|
SAXS Tutorial
|
| The tutorial
teaches the modeling and visualizaton
of low resolution bead models
of
protein structures derived from small angle X-ray scattering. The
results
can be compared to solutions distributed with the tutorial software. In
the demonstration below we use two cross-correlation based rigid body
strategies for the docking. However, the user may employ also
other fitting strategies as discussed under Outlook.
Once density maps are created, the rigid-body and flexible docking of
structures
to SAXS bead models is very similar to the approach used for electron
microscopy
maps. More documentation is available in the user
guide, in the Methodology page, and in
the published articles. |
|
Content:
|
| Download
and Installation
Follow first the
simple registration
and download steps .
In addition to
the executables, the
Situs_2.3_saxs_tutorial/bin
directory contains four data files:
- 0_tnc.pdb:
Atomic coordinates
of troponin C.
- 0_rib.pdb:
Atomic coordinates
of ribonuclease inhibitor.
- 0_tnc_sph.pdb:
Bead model
of troponin C.
- 0_rib_sph.pdb:
Bead model
of ribonuclease inhibitor.
Note that the bead
model files are
in PDB format, with the bead sphere radius in the occupancy field. In
the
following, we will perform various modeling tasks.
The user can compare all generated files to the files in the
"solutions"
directory.
|
Data
Flow and Design
The series
of steps and the utilities that are required for the modeling with
single-molecule SAXS bead models are shown
schematically
in the following figure. Bead models are expected to result
from experimental reconstructions. Simulated bead models for validation
of the modeling strategies can also be created with pdb2sax. Detailed program explanations are
given
in the user guide.

Schematic
diagram of SAXS related
routines. Major Situs components (blue) are classified by their
functionality.
The main data flow is indicated by brown arrows. The visualization
(orange) for the rendering of the bead models requires a molecular
graphics viewer (we
recommend the free VMD
graphics program, version
1.8.4 or higher; Chimera and Sculptor also support Situs
format).
Visualization and modeling of
atomic structures into SAXS bead models
are supported through a conversion into 3D volumes with the pdb2vol kernel convolution tool.
A docking between atomic structures to 3D maps can be achieved with a
number of approaches (see below). The resulting docked complex can be
inspected using a
molecular graphics viewer. The data can be prepared further
for the visualization using a variety of analysis and editing
tools. Kernel convolution facilitates the smoothing of bead surfaces
for
their visualization in the form of density isocontours.
|
Converting
Volumetric Bead Maps
The creation of simulated bead models
on a hexagonal lattice with pdb2sax
is straightforward and will not be discussed here in further detail. We assume that bead models are
already available from experimental reconstructions. We first convert SAXS
bead models to
volumetric Situs format with the pdb2vol
kernel convolution utility. Enter at the shell prompt:
| ./pdb2vol 0_rib_sph.pdb
1_rib_sph.situs |
Select no
mass-weighting (enter
1) and no B-factor thresholding (enter 1), then enter the desired voxel
spacing of the output map. Given the
dimensions
of the structure and the bead radius (6 Å), 1Å appears
to
be a good compromise between bead sampling accuracy and storage
requirement (you may have to adjust this value upwards for other cases
to avoid oversampling of beads and resulting large maps).
Next, enter the kernel width (bead radius): +6 Å. This is the
half-max
radius where the kernel amplitude drops to its half maximal
value.
Next, select the "Hard Sphere" smoothing kernel (enter 5). Turn lattice
correction off (enter 2), and enter the maximum amplitude of the kernel
(enter
1 and keep a note of this).
The program
projects the atomic
structure to the lattice, computes the hard sphere kernel, and carries
out the real-space convolution, writing the resulting map to the file
1_rib_sph.situs.
Now repeat this
calculation with
0_tnc_sph.pdb (troponin C), creating the map file 1_tnc_sph.situs. Note
that troponin C beads have a radius of only 4 Å!
