Flexible Docking Tutorial, Part I
The tutorial introduces the basic ideas of the landmark-based flexible docking strategy using actin as a test system. It is helpful for the understanding of the tutorial if the user is already familiar with the classic EM tutorial and the correlation-based docking tutorial. This tutorial uses the qplasty tool for approximative flexing at carbon alpha level of detail, we offer alternative (and more stereochemically accurate) Molecular Dynamics protocols at Situs Flavors. The results of the flexing can be compared to solutions distributed with the tutorial software. More documentation is available in the user guide, on 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_flex_tutorial/bin directory will contain the executables as well as four input data files and an executable shell script:
  • 0_actin_orig.pdb: Original actin (start) structure.
  • 0_actin_target.pdb: Target structure for flexible docking.
  • 0_rnap1.pdb: atomic structure of RNA polymerase in "closed" conformation.
  • 0_rnap2.situs: simulated EM map of RNA polymerase in "open" conformation.
  • run_tutorial.bash: Bash shell script containing all commands of this tutorial.

In the following, we will use the first two files to dock actin to various low-resolution maps. The user can compare all generated files to the files in the "solutions" directory. (The two files highlighted in brown color are used in part II of this tutorial.)

Data Flow and Design

The series of steps and the programs that are required to dock an atomic-resolution structure flexibly to single-molecule, low-resolution data are shown schematically in the following figure. Detailed program explanations are given in the user guide .

Schematic diagram of flexing related routines. Major Situs components (blue) are classified by their functionality. The main work flow is indicated by brown arrows. The advanced modeling of distance constraints for the motion capture skeleton is shown in dark blue. Visualization (orange) for the rendering of the data requires a molecular graphics viewer (we use here the VMD graphics program, Chimera and Sculptor also support Situs format). 

Standard EM formats are supported and are converted to cubic lattices in Situs format. This is done with the map2map utility. Subsequently, the data is inspected and, if necessary, prepared for the vector quantization using a variety of visualization and analysis tools. Atomic coordinates in PDB format can be transformed to low-resolution maps, if necessary, and vice versa. During vector quantization of the high-resolution structure, distances can be learnt that are sent to the vector quantizer of the low-resolution structure to enable skeleton-based fitting. After the vector quantization, the high-resolution structure is flexibly docked by the qplasty tool to the low-resolution density by the corresponding codebook vectors.

Creating a Simulated Target Map for Validation

First we create a simulated EM map from a known atomic structure for later validation. We lower the resolution of the target structure to 15 with the pdb2vol kernel convolution utility. Enter at the shell prompt:

./pdb2vol 0_actin_target.pdb 1_actin_target.situs

Select mass-weighting (enter 2) and select no B-factor cutoff (enter 1). Next enter the desired voxel spacing of the output map. Given the dimensions of the structure, 2 appears to be a good compromise between lattice accuracy and storage requirement. Next, enter the desired output resolution as a negative number: -15 . Next, select the Gaussian smoothing kernel (enter 1). Select lattice correction (enter 1), and enter the maximum amplitude of the kernel (enter 1). 
You can also automate this  procedure in a script by overloading the expected input (see run_tutorial.bash for details):

The program projects the atomic structure to the lattice, computes the Gaussian kernel, and carries out the real-space convolution, writing the resulting volumetric map to the file 1_actin_target.situs.

Here is the full program output:

