Flexible Fitting Tutorial, Part I
The tutorial introduces various current and older flexible fitting strategies implemented in Situs. Part I introduces damped dynamics flexible fitting useful for intermediate resolution maps. Part II provides some examples of using predicted features in low-resolution data.

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. 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_3.1_flex_tutorial/bin directory will contain the executables as well as four input data files and an executable shell script:
  • 0_lactoferrin_orig.pdb: Start structure of lactoferrin basen on PDB entry 1lfg.
  • 0_lactoferrin_target.situs: Target structure for flexible fitting (PDB entry 1lfh blurred to 7A).
  • 0_residue_codes_flexible.txt: Residue codes that keep the structure flexible.
  • 0_residue_codes_rigid.txt: Residue codes that impose full rigidity.
  • 0_residue_codes-H+S_rigid-rest_flexible.txt: Residue codes for partial rigidity.
  • 0_actin_orig.pdb: Original (start) structure of actin used in part II.
  • 0_actin_target.pdb: Target structure for flexible fitting.
  • 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 (parts I and II).

In the following, we will use the first two files to flexibly fit lactoferrin as controlled by various residue constraint files that impose varying degrees of rigidity (see ddforge user guide). The user can compare all generated files to the files in the "solutions" directory. (The four 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 with ddforge 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 optional rebuillding of truncated side chains with the third party SCRWL4 tool 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 can be inspected and, if necessary, prepared for the fitting using a variety of visualization and analysis tools. The ddforge tool requires one volume and one PDB structures for the fitting, where all density must be accounted for. Atomic coordinates in PDB format can be transformed to low-resolution maps, if necessary, and vice versa, to allow docking of maps to maps or structures to structures. The resulting docked complex can be inspected in the graphics program.

Preparing the Volume with Map Editing

The ddforge tool requires that all density must be accounted for by the fitted PDB file. Situs provides a number of map tools to adjust the map volume. For an example how this is done, we refer to the classic Situs tutorial and Fig.1 of Wriggers et al. (2011).

Preliminary Rigid-Body Registration

Before we start fitting the original lactoferrin structure to the target map, 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. For an illustrative example, see the actin fitting example in part II of this tutorial.

Flexible Refinement with ddforge

This example runs ddforge to fit the PDB structure "0_lactoferrin_orig.pdb" into the EM map "0_lactoferrin_target.situs", and uses the residue data from the file "0_residue_codes_flexible.txt".  The remaining parameters used here are:

    1:    minimum displacement between output conformations (Angstrom)
    7:    map resolution (Angstrom)
    12:  density threshold
    50:  damp/drag ratio
    0:    side-chain rebuild flag (0 -> none)
    10:  force-field cutoff distance (Angstrom)
    1:    maximum displacement per step (Angstrom)

At the shell prompt enter the following command (see also run_tutorial.bash):

./ddforge 0_lactoferrin_orig.pdb 0_lactoferrin_target.situs 1 7 12 50 0 10 1 \
-rdfile 0_residue_codes_flexible.txt

Watch the program compute a number of iterations until the stopping criterion is satisfied. The screen output will look like this:

./ddforge 0_lactoferrin_orig.pdb 0_lactoferrin_target.situs 1 7 12 50 0 10 1 -rdfile 0_residue_codes_flexible.txt
ddforge>
ddforge> Atomic structure file: 0_lactoferrin_orig.pdb
ddforge> Density map file:      0_lactoferrin_target.situs
ddforge> Min. displacement between output confs: 1.000000
ddforge> Map resolution: 7.000000 A
ddforge> Density threshold: 12.000000
ddforge> Damp/drag ratio: 50.000000
ddforge> Side-chain optimization flag: 0
ddforge> Force-field distance cutoff: 10.000000 A
ddforge> Max. displacement per time step: 1.000000 A
ddforge>
ddforge> Reading 0_lactoferrin_orig.pdb
lib_pio> 5332 atoms read from file 0_lactoferrin_orig.pdb.
ddforge>
ddforge> Reading 0_lactoferrin_target.situs
lib_vio> Situs formatted map file 0_lactoferrin_target.situs - Header information:
lib_vio> Columns, rows, and sections: x=1-103, y=1-96, z=1-82
lib_vio> 3D coordinates of first voxel: (-33.000000,-33.000000,-64.000000)
lib_vio> Voxel size in Angstrom: 1.000000
lib_vio> Reading density data...
lib_vio> Volumetric data read from file 0_lactoferrin_target.situs
ddforge> Setting density values below 12.000000 to zero.
ddforge> Optimization of sigma and threshold:
ddforge> iter =  0,  sigma =  2.02,  threshold_g = 1.42e+01,  max_g = 1.14e+02,  thr/max(PDB) = 0.124,  Gext = 29
ddforge> iter =  1,  sigma =  2.42,  threshold_g = 3.10e+01,  max_g = 1.81e+02,  thr/max(PDB) = 0.171,  Gext = 35
ddforge> iter =  2,  sigma =  2.06,  threshold_g = 1.55e+01,  max_g = 1.20e+02,  thr/max(PDB) = 0.129,  Gext = 29
ddforge> iter =  3,  sigma =  2.05,  threshold_g = 1.51e+01,  max_g = 1.18e+02,  thr/max(PDB) = 0.128,  Gext = 29
ddforge> Number of atoms: 5332
ddforge> Number of pseudo-atoms: 3282
ddforge> Number of residues: 691
ddforge> Read residue-data file '0_residue_codes_flexible.txt'
ddforge> Number of free variables: 1888
ddforge> Number of chains: 1

ddforge> Conf#  Step#      Time       Speed       Disp.      Dist_cut  Overlap     Cos      Compute time (sec)

