David L. Bostick
dbostick at physics.unc.edu
Thu Nov 20 03:19:00 CET 2003
If we take, for simplicity, x,y, and z as our coordinates. If
we wish to find a PMF for say, the center of mass of a molecule moving
along z, it should not matter if you constrain motion in x or y iff there
is isotropy in these two directions. For example, if you want the PMF of a
molecule crossing a bilayer and the bilayer plane is the xy-plane, for all
practical purposes, the system is isotropic in x and y. Thus you should see
very little difference whether or not you constrain motion of the molecule
in x and y as you sample z.
However, you might expect that if you allow motion in x and y, the molecule
might find a more natural path as you sample z, thus allowing faster
convergence in sampling z, even though the end result is the same.
If the system is anisotropic in the other 2 dimensions (x and y) like for
example if you want to sample a molecule travelling through a transmembrane
channel, then you may only constrain motion in x and y if you KNOW for sure
that this is the appropriate order parameter to sample. Otherwise, it is
safer to allow motion in x and y in this case as you sample z. This way the
molecule will find the appropriate path if you can verify that for each
point along z you are in equilibrium.
David Bostick Office: 262 Venable Hall
Dept. of Physics and Astronomy Phone: (919)962-0165
Program in Molecular and Cellular Biophysics
CB #3255 Phillips Hall dbostick at physics.unc.edu
Chapel Hill, NC 27599 http://www.unc.edu/~dbostick
On 19 Nov 2003, Ilya Chorny wrote:
> I'm less concerned about the sampling and more about the affect on
> freezing movement in two of the dimensions. How removing those
> contributions will effect the results.
> On Wed, 2003-11-19 at 14:30, David L. Bostick wrote:
> > Hi Ilya,
> > How do you mean? ... If you have adequate sampling along the degree of
> > freedom over which you wish to calculate the PMF, it is easily done .. Say,
> > for example the coordinate is z. Then ,
> > PMF(z) = -kT log(P(z)), where P(z) is the probability (or normalized
> > density) along the coordinate.
> > But if you do not have adequate sampling along z, you must devise a way to
> > sample it. Then you must look into free energy methods, such as umbrella
> > sampling, monitoring the constraint force along z and then integrating it,
> > or thermodynamic integration at points along the reaction path, etc....
> > David
> > -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
> > David Bostick Office: 262 Venable Hall
> > Dept. of Physics and Astronomy Phone: (919)962-0165
> > Program in Molecular and Cellular Biophysics
> > UNC-Chapel Hill
> > CB #3255 Phillips Hall dbostick at physics.unc.edu
> > Chapel Hill, NC 27599 http://www.unc.edu/~dbostick
> > =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
> > On 19 Nov 2003, Ilya Chorny wrote:
> > > Has anyone attempted to calculate PMF's by freezing the movement along
> > > two dimensions and allowing movement along one dimension?
> > >
> > > Ilya
> > >
> > >
> > >
> > >
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