J. Phys. Chem. B 2005, 109, 4279-4284
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Conformations and Tautomers of 5a,6-Anhydrotetracycline Kathrin Meindl and Timothy Clark* Computer-Chemie-Centrum, Friedrich-Alexander-UniVersita¨t Erlangen-Nu¨rnberg, Na¨gelsbachstrasse 25, 91052 Erlangen, Germany ReceiVed: October 27, 2004; In Final Form: December 9, 2004
Ab initio and density functional theory (DFT) calculations have been used to investigate the conformations and tautomeric forms of neutral anhydrotetracycline in aqueous solution.
Introduction 5a,6-Anhydrotetracycline (anhydrotetracycline or Atc), 1, is a toxic degradation product, formed either by photolysis1 or under acidic conditions2 from members of the tetracycline class of antibiotics3 with an active group in the 6-position.
within a free energy range of 10 kcal mol-1. We now report an analogous study for neutral 5a,6-anhydrotetracycline, 1, that is designed to detect differences in behavior, tautomerism, and conformations between the two tetracyclines. Some of these differences may be relevant for the contrasting behavior of the two molecules in biological systems. Experimental Procedures
Atc shows reduced antibacterial activity compared to tetracycline but binds to the tetracycline repressor protein (TetR) about 500 times more strongly than the parent compound4 and induces the tetracycline repressor system about 24 times more efficiently than tetracycline.5 This characteristic is important in view of the interest in tetracyclines as “gene switches”6 that arises from the regulatory function of TetR in the expression of the tetracycline antiporter protein, which actively transports tetracyclines from within resistant bacteria.7 A further fascinating aspect of Atc is that it is able to bind to TetR without a complexed Mg2+ ion,5 which is necessary for tetracycline to bind. Although an X-ray structure of Atc as its monohydrated hydrobromide is available,8 the exact chemical constitution [i.e., which tautomer(s) is(are) present under physiological conditions] and conformations of Atc remain unclear. There have been many experimental studies, ranging from 1H9 and 13C NMR10 to circular dichroism11 to numerous X-ray12 and a combined experimental and theoretical analysis of the vibrational spectra13 studies on tetracycline and its derivatives, but these have failed to provide a consistent and complete picture of the tautomeric and conformational equilibria available to the tetracyclines. We recently reported14 a comprehensive density functional theory (DFT) and ab initio study of neutral tetracycline in water, in which we concluded that two conformations each (the twisted and extended conformations11,15) of up to six different tautomers of neutral tetracycline can exist in water at room temperature * Corresponding author: e-mail
[email protected].
Density functional calculations all used the Becke threeparameter hybrid functional16 in conjunction with the LeeYang-Parr correlation functional17 (B3LYP) and the 6-31G(d) basis set.18 Geometries were optimized fully in vacuo by use of Gaussian 98.19 The structures obtained were confirmed as local minima by calculating their normal vibrations within the harmonic approximation. Single-point calculations on the optimized geometries by use of the self-consistent reaction field (SCRF) technique in a simulated water continuum were used to obtain energies “in solution”. The SCRF calculations used the standard polarizable continuum model (PCM) with a cavity generated with the united-atom topological model.20 Single-point calculations with the same basis set were also performed with a second-order Møller-Plesset (MP2)21 correction for electron correlation. Corrected MP2 relative energies were calculated by use of the gas-phase Born-Oppenheimer relative energies from these calculations and application of the vibrational and solvation corrections calculated with B3LYP. NMR chemical shifts were calculated by the gauge-independent atomic orbital (GIAO) approach.22 The calculated shieldings, σ, for carbon atoms were converted to 13C chemical shifts relative to tetramethylsilane, δ, by use of the regression formula23
δ ) 208.68 - (1.0716σ)
(1)
Finally, the absorption and fluorescence spectra of the B3LYP/ 6-31G(d) structures were calculated by use of a singles-pluspair-doubles configuration interaction (CI)24 within the program VAMP 8.1,25 with the AM1 Hamiltonian26 and our SCRF model for excited states27 as extended by Gedeck and Schneider28 to treat nonequilibrium solvation. Sixteen occupied and 16 virtual orbitals were included in the CI. Tests with larger and smaller numbers of active orbitals suggested that the results are converged for all calculations with more than 24 orbitals in the active space. Starting structures for the geometry optimizations were selected from the six conformations found in an AM1 study17 analogous to our earlier one for tetracycline.18 The 19 most likely