./pdb2vol 0_actin_target.pdb 1_actin_target.situs
lib_pio> 3572 atoms read.
pdb2vol> Found 639 hydrogens, 0 water atoms, 0 codebook vectors, 0 density atoms
pdb2vol> Hydrogens will be ignored.
pdb2vol> Do you want to mass-weight the atoms ?
pdb2vol>
pdb2vol> 1: No
pdb2vol> 2: Yes
pdb2vol> 2
pdb2vol> Do you want to select atoms based on a B-factor threshold?
pdb2vol>
pdb2vol> 1: No
pdb2vol> 2: Yes
pdb2vol> 1
pdb2vol> 2933 out of 3572 atoms selected for conversion.
pdb2vol>
pdb2vol> The input structure measures 74.971 x 62.460 x 38.249 Angstrom
pdb2vol>
pdb2vol> Please enter the desired voxel spacing for the output map (in Angstrom): 2
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: -15
pdb2vol>
pdb2vol> Please select the type of smoothing kernel:
pdb2vol>
pdb2vol> 1: Gaussian, exp(-1.5 r^2 / sigma^2)
pdb2vol> sigma = 7.500A, r-half = 5.098A, r-cut = 12.990A
pdb2vol>
pdb2vol> 2: Triangular, max(0, 1 - 0.5 |r| / r-half)
pdb2vol> sigma = 7.500A, r-half = 5.929A, r-cut = 11.859A
pdb2vol>
pdb2vol> 3: Semi-Epanechnikov, max(0, 1 - 0.5 |r|^1.5 / r-half^1.5)
pdb2vol> sigma = 7.500A, r-half = 7.331A, r-cut = 11.637A
pdb2vol>
pdb2vol> 4: Epanechnikov, max(0, 1 - 0.5 r^2 / r-half^2)
pdb2vol> sigma = 7.500A, r-half = 8.101A, r-cut = 11.456A
pdb2vol>
pdb2vol> 5: Hard Sphere, max(0, 1 - 0.5 r^60 / r-half^60)
pdb2vol> sigma = 7.500A, r-half = 9.722A, r-cut = 9.835A
pdb2vol> 1
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> 1
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): 1.408 Angstrom
pdb2vol>
pdb2vol> Computing Gaussian kernel (correcting sigma for lattice smoothing)...
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: 15.000A
pdb2vol>
lib_vio> Writing density data...
lib_vio> Volumetric data written to file 1_actin_target.situs
lib_vio> Situs formatted map file 1_actin_target.situs - Header information:
lib_vio> Columns, rows, and sections: x=1-57, y=1-52, z=1-39
lib_vio> 3D coordinates of first voxel (1,1,1): (-58.000000,-50.000000,-36.000000)
lib_vio> Voxel size in Angstrom: 2.000000


By loading the resulting map into VMD (see below), one can vary the density threshold. A threshold of 10 (~15% of the maximum value) corresponds approximately to the surface of the molecule.
Preliminary Rigid-Body Registration

Before we start fitting the original actin structure to the target structure, it is important to roughly align the atomic structure and the target map by rigid-body fitting.

An initial alignment "by eye" can e.g. be done with VMD (move a loaded molecule by selecting the VMD 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).

Alternatively, an automated rigid-body fitting procedure can also be employed, e.g. using colores, collage, or matchpt as explained in other tutorials. It is a good idea to export a number of best-scoring rigid body fits, and to explore the alignment of these fits by eye, before selecting one for subsequent flexible fitting.

For example, using colores at the shell prompt enter:

./colores 1_actin_target.situs 0_actin_orig.pdb -res 15.0 -deg 20 -explor 1


After this run we rename the resulting fit and remove the auxiliary files of the colores run:

mv col_best_001.pdb 2_actin_orig_dock_target.pdb
rm col_*

Vector Quantization of the High-Resolution Structure with quanpdb

Now, we perform the vector quantization of the rigid fitted structure with the quanpdb utility.

At the shell prompt, enter

./quanpdb 2_actin_orig_dock_target.pdb 2_actin_orig_dock_target.qpdb

and select mass-weighting (enter 2), ignore the B-factor cutoff (enter 1). Next, enter the number of codebook vectors: 4 (one for each of actin's subdomains). Watch the program compute a number of datasets for statistical averaging. The file 2_actin_orig_dock_target.qpdb now contains the four 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 twice enter 1 (don't save the connectivities or Voronoi cells). See also run_tutorial.bash.

