Recent Developments in N NMR Relaxation Studies that Probe Protein Backbone Dynamics - NMR of Proteins and Small Biomolecules - page 102

determined from the observed relaxation rate using known R 1 , t CP , and the CPMG

pulse width. Application of the sequence to relaxation dispersion has also been
proposed [ 45 ]. Dissection of the relaxation contribution in the R 2 dispersion
determined using the sequence has been described [ 46 ].
Cross-correlation of 1 H- 15 N dipolar interaction (DD) and 15 N CSA in CPMG R 2
experiments has been suppressed by applying 1 H 180 pulses [ 35 - 37 ]. Since CSA
relaxation increases as a function of the magnetic field strength (Fig. 1 ), relative
contribution of DD/CSA cross-correlation in the 15 N transverse relaxation increases
up to an external field strength.

2.1.3 Practical Relaxation Delay at High Magnetic Field Strength

Propagation of experimental noise, R , of a relaxation rate,

R , in an experiment where signal is measured at only two relaxation time points is
calculated using ( 2 ). Here, a two-point single exponential decay function, I ( t ) ¼
I 0 exp(

D I , to the uncertainty, D

RT ), is assumed [ 46 , 47 ]:

I 0

1 = 2

D R = R ¼ðD I = Þ½ 1 þ exp ð 2 RT Þ =ð RT Þ: (2)

I , is proportional to ( B 0 ) 3/2 (the magnetic field strength
is B 0 )[ 48 ]. By taking the advantage of the gain of the signal-to-noise ratio, the time
T can be reduced in the experiments performed at a higher magnetic field strength
when similar fractional error,

Signal-to-noise ratio, I 0 / D

R / R , to that obtained at a lower magnetic field
strength is desired. Assuming that R at 600 MHz is determined by a two-point
exponential fitting at T

D

¼ 0 and the optimal T ( ¼ 1/ R ), the R X T X at X MHz is

determined by the following function:

B 0 = B 600

0

3 = 2 1 = 2

ð Þ ¼ 2 : 86 R X T X =½ 1 þ exp ð 2 R X T X Þ : (3)

This equation predicts how much T can be reduced to have R X value with a
similar uncertainty to that at 600 MHz (Fig. 2 ). For example, when R at 600 MHz is
determined by a two-point exponential fitting at T

¼ 0and T ¼ 1/ R ,the R X T X at

X 1/ R X .

Since there are other factors that contribute to actual signal-to-noise ratio of relaxing
magnetization and that determine sensitivity of two different magnetic fields, this
calculation is a rough estimate.

¼ 900 MHz can be reduced by a factor of 0.32 times the optimal value, T X ¼

2.2 Practical Aspects in 15 N R 1 Experiment

15 N R 1 depends upon J (

o H ), but not on either J (0) or chemical exchange.
The pulse sequence used to measure R 1

o N ) and J (

in proteins usually incorporates