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#841 - 01/26/04 04:07 PM How to build IMAGE file using symmetric matrices ?
George Offline
Forum Member

Registered: 01/26/04
Posts: 2
I want to build a system with globular symmetry defining by some rotate axes. First, I need use a 2-fold axis (A2) to build a dimer. Then, I need to use a 5-fold axis (A5) to generate 10 copy of monomers. Finally, I need to use a 2-fold axis (B2) to generate total 20 copy.
As stated in CHARMM manu., IMAGE part, these axes can be useed in a IMAGE file to perform these image transformation. But I have all 20 symmetric matrices to generate these images now. It is not convenient to figure out these axes. Does someone can tell me how to use the MATRIX in IMAGE file, instead of axes?

If I have to use axes in CHARMM, How can I build most efficiently the image file using the three axes ?

Thanks a lot,

George

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#842 - 01/27/04 05:05 PM Re: How to build IMAGE file using symmetric matric [Re: George]
BRBrooks Offline

Forum Member

Registered: 09/02/03
Posts: 394
Loc: Rockville, Maryland
The array in CHARMM that needs to be filled is IMTRNS (in image.fcm). This array has 12 elements per image. There is no code to do what you've asked for, but it is easy to create. So,

1. I will add an option to the IMREAD subroutine that directly reads the IMTRNS elements. You can do this yourself with the USER command (or in several other ways) if you need it right away.

2. You can also figure out what translation/rotations you have in your matrix. This is perhaps easier than you realize. You can create the corresponding image file. If you post the list of transformations, I'll take a stab at it.

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#843 - 01/29/04 02:34 PM Re: How to build IMAGE file using symmetric matric [Re: BRBrooks]
George Offline
Forum Member

Registered: 01/26/04
Posts: 2
Thanks a lot.

Here is the transformations I need to do.

LET P1 = COORDINATES OF ANY ATOM AS LISTED IN ENTRY
1.
TRNSF1 1 .500000 -.809017 .309017
TRNSF2 1 .809017 .309017 -.500000
TRNSF3 1 .309017 .500000 .809017

P2 = TRNSF 1 * P1
P3 = TRNSF 1 * P2
P4 = TRNSF 1 * P3
P5 = TRNSF 1 * P4

APPLY THE FIVE-FOLD GIVEN BY TRNSF 1
P1 THROUGH P5 CONSTITUTE AN ENTIRE PENTAMER,
CONSISTING OF FIVE UNITS. ONE COMPLETE
PENTAMER SET OF COORDINATES WILL CONTAIN FIVE
CHAINS EACH OF A, B, AND C.

P1 THROUGH P5 CONSTITUTE AN ENTIRE PENTAMER,
CONSISTING OF FIVE UNITS.
2.
TRNSF1 2 0.309017 -0.500000 0.809017
TRNSF2 2 -0.500000 -0.809017 -0.309017
TRNSF3 2 0.809017 -0.309017 -0.500000

APPLY THE TWO-FOLD GIVEN BY TRNSF 2 TO P1 THROUGH
P5 TO GENERATE P6 THROUGH P10 FOR A SECOND ENTIRE
PENTAMER.

P6 = TRNSF 2 * P1
P7 = TRNSF 2 * P2
P8 = TRNSF 2 * P3
P9 = TRNSF 2 * P4
P10 = TRNSF 2 * P5

3.
TRNSF1 3 -0.500000 -0.809017 0.309017
TRNSF2 3 -0.809017 0.309017 -0.500000
TRNSF3 3 0.309017 -0.500000 -0.809017

APPLY THE TWO-FOLD GIVEN BY TRNSF 3 TO EACH OF THE
FIRST TEN UNITS (WILL YIELD TOTAL OF TWENTY
UNITS, FOUR COMPLETE PENTAMERS).

P11 = TRNSF 3 * P1
P12 = TRNSF 3 * P2
P13 = TRNSF 3 * P3
P14 = TRNSF 3 * P4
P15 = TRNSF 3 * P5
P16 = TRNSF 3 * P6
P17 = TRNSF 3 * P7
P18 = TRNSF 3 * P8
P19 = TRNSF 3 * P9
P20 = TRNSF 3 * P10


4.

TRNSF1 4 0.000000 0.000000 1.000000
TRNSF2 4 1.000000 0.000000 0.000000
TRNSF3 4 0.000000 1.000000 0.000000

APPLY THE THREE-FOLD GIVEN BY TRNSF 4 TO EACH OF
THE TWENTY UNITS P1 THROUGH P20 TO GENERATE UNITS
THROUGH P40.