Here is the output of the entire quanpdb calculation:

./quanpdb 2_actin_orig_dock_target.pdb 2_actin_orig_dock_target.qpdb
lib_pio> 3580 atoms read.
quanpdb> Found 639 hydrogens, 0 water atoms, 8 codebook vectors, 0 density atoms
quanpdb> Hydrogens will be ignored.
quanpdb> Do you want to mass-weight the atoms ?
quanpdb>
quanpdb> 1: No
quanpdb> 2: Yes
quanpdb> 2
quanpdb> Do you want to select atoms based on a B-factor threshold?
quanpdb>
quanpdb> 1: No
quanpdb> 2: Yes
quanpdb> 1
quanpdb> 2954 equally weighted inputs out of originally 3580 atoms selected for conversion.
quanpdb>
quanpdb> Sphericity of the atomic structure: 0.52
quanpdb> Enter desired number of codebook vectors for data quantization: (0 to exit): 4
quanpdb> Computing 8 datasets, 100000 iterations each...
quanpdb> Now producing dataset 1
quanpdb> Now producing dataset 2
quanpdb> Now producing dataset 3
quanpdb> Now producing dataset 4
quanpdb> Now producing dataset 5
quanpdb> Now producing dataset 6
quanpdb> Now producing dataset 7
quanpdb> Now producing dataset 8
quanpdb>
quanpdb> Codebook vectors have been written to file 2_actin_orig_dock_target.quanpdb
quanpdb> The PDB B-factor field contains the equivalent spherical radii
quanpdb> of the corresponding Voronoi cells (in Angstrom).
quanpdb> Cluster analysis of the 8 independent calculations:
quanpdb> The PDB occupancy field in 2_actin_orig_dock_target.qpdb contains the rms variabilities of the vectors.
quanpdb> Average rms fluctuation of the 4 codebook vectors: 0.865 Angstrom
quanpdb> Radius of gyration of the 4 codebook vectors: 17.347 Angstrom
quanpdb>
quanpdb> Do you want to learn nearest-neighbor connectivities?
quanpdb> Choose one of the following options -
quanpdb> 1: No.
quanpdb> 2: Learn and save to a PSF file
quanpdb> 3: Learn and save to a constraints file
quanpdb> 4: Learn and save to both PSF and constraints files
quanpdb> 1
quanpdb>
quanpdb> Do you want to save the Voronoi cells?
quanpdb> Choose one of the following options -
quanpdb> 1: No. I'm done
quanpdb> 2: Yes. Save cells to a PDB file
quanpdb> 1
quanpdb> Bye bye!


Vector Quantization of the Low-Resolution Map with quanvol

For the vector quantization of the volumetric dataset with the quanvol utility we use the previous quanpdb codebook vectors as start positions. After entering

./quanvol 1_actin_target.situs 2_actin_orig_dock_target.qpdb \
3_actin_target.qvol

the user is prompted to enter the density cutoff value. We enter 100 which is an appropriate surface value for this map. Subsequently, the program asks whether we wish to optimize the data. or analyse it only. We enter 1 for LBG optimization. Next, the program asks if the users wishes to use distance constraints, we enter 1 (No). Finally, the user is asked whether nearest-neighbor connectivities should be learnt. For now we enter 1 (No). The file 3_actin_target.qvol now contains the codebook vectors.

Here is the output of this quanvol calculation:

./quanvol 1_actin_target.situs 2_actin_orig_dock_target.qpdb 3_actin_target.qvol
lib_vio> Situs formatted map file 1_actin_target.situs - Header information:
lib_vio> Columns, rows, and sections: x=1-57, y=1-52, z=1-39
lib_vio> 3D coordinates of first voxel: (-58.000000,-50.000000,-36.000000)
lib_vio> Voxel size in Angstrom: 2.000000
lib_vio> Reading density data...
lib_vio> Volumetric data read from file 1_actin_target.situs
quanvol> Density values below a user-defined cutoff value will not be considered
quanvol> Do you want to inspect the input density values before entering the cutoff value?
quanvol> Choose one of the following three options -
quanvol>      1: No (continue)
quanvol>      2: Show me the minimum and maximum density values only
quanvol>      3: Show me the voxel histogram
quanvol> 1
quanvol> Now enter the cutoff density value: 100
quanvol> Cutting off density values < 100.000000, remaining occupied volume: 12713 voxels (1.017040e+05 Angstrom^3)
lib_pio> 4 atoms read.
quanvol> Do you want to optimize the start vectors or skip and proceed to the connectivity analysis?
quanvol> Choose one of the following two options -
quanvol>      1: Optimize start vectors with LBG
quanvol>      2: Skip and proceed directly to connectivity analysis
quanvol> 1
quanvol>
quanvol> Using start vectors from file 2_actin_orig_dock_target.qpdb.
quanvol>
quanvol> Vector distance constraints restrict undesired degrees of freedom.
quanvol> Do you want to add distance constraints?
quanvol> Choose one of the following three options -
quanvol>      1: No
quanvol>      2: Yes. I want to enter them manually
quanvol>      3: Yes. I want to read connectivities from a PSF file and use start vector distances
quanvol>      4: Yes. I want to read them from a Situs constraints file
quanvol> 1
quanvol> Starting standard LBG vector quantization.
quanvol> It. 1 -- Average vector update: 3.794887e-01 Angstrom
quanvol> It. 2 -- Average vector update: 3.459883e-01 Angstrom
quanvol> It. 3 -- Average vector update: 3.164652e-01 Angstrom
quanvol> It. 4 -- Average vector update: 2.914341e-01 Angstrom
quanvol> It. 5 -- Average vector update: 2.667951e-01 Angstrom
quanvol> It. 6 -- Average vector update: 2.440749e-01 Angstrom
quanvol> It. 7 -- Average vector update: 2.238978e-01 Angstrom
quanvol> It. 8 -- Average vector update: 2.044688e-01 Angstrom
quanvol> It. 9 -- Average vector update: 1.876906e-01 Angstrom
quanvol> It. 10 -- Average vector update: 1.723334e-01 Angstrom
quanvol> It. 11 -- Average vector update: 1.587836e-01 Angstrom
quanvol> It. 12 -- Average vector update: 1.464327e-01 Angstrom
quanvol> It. 13 -- Average vector update: 1.345356e-01 Angstrom
quanvol> It. 14 -- Average vector update: 1.241281e-01 Angstrom
quanvol> It. 15 -- Average vector update: 1.145233e-01 Angstrom
quanvol> It. 16 -- Average vector update: 1.052219e-01 Angstrom
quanvol> It. 17 -- Average vector update: 9.707859e-02 Angstrom
quanvol> It. 18 -- Average vector update: 8.882026e-02 Angstrom
quanvol> It. 19 -- Average vector update: 8.154858e-02 Angstrom
quanvol> It. 20 -- Average vector update: 7.512557e-02 Angstrom
quanvol> It. 21 -- Average vector update: 6.959220e-02 Angstrom
quanvol> It. 22 -- Average vector update: 6.432284e-02 Angstrom
quanvol> It. 23 -- Average vector update: 5.972955e-02 Angstrom
quanvol> It. 24 -- Average vector update: 5.495829e-02 Angstrom
quanvol> It. 25 -- Average vector update: 5.124211e-02 Angstrom
quanvol> It. 26 -- Average vector update: 4.685754e-02 Angstrom
quanvol> It. 27 -- Average vector update: 4.316624e-02 Angstrom
quanvol> It. 28 -- Average vector update: 4.039170e-02 Angstrom
quanvol> It. 29 -- Average vector update: 3.792771e-02 Angstrom
quanvol> It. 30 -- Average vector update: 3.597380e-02 Angstrom
quanvol> It. 31 -- Average vector update: 3.496715e-02 Angstrom
quanvol> It. 32 -- Average vector update: 3.241709e-02 Angstrom
quanvol> It. 33 -- Average vector update: 3.048423e-02 Angstrom
quanvol> It. 34 -- Average vector update: 2.848838e-02 Angstrom
quanvol> It. 35 -- Average vector update: 2.647463e-02 Angstrom
quanvol> It. 36 -- Average vector update: 2.404363e-02 Angstrom
quanvol> It. 37 -- Average vector update: 2.244006e-02 Angstrom
quanvol> It. 38 -- Average vector update: 2.056871e-02 Angstrom
quanvol> It. 39 -- Average vector update: 1.959148e-02 Angstrom
quanvol> It. 40 -- Average vector update: 1.851113e-02 Angstrom
quanvol> It. 41 -- Average vector update: 1.725249e-02 Angstrom
quanvol> It. 42 -- Average vector update: 1.626679e-02 Angstrom
quanvol> It. 43 -- Average vector update: 1.602147e-02 Angstrom
quanvol> It. 44 -- Average vector update: 1.627645e-02 Angstrom
quanvol> It. 45 -- Average vector update: 1.567052e-02 Angstrom
quanvol> It. 46 -- Average vector update: 1.466849e-02 Angstrom
quanvol> It. 47 -- Average vector update: 1.390725e-02 Angstrom
quanvol> It. 48 -- Average vector update: 1.287678e-02 Angstrom
quanvol> It. 49 -- Average vector update: 1.187649e-02 Angstrom
quanvol> It. 50 -- Average vector update: 1.093469e-02 Angstrom
quanvol> It. 51 -- Average vector update: 1.013612e-02 Angstrom
quanvol> It. 52 -- Average vector update: 9.438498e-03 Angstrom
quanvol>
quanvol> Final clustering -- Average vector update: 0.000000e+00 Angstrom
quanvol>
quanvol> Codebook vectors have been written to file 3_actin_target.qvol
quanvol> The PDB B-factor field contains the equivalent spherical radii
quanvol> of the corresponding Voronoi cells (in Angstrom).
quanvol> Radius of gyration of the 4 codebook vectors: 19.685 Angstrom
quanvol>
quanvol> Do you want to update or save the input connectivities?
quanvol> Choose one of the following options -
quanvol>      1: No. I'm done
quanvol>      2: Update and save to a PSF file
quanvol>      3: Update and save to a constraints file
quanvol>      4: Update and save to both PSF and constraints files
quanvol> 1
quanvol> Bye bye!

