Flexible
Docking Tutorial, Part II
|
| The tutorial teaches skeleton-based
flexible docking using RNA polymerase as a test system. It is helpful
for the
understanding
of the tutorial if the user is already familiar with part I and has performed at least the installation
step (the rest of part I can be skipped if the
earlier
output files are copied from the "solutions" directory). More
documentation is available in
the user guide, on the Methodology
page, and in the published articles. |
|
Content:
|
| Introduction
In principle, the resolution of
flexible fitting of an atomic structure to a low-resolution map can be
improved by increasing the number of codebook
vectors. However, there are practical limitations. If there are
experimental limitations
(e.g. noise, missing parts) not all vectors converge towards equivalent
features in the two data sets if the vector number is substantially
increased.
The solution to this problem is to freeze
longitudinal
degrees of freedom, and to impose distance constraints on the
vectors.
This can be done very efficiently with the tools provided by Situs.
We consider here an interesting case,
the
flexible fitting of the closed RNA polymerase structure to a
(simulated) open form at low resolution. Inspection of this file
reveals that an isocontour value of 50 units is appropriate.
|
Preliminary
Rigid-Body Registration
Before we start the
flexing, it is mandatory to roughly
align the atomic structure and the target map by rigid-body fitting.
This
can be done "by eye" or with a fast tool like qrange, as described earlier. Here the structures are already
sufficiently aligned.
|
| Vector
Quantization of the High-Resolution Structure
Now, we perform the vector
quantization of the roughly aligned atomic structure with the qpdb
utility.
At the shell prompt, enter
| ./qpdb 0_rnap1.pdb 5_rnap1.qpdb |
and select mass weigthing (enter 2) and no B-factor cutoff (enter 1).
Next, enter the number
of codebook vectors: 15. Watch the program compute a number of datasets
(default: 8) for statistical averaging. The file 5_rnap1.qpdb
now contains the 15 new codebook vectors, their rms variability, and
the effective radius of their Voronoi cells, in
PDB format. Finally, the user is asked whether nearest-neighbor
connectivities
should be learnt, or whether the Voronoi cells should be saved. Here we
enter 2 to save the connectivities to file 5_rnap1.qpsf.
We do not wish to save the Voronoi cells (enter 1).
Here is the
output of the entire
qpdb calculation:
% ./qpdb
0_rnap1.pdb 5_rnap1.qpdb
lib_pio> 10760
atoms read.
...qpdb> Found
0 hydrogens, 0 water atoms, 0 codebook vectors, 0
density atoms
...qpdb> Do you
want to mass-weight the atoms ?
...qpdb>
...qpdb> 1: No
...qpdb> 2: Yes
...qpdb> 2
...qpdb> Do you
want to select atoms based on a B-factor threshold?
...qpdb>
...qpdb> 1: No
...qpdb> 2: Yes
...qpdb> 1
...qpdb> 10760
equally weighted inputs out of originally 10760 atoms
selected for conversion.
...qpdb>
...qpdb>
Sphericity of the atomic structure: 0.20
...qpdb> Enter
desired number of codebook vectors for data
quantization: (0 to exit): 15
...qpdb>
Computing 8 datasets, 100000 iterations each...
...qpdb> Now
producing dataset 1
...qpdb> Now
producing dataset 2
...qpdb> Now
producing dataset 3
...qpdb> Now
producing dataset 4
...qpdb> Now
producing dataset 5
...qpdb> Now
producing dataset 6
...qpdb> Now
producing dataset 7
...qpdb> Now
producing dataset 8
...qpdb>
...qpdb>
Codebook vectors have been written to file 5_rnap1.qpdb
...qpdb> The
PDB B-factor field contains the equivalent spherical
radii
...qpdb> of the
corresponding Voronoi cells (in Angstrom).
...qpdb>
Cluster analysis of the 8 independent calculations:
...qpdb> The
PDB occupancy field in 5_rnap1.qpdb contains the rms
variabilities of the vectors.
...qpdb>
Average rms fluctuation of the 15 codebook vectors: 3.732 Angstrom
...qpdb> Radius
of gyration of the 15 codebook vectors: 41.810
Angstrom
...qpdb>
...qpdb> Do you
want to learn nearest-neighbor connectivities?
...qpdb> Choose
one of the following options -
...qpdb> 1: No.
...qpdb> 2:
Learn and save to a PSF
file
...qpdb> 3:
Learn and save to a
constraints file
...qpdb> 4:
Learn and save to both PSF
and constraints files
...qpdb> 2
...qpdb> Enter
PSF filename: 5_rnap1.qpsf
...qpdb>
Connectivity data written to PSF file 5_rnap1.qpsf.
...qpdb>
...qpdb> Do you
want to save the Voronoi cells?
...qpdb> Choose
one of the following options -
...qpdb> 1: No.
