conformers have different values. The most interesting fact is that there are differences between the torsion angles in CysCAT1 and CysCAT2 and those in CysCAT3 and CysCAT4. These are due to the rotation of the –CH2–SH– group. Firstly, in CysCAT1 and CysCAT2, all of the angles have similar values except for the torsion angle τ4(H11S10C9C2), due to the rotation of the thiol group. There are two H-bonds that stabilize both conformers. Secondly the dihedral angles τ1(O4C3C2N1), τ4(H11S10C9C2), and τ5(H15O6C3C2) change in CysCAT3 and CysCAT4 due to rotations of the –COOH and thiol groups. These two conformers are also stabilized by two H-bonds. For CysAN (−1), the values of the τ2(H5N1C2C3) and τ3(C3C2C9S10) dihedral angles in CysAN1 and CysAN2 are different. In particular, τ3(C3C2C9S10) is an interesting angle which is associated with the –CH2–S− group. Changes in this angle allow the formation of intramolecular H-bonds between the thiolate and protonated amino groups. For the last structure, there are differences between the torsion angles of CysDAN1, CysDAN2, and CysDAN3, especially τ2(H5N1C2C3) and τ3(C3C2C9S10). τ3(C3C2C9S10)

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relates to the –CH2–S− group, which rotates. Once again, this rotation allows the formation of intramolecular H-bonds between the thiolate and protonated amino groups. CysDAN1 and CysDAN3 present this H-bond, while it is absent in CysDAN2. Finally, it is clear that the structures obtained in our work (via M062X and MP2) are in good agreement with the most stable structures obtained by the authors of [15, 16]: L-Cys

zwitterions:

L-Cys

anions

(−1):

L-Cys anions (−2):

Our four most stable structures (CysZW1, CysZW2, CysZW3, and CysZW4) correspond well with the four most stable conformers obtained by the authors of [16] (g+g+, g−g+, tg+, and g+g−, respectively, explicit model), i.e., the orientations of the SH, COO−, and NH3+ groups of the cysteine moiety are similar. Additionally, our three most stable conformers (CysZW1, CysZW2, and CysZW3) are the same as those found using the implicit model in [15]. The same authors performed an extensive conformational research with the explicit model (4H2O), and their most stable conformers according to the explicit model (a5, a4, c2, b2, b4, and b5) are comparable with the three most stable conformers obtained with our implicit model. Our two most stable structures (CysAN1 and CysAN2) correspond well with the two most stable conformers obtained in [16] (g− and g+ , respectively, explicit model), i.e., the orientations of the S−, COO−, and NH3+ groups of cysteine are the same. In other words, the two most stable conformers obtained with our implicit model are the same, in terms of structure and energy, as the two most stable conformers indicated by the explicit model in [16]. Our two most stable structures (CysDAN1 and CysDAN2) correspond with the two most stable conformers obtained in [16] (g− and g+ , respectively, explicit model), i.e., the orientations of the S−, COO−, and NH2 groups of cysteine are the same.

In our opinion, this similarity between the most stable conformers obtained by us and in [15, 16] is an important indicator of the good agreement between our experimental data and the theoretical results. Spectral features Figures 3, 4, 5, 6 show the experimental IR (including the farIR region for CysZW), Raman, and VCD spectra of L-Cys at

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Zwitterion (pH=5.21) a) IR SPECTRA, 2000-600 cm-1

b) FarIR SPECTRA, 700-50 cm-1

c) RAMAN SPECTRA, 3100-500 cm-1 region

d) RAMAN SPECTRA, 700-50 cm-1 region

Fig. 3a–d Experimental IR (a), far-IR (b), and Raman (c, d) spectra for the zwitterionic species of L-Cys compared with predicted scaled spectra in the 3100–500 cm−1 and 700–30 cm−1 spectral regions. The middle graph in each subfigure depict: a experimental IR spectra in aqueous solution (in black), film (in blue), and in the solid phase (in red); b experimental far-IR spectrum for the solid sample; c experimental Raman

spectra in aqueous solution (in black) and in the solid phase (in red); d experimental Raman spectrum in the solid phase. The top graph and the bottom graph in each subfigure depict predicted scaled spectra obtained at the B3LYP/6-311++G (d,p) (in black) and M062X/6-311++G (d,p) (in red) levels of theory

