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Contributions of internal motions to molecular dynamics in solution. A nuclear magnetic resonance investigation
Volume 193, number 6
CHEMICAL PHYSICS LETTERS
12 June 1992
Contributions of internal motions to molecular dynamics in solution. A nuclear magnetic resonance investigation Claudio Rossi Department of Chemistry, University ofsiena, Pian dei Mantellini, 44, 53100 Siena, Italy
Received 3 March 1992; in final form 1 April 1992
The dynamical properties of piroxicam in solution were investigated on the basis of carbon spin-lattice relaxation data. In order to account for the complex molecular motion, an analysis based on Woessner’s equation is proposed. Correlation times describing overall reorientation and internal motions were determined. Our results demonstrate the existence of a unique molecular axis for internal reorientation, and enable geometrical correlations based on the calculated effective correlation times to be defined.
Nuclear magnetic resonance spectroscopy (NMR ) is the most suitable technique for the structural investigation and analysis of the dynamical properties of biomolecules in solution. Several new experimental techniques, which extend the range of applicability of NMR to larger size macromolecules and permit the analysis of their motions, have been proposed [l-6]. Knowledge of the motional properties of ligand biomolecules is important because in some cases a clear definition of the ligand-target interaction can be obtained. Relaxation experiments have been used to detect anisotropic molecular motions [ 7-9 1. The analysis of the carbon spin-lattice relaxation rates of ligand molecules is a particularly appropriate method fro mapping the dynamical behaviour of different molecular moieties. For proton-bearing carbons, the main source of longitudinal relaxation is the intramolecular dipole-dipole interaction (IDD) with the bonded proton nucleus [ lo- 12 1. The use of a suitable equation [ lo] allows the calculation of the effective correlation time r, modulating the ‘H-13C dipolar coupling. The IDD interaction is affected to different extents by the presence of anisotropic internal motions, depending on the direction of the anisotropic vectors. In many small to medium size Correspondence to: C. Rossi, Department of Chemistry, University of Siena, Pian dei Mantellini, 44, 53100 Siena, Italy.
biomolecules in which the longitudinal and transversal dimensions are not equal, the reorientational motion of the molecule cannot be described by a single isotropic correlation time. In fact contributions due to internal rotation of the overall molecule and its moieties along the main longitudinal axis are expected to affect the experimentally observed carbon spin-lattice relaxation rate. The aim of this paper is to analyze the dynamical behaviour of a molecule in solution on the basis of the isotropic component and the component of motion due to internal reorientation. Piroxicam was used as a model compound because: (i) it seems to be a typical molecule in which both the isotropic and the internal reorientational components have to be considered in order to describe the molecular motion; (ii) it is a well-known anti-inflammatory drug and represents a class of natural and synthetic molecules able to modulate enzymatic and/or metabolic activities. Piroxicam (4-hydroxy-2-methyl-N-2-pyridinyl-2H1,2-benzothiazine-3-carboxamide- 1,2-dioxide) (fig. 1) was kindly donated by Pfizer and used without further purification as 0.15 mol dm’ 3 DMSO-d, solution. A Varian XL-200 spectrometer operating at 50.3 MHz was used to record 13C NMR spectra. Spin-lattice relaxation rates (R, ) were obtained using a ( 180”-T-90”-t). pulse sequence and computer fitting of the magnetization recovery curves.
0009-2614/92/S 05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
553
CHEMICAL PHYSICS LETTERS
Volume 193, number 6
12 June 1992
____4&&@~~-~-
2
CH 3
02
Fig. 1. Structure of piroxicam and atom numbering used in the present discussion. The main direction of internal motion is also shown.