Here is the full
pdblur session
for file 1_rib_sph.situs:
%
./pdb2vol 0_rib_sph.pdb
1_rib_sph.situs
lib_pio>
57 atoms read.
pdb2vol>
Found 0 hydrogens, 0 water atoms, 0 codebook vectors, 0 density atoms
pdb2vol>
Do you want to mass-weight the atoms ?
pdb2vol>
pdb2vol>
1: No
pdb2vol>
2: Yes
pdb2vol> 1
pdb2vol>
Do you want to select atoms based on a B-factor threshold?
pdb2vol>
pdb2vol>
1: No
pdb2vol>
2: Yes
pdb2vol> 1
pdb2vol>
57 out of 57 atoms selected for conversion.
pdb2vol>
pdb2vol>
The input structure measures 60.000 x 58.890 x 39.190 Angstrom
pdb2vol>
pdb2vol>
Please enter the desired voxel spacing for the output map (in
Angstrom): 1
pdb2vol>
pdb2vol>
Kernel width. Please enter (in Angstrom):
pdb2vol>
(as pos. value) kernel half-max radius or
pdb2vol>
(as neg. value) target resolution (2 sigma)
pdb2vol>
Now enter (signed) value: 6
pdb2vol>
pdb2vol>
Please select the type of smoothing kernel:
pdb2vol>
pdb2vol>
1: Gaussian, exp(-1.5 r^2 / sigma^2)
pdb2vol>
sigma = 8.826A, r-half = 6.000A, r-cut = 15.288A
pdb2vol>
pdb2vol>
2: Triangular, max(0, 1 - 0.5 |r| / r-half)
pdb2vol>
sigma = 7.589A, r-half = 6.000A, r-cut = 12.000A
pdb2vol>
pdb2vol>
3: Semi-Epanechnikov, max(0, 1 - 0.5 |r|^1.5 / r-half^1.5)
pdb2vol>
sigma = 6.139A, r-half = 6.000A, r-cut = 9.524A
pdb2vol>
pdb2vol>
4: Epanechnikov, max(0, 1 - 0.5 r^2 / r-half^2)
pdb2vol>
sigma = 5.555A, r-half = 6.000A, r-cut = 8.485A
pdb2vol>
pdb2vol>
5: Hard Sphere, max(0, 1 - 0.5 r^60 / r-half^60)
pdb2vol>
sigma = 4.629A, r-half = 6.000A, r-cut = 6.070A
pdb2vol> 5
pdb2vol>
pdb2vol>
Do you want to correct for lattice interpolation smoothing effects?
pdb2vol>
pdb2vol>
1: Yes (slightly lowers the kernel width to maintain target resolution)
pdb2vol>
2: No
pdb2vol> 2
pdb2vol>
pdb2vol>
Finally, please enter the desired kernel amplitude (scaling factor): 1
pdb2vol>
pdb2vol>
Projecting atoms to cubic lattice by trilinear interpolation...
pdb2vol>
... done. Lattice smoothing (sigma = atom rmsd): 0.679 Angstrom
pdb2vol>
pdb2vol>
Computing Hard Sphere kernel (no lattice correction) ...
pdb2vol>
... done. Kernel map extent 15 x 15 x 15 voxels
pdb2vol>
pdb2vol>
Convolving lattice with kernel...
pdb2vol>
... done. Spatial resolution (2 sigma) of output map: 9.356A
pdb2vol>
(slightly larger than target resolution due to uncorrected lattice
smoothing)
pdb2vol>
lib_vio>
Writing density data...
lib_vio>
Volumetric data written to file 1_rib_sph.situs
lib_vio>
File 1_rib_sph.situs - Header information:
lib_vio>
Columns, rows, and sections: x=1-80, y=1-78, z=1-59
lib_vio>
3D coordinates of first voxel (1,1,1):
(-42.000000,-37.000000,-27.000000)
lib_vio>
Voxel size in Angstrom: 1.000000
|
|
| Exhaustive Search
Docking
The colores
program performs an exhaustive search of all rigid-body degrees of
freedom.
This approach can be used for SAXS bead models, but care
must be taken in the case of SAXS to select volumetric correlation (option
"-corr 0"), since the default option (Laplacian filter) would
amplify the segmentation of the data caused by the SAXS beads. The use
of colores with EM data has already
been shown elsewhere, in
the correlation-based docking
tutorial.
As an example we perform
here an exhaustive rigid body docking of the above data with colores. For this
particular docking case
it will be sufficient to perform a reduced angular search (sampled at
the default 30°step size), and we set the target resolution to the
resolution of the bead model returned above by pdb2vol:
option "-res
9.356". After the exhaustive search is done, the best 6
on-lattice
maxima (option "-explor 6") will be refined (off-lattice) using
Powell optimization.
