Author: bugman
Date: Thu Nov 2 09:15:17 2006
New Revision: 2727
URL: http://svn.gna.org/viewcvs/relax?rev=2727&view=rev
Log:
Significant improvements and expansion of the 'pdb.create_tensor_pdb()' user
function docstring.
Modified:
branches/tensor_pdb/prompt/pdb.py
Modified: branches/tensor_pdb/prompt/pdb.py
URL:
http://svn.gna.org/viewcvs/relax/branches/tensor_pdb/prompt/pdb.py?rev=2727&r1=2726&r2=2727&view=diff
==============================================================================
--- branches/tensor_pdb/prompt/pdb.py (original)
+++ branches/tensor_pdb/prompt/pdb.py Thu Nov 2 09:15:17 2006
@@ -46,7 +46,7 @@
run: The run to assign the structure to.
- scale: Value to scale the diffusion rates into Angstroms.
+ scale: Value for scaling the diffusion rates.
file: The name of the PDB file.
@@ -57,26 +57,72 @@
Description
~~~~~~~~~~~
-
- IMPORTANT: As the units of the Brownian rotational diffusion tensor
is the rate of
- diffusion measured in inverse seconds, the size of the tensor
geometric object is hence
- proportional to the rate and is not a correlation time. Hence the
larger the geometric
- object, the faster the diffusion of a molecule. For example the
diffusion tensor of a water
- molecule is much larger than the diffusion tensor of a
macromolecule. Hence, XH bond
- vectors parallel to the longest axis of the tensor tumble the
fastest.
This function creates a PDB file containing an artificial geometric
structure to represent
the diffusion tensor. A structure must have previously been read
into relax. The diffusion
tensor is represented by an ellipsoidal, spheroidal, or spherical
geometric object with its
- origin located at the center of mass (of the selected residues).
This diffusion tensor PDB
+ origin located at the centre of mass (of the selected residues).
This diffusion tensor PDB
file can subsequently read into any molecular viewer.
- The scaling argument can be used to vary the size of the tensor
geometric object. The
- default value is 1.8e-6. For spherical diffusion with a global
correlation time of 10 ns
- (this is equivalent to a Diso diffusion rate of 1.66e7 s^-1), the
radius of the sphere then
- be equal to 30 Angstrom. When the global correlation time is 30 ns,
the radius is 10
- Angstrom. If the global correlation time is 3ns, the radius will be
100 Angstrom (hence the
- scaling may need to be adjusted).
+ As the Brownian rotational diffusion tensor is a measure of the rate
of rotation about
+ different axes - the larger the geometric object, the faster the
diffusion of a molecule.
+ For example the diffusion tensor of a water molecule is much larger
than that of a
+ macromolecule.
+
+ The effective global correlation time experienced by an XH bond
vector, not to be confused
+ with the Lipari and Szabo parameter tau_e, will be approximately
proportional to the
+ component of the diffusion tensor parallel to it. The approximation
is not exact due to the
+ multiexponential form of the correlation function of Brownian
rotational diffusion. If an
+ XH bond vector is parallel to the longest axis of the tensor, it
will be unaffected by
+ rotations about that axis, which are the fastest rotations of the
molecule, and therefore
+ its effective global correlation time will be maximal.
+
+ To set the size of the diffusion tensor within the PDB frame the
unit vectors used to
+ generate the geometric object are first multiplied by the diffusion
tensor (which has the
+ units of inverse seconds) then by the scaling factor (which has the
units of second
+ Angstroms and has the default value of 1.8e-6 s.Angstrom).
Therefore the rotational
+ diffusion rate per Angstrom is equal the inverse of the scale value
(which defaults to
+ 5.55e5 s^-1.Angstrom^-1). Using the default scaling value for
spherical diffusion, the
+ correspondence between global correlation time, Diso diffusion rate,
and the radius of the
+ sphere for a number of discrete cases will be:
+
+ _________________________________________________
+ | | | |
+ | tm (ns) | Diso (s^-1) | Radius (Angstrom) |
+ |___________|_______________|___________________|
+ | | | |
+ | 1 | 1.67e8 | 300 |
+ | | | |
+ | 3 | 5.55e7 | 100 |
+ | | | |
+ | 10 | 1.67e7 | 30 |
+ | | | |
+ | 30 | 5.55e6 | 10 |
+ |___________|_______________|___________________|
+
+
+ The scaling value has been fixed to facilitate comparisons within or
between publications,
+ but can be changed to vary the size of the tensor geometric object
if necessary. Reporting
+ the rotational diffusion rate per Angstrom within figure legends
would be useful.
+
+ To create the tensor PDB representation, a number of algorithms are
utilised. Firstly the
+ centre of mass is calculated for the selected residues and is
represented in the PDB by a C
+ atom. Then the axes of the diffusion are calculated, as unit
vectors scaled to the
+ appropriate length (multiplied by the eigenvalue Dx, Dy, Dz, Dpar,
Dper, or Diso as well as
+ the scale value), and a C atom placed at the position of this vector
plus the centre of
+ mass. Finally a uniform distribution of vectors on a sphere is
generated using spherical
+ coordinates. By incrementing the polar angle using an arccos
distribution, a radial array
+ of vectors representing latitude are created while incrementing the
azimuthal angle evenly
+ creates the longitudinal vectors. These unit vectors, which are
distributed within the PDB
+ frame and are of 1 Angstrom in length, are first rotated into the
diffusion frame using a
+ rotation matrix (the spherical diffusion tensor is not rotated).
Then they are multiplied
+ by the diffusion tensor matrix to extend the vector out to the
correct length, and finally
+ multiplied by the scale value so that the vectors reasonably
superimpose onto the
+ macromolecular structure. The last set of algorithms place all this
information into a PDB
+ file. The distribution of vectors are represented by H atoms and
are all connected using
+ PDB CONECT records. Each H atom is connected to its two neighbours
on the both the
+ longitude and latitude. This creates a geometric PDB object with
longitudinal and
+ latitudinal lines.
"""
# Function intro text.
r2727 - /branches/tensor_pdb/prompt/pdb.py