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Pharmaceutical Modeling
Planarity or Non-Planarity: Modulating Guanidine Derivatives as #2-Adrenoceptors Ligands Cristina Trujillo, Aoife Flood, Goar Sánchez-Sanz, Brendan Twamley, and Isabel Rozas J. Chem. Inf. Model., Just Accepted Manuscript • DOI: 10.1021/acs.jcim.9b00140 • Publication Date (Web): 17 Mar 2019 Downloaded from http://pubs.acs.org on March 17, 2019
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Planarity or Non-Planarity: Modulating Guanidine Derivatives as α2-Adrenoceptors Ligands Cristina Trujillo,*,a Aoife Flood,a Goar Sanchez-Sanz,b Brendan Twamley,a and Isabel Rozas*,a
aSchool
of Chemistry, Trinity College Dublin, 152-160 Pearse Street, Dublin 2, Ireland
bIrish
Centre of High-End Computing, Grand Canal Quay, Dublin 2, Ireland
KEYWORDS: Planarity; Non-planarity; Intramolecular Hydrogen Bonds; Thiophene; Thiazole; Guanidinium; α2-Adrenoceptors; Antagonists; Affinity.
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ABSTRACT A theoretical study has been carried out at M062X/6-311++G(d,p) computational level to search for a rationale on ligands’ affinity towards α2-adrenoceptors by estimating the nature and strength of intramolecular hydrogen bonds potentially formed (by means of the QTAIM and NBO approaches) as well as the degree of deviation from planarity that could be observed in some of the compounds. Four different families have been studied: thiophen-2-yl, 3carboxylatethiophen-2-yl
esters,
3-cyanothiophen-2-yl
and
2-thiazolyl
guanidinium
derivatives. In the case of the thiophen-2-yl guanidines not substituted in the 3 position, nonplanarity was always observed whereas in the thiazole series, intramolecular hydrogen bonds were identified between the guanidinium and the thiazole ring forcing the systems to planarity. Regarding the carboxylic esters, two different rotamers were found: quasi-planar and quasi-perpendicular systems with very similar energy. Both these isomers can form different nets of intramolecular hydrogen bonds and other types of non-covalent interactions. Different physicochemical properties such as basicity, solubility or lipophilicity were calculated for these systems, but no correlation to the degree of planarity was found. However, when comparing the α2-ARs affinity with the planarity of the molecules, a trend appears in the thiophen-2-yl guanidinium series indicating that lack of planarity seems to be optimal for α2-ARs engagement.
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INTRODUCTION In the recent years the use of intramolecular hydrogen bonds (IMHB) as design elements in drug discovery has become a very relevant issue.1,2,3 Formation of IMHB not only can affect solubility and pharmacokinetic properties by facilitating cell membrane crossing,4,5,6 distribution and excretion,7 but also can have an effect on the interaction with the actual target thus modulating ligand activity.8,9 Besides, the use of the ‘beyond Rule of 5’ chemical space is becoming more and more relevant in drug design and the use of IMHB in such type of drugs can help with absorption since it can ‘shield’ polarity.10 For that reason, many authors are looking at this structural feature to understand the biochemical/pharmacological behaviour of active compounds and are incorporating this element in the early stages of drug design.11 However, in some instances the absence of IMHBs drives a lack of planarity that can be responsible of a particular biological response or for drug-like properties such as enhanced solubility.12
Continuing with our research in arylguanidine derivatives as α2-AR antagonists,13,14,15,16,17,18 we have recently reported the pharmacological behaviour of a series of guanidine derivatives of benzene ring-equivalents such as thiophene or thiazole at the α2-AR.19 We found interesting results in terms of affinity and activity (agonism vs. antagonism) when comparing phenyl and pyridine cores within our in-house libraries. Previously, we had studied the formation of IMHBs between the guanidinium cation and pyridine cores finding this feature responsible of a decrease in α2-AR affinity, but always rendering antagonist or inverse agonist functional activity (Figure 1).17
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Thus, considering the structure of the thiophen-2-yl and thiazol-2-yl guanidinium derivatives, the possibility of IMHBs or other non-covalent interactions between the cation and the N or even the S atoms20,21,22,23 of the heterocycles cannot be discarded. Accordingly, we would like to explore the potential effect that the degree of planarity (regulated among other effects by the presence or not of IMHBs) can have in the α2-AR affinity of a series of thiophen-2-yl and thiazol-2-yl guanidinium derivatives (Figure 1).
