# Re: amber-developers: Truncated Octahedron box volume (fwd)

From: Thomas Cheatham <tec3.utah.edu>
Date: Thu, 26 Jul 2007 13:26:55 -0600 (Mountain Daylight Time)

> It is not so clear to me what u mean by "... however "truncated
^^^
I find it really distracting to read e-mail as text message vernacular.

> octahedron" can be defined in multiple ways....". Do u mean that in a
> different space where you have a different type of metric, the 'truncated
> octahedron' can be defined different? Or do u mean that the volume of a
> 'truncated octahedron' can be defined in multiple ways?

What I mean is that it can be implemented in different ways and hence how
to determine its volume will differ. In Allen & Tildesley, there is an
algorithm that implements a truncated octahedral geometry. This is not
equivalent to the triclinic/AMBER definition. LEaP used to be able to
produce this "other" kind of box.

> > V = x * y * z * sqrt(1.0 - cos(alpha)**2 - cos(beta)**2 - cos(gamma)**2 +
> > 2.0 * cos(alpha) * cos(beta) * cos(gamma))
> >
>
> Thanks for the .pdf file u sent. I am trying to understand/prove why the
> volume is defined by the above equation. I saw a message of Dave Case in
> the amber mailing list, where he is referencing a 1997 paper regarding
> 'truncated octahedrons'. As far as I understood, amber sim.s are done
> using triclinic cells. And in order to use the truncated octahedral
> solvation box, it is mapped to a triclinic cell (at least that is what I
> understood). I would like to understand how this mapping is done.
>
> Another question is, why to use triclinic cell? Is it hard to explicitly
> use truncated octahedrals in the simulations? By combining triclinic
> cells, someone can create a continous system; but this must be true for
> combining truncated octahedrons, too.

The triclinic is a general property that fits well within the PME
framework. Those other boxes in that previous table map to the triclinic.
The standard Allen & Tildesley could map, but it would require a different
orientation of the box and different definition of the "length of a side".

> Unfortunately, our library does not have this journal. Can u give me the
> full references of these papers published in this journal? I will ask from
> the library to get it for me, but they need the full reference
> information. Thanks again.

What I would worry about understanding is the box_to_recip() code in
PME/AMBER, PMEMD, sander, or ptraj. This will allow you to better
understand the box. If the angle is 109.47 it IS a truncated octahedron /
it is also a particular triclinic shape.

--tom

p.s. you may have Current Protocols in the lab there...

Current Protocols in Nucleic Acid Chemistry:

(20) T. E. Cheatham, III, B. R. Brooks & P. A. Kollman. "Molecular
modeling of nucleic acid structure" in Current Protocols in Nucleic Acid
Chemistry. (Wiley: New York) 7.5.1-7.5.13 (1999).

(25) T. E. Cheatham, III, B. R. Brooks & P. A. Kollman. "Molecular
modeling of nucleic acid structure: Energy and sampling" in Current
Protocols in Nucleic Acid Chemistry. (Wiley: New York) 7.8.1-7.8.21
(2001).
(26) T. E. Cheatham, III, B. R. Brooks & P. A. Kollman. "Molecular
modeling of nucleic acid structure: Electrostatics and solvation" in
Current Protocols in Nucleic Acid Chemistry. (Wiley: New York)
7.9.1-7.9.22 (2001).
(27) T. E. Cheatham, III, B. R. Brooks & P. A. Kollman. "Molecular
modeling of nucleic acid structure: Setup and analysis" in Current
Protocols in Nucleic Acid Chemistry. (Wiley: New York) 7.10.1-7.10.18
(2001).
Received on Sun Jul 29 2007 - 06:07:26 PDT
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