ddforge>     0      0   0.000e+00   1.153e-04   5.000e-01   6.543e+01   78.54    0.00000       1.028e+01
ddforge>            1   4.338e+03   8.880e-05   5.000e-01   6.543e+01   78.52    0.00000       1.983e+01
ddforge>     1      2   9.969e+03   6.337e-05   5.178e-01   6.543e+01   78.04    0.99497       2.933e+01
ddforge>            3   1.814e+04   3.954e-05   5.045e-01   5.150e+01   77.30    0.99455       3.917e+01
ddforge>     2      4   3.090e+04   1.650e-05   3.400e-01   3.357e+01   76.57    0.99040       4.861e+01
ddforge>            5   5.150e+04   2.554e-05   3.635e-01   1.679e+01   76.02    0.18558       5.830e+01
ddforge>            6   6.573e+04   9.684e-05   3.922e-01   9.188e+00   77.09    0.92269       6.780e+01
ddforge>     3      7   6.978e+04   9.483e-05   3.624e-01   8.570e+00   78.53    0.98451       7.714e+01
ddforge>            8   7.361e+04   9.614e-05   3.389e-01   7.926e+00   79.80    0.98523       8.662e+01
ddforge>            9   7.713e+04   9.862e-05   3.305e-01   7.372e+00   80.86    0.98511       9.602e+01
ddforge>     4     10   8.048e+04   1.002e-04   3.260e-01   6.926e+00   81.82    0.98767       1.056e+02
ddforge>           11   8.373e+04   1.006e-04   3.131e-01   6.650e+00   82.68    0.98744       1.155e+02
ddforge>           12   8.685e+04   9.459e-05   3.376e-01   6.650e+00   83.47    0.99249       1.251e+02
ddforge>           13   9.041e+04   9.159e-05   3.186e-01   6.650e+00   84.34    0.99389       1.345e+02
ddforge>     5     14   9.389e+04   8.860e-05   2.352e-01   6.650e+00   85.04    0.99161       1.441e+02
ddforge>           15   9.655e+04   8.319e-05   2.082e-01   6.650e+00   85.58    0.99406       1.542e+02
ddforge>           16   9.905e+04   8.123e-05   1.669e-01   6.650e+00   85.96    0.99633       1.639e+02
ddforge>           17   1.011e+05   7.806e-05   1.887e-01   6.650e+00   86.33    0.99706       1.739e+02
ddforge>           18   1.035e+05   7.820e-05   2.116e-01   6.650e+00   86.69    0.99220       1.840e+02
ddforge>     6     19   1.062e+05   8.350e-05   1.949e-01   6.650e+00   86.79    0.96132       1.938e+02
ddforge>           20   1.086e+05   8.142e-05   1.465e-01   6.650e+00   87.04    0.99321       2.039e+02
ddforge>           21   1.104e+05   7.949e-05   1.301e-01   6.650e+00   87.31    0.99604       2.136e+02
ddforge>           22   1.120e+05   7.504e-05   1.561e-01   6.650e+00   87.58    0.99720       2.233e+02
ddforge>           23   1.141e+05   7.323e-05   1.682e-01   6.650e+00   87.83    0.99721       2.327e+02
ddforge>           24   1.164e+05   7.032e-05   2.019e-01   6.650e+00   88.13    0.99642       2.423e+02
ddforge>           25   1.192e+05   6.535e-05   2.095e-01   6.650e+00   88.46    0.99518       2.518e+02
ddforge>     7     26   1.225e+05   6.240e-05   2.302e-01   6.650e+00   88.78    0.99470       2.614e+02
ddforge>           27   1.261e+05   5.973e-05   2.344e-01   6.650e+00   89.09    0.99569       2.713e+02
ddforge>           28   1.301e+05   5.748e-05   2.395e-01   6.650e+00   89.41    0.99602       2.807e+02
ddforge>           29   1.342e+05   5.092e-05   2.285e-01   6.650e+00   89.77    0.99314       2.901e+02
ddforge>           30   1.387e+05   4.595e-05   2.002e-01   6.650e+00   90.18    0.98007       2.995e+02
ddforge>     8     31   1.431e+05   4.240e-05   1.876e-01   6.650e+00   90.50    0.99542       3.090e+02
ddforge>           32   1.475e+05   3.862e-05   1.771e-01   6.650e+00   90.78    0.99702       3.190e+02
ddforge>           33   1.521e+05   3.563e-05   1.734e-01   6.650e+00   91.03    0.99561       3.285e+02
ddforge>           34   1.570e+05   3.163e-05   1.694e-01   6.650e+00   91.31    0.99563       3.381e+02
ddforge>           35   1.623e+05   2.706e-05   1.625e-01   6.650e+00   91.57    0.99145       3.476e+02
ddforge>           36   1.683e+05   2.366e-05   1.627e-01   6.650e+00   91.81    0.98367       3.571e+02
ddforge>     9     37   1.752e+05   1.923e-05   1.637e-01   6.650e+00   92.08    0.97900       3.667e+02
ddforge>           38   1.837e+05   1.676e-05   1.851e-01   6.650e+00   92.37    0.91134       3.766e+02
ddforge>           39   1.947e+05   1.461e-05   1.400e-01   6.650e+00   92.63    0.47895       3.861e+02
