This is the only specific program documentation available for SVEDBERG. Sorry, but this program was developed for in-house use at Amgen and I cannot justify the time it would take to document it more thoroughly. Other users have found most of the usage to be fairly obvious, and when it is not, just try it! You will want to read two articles describing this program and some examples of its usage. The first is Philo, J. (1994) "Measuring Sedimentation, Diffusion, and Molecular Weights of Small Molecules by Direct Fitting of Sedimentation Velocity Concentration Profiles" in "Modern Analytical Ultracentrifugation" (Schuster and Laue, eds., Birkhauser, Boston, pp. 156-170). This article describes the original version of the program (prior to version 5.00 in 1997). This article should be available as an Adobe Acrobat .PDF document, including figures, as the file SVEDBERG.PDF, from wherever you obtained the program files. The second article is Philo, J. (1997) "An Improved Function for Fitting Sedimentation Velocity Data for Low-Molecular-Weight Solutes", Biophysical J. 72:435-444. This article should also be available as an Adobe Acrobat .PDF file, SVEDDOC2.PDF, from the software distribution sites. This article describes a new form of fitting function, the "modified Fujita-MacCosham function" which gives more accurate diffusion coefficients for low molecular weight species, and which accounts for restricted diffusion at the meniscus and can therefore be used for scans before the meniscus is cleared. This function was implemented as a program option beginning with version 5.01, and the function formerly used is still availabe but now called the "Fujita function". This article also describes further tests of fitting multiple species, fitting when the sedimentation coefficient is concentration-dependent, and discusses the effects of both random and systematic noise on the results. Reprints for this article are available upon request. (Please note that there was an inadvertent sign error in equations 1 and 2 in that article: the second term in the large brackets that begins with 2/sqr(pi) should be negative, not positive.) ---------------------------------------------------------- Some notes about when the use of Svedberg is appropriate for your data: 1) This analysis is primarily intended for situations where diffusion makes the boundaries quite broad. For relatively sharp boundaries (e.g., proteins of >100 kDa at 60K rpm) the fitted diffusion coefficients will generally be significantly overestimated. However the sedimentation coefficients should always be correct. For larger molecules, if you want good diffusion coefficients you should run at a low rotor speed so that diffusion has a profound influence on the boundary shape. If you have a protein whose sedimentation coefficient is strongly concentration dependent, giving self-sharpening of the boundaries, then this analysis will underestimate the true diffusion constant. 2) The "Fujita" fitting function does not account for restricted diffusion at the meniscus. Therefore it is not appropriate to include data at times before the meniscus is nearly clear with this function. In practice it is probably okay to begin using data when the concentration at the meniscus is 10-20% of the loading concentration. 3) The new "modified Fujita-MacCosham" function is somewhat slower to compute, but gives much better D values for proteins < 20 kDa. It can also be used for scans earlier in the run, well before the meniscus is clear, but in practice one should probably not include scans before the meniscus concentration drops below ~60% of the loading concentration. 4) For fitting multiple species, the assumption of the method is that they do not interact. If this is not true, the results will be nonsense! "Not interact" in this context really means no significant redistribution of species during the time course of the experiment. Thus in some cases where the kinetics of dissociation/association are very slow (for example, some antigen/antibody systems) the approximation that no interaction occurs may well be valid even for interacting systems. --------------------------------------------------------- Features of current Svedberg versions not documented in the articles mentioned above: 1) It is now possible to use molecular weight (as determined from the ratio s/D) as the second fitting parameter for each species, in place of D. The choice of whether to fit D or s/D is determined by a radio button found in the "Options" box at the bottom of the "Set Model" dialog box. The only real difference between fitting D or s/D comes in the error estimates for the parameters. Since the uncertainties in s and D are correlated, when you fit s and D it is not possible to easily calculate the uncertainty in s/D. By fitting s/D directly you can get the true confidence interval for the molecular weight. 2) Because it is now possible to fit molecular weight, there is a new option regarding the units for molecular weight. You can leave the units as s/D (Svedbergs per Fick), or convert them to buoyant molecular weight (which only requires knowing the sample temperature), or convert them to true molecular weight (which requires knowing the solvent density and the vbar of each species in the sample). When needed, the printed reports of the fit results will include what temperature, solvent density, or vbar values were used to convert to buoyant or true molecular weight units. 