Large Molecules

NOESY Spectra

Large Molecules

NOESY Spectra

Small Molecules

NOESY Spectra

Small Molecules

NOESY Spectra

Hb

Ha

Hc

C

Hc

Ha

Hb

δ (f2)

δ (f1)

NOESY (NOE SpectroscopY)

(+)

(-) Small molecule (+) Large molecule

-1

-0.5

0

0.5

0.01 0.1 1 10 100

0.1 1 10 100

0.4

-0.5

-1.0

ωτc

Small molecules

Large molecules

Extreme narrowing limit

NOESY (NOE SpectroscopY)

Higher temperature Lower temperature

Lower viscosity Higher viscosity

Lower field Higher field

Changing τc

Changing ω

Transverse cross-relaxation

Transverse cross-relaxation

Spin locking

Spin-locking – Theory

z

x’

y’

z

x’

y’

90

BSL (x) BSL

• BSL is a fluctuating magnetic field • It is static in the rotating frame. This is why these experiments are commonly called rotating-frame experiments.

Transverse Solomon equations

90 90 90

t1 tm

NOESY t2

ROESY (Rotating framE SpectroscopY)

90

t1 tm

ROESY t2

-Izcos(ΩIt1) -Szcos(ΩIt1) B0

-Ixcos(ΩIt1) -Sxcos(ΩIt1) BSL

ROESY (Rotating framE SpectroscopY)

ROESY (Rotating framE SpectroscopY)

ROESY (Rotating framE SpectroscopY)

ROESY (Rotating framE SpectroscopY)

ROESY (Rotating framE SpectroscopY)

Hb

Ha

Hc

C

Hb

Ha

Hc

δ (f2)

δ (f1)

(+)

(-) Small molecule ~0 “intermediate” molecules

(+) Large molecule (-) Every molecule using ROESY

NOESY vs ROESY

NOESY vs ROESY

Comparison of diagonal-peak and cross-peak amplitudes for NOESY and ROESY for a set of rotational correlation times. All simulations are for the case of two protons separated by 2 Å @ 500 MHz.

Transferred NOEs and bound conformations

•  The information about the bound conformation is transferred to the free molecule by chemical exchange between bound and free species

•  In a typical TrNOE experiment a low concentration of protein (≤0.1mM) and 10 to 30 molar equivalents of ligand are used

Relaxation and molecular size

78910 ppm78910 ppm78910 ppm78910 ppm 78910 ppm78910 ppm78910 ppm78910 ppm

6-residue peptide 180-residue protein

Free M13

M13 bound to CaM

M. Ikura and A. Bax, J. Am. Chem. Soc. 114,2433 (1992)

Relaxation and molecular size

Transferred NOEs and bound conformations

IF SF

SB IB

NOE σF

σB

Exchange k

NOE Kinetics and correlation time

IF SF NOE

σF IB SB NOE σB

Transferred NOEs and bound conformations

NOE int.

time

Mixing time

L

L Measured TrNOE Intensity

NOE of free L

τ

LE

Applicability limits of TrNOE

•  The rate of exchange between free and bound states needs to be sufficient for an appreciable magnetization flux to occur between them.

•  In this case:

<σ> = xFσF + (1-xF)σB

Applicability limits of TrNOE •  <σ> should be dominated by the bound

term: xFσF <<(1-xF)σB

The extent to which this inequality is fulfilled depends on:

• the relative tumbling rates and distances in the free and bound states

• the equilibrium constant Kd

Transferred NOEs and bound conformations

D81

H57

S139

A157C159

R161

P6P5P4

P3

P2

P1

Basic aaAcidic aaHydrophobic aa

R161

D81

H57

C159

R155

F154 P6P5

P4P3P2

P1