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Cation (protonated L-Cys) (pH=1.00) a) IR SPECTRA, 2000-600 cm-1

b) RAMAN SPECTRA, 3100-500 cm-1

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ƒFig. 4a–b

Experimental IR (a) and Raman (b) spectra for the protonated species of L-Cys compared with predicted scaled spectra in the 3100– 500 cm−1 region. The middle graph in each subfigure depict: a experimental IR spectra in aqueous solution (in black) and in film (in blue); b experimental Raman spectrum in aqueous solution (in black). The top graph and the bottom graph in each subfigure depict predicted scaled spectra obtained at the B3LYP/6-311++G (d,p) (in black) and M062X/6-311++G (d,p) (in red) levels of theory

most stable conformers. The comparison confirms the presence of the most stable conformers of the CysZW (Figs. 3 and 6a), CysCAT (+1) (Fig. 4), CysAN (−1) (Figs. 5a, b and 6b), and CysDAN (−2) (Figs. 5c, d and 6c) forms of L-Cys in aqueous solution and in the solid phase (only for the zwitterionic structures), considering that there is good agreement between the calculated spectra and experimental results, especially when M062X calculations were considered. The single scaling factors from the NIST database [43] for the B3LYP/6311++G (d,p) (0.967) and M062X/6-311++G (d,p) (0.950) levels of theory were used in the vibrational analysis of the studied species. All the percentage contributions of normal modes were taken from the PED matrix obtained with the VEDA program [40, 41]. CysZW, CysCAT, CysAN (−1), and CysDAN (−2) have, respectively, 36, 39, 33, and 30 normal vibrational modes belonging to the unique irreducible representation (A) of its common symmetry point group, C1. Nonchiroptical analysis: IR–Raman spectra Zwitterionic and protonated species Figures 3 and 4 show experimental IR, Raman, and far-IR (only in the zwitterion case) spectra of L-Cys in aqueous solution at pHvalues of 5.21 and 1.00, respectively, data obtained in the solid phase, and a comparison of those data with the results of theoretical calculations of the two most stable zwitterionic (CysZW1 and CysZW2) and cationic (CysCAT1 and CysCAT2) forms performed at the B3LYP/6-311++G (d,p) and M062X/6-311++G (d,p) levels of theory. The latter level adequately reproduces the experimental spectra. Thus, we can conclude that zwitterions are present at pH5.21 and cations at pH1.00, based on several spectral differences that we point out below (see Figs. 3 and 4):

four different pH values and under different conditions, i.e., in H2O solution and in the solid phase (thin films and powder sample), as compared with the calculated spectra of the set of

(i) One feature which is common to both species, i.e., the zwitterion and cation of L-Cys, is the band at 2575 cm−1 (Raman) at neutral pH and at 2577 cm−1 (Raman) at acidic pH, which is assigned to a normal mode with a contribution from the PED matrix of 100 % of SH str. motion of the two most stable CysZW or CysCAT (+1) conformers. (ii) In the experimental spectra obtained at pH1.00, there is an experimental band at 1736 cm−1 (IR and Raman, 1752 cm −1 in VCD) that does not appear in the

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Anion (deprotonated L-Cys) (pH=8.84)

Anion (double deprotonated L-Cys) (pH=13.00)

a) IR SPECTRA, 2000-600 cm-1

c) IR SPECTRA, 2000-600 cm-1

b) RAMAN SPECTRA, 2000-500 cm-1

d) RAMAN SPECTRA, 3100-500 cm-1

Fig. 5a–d Experimental IR (a, c) and Raman (b, d) spectra for monodeprotonated anionic (a, b) and dideprotonated anionic (c, d) species of L-Cys, compared with predicted scaled spectra in the 2000– 500 cm−1 region. The middle graph in each subfigure depict: a, c experimental IR spectra in aqueous solution (in black) and in film (in

blue); b, d experimental Raman spectra in aqueous solution (in black). The top graph and the bottom graph in each subfigure depict predicted scaled spectra obtained at the B3LYP/6-311++G (d,p) (in black) and M062X/6-311++G (d,p) (in red) levels of theory

experimental spectra obtained at pH5.21. This can be assigned to a normal mode with an 87 % contribution

from C=O str. of the two most stable cationic forms. This band reveals the presence of C=O bond stretching, which

