SAXS Tutorial
The tutorial teaches the modeling and visualization 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
First, follow these registration and download steps (each Situs tutorial is separate and must be downloaded and compiled individually)!

Then, return to this page.

The Situs_2.8_saxs_tutorial/bin directory will contain the executables as well as four input data files and an executable shell script:

  • 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.
  • run_tutorial.bash: Bash shell script containing all commands of this tutorial.

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 use here the VMD graphics program, 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 ┼), 1┼ 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 ┼. 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.

Here is the full pdblur session for file 1_rib_sph.situs. You can also automate this  procedure in a script by overloading the expected input (see run_tutorial.bash for details):

./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> Situs formatted map 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: (-42.000000,-37.000000,-27.000000)
lib_vio> Voxel size in Angstrom: 1.000000


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 ┼. See run_tutorial.bash.
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 a possible 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 core 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> Standard cross correlation
colores> FFT grid size expansion factor 0.100 (thickness of additional zero layer as fraction of map dimensions)
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> Sculptor mode OFF
colores> Number of best fits explored  6
colores> Original peak search by sort and filter
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> Situs formatted map 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: (-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> Map interpolated from 80 x 78 x 59 to 33 x 33 x 25.
lib_vwk> Voxel spacings interpolated from (1.000,1.000,1.000) to (2.339,2.339,2.339).
lib_vwk> New map origin (coord of first voxel), in register with coordinate system origin: (-39.763,-35.085,-25.729)
lib_vwk> Setting density values below 0.000000 to zero.
lib_vwk> Remaining occupied volume: 27225 voxels.
lib_vwk> Map size changed from 33 x 33 x 25 to 33 x 31 x 23.
lib_vwk> New map origin (coord of first voxel): (-39.763,-32.746,-23.390)
lib_vwk> Map density info: max 1.200882, min 0.000000, ave 0.170563, sig 0.312096.
_____________________________________________________________________________
colores> Processing atomic structure.
lib_pio> 3411 atoms read.
colores> Geometric center: 13.643 37.649 18.051, radius: 40.408 Angstrom
_____________________________________________________________________________
lib_vwk> Generating Gaussian kernel with 7^3 = 343 voxels.
lib_vwk> Generating Gaussian kernel with 11^3 = 1331 voxels.
lib_vwk> Generating kernel with 7^3 = 343 voxels.
lib_vwk> Map size expanded from 33 x 31 x 23 to 47 x 45 x 35 by zero-padding.
lib_vwk> New map origin (coord of first voxel): (-56.136,-49.119,-37.424)
colores> Identifying inside or buried voxels and creating flipped mask...
colores> Found 4041 inside or buried voxels (out of a total of 74025).
colores> Identifying inside or buried voxels...
colores> Found 4041 inside or buried voxels (out of a total of 74025).
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 1.200882, min 0.000000, ave 0.054214, sig 0.203321.
lib_vwk> Map density info: max 11.054224, min 0.000000, ave 0.614863, sig 1.850482.
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 5.541246, min 0.000000, ave 0.250160, sig 0.938185.
lib_vwk> Map density info: max 5.463697, min 0.000000, ave 0.303904, sig 0.914625.
colores> Writing target and probe maps for inspection or debugging...
lib_vio> Writing density data...
lib_vio> Volumetric data written in Situs format to file col_hi_fil.sit
