How To Diffuse

Process and fit NMR data to obtain translational
diffusion constants and hydrodynamic radii

Written by Christiane Riedinger, but I am just summarising what Frank Delaglio
and Brian Volkman have done!
See also:
o Stejskal and Tanner, Journal of Chemical Physics
“Spin Diffusion Measurements: Spin Echoes in the Presence of a Time-
Dependent Field Gradient”, Volume 42, Number 1, January 1965.
o Christina Redfield’s Chapter in Protein NMR Techniques by A.K. Downing
o http://www.biochem.mcw.edu/people/faculty/volkman/methods/diffusion.html
o http://tech.groups.yahoo.com/group/nmrpipe/

1. Data collection: (sorry! It’s Oxford-specific!)
• Pulse Sequence Omegas: DSTE_TranDiff_2d.s, jaj_sledXXXXX.s
• Bruker: diff2_h2o, but our bruker might not have Z gradients…
• All acquired as a series of 1Ds in a pseudo 2d

OMEGAS
1. Peter’s sequence (DSTE_TrandDiff_2d.s) – which I’d rather not use!
• The diffusion gradient strength is incremented:
• Gradzini 5 initial GradZ amplitude (0,100)
• Gradzstep 5 Gradient Amplitude Stepsize (can’t be altered)
• Maximum nb:
• Gradzini+nb*Gradzstep < 100
• Acqmode –f na 0 nb 0
• Acquire enough scans so that there is still signal at maximum gradient
amplidude. E.g. 512 scans for a 500uM sample: acqmode –f 512 0 18 0…

2. Christina Redfield’s sequence (jaj_sled…) – use this one!!!
• Add 15ul of a 3.5% 2,4-dioxane solution (prepared in D2O) as an internal
standard for the hydrodynamic radius. See Protein NMR Techniques for more
information, as stated above.
• There is a special pulse sequence for the setup, called jaj_sledvalsh.s, load
this one first to setup your parameters.
• Use a sample prepared in D2O, since there is poor water suppression in the
sequence. If you absolutely have to use an aqueous sample, you have the
option of using water-presaturation: In this case, set F2 to the same value as
F1 and load the calibration file for hydrogen:
# f2cal f2_500
Then adjust f2sat for optimal water suppression (by monitoring gain).
• Parameters that need to be adjusted: tau, gradt (two gradient delays)
• Gradl is the gradient power, which will be incremented from 5 to 100, in steps
of 5. This results in a pseudo 2D experiment with 20 increments.
• Since gradient strengths vary between different omega spectrometers, you
might have to choose different values for tau and gradt when changing
spectrometer (also, don’t use the 600, since its gradients are too weak)…

• Set gain as usual
• 90* pulse: pw = f190
• Initially, leave default values for tau and gradt, set gradl to 5 and acquire
enough scans to get good signal
• Then set gradl to 100 and acquire the same number of scans.
• Compare the intensity of the signal. The aim is to obtain 8x signal reduction
for gradl of 100.
• Vary tau and gradt for desired signal reduction.
• Load sequence for recording the experiment, e.g. jaj_sled128sh.s. This
sequence will first acquire 8 dummy scans and then do 6 repeats of 20
increments.
• These experiments are best setup with a large blocksize (4K or 8K), in order
to give the dioxane signal enough time to decay.
• Enter the values for pw, gradt, tau as determined in the setup-sequence and
run the experiment as ‘acqmode –f na 0 128 0’.

Subsequent analysis depends on a few key acquisition parameters:
3. Diffusion delay: (stating the default values)
jaj_sled….s tau 100ms, can be varied
DSTE_Trandiff_2d.s real tau 200ms
Bruker d8 80ms
4. Gradient duration: : (stating the default values)
Jaj_sled….s gradt 4.9ms, can be varied
DSTE_Trandiff_2d.s real gradt 2.8ms
Bruker p15 5ms
5. Size of gradient steps:
Omegas: 5, can’t be varied unless seq. altered
Bruker: gradient strength increment - the diff2_h2o.bv sequence is hardcoded
to collect a series of 1D spectra with the strength of the p15 gradient pulses
increasing from 5% in 1% increments to a total of ~80%, depending on td1.