We start again with ribonuclease
inhibitor. We're using 2 processors on a dual CPU machine to speed up
the calculation. At the shell
prompt,
enter:
./colores
1_rib_sph.situs 0_rib.pdb -res 9.356
-corr 0 -explor 6 -nprocs 2
|
The output of colores has already been
described in detail in the corresponding tutorial.
We list here the
output of the entire
calculation as a reference:
%
./colores 1_rib_sph.situs 0_rib.pdb -res 9.356 -corr 0 -explor 6
-nprocs 2
_____________________________________________________________________________
colores>
Options read:
colores>
Target resolution 9.356
colores>
Resolution anisotropy 1.000
colores>
Low-resolution map cutoff 0.000
colores>
Grid size expansion factor 0.200
colores>
Standard (volumetric) correlation
colores>
Euler angles generation using Proportional method
colores>
Angular sampling accuracy 30.000
colores>
Euler angle range: [0.000:360.000] [0.000:180.000] [0.000:360.000]
colores>
Number of best fits explored 6
colores>
New peak search via filtering
colores>
Powell maximization ON
colores>
Powell tolerance 1.00E-06 Max iterations 25
colores>
Powell trans & rot initial step sizes set to default values
colores>
Powell correlation algorithm determined automatically
colores>
Peak sharpness estimation ON
colores>
Number of SMP processors requested: 2
_____________________________________________________________________________
colores>
Processing low-resolution map.
lib_vio>
File 1_rib_sph.situs - Header information:
lib_vio>
Columns, rows, and sectiord of (1,1,1) voxel): (-40.000,-35.000,-24.000)
lib_vwk>
Map density info: max 1.336620, min 0.000000, ave 0.731369, sig
0.356352.
_____________________________________________________________________________
colores>
Processing atomic structure.
lib_pio>
3411 atoms read.
colores>
COM: 13.592 37.670 18.081, radius: 40.402 Angstrom
_____________________________________________________________________________
lib_vwk>
Generating Gaussian kernel with 17^3 = 4913 voxels.
lib_vwk>
Generating Gaussian kernel with 27^3 = 19683 voxels.
lib_vwk>
Generating kernel with 17^3 = 4913 voxels.
lib_vwk>
Map size expanded from 75 x 73 x 53 to 129 x 125 x 95 by zero-padding.
lib_vwk>
New map origin (coord of (1,1,1) voxel): (-67.000,-61.000,-45.000)
colores>
Identifying inside or buried voxels and creating flipped mask...
colores>
Found 65521 inside or buried voxels (out of a total of 1531875).
colores>
Identifying inside or buried voxels...
colores>
Found 65521 inside or buried voxels (out of a total of 1531875).
colores>
Memory allocation for FFT.
colores>
FFT planning...
_____________________________________________________________________________
colores>
Testing the maps and correlations.
colores>
Projecting probe structure to lattice...
colores>
Low-pass-filtering probe map...
colores>
Target and probe maps:
lib_vwk>
Map density info: max 1.336620, min 0.000000,ons: x=1-80, y=1-78, z=1-59
lib_vio>
3D coordinates of first voxel (1,1,1):
(-42.000000,-37.000000,-27.000000)
lib_vio>
Voxel size in Angstrom: 1.000000
lib_vio>
Reading density data...
lib_vio>
Volumetric data read from file 1_rib_sph.situs
lib_vwk>
Setting density values below 0.000000 to zero.
lib_vwk>
Remaining occupied volume: 368160 voxels.
lib_vwk>
Map size reduced from 80 x 78 x 59 to 75 x 73 x 53.
lib_vwk>
New map origin (co ave 0.731369, sig
0.356352.
lib_vwk>
Map density info: max 0.888912, min 0.000000, ave 0.238482, sig
0.265116.
colores>
Projecting probe structure to lattice...
colores>
Applying filters to target and probe maps...
colores>
Normalizing target and probe maps...
colores>
Target and probe maps:
lib_vwk>
Map density info: max 7.706669, min 0.000000, ave 4.216920, sig
2.054652.
lib_vwk>
Map density info: max 7.062263, min 0.000000, ave 1.894701, sig
2.106307.
colores>
Computing correlation in direct space...
colores>
Correlation with structure centered in density map:
4.0550410E-01
colores>
Computing correlation in Fourier space...
colores>
FFT correlation with structure centered in density map:
4.0550410E-01
_____________________________________________________________________________
colores>
Getting Euler angles.
lib_eul>
Proportional Euler angles distribution, total number 552 (delta =
30.000000 deg.)
colores>
Total number of orientations sampled: 552
colores>
Euler angles saved in file col_eulers.dat.
