Just considering the 2D a b plane, because 120 degrees is 30 degrees bigger than a right-angle, the matrix to fractionalise your orthogonal (x, y) coordinates is
1 tan(30) 0 1/cos(30) To apply the symmetry operation you specified, the fractional coordinates have to be premultiplied by this matrix: -1 0 -1 1 Then 2/3 has to be added to the new fractional x and 1/3 added to the new fractional y. When you have done that you re-orthogonalise the coordinates by pre-multiplying with this matrix: 1 -sin(30) 0 cos(30) After a few pages of trigonometry, I think you do get the result that the pdb have given you ;-0 Best wishes, Jon Cooper. [email protected] Sent with [Proton Mail](https://proton.me/mail/home) secure email. On Saturday, 20 September 2025 at 16:37, Jon Cooper <[email protected]> wrote: > Hello, it's because your unit cell has a 120 degree angle and cos 120 = -0.5, > sin 120 = 0.866. It reminds me of an essay I wrote in the lockdowns: > > https://www.ucl.ac.uk/~rmhajc0/frorth.pdf > > Best wishes, Jon Cooper. > [email protected] > > Sent from Proton Mail Android > > -------- Original Message -------- > On 20/09/2025 14:45, Qixu Cai <[email protected]> > wrote: > >> Dear Thierry, >> >> Thank you for your reply. >> After I provided the symmetric operator to PDB staff, they updated the >> matrix as below: >> -0.500000 -0.866025 0.000000 89.06300 >> -0.866025 0.500000 0.000000 51.42055 >> 0.000000 0.000000 -1.000000 46.27767 >> The matrix is totally different with the matrix I provided. How was the >> symmetric operator (-X+2/3,-X+Y+1/3,-Z+1/3) transformed to the above matrix? >> The space group is H32 with cell constents of 178.126 178.126 138.833 90.00 >> 90.00 120.00. >> >> Thanks and best regards, >> Qixu Cai >> Email: [email protected] >> >> Fischmann, Thierry <[email protected]> 于2025年9月19日周五 23:37写道： >> >>> Hi, >>> >>> The matrix is correct for the operator you provide. >>> >>> Thierry >>> >>> From: CCP4 bulletin board <[email protected]> On Behalf Of Qixu Cai >>> Sent: Friday, September 19, 2025 11:30 AM >>> To: [email protected] >>> Subject: [ccp4bb] convert symmetric operator to matrix & coot1 >>> >>> You don't often get email from >>> [email protected]. [Learn why this is >>> important](https://aka.ms/LearnAboutSenderIdentification) >>> >>> EXTERNAL EMAIL– Use caution with any links or file attachments. >>> >>> Dear all, >>> >>> There is a dimer in the asymmetric unit of a structure, and applying the >>> symmetric operator (-X+2/3,-X+Y+1/3,-Z+1/3) can generate a tetramer, which >>> is a biological assembly. When I deposit the structure to PDB, I need to >>> provide a matrix to generate the biological assembly. Is the following >>> matrix correct for pdb format? >>> >>> -1 0 0 0.6667 >>> >>> -1 1 0 0.3333 >>> >>> 0 0 -1 0.3333 >>> >>> Another question is that I can use "Calculate --> Modelling --> New >>> molecule from symmetry op..." to generate new molecule in wincoot0.9.8. >>> However, I cannot find similar function in new wincoot1.18. I also found >>> that many useful functions in "Calculate --> Modelling" of coot0.9.8 are >>> not available in coot1. Will they come back in the following versions of >>> coot1? >>> >>> Thanks and best regards, >>> >>> Qixu Cai >>> Email: [email protected] >>> >>> --------------------------------------------------------------- >>> >>> To unsubscribe from the CCP4BB list, click the following link: >>> https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 >>> >>> This e-mail message, together with any attachments, contains information of >>> Merck & Co., Inc.,Rahway, NJ, USA, and/or its affiliates, known as MSD >>> outside of the United States and Canada, that may be confidential, >>> proprietary, copyrighted and/or legally privileged. (Direct contact >>> information for affiliates is available at - [Contact us - >>> MSD](https://www.msd.com/contact-us/).) It is intended solely for the use >>> of the individual or entity named on this message. If you are not the >>> intended recipient, and have received this message in error, please notify >>> us immediately by reply e-mail and then delete it from your system. >> >> --------------------------------------------------------------- >> >> To unsubscribe from the CCP4BB list, click the following link: >> https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 > > --------------------------------------------------------------- > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 ######################################################################## To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a mailing list hosted by www.jiscmail.ac.uk, terms & conditions are available at https://www.jiscmail.ac.uk/policyandsecurity/
