Biochemistry 530 NMR Theory and Practice

Biochemistry 530 NMR Theory and Practice Gabriele Varani Department of Biochemistry and Department of Chemistry University of Washington

1D spectra contain structural information.. but is hard to extract: need multidimensional NMR 1D spectrum Dispersed amides: protein is folded Ha: protein contains b-sheet Downfield CH 3 : Protein is folded

1D vs 2D homonuclear NMR Spectroscopy 1D NMR preparation t detection Basic structure of 1D experiment FID 2D NMR t 1 m Basic structure of 2D experiment (e.g. NOESY) preparation evolution mixing detection t 2 Jeener and Ernst, 1972

2D homonuclear NMR Spectroscopy 2D NMR t 1 m preparation evolution mixing detection t 2 Basic structure 90 90 90 NOESY t 1 m 90 90 FID Two basic experiments: NOESY and COSY COSY t 1

How to generate a 2D experiment: NOESY Typical number of repetitions (t1 increments) for homonuclear NMR: 256-512 1. Record numerous 1D experiments by systematically incrementing time t1 from 0 to t max ; the experiment generates a matrix of points S(t1,t2) which encodes the frequency information with respect to both t1 and t2

How to process the data to obtain a 2D spectrum 2. Execute the FT for each experiment (each t1 value) with respect to time t2 to generate an interferogram S(t1, w2) 3. Execute the FT with respect to t1 (for each w2 value) to generate the final 2D spectrum S(w1,w2)

1D vs 2D NMR spectra of a protein 1D spectrum amides NH2 Ha Side chain CH2 Side chain CH3

1D vs 2D NMR spectra of a protein 2D projection representation 2D contour representation

cross-peaks in multidimensional NMR carry structural information Diagonal is closely related to 1D spectrum 2D contour representation: peaks outside diagonal are called cross-peaks

Nuclear Overhauser Effect SpectroscopY (NOESY) 2D NMR t 1 m preparation evolution mixing detection t 2 90x 90x 90x A B t 1 C D m mixing E F t 2 acquire consider a two spin system, I & S: A z B The NOESY Iz experiments detects interactions between Sz t 1 free spins that are close 90x in space and dipolar precession coupled: the magnetization transfer mechanism is essentially the Iy same as FRET in optical spectroscopy (fluorescence) y z Sy x x

Nuclear 90x Overhause 90x 90x Effect SpectroscopY (NOESY) x A C Ix sin I t 1 Sx sin S t 1 x x E S I z z z Iz Sz A B Iy cos Sy cos I t 1 S t 1 S I Sz cos S t 1 Iz cos I t 1 (mixing) t 1 consider a two spin system, I & S: C D 90x y 90x 90x y m mixing I S x B x x E D F F S t 2 I z z z acquire Iy Sy y Sz cos S t 1 Iz cos I t 1 Iy (a II cos I t 1 + a SI cos S t 1 ) Sy (a SS cos S t 1 + a IS cos I t 1 ) t 1 free precession m mixing y y 1. Excite with 90 o pulse 2. During t1, spins are labeled with their Larmor frequency 3. The second 90 o pulse exchanges rotates magnetization to -z 4. Magnetization is exchanged between spin I and S during the mixing time 5. The final 90 o pulse makes the signal observable and signal is acquired in t2

Nuclear Overhause Effect SpectroscopY (NOESY) t 1 m t 2 90x free precession 90x mixing 90x acquire [Iy a II cos I t 1 + Sy a SS cos S t 1 + Iy a SI cos S t 1 + Sy a IS cos I t 1 ].[ cos I t 2 + cos S t 2 ] S I F 2 S I When magnetization is exchanged, spin I signal contains information on spin S and viceversa (crosspeaks) I a SI S, I ) diagonal peaks a II I, I ) I S a SS S, S ) crosspeaks a IS I, S ) S Cross-peaks appear between spins which are close in space (<5-6 A) (assignments and structure) S I F 1

Nuclear Overhause Effect SpectroscopY (NOESY) t 1 m t 2 90x free precession 90x mixing 90x acquire [Iy a II cos I t 1 + Sy a SS cos S t 1 + Iy a SI cos S t 1 + Sy a IS cos I t 1 ].[ cos I t 2 + cos S t 2 ] S I The mixing coefficients, a IS = a SI are proportional to the NOE between these two nuclei I F 2 a SI S S, I ) diagonal peaks I a II I, I ) I The NOE is related to the distance r between the two spins and the correlation time t c (the time for reorientation of the IS vector in the molecule): structure and motion S a SS S, S ) crosspeaks a IS I, S ) S NOE r IS -6 f (t c ) m S I F 1

