Icosahedral conventions

Submitted by dmbelnap on Thu, 2010-10-14 14:32

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Frealign

I thought I would try to write a little program to convert from PFT3DR (my adaptation of Tim Baker's PFT and EM3DR programs that uses the Bsoft format) to your convention and parameter files, so we can jump right into the refinement mode of FREALIGN. The Bsoft orientation convention is essentially the same as SPIDER, but I have a question about your icosahedral convention.

The PFT3DR programs use the icosahedral convention where, looking down on a 2-fold oriented along the z-axis, you have the order 2-5-3-2 as you move from the z-axis to the x-axis. I understand that FREALIGN uses the 2-3-5-2 convention. I can modify the angles appropriately, but does FREALIGN require icosahedral angles to be within a certain PHI,THETA range? Or, can the angles have any value as long as they conform to the 2-3-5-2 convention?

niko Thu, 2010-10-14 14:38

Frealign has two icosahedral conventions built in that are can be indicated using symmetry symbols I and I2. They are defined in the README file that comes with the distribution. The definitions are:

I = icosahedral 532 symmetry in setting 1 (5fold is closest to the X-axis) - same convention used by ViperDB (http://viperdb.scripps.edu/)
I2 = in setting 2 (Y) - as used by Crowther et al

The angles do not need to be within a particular symmetry-related range but should be between 0 and 360.

dmbelnap Thu, 2010-10-14 15:45

My apologies for missing the definitions in the README file. Because the first line was "new features in v8.09", I assumed it was simply a log of your updates. Perhaps putting a permanent title at the top would eliminate such confusion for others.

Would you please clarify these icosahedral definitions?

I = icosahedral 532 symmetry in setting 1 (5fold is on X)
Is one of the perpendicular 2-fold axis (to the 5-fold) on the Y or Z axis?

I1 = also in setting 1 (X) - as used by Imagic
What does "X" mean? Is a 2-fold axis oriented on Y?

I2 = in setting 2 (Y) - as used by Crowther et al
What does "Y" mean? Is a 5-fold axis oriented on Y? Crowther's software computed the icosahedral structure first with a 5-fold oriented on a Cartesian axis, then rotated the structure to put 2-folds on the Cartesian axes.

Thanks.

niko Thu, 2010-10-14 16:26

Symmetry settings I and I1 are the same (referred to here as setting 1). I just checked our rotavirus DLP reconstruction that used I2 symmetry. If I look down a 2-fold aligned along the z axis (using UCSF Chimera) and then follow in a direction towards the x axis, I first hit a 5-fold, then a 3-fold, and then a 2-fold. If I follow in a direction towards the y axis, I first hit a 3-fold, then a 5-fold and then a 2-fold. If I consider the PDH example included with the distribution and look down a 2-fold aligned along the z axis, I get the opposite behavior as this uses the I symmetry: If I follow in a direction towards the x axis, I first hit a 3-fold, then a 5-fold and then a 2-fold. If I follow in a direction towards the y axis, I first hit a 5-fold, then a 3-fold and then a 2-fold.

dmbelnap Thu, 2010-10-14 17:49

Thank you for defining I(I1) and I2 in that way. That definition is clear. However, the statement from the README file, "5fold is on X" suggests that a 5-fold axis lies on the Cartesian X-axis.

niko Thu, 2010-10-14 18:30

Yes, this is a bit unclear. This formulation was chosen by Richard Henderson. I assume that "5fold is on X" refers to the 5-fold that points more along the x axis, which would be the case in the "I" convention.