_____________________________________________________________________________
colores>
Time of one FFT calculation: 558.529000 ms
colores>
Average time spent on each rotation: 1.930565 s
colores>
Estimated time for full 6D (on-lattice) search: 0 h 8 m 52 s
colores>
Off-lattice Powell optimization will take significant extra time.
_____________________________________________________________________________
colores>
Starting 6D on-lattice search with 3D FFT scan of Euler angles.
colores>
Searching using 2 processors
colores>
|##################################################|
552/552 | 100% done
colores>
Actual time spent on 6D on-lattice search: 0 h 9 m 17 s
_____________________________________________________________________________
colores>
Translation function peak detection.
colores>
Peak filter contrast: maximum 1.466482, sigma 0.220214
colores>
Contrast threshold: 0.366620, candidate peaks: 6442
colores>
Found 2038 non-redundant peaks.
_____________________________________________________________________________
colores>
Off-lattice search (Powell's optimization method).
colores>
Determining fastest correlation function...
colores>
Original algorithm: Correlation = -0.40325570 Time = 801.346500 ms
colores>
Masked algorithm: Correlation = -0.37685866 Time =
769.456000 ms
colores>
One-step algorithm: Correlation = -0.40387978 Time = 339.170000 ms
colores>
Using original three-step correlation function.
colores>
Using 2 processors in SMP mode.
colores>
Parallel Powell optimization: The order of maxima is not preserved in
the output.
colores>
Shown are: offset (in A) from reference center (-2.500,1.500,2.500),
colores>
Euler angles (in degrees), and correlation value.
colores>
colores>
Performing optimizations...
colores>
colores>
Powell optimization for score maximum no. 2.
colores>
X
Y
Z Psi
Theta Phi Correlation
colores>
2.000 1.000 -2.000 150.000 90.000
120.000 7.2017062E-01 Initial
colores>
0.837 -0.260 -2.957 147.826 100.196
119.984 7.4344796E-01 1
colores>
1.064 -0.614 -3.393 146.070 100.800
119.948 7.4503033E-01 2
colores>
1.361 -0.570 -3.398 144.720 100.859
120.043 7.4539065E-01 3
colores>
1.558 -0.554 -3.351 144.043 100.667
120.162 7.4553672E-01 4
colores>
1.586 -0.560 -3.346 144.065 100.639
120.179 7.4554444E-01 5
colores>
1.653 -0.566 -3.338 144.007 100.630
120.221 7.4554937E-01 6
colores>
1.652 -0.572 -3.339 144.005 100.631
120.216 7.4554958E-01 7
colores>
1.652 -0.572 -3.339 144.005 100.631
120.216 7.4554958E-01 Final
colores>
colores>
Powell optimization for score maximum no. 1.
colores>
X
Y
Z Psi
Theta Phi Correlation
colores>
2.000 -2.000 -2.000 150.000 90.000
120.000 7.2380030E-01 Initial
colores>
0.992 -0.714 -2.912 147.397 100.100
119.950 7.4391271E-01 1
colores>
1.127 -0.608 -3.377 145.893 100.763
119.950 7.4512706E-01 2
colores>
1.385 -0.550 -3.393 144.582 100.880
120.072 7.4541740E-01 3
colores>
1.514 -0.540 -3.357 144.2.300.668
120.143 7.4552242E-01 4
colores>
1.609 -0.551 -3.323 144.014 100.510
120.202 7.4554278E-01 5
colores>
1.615 -0.560 -3.325 144.176 100.504
120.238 7.4554497E-01 6
colores>
1.624 -0.565 -3.331 144.229 100.531
120.250 7.4554673E-01 7
colores>
1.627 -0.569 -3.336 144.2.300.537
120.251 7.4554735E-01 8
colores>
1.627 -0.569 -3.336 144.2.300.537
120.251 7.4554735E-01 Final
colores>
colores>
Powell optimization for score maximum no. 3.