HH R agonists
N H
N H
S 1
N
N H H
H
N
N H
H N H
2-AR affinity H
antagonists/inverse agonists
EtO
H R1
R
O H N H N
H N H H
CN H
R1 S
N
N 2 H H
R1 = H (a), 4-CH3 (b),
H
R1
H N H
N
S
N 3 H H
(c),
(d),
R1
H N H
N S
H N N H
H H N H
4
(e)
Figure 1. Structures of phenyl and pyridine-2-yl guanidinium derivatives previously studied by Rozas et al.17 where the phenyl and guanidinium groups are out-of-plane while the pyridine-2-yl and the guanidinium are co-planar (above), and thiophen-2-yl (1a-e), 3carboxylatethiophen-2-yl ethyl esters (2a-e), 3-cyanothiophen-2-yl (3a-e) and 2-thiazolyl (4ae) guanidinium derivatives (below) investigated in this study.
Additionally, the crystallographic structures of the related N-(2-methoxycarbonylthien-3yl)guanidine (5) and N-(3-methoxycarbonylthien-2-yl)guanidine (6) hydrochlorides have been resolved and are discussed here to support the theoretical observations.
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METHODS Computational details Calculations have been carried out using the Gaussian16 computational package.24 All systems have been optimized at the M06-2X25 computational level using the 6-311++G(d,p)26 basis sets. Frequency calculations have been carried out to confirm that the structures obtained correspond to energetic minima. Effects of water solvation have been included by means of the SCFR-PCM approaches implemented in the Gaussian16 starting from the gasphase geometries and re-optimizing.
The Atoms in Molecules (AIM) methodology27 was used to analyse the electron density of the systems with the AIMAll program.28 The NCI (non-covalent interactions) index, based on the reduced gradient of the electron density, has been calculated to identify attractive and repulsive interactions with the NCI program29 and plotted with the VMD program.30
Crystallographic details Single crystals of thiophenes 5 and 6 were obtained. A suitable crystal was selected and mounted on a glass fibre on a Rigaku Saturn 724 diffractometer. The crystal was kept at 108(2) K during data collection. Using Olex2,31 the structure was solved with the XS32 structure solution program using Direct Methods and refined with the XL33 refinement package using Least Squares minimisation.
Crystal Data for 5, C7H10ClN3O2S (M = 235.69 g mol-1): orthorhombic, space group P212121 (no. 19), a = 7.361(3) Å, b = 10.015(3) Å, c = 13.821(5) Å, V = 1018.9(6) Å3, Z = 4, T = 108.15 K, μ(MoKα) = 0.558 mm-1, Dcalc = 1.536 g cm-3, 4063 reflections measured (5.896°
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≤ 2Θ ≤ 50.484°), 1743 unique (Rint = 0.0211, Rsigma = 0.0194) which were used in all calculations. The final R1 was 0.0220 (I > 2σ(I)) and wR2 was 0.0579 (all data). CCDC no. 1530438.
Crystal Data for 6, C7H10ClN3O2S (M = 235.69 g mol-1): monoclinic, space group C2/c (no. 15), a = 11.739(4) Å, b = 9.691(3) Å, c = 18.765(6) Å, β = 107.522(4)°, V = 2035.7(11) Å3, Z = 8, T = 108.15 K, μ(MoKα) = 0.558 mm-1, Dcalc = 1.538 g cm-3, 7702 reflections measured (5.56° ≤ 2Θ ≤ 50.496°), 1750 unique (Rint = 0.0205, Rsigma = 0.0213) which were used in all calculations. The final R1 was 0.0235 (I > 2σ(I)) and wR2 was 0.0607 (all data). CCDC no. 1530439.
RESULTS AND DISCUSSION Structural and electron density results We have optimised all the structures of the four sets of compounds shown in Figure 1 at M062X/6-311++G(d,p) computational level (including water solvation by means of the PCM approach). Cartesian coordinates and molecular graphs for all the compounds calculated are shown in Table S1 (see ESI). Additionally, the degree of co-planarity between the heteroaromatic rings and the guanidinium cation has been assessed by measuring the (S,N)ringCring-Ngua-Cgua dihedral angle and the values obtained are presented in Table 1.
