NMR Spectroscopy. Applications. Drug design MRI. Food quality. Structural biology. Metabonomics

Transcription

1 Applications Drug design MRI Food qualit Metabonomics Structural biolog

2 Basic Principles N.M.R. = Nuclear Magnetic Resonance Spectroscopic technique, thus relies on the interaction between material and electromagnetic radiation The nuclei of all atoms possess a nuclear quantum number, I. (I 0, alwas multiples of.) Onl nuclei with spin number (I) >0 can absorb/emit electromagnetic radiation. Even atomic mass & number: I = 0 ( 12 C, 16 O) Even atomic mass & odd number: I = whole integer ( 14 N, 2 H, 10 B) Odd atomic mass: I = half integer ( 1 H, 13 C, 15 N, 31 P) The spinning nuclei possess angular momentum, P, and charge, and so an associated magnetic moment,. = P Where is the gromagnetic ratio

3 Basic Principles B0 The spin states of the nucleus are quantified: I, (I - 1), (I - 2),, -I I= (e.g. 1 H) Energ E=h =h B0/2 B0=0 B0>0

4 Basic Principles In the ground state all nuclear spins are disordered, and there is no energ difference between them. The are degenerate. B o Since the have a magnetic moment, when we appl a strong eternal magnetic field (Bo), the orient either against or with it: There is alwas a small ecess of nuclei (population ecess) aligned with the field than pointing against it.

5 Basic Principles E=h 0=h B0/2 B o =0 B o >0 0 is the Larmor Frequenc 0= B0, angular velocit B0 z

6 Basic Principles Each level has a different population (N), and the difference between the two is related to the energ difference b the Boltzmman distribution: N /N = e E/kT E for 1 H at 400 MHz (B0 = 9.5 T) is Kcal/mol N /N = The surplus population is small (especiall when compared to UV or IR). That renders NMR a rather insensitive technique!

7 The electromagnetic spectrum -ras X-ras ultraviolet visible infrared microwave Mossbauer electronic vibrational rotational H 19 F 31 P 13 C /MHz 10 aldehdic 8 aromatic 6 olefinic 4 acetlenic 2 aliphatic 0 /ppm radiofrequenc NMR /Hz

8 The Vector Model M 0

9 NMR ecitation M o z B 1 = C * cos ( o t) B 1 B o i Transmitter coil () B 1 is an oscillating magnetic field + 0-0

10 Laborator vs. Rotating frame z z + 0 M 0 M 0 B Laborator frame Rotating frame

11 Effect on an rf pulse z M 0 z = 1 t p (degrees) =90 B 1 B 1 =180

12 Magnetization properties z 1H=400,000,000 Hz A=400,000,005 Hz A M A B 1 M A =5 Hz

13 Magnetization properties z 1H=400,000,000 Hz A=400,000,005 Hz A M A B 1 M A =5 Hz detector M A =M A cos t M A =M A sin t I M I M M A M A t t t

14 The Fourier Transform time domain FT frequenc domain I M t =1/ t FT t time frequenc

15 The Fourier Transform I M Signal Induction Deca (FID) time

16 The Fourier Transform FT

17 Continuous wave vs. pulsed NMR o or B o o or B o time

18 Continuous wave vs. pulsed NMR For cos( t) FT absorptive lines For sin( t) FT despersive lines

19 Continuous wave vs. pulsed NMR A monochromatic radiofrequenc pulse is a combination of a wave (cosine) of frequenc 0 and a step function * = t p Since f=1/t, a pulse of 10 s duration ecites a frequenc bandwidth of 10 5 Hz! FT o

20 Continuous wave vs. pulsed NMR E t ~ h or t ~1

21 Single-channel signal detection z FT

22 Quadrature detection z M M + M M

23 Quadrature detection cos + sin Hz + 0 Hz

24 The Chemical Shift The NMR frequenc of a nucleus in a molecule is mainl determined b its gromagnetic ratio and the strength of the magnetic field B The eact value of depends, however, on the position of the nucleus in the molecule or more precisel on the local electron distribution this effect is called the chemical shift

25 The Chemical Shift E=h =h B/2 Nuclei, however, in molecules are never isolated from other particles that are charged and are in motion (electrons!). Thus, the field actuall felt b a nucleus is slightl different from that of the applied eternal magnetic field!!