P21 = TRNSF 4 * P1
P22 = TRNSF 4 * P2
P23 = TRNSF 4 * P3
P24 = TRNSF 4 * P4
P25 = TRNSF 4 * P5
P26 = TRNSF 4 * P6
P27 = TRNSF 4 * P7
P28 = TRNSF 4 * P8
P29 = TRNSF 4 * P9
P30 = TRNSF 4 * P10
P31 = TRNSF 4 * P11
P32 = TRNSF 4 * P12
P33 = TRNSF 4 * P13
P34 = TRNSF 4 * P14
P35 = TRNSF 4 * P15
P36 = TRNSF 4 * P16
P37 = TRNSF 4 * P17
P38 = TRNSF 4 * P18
P39 = TRNSF 4 * P19
P40 = TRNSF 4 * P20

FINALLY, UNITS P41 THROUGH P60 MAY BE GENERATED
BY APPLYING TRNSF 4 TO UNITS P21 THROUGH P40.

P41 = TRNSF 4 * P21
P42 = TRNSF 4 * P22
P43 = TRNSF 4 * P23
P44 = TRNSF 4 * P24
P45 = TRNSF 4 * P25
P46 = TRNSF 4 * P26
P47 = TRNSF 4 * P27
P48 = TRNSF 4 * P28
P49 = TRNSF 4 * P29
P50 = TRNSF 4 * P30
P51 = TRNSF 4 * P31
P52 = TRNSF 4 * P32
P53 = TRNSF 4 * P33
P54 = TRNSF 4 * P34
P55 = TRNSF 4 * P35
P56 = TRNSF 4 * P36
P57 = TRNSF 4 * P37
P58 = TRNSF 4 * P38
P59 = TRNSF 4 * P39
P60 = TRNSF 4 * P40


