[gmx-users] gyration radius

[David van der Spoel]

On Wed, 2005-07-20 at 12:18 -0400, Ran Friedman wrote:
> Sorry for insisting, but I still don't get it:
> 
> If I only take a single frame, e.g.:
> 
> @ s0 legend "Rg"
> @ s1 legend "RgX"
> @ s2 legend "RgY"
> @ s3 legend "RgZ"
>          1     1.76618     1.21448     1.50536     1.58042
> 
> I get Rg= sqrt ((Rx^2 + Ry^2 + Rz^2) * 0.5)
Actually your equation is correct....

RgX is the radius of gyration for rotation around the X axis (i.e. the
sum of the Y and Z components):

RgX = sum ( m Y^2 + m Z^2 )

therefore if you sum their squares you get all terms twice.

> 
> Thanks,
> Ran.
> 
> David van der Spoel wrote:
> > On Wed, 2005-07-20 at 10:58 -0400, Ran Friedman wrote:
> >   
> > > Hello,
> > > 
> > > I'm trying to understand the relation between the total radius of 
> > > gyration and its components. Searching to the mailing list, I found     
> > > that Rg = sqrt (Rx^2 + Ry^2 + Rz^2), see 
> > > http://www.gromacs.org/pipermail/gmx-users/2003-October/007376.html
> > > 
> > > But what I got was:
> > > 
> > > set     average              stddev
> > > SS1   1.744821e+00   2.028432e-02   (Rg)
> > > SS2   1.195420e+00   1.366429e-02   (Rx)
> > > SS3   1.485673e+00   2.606876e-02   (Ry)
> > > SS4   1.565914e+00   2.048274e-02   (Rz)
> > > 
> > > which means:
> > > Rg = sqrt ((Rx^2 + Ry^2 + Rz^2) * 0.5)
> > > 
> > > What's wrong?
> > > 
> > >     
> > You should do the averaging after summing up the components.
> > 
> > 
> >   
> > > Thanks,
> > > Ran.
> > > 
> > >     
> 
> -- 
> ------------------------------------------------------
> Ran Friedman
> Laser Laboratory for Fast Reactions in Biology
> Department of Biochemistry
> Faculty of Life Sciences
> Tel-Aviv University
> Tel. +972-3-6409824
> Fax. +972-3-6409875
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-- 
David.
________________________________________________________________________
David van der Spoel, PhD, Assoc. Prof., Molecular Biophysics group,
Dept. of Cell and Molecular Biology, Uppsala University.
Husargatan 3, Box 596,          75124 Uppsala, Sweden
phone:  46 18 471 4205          fax: 46 18 511 755
spoel at xray.bmc.uu.se    spoel at gromacs.org   http://xray.bmc.uu.se/~spoel
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