26 The Chemical Shift E=h =h Be /2 Beff, is given b B0-B = B0-B0 =B0(1- ) = B 0 (1- ) 2 and is the chemical shift = ( - ref ) ref ( ref - )

27 The Chemical Shift methl protons amide protons aromatic ring protons methlene protons 750 MHz 1 H spectrum of a small protein shielding frequenc magnetic field

28 The Chemical Shift

29 The Chemical Shift

30 Nuclear Shielding = dia + para + nb + rc + ef + solv diamagnetic contribution paramagnetic contribution neighbor anisotrop effect ring-current effect electric field effect solvent effect

31 Nuclear Shielding - diamagnetic contribution The eternal field B0 causes the electrons to circulate within their orbitals B 0 h B 0 h B 0 (1- ) B The higher is the electron densit close to the nucleus, the larger the protection is!

32 Nuclear Shielding - diamagnetic contribution Depends on the electronegativit CH3X

33 Nuclear Shielding - paramagnetic contribution The eternal field B0 mies the wavefunction of the ground state with that of the ecited state The induced current generates a magnetic field that enhances the eternal field and deshields the nucleus LUMO B 0 HOMO p = 1 1 R 3

34 Chemical shift range 1 H; ~10 ppm 13 C; ~200 ppm 19 F; ~300 ppm 31 P; ~500 ppm Local diamagnetic and paramagnetic currents make onl modest contributions to 1 H shielding!

35 Chemical Shift Anisotrop Nuclear shielding,, is a tensor. The distribution of the electrons about the nucleus is non-sperical- thus, the magnitude of the shielding depends on the relative orientation of the nucleus with respect to the static field. In isotropic cases: = ( ) In static cases, e.g. solid state

36 Nuclear Shielding - neighboring group B 0 A B B A μ par > μ per μ par < μ per

37 Nuclear Shielding - neighboring group - C + + C - μ par > μ per - + C - C + μ par < μ per C 2 H 4 C 2 H 2 C 2 H ppm

38 Nuclear Shielding - ring-current effect More pronounced in aromatic rings due to the electron clouds B o 9.28 e

39 Nuclear Shielding - hdrogen bonding Hdrogen bonding causes deshielding due to electron densit decrease at the proton site OH CH 2 CH 3 [EtOH] in CCl 4 1M 0.1M 0.01M 0.001M ppm

40 Spin-spin (scalar) coupling HF ( 1 H- 19 F) H F J HF J HF

41 Spin-spin (scalar) coupling HF ( 1 H- 19 F) B o 19 F 1 H H F H H F 19 F 1 H H F H H F Nuclear moment Magnetic polarization of the electron E=h J AX m A m X where m is the magnetic quantum number J AX is the spin-spin coupling constant

42 Spin-spin (scalar) coupling AMX AX 2 AX 3

43 Spin-spin (scalar) coupling Strong coupling <10 J

44 Spin-spin (scalar) coupling The principal source of scalar coupling is an indirect interaction mediated b electrons involved in chemical bonding The magnitude of interaction is proportional to the probabilit of finding the electron at the nucleus (R=0) Magnitude in Hz- independent of the eternal magnetic field H3C CH3 H2C CH2 HC CH 125 Hz 160 Hz 250 Hz

45 Spin-spin (scalar) coupling Three-bond coupling most useful since it carries information on dihedral angles Empirical relationship: the Karplus relation 3 J = A + B cos + C cos 2

46 Chemical shifts on the rotating frame z 500 MHz 3 2 t z 0 =500 Hz

47 Spin couplings on the rotating frame z J 0 t z =-J/2 Hz =+J/2 Hz

48 The basic spin-echo pulse sequence 90 applied along ais 180 applied along ais acquisition dela

49 Effect of spin echo on chemical shift evolution 90 applied along ais 180 applied along ais acquisition dela z z 90 z z z A 180 A

50 Effect of spin echo on scalar coupling evolution 90 applied along ais 180 applied along ais acquisition dela z z 90 1 H-X z z z (onl 1 H) -J/2 +J/ J/2 -J/2

51 Effect of spin echo on scalar coupling evolution 90 applied along ais 180 applied along ais acquisition dela z z 90 1 H-X z z z (both 1 H and X) 180 -J/2 +J/2 -J/2 +J/2