THIS YIELDS A TOTAL OF 60 UNIT COPIES IN
AN ICOSAHEDRAL VIRUS PARTICLE
APPLY THE FOLLOWING TO CHAINS: A, B, C



BIOMT1 1 1.000000 0.000000 0.000000 0.00000
BIOMT2 1 0.000000 1.000000 0.000000 0.00000
BIOMT3 1 0.000000 0.000000 1.000000 0.00000
BIOMT1 2 0.500000 -0.809017 0.309017 0.00000
BIOMT2 2 0.809017 0.309017 -0.500000 0.00000
BIOMT3 2 0.309017 0.500000 0.809017 0.00000
BIOMT1 3 -0.309017 -0.500000 0.809017 0.00000
BIOMT2 3 0.500000 -0.809017 -0.309017 0.00000
BIOMT3 3 0.809017 0.309017 0.500000 0.00000
BIOMT1 4 -0.309017 0.500000 0.809017 0.00000
BIOMT2 4 -0.500000 -0.809017 0.309017 0.00000
BIOMT3 4 0.809017 -0.309017 0.500000 0.00000
BIOMT1 5 0.500000 0.809017 0.309017 0.00000
BIOMT2 5 -0.809017 0.309017 0.500000 0.00000
BIOMT3 5 0.309017 -0.500000 0.809017 0.00000
BIOMT1 6 -0.809017 -0.309017 0.500000 0.00000
BIOMT2 6 -0.309017 -0.500000 -0.809017 0.00000
BIOMT3 6 0.500000 -0.809017 0.309017 0.00000
BIOMT1 7 -0.500000 0.809017 0.309017 0.00000
BIOMT2 7 -0.809017 -0.309017 -0.500000 0.00000
BIOMT3 7 -0.309017 -0.500000 0.809017 0.00000
BIOMT1 8 0.500000 0.809017 -0.309017 0.00000
BIOMT2 8 -0.809017 0.309017 -0.500000 0.00000
BIOMT3 8 -0.309017 0.500000 0.809017 0.00000
BIOMT1 9 0.809017 -0.309017 -0.500000 0.00000
BIOMT2 9 -0.309017 0.500000 -0.809017 0.00000
BIOMT3 9 0.500000 0.809017 0.309017 0.00000
BIOMT1 10 0.000000 -1.000000 0.000000 0.00000
BIOMT2 10 0.000000 0.000000 -1.000000 0.00000
BIOMT3 10 1.000000 0.000000 0.000000 0.00000
BIOMT1 11 -0.809017 0.309017 -0.500000 0.00000
BIOMT2 11 0.309017 -0.500000 -0.809017 0.00000
BIOMT3 11 -0.500000 -0.809017 0.309017 0.00000
BIOMT1 12 -0.309017 0.500000 -0.809017 0.00000
BIOMT2 12 -0.500000 -0.809017 -0.309017 0.00000
BIOMT3 12 -0.809017 0.309017 0.500000 0.00000
BIOMT1 13 0.000000 0.000000 -1.000000 0.00000
BIOMT2 13 -1.000000 0.000000 0.000000 0.00000
BIOMT3 13 0.000000 1.000000 0.000000 0.00000
BIOMT1 14 -0.309017 -0.500000 -0.809017 0.00000
BIOMT2 14 -0.500000 0.809017 -0.309017 0.00000
BIOMT3 14 0.809017 0.309017 -0.500000 0.00000
BIOMT1 15 -0.809017 -0.309017 -0.500000 0.00000
BIOMT2 15 0.309017 0.500000 -0.809017 0.00000
BIOMT3 15 0.500000 -0.809017 -0.309017 0.00000
BIOMT1 16 0.309017 0.500000 -0.809017 0.00000
BIOMT2 16 -0.500000 0.809017 0.309017 0.00000
BIOMT3 16 0.809017 0.309017 0.500000 0.00000
BIOMT1 17 0.309017 -0.500000 -0.809017 0.00000
BIOMT2 17 0.500000 0.809017 -0.309017 0.00000
BIOMT3 17 0.809017 -0.309017 0.500000 0.00000
BIOMT1 18 -0.500000 -0.809017 -0.309017 0.00000
BIOMT2 18 0.809017 -0.309017 -0.500000 0.00000
BIOMT3 18 0.309017 -0.500000 0.809017 0.00000
BIOMT1 19 -1.000000 0.000000 0.000000 0.00000
BIOMT2 19 0.000000 -1.000000 0.000000 0.00000
BIOMT3 19 0.000000 0.000000 1.000000 0.00000
BIOMT1 20 -0.500000 0.809017 -0.309017 0.00000
BIOMT2 20 -0.809017 -0.309017 0.500000 0.00000
BIOMT3 20 0.309017 0.500000 0.809017 0.00000
BIOMT1 21 0.000000 0.000000 1.000000 0.00000
BIOMT2 21 1.000000 0.000000 0.000000 0.00000
BIOMT3 21 0.000000 1.000000 0.000000 0.00000
BIOMT1 22 0.000000 1.000000 0.000000 0.00000
BIOMT2 22 0.000000 0.000000 1.000000 0.00000
BIOMT3 22 1.000000 0.000000 0.000000 0.00000
BIOMT1 23 0.309017 0.500000 0.809017 0.00000
BIOMT2 23 0.500000 -0.809017 0.309017 0.00000
BIOMT3 23 0.809017 0.309017 -0.500000 0.00000
BIOMT1 24 0.809017 0.309017 -0.500000 0.00000
BIOMT2 24 0.309017 0.500000 0.809017 0.00000
BIOMT3 24 0.500000 -0.809017 0.309017 0.00000
BIOMT1 25 0.809017 0.309017 0.500000 0.00000
BIOMT2 25 -0.309017 -0.500000 0.809017 0.00000
BIOMT3 25 0.500000 -0.809017 -0.309017 0.00000
BIOMT1 26 0.500000 -0.809017 -0.309017 0.00000
BIOMT2 26 0.809017 0.309017 0.500000 0.00000
BIOMT3 26 -0.309017 -0.500000 0.809017 0.00000
BIOMT1 27 0.809017 -0.309017 0.500000 0.00000
BIOMT2 27 -0.309017 0.500000 0.809017 0.00000
BIOMT3 27 -0.500000 -0.809017 0.309017 0.00000
BIOMT1 28 -0.500000 -0.809017 0.309017 0.00000
BIOMT2 28 0.809017 -0.309017 0.500000 0.00000
BIOMT3 28 -0.309017 0.500000 0.809017 0.00000
BIOMT1 29 0.309017 -0.500000 0.809017 0.00000
BIOMT2 29 0.500000 0.809017 0.309017 0.00000
BIOMT3 29 -0.809017 0.309017 0.500000 0.00000
BIOMT1 30 -0.809017 0.309017 0.500000 0.00000
BIOMT2 30 0.309017 -0.500000 0.809017 0.00000