Both the thiophen-2-yl (1a-e) and 3-cyanothiophen-2-yl (3a-e) guanidinium families, show these dihedral angles to be around 90° indicating that the thiophene and the guanidinium systems are perpendicular. On the contrary, all the thiazole guanidinium derivatives (4a-e) show dihedral angles near 180° indicating planar molecules.
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Table 1.- Calculated (S,N)ring-Cring-Ngua-Cgua dihedral angles (°) for thiophen-2-yl (1a-e), 3carboxylatethiophen-2-yl ethyl esters (2a-e), 3-cyanothiophen-2-yl (3a-e) and 2-thiazolyl (4ae) guanidinium derivatives optimised at M06-2X/6-311++G(d,p) computational level. (Y) H2N
X
R1
C S
C N
NH2
H
R1-
1 (X= C; Y= H)
2 (X= C; Y= CO2Et) (perpend./planar)
3 (X= C; Y= CN)
4 (X= N)
H-
(a)
96.6
92.4 / 6.3 [6 (Y= CO2Me): 108.6 (2)]a
104.3
175.2
H3C-
(b)
95.8
108.7 / 32.0
96.0
179.5
(c)
96.4
112.7 / 37.0
96.2
180.0
(d)
96.9
111.1 / 24.0
97.7
179.6
(e)
93.8
116.7 / 53.0
96.3
176.1
aExperimental
torsion from X-ray structure of related methyl ester 6
A different scenario is observed for the 3-carboxylatethiophen-2-yl ethyl esters. In most of these thiophenes (2a-d), two different conformations of minimum energy were found for each compound, one quasi-planar (dihedral angles between 6.3° and 37.0°) and one quasiperpendicular (dihedral angles between 92.4° and 112.6°). Compound 2e was an exception with both rotamers being quasi-perpendicular (53.0° and 116.7°).
However, when looking at the relative energies for each pair of conformations, we found that this was very small for compounds 2b-e (0.8, 2.0, 0.9 and 1 kJ mol-1, respectively) indicating that both conformations may be equally possible in aqueous solution. In the case of
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compound 2a, this energy difference is larger (12.7 kJ mol-1). Yet, it is well-known that when a ligand binds to a target, it is usually not in its minimum energy conformation and that a loss of conformational degrees of freedom occurs; additionally, in a large-scale study of ligandreceptor complexes it was found that the bound conformation of ligands was around 20 kJ mol-1 higher in energy than the corresponding minimum energy conformation.34,35 Thus, bearing all this in mind, it can be considered that the energy difference observed between the two conformers of 2a can be overpassed. Therefore, we should take into account both quasiplanar and quasi-perpendicular conformers for the rest of the study.
It should be noted that the degree of non-planarity calculated for the perpendicular ethyl ester 2a (96.6°) is in good agreement with the experimental value obtained for the crystallographic structure of the related methyl ester 6 [108.6 (2)°].
Structures for 5 and 6 are shown in Figure 2. The solid state structure of 5 shows how the ester group and the guanidine moiety form an IMHB forcing the guanidinium slightly out of the thiophene plane (torsion 153.6 (2)°, approximately 40° thiophene ring plane to guanidinium plane). However, in the isomer 6 (related to the ethyl ester 2a), the guanidine moiety is almost perpendicular to the thiophene carboxylate system (approximately 74° thiophene ring plane to guanidinium plane), in agreement with our computational results for compound 2a. Probably, the strong ionic interaction between the guanidinium and the counter ion Cl- in the crystal unit (Figure 2), force the cation out-of-plane.
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A
B
Figure 2.- Symmetry generated full Cl- anion environments in the structures of (A) N-(2methoxycarbonylthien-3-yl)guanidine hydrochloride (5) (symmetry transformations used to generate equivalent atoms = –x, 0.5+y, 1.5-z; 0.5-x, -y, 0.5+z) and (B) N-(3methoxycarbonylthien-2-yl)guanidine hydrochloride (6) (symmetry transformations = 1.5-x, 0.5-y; -z; -x, -y, -z). IMHBs shown as dotted lines with atomic displacement shown at 50% probability.