A simple example: a small immunogenic peptide

COSY and NOESY connectivities in the polypeptide unit COSY (broken lines) and NOESY (continuous lines)

Protein chemical structure dictates local NOE interactions Sequential and medium range interactions in polypeptides

Protein secondary structure determines local NOE interactions Sequential and medium range NOE interactions in regular turns

Protein 3D structure determines local NOE interactions Sequential and medium range NOE interactions in an a-helix

Protein 3D structure determines NOE interactions Medium and long range NOE interactions in a parallel and anti-parallel b-sheets

Patterns of NOE interactions define protein secondary structure Observable NOE interactions (<5 A) in regular protein secondary structures

NOE interactions, scalar couplings (and chemical shifts) can be combined to define protein secondary structure NOE interactions (<4.5 A) and scalar coupling patterns in regular protein secondary structures

A simple example: a small immunogenic peptide

COherence transfer SpectroscopY (COSY) Cross-section of cross-peak between HN and Ha proton allows measurement of scalar couplings for residue C57

COherence transfer SpectroscopY (COSY) 2D NMR t 1 m preparation evolution mixing detection t 2 90x 90x A B t 1 C D t 2 acquire consider a two spin system, I & S: z The A z COSY experiments detects B interactions Iz (correlation) Sz between spins that are scalar t 1 90x coupled: beware, it can only be understood through quantum mechanics Iy Sy free precession y

90x 90x t COherence 1 t 2 transfer SpectroscopY (COSY) A B C D acquire x consider a two spin system, I & S: A z Iz Sz + Ix sin ( I _ J IS )t 1 Sx sin ( + S _ J IS )t 1 x C + z 90x x S Ix sin ( I _ J IS )t 1 Sx sin ( S + _ J IS )t 1 Iy cos ( I _ J IS )t 1 Sy cos ( S _ + J IS )t 1 S I D I x B z + y z y Iy Sy 90x t 2 acquire t 1 free precession y 1. Excite with 90 o pulse 2. During t1, spins are labeled with their Larmor frequency 3. During t1, if spins are scalar coupled, the signal encodes this information as well 4. The second 90 o pulse exchanges magnetization between spins: spin I now has memory of spin S and viceversa 5. Signal is acquired in t2

COherence transfer SpectroscopY (COSY) 90x JIS t 1 free precession 90x t 2 acquire Ix.1/2[sin ( I - J IS ) t 1 - sin ( I + J IS ) t 1 ].1/2[sin ( I - J IS ) t 2 - sin ( I + J IS ) t 2 ] Sx.1/2[sin( S - J IS ) t 1 - sin ( S + J IS ) t 1 ].1/2[sin ( S - J IS ) t 2 - sin ( S + J IS ) t 2 ] S JIS I When magnetization is exchanged, spin I signal contains information on spin S and viceversa (crosspeaks) I F 2 S ± J IS/2 S, I ) I ± J IS/2 diagonal peaks I, I ) I ± J IS/2 Cross-peaks appear between spins which are scalar coupled (assignments) S S S, S ) crosspeaks I I, S ) F 1 S ± J IS/2 The cross-peak fine structure contains information on scalar coupling (structure)

Structural information: scalar couplings directly gives you the torsion angles that define protein or n.a. structure C a N H O C H C 1 a R H N C f b H C H O C a 3 J HaN =5.9cos 2 f-1.3cosf +2.2 3 J ab =9.5cos 2 1-1.6cos 1 +1.8 (Karplus, 1958) Cross-peaks in COSY experiments occur only between residues that are scalar coupled; in turns, these couplings can be measured in COSY experiments

COSY and NOESY connectivities in the polypeptide unit COSY (broken lines) and NOESY (continuous lines)

Amino acid chemical structure Different pattern of scalar couplings

Amino acid identification from scalar coupling patterns Different pattern of scalar couplings allows amino acid type identification in correlated spectra (COSY, 2QF-COSY, TOCSY) This is the first step towards complete spectral assignments of a protein spectrum (at least before heteronuclear NMR)

Amino acid chemical structure leads to distinct shift for each residue: random coil chemical shift values Residue NH ah bh Others Gly 8.39 3.97 Ala 8.25 4.35 1.39 Val 8.44 4.18 2.13 CH3 0.97, 0.94 Ile 8.19 4.23 1.90 CH2 1.48, 1.19 CH3 0.95 CH3 0.89 Leu 8.42 4.38 1.65,1.65 H 1.64 CH3 0.94, 0.90 Prob 4.44 2.28,2.02 CH2 2.03, 2.03 CH2 3.68, 3.65