I'm done
...qpdb> 2:
Yes. Save cells to a PDB
file
...qpdb> 1
...qpdb> Bye
bye..
|
|
| Assigning
Corresponding Vectors and Distance Constraints
We now have codebook vectors and the
distance information for the atomic structure. To proceed with the
flexible docking, two problems
must be solved:
- We need to
generate low-resolution vectors that are in correspondance with
the atomic ones, i.e. here we must form 15 pairs
of vectors that will be used as refinement parameters.
- Modeling of
the
skeleton. The distance
connectivity file 5_rnap1.qpsf contains connectivity information about
adjacent high-resolution vectors. This file is only a starting point.
E.g. enforcing all of these constraints
would
make the structure rather rigid, so we must select a sparse set of
non-redundant
distances, i.e. a skeleton, that enables flexible fitting.
There is no
automated
Situs routine for assigning corresponding vectors and for modeling the
skeleton. It is recommended to select these vectors by visual
inspection
with a graphics program.
Vector
connectivities in PSF format
(recognized by Molecular Dynamics related programs such as VMD, CHARMM,
X-PLOR, CNS, NAMD) can be visualized and edited as bond connections
(together with the
corresponding codebook vector PDB file) using the molecular graphics
program VMD. Here we
overload
the
PSF file into the PDB file in the VMD command console:
mol load pdb
5_rnap1.qpdb psf 5_rnap1.qpsf
mol load pdb 0_rnap1.pdb
mol modstyle 0 1 Tube 0 1
mol modcolor 0 0 ColorID 10
mol modcolor 0 1 ColorID 2
display projection orthographic
|
Then
rotate your molecule such that it is oriented as in the figures below
(you should recognize the pattern):
(click images to enlarge)
Then toggle the display of molecule 0_rnap1.pdb (in the VMD Molecule menu)
so that only the blue connectivities remain. Don't rotate the molecule. Under the
'Mouse' menu select 'Add/Remove Bonds'. Remove any "red" bonds shown
above by clicking on both end points. Then add the "green" bonds the
same way. You should have a proper balance
between freedom of motion and stability of the skeleton. This takes
some experience, trial and error. The blue connectivities give a
reasonable fit that can be improved later. The edited
connectivity can then be saved into a PSF file from the VMD
command console (assuming your connectivity molecule
is still 'top'):
set sel
[atomselect top all]
$sel writepsf 6_rnap1.qpsf
|
|
| LBG
Vector Quantization of the Low-Resolution Map
Now that the
skeleton connectivities have been
determined, the skeleton distances can be enforced with the local LBG
optimization algorithm of the qvol
utility.
After entering
./qvol
0_rnap2.situs 5_rnap1.qpdb
7_rnap2.qvol
|
the user is
prompted to enter
the density cutoff value. We enter the approximate surface threshold,
50. The start vectors are taken
from file 5_rnap1.qpdb and the user has the choice
optimization with LBG (enter 1) and of assigning vector distances. We
read them from the file 6_rnap1.qpsf
(option 3). Finally, the user is asked whether
nearest-neighbor connectivities should be learnt, we don't need this
option at the moment (enter 1). The file 7_rnap2.qvol
now contains the newly placed "QVOL" codebook vectors with the distance
constraints enforced. As an exercise you should load both this file and
6_rnap1.qpsf,
together with 0_rnap2.situs into VMD:
(click image to enlarge)
Below is the
output of the entire
qvol LBG calculation. LBG is an iterative "gradient descent" method
that converges slowly, whereas
TRN (without the second argument as start vectors) uses a prespecified
number of calculations. The additional SHAKE statements
describe the convergence of the distance constraints:
% ./qvol
0_rnap2.situs 5_rnap1.qpdb 7_rnap2.qvol
lib_vio> File 0_rnap2.situs - Header information:
lib_vio> Columns, rows, and sections: x=1-44, y=1-47, z=1-45
lib_vio> 3D coordinates of first voxel (1,1,1):
(140.000000,12.000000,0.000000)
lib_vio> Voxel size in Angstrom: 4.000000
lib_vio> Reading density data...
lib_vio> Volumetric data read from file 0_rnap2.situs
...qvol> Density values below a user-defined cutoff value will not
be considered
...qvol> Do you want to inspect the input density values before
entering the cutoff value?
...qvol> Choose one of the following three options -
...qvol> 1: No (continue)
...qvol> 2: Show me the minimum and
maximum density values only
...qvol> 3: Show me the voxel histogram
...qvol> 1
...qvol> Now enter the cutoff density value: 50
...qvol> Cutting off density values < 50.000000, remaining
occupied volume: 10005 voxels (6.403200e+05 Angstrom^3)
lib_pio> 15 atoms read.
...qvol> Do you want to optimize the start vectors or skip and
proceed to the connectivity analysis?
...qvol> Choose one of the following two options -
...qvol> 1: Optimize start vectors
with LBG
...qvol> 2: Skip and proceed directly
to connectivity analysis
...qvol> 1
...qvol>
...qvol> Using start vectors from file 5_rnap1.qpdb.
...qvol>
...qvol> Vector distance constraints restrict undesired degrees of
freedom.
...qvol> Do you want to add distance constraints?