lib_vio> Situs formatted map file col_hi_fil.sit - Header information:
lib_vio> Columns, rows, and sections: x=1-47, y=1-45, z=1-35
lib_vio> 3D coordinates of first voxel: (-56.136000,-49.119000,-37.424000)
lib_vio> Voxel size in Angstrom: 2.339000
lib_vio> Writing density data...
lib_vio> Volumetric data written in Situs format to file col_lo_fil.sit
lib_vio> Situs formatted map file col_lo_fil.sit - Header information:
lib_vio> Columns, rows, and sections: x=1-47, y=1-45, z=1-35
lib_vio> 3D coordinates of first voxel: (-56.136000,-49.119000,-37.424000)
lib_vio> Voxel size in Angstrom: 2.339000
colores> Computing correlation between maps in direct space...
colores> Correlation with structure centered in density map:   4.1225703E-01
colores> Computing correlation in Fourier space...
colores> FFT correlation with structure centered in density map:   4.1225703E-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: 6.597000 ms
colores> Average time spent on each rotation: 16.877600 ms
colores> Estimated time for full 6D (on-lattice) search: 4.658218 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: 8.505492 s
_____________________________________________________________________________
colores> Translation function peak detection.
colores> Peak filter contrast: maximum 2.217902, sigma 0.400741
colores> Contrast threshold: 0.554475, candidate peaks: 554
colores> Found 168 non-redundant peaks.
_____________________________________________________________________________
colores> Off-lattice search (Powell's optimization method).
colores> Determining most efficient correlation algorithm based on convergence and time...
colores>    Original algorithm: Correlation = 0.41891119  Time = 3.727500 ms
colores>    Masked algorithm:   Correlation = 0.33195710  Time = 3.631000 ms
colores>    One-step algorithm: Correlation = 0.41907229  Time = 6.050000 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 (-1.169,3.508,3.508),
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>   2.339  -4.678  -4.678 150.000  90.000 120.000    7.2495764E-01 Initial
colores>  -0.303  -2.663  -3.804 147.314 100.244 120.322    7.6652249E-01 1
colores>  -0.116  -2.617  -4.290 145.170 100.816 120.054    7.6795897E-01 2
colores>   0.079  -2.640  -4.265 144.752 100.707 120.004    7.6810865E-01 3
colores>   0.119  -2.542  -4.245 144.666 100.578 119.991    7.6813893E-01 4
colores>   0.119  -2.549  -4.245 144.671 100.578 119.989    7.6813929E-01 5
colores>   0.119  -2.549  -4.245 144.671 100.578 119.989    7.6813929E-01 Final
colores>
colores> Powell optimization for score maximum no.  1.
colores>   X       Y       Z       Psi     Theta   Phi      Correlation
colores>   2.339  -4.678  -2.339 180.000  60.000 300.000    7.2601146E-01 Initial
colores>   0.734  -3.122  -3.567 181.789  59.488 293.147    7.4924440E-01 1
colores>   0.492  -2.697  -3.699 188.064  57.820 291.198    7.5499423E-01 2
colores>  -0.619  -2.532  -3.939 192.661  57.826 290.023    7.5910809E-01 3
colores>  -0.777  -2.770  -3.877 193.196  58.068 290.045    7.5942694E-01 4
colores>  -0.816  -2.874  -3.891 193.398  58.565 290.008    7.5948509E-01 5
colores>  -0.870  -2.946  -3.919 193.683  58.713 289.896    7.5952242E-01 6
colores>  -0.893  -2.957  -3.911 193.671  58.714 289.890    7.5952748E-01 7
colores>  -0.892  -2.957  -3.913 193.671  58.714 289.890    7.5952750E-01 8
colores>  -0.892  -2.957  -3.913 193.671  58.714 289.890    7.5952750E-01 Final
colores>
colores> Powell optimization for score maximum no.  3.
colores>   X       Y       Z       Psi     Theta   Phi      Correlation
colores>   4.678  -2.339  -2.339 120.000  90.000 120.000    7.0052552E-01 Initial
colores>   3.625  -1.707  -3.065 135.528 100.170 122.590    7.4422417E-01 1
colores>   1.397  -2.290  -3.871 141.039  99.884 120.912    7.6534903E-01 2
colores>   0.127  -2.485  -4.242 144.794 100.571 119.988    7.6811939E-01 3
colores>   0.128  -2.579  -4.243 144.740 100.571 119.981    7.6813917E-01 4
colores>   0.130  -2.574  -4.243 144.742 100.571 119.982    7.6813926E-01 5