colores>
X
Y
Z Psi
Theta Phi Correlation
colores>
2.000 -2.000 -5.000 150.000 90.000
120.000 7.1574640E-01 Initial
colores>
1.074 -0.482 -2.946 147.244 100.169
120.084 7.4413757E-01 1
colores>
1.155 -0.601 -3.382 145.715 100.680
120.047 7.4517064E-01 2
colores>
1.406 -0.545 -3.377 144.515 100.756
120.119 7.4544158E-01 3
colores>
1.546 -0.547 -3.340 144.142 100.623
120.150 7.4553421E-01 4
colores>
1.600 -0.550 -3.336 144.098 100.626
120.209 7.4554627E-01 5
colores>
1.604 -0.566 -3.336 144.033 100.629
120.205 7.4554756E-01 6
colores>
1.612 -0.571 -3.336 144.012 100.633
120.152 7.4554819E-01 7
colores>
1.612 -0.571 -3.336 144.012 100.633
120.152 7.4554819E-01 Final
colores>
colores>
Powell optimization for score maximum no. 4.
colores>
X
Y
Z Psi
Theta Phi Correlation
colores>
1.000 -4.000 -2.000 150.000 90.000
120.000 7.1089411E-01 Initial
colores>
1.091 -0.720 -2.917 147.207 100.152
120.118 7.4408655E-01 1
colores>
1.190 -0.615 -3.372 145.683 100.656
120.068 7.4520931E-01 2
colores>
1.408 -0.533 -3.374 144.536 100.721
120.133 7.4544507E-01 3
colores>
1.518 -0.559 -3.341 144.225 100.621
120.134 7.4552536E-01 4
colores>
1.600 -0.577 -3.327 144.200 100.598
120.196 7.4554599E-01 5
colores>
1.634 -0.564 -3.335 144.027 100.627
120.200 7.4554919E-01 6
colores>
1.636 -0.565 -3.335 144.026 100.628
120.200 7.4554925E-01 7
colores>
1.636 -0.565 -3.335 144.026 100.628
120.200 7.4554925E-01 Final
colores>
colores>
Powell optimization for score maximum no. 5.
colores>
X
Y
Z Psi
Theta Phi Correlation
colores>
4.000 0.000 -3.000 180.000 60.000
300.000 7.0387882E-01 Initial
colores>
2.733 -0.707 -2.647 180.253 58.785
293.652 7.2366609E-01 1
colores>
2.032 -0.522 -2.645 187.353 57.663
291.467 7.3116989E-01 2
colores>
0.502 -0.746 -2.906 193.829 58.599
289.965 7.3689413E-01 3
colores>
0.435 -0.893 -2.919 193.788 58.822
290.013 7.3695839E-01 4
colores>
0.430 -0.896 -2.934 193.783 58.831
290.007 7.3695933E-01 5
colores>
0.431 -0.896 -2.932 193.783 58.831
290.007 7.3695934E-01 6
colores>
0.431 -0.896 -2.932 193.783 58.831
290.007 7.3695934E-01 Final
colores>
colores>
Powell optimization for score maximum no. 6.
colores>
X
Y
Z Psi
Theta Phi Correlation
colores>
2.000 -3.000 0.000 150.000 90.000
120.000 7.0376503E-01 Initial
colores>
1.008 -1.009 -1.270 146.806 98.464
119.965 7.3342647E-01 1
colores>
1.252 -0.976 -2.536 145.586 100.521
119.984 7.4314829E-01 2
colores>
1.548 -0.564 -3.343 144.045 100.699
120.162 7.4553381E-01 3
colores>
1.627 -0.572 -3.343 143.979 100.637
120.162 7.4554842E-01 4
colores>
1.629 -0.574 -3.338 144.029 100.626
120.160 7.4554908E-01 5
colores>
1.629 -0.574 -3.338 144.029 100.626
120.160 7.4554908E-01 Final
colores>
colores>
Powell optimization time (6 runs): 1 h 50 m 25 s
colores>
Removing 4 redundant fits, keeping 2 unique fits.
