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
H
H
H
H
H
C
H
H
H
H
C
H
C
H
C
H
C
N
C
C
C
N
C
H
N
C
C
H
H
N
C
H
H
H
H
H
1H spectrum
15N
2D HSQC yields one resonance for each amide N-H
1H
4
Line width at half maximum
15N spectrum
15N
1H
5
T2 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.
6
Relaxation, line width and correlation times
hw viscosity of the solvent
r3H hydrated radius
For ubiquitin, 76 residues Mw 8565 1H line
width 6 Hz tc 4.0 ns rH 17 Å Correct
for ubiquitin monomer. What would the line width
be for a tetramer?
7
mobile, flexible chain has narrower line widths
than globular protein
15N
1H
8
Mobility is also expressed in T1 relaxation times.
How do you measure T1?
9
Concept 6 When the B1 field is turned off, the
net magnetization relaxes back to the Z axis with
the time constant T1
T1 is the longitudinal relaxation time constant
which results from spin-lattice relaxation
10
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11
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12
Measure T1 with an inversion recovery pulse
sequence 180 - t - 90 - measure intensity
acquire spectrum
acquire spectrum
13
180
Inversion Recovery
14
Inversion Recovery - Measure NMR Intensity as a
function of the delay time t
0
t
15
Inversion Recovery - Measure NMR Intensity as a
function of the delay time t and fit to an
exponential function
0
t
Mz
Mz Mo (1- 2e -t/T1 )
0
t
16
Mobility is also expressed in T1 relaxation times.
t 10 us
t 100 us
t 1000 us
t 5000 us
17
Secondary Structure
Sequence MALRRVETTYGDAWCSTQNLIVWRSTERLN
daN 3JHNa gt 7 Hz T1
loop
sheet
sheet
18
Amide Exchange
15N-1H HSQC
Add D20 and collect time series of spectra
19
D20
mobile, flexible chain is more exposed to
solvent and will exchange faster
D20
D20
D20
15N
1H
20
Chemical Exchange
Slow exchange - two distinct resonances
21
mobile, flexible chain transiently forms
helix in the limit of slow exchange, you will
observe two distinct resonances
15N
What is slow?
1H
22
Chemical Exchange
Fast exchange - one sharp average resonance
temp
Intermediate exchange - one broad resonance
Slow exchange - two distinct resonances
23
mobile, flexible chain forms helix upon
phosphorylation You can measure the kinetics by
NMR
P
P04-2
1H
1H
24
Kinetics
O
O
H
N
N
OH
time
25
T2 - spin-spin or transverse relaxation
26
Recall first lecture. One spin precessing in the
x-y plane will induce an oscillating current
Current amplitude
time
27
Recall first lecture. Fourier transform of an
infinite sine wave is a delta function, ie. a
sharp line with a single frequency
Current amplitude
frequency
time
28
Now imagine you have many spins with
different orientations in the x-y plane and all
precessing at the same frequency. The net
current is zero and therefore there is no
signal.
Current amplitude

time
time
29
Immediately after all of spins are put into the
X-Y plane, they are in phase.
Current amplitude
time
30
The time it takes for the Individual spins to
dephase in the x-y plane is the T2 relaxation
time.
Current amplitude
time
31
Current amplitude
frequency
time
Current amplitude
frequency
time
Fourier transform of a decaying sine wave gives a
broad line in the frequency domain.
32
Current amplitude
frequency
time
The faster the dephasing, the faster the decay of
the time domain signal, the broader the line.
Line widths are related to T2 relaxation. T2
is always faster than or equal to T1
33
Quantum mechanical picture

Mz

Mz
34
Quantum mechanical picture
T1 - not energy conserving
T2 - energy conserving
35
T1 and T2 at short correlation times
T1 or T2 relaxation time
T1
T1 minimum
T2
long
short
Correlation time
optimal frequency for T1 relaxation (MHz
frequencies)
36

• NMR concepts
• Basics
• magnetic fields.
• What is the difference between B0 and B1?
• chemical shifts
• J-couplings
• dipolar couplings
• Protein structure determination
• what is the basic strategy?
• collect a series of 2D and 3D spectra
• assign protons to amino acids in a sequence
  specific manner
• assign secondary structure (how?)
• collect and catalog long range (non trivial)
  NOEs
• assign tertiary contacts
• MD simulations using structural constraints

37

• NMR concepts
• Protein structure determination
• collect a series of 2D and 3D spectra
• 2D 3D
• COSY HSQC - NOESY
• NOESY HSQC - TOCSY
• TOCSY
• HSQC
• HNCOCACB
• HNCACB
• assign protons to amino acids in a sequence
  specific manner
• What are the differences in these sequences and
  how can
• they be used for assignments?

38

• NMR concepts
• Relaxation and dynamics
• T1 and T2 relaxation
• amide exchange
• How do you tell if a protein is folded?
• How do you tell what regions are more mobile/less
  mobile?

39
Quiz
H
H
H
H
H
H
CH3 - C - CH3
H
OH

O
O
O
O
C
C
C
N
C
C
N
C
N
C
N
C
H
H
H
H
H
H
H
H
Draw the amino acid spin systems for each
residue? What would the COSY spectrum look like
if the assigments for the resonances were as
follows NH CaH Phe 8.2 4.5 Ser 8.0 3.7 Al
a 8.4 4.0 Leu 7.9 5.2
40
Amino Acid Spin Systems Ala
H
O
C
N
C
H
H
bCH3
aH
41
Hc
Amino Acid Spin Systems Phe
Hb
Hb
Ha
Ha

O
bH
C
N
C
bH
H
H
aH
Hb
42
Amino Acid Spin Systems Ser
OH
O
C
N
C
H
H
bH
bH
aH
43
Amino Acid Spin Systems Leu
H
CH3 - C - CH3
O
C
N
C
H
H
dCH3
dCH3
gH
bH
bH
aH
44
What would the COSY spectrum look like if the
assigments for the resonances were as
follows NH CaH Phe 8.2 4.5 Ser 8.0 3.7 Al
a 8.4 4.0 Leu 7.9 5.2
Ser
Ala
Phe
Leu
Leu
Ser
Phe
Ala
45
Phe-Ser-Ala-Leu
What would the NOESY spectrum look like
COSY
Ser
Ala
Phe
Leu
AlaCaH-NHLeu
Leu
Ser
Phe
NOESY
Ala
46
Phe-Ser-Ala-Leu
What about HNCOCA?
HNCOCA
Ser-Ala Ser CaH is Correlated with Ala NH
Ser
Ala
Phe
Leu
Leu
Ser
Phe
Ala