**From:** Giacomo Fiorin (*giacomo.fiorin_at_gmail.com*)

**Date:** Thu Feb 21 2013 - 10:10:24 CST

**Next message:**Rawan Al Nsour: "Epoxy CHARMM"**Previous message:**JÃ©rÃ´me HÃ©nin: "Re: Orientation colvar + metadynamics questions"**In reply to:**JÃ©rÃ´me HÃ©nin: "Re: Orientation colvar + metadynamics questions"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Yeah, that distance is simply the angle w (in radians) between Q1 and Q2 as

unit vectors in R^4. Because of the symmetry, the actual distance is the

lower number between w and (pi - w), so as Jérôme already said, values of

the distance range from 0 to pi/2.

Benjamin: apart from the lack of grids, no problems using quaternions for

metadynamics, if you need a completely isotropic variable. Check however

if you could simplify it by ignoring e.g. one axis of rotation and using

tilt and/or spinAngle.

Regarding the grid implementation of the PMF: a grid for the energy (scalar

function of a quaternion variable) is a bit complex, but doable. For

instance, you can find in the literature that people use multiple 3-d

projections of the 4-d unit sphere, switching from one projection to the

other to preserve the resolution. Also, because the metadynamics PMF is

essentially a histogram, the symmetry is automatically taken care of, by

incrementing the grid's value at both locations, Q and (-Q).

However, things start getting messier with the grid for the energy

gradients (quaternion function of a quaternion variable...).

Essentially, if you can live with the performance loss of using explicit

gaussian functions instead of the grid, I think your best bet is to get the

quaternion values from the colvars.traj file, and calculate the histogram

(i.e. the PMF) choosing the 3-d projection that it's best for your case. I

can send you a python script for that, if you like.

Bests

Giacomo

On Thu, Feb 21, 2013 at 10:21 AM, Jérôme Hénin <jerome.henin_at_ibpc.fr> wrote:

*> ----- Original Message -----
*

*> > Thanks for the answers Jérôme. One last question, if I may - in
*

*> > quaternion
*

*> > space, is the biasing Gaussian function 'isotropic' (ie, same width
*

*> > applied to all 4 dimensions), or are the scalar and vector parts
*

*> > treated
*

*> > differently?
*

*>
*

*> The four components are treated in a symmetric way, but not as a Euclidean
*

*> distance: since the orientation quaternions are always unit, their distance
*

*> is defined as the geodesic distance on the unit sphere (4D hypersphere).
*

*> More precisely, the distance between Q1 and Q2 is the min of d(Q1, Q2) and
*

*> d(Q1, -Q2), as Q2 and -Q2 have the same meaning in terms of rotations. So
*

*> unless I am mistaken, it should be between 0 and pi/2.
*

*>
*

*> Best,
*

*> Jerome
*

*>
*

*>
*

*>
*

*> > On Thu, 21 Feb 2013 13:53:28 +0100, Jérôme Hénin
*

*> > <jerome.henin_at_ibpc.fr>
*

*> > wrote:
*

*> >
*

*> > > Hi Benjamin,
*

*> > >
*

*> > > ----- Original Message -----
*

*> > >> Hello all,
*

*> > >>
*

*> > >> I'm attempting to use quaternions (colvar 'orientation') as a
*

*> > >> biasing
*

*> > >> coordinate for a metadynamics simulation, to control the
*

*> > >> orientation
*

*> > >> of a
*

*> > >> molecule with respect to another. I have a few questions that
*

*> > >> neither
*

*> > >> the
*

*> > >> documentation nor my first results have completely answered:
*

*> > >>
*

*> > >> - Am I correct in assuming that the 'orientation' colvar is
*

*> > >> affected
*

*> > >> by
*

*> > >> the overall rotation of the system, meaning that if I want to
*

*> > >> control
*

*> > >> the
*

*> > >> orientation of B relative to A, I have to restrain the rotation of
*

*> > >> A
*

*> > >> (using, e.g., another 'orientation' colvar and a 'harmonic'
*

*> > >> restraint)?
*

*> > >
*

*> > > You are correct that the 'orientation' colvar is, in general,
*

*> > > sensitive
*

*> > > to overall rotations of the system, but incorrect in concluding
*

*> > > that you
*

*> > > need restraints. As with all colvars, you can define this
*

*> > > orientation
*

*> > > based on rotated coordinates, in the frame of reference of group A.
*

*> > > to
*

*> > > that effect, use the rotateReference and refPositionsGroup
*

*> > > keywords,
*

*> > > providing group A as the the refPositionsGroup.
*

*> > >
*

*> > >
*

*> > >> - How exactly is the width of the hill Gaussians (in R^4) defined
*

*> > >> from the
*

*> > >> scalar 'width' parameter? I could find no trivial relationship
*

*> > >> between
*

*> > >> this parameter and the width of the hills (also scalar) given in
*

*> > >> the
*

*> > >> colvars.state file.
*

*> > >
*

*> > > The width of each Gaussian is considered to be twice its standard
*

*> > > deviation, and it is obtained as the hillWidth parameter of
*

*> > > metadynamics, times that colvar's width parameter. So the std. dev.
*

*> > > is:
*

*> > > 1/2 * hillWidth * colvar->width
*

*> > >
*

*> > >
*

*> > >> - Since 'orientation' is not grid-compatible, PMF output seems
*

*> > >> disabled.
*

*> > >> Is there a utility program to convert the hills file to a PMF, or
*

*> > >> should I
*

*> > >> write my own (which would require me to understand the
*

*> > >> aforementioned
*

*> > >> hill-width thing...)?
*

*> > >
*

*> > > I don't think there is such a utility at this point, but I hope the
*

*> > > info
*

*> > > above is enough for you to compute the PMF.
*

*> > >
*

*> > > Best,
*

*> > > Jerome
*

*> >
*

*>
*

*>
*

**Next message:**Rawan Al Nsour: "Epoxy CHARMM"**Previous message:**JÃ©rÃ´me HÃ©nin: "Re: Orientation colvar + metadynamics questions"**In reply to:**JÃ©rÃ´me HÃ©nin: "Re: Orientation colvar + metadynamics questions"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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