Proton-carbon “broad-band” nuclear Overhauser effect values (NOEBB), determined by the equation NOEBB= (I, - IO)/I,, (where Z, and IO are the peak intensities measured under continuous and gated proton decoupling conditions, respectively) show a complete dipolar relaxation pathway for all the protonated carbon nuclei of piroxicam. There was an estimated experimental error of 3O/6in the R, measurements. All measurements were performed at a temperature of 22’ C. The dipolar contribution to the experimental carbon relaxation rate R, can be calculated by the equation RpD=f
DDRl,
(1)
where f DD,the fractional dipolar contribution, is determined by comparing the experimental and theoretical NOEBBvalues (calculated of carbon nuclei relaxing entirely by a dipolar mechanism). Under the present experimental conditions, f DD was equal to 1 for all the proton-bearing carbons. Table 1 shows the 13Cchemical shifts and dipolar relaxation rates of protonated carbon nuclei. The effective correlation time r, modulating the protoncarbon dipolar coupling can be determined by the equation
Table 1 Spin-lattice relaxation rates of protonated carbons, correlation times and angles @for a 0.15 mol dm-’ DMSO-d, solution of piroxicam at 22°C Carbon No.
6”) (ppm)
14 12 4 3 5 2 13 11
145.43 139.93 133.13 132.63 126.45 123.80 119.97 116.24
2.1 2.1 3.2 4.0 2.6 .,2.6 5.1 2.0
4 b) ;‘s, 9.10x lo-” 9.10x lo-” 1.42x IO-” 1.80x lo-“’ 1.14x10-‘0 1.14x IO-I0 2.40x lo-” 8.70x lo-”
60 -60 40 -20 100 -80 0 -120
a) ppm from TMS. b, The angles 4 reported are defined by the internal rotation axis and the C-H, bond direction. The o values are taken as positive if obtained moving in a clockwise direction from the internal rotation axis, otherwise they are taken as negative.
29~and rC_Hthe proton-carbon distance, assumed constant in this case. For molecules experiencing internal reorientation the effective correlation time r, reported in eq. (2) is given by Woessner’s equations [ 7,13 ] : T~=A~,+BT,+DT,,
(3)
where the geometrical factors A, B and D are
B,,,,= rn2r&y:: I 10 rIH
A=~(~cos*@-I)*,
(4)
B= a sin*( 2@) ,
(5)
D= $ sin4@.
(6)
(2) where w, and IS, and yH and yc are the proton and carbon Larmor frequencies and the magnetogyric ratios respectively, fi is Plan&s constant divided by 554
RFD (s-1)
The angle @is the angle defined by the proton-carbon bond direction and the molecular rotor axis. It may be noted that A + B + D = 1. The three correla-
Volume 193, number 6
tion times reported in eq. (3) are given by (7)
rA=TR,
12 June 1992
CHEMICAL PHYSICS LETTERS
Tg’ =rR’ +&’
)
(8)
z,‘=ri’+&’
)
(9)
Table 2 Correlation time values (s) describing the dynamical behaviour of piroxicam determined from carbon spin-lattice relaxation rates of 0.15 mol dm-’ DMSO-d, piroxicam solution at 22°C 2.4x 1.2x 4.7x 2.4x 4.0x 2.4x 3.4x
7,
where rI = rR is the correlation time for the isotropic tumbling molecular reorientation and rr ’ = ZK ’ + TG’. In the last equation ro is the diffusional correlation time for the internal reorientation and rlIdescribes the motion along the main molecular axis. The first term of eq. (3) gives the isotropic contribution to the effective correlation time whereas the second and third terms are mainly related to the internal reorientational motion, The dynamical properties of both the pyridinyl and the benzothiazine moieties of piroxicam were analyzed with the use of the above equations. (A) Pyridinyl moiety. From the results reported in table 1 can be observed that C”, Cl2 and Cl4 nuclei show similar rc values. This suggests a similar contribution of the second and third terms of eq. (3) to r,. Given that the proton-carbon pairs are aligned in directions shifted by about 60” moving from C’ l to C14,a similar contribution by the second term of eq. (3) to Cl’, Cl2 and Cl, is observed only if the axis of the internal rotation is aligned with the direction of Cl 3-H l 3 bond. Under these conditions $ is 60 ’ for C 12, -60” for Cl.,, 120” for Cl’ and 0” for C’3. The isotropic correlation time rR=rA=rI can then be calculated from the rc value of C13. In this case the second and the third terms of eq. (3) do not contribute to 7, and the effective correlation time assumes the value of the isotropic reorientational motion rR. For C’,, CIZ and C4 carbons r, and ?‘, can be obtained by solving a system of three equations, i.e. (3), (8) and (9) with three unknowns rB, rD and rG. The results are reported in table 2. (B) Benzothiazine moiety. For the benzothiazine moiety the interpretation of the correlation time rc modulating the ‘H-13C dipolar interactions of C2, C3, C, and C5 carbons, requires deeper investigation. On the basis of eq. (3) and using the T,+ r, nd rD correlation times calculated from analysis of the carbon relaxation of the pyridinyl moiety, the theoretical dependence curve of T=on the angle $ between the internal reorientational axis and the proton-carbon bond direction can be calculated (fig. 2).
