1. 1 Introduction to Biomolecular NMR

2. 2 Nuclear Magnetic Resonance Spectroscopy Certain isotopes ( 1 H, 13 C, 15 N, 31 P ) have intrinsic magnetic moment Precess like tops in magnetic field B 0 In a 600 MHz spectrometer –protons precess at 600 MHz – 15 N nuclei precess at ~60 MHz – 13 C nuclei precess at ~125 MHz BoBo   =  B o

3. 3 Creating coherence Unless the spins are aligned (coherent), their nett effect will be zero B 0 field aligns spins M 0 B 1 field rotates M 0 into x-y plane M 0 rotates at speed in x-y plane Coils in x-y plane record fluctuating magnetic field B 1 field must rotate about z-axis at precession frequency MoMo z x i B1B1 y BoBo

4. 4 1D NMR experiment z x M xy y z x y MoMo Free Induction Decay (FID) 90 y pulse

5. 5 Free Induction Decay t M M(t) = cos(  t) exp(- t/T)  FT 

6. 6 Fourier transform spectroscopy System resonates at many different frequencies (c.f. church bell) Excite all frequencies simultaneously using a ‘hard’ pulse Frequency analyse (Fourier transform) to yield component frequencies t 

7. 7 Two major causes of decay of signal Spin-lattice relaxation (T 1 decay) –loss of energy by spins leads to return of M to z axis –happens with time constant T 1 Loss of coherence due to dephasing (T  decay) T 1 >> T 2 T 2 inversely related to homogeneity of B 0 No energy is lost during dephasing  signal may be refocused M(t) = M(0) e -t / T 1 M(t) = M(0) e -t / T 2 M z x y M z x y

8. 8 NMR of proteins A sample of protein contains many protons –H N proton attached to N on backbone –H  proton attached to C  on backbone –H  proton attached to C  on backbone (typically 2) –H  proton attached to C  on backbone –Protons in H 2 O molecules (concentration 110 M as compared to ~1mM for protein) Different protons precess at different frequencies, depending on their chemical environment –  depends on the chemical shielding; e.g. how exposed the nucleus is to the solvent or how close it is to a heavy atom such as C or N –protons in water correspond to  =0 (no chemical shielding) –protons in the protein may have  >0 (to the right of the water peak) or  <0 (to the left) Define a B 0 -independent scale: –known as ppm’s  = -  B 0  =  H2O -  ) / ( 10 6  H2O ) =  / 10 6

9. 9 1D NMR spectrum of a protein In terms of ppm scale, peaks appear at same place irrespective of the strength of B 0  larger proteins have more overlapping peaks But line width is independent of B 0 –roughly  T 2 -1 –increases with size of protein  less overlap at higher field Also strength of signal increases with B 0 Conclusion: going to higher field increases sensitivity and resolution

10. 10 Interactions between nuclei (couplings) Coupled springs –transfer of energy back and forth Scalar coupling –mediated through overlap of electronic orbitals –“through bond” coupling –useful for assigning particular peaks to particular protons –determine covalent structure of the protein molecule Dipolar coupling –results from interaction of dipolar fields of nuclei –“through space” coupling –useful for determining non-covalent structure (folded shape) of molecule

11. 11 Simplest 2D experiment Correlation spectrOScopY experiment Pair of coupled nuclei s 1 and s 2 Record whole series of 1D experiments, each with a different value of t 1 Second 90 pulse transfers magnetization from s 1 to s 2 Data acquired during t 2 tells us the precession frequency (  2 ) of s 2 During t 1 magnetization is on s 1 and therefore precesses at frequency  1 –initial magnitude at beginning of t 2 depends on t 1 and  1 S(t 2 ) = cos(  2 t 2 ) S(t 1,t 2 ) = cos(  1 t 1 ) cos(  2 t 2 ) COSY pulse sequence 90 x 90 y t1t1 t2t2