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L-Cys VCD a) VCD ZWITTERION

ƒFig. 6a–c

The middle graph in each subfigure depict experimental VCD spectra for the zwitterionic (a), monodeprotonated anionic (b), and dideprotonated anionic (c) species of L-Cys compared with predicted scaled spectra in the 2000–900 cm−1 region. The top graph and the bottom graph in each subfigure depict predicted scaled spectra obtained at the B3LYP/6-311++G (d,p) (in black) and M062X/6-311++G (d,p) (in red) levels of theory

(iii)

b) VCD AN(-1)

(iv)

(v)

c) VCD AN(-2)

(vi)

is not present in the zwitterionic structures. This means that, as expected, protonation of the carboxylate group occurs at highly acid pH. Another relevant spectral difference is the experimental band that appears at 1611 cm−1 (in the IR; 1618 cm−1 in the Raman spectrum) at neutral pH. This is assigned to a normal mode with an 88 % contribution from asym. COO− str. of the two most stable zwitterionic structures. This band is important because it can prove the presence of zwitterions, considering that it involves the carboxylate group. However, a different band can be observed at acid pH at 1620 cm −1 (in the IR; broad band at 1634 cm−1 in the Raman spectrum), which can be assigned to a combination of two normal modes with the same contributions for the CysCAT1 and CysCAT2 conformers: 75 % asym. NH3+ bend. and 22 % HNCC torsion motions. Moreover, the experimental band observed at 1255 cm−1 (broad band in IR, 1213 cm−1 in VCD and 1218 cm−1 in Raman) at acid pH is absent at neutral pH. This can be assigned to a normal mode with a 45 % contribution from HOC bend. (COOH group) and a 30 % contribution from OC str. due, mainly, to the presence of CysCAT1 and CysCAT2 conformers. In addition, there are bands that separately seem to prove the presence of only one conformer. The band mentioned in (iii) is an example, as is the experimental band at 1400 cm−1 (IR and Raman) at neutral pH, which can be assigned to two normal modes due mainly to the presence of CysZW2. The first has the following contributions: 52 % sym. NH3+ bend., 17 % CH2 rock., 10 % sym. COO− str., and 9 % HCSH torsion motions; the second has the following contributions: 40 % sym. NH3+ bend., 47 % CH2 rock., and 6 % HCSH torsion motions. Finally, other bands are common to both species, i.e., the zwitterion and cation of L-Cys; for instance, the band at 1517 cm−1 (IR, and solid Raman) at neutral pH and at 1530 cm−1 (IR, and Raman) at acid pH. At neutral pH, the band at 1517 cm−1 can be assigned to two normal modes with the same contributions for the two most stable CysZW conformers; that is, 71 % asym. NH3+ bend. and 20 % HNCC torsion. At acid pH, the band at 1530 cm−1 can be assigned to a normal mode with a contribution from 96 % sym. NH3+ bend. motion of the two most stable CysCAT (+1) conformers.

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For the zwitterionic structures, we highlight the utility of the low-wavenumber region, far-IR, and Raman spectra of the solid L-Cys for discerning differences between different conformers (see Figs. 3b and d). This region presents normal modes with contributions from waggings, rockings, and torsions. We will consider one of the most strong and relevant normal modes: HSCC torsion. This appears at different wavenumbers depending on the CysZW conformer: at 166 cm−1 (far-IR, 164 cm−1 for Raman spectroscopy of the solid) for CysZW1, with theoretical contributions of 67 % and 10 % from HCCO torsion, and at 365 cm−1 (far-IR and Raman spectroscopy of the solid) for CysZW2, with contributions of 73 % and 10 % HCSH torsion. Furthermore, the –NH3+ torsion normal mode of the two most stable conformers of L-Cys also appears at 262 cm−1 (far-IR and Raman of the solid), with 61 % HNCC and 13 % CNCC torsions, for both CysZW1 and CysZW2. Small additional contributions from 11 % OCC bend. and 8 % CCC bend. are present for CysZW1 and CysZW2, respectively. However, in Raman spectroscopy of the solid, these two normal modes are predicted to be so weak for CysZW2 that they cannot be identified in its experimental spectrum. Another interesting band is observed at 693 cm−1 (far-IR and Raman of the solid), which can be assigned to a normal mode with contributions from 65 % SC str. and 9 % OCOC torsion motions, due to the presence of the CysZW2 conformer. Finally, the experimental band observed at 635 cm−1 (far-IR and Raman of the solid) can be assigned to a normal mode with contributions from 38 % OCO bend., 13 % NC str., 8 % HSCH torsion, and 8 % CNCC torsion motions, due mainly to the presence of CysZW1. As can be seen, the low-frequency region (IR and Raman) is suitable for assigning different conformers [44]. Figures 12–13 in [15] and Figures 4–13 in [16] show the IR–Raman spectra obtained for the zwitterionic forms of LCys (neutral conditions). Upon comparing their calculated spectra (B3LYP with an explicit solvation model), the authors conclude that four conformers contribute to the experimental IR–Raman spectra (i.e., they accurately reproduce their experimental spectra). Moreover, our data include both IR and Raman spectra in aqueous solutions and a comparison with the spectra obtained in the solid phase (which are less interesting in terms of biological importance). Figure 3 shows our experimental/theoretical comparison. The Raman data yield a lot of information, and we can see how the regions around 1400 cm−1 (see also IR data) and 650 cm−1 are built from the contributions of the two most stable conformers. In our opinion, this fact is due to the similar sets of most stable conformations obtained with the M062X and MP2 methods, which are comparable to that given in [15, 16]. Monodeprotonated and dideprotonated species Figure 5 shows experimental IR (panels a and c) and Raman (panels b and d) spectra of L-Cys in aqueous solutions at pH8.84

