Magnetisation Transfer Schemes

Transcription

1 Magnetisation Transfer Schemes P. K. Madhu Department of Chemical Sciences Tata Institute of Fundamental Research Homi Bhabha Road Colaba Mumbai , India

2 Sensitivity of NMR Spectroscopy S/N Nγ exc γ det B 3/2 0 NST 1/2 2 S/N N γ exc γ det B 3/2 0 NS T 1/2 2 signal-to-noise ratio number of spins gyromagnetic ratio of excited spins gyromagnetic ratio of detected spins static magnetic field number of scans transverse relaxation time sample concentration isotope labeling magnet size measurement time molecular weight

3 Sensitivity of NMR Spectroscopy Spin-1/2 nucleus β> α> N β =e E kt N α ΔE=(h/2π) γb =e γhb kt Preferred N β <<N α For 1 H: γ=26.75 rad T -1 s -1 ΔE=2.65*10-25 J for B=9.4 T kt= 4.14*10-21 J ΔE/kT=6.4*10-5 Hence, the energy required to reorient the spins is dwarfed by the thermal energy, little tendency for the spins to become ordered in the lower energy level

4 Sensitivity of NMR Spectroscopy Spin-1/2 nucleus β> α> ΔE=(h/2π) γb Preferred N β <<N α For 1 H: γ=26.75 rad T -1 s -1 ΔE=2.65*10-25 J for B=9.4 T kt= 4.14*10-21 J ΔE/kT=6.4*10-5 N β =e E kt N α 1 E 2kT N α N β N α +N β = E 2kT 3.2*10-5 (one in 31000)

5 Energy Levels, Magnetic Field, and Relative Population Spin-1/2 nucleus 1 million 1 million 2 million 1 million ΔE 1 million+16 1 million+64 B 0 (Tesla) 1 million T 2.35 T 9.4 T 18.8 T

6 NMR Active Nuclei: Properties

7 NMR Concentrations Sensitivity of NMR Spectroscopy: How to Increase? Higher magnetic fields Lower temperatures Hyperpolarised NMR Cryoprobes/sample cooling Transfer of abundant population from some source to rare nuclei Can the polarisation from an abundant spin, like 1 H, be transferred to a rare spin, like 13 C? Polarisation Transfer

8 Selective Population Transfer (SPT) Consider two proton spins, homonuclear 1 H- 1 H spin system, weakly J coupled (having a large chemical-shift difference), forming an AX spin system αβ 2 A x 4 1 ββ X A αα 3 βα 1,3 2,4 A 1,2 3,4 X RF irradiation leading to saturation Of 1-3 transition αβ 2 A X 4 1 ββ X A αα 3 βα 1,3 2,4 A 1,2 X 3,4 Population is transferred from one nuclues to the other 3-4 transition gets a 50% increase

9 Selective Population Inversion (SPI) Soft pulse, transition selective αβ 2 A X 4 1 ββ X A αα 3 1,3 2,4 1,2 3,4 βα A X Soft pulse, transition selective 3,4 3-4 transition gets a two-fold increase αβ 2 I S 4 1 ββ S I αα 3 βα 1,3 2,4 1,2

10 Polarisation Transfer Both SPT and SPI can lead to polarisation transfer, but we are only dealing with homonuclear spin systems, not really interesting SPT and SPI can identify scalar coupled spin systems in crowded dpectral regions But the real use of these are in heteronuclear spin systems

11 αβ SPI in Heteronuclear Spin Systems 2 13 C 4 ββ 1 H 13 C 1,2 3,4 180, soft pulse on 1 H αβ 13 C 1 H 2 αα C ββ 1 H 3 βα 1,3 2,4 A 2,4 1 H X 3,4 1 H αα 1 13 C 3 Overall 13 C intensity: Before perturbation=2+2=4 And after pertrubation=6+10=16 Four-fold enhancement! βα 1,3 13 C A 1,2 1 H X