___________________________________________________________________
colores>
Renormalizing correlation values by highest score.
colores>
Writing translation function lattice to Situs file.
lib_vio>
Writing density data...
lib_vio>
Volumetric data written to file col_trans.sit
lib_vio>
File col_trans.sit - Header information:
lib_vio>
Columns, rows, and sections: x=1-129, y=1-125, z=1-95
lib_vio>
3D coordinates of first voxel (1,1,1):
(-67.000000,-61.000000,-45.000000)
lib_vio>
Voxel size in Angstrom: 1.000000
colores>
Writing translation function lattice information to log file.
___________________________________________________________________
colores>
Saving the best results.
colores>
Estimating peak sharpness and writing best fit no. 1 to
file col_best_001.pdb.
colores>
Estimating peak sharpness and writing best fit no. 2 to
file col_best_002.pdb.
___________________________________________________________________
colores>
Output files:
col_best*.pdb => best docking results in PDB format with
info in header
col_eulers.dat => colores-readable list of Euler angles
col_rotate.log => Rotation function (unnormalized) log file
col_trans.log => Translation function (norm. by best
fit) log file
col_trans.sit => Translation function (norm. by best
fit) in Situs format
col_powell.log => Powell optimization log file
___________________________________________________________________
colores>
All done!
|
Note that 4 of the found results were
redundant so only two solutions remain. Note that each run of colores or colacor overwrites the col_* files in your
directory. Therefore, you should save these files after each run into a
separate subdirectory:
| mkdir exhaustive ; mv col_*
exhaustive |
As an additional exercise you
may do the same
for troponin C.
|
| Visualization
One of the problems with SAXS bead
models is the rendering of an outer contour that does not occlude the
interior. In the
following, we use again pdb2vol to create a low-resolution map from
the bead model, but this
time
we apply a "soft" smoothing kernel that will allow us to render a
smooth
envelope of the bead model surface without cluttering up the image with
individal spheres. For this we use the VMD
graphics program (version
1.8.4 or higher). Chimera and Sculptor also support Situs
format.
At the command
prompt, enter:
| ./pdb2vol 0_rib_sph.pdb
3_rib_sph.situs |
Select no
mass-weighting (enter
1), no B-factor threshold (enter 1) and enter the desired voxel spacing
of the output map. For the
visualization
we choose this time a larger voxel spacing of 2 Å. Next, enter
the kernel
width
(half-max radius): +6 Å. Next, select the Gaussian smoothing
kernel
(enter 1). Since we are using a larger grid spacing now select lattice
correction (enter 1), and enter the maximum
amplitude
of the kernel (enter 1 and keep a note of this).
The following
sequence of commands
in the VMD text console (cf. VMD user
guide ) will load the docked structure 2_rib_1.pdb and render
it in cartoon representation, coded by color. The script then instructs
VMD to render the file 3_rib_sph.situs:
mol load
pdb exhaustive/col_best_001.pdb
mol load
situs 3_rib_sph.situs
mol top 0
rotate stop
display
resetview
display
projection orthographic
mol modstyle
0 0 Cartoon 2.1 11
5
mol modstyle
0 1 Isosurface 0.5 0 0 1 2 1
mol modcolor
0 0 Structure
mol
modcolor 0 1 ColorID 0
|
The result
should look like the following figure. Note the smooth surface that
wraps around the beadmodel without penetrating into it:

(Click image to
enlarge)
Now inspect the
alternative solution col_best_002.pdb. The second ribonuclease
inhibitor
structure is "flipped" about the pseudo-symmetry axis of the U-shaped
molecule.
This kind of degeneracy of the best fit can be expected in the case of
symmetric shapes. One
should expect unique fits only in cases where the shape of the molecule
clearly determines the registration.
|
Manual Docking and
Refinement
In many fitting applications an expert
user may have a pretty good idea where to place a biomolecule.
Therefore, it is still quite popular to manually dock atomic structures
into low resolution maps. (In VMD one can move a
loaded molecule by selecting the menu Mouse -> Move -> Molecule,
then translate it with the mouse and rotate it by pressing the Shift
key; the new coordinates can then be saved by selecting File -> Save
Coordinates).