Analysis of the electron density properties of all these compounds (and conformers) by means of the QTAIM theory was performed in order to identify possible IMHBs. All interactions found were characterised by the presence of a bond critical point (BCP) and the corresponding QTAIM molecular graphs are presented in Figure 3 for compounds 1a, 2c(planar), 3d and 4e and in Table S1 (see ESI) for the rest of the compounds and isomers studied. In the case of the families 1 and 3 neither IMHB nor other type of non-covalent interaction was identified between the guanidinium and the heterocycle or the CN substituent, in agreement with the lack of planarity observed. In the case of the carboxylate ethyl esters (family 2), IMHBs were identified between the carbonyl group of the ester and a NH of the guanidinium cation; additionally, a BCP between the S atom of the thiophene ring and an N atom of the guanidinium moiety was found. This could indicate a stabilizing interaction in which the lone pairs of S are donating into the cationic moiety (Figure 3). Also, the existence of a BCP is observed between the carbonyl O atom and an N of the guanidinium in those
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compounds with the thiophene ring perpendicular to the guanidinium. This has been previously reported by Diederich in 200536,37,38 and computationally studied by some of us.39 All these interactions are in agreement with the quasi-planarity observed in these derivatives and their rotamers. Regarding the thiazole core family 4, IMHBs were found in the five derivatives between the N atom of the heteroaromatic ring and a NH of the guanidinium cation.
The corresponding calculated electron density parameters at the BCPs (i.e. electron density, ρBCP and Laplacian of the electron density, 2ρBCP) are summarised in Table S2 (see ESI). The 2ρBCP values are positive for all these interactions indicating closed shell interactions. Looking at the ρBCP and at the corresponding intramolecualr interaction distances, it was possible to distinguish between IMHBs (i.e. O…HN or N…HN) with ρBCP values between 0.02-0.03 a.u. and distances between 1.89-2.06 Å, and other non-covalent interactions (i.e. N…O or N…S) with ρBCP values around 0.01 a.u. and distances between 2.81-3.12 Å. The extremely short intramolecular N···HN distances found in compounds 4a-e (1.93 Å compared with the sum of the van der Waals radii of N and H which is 2.75 Å), together with the large ρBCP and 2ρBCP values obtained (Table S2) indicate very strong IMHBs that force these molecules to planarity coherent with a HB in a positively charged system.
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Journal of Chemical Information and Modeling
1a
2c(planar)
3d
3e
Figure 3.- QTAIM molecular graphs of compounds 1a, 2c(planar), 3d and 4e. Bond critical points (BCPs) are indicated by green dots.
Investigation of the total energy density at the BCPs (HBCP) can provide further information on the nature of these interactions; thus, HBCP values 0.0 a.u. (Table S2, ESI) we can conclude that these interactions do not have any partial covalent character; however, it should be noticed that in the IMHBs found in the thiazole derivatives 4a-e, the HBCP values are very small (0.0009-0.0012 a.u.) and thus these interactions could be at the limit of having a certain covalent character.43,44
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In order to provide further information on the interactions found in these guanidinium systems, the Non-Covalent Interaction index (NCI)45 was analysed for two sample compounds with related structure, the thiophene 3d, which does not exhibit any IMHB interaction, and the thiazole 4d, which presents a strong IHMB. The resulting plots are shown in Figure 4.
Figure 4. NCI plots of the interactions found for compounds 3d (left), 4d (right). Green areas correspond to λ2 ≈ 0 (weak interactions) while blue areas are characteristic of λ2 > 0 (strong interactions). The λ2 value is one of the three eigenvalues of the electron density Hessian (λ1 ≤ λ2 ≤ λ3).
The plot corresponding to compound 3d shows a green area between one N-H of the guanidinium and the attached C atom of the thiophene maybe indicating a weak electron donation. A strong IMHB can be observed in compound 4d, as evidenced by the blue area found between the N-H of the guanidinium and the N atom of the thiazole ring.
Summarising, different IMHBs have been identified that can play a role in the planarity of the thiazo-2-yl guanidines (4a-e) and some of the rotamers of the ethyl 3-carboxylate thiophen-2yl guanidines (2a-e(planar)), whereas lack of IMHBs was observed for the non-planar systems such as the 3-unsubstituted or 3-cyano thiophen-2-yl guanidines (1a-e and 3a-e, respectively).
