Hi Katherine I think this topic has been touched on before on CCP4BB. Any rigid body motion can be decomposed into a single translation and a rotation about that vector. In the case of a two-domain protein with a flexible hinge, the translation component is often close to zero and a pure rotation results. Like Herman I have an old program to decompose rigid transformations into the screw axis form, but I believe Chimera will also do it for you with a "measure rotation" command. There are cases such as haemoglobin where the direction of the rotation axis as well as the rotation angle is pertinent.
Note that the angle you are calculating from your R matrix is different, since it is about the origin. Google "Chasles theorem" for more information. best wishes Jeremy On Aug 6, 2014, at 6:22 AM, Katherine Sippel wrote: > Hi Herman, > > I have done a categorically awful job at explaining the problem. I'll just > copy and paste my explanation from an off-board conversation. > > Normally I would use the angle = cos^-1((a11+a22+a33-1)/2) formula on the > rotation matrix to get the shift angle. My problem is that the shift is > occurring in not quite opposite directions between the three different models > (see attached). Saying that "the dimer orientation shifted 15 degrees between > apo and the homolog versus 11 degrees between the apo and bound" is > misleading because there is a directional component that isn't being > accounted for in that statement. I'm trying to figure the best way to express > the dimer orientation changes in a results section so that it won't be > confusing for the reader. > > At the moment I'm attempting to co-opt DynDom 3D into identify a rotation > axis, but I am open for suggestions. > > > On Tue, Aug 5, 2014 at 1:50 AM, <herman.schreu...@sanofi.com> wrote: > Hi Katherine, > > > > Just reporting the translation vector is not very useful, since it depends on > how far your protein molecule is away from the origin (rotation center). I do > have an ancient program which reports the translation vector when rotation > axis through centroid and the component of the translation vector parallel to > the rotation axis. > > > > However, in your case, I would critically examine the structures. Usually, > most of the movements can be explained by rotations and in this case I would > only report rotations. However, if it looks like there is a significant > translation component, or the center of rotation is away from the hinge, I > would try to quantify this translational component as well. > > > > My 2 cents, > > Herman > > > > > > > > Von: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] Im Auftrag von > Katherine Sippel > Gesendet: Montag, 4. August 2014 19:02 > An: CCP4BB@JISCMAIL.AC.UK > Betreff: [ccp4bb] reporting rotational and translational interface shifts > > > > Hi all, > > I am trying to figure out the best way of reporting changes in dimer > orientations between three structures. I have an apo, a drug-bound, and a > homolog dimer structure. I had originally decided to calculate the angle from > the rotation matrix generated by LSQKAB, but the translational component is > oriented in opposite directions (translation vector of -22.9, 3.2, 10.8 > versus 22.4, -3.4, -17.1). I've only ever seen these types of orientation > shifts reported in degrees, so I was wondering how other people dealt with > accurately reporting these numbers in their manuscripts. Did you include the > translation vectors in the text or just rely on figures and arrow to make > your point? > > Thanks for your time, > > Katherine > > > > -- > > "Nil illegitimo carborundum" - Didactylos > > > > > -- > "Nil illegitimo carborundum" - Didactylos > <dimer_shifts.jpg>