We support this
manual docking by providing a tool, colacor, that calculates the
cross correlation (as a way to provide quantitative feedback) and
performs a single optimization run to the nearest maximum of the
cross-correlation coefficient (if a refinement after manual docking is
desired). As with colores above, care
must be taken in the case of SAXS to select volumetric correlation (option
"-corr 0"), since the default option (Laplacian filter) would
amplify the segmentation of the data caused by the SAXS beads. colacor is essentially a stripped down
version of colores, but it does not center the input map
and PDB as in a global 6D search, instead it proceeds based on the
local geometry.
Inspection of the troponin C files
0_tnc.pdb and 1_tnc_sph.situs
reveals that 0_tnc.pdb is
slightly misplaced relative to the volumetric map, although the
structures do overlap. This is a good start situation for manual
refinement with colacor. Here we give the results of a colacor
run based on these two input files (note the -corr 0 and -sizef 0.5 for
avoiding limited initial overlap problems, and the resolution
-res 6.333 which is the value returned by the earlier pdb2vol
conversion of 1_tnc_sph.situs):
./colacor 1_tnc_sph.situs 0_tnc.pdb
-res 6.333 -corr 0 -sizef 0.5
_____________________________________________________________________________
colacor> Options read:
colacor> Target resolution 6.333
colacor> Resolution anisotropy 1.000
colacor> Powell correlation algorithm determined automatically
colacor> Low-resolution map cutoff 0.000
colacor> Powell maximization ON
colacor> Grid size expansion factor 0.500
colacor> Standard (volumetric) correlation
colacor> Powell tolerance 1.00E-06 Max iterations 25
colacor> Powell trans & rot initial step sizes set to default
values
_____________________________________________________________________________
colacor> Processing low-resolution map.
lib_vio> File 1_tnc_sph.situs - Header information:
lib_vio> Columns, rows, and sections: x=1-90, y=1-46, z=1-45
lib_vio> 3D coordinates of first voxel (1,1,1):
(-48.000000,-19.000000,-39.000000)
lib_vio> Voxel size in Angstrom: 1.000000
lib_vio> Reading density data...
lib_vio> Volumetric data read from file 1_tnc_sph.situs
lib_vwk> Setting density values below 0.000000 to zero.
lib_vwk> Remaining occupied volume: 186300 voxels.
lib_vwk> Map density info: max 1.142575, min 0.000000, ave 0.646634,
sig 0.367731.
_____________________________________________________________________________
colacor> Processing atomic structure.
lib_pio> 1271 atoms read.
colacor> COM: -0.731 2.042 1.980, radius: 36.731 Angstrom
_____________________________________________________________________________
lib_vwk> Generating Gaussian kernel with 11^3 = 1331 voxels.
lib_vwk> Generating Gaussian kernel with 19^3 = 6859 voxels.
lib_vwk> Generating kernel with 11^3 = 1331 voxels.
lib_vwk> Map size expanded from 90 x 46 x 45 to 144 x 94 x 93 by
zero-padding.
lib_vwk> New map origin (coord of (1,1,1) voxel):
(-75.000,-43.000,-63.000)
colacor> Projecting probe structure to lattice...
colacor> Computing fraction of PDB contained within the map (above
cutoff density) ...
colacor> Overlap fraction: 1.1210593E-01
colacor> Warning: Less than half of the input PDB is contained
within the map!
colacor> Applying filters to target and probe maps...
colacor> Normalizing target and probe maps...
colacor> Target and probe maps:
lib_vwk> Map density info: max 9.854325, min 0.000000, ave 5.577000,
sig 3.171556.
lib_vwk> Map density info: max 12.963925, min 0.000000, ave
2.800532, sig 3.306156.
colacor> Computing correlation value ...
colacor> Correlation value: 9.4975131E-02
_____________________________________________________________________________
colacor> Identifying inside or buried voxels...
colacor> Found 29788 inside or buried voxels (out of a total of
1258848).
colacor> Powell's optimization method.
colacor> Determining fastest correlation function...
colacor> Original algorithm: Correlation =
-0.10394427 Time = 51.405500 ms
colacor> Masked algorithm: Correlation
= -0.08669810 Time = 43.978500 ms
colacor> One-step algorithm: Correlation =
-0.10394609 Time = 21.852000 ms
colacor> Using original three-step correlation function.