colores>   0.130  -2.574  -4.243 144.742 100.571 119.982    7.6813926E-01 Final
colores>
colores> Powell optimization for score maximum no.  4.
colores>   X       Y       Z       Psi     Theta   Phi      Correlation
colores>   4.678   2.339   0.000 108.000 120.000 120.000    6.5674961E-01 Initial
colores>   3.683  -0.639  -2.610 124.278 103.785 125.292    7.3451722E-01 1
colores>   2.633  -1.449  -3.418 135.307  99.906 121.989    7.5425408E-01 2
colores>   0.671  -2.538  -4.082 141.777 101.419 120.344    7.6748934E-01 3
colores>   0.405  -2.615  -4.308 143.719 100.935 120.064    7.6791881E-01 4
colores>   0.126  -2.523  -4.277 144.651 100.634 120.003    7.6813210E-01 5
colores>   0.120  -2.556  -4.247 144.657 100.594 119.998    7.6813902E-01 6
colores>   0.124  -2.554  -4.248 144.670 100.585 119.996    7.6813930E-01 7
colores>   0.124  -2.554  -4.248 144.670 100.585 119.996    7.6813930E-01 Final
colores>
colores> Powell optimization for score maximum no.  5.
colores>   X       Y       Z       Psi     Theta   Phi      Correlation
colores>  -4.678  -9.356  -4.678 216.000  60.000 270.000    6.4289230E-01 Initial
colores>  -1.884  -3.350  -4.554 210.826  47.059 279.904    7.3771509E-01 1
colores>  -1.612  -3.166  -4.290 206.022  52.989 283.709    7.4682258E-01 2
colores>  -1.621  -3.400  -3.916 199.130  58.790 287.895    7.5662388E-01 3
colores>  -1.355  -3.248  -3.850 197.525  58.590 288.544    7.5803446E-01 4
colores>  -0.906  -2.920  -3.889 193.943  58.470 289.803    7.5950836E-01 5
colores>  -0.922  -2.911  -3.904 193.803  58.633 289.864    7.5951913E-01 6
colores>  -0.908  -2.949  -3.912 193.735  58.714 289.900    7.5952662E-01 7
colores>  -0.910  -2.954  -3.911 193.735  58.714 289.900    7.5952682E-01 8
colores>  -0.910  -2.954  -3.911 193.735  58.714 289.900    7.5952682E-01 Final
colores>
colores> Powell optimization for score maximum no.  6.
colores>   X       Y       Z       Psi     Theta   Phi      Correlation
colores>   2.339   4.678   0.000 144.000  60.000 300.000    6.3339013E-01 Initial
colores>   2.711   1.663  -2.931 162.393  52.646 297.109    7.0955659E-01 1
colores>   1.742  -1.054  -3.399 172.749  54.899 294.759    7.3971360E-01 2
colores>   0.250  -3.683  -3.871 186.763  58.300 291.658    7.5333631E-01 3
colores>  -0.310  -3.659  -3.970 190.441  58.829 291.047    7.5683888E-01 4
colores>  -0.797  -3.218  -3.787 192.449  58.942 290.514    7.5918823E-01 5
colores>  -0.810  -3.122  -3.877 192.778  58.965 290.301    7.5939956E-01 6
colores>  -0.849  -3.036  -3.915 193.166  58.900 290.067    7.5949853E-01 7
colores>  -0.883  -2.968  -3.941 193.501  58.806 289.926    7.5951907E-01 8
colores>  -0.893  -2.973  -3.947 193.595  58.793 289.937    7.5952157E-01 9
colores>  -0.892  -2.967  -3.949 193.615  58.773 289.925    7.5952213E-01 10
colores>  -0.892  -2.967  -3.949 193.615  58.773 289.925    7.5952213E-01 Final
colores>
colores> Powell optimization time (6 runs): 34.629978 s
colores> Removing 4 redundant fits, keeping 2 unique fits.
_____________________________________________________________________________
colores> Renormalizing correlation values by highest score.
colores> Writing translation function lattice to density file in Situs format.
lib_vio> Writing density data...
lib_vio> Volumetric data written in Situs format to file col_trans.sit
lib_vio> Situs formatted map file col_trans.sit - Header information:
lib_vio> Columns, rows, and sections: x=1-47, y=1-45, z=1-35
lib_vio> 3D coordinates of first voxel: (-56.136000,-49.119000,-37.424000)
lib_vio> Voxel size in Angstrom: 2.339000
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_lo_fil.sit     => Filtered target volume in Situs format, just prior to correlation calculation
   col_hi_fil.sit     => Filtered (and centered) probe structure in Situs format, just prior to correlation calculation
   col_powell.log     => Powell optimization log file
_____________________________________________________________________________
colores> All done!