12 SPI in Heteronuclear Spin Systems Overall 13 C intensity: Before perturbation=2+2=4 And after pertrubation=6+10=16 Four-fold enhancement! 2,4 3,4 By manipulating the polarisation of the protons, we have accomplished a four-fold enhancement for 13 C signals, counting both positive and negative signals 1,3 13 C A 1,2 1 H X The factor of 4 comes from γ H /γ C ratio; it will be 10 for 1 H to 15 N polarisation transfer This is all fine, but we have up and down signals, not quite interesting

13 Echo Modulations AX spin system, heteronuclear y y A X 90 τ 180 τ y α M Xα A β x M Xβ A M Xβ A M Xα A x y M Xα A x M Xβ A α M Xα A β x M Xβ A Everything is refocussed, chemical shifts, RF and B 0 inhomogeneities, and coupling (scalar) effects- The spin-echo phenomenon

14 Echo Modulations AX spin system, homonuclear y y A τ τ X τ τ No J refocussing 180 α M Xα A β x M Xβ A y M Xα A M Xβ A x AX spin system, heteronuclear y M Xα A x M Xβ A M Xβ A φ x M Xβ A The difference in angular frequency between the two components is 2πJ AX φ(2 τ) = 4πJ τ AX

15 J-Modulation and Polarisation Transfer y y J / 2 x t D = 1 / 2J x 13 C magnetisation vectors, +5 and -3 in length in the xy plane 90 t p 180 NO REFOCUSSING REFOCUSSING BEFORE DECOUPLING BEFORE DECOUPLING

16 J-Modulation and Polarisation Transfer 180 A, 1 H x τ τ 180 x τ=1/4j X, 13 C y 13 C signal of lengths -3 and 5 created along the z-axis y M Aα X τ=j/4 180 x A x x x 90 M Aβ 0 X x τ=j/4 x 180 x X

17 J-Modulation and Polarisation Transfer We achieve polarisation transfer and signal enhancement, but: The proton 180 pulse has to be selective Lack of generality The need is to set up appropriate polarisation of all the proton transitions regardless of frequency/selectivity Hence, we need a pulse sequence that generates anti-phase proton transition for every 1 H- 13 C spin pairs, but non-selectively

18 INEPT Insenstive nuclei enhanced by polarisation transfer A, 1 H 90 x τ τ 180 x 90 y X, 13 C 180 x 90 x τ=1/4j The idea is to create an antiphase doublet for the proton magnetisation and then a 90 pulse on 13 C will create the (-3,5) carbon magnetisation

19 INEPT 90 x τ A, 1 H 180 x τ 90 y Monitor the 1 H magnetisation vectors z 180 x 90 x X, 13 C 90 x A y τ=j/ z y x z z x 180 x A,X z 90 y A τ=j/4 y y y x x x Anti-phase proton magnetisation and the subsequent 90 on 13 C creates the (-3,5) carbon vectors as earlier Here, we achieve uniform polarisation transfer

20 INEPT A δ 180 x δ 90 y 2,4 180 x 90 x X a b c 13 C A INEPT 1 2 A X ( δ = ) 4J x z y AX 1,3 Factor of 4 as enhancement

21 INEPT A z 90 A x 90 x δ A, 1 H 180 x δ 90 y -A y -A y cos πjδ A y cos πjδ A y cos πjδ 2πJA z X z 180 A x 180 X x 2πJA z X z 2A x X z sin πjδ 2A x X z sin πjδ -2A x X z sin πjδ X, 13 C 180 x 90 x δ = 1 4J A y cos 2 πjδ -2A x X z cos πjδ sin πjδ -2A x X z sin πjδ cos πjδ -A y sin 2 πjδ A y cos 2 πjδ 90 A y -4A z X z cos πjδ sin πjδ -A y sin 2 πjδ A y cos 2 πjδ 0.5A y 90 X x δ = 1 4J -4A z X y cos πjδ sin πjδ 2A z S y -A y sin 2 πjδ -0.5A y

22 INEPT Enhances polarisation Basic building block in most pulse schemes Spectral editing To select functional groups of our choice Establishes correlation between sets of coupled spins Most important in multi-dimensional experiments