colacor> Shown are: offset (in A) from reference center
(-3.000,4.000,-16.500),
colacor> Euler angles (in degrees), and correlation value.
colacor>
colacor> Performing optimizations...
colacor>
colacor> Powell optimization
colacor> X
Y
Z Psi
Theta Phi Correlation
colacor> 0.000 0.000
0.000 0.000 0.000
0.000 9.4975131E-02 Initial
colacor> -1.032 -1.254 -1.261 12.330
-4.039 2.313 1.4519657E-01 1
colacor> 1.949 -3.211 -1.971
9.831 -14.848 6.502 1.7328373E-01 2
colacor> 4.011 -6.074 -3.061
9.346 -45.961 2.042 2.0509940E-01 3
colacor> 1.458 -7.180 -3.668 17.412
-39.793 -3.288 2.3513902E-01 4
colacor> -0.159 -7.805 -4.612 26.679 -32.417
-19.213 2.5908911E-01 5
colacor> -0.123 -8.814 -6.306 38.161 -46.973
-33.870 3.0745488E-01 6
colacor> -0.140 -8.945 -7.126 42.410 -48.590
-35.654 3.2619263E-01 7
colacor> -1.325 -7.790 -9.069 54.285 -43.789
-40.911 3.6114242E-01 8
colacor> -0.965 -7.014 -10.459 64.302 -32.914
-50.010 3.7981803E-01 9
colacor> 0.957 -4.130 -16.037 103.995
9.719 -98.146 5.3222052E-01 10
colacor> 2.351 -3.289 -17.509 109.815
8.594 -103.848 5.7116303E-01 11
colacor> 3.317 -2.474 -19.099 116.936
6.569 -112.326 5.9388999E-01 12
colacor> 3.212 -2.343 -19.331 118.381
5.935 -114.200 5.9653099E-01 13
colacor> 2.892 -1.987 -19.581 120.267
4.679 -117.086 5.9968876E-01 14
colacor> 2.857 -1.866 -19.566 120.267
4.878 -116.890 6.0022909E-01 15
colacor> 2.726 -1.423 -19.387 119.474
5.332 -115.413 6.0112616E-01 16
colacor> 2.712 -1.392 -19.376 119.346
5.120 -115.168 6.0120951E-01 17
colacor> 2.704 -1.375 -19.338 119.085
4.959 -114.849 6.0124580E-01 18
colacor> 2.705 -1.373 -19.336 119.061
4.927 -114.818 6.0124667E-01 19
colacor> 2.706 -1.373 -19.337 119.067
4.934 -114.832 6.0124681E-01 20
colacor> 2.706 -1.373 -19.337 119.067
4.934 245.168 6.0124681E-01 Final
colacor>
colacor> Powell optimization time: 0 h 7 m 34 s
_____________________________________________________________________________
colacor> Writing result to file col_best_001.pdb.
_____________________________________________________________________________
colacor> All done!!!
|
The program output shows how the
initial correlation of 0.1 increases to 0.6 while the structure is
matched. The output is again written to the file col_best_001.pdb. As
before, we create a directory "manual" and move the col_* files into it.
When inspected
with VMD as above the results should look similar to the following
figure:

(Click image to
enlarge)
|
| Outlook:
Alternative Fitting Strategies
Using simulated markers (feature points)
for docking
The programs qpdb, qvol,
qdock are specialized tools that
perform vector quantization based docking
for a given number of feature vectors (simulated markers).
Most of the functionality of these routines is included in the combined
qrange
tool.
The
usage of these routines is demonstrated elsewhere
in the context of electron microscopy docking, but are also applicable
to SAXS.
Flexible
docking
It is well known
that proteins
can adopt a solution conformations that deviate from a known crystal
structure.
Consider e.g. the case of calmodulin which was first shown by SAXS to
compact
in solution (Heidorn & Trewhella, Biochemistry 1988 Feb 9; 27(3):
909-15)
and whose first solved crystal structure was not in the
"physiologically
relevant" conformation. For cases like this the flexible docking tools
described in the flexible docking tutorial,
although developed with electron microscopy in mind, may also become
very useful to SAXS modelers.
|
| Return
to the front page . |
|