A.2.1
Introduction.
As discussed in Apendix A.1, exrate requires a data input table that contains, among other things,Reff
2 and the associated error for each residue. However, only a subset of residues within a given protein exhibit linebroadening in the R2 relaxation dispersion pulse sequences. Early relaxation dispersion efforts required thatReff2 values and the associated error be calculated on a per-residue basis. This process was very time consuming, error prone and required use of a program such as Excell or Matlab. Additionally, residues were often excluded from the analysis based on an “eye-ball” test as opposed to any statistical metric.
This prompted the development of the python scripts rlx tab extract.py and rlx- cat.py for calculating and formatting the data table and the FORTRAN program hffit for assessing the statistical significance of linebroadening in theR2 dispersion experi- ment. The user must begin the analysis procedure with a NMRDraw peak table that contains the fitted peak intensities from a pseudo-3D relaxation dispersion spectra that contains a reference experiment (I0), dispersion planes (I) and duplicate planes for error analysis.
A.2.2
Methods.
The python scripts were written in Python 2.x language format and require the numpy module(numpy.scipy.org). The statistical testing program, hffit, was programed in FORTRAN 77 using the sMINPACK libraries discussed in Apendix A.1. The F- tables are hard coded in the program and can handle datasets ranging from 4-17 relaxation points per residue. The F-tables correspond to alpha-critical values of 0.001, 0.01, 0.025, 0.05 and 0.1.
A.2.3
Protocol.
A peak table that contains resonance assignments and intensities associated with a pseudo-3D dataset is required for executing rlx tab extract.py. This table is generated by executing the nLinLS fitting program in NMRDraw using the autofit.tcl script. A simple text file that associates each relaxation plane in the 3D matrix with the corresponding τcp value is also required. The program assumes the first plane of the 3D matrix corresponds to the reference experiment. The user should modify rlx tab extract with the appropriate length of the constant time relaxation period (T), input table and output table names, and the field strength at which the data was acquired. Upon execution rlx tab extract.py, calculates Reff
using the equation: Ref f2 =−1 T ln( I I0 ) (A.3)
where I and I0 are the peak intensities of the CPMG plane and reference plane, respectively.
Duplicate planes are identified and used to calculate the root mean square (rms) error (σ) in the peak intensities. The error is propagated using the equation:
error= √ ( 1 T I0 2 σ2) + ( 1 T I 2 σ2) (A.4)
Prior to printing, the data is sorted by τcp value and residue number. The data is printed in an output file that is appropriate for direct input to exrate or hffit for further analysis. As discussed above, the fitted relaxation dispersion exchange parameters are more accurate with two or more field strengths. The program rlxcat.py was developed to contatenate two exrate input tables into a single file.
The problem remains that each measurable residue in the average protein does not experience conformational exchange on theµs-ms timescale. While these residues
can be fit to an exchange rate, the fitted value would be meaningless and waste computational resources. The Fortran program hffit is used to determine if a residue has statistically significant conformational exchange and excludes those that should not be analyzed. Upon executing hffit, the user is asked for an input data table and to choose their desired alpha-critical value for F-testing. The strictest cutoff is α = 0.001 which corresponds to a 99.9% confidence interval. This is the recommended value if the user is not very familiar with relaxation dispersion analysis. The program then calculates the difference between the first and last data point for each residue, which corresponds to the largest and smallest CPMG field strength. If the difference is less than 2 s−1 then the residue is excluded from further analysis. The data is best
Figure A.3: An example of the log output file from hffit. Residues that show little change in R2 or fit well to a horizontal line are indicated by an “x”.
fitted to a horizontal line (Reff
2 = R02) and a simple model for two state exchange. The goodness-of-fit to each model is judged by the Chi-squared value. An F test is used to test the hypothesis that the data fits as well or better to a straight line than a model for two state exchange. If the calculated F-value is greater than the F value corresponding to the predetermined alpha-critical value then we reject the null hypothesis indicating the residue experienced significantR2 dispersion.
As mentioned above, the program hffit generates an output file and a log file (Figure A.3). This output file can be directly used as the exrate input table. Residues that do not show statistically significant conformational exchange are excluded using the “{, }” format discussed in Appendix A.1. It should be noted that data is never deleted by hffit. The log file reports the results of the statistical testing as shown in Figure A.3. The alpha critical value and critical F value are recorded for the users reference. The first and second column represent the residue name and the difference inReff2 values, respectively. TheX2values for the linear (X2(l)) and nonlinear (X2(nl))
fits and the caluclated F value are listed. If the difference inR2 is not greater than 2 s−1 an “x” will appear in the “Failed dR20” column. The log file also records whether the residue passed or failed the F-test. The results in the log file can then be used to asses the appropriateness of the alpha-critical value and the quality of the data.
These programs generally streamline the process of fitting relaxation dispersion data. In addition, hffit allows the user to statistically test the data and determine whether the residue is experiencing µs-ms conformational exchange. Together, they aid in formatting and parsing through the data within the generally rigid exrate data format.