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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.
Created and maintained by Dr. Xiang-Jun Lu [律祥俊] (xiangjun@x3dna.org)
The Bussemaker Laboratory at the Department of Biological Sciences, Columbia University.