Note that four of the found results were redundant so only two solutions remain. Also, note that each run of colores overwrites the col_* files in your directory. Therefore, you should save these files after each run into a separate subdirectory:

mkdir 2_exhaustive ; mv col_* 2_exhaustive

As an optional exercise (not in the solutions directory) 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. We show the results with the VMD graphics program. 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 ┼. Next, enter the kernel width (half-max radius): +6 ┼. 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 (this is arbitrary, we use here an amplitude of 1).

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 volumetric map 3_rib_sph.situs by its isocontour value 0.5 (the suggested isocontour value, which can be adjusted in an intensity range slider, is half of the kernel amplitude chosen above):

mol load pdb 2_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


Don't forget to hit "enter" after the last line!

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)

(You can change the rendering style and transparency of the wrapped isocontour and PDB in the VMD Graphics menu).

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.

As an additional exercise you may do the same for troponin C using a 4┼ bead radius.

Manual Docking and Refinement

In many fitting applications an expert user may have a pretty good idea where to place a biomolecule. Therefore, manu users wish 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 refinement tool, collage, that 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 always select standard correlation (option "-corr 0"), since a possible default option (Laplacian filter) would amplify the segmentation of the data caused by the SAXS beads. collage can take one or more PDB files as input.

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 collage. Here we give the results of a collage run based on these two input files (note the -corr 0 and the resolution -res 6.333 which is the value returned by the earlier pdb2vol conversion of 1_tnc_sph.situs):

./collage 1_tnc_sph.situs 0_tnc.pdb -res 6.333 -corr 0
_____________________________________________________________________________
collage> Options read:
collage> Target resolution 6.333
collage> Resolution anisotropy 1.000
collage> Powell correlation algorithm determined automatically
collage> Low-resolution map cutoff 0.000
collage> Powell maximization ON
collage> Standard cross correlation
collage> Powell tolerance 1.00E-06  Max iterations 50
collage> Powell trans & rot initial step sizes set to default values
_____________________________________________________________________________
collage> Processing low-resolution map.
lib_vio> Situs formatted map 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: (-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> Map interpolated from 90 x 46 x 45 to 56 x 29 x 28.
lib_vwk> Voxel spacings interpolated from (1.000,1.000,1.000) to (1.583,1.583,1.583).
lib_vwk> New map origin (coord of first voxel), in register with coordinate system origin: (-47.498,-18.999,-37.998)
lib_vwk> Setting density values below 0.000000 to zero.
lib_vwk> Remaining occupied volume: 45472 voxels.
lib_vwk> Map size changed from 56 x 29 x 28 to 55 x 27 x 25.
lib_vwk> New map origin (coord of first voxel): (-47.498,-17.416,-36.415)
lib_vwk> Map density info: max 1.016194, min 0.000000, ave 0.133514, sig 0.273129.
_____________________________________________________________________________
collage> Processing atomic structures.
lib_pio> 1271 atoms read.
collage> One atomic input structure detected:
collage>   1. 0_tnc.pdb (1271 atoms)
_____________________________________________________________________________
lib_vwk> Generating Gaussian kernel with 7^3 = 343 voxels.
lib_vwk> Generating Gaussian kernel with 11^3 = 1331 voxels.
lib_vwk> Generating kernel with 7^3 = 343 voxels.
lib_vwk> Map size expanded from 55 x 27 x 25 to 61 x 33 x 31 by zero-padding.
lib_vwk> New map origin (coord of first voxel): (-52.247,-22.166,-41.165)
collage> Projecting probe structure to lattice...
collage> (no steric exclusion boosting of density)
collage> Computing fraction of PDB contained within the map (above cutoff density) ...
collage> Overlap fraction:   1.4844269E-01
collage> Warning: Less than half of the input PDB is contained within the map!
collage> Applying filters to target and probe maps...
collage> Normalizing target and probe maps...
collage> Target and probe maps:
lib_vwk> Map density info: max 4.056848, min 0.000000, ave 0.317103, sig 0.902745.
lib_vwk> Map density info: max 7.805456, min 0.000000, ave 0.257985, sig 0.937638.
collage> Initial correlation coefficient:   1.4506603E-01
_____________________________________________________________________________
collage> Identifying inside or buried voxels...
collage> Found 7696 inside or buried voxels (out of a total of 62403).
collage> Powell conjugent gradient maximization.
collage> Determining most efficient correlation algorithm based on convergence and time...
collage>   Original algorithm: Correlation = 0.15601827  Time = 1.894500 ms
collage>   Masked algorithm:   Correlation = 0.12867513  Time = 1.853000 ms
collage>   One-step algorithm: Correlation = 0.15139914  Time = 1.120000 ms
collage> Using original three-step correlation function.
collage>
collage> Performing Powell conjugate gradient maximization...
collage>
collage> Single-body Powell
collage>   X       Y       Z       Psi     Theta   Phi      Correlation   Iteration   PDB (Body) Nr.
collage>   0.000   0.000   0.000   0.000   0.000   0.000    1.4506603E-01 Initial     1     
collage>   2.284  -1.190 -18.364  36.872  11.519 328.383    6.3113920E-01 Final       1     
collage> Total number of Powell steps: 26
collage> Total optimization time: 28.654045 s
_____________________________________________________________________________
collage> Writing body number 1 to file cge_001.pdb.
collage> Writing Powell log to file cge_powell.log.
_____________________________________________________________________________
collage> All done!!!

The program output shows how the initial correlation of 0.1 increases to 0.6 while the structure is fitted. The output is written to the file cge_best_001.pdb. To avoid over writing this file, we create a directory "4_manual" and move the cge_* files into it (see run_tutorial.bash script).

When inspected with VMD as above, the results should look similar to the following figure:


(Click image to enlarge)

Outlook: Alternative Fitting Strategies

Enforcing symmetry

The collage tool and the pdbsymm tool can be combined to impose symmetry constraints on the fragments during multi-fragment docking. Currently we support C, D, and helical symmetry. This feature should be very useful for many oligomeric assemblies. See the multi-fragment tutorial for details.

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 .