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(panels a and b) and pH13.00 (panels c and d). Some of the bands in the IR and Raman spectra suggest the existence of two different anions, i.e., monodeprotonated CysAN (−1) (deprotonated thiol group and protonated amino group) and dideprotonated CysDAN (−2) (deprotonated thiol and amino groups), when we carried out the analysis of the PED matrix obtained with the VEDA program: (i) One feature which is common to both species, i.e., CysAN (−1) and CysDAN (−2) of L-Cys, is the absence of SH stretching for both anions. A very weak SH band is observed at pH8.84, which is probably due to a contribution from the zwitterionic structure. (ii) In the experimental IR spectra obtained at pH8.84, one band is seen at 1582 cm−1, whereas two bands are observed at 1655 cm−1 and 1546 cm−1 in the experimental IR spectra at pH13.00. These differences are due to the deprotonation of the amino group. Asym. COO− str. contributes to the three bands, but NH2 scissor. only does so for the bands obtained at pH13.00. The band at 1582 cm−1 can be assigned to a normal mode that has an 87 % contribution from asym. COO− str. of the two most stable CysAN (−1) conformers. However, the band at 1655 cm−1 can be assigned to a combination of three different normal modes of the two most stable CysDAN (−2) conformers. The first normal mode arises from CysDAN1, with a 69 % contribution from asym. COO− str. and 16 % from NH2 scissor. The second and third normal modes are due to CysDAN2, and show different contributions from the different motions. The second normal mode has an 86 % contribution from NH2 scissor. and a 15 % contribution from HNCC torsion, whereas the third normal mode has a 90 % contribution from asym. COO− str. and a 7 % contribution from CCO bending. The band at 1546 cm−1 arises from the CysDAN1 conformer and can be assigned to a normal mode with a 52 % contribution from NH2 scissor., 25 % from asym. COO− str., and 16 % from HNCC torsion motions. Because of the deprotonation of the amino group, the Raman and VCD spectral bands at 1620 cm−1 and 1580 cm−1, respectively, appear broader at pH8.84 than at pH13.00. (iii) At pH8.84 there is a band at 1434 cm−1 (IR and Raman) which is absent at pH13.00, as predicted theoretically. This can be assigned to different normal modes depending on the conformer. For CysAN1, the normal mode has the following contributions: 63 % sym. NH3+ bend., and 22 % sym. COO− str. For CysAN2, the contributions to the normal mode are: 17 % sym. NH3+ bend., 63 % sym. COO− str., and 7 % OCO bending. (iv) Other interesting bands are also observed at both pH values. For instance, the experimental bands at 1400 cm −1 (IR and Raman) at pH 8.84 and at 1411 cm−1 (IR and Raman) at pH13.00 are due mainly