7B 7D 7R 7, 7L 7u
lo-” lo-I0 lo-” lo-“’ lo-” lo-“’ lo-”
From the curve in fig. 2 a good fit is observed between the effective correlation times calculated for C2, C3, C, and C5 carbons and the geometrical parameters. If an angle of - 80” between the protoncarbon bond direction and the direction of the internal motion is assumed for the C2 nuclei, the theoretical rc values for C3, C, and C5 are obtained by increasing the angle $ considered for the CZ carbon by 60” each time. Using fig. 2 we can observe that for 9 of - 80’) - 20’) 40’ and 100 ’ respectively, the theoretical 7, values are in good agreement with the
-: 0-160 L
-90
0
90
’
180
f#
Fig. 2. Plot of the effective correlation time 7, as expressed by eq. (3) versus @,the angle between the internal reorientational axis and the proton-carbon bond direction. The correlation times used were7,=2.4x10-‘0s,7B=1.2~10-‘0sand7,=4.7~IO-”s. 555
Volume 193, number 6
CHEMICAL PHYSICS LETTERS
experimentally determined effective 7c for Cz, C3, C, and C5. From these results two considerations are possible: (i ) The curve reported in fig. 2 is calculated on the basis of dynamical parameters obtained from the pyridinyl moiety. Since this curve can be used for describing the dynamical behaviour of the benzothiazine moiety, it must be assumed that a unique internal reorientational motion about the same axis occurs in the molecule (fig. 1). (ii) The fit of the 7c values for C2, C3, C4 and C5, obtained by adding standard degrees to the angle 9 of the C2 carbon, shows good correspondence between the theoretical structure and the experimental one. Conclusions. From the carbon spin-lattice relaxation experiments reported in table 1, a set of correlation times describing the entire molecular dynamics can be derived. These calculated correlation times are reported in table 2. The proposed method of analysis can be used to obtain information about the direction of internal reorientational axes in the presence of internal motions. This approach can also be used to calculate the angle between the reorientational axis and the proton-carbon bond direction,
556
12 June 1992
information which can define molecular geometry in solution.
References [ 1] B.A. Borgias and T.L. James, J. Magn. Reson. 79 (1988) 493.
[ 21 C. Rossi, M.R. Sansoni and A. Donati, Chem. Phys. Letters 187 (1991) 439. [3] N.J. Oppenheimer and T.L. James, eds., Nuclear magnetic resonance, spectral techniques and dynamics, Vol. 176 (Academic Press, New York, 1989). [4] N. Marchettini, Y. Yang and C. Rossi, J. Phys. Chem. 95 (1991) 10811. [ 5 ] K. Wiithrich, NMR of proteins and nucleic acid (WileyInterscience, New York, 1986), and references therein. [6] V. Sklenar, D. Torchia and A. Bax, J. Magn. Reson. 73 (1987) 375. [7] D.E. Woessner, J. Chem. Phys. 36 (1962) 1. [ 8 ] D. Lipari and A. Szabo, J. Am. Chem. Sot. 104 ( 1982) 4546. [ 91 G. Lipari and A. Szabo, J. Am. Chem. Sot. 104 ( 1982) 4559. [IO] A. Allerhand and R.A. Komoroski, J. Am. Chem. Sot. 95 (1973) 8228. [ 111 C. Ross, N. Niccolai and F. Laschi, J. Phys. Chem. 9 1 ( I987 ) 3903. [ 12 ] C. Rossi and N. Niccolai, Chem. Phys. Letters 142 ( 1987 ) 4181. [ 131 R.K. Harris, NMR spectroscopy (Pitman, London, 1983) pp. 113-116.
