# Re: [AMBER] using internal geometry

From: Jason Swails <jason.swails.gmail.com>
Date: Mon, 2 Mar 2015 13:35:10 -0500

On Mon, Mar 2, 2015 at 1:07 PM, newamber list <newamberlist.gmail.com>
wrote:

> Dear All,
>
> I am sure this is irrelevant question for AMBER but tleap functionality in
> AMBERTools does this job. For example if there is any missing atom in the
> loaded pdb then tleap can add that missing atom using residue library.
>
> I think this tleap module uses internal geometry (Z matrix) of the residue
> and generates a new Cartesian coordinate in space for missing atom. I have
> similar problem which I tried to ask in babel community but no reply.
>
> Lets say I have a,b,c,d four atoms (or even more). I can use babel to
> generate Z matrix which is internal geometry coordinates. I have many cases
> when I need to find Cartesian coordinate of atom 'a' given that I know
> Cartesian coordinate for b,c and d (other atoms too).
>

​Do you have the internal geometry representation for that residue and you
just want to "fill in" the missing atom from that template?

> This is very simple problem but am not able to come up with a solution.
> Also a mathematical explanation would help.
>

​Basically what the process boils down to is generating a system of
equations to solve for the x, y, and z coordinates of the missing atom (a)
by creating 3 equations (since you have 3 unknowns). If you know the
positions of ​
3 atoms (b, c, d) and the b-a bond, a-b-c angle, and a-b-c-d torsion
angles, then you can create 3 equations by computing the distance, angle,
and dihedral expressions and solving for xa, ya, and za. Of course, this
*assumes* that you know the internal coordinate representation (e.g., from
the template).

Another way mathematicians often frame this type of problem is to use a
'coordinate system' that is convenient for your problem (in your case, a
set of internal coordinates) and then using the Jacobian to translate
between the two different coordinate systems.​

HTH,
Jason

```--
Jason M. Swails
BioMaPS,
Rutgers University
Postdoctoral Researcher
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Received on Mon Mar 02 2015 - 11:00:03 PST
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