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to the presence of the most stable conformer in both species. On the one hand, the band at 1400 cm−1 at pH 8.84 can be assigned to a normal mode with contributions from: 39 % sym. COO− str., 8 % sym. NH3+ bend., 8 % HCCO torsion, and 7 % CC stretching. On the other hand, the band at 1411 cm−1 at pH13.00 can be assigned to a combination of two normal modes. The first has an 81 % contribution from CH2 rock. and a 14 % contribution from HCCN torsion, and the second has contributions of: 67 % sym. COO− str., 7 % HNC bend., and 7 % OCO bending. In addition, the experimental band observed at 1346 cm−1 (IR and Raman, 1350 cm−1 in VCD) at both pH values arises from the two most stable CysAN (−1) conformers and CysDAN1, depending on the pH. This can be assigned to a normal mode with contributions from: 46 % HCCO torsion, 12 % sym. COO− str., and 9 % CH wagg. at pH8.84. At pH13.00, it can be assigned to a normal mode with a contribution from: 34 % CH wagg., 20 % sym. COO− str., and 17 % HNC bending. (v) Finally, there are bands which are absent from the spectra of both species at pH5.21 and pH1.00, that indicate the formation of anions. An example is the band at 1032 cm−1 (IR and Raman) obtained at pH13.00, which can be assigned to two normal modes of the two most stable dideprotonated conformers. These modes show the same contributions: 23 % HNCC torsion, 16 % HCS bend., 13 % CC str., and 12 % NC stretching. All of these bands confirm the presence of the monodeprotonated L -Cys species at pH 8.84 and the dideprotonated one at pH13.00. Figure 14 in [15] shows the Raman spectrum obtained for the anionic L-Cys (pH 12), which can be assigned to the diprotonated form of cysteine (CysDAN (−2)). By comparing their calculated spectra (B3LYP with an explicit solvation model) with the experimentally recorded spectra, the authors concluded that three conformers contribute to the experimental IR-Raman spectra, and that these three structures reproduce their experimental spectra in a suitable way. Moreover, our data include both IR and Raman spectra in aqueous solutions. Figure 5 shows our experimental/theoretical comparison. The Raman data newly reveal a lot of information, and we can see how the regions around 1400 cm−1 (see also the IR data) and 900–600 cm−1 are built from the contributions of the two most stable conformers. As said before, in our opinion, this is due to the similar sets of most stable conformations obtained with the M062X and MP2 methods, which are comparable to those given in [15, 16]. Chiroptical response: VCD We observe reasonable agreement between the experimental VCD spectra (thin films in KCl supports) and the predicted

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scaled VCD spectra of the different forms of L-Cys. Figure 6 displays the experimental and calculated VCD spectra of zwitterions (a), monodeprotonated anions (b), and dideprotonated anions (c) in the 2000–900 cm−1 spectral region. In this figure, the bottom and top panels show the predicted scaled VCD spectra for the most stable conformers, and the middle panels show the experimental VCD spectra. It seems that the presence of the two most stable conformers of each form is sufficient to be able to reproduce the experimental VCD spectra. A few experimental VCD bands indicate the presence of the CysZW (Fig. 6a), CysAN (−1) (Fig. 6b), or CysDAN (−2) (Fig. 6c) chiral structures, taking into account the two most stable conformers of these species: (i) In the case of the zwitterion, the (−,−,+,−,−,+) VCD bands that follow at 1635 cm−1, 1525 cm−1, 1345 cm−1, 1323 cm−1, 1295 cm−1, and 1284 cm−1 are reasonably well reproduced by the calculations. (ii) For the cation, we did not obtain a suitable film, and all of the measured films taken at different positions and orientations showed many undesirable bands, meaning that we are not able to present a reasonable VCD spectrum for this species. (iii) Regarding the monodeprotonated anion, we point out that the (−,−,−,+,−) bands at 1600 cm−1, 1495 cm−1, 1350 cm−1, 1310 cm−1, and 1055 cm−1 are reasonably well reproduced by the calculations. (iv) Concerning the dideprotonated anion, we can discern the (−,+,−,+,−,−) bands at 1575 cm − 1 , 1510 cm −1, 1405 cm−1, 1380 cm −1, 1300 cm−1, and 1260 cm−1 are reasonably well reproduced by the calculations. Figure 9 in [15] shows the IR-VCD spectra obtained for the zwitterionic forms of L-Ser (under neutral conditions). The best theoretical/experimental agreement obtained was with the explicit solvation model and not with the PCM implicit model. It is notable that the most stable conformer obtained with the PCM model corresponds to our second most stable conformer, and that our first conformer—in terms of functional group orientations—corresponds to the first conformer obtained with the explicit model. Additionally, Fig. 10a in [15] shows how conformers 6ZW5 and 6ZW6 (which comprise less than 5 % of the population) fit better to the experimental data than the most stable conformers 6ZW1 and 6ZW3 do. This fact highlights the great difficulties associated with this topic. Moreover, our data include both IR and Raman spectra in aqueous solutions and a comparison with the solid-phase spectra (less interesting from a biological perspective). Figures 3a and c show our experimental/theoretical comparison. Here, the Raman data reveal a lot of information, and we can see how the band at 1200 cm−1 is due to the second conformer. In our opinion, this is due to the similar sets of