23 INEPT Spectrum INEPT INEPT 13 C coupled

24 INEPT Spectral Patterns 13 C spectrum -1:1-1: 0:1-1: -1: 1:1 CH CH 2 CH 3

25 Refocused INEPT For CH spin systems, the optimum value for Δ=1/2J CH In case of CH, CH 2, and CH 3 groups, optimum value for Δ=1/3J CH Refocused NEPT I 90 x δ 180 x δ 90 x 180 x Δ/2 Δ/2 180 x 90 x 180 x S a b c d I x ( = ) ref. INEPT 1 S δ x 4J IS

26 Behaviour of CH, CH 2 and CH 3 Groups Spectral Editing

27 Distortionless Enhancement by Polarisation Transfer The relative intensities of the mulitplet components in INEPT spectra differ from the normal spectra, hence, DEPT DEPT I, 1 H 90 x τ 180 x τ θ y τ S, 13 C 90 x 180 x In DEPT, the θ pulse takes the role of Δ in INEPT, so the t delay is set to 1/2J and depending on the values of θ one gets various functional group spectra

28 DEPT45 DEPT45 experiment yields a positive peak for every carbon with attached protons: C a at 16 ppm, C b at 29 ppm, and C d, C e, and C f at 128.5, 128.9, and 129 ppm, respectively. Note in the spectrum below that carbon in the CDCl 3 solvent does not give a signal, since it has no attached protons

29 DEPT90 Dept 90 yields only CH yields peaks; CH 0, CH 2, and CH 3 are invisible. In our example we see only three lines due to C d, C e, and C f in the aromatic range from 126 to 129 ppm.

30 DEPT135 With DEPT135 CH 2 yields negative peaks, whereas CH and CH 3 are positive. Thus, we see C a, C d, C e, and C f as positive peaks, while C b is negative.

31 DEPT: Spectral Editing To distinguish the various multiplicity patterns in 13 C NMR, three DEPT spectra are acquired

32 DEPT: Spectral Editing CH 3 =FID(45)+FID(135) FID(90)

33 DEPT: Spectral Editing

34 Major Relaxation Pathways 1. Dipole-dipole coupling 2. Scalar coupling 3. Chemical shift anisotropy 4. Chemical exchange 5. Paramagnetic interactions 6. Spin rotation

35 Nuclear Overhauser Effect NOE is the change in the intensity of an NMR resonance when the transitions of a dipolar coupled spin are perturbed (saturated/inverted) The NOE enhancement of I spin upon saturating S spin is defined as η { S} = I I I I 0 0 Perturbed spin Equilibrium I intensity Observed spin

36 NOE: Transition Probabilities ββ ( ) ( ) αβ W 1A W 0AX W 2AX W 1X βα ( ) W 1X W 1A αα ( ) W 0AX and W 2AX are determined by dipolar couplings and have a distance dependence, r -6, and rotational correlation time dependence, τ c

37 NOE and Molecular Motion Relaxation Small molecules lead to positive NOE Big molecules lead to negative NOE Somewhere in between null NOE W 2 W 1 W 0 Depends on the strength of the local (dipolar) fields fluctuating at that frequency, ω Depends on the molecular motion at that frequency, ω W 0 transition will be predominant when the molecules tumble at ω A -ω X frequency, khz, for large molecules W 1 for molecules tumbling at Larmor frequencies W 2 for molecules tumbling at twice the Larmor frequencies, small molecules, fast tumbling

38 NOE: Some Expressions W 2AX -W 0AX η A = = f A {X} 2W 1X + W 2AX + W 0AX W n 1 r 6 J(nω) σ AX = AX W 2AX -W 2AX -W 0AX 0AX ρ AX = AX 2W 2W 1X + 1X W 2AX + 2AX W 0AX 0AX η A = A σ AX / AX / ρ AX = AX f A f {X} A {X} J(nω) = τ c 1+(nωτ c ) 2

