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