Walter F. Stafford
BOSTON BIOMEDICAL RESEARCH INSTITUTE
ANALTYICAL ULTRACENTRIFUGATION RESEARCH LABORATORY
64 GROVE STREET, WATERTOWN, MA 02472
Voice 617 - 658 - 7808
E-mail: stafford@bbri.org
April 29, 1997; revised May 24, 1999
Revised November 12, 2000
Software may be obtained from our anonymous FTP site:
>FTP rasmb.bbri.edu
>log anonymous
>password
/rasmb/spin/mac or /rasmb/spin/ms_dos
g(s*) Analysis for the XL-A and XL-I [PC Version]. PROGRAM DCDT
1. Before you run the program, you will have to create a text file
containing a list of the file names of the group of files to be processed.
The minimum number of files is 2. The maximum number is 30 or 60 for the
versions DCDT_30Z.EXE and DCDT_60Z.EXE, respectively. If you create a list
with an odd number of file names, it will ignore the last one. If you end
the file with a blank line, you will get a cryptic error message about a
file not found. Delete the extra carriage return, and try again. A version
called DCDT_100Z.EXE is now available for interference data.
2. For presentation purposes, be sure to check that the time difference
between the first and last scan being processed does not exceed a value of
about
delta = t(last)-t(first) < 90*[t(first)+t(last)]/(sqrt(M)*speed)
where M is in kilograms/mole and speed is in rpm/1000. This rule of thumb
assures that a boundary in the middle of the cell will move no more than
one standard deviation during the time interval chosen. The best thing to
do (within the limits imposed by the sample) is to take scans as often as
the XL-A/XL-I is capable at the lowest speed that will still give you the
resolution you need. Since separation increases as the first power of time
and diffusion only as the square root of time, resolution will increase
with the square root of time. (Don't be fooled by those sharp peaks at the
beginning of the run.) Therefore, the best data (i.e. with the highest
resolution) will be collected near the end of the run just before the
plateau dissapears. So, start with a small set of scans taken as late as
possible in the run and add pairs of scans to the data set (going backwards
in time) until you just exceed the value of delta-t given by the rule of
thumb. If you are looking for aggregates, then use only one or two pairs of
scans at the earliest times.
3. This rule should be made a little more stringent if the curves are to be
fit for molar mass determination: Try
delta = t(last)-t(first) < 40*[t(first)+t(last)]/(sqrt(M)*speed)
^^
4. After choosing the meniscus, the first plot you will see is a graph of
dc/dt vs s*. If the XL-A is functioning properly, the only item from the
menu items you may have to deal with is "E". "E" allows you to select the end
points for the data subset that will be used to compute g(s*). It is
important that you eliminate garbage data points near the meniscus before
you select "D" from the menu, since they will be propagated into the entire
g(s*) pattern in the process of computing g(s*) from dc/dt. The level of
smoothing can be changed here. A a good smoothing level for scanner data
is with a window spanning 2% of the total span of the data. If you are a
purist, you should set this to 0 (zero)(the default) to see the noise in all
its glory. On the XL-I with Rayleigh optics, you usually won't need any
smoothing. If you don't like what you see, you can smooth the data even more,
but be aware that the smoothed data contain less information than the
unsmoothed data. The error bars for g(s*) mentioned below are based on the
original unsmoothed data, so you won't loose everything by smoothing. Do
*NOT* curve fit to smoothed data if you are computing the molecular weight
from s and D.
4.05 It is highly recommended that the whole interference image be
collected (all 2048 pixels) so that the whole air-air space is available
for aligning the patterns to remove the instrumental jitter.
4.1 With Rayleigh data, re-zeroing of the dcdt pattern will generally be
required. First, however, the fringe displacement data must be aligned in
the air-air space. Choose a relatively flat spot for this. This takes care
of some instrumental vertical "jitter" in the fringe patterns.