52 Water suppression b the Jump and Return method z z 90 z z z 90 - A

53 Water suppression

54 Spin decoupling 1 H decouple 13 C H C H H C H C H H C

55 The J-modulated spin echo 1 H decouple 13 C

56 1 H decouple The J-modulated spin echo 13 C

57 1 H decouple The J-modulated spin echo 13 C If =180J degrees C: I=1 CH: I cos CH 2 : I cos 2 CH 3 : I cos 3

58 1 H decouple The J-modulated spin echo 13 C =1/J 13 C (ppm)

59 Sensitivit enhancement NMR has poor sensitivit compared to other analtical techniques The intrinsic sensitivit depends upon the gromagnetic ratio, A greater contributes to: a high resonant frequenc- large transition energ difference- greater Boltzmann population difference high magnetic moment and hence a stronger signal high rate of precession which induces a greater signal in the detection coil So, the strength of NMR signal is proportional to 3 Noise increases a square-root of observed frequenc} S/N 5/2

60 Sensitivit enhancement b polarization transfer Signal sensitivit enhancement b transferring the greater population differences of high- spins onto their spin-coupled low- partners. C 2 H 2 1 H- 13 C spin pair H 1 C 1

61 Sensitivit enhancement b polarization transfer Signal sensitivit enhancement b transferring the greater population differences of high- spins onto their spin-coupled low- partners. + C 2 C C 2 H 2 C 2 + C 2 +2 C C 2 H 2 C 2 2 H 1 C 1 2 C C 2 (inverted) H 1 C 1 C 2 +2 C + C H 1 H 2 + C C 1 C 2 H 1 H 2 C 1 C 2-3:5

62 Sensitivit enhancement b polarization transfer Signal sensitivit enhancement b transferring the greater population differences of high- spins onto their spin-coupled low- partners. coupled decoupled INEPT refocused INEPT refocused, decoupled INEPT

63 Relaation When perturbed, the nuclear spins need to rela to return to their equilibrium distribution E.g. when the sample is put into a magnet, the Boltzmann distribution of spins among the energ levels changes due to a change in the energ of the various levels E.g. after appling electromagnetic radiation, which induces transitions between energ levels, the sstem returns to its equilibrium This process is called relaation

64 Longitudinal Relaation: Establishing Equilibrium z z z z z

65 Longitudinal Relaation: Establishing Equilibrium Recover of the z-magnetization follows eponential behavior dm z (M 0 -M z ) = M z =M 0 (1-2e -t/t1 ) dt T 1 where T 1 is the longitudinal relaation time

66 Longitudinal Relaation: Measurement z z z z z z 90

67 Longitudinal Relaation: Measurement

68 Longitudinal Relaation: Eponential growth M z =M 0 (1-2e -t/t1 ) B the end of 5T 1 sec, the magnetization has recovered b 99.33%

69 Longitudinal Relaation: optimizing sensitivit

70 Longitudinal Relaation: optimizing sensitivit

71 Longitudinal Relaation: optimizing sensitivit optimum pulse repetition time when using 90º Quantitative measurements and integration

72 Transverse Relaation: magnetization loss in the - plane time

73 Transverse Relaation: magnetization loss in the - plane = 1 T 2 *

74 Transverse Relaation: Measurement z z z z z -

75 Transverse Relaation: Measurement

76 T1 vs T2 Relaation T 1 T 2 For small molecules, T 1 T 2 For large molecules, T 1 >> T 2 Longitudinal relaation causes loss of energ from the spins (enthalpic) Transverse relaation occurs b mutual swapping of energ between spins (entropic)

77 Relaation mechanisms Nuclear spin relaation is not a spontaneous process; it requires stimulation b suitable fluctuating fields to induce the necessar spin transitions Two main mechanisms Dipole-dipole Chemical shift anisotrop

78 Relaation mechanisms Longitudinal relaation requires a time-dependent magnetic field fluctuating at the Larmor frequenc The time-dependence originates in the motions of the molecule (vibration, rotation, diffusion etc) Molecules in solution tumble. This tumbling can be characterized b a rotational correlation time c c is the time needed for the rms deflection of the molecules to be ~ 1 radian (60 )