39 Steady-State NOE ωτ c <<1 ωτ c =1.12 ωτ c >>1

40 NOE Difference Spectroscopy 13 C Ha Hb Hc Hb Ha C 1 H Hc _ = Steady-state NOE η ab η ac Knowing a reference distance, other distances may be calculated η ab ab r -6 ab -6 ab η ac ac r -6 ac -6 ac r ac ac = r ab ab * (( η ab ab // η ac ac )) -1/6-1/6

41 Transient NOE ( ) αβ ββ ( ) W 1A W 1X W 2AX βα () W 0AX 180 X 90 τ m W 1X W 1A αα ( ) selective inversion Intensity Monitor the magnetisation of the dipolar coupled spin by inverting the other spin as a function of the mixing time. The initial rate of growth is proportional to r -6 τ m Steady-state NOE could give ambiguous results in big molecules due to other magnetisation transfer processes, such as, spin diffusion. Hence, transient NOE much more desirable and useful

42 Nuclear Overhauser Effect

43 Nuclear Overhauser Effect

44 Nuclear Overhauser Effect

45 Nuclear Overhauser Effect

46 Nuclear Overhauser Effect

47 Nuclear Overhauser Effect Useful to identify spins undergoing cross-relaxation Direct dipolar couplings provide primary means of cross relaxation Cross relaxation manifests in the form of cross peaks in the NOESY spectrum

48 Overhauser being awarded the National Medal of Science, 1994

49 "Overhauser proposed ideas of startling originality, so unusual that they initially took portions of the scientific community back, but of such depth and significance that they opened vast new areas of science." The consequences of this discovery---known as the Overhauser Effect---for nuclear magnetic resonance, and through nuclear magnetic resonance for chemistry, biology and high-energy physics have been enormous. The idea, which has also had very practical consequences, was so unexpected that it was originally resisted vehemently by the authorities in the field. Not until its existence was demonstrated experimentally by Slichter and Carver in 1953 was it fully accepted. It has been said that one can judge the importance of a new discovery in physics by the number of other fields of science and engineering it impacts. From this point of view this contribution of Overhauser ranks among the highest.

50 When first proposed as a contributed paper at an APS meeting in April 1953, the proposal was met with much skepticism by a formidable array of physics talent. Included among these were notables such as: Felix Bloch (recipient of 1952 Physics Nobel Prize), Edward M. Purcell (recipient of Nobel Prize 1952 with Bloch and session chair), Isidor I. Rabi (recipient of Physics Nobel Prize, 1944) and Norman F. Ramsey (recipient of Physics Nobel Prize, 1989). Eventually everyone was won over. In a letter dated 27 July 1953, Norman F. Ramsey stated the matter succinctly2,3:

51 July 27, 1953 Dear Dr. Overhauser: You may recall that at the Washington Meeting of the Physical Society, when you presented your paper on nuclear alignment, Bloch, Rabi, Pearsall, and myself all said that we found it difficult to believe your conclusions and suspected that some fundamental fallacy would turn up in your argument. Subsequent to my coming to Brookhaven from Harvard for the summer, I have had occasion to see the manuscript of your paper. After considerable effort in trying to find the fallacy in your argument, I finally concluded that there was no fundamental fallacy to be found. Indeed, my feeling is that this provides a most intriguing and interesting technique for aligning nuclei. After considerable argument, I also succeeded in convincing Rabi and Bob Pound of the validity of your proposal and I have recently been told by Pound that he subsequently converted Pearsall shortly before Pound left for Europe. I hope that you will have complete success in overcoming the rather formidable experimental problems that still remain. I shall be very interested to hear of what success you have with the method. Sincerely, Norman F. Ramsey

