Topics Covered
• Relaxation Time Constants (T1 and T2)
• Mechanisms of relaxation (dipole-dipole)
• Relaxation  protein/nucleic acid dynamics
2/18/14
Clubb
Typical one dimensional (1D) experiment
90 o
(FID)
Delay to enable system to relax back to equilibrium
90 o
Mz=Mo equilibrium
Mz=0
Return to equilibrium via relaxation processes
Mz=Mo equilibrium
1

T1: Longitudinal (also called spin-lattice) relaxation. It is a measure of rate of return of the magnetization to the Z-axis.
Importance:
1)
2)
Dynamics
Determines delay times between subsequent NMR experiments
90 o
90 o
(FID)
(FID)
~100ms ~900ms
Total recycle time
~1 s
T2: Transverse (also called spin-spin) relaxation. It is a measure of
The rate of decay of magnetization in the x-y plane.
Importance:
1)
2)
Dynamics
Determines line-width of peaks
Linewidth

1/ (
 x T2*)
FID
Mz=Mo
Behavior of magnetization during the free induction decay as it returns to its equilibrium state along the z-zaxis
Mz=Mo
Mz
Note: formula describes reappearance of Mz when it starts from X-Y plate
2

• During T1 relaxation the spins lose energy to the lattice (surroundings) as a result of spins “flipping” from the high energy (beta) state to lower energy (alpha) state
• Spins “flip” during relaxation process as a result of fluctuating magnetic fields that generate RF at the appropriate frequency
Mz=Mo
Mz = 0
T1 relaxation
Mz=Mo
Each atom produces its own magnetic field
Tumbling of protein
Tumbling of protein causes magnetic field from proximal atoms to vary.
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Other sources of fluctuating magnetic fields that cause relaxation
(not as important as dipolar relaxation in macromolecules)
Chemical shift anisotropy (CSA ). Negligible for protons, but important for nuclei with large chemical shift ranges such as carbon-13.
Quadrupolar (negligible in proteins ). Atoms with I > ½ have non-spherical charge. Interaction of resultant quadrupole moment with electric field gradients can cause relaxation.
Scalar relaxation (negligible in proteins ): caused by time dependent fluctuations in coupling constants
Paramagnetic (negligible for most proteins): Relaxation caused by very large magnetic moment of unpaired electrons. Similar to nuclear dipole-dipole interaction.
Not significant in most proteins because they do not contain unpaired electrons.
Importance: Choose recycle times in multi-scan experiments to be
~5x T
1 value of 1 H atom
Total Recycle time
FID t
Scan #1 #2 t
#3 t
#4
Delay between scans to enable relaxation (t)
•Choose total recycle time to be
~5x T
1
•1H T
1 value of 1H atom times in proteins are typically ~200ms
Summed FID
FT
NMR Spectrum
4

Recycle time = 5 * T1
At recycle time = 5 * T1 e (-t/T1) = 0.0067
Mz ~ M0
Note: Eqn. describes return to Z-axis from XY plane
Recall:
Describes return to Z-axis from the XY plane
FID
Mz=Mo
Behavior of magnetization during the free induction decay as it returns to its equilibrium state along the z-zaxis
Mz=Mo
Mz
5

180 o 90 o
Perform a series of 1D experiments using different times for

Inversion recovery spectra at various values of the
 delay
 when M t
= 0
Note: formula describes reappearance of Mz when it starts from –Z axis
6

Review: pulses of different
Flip angles (90 o and 180 o )
90 o dM(t)/dt = M(t) X

B1
180 o
Mz = -Mo at very long
 values complete recovery to Mo occurs
Mz = Mo
FT
Detector
7


Short values
Mz = -Mo Mz > -Mo
Very long
 values
At shorter
 values Mz does not fully recover to Mo. Can give rise to negative signal
FT
Detector
FT
Recall:
Sign and phase of signal depends upon where magnetization starts at the beginning of detection.
Detector
8

T
2 relaxation constant (spin-spin or transverse ): Time constant describing rate of decay in the transverse (XY) plane.
Larger T
2 values slower decay of magnetization
Rate of dephasing characterized by the time constant T2 (transverse relaxation time or spin-spin relaxation time)
*
Intrinsic time constant for decay (transverse relaxation time, also called spin-spin relaxation time)
Signal decay caused by field inhomogeneity
Linewidth at half-maximal intensity

1/ (
 x T2*)
9

Spin-Echo experiments to selectively measure intrinsic T
2 value of a nucleus. Experiment eliminates contribution from field inhomogeneity
Dephasing from field inhomogeneity
Field inhomogeneity effects refocused.
However intrinsic dephasing caused by T
2 is not.
Therefore the magnitude of the vector has decreased.
(note in relation to a simple one-pulse experiment the spectrum would be of opposite sign. This can be corrected by properly phasing the spectrum
10