3) For multiple-species fits here is a new entry on the Analysis menu that allows you to constrain the ratio of the sedimentation coefficient and/or molecular weight value of one species relative to another. For example, suppose you believe your sample contains a small amount of a dimer of the primary species (perhaps a disulfide-linked dimer). The amount of the dimer may be too small to independently determine its s and/or D values from the data. Therefore you may be able to obtain more accurate estimates of the s and D values for the monomer, and a more accurate estimate of the amount of the dimer, by constraining the dimer's s value to be an appropriate multiple of the s value of the monomer, and/or by constraining the dimer D value to be consistent with a dimer molecular weight exactly twice that of the monomer. 4) Starting with version 5.01 the program can read and fit refractometric data. With refractometric data the relatively large baseline offsets and shifts due to the windows can be a significant problem (see the discussion in the 1997 Biophys. J. article). In addition, the fact that the XL-I data acquisition defines the fringe count for the first radial position in each scan to be zero must be accounted for. This property means that if you start the scan below the meniscus (as Beckman recommends) then the plateaus of successive scans will shift as the meniscus region is depleted. The program now detects this problem and attempts to correct for it. Whenever the program is using interference data, and when the position of the meniscus is below the first data point in the scans, then the fitting function automatically substracts the computed concentration at the radial position of the first data point from all computed concentration values, thus forcing that first data point to be zero in the same fashion as the Beckman data acquisition does. Whenever this is being done that fact will be noted in the printed results from fits. In order to accomodate refractometric data, it is now possible to manually enter meniscus positions at radii below the first data point radius from the "Set Meniscus" choice. 5) Starting with version 5.01 there is a choice under the File menu to specify whether the program is using the data file naming conventions of the old Beckman DOS XL-A data acquisition program or the file naming conventions of the new Windows XL-A and XL-I data acquisition. Selecting this menu item toggles between the two, and the program also detects and sets the naming convention as each data file is read. 6) It is now possible to set the radial range of data to be included in the fit separately for each individual data set. Generally I still recommend using the same data range for all sets, but this option allows you to isolate a specific boundary as it moves down the cell in situations where you have faster sedimenting species that you do not want to include in the analysis. 7) A fitting parameter, "slope correction", is available for absorbance data, BUT IT IS NOT FOR GENERAL USE! This is an attempt to correct for an optical problem in some XL-As that causes the absorbance in the plateau regions to rise toward the bottom of the cell even when the concentration is actually uniform. The origin of this artifact is not entirely clear, but it is probably a stray light problem. The best diagnostic test is: if you see a slope in a low speed scan (e.g. 3000 rpm), go immediately to high speed and scan again. If you find the same slope, and no significant decrease in absorbance, it implies that the slope at low speed could not have been due to rapidly sedimenting material and therefore it is an artifact. When this parameter is non-zero, the data are treated as though the path length of the cell varies linearly with radius, and the loading concentration becomes the value at 6.5 cm. The units of the parameter are "%/cm"; i.e. a value of 6 (typical on my XL-A) means that a true constant plateau will have an apparent rise of 6% over a radial distance of 1 cm. There is no real theoretical justification for this correction, so I don't recommend using it unless a) you have convinced yourself that your machine has this same problem; and b) you are desperate and unable to get Beckman to fix it. (My XL-A had this problem intermittently for over 3 years and we could never diagnose or fix it. It was only "cured" when I traded in for an XL-I.) 8) Svedberg follows the "UConn convention" for marking bad data points (such as the spikes in absorbance data when the lamp misfired) as not to be included in the analysis. By this convention, any data point in which the value of the third column in the data file is negative will be ignored when the file is read. For absorbance data, this third column normally contains either zero (when no averaging is used) or the standard deviation of the absorbance value (when multiple flashes are being averaged). For interference data, there normally is no third column entry. However, this software checks each line of data for a third column, and will ignore any data point where a third column exists and is negative. Thus to mark a data point as "bad" you may use Notepad or some other text editor to manually change the entry in the third column to a negative value (or add a third column for that line with -1 as the value for interference data). In the case of absorbance data, simply changing the sign of the standard deviation allows you to later restore the original raw data if needed, without loss of information. Some people in the AU community have recommended replacing "bad" data points with a point corresponding to the interpolated value between the neighboring "good" data points. In my view, such a procedure invalidates the statistics of the fit, since one is adding a data point that is not based on any independent