10.1021/jp0451039 CCC: $30.25 © 2005 American Chemical Society Published on Web 02/10/2005
4280 J. Phys. Chem. B, Vol. 109, No. 9, 2005
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TABLE 1: Calculated Relative Energies for Neutral 5a,6-Anhydrotetracycline Conformations and Tautomersa hydrogen bond species conformation N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11 N12 N13 N14 N15 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Z13 Z14 Z15 Z16 Z17 Z18 Z19 Z20 Z21 Z22 Z23 Z24 Z25 Z26 Z27 Z28 Z29 Z30 Z31 Z32 Z33 Z34 Z35
t t e e e t t t e t t t e e e t t e e e e t t t t e e e t t e t t e t t e e t t t e e e e e e e e t
O12a O1 O1 O12 O12 O12 xb O1 O1 N O1 x O1 O1 x x O1 O1 O12 O12 O12 O12 O1 O1 O1 O1 O12 O12 O12 O1 O1 O12 O12 O12 O1 O1 O1/O12 O12 O12 O1/O12 O1 O1 O1 O12 O12 O12 O12 O12 O12 O12 O12
O1 O3 O11
O12
A O11 A O11 A O11 A O11 A O11 A O11 N O12 N O11 A O12a A O1 A O1 A O1 A O1 A O12a A O1/O12a O12 O11 O12 O12 O11 O11 O12 O11 O12 O11 A O1 O1 A A A O1 A
O1 O1 O12 O1 A A O12 A O12
relative energy
amine amide O amide N 0 K 298 K 298 K, PCM MP2-corrected (298 K, PCM)
O3 O3 O12 O3 O12a O3 x x x x O12a O12a O12a O3 O3 O12a O3 x O12a O3 x O3 O3 x O3 x O12a O12a O3 O3 O3 x O3 x x
O1 O3
O1 O1 O1 O3 O3
O3
O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O3 O3 O1 O1 O1 O1 O3 O3 O1 O3 O3 O3 O3 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1 O1
0.0 3.9 5.5 6.8 8.2 8.4 13.5 15.0 15.7 15.9 18.9 19.5 21.8 23.4 23.6 19.8 21.1 24.8 24.0 27.1 26.2 30.0 30.6 30.7 31.3 30.8 30.8 31.6 32.8 32.9 33.2 35.5 36.3 37.0 35.8 36.6 37.1 37.2 38.0 37.9 39.5 39.4 38.9 38.8 39.5 42.2 43.7 43.1 43.6 45.0
0.0 3.4 5.0 6.6 8.0 8.1 13.3 14.9 15.4 15.4 18.4 19.1 21.6 22.7 22.5 19.4 21.0 24.5 23.4 27.0 25.8 29.7 30.6 30.0 30.6 31.0 30.7 31.9 32.6 32.5 33.4 35.4 36.7 36.7 35.6 36.9 36.6 36.8 38.3 37.7 39.4 38.8 38.4 38.4 38.4 41.8 43.8 42.2 43.5 44.8
0.0 3.6 4.9 6.9 5.9 3.9 7.8 10.7 7.9 12.0 12.5 14.4 16.3 14.8 17.1 8.7 9.7 8.7 8.5 10.1 11.2 11.8 13.1
0.0 4.1 6.9 8.8 6.9 3.5 3.1 8.3 5.6 11.5 11.8 14.2 14.6 15.2 18.3 2.5 5.8 0.0 3.8 4.0 9.1 4.3 7.7
c
c
11.3 5.3 7.9 6.1 16.6 16.1 8.1 13.5 19.0 17.2 10.9 42.9 11.2 6.4 19.6 12.0 24.6 17.4 18.3 9.1 18.7 9.1 11.0 18.9 9.9 17.2
6.8 2.1 4.8 2.5 11.2 10.8 3.4 9.3 11.6 9.9 5.9 35.2 9.6 4.3 11.3 6.2 17.3 11.3 10.2 6.4 16.1 5.2 6.3 15.4 5.2 8.5
a Energies are given in kilocalories per mole. The extended conformation11,14 is designated as e and the twisted one as t. The column headed O12a defines the atom to which the proton bonded to O12a (always protonated) makes a hydrogen bond. The columns headed Hydrogen Bond indicate that the atom given is protonated if an entry is present. The entries for the individual conformations indicate the atom to which the relevant proton makes a hydrogen bond. The Me2N nitrogen is indicated by N and the amide oxygen atom by A. The MP2-corrected relative energy was calculated as described in the methods section. Completely un-ionized structures are designated N and zwitterionic ones Z. b The atom is protonated but does not form a hydrogen bond. c The UAHF-PCM calculation failed consistently for structure Z9.
tautomers (three un-ionized and 16 zwitterionic, obtained by considering the protonation positions N4, O1, O2, O3, O11, and O12) were constructed for each of the conformations by shifting protons without changing the geometries of the non-hydrogen atoms. This gave a total of 114 starting structures, 64 of which optimized to local minima found for other starting geometries. This procedure resulted in 50 unique combinations of the ring conformation and tautomeric form. These 50 structures (15 unionized and 35 zwitterionic) were then characterized in terms of their calculated energies at 298 K in aqueous solution and their spectroscopic properties.
Results Conformations Obtained. Table 1 shows the calculated relative energies for the 50 minima obtained for neutral Atc. Table S1 of the Supporting Information gives the calculated total and zero-point vibrational energies. The most stable completely un-ionized structure found, N1, is shown in Figure 1. It is found to be the “conventional” tautomer with O10 and O12 both protonated and making hydrogen bonds to O11. The twisted conformation is fixed by the network of O12aH‚‚‚O1, amide-NH‚‚‚O1, and O3H‚‚‚amide-O hydrogen bonds. Note that the O12aH‚‚‚N hydrogen bond found for the
Conformations of 5a,6-Anhydrotetracycline
Figure 1. Most stable structure (N1, twisted) calculated for the unionized form of anhydrotetracycline. Hydrogen bonds are indicated by dashed lines.