CHEMICAL PHYSICS LETTERS
12 June 1992
Contributions of internal motions to molecular dynamics in solution. A nuclear magnetic resonance investigation Claudio Rossi Department of Chemistry, University ofsiena, Pian dei Mantellini, 44, 53100 Siena, Italy
Received 3 March 1992; in final form 1 April 1992
The dynamical properties of piroxicam in solution were investigated on the basis of carbon spin-lattice relaxation data. In order to account for the complex molecular motion, an analysis based on Woessner’s equation is proposed. Correlation times describing overall reorientation and internal motions were determined. Our results demonstrate the existence of a unique molecular axis for internal reorientation, and enable geometrical correlations based on the calculated effective correlation times to be defined.
Nuclear magnetic resonance spectroscopy (NMR ) is the most suitable technique for the structural investigation and analysis of the dynamical properties of biomolecules in solution. Several new experimental techniques, which extend the range of applicability of NMR to larger size macromolecules and permit the analysis of their motions, have been proposed [l-6]. Knowledge of the motional properties of ligand biomolecules is important because in some cases a clear definition of the ligand-target interaction can be obtained. Relaxation experiments have been used to detect anisotropic molecular motions [ 7-9 1. The analysis of the carbon spin-lattice relaxation rates of ligand molecules is a particularly appropriate method fro mapping the dynamical behaviour of different molecular moieties. For proton-bearing carbons, the main source of longitudinal relaxation is the intramolecular dipole-dipole interaction (IDD) with the bonded proton nucleus [ lo- 12 1. The use of a suitable equation [ lo] allows the calculation of the effective correlation time r, modulating the ‘H-13C dipolar coupling. The IDD interaction is affected to different extents by the presence of anisotropic internal motions, depending on the direction of the anisotropic vectors. In many small to medium size Correspondence to: C. Rossi, Department of Chemistry, University of Siena, Pian dei Mantellini, 44, 53100 Siena, Italy.
biomolecules in which the longitudinal and transversal dimensions are not equal, the reorientational motion of the molecule cannot be described by a single isotropic correlation time. In fact contributions due to internal rotation of the overall molecule and its moieties along the main longitudinal axis are expected to affect the experimentally observed carbon spin-lattice relaxation rate. The aim of this paper is to analyze the dynamical behaviour of a molecule in solution on the basis of the isotropic component and the component of motion due to internal reorientation. Piroxicam was used as a model compound because: (i) it seems to be a typical molecule in which both the isotropic and the internal reorientational components have to be considered in order to describe the molecular motion; (ii) it is a well-known anti-inflammatory drug and represents a class of natural and synthetic molecules able to modulate enzymatic and/or metabolic activities. Piroxicam (4-hydroxy-2-methyl-N-2-pyridinyl-2H1,2-benzothiazine-3-carboxamide- 1,2-dioxide) (fig. 1) was kindly donated by Pfizer and used without further purification as 0.15 mol dm’ 3 DMSO-d, solution. A Varian XL-200 spectrometer operating at 50.3 MHz was used to record 13C NMR spectra. Spin-lattice relaxation rates (R, ) were obtained using a ( 180”-T-90”-t). pulse sequence and computer fitting of the magnetization recovery curves.
0009-2614/92/S 05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
553
CHEMICAL PHYSICS LETTERS
Volume 193, number 6
12 June 1992
____4&&@~~-~-
2
CH 3
02
Fig. 1. Structure of piroxicam and atom numbering used in the present discussion. The main direction of internal motion is also shown.