52 April 20, 1993 Dear Al: I greatly appreciate your thoughtful remarks about the letter I wrote you forty years ago. Although I clearly remember surprising some of my friends by writing a very favorable referee report, I had forgotten that I also had written you a letter. You might be interested in how I came to get the matter straight and avoid the lifelong embarrassment of being responsible for the rejection of a great pioneering paper. After the APS meeting I did not understand your paper and was thoroughly convinced by the vigorous arguments of Bloch, Rabi and others that a radio frequency field always produces heating. I was consequently annoyed when I was asked to referee the paper and therefore would have to find exactly what was wrong. I started my study with strong prejudices against you but I then remembered that in high school physics I had always had trouble remembering how a Servel (gas) refrigerator worked. I decided that I could not write a negative referee report until I understood once again how the Servel worked. By the time I understood that, I had lost my prejudice against your paper and on further study was convinced you were right. Incidentally the easiest way for me to remember how in principle a gas refrigerator can work without violating thermodynamics is to remember one could use the heat of the gas flame to operate a steam engine which in turn could operate a mechanical refrigerator. Sincerely yours, Norman F. Ramsey

53 13 C Chloroform Spectra INEPT NORMAL, NO NOE REFOCUSSED INEPT REFOCUSSED INEPT AND DECOUPLING NORMAL DECOUPLING FULL NOE

54 29 Si with INEPT Scheme INEPT

55 INEPT and NOE Transfers Enhancement via INEPT NOE I=I 0 γ A γx I=I 0 (1 + γ A 2γ X ) NOE INEPT T 1 of interest is that of observed nucleus T 1 of interest is that of proton

56 INEPT and NOE Transfers Signal strength available by direct observation in the presence of full NOE from protons and from polarisation transfer from protons to the heteronucleus Nucleus Maximum NOE Polarisation Transfer 31 P C Si N Fe Rh

57 Dynamics and Relaxation Time scales and molecular motions Atomic fluctuations, vibrations. Group motions. (covalently linked units) Molecular rotation, reorientation Molecular translation, diffusion Rotation of methyl groups. Flips of aromatic rings. Domain motions. Chemical exchange, proline isomerization Amide exchange Ligand binding Influences bond length measurements Relaxation, linewidths, correlation times DOSY NMR 2 H NMR 2 H NMR 2 H NMR Chemical shifts 15 N- 1 H HSQC Transferred NOE measurements

58 Motional Timescales Slow Very slow Slow Fast Very fast Ultra fast s ms μs ns ps fs Fast Macroscopic Diffusion, Flow Chemical exchange Molecular rotations Molecular vibrations

59 Chemical Exchange Motional process leading to formation or rupture of chemical bonds: Chemical exchange The electronic structure is different in both the forms leading to difference chemical shifts and coupling constants when the exchange process takes place: Detectable by NMR provided the process is on an appropriate time scale

60 NMR and Dynamic Processes K ex Conformational equilibrium K B Chemical equilibrium This could be a chemical reaction, conformational equilibrium, exchange between the bound and free states of a ligand/protein complex, ligand binding of drugs to proteins.

61 NMR: Measurement of Rate Constants Inversion of NN-dimethylformamide O O N H N H The two methyl groups exchange due to the double-bond nature of the amide bond. They give two distinct resonance lines as long as the rate of exchange is longer than the relative difference in frequency of the two resonances 1 1 Rate Rate (s) (s) >> >> or or δ r - r -δ Δδ b Δδ b

62 NMR: Measurement of Rate Constants Lets now start increasing the temperature. Since the rate depends on the ΔG of the inversion, and the ΔG is affected by T, higher temperature will make things go faster. What we see in the NMR looks like this: At a certain temperature, called the coalecense temperature, the rate of the exchange between the two species becomes comparable to the difference in chemical shifts of the sites: T T C Past this point, the NMR measurement cannot distinguish between things in either site, because things are exchanging faster than the difference in relative frequencies. Rate Rate (s) (s) 1 1 or or δ r - r -δ Δδ b Δδ b

63 NMR: Measurement of Rate Constants Δδ * Rate > 1 Δδ * Rate = 1 Δδ * Rate < 1 Slow exchange Transition Fast exchange Now, since we can estimate the temperature at which we have the transition taking place, we can get thermodynamic and kinetic data for the exchange process taking place. If we did a very detailed study, we see that we have to take into account the populations of both sites (one site may be slightly favored over the other energetically), as well as the peak shape. Assuming equally populated sites (equal energies) simple relationships could be obtained.