2. Data Processing in nmrPipe
1. Export Omega data: (has to be on a Sun computer!)
# export –f f <your file>.dat <your file>.header <your file>.bin

2. Data Conversion:
#!/bin/csh
#conversion script for translational diffusion experiment
bin2pipe -in <your file>.bin -ge -neg
-xN 2048 -yN <your nb>
-xT <your cb> -yT <your nb>
-xMODE Complex -yMODE Real #this is important!
-xSW <yoursw> -ySW <does not matter>
-xOBS <your f1@0ppm> -yOBS <does not matter>
-xCAR <carrier ppm> -yCAR <does not matter>
-xLAB H -yLAB H-pseudo
-ndim 2 -aq2D States
-out <your file>.fid -verb -ov

To convert bruker-data, use the nmrPipe utility to generate a conversion script
(execute from command line, typing “bruker”).

3. Processing:
In case you use dioxane as an internal standard, process each spectrum twice,
once with sinebell window function (as below) for optimal apodisation of the
protein signal, once with exponential window function for the dioxane signal.
Furthermore, in case you use the experiment jaj_sled128sh.s (8 dummy scans, 6
repeats of 20 increments), you need to extract each repeat individually:

In order to do this, insert the following line (this is for the first repeat):
# nmrPipe –fn EXT –y1 9 –yn 28
Example processing script:
#!/bin/csh
# You will find answers to many questions by searching
# here: http://groups.yahoo.com/group/nmrpipe/messages
# processing script for processing translational diffusion pseudo -2d
# omitting solvent suppression, caused distortion of the baseline

nmrPipe -in <your file>.fid -ov
| nmrPipe -fn SP -off 0.389 -pow 1 -c 0.5
| nmrPipe -fn ZF -auto
| nmrPipe -fn FT -auto
| nmrPipe -fn PS -p0 <your value> -p1 <your value> -di -verb
| nmrPipe -fn POLY -auto
| nmrPipe -fn EXT -x1 <your max>ppm -xn <your min>ppm -sw -verb
#| nmrPipe –fn EXT –y1 1 –yn 28
| nmrPipe -out <your file>.ft -ov

3. Analyse Data with the nmrPipe DOSY Viewer
In case you don’t like that, export your 1d’s to ascii format and analyse them in a
fitting program of your choice. Check under:
# pipe2txt.tcl -help
For the analysis with the DOSY viewer, you have two choices:
• use Brian Volkman’s tool for analysing translational diffusion data
• use nmrPipe’s general tool to fit XY data pairs to a simple model

1. Using nmrPipe
This involves using the scripts DosyView.tcl and FitXY.tcl.
For more information see:
# FitXY.tcl –help
# DosyView.tcl –help
Launch the Dosy-Viewer as follows:
# dosyView.tcl –in <your file>.ft
The default input filename is test.ft1.

The following windows will be launched:

The DOSY Viewer 2D window should
display a contour plot of the
tting diffusion curves with dsView an processed data, where the horizontal
axis is 1H chemical shift and the
vertical axis corresponds to increasing
gradient strength.

Move vertical cursor along the 2D window to select an appropriate column for
fitting. A plot of column intensity vs. gradient strength is shown in the DOSY
Viewer 1D window.

You need to input the parameters of your experiment to fit your data. The delays
are specified via the –tau argument. See the answers of Frank Delaglio and Mike
Osborne to my e-mail “translational diffusion analysis” on the nmrPipe mailing
list. Also check the file ‘dosyFit.com’ for more information (this file is created
when running fitXY.tcl), -x states the gradient stepsize, -y the intensities…
The rest, you can figure out for yourself! :-)

2. Using dsFit1D.tcl by Brian Volkman
You need to launch DosyView and invoke dsFit1D.tcl:
# dosyView.tcl –in <your file>.extension –fit dsFit1D.tcl
(you need to amend dosyView.tcl to invoke dsFit1D.tcl!!!)

After having chosen the appropriate column for fitting, click the Fit1D button to
perform an automated nonlinear fit to the curve using the standard bruker
parameters (delay=80 ms; pulse=5 ms; 5-80% gradient strength in 1%
increments). Results of the iterative fitting process and Monte Carlo simulations
are displayed in one window. A second window plots the experimental data and
simulated values obtained from the optimal fit, along with a value for Ds, the self-
diffusion constant. If desired, the fitted data may be saved to a text file for plotting
or further analysis in another program.