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most stable conformations obtained with the M062X and MP2 methods, which are comparable in terms of the most stable conformers to those given in [15, 16]. To sum up, by analyzing the chiroptical properties of L-Cys in relation to its structure, we can confirm the presence of zwitterions at pH5.21, monodeprotonated anions at pH 8.84, and dideprotonated anions at pH13.00. IR and Raman spectroscopic results also confirm this fact and the presence of cations at pH1.00.

Conclusions (i) The experimental far-IR, IR, and Raman spectra of L-Cys in aqueous solution at different pH values and in the solid phase present evidence of the presence of the two most stable conformers of the species present at each pH, i.e., zwitterions at pH 5.21, cations at pH 1.00, monoprotonated anions at pH 8.84, and dideprotonated anions at pH 13.00. Analysis of the chiroptical properties of L-Cys by means of vibrational circular dichroism (VCD) spectroscopy confirmed this conclusion. (ii) It was necessary to analyze the conformational preference of L-Cys at each protonation state from both theoretical and experimental points of view. The most stable set of conformers of each species was identified by performing an exhaustive analysis of the quantum chemical calculations carried out. The experimental spectra were compared with a set of quantum chemical calculations realized using the DFT (B3LYP and M062X functionals) and MP2 methods with the same 6-311++G (d,p) basis set. All of the experimental spectra were found to be in good agreement with the calculated spectra (especially those obtained with the M062X functional), as also observed for other similar systems. (iii) Applying the theoretical implicit model IEF-PCM to simulate the water seems to lead to a reasonable reproduction of our experimental data. In our opinion, this is due to the good agreement between the set of most stable conformers we obtained using the M062X and MP2 methods and the set calculated in the literature using both implicit and explicit solvation models [15, 16]. It is well known that combining both models leads to better agreement between theory and experiment, and thus conclusive information about the conformational landscape of the molecule in water and about hydrogenbonding interactions between the molecule and water [14, 45–49]. In fact, in [45], the authors reported that “while the observed VA spectra under three pHs can be well interpreted with the inclusion of the implicit solvation model, both implicit and explicit solvation models have been found to be crucial for the adequate interpretation of the complex VCD features observed.”

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(iv) Our results suggest that the M062X functional gives better results than the B3LYP functional in terms of interpreting far-IR, IR, VCD, and Raman spectra. We can also conclude that the MP2 and M062X approaches yield the same relative energies. In addition, even though the B3LYP functional calculates the same structures as the MP2 and M062X approaches, the relative energies obtained using B3LYP appear to be very different to those obtained using the other approaches, and the experimental data agree better with the M062X and MP2 results than the B3LYP results. However, for the CysZW conformers, the relative energies obtained using MP2 and B3LYP show better agreement, although the closest agreement between the experimental and calculated spectra is again attained using M062X. (v) The results obtained in this work should be useful when studying building blocks that contain L-cysteine. The present work reveals that IR, Raman, and (especially) far-IR and VCD spectroscopies are complementary techniques in the study of species of biological interest. Applying them in combination with quantum chemical calculations may help to clarify the conformational landscape of flexible biological species such as those described here. Thus, this methodology can be followed to analyze other amino acids under conditions similar to those present in biological environments. Acknowledgments This work was supported by the Junta de Andalucía (project P08-FQM-04096). The authors thank the University of Jaén for its continuing financial support, and its CICT for allowing them to use its instrumental facilities. Mª del Mar Quesada Moreno thanks the University of Jaén for a predoctoral fellowship. The authors also thank D. Francisco Hermoso Torres for his help in the laboratory.

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