BIOMT3 30 0.500000 0.809017 0.309017 0.00000
BIOMT1 31 0.500000 -0.809017 0.309017 0.00000
BIOMT2 31 -0.809017 -0.309017 0.500000 0.00000
BIOMT3 31 -0.309017 -0.500000 -0.809017 0.00000
BIOMT1 32 -0.309017 -0.500000 -0.809017 0.00000
BIOMT2 32 0.500000 -0.809017 0.309017 0.00000
BIOMT3 32 -0.809017 -0.309017 0.500000 0.00000
BIOMT1 33 -0.309017 -0.500000 0.809017 0.00000
BIOMT2 33 -0.500000 0.809017 0.309017 0.00000
BIOMT3 33 -0.809017 -0.309017 -0.500000 0.00000
BIOMT1 34 -0.809017 -0.309017 -0.500000 0.00000
BIOMT2 34 -0.309017 -0.500000 0.809017 0.00000
BIOMT3 34 -0.500000 0.809017 0.309017 0.00000
BIOMT1 35 -0.309017 0.500000 0.809017 0.00000
BIOMT2 35 0.500000 0.809017 -0.309017 0.00000
BIOMT3 35 -0.809017 0.309017 -0.500000 0.00000
BIOMT1 36 -0.809017 0.309017 -0.500000 0.00000
BIOMT2 36 -0.309017 0.500000 0.809017 0.00000
BIOMT3 36 0.500000 0.809017 -0.309017 0.00000
BIOMT1 37 0.500000 0.809017 0.309017 0.00000
BIOMT2 37 0.809017 -0.309017 -0.500000 0.00000
BIOMT3 37 -0.309017 0.500000 -0.809017 0.00000
BIOMT1 38 -0.309017 0.500000 -0.809017 0.00000
BIOMT2 38 0.500000 0.809017 0.309017 0.00000
BIOMT3 38 0.809017 -0.309017 -0.500000 0.00000
BIOMT1 39 1.000000 0.000000 0.000000 0.00000
BIOMT2 39 0.000000 -1.000000 0.000000 0.00000
BIOMT3 39 0.000000 0.000000 -1.000000 0.00000
BIOMT1 40 0.000000 0.000000 -1.000000 0.00000
BIOMT2 40 1.000000 0.000000 0.000000 0.00000
BIOMT3 40 0.000000 -1.000000 0.000000 0.00000
BIOMT1 41 -0.500000 -0.809017 0.309017 0.00000
BIOMT2 41 -0.809017 0.309017 -0.500000 0.00000
BIOMT3 41 0.309017 -0.500000 -0.809017 0.00000
BIOMT1 42 0.309017 -0.500000 -0.809017 0.00000
BIOMT2 42 -0.500000 -0.809017 0.309017 0.00000
BIOMT3 42 -0.809017 0.309017 -0.500000 0.00000
BIOMT1 43 -0.809017 0.309017 0.500000 0.00000
BIOMT2 43 -0.309017 0.500000 -0.809017 0.00000
BIOMT3 43 -0.500000 -0.809017 -0.309017 0.00000
BIOMT1 44 -0.500000 -0.809017 -0.309017 0.00000
BIOMT2 44 -0.809017 0.309017 0.500000 0.00000
BIOMT3 44 -0.309017 0.500000 -0.809017 0.00000
BIOMT1 45 0.000000 1.000000 0.000000 0.00000
BIOMT2 45 0.000000 0.000000 -1.000000 0.00000
BIOMT3 45 -1.000000 0.000000 0.000000 0.00000
BIOMT1 46 -1.000000 0.000000 0.000000 0.00000
BIOMT2 46 0.000000 1.000000 0.000000 0.00000
BIOMT3 46 0.000000 0.000000 -1.000000 0.00000
BIOMT1 47 0.809017 0.309017 -0.500000 0.00000
BIOMT2 47 -0.309017 -0.500000 -0.809017 0.00000
BIOMT3 47 -0.500000 0.809017 -0.309017 0.00000
BIOMT1 48 -0.500000 0.809017 -0.309017 0.00000
BIOMT2 48 0.809017 0.309017 -0.500000 0.00000
BIOMT3 48 -0.309017 -0.500000 -0.809017 0.00000
BIOMT1 49 0.500000 -0.809017 -0.309017 0.00000
BIOMT2 49 -0.809017 -0.309017 -0.500000 0.00000
BIOMT3 49 0.309017 0.500000 -0.809017 0.00000
BIOMT1 50 0.309017 0.500000 -0.809017 0.00000
BIOMT2 50 0.500000 -0.809017 -0.309017 0.00000
BIOMT3 50 -0.809017 -0.309017 -0.500000 0.00000
BIOMT1 51 0.809017 0.309017 0.500000 0.00000
BIOMT2 51 0.309017 0.500000 -0.809017 0.00000
BIOMT3 51 -0.500000 0.809017 0.309017 0.00000
BIOMT1 52 -0.500000 0.809017 0.309017 0.00000
BIOMT2 52 0.809017 0.309017 0.500000 0.00000
BIOMT3 52 0.309017 0.500000 -0.809017 0.00000
BIOMT1 53 0.809017 -0.309017 0.500000 0.00000
BIOMT2 53 0.309017 -0.500000 -0.809017 0.00000
BIOMT3 53 0.500000 0.809017 -0.309017 0.00000
BIOMT1 54 0.500000 0.809017 -0.309017 0.00000
BIOMT2 54 0.809017 -0.309017 0.500000 0.00000
BIOMT3 54 0.309017 -0.500000 -0.809017 0.00000
BIOMT1 55 0.309017 -0.500000 0.809017 0.00000
BIOMT2 55 -0.500000 -0.809017 -0.309017 0.00000
BIOMT3 55 0.809017 -0.309017 -0.500000 0.00000
BIOMT1 56 0.809017 -0.309017 -0.500000 0.00000
BIOMT2 56 0.309017 -0.500000 0.809017 0.00000
BIOMT3 56 -0.500000 -0.809017 -0.309017 0.00000
BIOMT1 57 0.000000 0.000000 1.000000 0.00000
BIOMT2 57 -1.000000 0.000000 0.000000 0.00000
BIOMT3 57 0.000000 -1.000000 0.000000 0.00000
BIOMT1 58 0.000000 -1.000000 0.000000 0.00000
BIOMT2 58 0.000000 0.000000 1.000000 0.00000
BIOMT3 58 -1.000000 0.000000 0.000000 0.00000
BIOMT1 59 0.309017 0.500000 0.809017 0.00000
BIOMT2 59 -0.500000 0.809017 -0.309017 0.00000
BIOMT3 59 -0.809017 -0.309017 0.500000 0.00000
BIOMT1 60 -0.809017 -0.309017 0.500000 0.00000
BIOMT2 60 0.309017 0.500000 0.809017 0.00000
BIOMT3 60 -0.500000 0.809017 -0.309017 0.00000