NOTE: if non-standard parameters were used in the acquisition, copy the
dsFit1D.tcl program to your own directory and modify the values contained at the
top of the script:

#!/bin/sh
# The next line restarts using nmrWish
exec nmrWish "$0" -- "$@"
set auto_path "[split $env(TCLPATH) :] $auto_path"
set ARGV [concat $argv0 $argv]
set ARGC [llength $ARGV]

# dosyFit1D.tcl: fit a given 1D DOSY vector to a Gaussian
# equation for determination of Ds, the translational self-
# diffusion coefficient. Standard experimental parameters are
# set below (diffusion delay, 80 ms; PFG duration, 5 ms; max
# gradient strength, 60 G/cm). If data are collected with non-
# standard values, change on the lines below.
#---------------------------------------------------------------------
proc modelProc {}
{
global xList pList yModel gmax
set amp [lindex $pList 0]
set alpha [lindex $pList 1]
set delay 0.2 # 0.055 (tau, diffusion delay)
set pfg 0.0028 # 0.0049 (gradt, gradient duration)
set gmax 95 # 100 (maximal gradient strength)
set gstart 5 # 5 (minimal gradient strength)
foreach x $xList
{
set y [expr $amp*exp( -0.000001*715616000*($delay-

($pfg/3))*pow(($pfg*$gmax*($x+$gstart)/100),2)*$alpha )]

lappend yModel $y (# → this must be δ2 ⋅ G2)
}
}
proc dosyExit {}
# …and so on!!!

• Alter the bold lines with the parameters used in your experiment
• The underscored part contains the equation used for the fit:
Set y y =
Expr evaluate expression
-0.00001*715616000 γ2 (26.7519^2), [107rad T-1 S-1]
pow (x,2) x2
• This equation is the Bloch-Torrey-Equation!
- γ 2 ⋅ G2 ⋅ δ 2 ⋅ ( Δ - 1/3 ⋅ δ ) ⋅ D
signal i = signal (i = 0) ⋅ e

signal i signal after application of gradient
signal i = 0 signal for lowest gradient strength (5%)
γ gyromagnetic ratio of 1H
G gradient strength
δ gradient duration (gradt)
Δ (tau) Abstand der Mitten der Gradientenpulse
D Self-Diffusion Coefficient

Record the fitted values for Ds from a series of columns in different regions of the
spectrum to gauge the precision of the resulting values. Ideally, the experiment
should be recorded multiple times so that experimental uncertainties can be
derived from the standard deviation of Ds values from separate datasets.

Example output:
#
# amp*exp( -1.0*|alpha|*x ) + C
# amp: 5.97709e+04 +/- 3.33%
# alpha: 0.08321 +/- 0.00322
# C: 0.0 Fixed

DATA MODEL exp amp 5.977095e+04 1.992117e+03 alpha 8.320961e-02
3.218234e-03

VARS INDEX X Y Y_MODEL NOISE
FORMAT %4d %.5e %.5e %.5e %.5e

1 0.00000e+00 5.25887e+04 5.97709e+04 1.71656e+03
2 1.00000e+00 5.19514e+04 5.49987e+04 1.71656e+03
3 2.00000e+00 4.78349e+04 5.06075e+04 1.71656e+03
4 3.00000e+00 4.79348e+04 4.65669e+04 1.71656e+03
5 4.00000e+00 4.82115e+04 4.28490e+04 1.71656e+03
6 5.00000e+00 4.47816e+04 3.94278e+04 1.71656e+03
7 6.00000e+00 4.15594e+04 3.62798e+04 1.71656e+03
8 7.00000e+00 3.84508e+04 3.33832e+04 1.71656e+03
9 8.00000e+00 3.51482e+04 3.07178e+04 1.71656e+03
10 9.00000e+00 3.05485e+04 2.82653e+04 1.71656e+03
11 1.00000e+01 2.75489e+04 2.60085e+04 1.71656e+03
12 1.10000e+01 2.46001e+04 2.39319e+04 1.71656e+03
13 1.20000e+01 2.11248e+04 2.20212e+04 1.71656e+03
14 1.30000e+01 1.92972e+04 2.02630e+04 1.71656e+03
15 1.40000e+01 1.67549e+04 1.86451e+04 1.71656e+03
16 1.50000e+01 1.44539e+04 1.71565e+04 1.71656e+03
17 1.60000e+01 1.16205e+04 1.57867e+04 1.71656e+03
18 1.70000e+01 1.03331e+04 1.45262e+04 1.71656e+03
19 1.80000e+01 8.07764e+03 1.33664e+04 1.71656e+03
20 1.90000e+01 6.89481e+03 1.22992e+04 1.71656e+03

How To Diffuse

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