Figure 2. Most stable extended structure (N3) calculated for the unionized form of anhydrotetracycline. Hydrogen bonds are indicated by dashed lines.
two most stable un-ionized twisted conformations of tetracycline14 is only found in one relatively unstable structure (N9) for Atc. The next most stable un-ionized structure N2 differs from N1 only in that the dimethylamine group is inverted, so that in N2 the nitrogen lone pair points toward O3. The most stable extended conformation N3 is shown in Figure 2. This structure differs from N1 in that the hydrogen bond from O12aH has shifted to O12, providing a stable network of three hydrogen bonds (O10H‚‚‚O11, O12H‚‚‚O11, and O12aH‚‚‚O12) that appear to stabilize the extended conformation effectively, as conformations N3-N5 all exhibit this hydrogen-bond pattern. However, whereas for the un-ionized form of tetracycline the difference between the lowest twisted and extended conformations was found to be only 3.7 kcal mol-1 (MP2-corrected relative energy at 298 K),14 the free-energy difference between structures N1 and N3 for Atc is found to be 6.9 kcal mol-1 at the same level of theory. Thus, un-ionized Atc is conformationally more rigid (in the sense that the extended conformation is less accessible energetically) than un-ionized tetracycline. Note also that the extended conformation of tetracycline was found to be the more stable in the gas phase,14 an effect not found for Atc. N1 is found to be the most stable un-ionized structure in both the gas phase and solution. The strong solvation preference for the extended conformation observed for tetracycline14 is not found for Atc. This results in the preferred conformation for un-ionized Atc in solution being the twisted one, whereas tetracycline was found to prefer the extended conformation.14 The zwitterionic tautomers of Atc, on the other hand, behave far more similarly to tetracycline. The most stable gas-phase structure, Z1, has the twisted conformation, but solvation stabilizes the extended conformation preferentially, so that the most stable zwitterionic structure in solution is found to be Z3, which exhibits the extended conformation. Figure 3 shows the structure of the most stable gas-phase structure, Z1. The
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Figure 3. Most stable structure (Z1, twisted) calculated for the zwitterionic form of anhydrotetracycline in the gas phase. Hydrogen bonds are indicated by dashed lines.
Figure 4. Most stable structure (Z3, extended) calculated for the zwitterionic form of anhydrotetracycline in solution. Hydrogen bonds are indicated by dashed lines.
hydrogen-bond network resembles that found for N1 with the exception that the O3H‚‚‚amide-O hydrogen bond from the neutral structure is replaced by an amine-NH‚‚‚O3 link in the zwitterion and the proton found on O12 in the un-ionized structure shifts to O11 in the zwitterion. The most stable zwitterionic structure in solution, Z3, is shown in Figure 4. This structure shows an extended hydrogenbond network from O10H‚‚‚O11 via O11H‚‚‚O12 and O12aH‚‚‚ O12 to amine-NH‚‚‚O12a. The latter was also found to be indicative of the extended conformation in tetracycline.14 It is, however, not as prevalent for Atc as for tetracycline. The energy difference between the most stable zwitterionic extended structure (Z3) and its twisted counterpart (Z1) is calculated to be 2.5 kcal mol-1, compared with 3.2 kcal mol-1 for tetracycline.14 Calculated Spectra. As for tetracycline,14 the vibrational, NMR, and UV/vis spectra were calculated for the 50 structures found for Atc. Also as for tetracycline, no significant trends could be found in the vibrational frequencies and IR intensities, so that we simply include the data in the Supporting Information for those who wish to analyze them. NMR Spectra. All calculated chemical shifts (13C, 15N, and 17O) are given in Tables S4 and S5 of the Supporting Information. We will discuss only the 13C shifts here. As for tetracycline,14 the 13C chemical shifts for C4a, C5, and C6 are diagnostic for the molecular conformation. Figure 5 shows a 3D plot of the chemical shifts of these three carbons in which the extended conformations are shown in gray and the twisted in black. The twisted and extended conformations cluster together, as for tetracycline. The one exception is structure Z28, which clearly adopts a twisted conformation but lies in the extended cluster. The geometry of the ring scaffold of this structure is not unusual, so we have no explanation for the deviation. However, Z28 is calculated to be a high-energy structure, so the deviation probably has no experimental consequences.
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Figure 5. Plot of the calculated 13C chemical shifts for C4a, C5, and C6 for the 50 structures reported here. Extended conformations are shown as gray dots; twisted conformations as black dots. Structure Z28 is circled.
TABLE 2: Calculated (AM1/CI) Vertical Excitation Energies and Oscillator Strengths in Water for the Ten Most Stable Structures of Anhydrotetracyclinea species >310 nm Z3
375 (0.226)
N1 Z11
383 (0.420) 378 (0.418)
Z1
367 (0.201)
Z13
377 (0.405)
Z16 N7 N6 Z4 Z5
368 (0.432) 369 (0.205) 382 (0.434) 373 (0.228) 395 (0.478)
260-310 nm