The chain A, B, and C are identical and form a trimer. Chain A will be used as primary atoms and chain B and C will be generated images from A. The two matrices are used to generate B and C from A are:

0.97096634 0.02672976 0.23769738 -8.78279209
0.02672516 0.97538936 -0.21884929 16.99122429
-0.23770490 0.21885435 0.94636488 1.57086122

-0.96256614 -0.02893539 0.26949260 -15.66497803
-0.04114059 -0.96716338 -0.25079200 24.54845047
0.26789939 -0.25248924 0.92977130 5.53630066

They are some complicated. But I can use following two 2-fold axes to simplify the situation.

Axis1. 21.83283 -15.3937 216.225 0.0
Axis2. 44.24117 -31.5773 212.7333 0.0

Rotat axis1 for 180 degree to generate B from A and rotate axis2 for 180 degree to generate C from B chain.



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#844 - 01/29/04 05:31 PM Re: How to build IMAGE file using symmetric matric [Re: George]
BRBrooks Offline

Forum Member

Registered: 09/02/03
Posts: 394
Loc: Rockville, Maryland
This isn't too hard... But first, why don't you use the "standard" icosohedral image files (both 60-fold and 12-fold) that Carol has?
This problem was solved many years ago.

Anyway...
rotation #1 is 72 degrees about the -0.525731 0.00000 -0.850651 axis
roataion #2 is 180 degrees about 0.809017 -0.309017 0.500000 axis
rotation #3 is 180 degrees about 0.500000 -0.809017 0.309017 axis
rotation #4 is 120 degrees about -1. -1. -.1 axis

(You need these numbers with more precision for large systems)...
0.309... is sin(18 deg) and 0.809... is sin(54 deg) and axis 1 is orthogonal to axis 2. Work out these numbers in high precision
and substitute into the image file.

The image transformation file would be something like (note: not checked);

* icosohedral image file
*
image p2
rotate -0.525731... 0.00000 -0.850651... 72.0
image p3
define p1 p1
image p4
define p1 p2
image p5
define p1 p4
image p6
rotate 0.809017... -0.309017... 0.500000 180.0
image p7
define p6 p2
image p8
define p6 p3
image p9
define p6 p4
image p10
define p6 p5
image p11
rotate 0.5 -0.809017... 0.309017... 180.0
image p12
define p11 p2
...
...
image p21
rotate -1. -1. -1. 120.0
image p22
define p21 p2
...
...
image p41
define p21 p21
image p42
define p41 p2
...
...
end


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