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Effect of planarity/non-planarity in the pharmacology at the α2-AR and drug-like properties We have previously found that the introduction of a heteroatom in the aromatic system connected to the guanidinium is detrimental for the α2-AR affinity since phenylguanidine shows the largest affinity compared to pyridine-2-ylguanidine (see Figure 1) or even thien-2ylguanidine.17,19 However, we also found that the introduction of an IMHB, reducing the basicity of the guanidinium, could result in an improvement of the α2-AR affinity as can be observed when comparing pyridin-2-ylguanidine (IMHB, experimental pKi = 5.74,17 calculated pKaH = 9.5446) and pyridine-3-ylguanidine (no IMHB, experimental pKi = 3.79,17 calculated pKaH = 10.1446). Therefore, considering the previously evaluated α2-AR affinity (pKi values) of some of the computationally studied guanidinium derivatives (Table 2) we have searched for any possible relation with different structural and physicochemical features.
Thus, α2-AR engagement (pKi) has been compared to molecular planarity (measured by the dihedral angle between the ring and the guanidinium system, Table 1), basicity (calculated pKaH of guanidinium, Table 2) as well as other physicochemical calculated parameters such as molecular weight (Da), lipophilicity (logP and logD(7.4)), polar surface area (PSA, Å) and solubility (g/L). The full set of physicochemical data, which was calculated using the Marvin package,46 is presented in Table S3 and data corresponding to compounds whose α2-AR affinity was known is shown in Table 2.
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Table 2.- Binding affinity for the human α2-ARs expressed as pKi calculated from [3H]RX821002 (≈ 2 nM) competition binding experiments,19 molecular planarity (computed dihedral angles, Table 1), calculated solubility (g/L) and basicity (calculated pKaH of the guanidinium). Compd.
Structure NH HCl
1c
2c (planar/ perpend.) 2d (planar/ perpend.) 2e (planar/ perpend.)
S
N H
Solubility (g/L)b
Basicity (pKaH gua.)b
7.06
96.4
79.6
9.83
7.50
96.9
24.7
9.76
S
N H
6.81
93.8
7.1
9.74
4.18
108.7/32.0
3.7
9.71
3.93
112.7/37.0
0.9
9.66
4.58
111.1/24.0
0.3
8.13
1 g/L) water soluble. This is independent of the degree of planarity and could be attributed to the presence of the guanidinium system that is highly hygroscopic.
Additionally, no correlation was found between MW, PSA or logP and the α2-AR receptor engagement (pKi). However, it was possible to find a certain relation between the calculated logD(7.4) values and the α2-AR affinity (pKi = 7.14 e-0.21 logD(7.4); R² = 0.6588), what makes sense since it is well established that druggability is dependent on lipophilicity, and logD(7.4) is the most reliable descriptor for lipophilicity.47 When comparing the basicity of the compounds studied (calculated pKaH) with the α2-ARs affinity, we found a linear correlation (pKi = - 0.61 + 0.79 pKaH; R² = 0.8477), but only for those systems (1c-e, 3c-e and 4c-d) that exclusively present planar or perpendicular conformations, not including the ethyl esters (2be) which can adopt both of those conformations.
Finally, comparing the α2-ARs affinity with the planarity of the molecules (Figure 5) three different clusters can be identified based on the dihedral angles between heterocycle and guanidinium moieties. First, quasi-planar compounds with dihedral angles between 24-53° (green cluster in Figure 5), then compounds that show a perpendicular conformation with dihedral angles between 93-116° (red cluster in Figure 5) and, finally, the planar thiazoles (purple cluster in Figure 5). Compounds 2b-e can exist as two different rotamers (see torsions in Table 1) and, from an energetic point of view, both could equally engage with the target; therefore, in the experimental assays both rotamers for each compound would provide only
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one α2-AR’s affinity value. Accordingly, each rotamer (denoted as 2b-e and 2b’-e’ in Figure 5) has been represented in the graph vs. the α2-AR pKi experimental value of the compound.
Figure 5.- Relation between planarity (measured as the dihedral angles in Table 1) and α2AR’s affinity (expressed as pKi) for compounds 1c-e, 2b’-e’/2b-e (planar/perped.), 3c-e and 4c-d. The green cluster gathers quasi-planar compounds with torsions between 24-53°; the red cluster groups compounds with torsions between 93-116°; the purple cluster assembles the planar thiazoles.
