Time scales and molecular motions

1
Dynamics and Relaxation

• Time scales and molecular motions
• Atomic fluctuations, vibrations. 10-15 to
  10-12 s lt1Å
• Group motions. (covalently linked units)
  10-12 10-3 s lt 1 Å 50 Å
• Molecular rotation, reorientation 10-12 10-9 s
• Molecular translation, diffusion
• Rotation of methyl groups. 10-12 10-9 s
• Flips of aromatic rings. 10-9 10-6 s
• Domain motions. 10-8 10-3 s
• Proline isomerization. gt 10-3 s
• Chemical exchange (e.g. two protein
  conformations)
• Amide exchange
• Ligand binding

2
Dynamics and Relaxation

• Time scales and molecular motions
• Atomic fluctuations, vibrations. Influences
  bond length measurements
• Group motions. (covalently linked units)
• Molecular rotation, reorientation Relaxation,
  linewidths, correlation times
• Molecular translation, diffusion DOSY NMR
• Rotation of methyl groups. 2H NMR
• Flips of aromatic rings. 2H NMR
• Domain motions. 2H NMR
• Chemical exchange, proline isomerization Chemical
  shifts
• Amide exchange 15N-1H HSQC
• Ligand binding Transferred NOE measurements

3
Relaxation, line width and correlation times
Large molecule, long tc, J(w) dominated by low
frequency fluctuations.
Small molecule, short tc, high frequency and
low frequency fluctuations.
4
Relaxation, line width and correlation times
hw viscosity of the solvent
r3H hydrated radius
25
20
Dn FWHM (Hz)
15
10
5
0
2
6
8
10
12
14
4
tc (ns)
See Cavanagh et al. Protein NMR spectroscopy,
pages 16-19.
5
Molecular Diffusion
Hahn echo in absense of gradient pulses
180y
90x
reverse gradient
gradient pulse
t2
t1
If there is no diffusion, a second gradient
pulse, will result in full Hahn echo.
With gradient pulse, magnetization evolves at
different frequencies (it is labeled depending
on its location).
DOSY diffusion ordered nmr spectroscopy (see
Prog. Nucl. Mag. Reson. Spec. 34203)
6
Secondary Structure
Sequence MALRRVETTYGDAWCSTQNLIVWRSTERLN
daN 3JHNa gt 7 Hz T1
loop
sheet
sheet
7
13C Chemical Shift Anisotropy
Many orientations in xy plane
z
Only one orientation along z-axis
x
y
chemical shift (Hz or ppm)
8
13C Chemical Shift Anisotropy
More orientations with x component
z
than y component
Only one orientation along z-axis
O
C
x
y
chemical shift (Hz or ppm)
9
13C Chemical Shift Anisotropy
X and Y are averaged
Nothing happens
z
O
C
x
chemical shift (Hz or ppm)
y
Rotation about z
10
13C Chemical Shift Anisotropy
z
O
C
x
chemical shift (Hz or ppm)
y
x has a unique chemical shift
z and y are averaged
Rotation about x
11
13C Chemical Shift Anisotropy
z
O
C
x
chemical shift (Hz or ppm)
y
Isotropic Chemical shift
Rotation about angle of 54.7 relative to z-axis
12
MAS NMR
Static
13CH2
13COOH
512 scans
10 kHz MAS
4 scans
Chemical Shift
MAS improves resolution and sensitivity
13
Deuterium NMR
D
D
C
D
D
D
C
D
Rigid Isotropic
Z
14
Deuterium NMR
D
D
D
Axially Symmetric Axially Asymmetric
C
c2
Z
D
D
D
C
c2
c1
15
Experimental (a) and simulated (b) MAS spectrum
of Val80
Only fast methyl rotation
16
Deuterium NMR
CD3
D
trans (90)
C
CD3
CD3
D
gauche (7)
C
CD3
CD3
CD3
gauche - (3)
C
D
Rotamer distribution of valine in a-helices
obtained from an analysis of soluble protein
crystal structure. (Lovell et al., Proteins
40389-408, 2000)
17
Static NMR simulations
CD3
Populations Jump rate (s-1) 751510 105
9073 102 (slow) 9073
105(intermediate) 9073 108(fast)
D
C
CD3
c1

• Simulations
• assume fast methyl group rotation
• vary rotamer populations
• vary the rate of rotation about c1

18
Experimental (a) and simulated (b) MAS spectrum
of Val82
Motion about the Ca-Cb bond is fast on the 2H NMR
time scale Unequal populations (9073) for
occupancy of the three dominant rotamers.
Valine is not locked into a single rotamer
state. Trans conformer is thermodynamically
favored.
19
Chemical Exchange
20
Chemical Exchange
Slow exchange - two distinct resonances
21
Chemical Exchange
Fast exchange - one sharp average resonance
temp
Intermediate exchange - one broad resonance
Slow exchange - two distinct resonances
22
Amide Exchange
15N-1H HSQC
Add D20 and collect time series of spectra
23
Transferred NOEs
24
Transferred NOEs
25
Kinetics
O
O
H
N
N
OH
time