Applications Drug design MRI Food qualit Metabonomics Structural biolog
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
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
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.
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
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 3.8 10-5 Kcal/mol N /N =1.000064 The surplus population is small (especiall when compared to UV or IR). That renders NMR a rather insensitive technique!
The electromagnetic spectrum -ras X-ras ultraviolet visible infrared microwave 10 22 10 20 10 18 10 16 10 14 10 12 10 10 Mossbauer electronic vibrational rotational 600 500 400 300 200 100 1 H 19 F 31 P 13 C /MHz 10 aldehdic 8 aromatic 6 olefinic 4 acetlenic 2 aliphatic 0 /ppm radiofrequenc 10 8 10 6 NMR /Hz
The Vector Model M 0
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
Laborator vs. Rotating frame z z + 0 M 0 M 0 B 1 + 0-0 -2 0 Laborator frame Rotating frame
Effect on an rf pulse z M 0 z = 1 t p (degrees) =90 B 1 B 1 =180
Magnetization properties z 1H=400,000,000 Hz A=400,000,005 Hz A M A B 1 M A =5 Hz
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
The Fourier Transform time domain FT frequenc domain I M t =1/ t FT t time frequenc
The Fourier Transform I M Signal Induction Deca (FID) time
The Fourier Transform FT
Continuous wave vs. pulsed NMR o or B o o or B o time
Continuous wave vs. pulsed NMR For cos( t) FT absorptive lines For sin( t) FT despersive lines
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
Continuous wave vs. pulsed NMR E t ~ h or t ~1
Single-channel signal detection z FT + + 0 -
Quadrature detection z M M + M M
Quadrature detection cos + sin 0 + - Hz + 0 Hz
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
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!!
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 10 6 10 6 ( ref - )
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
The Chemical Shift
The Chemical Shift
Nuclear Shielding = dia + para + nb + rc + ef + solv diamagnetic contribution paramagnetic contribution neighbor anisotrop effect ring-current effect electric field effect solvent effect
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!
Nuclear Shielding - diamagnetic contribution Depends on the electronegativit CH3X
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
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!
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: = ( 11 + 22 + 33) In static cases, e.g. solid state
Nuclear Shielding - neighboring group B 0 A B B A μ par > μ per μ par < μ per - + + + - - - +
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 6 7 6 5 4 3 2 1 0 ppm
Nuclear Shielding - ring-current effect More pronounced in aromatic rings due to the electron clouds B o 9.28 e - -2.99
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 6 4 2 0 ppm
Spin-spin (scalar) coupling HF ( 1 H- 19 F) H F J HF J HF
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
Spin-spin (scalar) coupling AMX AX 2 AX 3
Spin-spin (scalar) coupling Strong coupling <10 J
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
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
Chemical shifts on the rotating frame z 500 MHz 3 2 t z 0 =500 Hz
Spin couplings on the rotating frame z J 0 t z =-J/2 Hz =+J/2 Hz
The basic spin-echo pulse sequence 90 applied along ais 180 applied along ais acquisition dela
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
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/2 180 +J/2 -J/2
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
Water suppression b the Jump and Return method z z 90 z z z 90 - A
Water suppression
Spin decoupling 1 H decouple 13 C H C H H C H C H H C
The J-modulated spin echo 1 H decouple 13 C
1 H decouple The J-modulated spin echo 13 C
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
1 H decouple The J-modulated spin echo 13 C =1/J 13 C (ppm)
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
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
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
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
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
Longitudinal Relaation: Establishing Equilibrium z z z z z
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
Longitudinal Relaation: Measurement z z z z 180 90 z z 90
Longitudinal Relaation: Measurement
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%
Longitudinal Relaation: optimizing sensitivit
Longitudinal Relaation: optimizing sensitivit
Longitudinal Relaation: optimizing sensitivit optimum pulse repetition time when using 90º Quantitative measurements and integration
Transverse Relaation: magnetization loss in the - plane - - - + + + time
Transverse Relaation: magnetization loss in the - plane = 1 T 2 *
Transverse Relaation: Measurement z z z 90 - + z 180 + z -
Transverse Relaation: Measurement
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)
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
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 )
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( )
Spectral densit function Frequenc distribution of the fluctuating magnetic fields
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)
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
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)
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
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
Relaation mechanisms: Dipole-dipole Molecules in liquids rotate, tumble rapidl with tpical frequencies between 10 12 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
Relaation mechanisms: Dipole-dipole R1 depend of the gromagnetic ratio of the nuclei (e.g. H-H relaation more efficient than C-H)
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
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
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
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
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
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!
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
Nuclear Overhauser Effect (NOE) c =1.12 Variation in NOE as a function of molecular tumbling rates
Field gradient B g Variation of magnetic field strength along the z ais
Field gradient +!B g -!B g 90º B g,! g -B g,! g -!B g +!B g defocused (dephased) refocused (rephased)
Field gradient RF G z stronger gradient
Field gradient RF G z Variation of the second gradient pulse (90 to 110% of the first)
Diffusion-ordered spectroscop B g!!!! "! "!!! #! #! G gradient strength D diffusion coefficient
Diffusion-ordered spectroscop mobilit
Multi-dimensional NMR One dimension Two dimensions
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
Multi-dimensional NMR A hv B
Multi-dimensional NMR
COSY (COrrelated SpectroscopY) Correlation through bonds (J-coupling)
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
COSY vs. TOCSY Correlation through bonds (J-coupling) COSY TOCSY
COSY vs. TOCSY Correlation through bonds (J-coupling)
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 1 1 1 1 X t 2 b) H t 1 2.5 4 10 X t 2 (traditional) c) H X t 1 t 2 4 8 30 d) H X t 1 t 2 10 32 300 (inverse) modern
Heteronuclear Single Quantum Coherence (HSQC) 13 C 1 H
Protein NMR 2D NOESY
Protein NMR 2D NOESY
Protein NMR Isotopicall labeled proteins
Protein NMR 1 H- 15 N HSQC (protein s fingerprint) 15 N 1 H
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
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)
Protein NMR Signal overlap problem alleviated b 3D & 4D NMR
Protein NMR Signal overlap problem alleviated b 3D & 4D NMR
Protein NMR Assignment - Triple Resonance Eperiments N H H C C H H C O 3D HNCA
Protein NMR Assignment - Triple Resonance Eperiments
Protein NMR Assignment - Triple Resonance Eperiments 15 N ppm 115 118 122 125 116 130 128 40 45 13 C ppm 50 55 6.5 6.2 7.0 7.2 7.8 8.5 8.0 1 H ppm
NMR Spectroscop Protein NMR Assignment - Triple Resonance Eperiments
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 40 45 45 45 50 50 50 55 55 55 8.5 8.5 7.5 7.5 7.5 7.5 i-1 i i+1