The number of protons yielding correlations in a 2D NOESY spectrum quickly overwhelms the space available onA 2D map. 15N labeling can help simplify the fingerprint region but not the aliphatic region

NH HH HCβ CβCα C' CαONH HHHN1JNH1JNCα

1JNC'1JC'Cα1JHCαα

2JNCα

Coupling Magnitude (Hz)1JNH 931JNCα 7 - 112JNCα 4 - 91JNC’ 151JCαC’ 551JHαCα 140

These methods take advantage of large 1J coupling constants

NH H

HN NH H

H HHCβ CβCα CαO

i ii-112 23CHNCA

Backbone assignment via 1J couplings

Start here – exciteprotons with aproton 90o pulse

HN(CO)CA

N Cα

Cβ

H

C N Cα

HH

H OH

H

Cβ HH

1 2

3

ii-1i-1

Slice from HNCA (at the 15N shiftof I44, T14, R74..). Each pair ofpeaks correlates a Cαi) and Cαi-1) with the 1H and 15N shift of residue i.

Slice from HN(CO)CA (at the 15N shift of I44, T14, R74..). Each pair of peaks correlates the Cαi-1) with the 1H and 15N shift of residue i.

Stage 2. Sidechain assignments completed with HCCH-COSY andHCCH-TOCSY for example.

The HCCH experiments provide connectivities of the aliphatic sidechains of individual amino acid residues.

Complete assignments can be obtained if the backbone assignments and the side-chain assignments can be connected via the 13Cα shifts.

An example. 13C shifts of Isoleucine

We know the 13Cα shifts from the backbone assignment

13CH3

13CH2

13CH 13CH3

13C

H

13C

O

15N

H

δ 5-15ppm

γ1 25-30ppmγ2 15-20ppm

β 30-35ppm

α 50-65ppm

Attempt to gain complete 1H, 15N and 13C chemical shift assignments. We can now resolve uncertainty in NOEs we observe.

These 4 methyls would give an ambiguous network of possible NOEs. But suppose we knew that the 13C shift of the δCH3 of Ile 1 was 9.3ppm and the δCH3 of Ile 2 was 13 ppm.

CH3

H3CCH3

CH30.82ppm

1H 0.55ppm

1H 0.55 ppm

0.82 ppm

3 Αngstroms

8 AngstromsδCH3 of Ile 1

δCH3 of Ile 2

Far larger proteins can now be tackled…44kDa

Simian immuodeficiencyvirus (SIV) ectodomainused to fuse with hostwhite blood cells

Types of Spin Relaxation

•Longitudinal or spin-lattice relaxation (T1 )- recovery of longitudinal magnetization- establishment of thermal equilibrium populations- exchange of energy

•Transverse or spin-spin relaxation (T2 )-decay of transverse magnetization- no exchange of energy- increase of entropy

T1. Build up of longitudinal magnetization when field is

switched on

Mz (t) = Mzeq [1- exp{- (t-ton) / T1}]

Equilibrium longitudinal magnetization Spin-lattice relaxation time OR longitudinal relaxation time

Inversion of longitudinal magnetization by π pulse

180o rotation about x-axis

Recovery of longitudinal magnetization after π pulse

1

2

Simple theory of T1

rotational correlation time

€

T1−1 = γ 2 Bran

2 τ c

1+ ωo τ c( )2

mean square amplitude of fluctuating fields

spin-lattice relaxation rate constant

Larmor frequency

rotational correlation time [in ns] approx. equal to 0.5 molecular mass [in kDa]

1 kDa = 1000 atomic mass units

large molecules tumble more slowly

small molecules tumble more quickly

Rotational correlation time c

Precession of Transverse Magnetization

The transverse magnetization components oscillate and decay

Mx

My

Time

Time

x

y

z

x

y

z

x

y

zBo

xy plane

My (t) = -Mzeq cos(t) exp{-t / T2}

Mx (t) = Mzeq sin(t) exp{-t / T2}

oscillation at the Larmor frequency

decay time constant = spin-spin relaxation time OR transverse relaxation time

Transverse relaxation or T2 decay

transverse magnetization is excited by first pulse along –y-axis

transverse magnetization dephases due to field inhomogeneity during the interval /2. “Black” vectors rotate

faster than “grey” vectors

Problems with higher molecular weights and how toovercome them

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Δv ≅1

πT2is the line-width in Hz at half peak height

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Δv

Comparison of T1 and T2

rapid motion (small molecule non-viscous liquids), T1 and T2 are

equal

Slow motion (large molecules, viscous

liquids): T2 is shorter

than T1.

Sensitivity of an NMR Experiment

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S N ≈ Nγ excγ det3 / 2Bo

32NS

12T2

12

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S /N

N

γ exc

γ det

Bo

NS

T2

Signal to noise ratio

Number of spins sample concentration

Gyromagnetic ratio of excited spins isotope labeling

Gyromagnetic ratio of detected spins out and back experiments

Static magnetic field strength magnet “size”

Number of scans measurement time

Transverse relaxation time molecular weight

Rattle page 46 and 47