...qvol> Choose one of the following three options -
...qvol> 1: No
...qvol> 2: Yes. I want to enter them
manually
...qvol> 3: Yes. I want to read
connectivities from a file and use start vector distances
...qvol> 4: Yes. I want to read them
from a Situs constraints file
...qvol> 3
...qvol> Enter filename: 6_rnap1.qpsf
...qvol> 30 connectivities read from file 6_rnap1.qpsf
...qvol> The corresponding distances were assigned from file
5_rnap1.qpdb
...qvol> Distance preconditioning step 1 -- 48 SHAKE distance
iterations
...qvol> Distance preconditioning step 2 -- 39 SHAKE distance
iterations
...qvol> Distance preconditioning step 3 -- 37 SHAKE distance
iterations
...qvol> Distance preconditioning step 4 -- 40 SHAKE distance
iterations
...qvol> Distance preconditioning step 5 -- 39 SHAKE distance
iterations
...qvol> Distance preconditioning step 6 -- 37 SHAKE distance
iterations
...qvol> Distance preconditioning step 7 -- 35 SHAKE distance
iterations
...qvol> Distance preconditioning step 8 -- 34 SHAKE distance
iterations
...qvol> Distance preconditioning step 9 -- 33 SHAKE distance
iterations
...qvol> Distance preconditioning step 10 -- 33 SHAKE distance
iterations
...qvol> Starting standard LBG vector quantization.
...qvol> It. 1 -- 53 SHAKE distance iterations
...qvol> It. 1 -- Average vector update: 6.108390e-01 Angstrom
...qvol> It. 2 -- 48 SHAKE distance iterations
...qvol> It. 2 -- Average vector update: 5.948577e-01 Angstrom
...qvol> It. 3 -- 48 SHAKE distance iterations
...qvol> It. 3 -- Average vector update: 5.773613e-01 Angstrom
...qvol> It. 4 -- 49 SHAKE distance iterations
...qvol> It. 4 -- Average vector update: 5.605641e-01 Angstrom
...qvol> It. 5 -- 52 SHAKE distance iterations
...qvol> It. 5 -- Average vector update: 5.440111e-01 Angstrom
...
...qvol> It. 118 -- 89 SHAKE distance iterations
...qvol> It. 118 -- Average vector update: 1.105221e-02 Angstrom
...qvol> It. 119 -- 89 SHAKE distance iterations
...qvol> It. 119 -- Average vector update: 9.938773e-03 Angstrom
...qvol>
...qvol> Final clustering -- 71 SHAKE distance iterations
...qvol> Final clustering -- Average vector update: 2.273772e-03
Angstrom
...qvol> Final clustering -- 71 SHAKE distance iterations
...qvol> Final clustering -- Average vector update: 2.607668e-07
Angstrom
...qvol>
...qvol> Codebook vectors have been written to file 7_rnap2.qvol
...qvol> The PDB B-factor field contains the equivalent spherical
radii
...qvol> of the corresponding Voronoi cells (in Angstrom).
...qvol> Radius of gyration of the 15 codebook vectors: 42.462
Angstrom
...qvol>
...qvol> Do you want to update or save the input connectivities?
...qvol> Choose one of the following options -
...qvol> 1: No. I'm done
...qvol> 2: Update and save to a PSF
file
...qvol> 3: Update and save to a
constraints file
...qvol> 4: Update and save to both
PSF and constraints files
...qvol> 5: Just save (don't update)
to a PSF file
...qvol> 1
...qvol> Bye bye!
|
|
Flexible,
Skeleton-Based Docking with Interpolation
As described earlier, the
flexible docking is performed here in an approximative way by
interpolation from the 15 pairs of codebook vectors.
To start the qplasty optimization,
enter at the shell prompt
| ./qplasty 0_rnap1.pdb
5_rnap1.qpdb 7_rnap2.qvol 8_flexed_rnap.pdb |
The flexed
structure will be written
to the file 8_flexed_rnap.pdb.
|
Visualization
The following sequence of commands
in the VMD text console (cf. VMD
user guide) will load the original and flexibly docked rnap
structures, 0_rnap1.pdb (red) and 8_flexed_rnap.pdb (green), and
render them in colored tube representation. The script also renders the
target density map 0_rnap2.situs in gray:
mol
load
pdb 8_flexed_rnap.pdb
mol load
pdb 0_rnap1.pdb
mol load
situs 0_rnap2.situs
mol top 0
rotate stop
display
resetview
display
projection orthographic
mol modstyle
0 0 Tube 0.3 6
mol modstyle
0 1 Tube 0.3 6
mol modstyle
0 2 Isosurface 50 0 0 1 2 1
mol
modcolor 0 0 ColorID 7
mol
modcolor 0 1 ColorID 1
mol
modcolor 0 2 ColorID 2
|
The final result
should look like this:
(click image to
enlarge)
Note
that some density regions are not optimally filled by the flexed
structure. As an exercise, manually edit the connectivities or codebook
vector positions to optimize the fit.
|
| Return
to the front page . |
|