79 Spectral densit function Rotational diffusion in solution occurs at a range of frequencies 1/ c ~ rms rotational frequenc (radians s -1 ) The probabilit function of finding motions at a given angular frequenc can be described b the spectral densit function J( )

80 Spectral densit function Frequenc distribution of the fluctuating magnetic fields

81 Spectral densit function: Longitudinal relaation Spins are relaed b local fields fluctuating at the Larmor frequenc 0 So, the relaation rate (R1) will be proportional to the J( 0) 1/T 1 = R 1 = 2 <B 2 > J( 0 ) Knowing the form of J( ) we can predict the dependence of the spin-lattice relaation time (T1=1/ R1) on the correlation time c for a given NMR frequenc 0 0 c =1,J( 0 ) = c = 1/ 0 and T 1 is minimum (R 1 maimum) 0 c <<1 (small molecules), J( 0 ) ~ 2 c and T 1 decreases (R 1 increases) with increasing c (e.g.b decreasing the temperature) 0 c <<1 0 c >>1 0 c =1 0 c >>1 (large molecules), J( 0 ) ~ 2/ 02 c and T 1 increases (R 1 decreases) with increasing c (e.g. b decreasing the temperature)

82 Relaation mechanisms: Dipole-dipole Nuclei with non-zero quantum numbers have magnetic dipoles The behave like small magnets and induce small magnetic fields that affect neighboring nuclei Magnetic field, B, generated b a magnetic dipole

83 Relaation mechanisms: Dipole-dipole Representation of the dipolar magnetic field B, generated b a magnetic dipole lines of force densit plots B μz B μ B μz is zero for =±54.7 (magic angle)

84 Relaation mechanisms: Dipole-dipole The z component of their dipole magnetic field will affect the field eperienced b the other nucleus and cause splitting X ± sign refers to the quantum number of A (± ) A B μ A Thus, the splitting in the spectrum of X is KAX var with the distance e.g. KCH is 9000 Hz at 1.5 Å and 30 Hz at 10 Å

85 Relaation mechanisms: Dipole-dipole Splitting of the AX spectrum depends on In a crstal with fied distances and angles the dipolar splitting var with the crstal orientation with respect to the eternal magnetic field

86 Relaation mechanisms: Dipole-dipole Molecules in liquids rotate, tumble rapidl with tpical frequencies between to 10 8 Hz for small molecules and proteins, respectivel. Those frequencies are much larger than tpical dipolar couplings (10 5 Hz) The angular part of the dipolar splitting is averaged over all possible orientation to 0 Although the are not directl observed in solution, dipolar couplings pla an important role in spin relaation The local field eperienced at one nucleus as a result of its neighbor will fluctuate as the molecule tumbles

87 Relaation mechanisms: Dipole-dipole R1 depend of the gromagnetic ratio of the nuclei (e.g. H-H relaation more efficient than C-H)

88 Relaation mechanisms: Chemical shift anisotrop The distribution of the electrons about the nucleus is non-sperical- thus, the magnitude of the shielding depends on the relative orientation of the nucleus with respect to the static field. As the molecule tumbles, it creates a fluctuating magnetic field

89 Nuclear Overhauser Effect (NOE) NOE: change in intensit of one resonance when the spin transitions of another are perturbed from their equilibrium populations perturbation: saturation or inversion The two spins should communicate through dipole-dipole interaction NOE is observed for spin I when spin S is perturbed

90 Nuclear Overhauser Effect (NOE) Origin of the NOE N S I N- I S N N /2 S 0 I N- /2 I 0 S N+ /2 N+ N+ /2 S I S I

91 Nuclear Overhauser Effect (NOE) Si possible transitions in a two-spin sstem W 1 S W 1 I W 0 W 2 W 1 I W 1 S Onl single transitions can b observed b NMR (W1) W0 and W2 are cross-relaation pathwas, responsible for the NOE

92 Nuclear Overhauser Effect (NOE) N- N- /2 N S I N N /2 S 0 I N+ /2 I S I 0 S N+ N+ /2 S I S I S 0 > I S 0 < I W 0 W 2 I > 0 S I < 0 S positive NOE negative NOE S I S I

93 Nuclear Overhauser Effect (NOE) W 1 tends to reduce the magnitude of the NOE Saturating for a period of time that is long relative to the relaation times allows a new stead-state of populations to arise IS, cross-relaation rate: dictates the sign of the NOE IS, dipolar longitudinal relaation rate of spin I: it serves to reduce the magnitude Thus, NOE is related to molecular motion!

