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I am currently trying to repeat the base-stepping calculation in 3DNA. I read the "technical details" document associated with 3DNA and try to follow "5.5 Step parameters" section. I am doing OK until step 4, where the document states that the axes of "middle-frame" are simply the average between those of R1’ and R2’. When I computed that myself, I got a different Rm compared to the one given in the document. For example the first element of Rm was calculated as (-0.6616 -0.1982)/2 =-0.4299, which was different to the given value -0.4490. Therefore I was unable to follow the rest of the calculation and get the correct base-step parameters myself.
I am wondering if I misunderstood anything or this is an error of the document. I look forward to your response. Thank you very much!
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Thanks for reading the "technical details" -- you are one of the very few users I am aware of who actually work through the examples.
Regarding your specific question, you are right in noticing that the x- and y-axes (the first two columns) of Rm are not the raw average of the corresponding columns of R1' and R2':
(-0.6616 -0.1982)/2 =-0.4299, which was different to the given value -0.4490
Here Rm, as a proper rotation matrix (http://en.wikipedia.org/wiki/Rotation_matrix), is orthonormal (http://en.wikipedia.org/wiki/Orthonormality); its x-axis and y-axis are normalized, which is precisely where the discrepancy comes from.
HTH,
Xiang-Jun
PS. In going through the doc, I've also noticed a typo in step #2 of section 5.5, where the RollTilt angle should be in degrees instead of Angstroms. I am planning to update the technical details and put it on the web. If you notice anything that can be improved, please post back.
Funded by the NIH R24GM153869 grant on X3DNA-DSSR, an NIGMS National Resource for Structural Bioinformatics of Nucleic Acids
Created and maintained by Dr. Xiang-Jun Lu, Department of Biological Sciences, Columbia University