Flexible Fitting using Interpolation

The flexible docking is approximated, based on the sparsely sampled displacements from the above quanvol and quanpdb codebook vectors, by interpolation with qplasty. This is sufficient for carbon alpha level accuracy. We use here the default parameters for qplasty. For more information on the algorithm see Rusu et al., 2008.

To start the flexing, enter at the shell prompt:

./qplasty 2_actin_orig_dock_target.pdb 2_actin_orig_dock_target.qpdb \
          3_actin_target.qvol 4_flexed_to_target.pdb

The flexed structure has been written to file 4_flexed_to_target.pdb.

Visualization

We now inspect the above results with VMD. The following sequence of commands in the VMD text console (cf. VMD user guide) will load the original and flexed actin structures, 2_actin_orig_dock_target.pdb (red) and 4_flexed_to_target.pdb (green), and render them in colored tube representation. The script also renders the target density map, 1_actin_target.situs, in gray:

mol load pdb 4_flexed_to_target.pdb
mol load pdb 2_actin_orig_dock_target.pdb
mol load situs 1_actin_target.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 100 0 0 1 2 1
mol modcolor 0 0 ColorID 7
mol modcolor 0 1 ColorID 1
mol modcolor 0 2 ColorID 2


Don't forget to hit "enter" after the last line! The result should look very similar to this image:


(Click image to enlarge)

Part II: Skeleton-Based Docking

We are now prepared to improve the stereochemical quality of the flexing. It is possible to constrain the distances between the landmarks to reduce the effect of noise and experimental limitations on the codebook vector positions. This "skeleton" based approach, as described on the Vector Quantization page, is related to 3D motion capture technology used in the entertainment industry and in biomechanics. The application is demonstrated in the Flexible Docking Tutorial, Part II.

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