Proton-carbon “broad-band” nuclear Overhauser effect values (NOEBB), determined by the equation NOEBB= (I, - IO)/I,, (where Z, and IO are the peak intensities measured under continuous and gated proton decoupling conditions, respectively) show a complete dipolar relaxation pathway for all the protonated carbon nuclei of piroxicam. There was an estimated experimental error of 3O/6in the R, measurements. All measurements were performed at a temperature of 22’ C. The dipolar contribution to the experimental carbon relaxation rate R, can be calculated by the equation RpD=f
DDRl,
(1)
where f DD,the fractional dipolar contribution, is determined by comparing the experimental and theoretical NOEBBvalues (calculated of carbon nuclei relaxing entirely by a dipolar mechanism). Under the present experimental conditions, f DD was equal to 1 for all the proton-bearing carbons. Table 1 shows the 13Cchemical shifts and dipolar relaxation rates of protonated carbon nuclei. The effective correlation time r, modulating the protoncarbon dipolar coupling can be determined by the equation
Table 1 Spin-lattice relaxation rates of protonated carbons, correlation times and angles @for a 0.15 mol dm-’ DMSO-d, solution of piroxicam at 22°C Carbon No.
6”) (ppm)
14 12 4 3 5 2 13 11
145.43 139.93 133.13 132.63 126.45 123.80 119.97 116.24
2.1 2.1 3.2 4.0 2.6 .,2.6 5.1 2.0
4 b) ;‘s, 9.10x lo-” 9.10x lo-” 1.42x IO-” 1.80x lo-“’ 1.14x10-‘0 1.14x IO-I0 2.40x lo-” 8.70x lo-”
60 -60 40 -20 100 -80 0 -120
a) ppm from TMS. b, The angles 4 reported are defined by the internal rotation axis and the C-H, bond direction. The o values are taken as positive if obtained moving in a clockwise direction from the internal rotation axis, otherwise they are taken as negative.
29~and rC_Hthe proton-carbon distance, assumed constant in this case. For molecules experiencing internal reorientation the effective correlation time r, reported in eq. (2) is given by Woessner’s equations [ 7,13 ] : T~=A~,+BT,+DT,,
(3)
where the geometrical factors A, B and D are
B,,,,= rn2r&y:: I 10 rIH
A=~(~cos*@-I)*,
(4)
B= a sin*( 2@) ,
(5)
D= $ sin4@.
(6)
(2) where w, and IS, and yH and yc are the proton and carbon Larmor frequencies and the magnetogyric ratios respectively, fi is Plan&s constant divided by 554
RFD (s-1)
The angle @is the angle defined by the proton-carbon bond direction and the molecular rotor axis. It may be noted that A + B + D = 1. The three correla-
Volume 193, number 6
tion times reported in eq. (3) are given by (7)
rA=TR,
12 June 1992
CHEMICAL PHYSICS LETTERS
Tg’ =rR’ +&’
)
(8)
z,‘=ri’+&’
)
(9)
Table 2 Correlation time values (s) describing the dynamical behaviour of piroxicam determined from carbon spin-lattice relaxation rates of 0.15 mol dm-’ DMSO-d, piroxicam solution at 22°C 2.4x 1.2x 4.7x 2.4x 4.0x 2.4x 3.4x
7,
where rI = rR is the correlation time for the isotropic tumbling molecular reorientation and rr ’ = ZK ’ + TG’. In the last equation ro is the diffusional correlation time for the internal reorientation and rlIdescribes the motion along the main molecular axis. The first term of eq. (3) gives the isotropic contribution to the effective correlation time whereas the second and third terms are mainly related to the internal reorientational motion, The dynamical properties of both the pyridinyl and the benzothiazine moieties of piroxicam were analyzed with the use of the above equations. (A) Pyridinyl moiety. From the results reported in table 1 can be observed that C”, Cl2 and Cl4 nuclei show similar rc values. This suggests a similar contribution of the second and third terms of eq. (3) to r,. Given that the proton-carbon pairs are aligned in directions shifted by about 60” moving from C’ l to C14,a similar contribution by the second term of eq. (3) to Cl’, Cl2 and Cl, is observed only if the axis of the internal rotation is aligned with the direction of Cl 3-H l 3 bond. Under these conditions $ is 60 ’ for C 12, -60” for Cl.,, 120” for Cl’ and 0” for C’3. The isotropic correlation time rR=rA=rI can then be calculated from the rc value of C13. In this case the second and the third terms of eq. (3) do not contribute to 7, and the effective correlation time assumes the value of the isotropic reorientational motion rR. For C’,, CIZ and C4 carbons r, and ?‘, can be obtained by solving a system of three equations, i.e. (3), (8) and (9) with three unknowns rB, rD and rG. The results are reported in table 2. (B) Benzothiazine moiety. For the benzothiazine moiety the interpretation of the correlation time rc modulating the ‘H-13C dipolar interactions of C2, C3, C, and C5 carbons, requires deeper investigation. On the basis of eq. (3) and using the T,+ r, nd rD correlation times calculated from analysis of the carbon relaxation of the pyridinyl moiety, the theoretical dependence curve of T=on the angle $ between the internal reorientational axis and the proton-carbon bond direction can be calculated (fig. 2).
