[Chimera-users] Angles

Greg Pintilie pintilie at mit.edu
Mon Nov 5 16:44:49 PST 2007

```If you think of the line connecting the two atoms as a vector (with no
position in space), then it's angle to another vector (e.g. the x-axis
(1,0,0)) can be computed from the definition of dot product:

u . v = |u| * |v| * cos ( theta)

where u . v is the dot product between the vectors u and v, theta is
the angle between the vectors u and v, and |u| is the magnitude
(length) of u

so

cos ( theta) = u . v / ( |u| * |v| )
theta = arccos ( u.v / ( |u| * |v| ) )

if the vectors u and v are normalized / have unit length of 1 then you
can simplify:

theta = arccos ( u.v )

within chimera, in the python interpreter IDLE, you first need to get
the coordinates of the two atoms, for example, to get the vector from
the alpha carbon in residue 32 to the alpha carbon in residue 33:

at1 = chimera.selection.OSLSelection(":32.A at CA").atoms()[0]
at2 = chimera.selection.OSLSelection(":33.A at CA").atoms()[0]
v = at2.coord() - at1.coord()
v.normalize()
import numpy
theta_to_x_in_degrees = numpy.arccos ( v * chimera.Vector(1,0,0) ) *
180 / numpy.pi

hope that helps...

Greg

On Nov 5, 2007 3:24 PM,  <hsosa at aecom.yu.edu> wrote:
> Hi,
> I have a couple of questions:
>
> Is there a simple  way to determine the angle between  any of the three
> axes, X,Y or Z and the line connecting two selected atoms?. I know you
> can use the Angles/Torsions tools to determine the angle formed between
> 3 sets of atoms, but I wonder if  you could use that tool, or some
> other,  to  report the angle of two atoms with the axes?.
>
> Is it possible to draw a box with the axes around a structure as it can
> be done with a volume ?.
>
> Thanks
>
> Hernando
>
> --
> -----------------------------------
> Hernando Sosa
> Dept. of Physiology and Biophysics
> Albert Einstein College of Medicine
> 1300 Morris Park Av.
> Bronx NY 10461
> phone   (718) 430-3456
> FAX     (718) 430-8819
> email   hsosa at aecom.yu.edu
> -----------------------------------
>
>
>
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>

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