Extensions to 3Dand

Improving Efficiency with Pulsed Field Gradients

BCMB/CHEM 8190

2D NMR spectra can get very crowded

2D NOESY of Staph- Nuclease

156 AA

Solution: go to 3D

- - - C N C C N - - -

H

C

= =

- -

O O

H

H H

HH

- - - C N C C N - - -

H

C

= =

- -

O O

H

H H

HH

(HB)CBCA(CO)NH

HNCACB

3D experiments used for sequential resonance assignments: Can detect C in 3D by INEPT transfer from 13C to 15N then from 15N to 1H. Sequential connections from: HNCA plus HN(CO)CA

1D2D

3D

f3 (1H)

f1 (13C)

f2 (15N)

HN(CO)CA

Strategy for Constructing 3D Experiments:Combine various 2D Experiments

4D

combine more?

Cavanagh et al 1996

3D TOCSY-HSQC

Cavanagh et al 1996

TOCSY-HSQC for 15N-Labeled Ubiquitin

Cavanagh et al 1996

Pulsed Field Gradients: More Efficiency in Multidimensional Spectra

• Coherence selection using pulsed field gradients. J. R. Tolman & J. H. Prestegard, Concepts in Magnetic Resonance, 7, 247-262 (1995).

• Water suppression (WATERGATE), M. Piotto, V. Saudek & V. Sklenar, J. Biomol. NMR, 2, 661-665 (1992).

• Diffusion measurements. Altieri, Hinton & Byrd, J. Am. Chem. Soc., 117, 7566-7567 (1995).

Pulsed Field Gradients – How they Work

i

iB0(z)

B’

z

B0

time

G(z)

Magnetization vectors precess at different rates depending on G(z) and for each volume element. They dephase - net Mx, My = 0. Reversal of gradient refocuses magnetization.

Effects of Gradients can be Refocussed Application: Water Suppression

90x 90-y 180y 90-y

x y

z

a b x y

ab

zG1 G1

Resonance notaffected by 90refocuses

x y

z

b

a

x yb

a

zResonance affected by 90dephases (H2O)

x ya

b

z

x y

z

a

b

x y

z

b

a

1D 1H Water-Suppressed Spectrum Pf-Rubredoxin in 1H2O

ppm-2024681012

Translational Diffusion Constants for Macromolecules

• Determine aggregate size• Determine protein-protein interactions• Screen for bound ligands

• <(X1-X0)2> = nDt where D = kT/(6r)• Key: if molecule moves, field is different,

magnetization doesn’t refocus

r

90x 180y

gz gz

∆

•ln[S/S0] = -2g2D2(∆ - /3)

Stejskal and Tanner Pulse Sequencefor Diffusion Measurement

Diffusion Measurement Continued

• Measurements are limited by natural T2

• Improved sequence uses z storage(Altieri, Hinton and Byrd, 1995)

ln(S/S0)

g2

Large molecule

Small molecule

Coherence Selection Using Pulse Field Gradients

• H(r) = -kk [B0 + Bz(r)]Ikz

(in radians s-1 and neglecting chemical shifts)• Effects on product operators for a z gradient:

• Ikz -k Bz(z) Ikz Ikz

• Ikx = (Ik+ + Ik- )/2

• Ik+ -k Bz(z) Ikz exp[i k Bz(z) ] Ik+

• Ik- -k Bz(z) Ikz exp[-i k Bz(z) ] Ik-

• For linear gradients Bz(z) = Gz z• Observables are integrals over z – zero for Ik+ , Ik-

B’

z

B0

1H(I)

15N(S)90-x 180y 90y

90y

t1/2 t1/2 decouple180x 90-x 180x

180y 90-x 180x

t2

GG1

-G1G2

Gradient Selected HSQC

I+(t2) Integralz {S+(t1) exp[iN2G1z] exp[-iHG2z]}

Integralz {S+(t1) exp[i(N2G1z- HG2z)]}

I+(t2) finite only if N2G1 = HG2All 1Q proton transverse magnetization eliminatedNo phase cycling needed to suppress unwanted signals