7B 7D 7R 7, 7L 7u
lo-” lo-I0 lo-” lo-“’ lo-” lo-“’ lo-”
From the curve in fig. 2 a good fit is observed between the effective correlation times calculated for C2, C3, C, and C5 carbons and the geometrical parameters. If an angle of - 80” between the protoncarbon bond direction and the direction of the internal motion is assumed for the C2 nuclei, the theoretical rc values for C3, C, and C5 are obtained by increasing the angle $ considered for the CZ carbon by 60” each time. Using fig. 2 we can observe that for 9 of - 80’) - 20’) 40’ and 100 ’ respectively, the theoretical 7, values are in good agreement with the
-: 0-160 L
-90
0
90
’
180
f#
Fig. 2. Plot of the effective correlation time 7, as expressed by eq. (3) versus @,the angle between the internal reorientational axis and the proton-carbon bond direction. The correlation times used were7,=2.4x10-‘0s,7B=1.2~10-‘0sand7,=4.7~IO-”s. 555
Volume 193, number 6
CHEMICAL PHYSICS LETTERS
experimentally determined effective 7c for Cz, C3, C, and C5. From these results two considerations are possible: (i ) The curve reported in fig. 2 is calculated on the basis of dynamical parameters obtained from the pyridinyl moiety. Since this curve can be used for describing the dynamical behaviour of the benzothiazine moiety, it must be assumed that a unique internal reorientational motion about the same axis occurs in the molecule (fig. 1). (ii) The fit of the 7c values for C2, C3, C4 and C5, obtained by adding standard degrees to the angle 9 of the C2 carbon, shows good correspondence between the theoretical structure and the experimental one. Conclusions. From the carbon spin-lattice relaxation experiments reported in table 1, a set of correlation times describing the entire molecular dynamics can be derived. These calculated correlation times are reported in table 2. The proposed method of analysis can be used to obtain information about the direction of internal reorientational axes in the presence of internal motions. This approach can also be used to calculate the angle between the reorientational axis and the proton-carbon bond direction,
556
12 June 1992
information which can define molecular geometry in solution.
References [ 1] B.A. Borgias and T.L. James, J. Magn. Reson. 79 (1988) 493.
[ 21 C. Rossi, M.R. Sansoni and A. Donati, Chem. Phys. Letters 187 (1991) 439. [3] N.J. Oppenheimer and T.L. James, eds., Nuclear magnetic resonance, spectral techniques and dynamics, Vol. 176 (Academic Press, New York, 1989). [4] N. Marchettini, Y. Yang and C. Rossi, J. Phys. Chem. 95 (1991) 10811. [ 5 ] K. Wiithrich, NMR of proteins and nucleic acid (WileyInterscience, New York, 1986), and references therein. [6] V. Sklenar, D. Torchia and A. Bax, J. Magn. Reson. 73 (1987) 375. [7] D.E. Woessner, J. Chem. Phys. 36 (1962) 1. [ 8 ] D. Lipari and A. Szabo, J. Am. Chem. Sot. 104 ( 1982) 4546. [ 91 G. Lipari and A. Szabo, J. Am. Chem. Sot. 104 ( 1982) 4559. [IO] A. Allerhand and R.A. Komoroski, J. Am. Chem. Sot. 95 (1973) 8228. [ 111 C. Ross, N. Niccolai and F. Laschi, J. Phys. Chem. 9 1 ( I987 ) 3903. [ 12 ] C. Rossi and N. Niccolai, Chem. Phys. Letters 142 ( 1987 ) 4181. [ 131 R.K. Harris, NMR spectroscopy (Pitman, London, 1983) pp. 113-116.