information. Therefore Svedberg simply omits the bad points totally, leaving a corresponding small gap in the raw data. Remember that if you mark data points as bad after you have already read that file from the "Data Included in Fit" form, you will need to re-load that data set by simply clicking on the file name and re-loading the same file. -------------------------------------------------------- Other notes about Svedberg program usage: 1) This program will work with Windows running at VGA resolution (640 x 480), BUT it is really designed to run at 800 x 600 resolution or higher. At VGA resolution the Results form displayed at the end of each fit has so much information that a very small font must be used, which is hard to read. Windows 3.1 or or higher or Windows95 is required; Windows 3.0 will not work! 2) There is now a help file for the graphing window that explains the menus and features of the graphing package. 3) Fits can be saved and restored from disk. This saves all the raw data from whatever data files were loaded, and all the results and information about the last fit done. This is highly recommended as a way of archiving what you have done. These files may have any 8-character file name, and are given a .FIT extension. 4) The fitting routine largely follows the "preferred method" outlined in the Johnson & Faunt article, Methods Enzymol. 210:1-37 (1992). The "increment reduction factor" displayed during fitting corresponds to the lambda scaling factor in their notation (eq. 26). If the next guess for the parameters results in an increase in variance rather than a decrease (which may happen when you are far from the minimum or the parameters are too highly correlated), the incremental change in the parameters is reduced by factors of two until the variance decreases, and then the shape of the variance curve is used to estimate the value for lambda which will give the minimum variance for that iteration. Thus, when the fit is proceeding well the "increment reduction factor" will remain at one. When you see it being reduced, the fit is having trouble (although at convergence it often does this as it unsuccessfully hunts for a lower variance). When the increment reduction factors falls below 1/128, your fit is probably in BIG trouble and the program tries the opposite direction to see if that is better. The routines try to always reduce the variance with each iteration, but if things go very badly it is possible that this will not happen. 5) During fitting each parameter is restrained to stay within an upper and lower bound, in order to try to prevent the fitting from straying into regions where the parameters make no physical sense. If the next iteration would place the parameter outside those bounds, a yellow warning flag will display on the fit monitor form next to the value of that parameter. The "increment reduction factor" discussed above will be reduced by factors of two until the parameter is in bounds. Often if the bounds are exceeded the fit will keep trying to go in that direction and will never converge. You can alter the bounds for the parameters using the "Alter Bounds" choice under the Analysis menu. 6) At the completion of a fit, a simple estimate of the standard error in each parameter is made using the covariance matrix (the "asymptotic standard errors" method in Johnson & Faunt's article). This will always be an underestimate for any non-linear problem. You may do a more rigorous calculation of the uncertainty in the parameters by clicking the "Compute Confidence Intervals" button. This is very slow, so you will usually only do this for final results. This uses a search method, corresponding to the "preferred method" of Johnson and Faunt. The default is to compute 95% confidence intervals, but you may change this using the "Set Confidence Probability..." choice under the Preferences menu, and permanently change the default using the "Save Defaults to Disk..." choice in the File menu. 7) The "Simulate" choice under analysis allows you to use the current fitting model/function to calculate simulated curves for any set of parameters, over the data ranges currently in use for the experimental data. Svedberg also incorporates the finite element Claverie method for a more rigorous simulation of sedimentation velocity data, but this takes much longer to compute. This Claverie routine was kindly provided by Walt Stafford and David Cox. You can use the Claverie routine to simulate either synthetic boundary or convention cell data by placing the initial boundary either at, or outside, the inner radius for the simulation. You can simulate multiple species by summing the results of two successive simulations, and you may optionally add random noise. At the end of a simulation you may optionally write out the simulation as XL-A data files (the S and D values are written into the XLA comment line). The calculation interval setting determines the number of seconds between successive iterations in the calculation, and the number of data points determines the radial spacing of the simulation. Decreasing the interval and increasing the data points will increase the accuracy of the simulation, but also will correspondingly increase the calculation time. 8) I DO want to know about bugs (and there always will be some). I won't promise to fix them (and what you consider a "bug" I might consider a "feature"!), but I can't fix them if I don't know about them. I am also open to suggestions for improvements/new features. E-mail is preferred, to jphilo@earthlink.net My fax # is 805-492-6413 ------------------------------ I hope you find this program useful! John Philo