4.2 After doing the fringe alignment, you will get the first look at dcdt
vs. s*. Now, choose the "Z" option and reselect what you think is the best
zero level for the data. Very little, if any, re-zeroing should be
required if the alignment in the air-air space was carried out succesfully.
Keep in mind that dc/dt must be slightly above zero in the plateau region on
this plot. (At this point dc/dt hasn't yet been corrected for radial dilution,
which makes a small but significant contribution to dc/dt in the region
centrifugal to the boundary.)
5.00 The last plot is a graph of g(s*) vs s*. [Use the "Z" rezero option
with caution here.] You will find that rezeroing near the meniscus produces
smaller variations than rezeroing near the base. This because the
rezeroing is done on dc/dt which is divided by s* to get g(s*). (c.f Anal.
Biochem. 203, 295-301 (1992).) [Your version may not have this
option working. So you can just jump back to step 4 to rezero.]
5.10 Computing the weight average sedimentation coefficient:
The weight average sedimentation coefficient (with the caveat given
below) can be computed by
Sw = SUM[ s(i)*gs(i) ] / SUM[ gs(i) ] for non-interacting systems.
and
Sw = SUM[ s(i)*gs_hat(i)]/SUM[gs_hat(i) ] for interacting systems.
where
SUM[gs(i)] = loading concentration
and
SUM[gs_hat(i)] = plateau concentration
6. The output will be a file with the same name as the list file but with the
extension ".GS0" The first few lines should be skipped when reading it into a
plotting program. The line containing the column headers and the subsequent
data containing lines will be 5 columns long;
The 1st column is s*
The 2nd column is g(s) (This has been corrected for radial dilution.)
The area under this curve is the laoding concentration.
The 3rd column is SEM the standard error of the mean value of g(s*) at
each value of s. It is computed as the standard
deviation of the original data (i.e. not affected by
any smoothing) divided by the square root of the
number of pairs of scans used in computing the average.
The 4th column is g^(s) ( uncorrected for radial dilution)
The Area under this curve is the plateau concentration.
The 5th column is sg^(s). can be used for computing Sw.
7. Molar Mass Determination from the g(s*) vs s* curves:
The molar mass can be computed using the Svedberg equation after
the diffusion coefficient is determined by curve fitting the g(s*) curve.
The g(s*) vs. s* curves are essentially gaussian; The standand deviation,
sigma, can be related to the diffusion coefficient:
D = [ sigma * w^2*t * Rm ]^2/[2*t]
where Rm, (w^2*t) and t are given in the header of the output file, Rm is the
radius of the meniscus and sigma is defined by:
g(s) = A * exp[ -0.5 * ( (s_peak - s)/(sigma) )^2 ]
Use this equation for fitting to get sigma.
The values of s and D can be substituted into the Svedberg equation to get the
molecular weight.:
M = [ R*T*s_peak ]/[ D*(1-vBar*rho)*w^2*t ]
8. Let me know how you make out with this even if you don't have any problems
with it. I have found for samples with low molecular weight that the maximum in
g(s*) is slightly skewed to lower values than expected. The magnitude of
the shift is dependent only on the product of the molecular weight and the
square of the speed and approahces zero as the molecular weight and speed
are increased. Therefore, for slowly sedimenting samples for precise work,
I would recommend using the second moment boundary positions obtained from
a synthetic boundary run to compute Sw or using John Philo's curve fitting
program called SVEDBERG of which there is a DOS version on this FTP site.
The following table gives the factional factional shift in s-peak at 60,000 rpm
for a boundary located in the middle of the cell.
MW fractional error in s-peak
-----------------------------------------------------
60 kg/mole - 0.01
35 - 0.02
25 - 0.03
18 - 0.04
Updated May 24, 1999
Walter Stafford
Analytical Ultracentrifugation Laboratory
Boston Biomedical Research Institute
20 Staniford Street
Boston MA 02114-2500 USA
voice: (617)-912-0386
fax: (617)-912-0335
E-mail: stafford@bbri.bbri.org