12. 12 The amplitiude of the 1D spectrum acquired during t 2 varies sinusoidally with a different frequency as a function of the interval t 1, indicating that during t 1 the magnetization is on a spin with the corresponding frequency

13. 13 2D NMR spectrum Fourier transform in both t 1 and t 2 gives S(  1,  2 ), which when plotted as contour function gives a peak at coordinates  1 and  2 11 22

14. 14 2D COSY spectrum Magnetization which stays on same nucleus during t 1 and t 2 has the same frequency in both dimensions  along the diagonal Magnetisation which jumps from a nucleus with frequency  1 during t 1 to one with frequency  2 during t 2 is represented by a cross-peak at cooordinates (  1,  2 ) The furthest that magnetisation is able to jump is the distance of 3 bonds; i.e –H N - H  –H  - H  –H  - H 

15. 15 COSY spectrum of a small molecule COSY spectrum directly confirms covalent structure of molecules

16. 16 TOCSY TOtal Correlation SpectroscopY TOCSY is an ‘relayed’ extension of COSY –uses scalar coupling Cross-peaks appear between all spins which can be connected by relaying Magnetisation still can’t be transferred across peptide bond (3-bond limit still applies)  amino acids still form isolated spin systems Useful for recognising particular amino acids

17. 17 Heteronuclear NMR 3-bond limit means that cross- peaks are never observed between protons in different amino acids; i.e. there is no magnetization transfer across the peptide bond Magnetization can be transferred if the intervening nuclei are magnetic; i.e. 13 C and 15 N. This is achieved by producing the protein recombinantly in bacteria grown with 15 N-ammonium chloride and 13 C-glucose as the sole nitrogen and carbon sources respectively Peptide bond

18. 18 3D experiments The previous experiments can be extended to two indirect dimensions, t 1 and t 2 The real time interval during which all the FID’s are recorded is called t 3, or the direct dimension. S is a function of t 1, t 2, and t 3 ; to get the spectrum it must be Fourier transformed inall three time dimensions. If the magnetization is on a nucleus with frequency  1 in t 1,  2 in t 2 and  3 in t 3, the spectrum will have a ‘peak’ centred at coordinates (  1,  2,  3 ) In 3D a peak is more like a ball CC  HN NN

19. 19 Heteronuclear assignment experiments 3D HNCA experiment –protein must be isotopically enriched with 1 H, 13 C and 15 N Peaks represented as balls in 3D space at coordinates corresponding to: – 1 H shift of an amide proton (H N ) – 15 N shift of attached N – 13 C shift of attached C  At same 1 H and 15 N values, another peak corresponding to 13 C shift of C  of preceding residue  makes it possible to walk along sequence to assign entire backbone residue i-1 residue i

20. 20         1 2 3 4 5 Assignment of all H N, N and C  resonances of a pentapeptide in a HNCA spectrum by ‘walking’ along the backbone. In each case the black sphere represents the in-residue C , the grey sphere the C  of the preceding residue  HN NN CC

21. 21 NOE effect provides structural information Nuclear Overhauser Effect produces coupling between protons which are close in space (though not necessarily covalently bonded) NOE cross-peaks  R -6  only observed for R < 5 Å NOESY is 2D experiment in which cross peak intensities are proportional to NOE between corresponding protons NOESY spectrum of lysozyme

22. 22 Basic method for protein structure determination by NMR ASSIGN all peaks using COSY-type spectra Identify all cross peaks between assigned diagonal peaks on NOESY spectra Convert NOESY cross-peaks to distance constraints between corresponding protons Find 3D structure which optimally satisfies distance constraints as well as protein stereochemistry

23. 23 Structure determination Molecular modelling with energy function E total = E covalent geometry + E NOE restraints Use optimisation algorithm to find molecular structure with lowest value of E total which still satisfies all NMR-derived distance constraints Generate family of structures Resolution generally not as good as X-ray, but may be better reflection of molecules in-vivo