94 Nuclear Overhauser Effect (NOE) 1 H at 400 MHz W 1 at 400 MHz W 2 at 800 MHz (W I +W S )- stimulated b rapidl tumbling molecules W 0 at Hz-kHZ ( W I -W S )- stimulated b slowl tumbling molecules Small molecules ehibit positive NOEs Large molecules ehibit negative NOEs

95 Nuclear Overhauser Effect (NOE) c =1.12 Variation in NOE as a function of molecular tumbling rates

96 Field gradient B g Variation of magnetic field strength along the z ais

97 Field gradient +!B g -!B g 90º B g,! g -B g,! g -!B g +!B g defocused (dephased) refocused (rephased)

98 Field gradient RF G z stronger gradient

99 Field gradient RF G z Variation of the second gradient pulse (90 to 110% of the first)

100 Diffusion-ordered spectroscop B g!!!! "! "!!! #! #! G gradient strength D diffusion coefficient

101 Diffusion-ordered spectroscop mobilit

102 Multi-dimensional NMR One dimension Two dimensions

103 Multi-dimensional NMR To generate a spectrum with two frequenc domains, f 1 and f 2, it is necessar to sample data as a function of two separate time variables, t 1 and t 2. General scheme for 2D NMR eperiment P: Preparation E: Evolution M: Miing D: Detection P E M D t 1 t 2

104 Multi-dimensional NMR A hv B

105 Multi-dimensional NMR

106 COSY (COrrelated SpectroscopY) Correlation through bonds (J-coupling)

107 TOCSY (Total COrrelated SpectroscopY) Correlation through bonds (J-coupling)! m t 2 t 1 spin-lock J AB A B C D E! m J BC A B C D E J CD A B C D E J DE A B C D E

108 COSY vs. TOCSY Correlation through bonds (J-coupling) COSY TOCSY

109 COSY vs. TOCSY Correlation through bonds (J-coupling)

110 General schemes for 2D NMR Relative sensitivit P E M D 1 H- 31 P 1 H- 13 C 1 H- 15 N a) H t X t 2 b) H t X t 2 (traditional) c) H X t 1 t d) H X t 1 t (inverse) modern

111 Heteronuclear Single Quantum Coherence (HSQC) 13 C 1 H

112 Protein NMR 2D NOESY

113 Protein NMR 2D NOESY

114 Protein NMR Isotopicall labeled proteins

115 Protein NMR 1 H- 15 N HSQC (protein s fingerprint) 15 N 1 H

116 Protein NMR Signal overlap problem alleviated b 3D & 4D NMR 110 ppm 120 ppm 130 ppm 120 ppm 15 N 130 ppm 15 N 110 ppm 15 N 1 H 6.5 ppm 1 H 6.5 ppm 1 H 6.5 ppm

117 Protein NMR Signal overlap problem alleviated b 3D & 4D NMR 2D 110 ppm 3D 120 ppm 130 ppm 120 ppm 130 ppm 110 ppm 15 N 15 N 15 N 1 H 1 H 1 H 6.5 ppm 6.5 ppm 6.5 ppm F2 ( 15 N) F3 (NH)

118 Protein NMR Signal overlap problem alleviated b 3D & 4D NMR

119 Protein NMR Signal overlap problem alleviated b 3D & 4D NMR

120 Protein NMR Assignment - Triple Resonance Eperiments N H H C C H H C O 3D HNCA

121 Protein NMR Assignment - Triple Resonance Eperiments

122 Protein NMR Assignment - Triple Resonance Eperiments 15 N ppm C ppm H ppm

123 NMR Spectroscop Protein NMR Assignment - Triple Resonance Eperiments

124 Protein NMR Assignment - Triple Resonance Eperiments HNCA HN(CO)CA 130 ppm 130 ppm 40 HNCA HN(CO)CA 125 ppm 125 ppm 40 HNCA HN(CO)CA 125 ppm 125 ppm i-1 i i+1