the number of protons yielding correlations in a 2d noesy spectrum quickly overwhelms the space...
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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
€
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