It is interesting that the planar thiazole derivatives are in a cluster by themselves with a good to medium α2-ARs affinity (pKi around 6); hence, they should be treated separately. Even though not a clear correlation is found among the thiophen-2-yl series, it seems that the red cluster (non-planar systems) has more compounds with good α2-ARs affinity (pKi > 6) than the green cluster (all pKi < 5). Therefore, the formation of IMHBs seems to be detrimental for the α2-ARs affinity of thiophen-2-yl guanidines.
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CONCLUSIONS Considering the potential planarity imposed by IMHBs that can be achieved by S-containing five membered heterocyclic guanidines, four families of these derivatives with thiophen-2-yl (1), 3-carboxylatethiophen-2-yl ethyl esters (2), 3-cyanothiophen-2-yl (3) and 2-thiazolyl (4) cores were computationally studied at M062X/6-311++G(p,d) level and the nature of the interactions found was analysed by means of the QTAIM and NBO approaches.
Different types of interactions were observed in these derivatives depending on the nature of the S-containing heterocycle and the substituents in position 3. In the case of thiophen-2-yl guanidines with no substituent (1a-e) or with a CN (3a-e) in position 3, lack of planarity is observed in all the compounds studied; this is in agreement with the solid state structure determined by crystallography for compound 6. On the contrary, all thiazo-2-yl guanidines studied (4a-e) are found to establish strong IMHBs, locking the guanidinium cation in a planar restricted conformation. Finally, two different rotamers were found for the ethyl 3carboxylate thiophen-2-yl guanidines 2a-e, one quasi-planar (exhibiting IMHBs and other non-covalent interactions between guanidinium and ester groups) and another quasiperpendicular, and, from an energy point of view, both could equally engage with the target.
No correlation was found between the degree of planarity and most of the calculated physicochemical properties. Regarding aqueous solubility, we found that most of the compounds can be classified as moderately to highly water soluble, independently of the degree of planarity and probably more related to the presence of the guanidinium system.
Comparison of the α2-ARs affinity with the dihedral angle between the heterocyclic and guanidinium moieties yielded no correlation; however, three different clusters were observed:
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compounds with dihedral angles between 24-53°, perpendicular compounds with dihedral angles between 93-116° and planar thiazoles. Thiazoles, which are in a cluster by themselves showed a good to medium α2-ARs affinity (pKi around 6) and they should be treated separately. In the case of the thiophen-2-yl series, it seems that there are more compounds with good α2-ARs affinity (pKi > 6) among the non-planar systems than among the quasiplanar compounds (all pKi < 5). Therefore, the formation of IMHBs seems to be detrimental for the α2-ARs affinity of thiophen-2-yl guanidines.
ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge from the ACS Publications website at DOI: ??. CCDC 1530438-1530439 contains the supplementary crystallographic data for this work. The data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/structures.
AUTHOR INFORMATION Corresponding Authors Cristina Trujillo, email:
[email protected]; Phone: +353 1 896 4508, and Isabel Rozas, email:
[email protected]; Phone: +353 1 896 3731.
ORCID Cristina Trujillo: 0000-0001-9178-5146 Isabel Rozas: 0000-0002-6658-6038
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Author Contributions C.T. contributed to the development of the idea, performed all computational studies and participated in the manuscript writing; A.F. did all the original synthesis work, discussed the pharmacological results and participate in the manuscript writing; G.S.S participated in the computational studies and performed all correlations and NCI studies; B.T. carried out the Xray study and participated in the manuscript writing; I.R. conceived the idea, supervised all chemical and medicinal chemistry work and wrote the manuscript. All authors have given approval to the final version of the manuscript.
ACKNOWLEDGEMENTS Thanks are given to the Irish Research Council for postgraduate support (A.F., “IRCSET 2007-Aoife_Flood-PG-EMBARK”). The authors thank Dr. Thomas McCabe for his preliminary work solving the crystallographic structures reported. Thanks are also given to the Irish Centre for High-End Computing (ICHEC) for the provision of computational facilities.
ABBREVIATIONS USED α2-ARs: α2-adrenoceptors; [3H]RX821002: 2-methoxyidazoxan; pKi: minus logarithm of the affinity constant; pKaH: minus logarithm of the acid constant; NCI: non-covalent interaction index; QTAIM: quantum theory of atoms in molecules.
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