64 NMR: Measurement of Rate Constants From the Δδ value (in Hz) at the limit of slow exchange we estimate the rate constant at the coalecense temperature: K ex = ex π ** Δν Δν // 2 2 = ** Δν Δν Since we have the coalecense temperature, we can calculate the ΔG of the process: ΔG ΔG = R ** T C * C *[[ ln ln (( T C / C / Δν Δν ))]] With NMR we can measure rates from 10-2 to 10 8 s -1.

65 Ligand Conformation: Transfer NOE Ligand binding to a receptor? Eg. Drug binding to protein, helpful in the design of drugs provided the chemical requirements of activity and conformational requirements of binding are known + Free Bound Often the bound ligand-receptor form cannot be solved as the protein could be very large. Monitor the NOE rates!

66 Ligand Conformation: Transfer NOE * * H I H S When bound, the protons in the marked carbons will have an NOE interaction. It will be very hard to see it with the protein also having tons of other NOE correlations As the ligand dissociates from the protein, it adopts another conformation in a jiffy H I * * H I H * H S k off * * H k unf * Usually, k off <k unf, hence, if k off is faster than T 1, the relaxation time, the NOE information will stay put with the ligand even Outside of the protein H S

67 Ligand Conformation: Transfer NOE Besides retaining NOE, sharp NMR spectral lines of the ligand could be obtained outside of the protein bound L free L protein The ligand cannot bind tightly to the receptor (we need constant exchange between bound and free ligand). The k off rate has to be much smaller than the spin-lattice relaxation rate, otherwise the NOE dies before we can detect it. Size of the receptor is not an issue.

68 Correlation Experiments: Magnetisation Transfer Correlation experiments, homocorrelation/heterocorrelation Assignments, connectivities Single-quantum/multiple-quantum correlation Magnetisation transfer Coherent Incoherent Mediated via scalar couplings through one or more coherent transfer steps Mediated via dipolar couplings, NOE/ROE/chemical exchange Essentially four building blocks: COSY, TOCSY, INEPT, and HMQC

69 Building Blocks, Spin Echo Schemes I τ 180 x a b c d τ Dec. SE I x Dec. SE I x I τ 180 x τ J IS SE I S 180 x a b c d JIS. SE 1 x 2 IySz( τ = 4J ) I S IS 180 x Dec. CS a b c d Dec. CS x x Ω I + y ΩI I I τ I cos( 2 ) sin( 2 τ )

70 Heteronuclear Multiple-Quantum Correlation, HMQC HMQC building block which takes as input transverse I magnetisation and frequency labels it with S I 180 x 90 x 90 x S Δ t/2 t/2 Δ a b c d e f Essentially HMQC does the following: HMQC I I cos( Ω t) x x s

71 INEPT INEPT I δ 180 x δ 90 y 180 x 90 x S a b c I INEPT 1 2 I S ( δ = ) 4J x z y IS

72 Refocused INEPT Refocused NEPT I δ 180 x δ 90 y δ 180 x δ 180 x 90 x 180 x S a b c d I x ( = ) ref. INEPT 1 S δ x 4J IS

73 Reverse INEPT Reverse INEPT I 90 y δ 180 x δ 90 x 180 x S a b c 2 IS ( ) rev. INEPT 1 z y I δ x = 4J IS

74 Reverse Refocused INEPT Reverse refocused INEPT I δ 180 x δ 90 y δ 180 x δ 180 x 90 x 180 x S a b c d S x ( = ) rev. ref. INEPT 1 I δ x 4J IS

75 Conclusions It is possible to manipulate the spin populations Transfer of polarisation possible from one nucleus to another Polarisation transfer mediated by J or dipolar coupling In the case of dipolar coupling, NOE, distance information is present These form the building blocks in experiments to determine the structure of big molecules