ddforge>           40   2.043e+05   1.762e-05   1.503e-01   6.650e+00   92.87   -0.04687       3.955e+02
ddforge>           41   2.129e+05   1.473e-05   6.346e-02   6.650e+00   92.99   -0.36297       4.054e+02
ddforge>           42   2.172e+05   9.249e-06   6.413e-02   6.650e+00   93.15    0.60304       4.155e+02
ddforge>           43   2.241e+05   7.082e-06   7.695e-02   6.650e+00   93.27    0.80377       4.258e+02
ddforge>           44   2.350e+05   6.980e-06   7.109e-02   6.650e+00   93.48    0.71865       4.359e+02
ddforge>           45   2.452e+05   7.484e-06   4.648e-02   6.650e+00   93.66    0.51553       4.455e+02
ddforge>           46   2.514e+05   6.583e-06   5.578e-02   6.650e+00   93.73    0.40252       4.551e+02
ddforge>    10     47   2.598e+05   1.375e-05   6.693e-02   6.650e+00   93.77    0.59082       4.646e+02
ddforge>           48   2.647e+05   6.881e-06   5.812e-02   6.650e+00   93.89    0.84670       4.744e+02
ddforge>           49   2.732e+05   4.894e-06   5.951e-02   6.650e+00   93.99    0.42948       4.839e+02
ddforge>           50   2.853e+05   5.888e-06   7.142e-02   6.650e+00   94.12    0.38010       4.934e+02
ddforge>           51   2.974e+05   1.248e-05   8.570e-02   6.650e+00   94.18    0.19590       5.029e+02
ddforge>           52   3.043e+05   8.516e-06   5.487e-02   6.650e+00   94.28    0.54021       5.125e+02
ddforge>           53   3.108e+05   5.036e-06   2.536e-02   6.650e+00   94.35    0.10986       5.220e+02
ddforge>           54   3.158e+05   5.468e-06   3.044e-02   6.650e+00   94.37    0.31836       5.315e+02
ddforge>           55   3.214e+05   3.696e-06   3.296e-02   6.650e+00   94.43    0.55588       5.410e+02
ddforge>           56   3.303e+05   5.558e-06   3.955e-02   6.650e+00   94.47    0.39599       5.506e+02
ddforge>           57   3.374e+05   4.650e-06   3.239e-02   6.650e+00   94.51   -0.02584       5.601e+02
ddforge>           58   3.444e+05   5.185e-06   2.525e-02   6.650e+00   94.56   -0.34213       5.698e+02
ddforge>           59   3.492e+05   3.635e-06   1.499e-02   6.650e+00   94.60   -0.25787       5.797e+02
ddforge>           60   3.533e+05   3.001e-06   1.653e-02   6.650e+00   94.64    0.30421       5.895e+02
ddforge>           61   3.589e+05   2.683e-06   1.983e-02   6.650e+00   94.66    0.46938       5.992e+02
ddforge>           62   3.662e+05   4.374e-06   2.380e-02   6.650e+00   94.70    0.21611       6.088e+02
ddforge>           63   3.717e+05   2.999e-06   2.443e-02   6.650e+00   94.74    0.48411       6.186e+02
ddforge>           64   3.798e+05   4.804e-06   2.931e-02   6.650e+00   94.79    0.12163       6.283e+02
ddforge>           65   3.859e+05   4.121e-06   2.018e-02   6.650e+00   94.81   -0.28679       6.379e+02
ddforge>           66   3.908e+05   4.084e-06   1.948e-02   6.650e+00   94.86   -0.02655       6.479e+02
ddforge>           67   3.956e+05   2.573e-06   1.360e-02   6.650e+00   94.87    0.15455       6.577e+02
ddforge>           68   4.009e+05   3.510e-06   1.632e-02   6.650e+00   94.89    0.13058       6.675e+02
ddforge>           69   4.055e+05   2.871e-06   1.422e-02   6.650e+00   94.93    0.07488       6.774e+02
ddforge>           70   4.105e+05   3.778e-06   1.707e-02   6.650e+00   94.95    0.05679       6.870e+02
ddforge>           71   4.150e+05   2.521e-06   1.266e-02   6.650e+00   94.98    0.15003       6.973e+02
ddforge>           72   4.200e+05   3.776e-06   1.519e-02   6.650e+00   95.02    0.18649       7.077e+02
ddforge>           73   4.241e+05   2.286e-06   1.168e-02   6.650e+00   95.03    0.35089       7.185e+02
ddforge>           74   4.292e+05   3.022e-06   1.401e-02   6.650e+00   95.05    0.22285       7.290e+02
ddforge>           75   4.338e+05   2.827e-06   1.347e-02   6.650e+00   95.07    0.02903       7.395e+02
ddforge>           76   4.386e+05   3.150e-06   1.616e-02   6.650e+00   95.10    0.06866       7.501e+02
ddforge>           77   4.437e+05   2.682e-06   1.260e-02   6.650e+00   95.11   -0.10886       7.610e+02
ddforge>           78   4.484e+05   2.519e-06   1.134e-02   6.650e+00   95.14   -0.04633       7.718e+02
ddforge>           79   4.529e+05   2.075e-06   1.157e-02   6.650e+00   95.15    0.23405       7.826e+02
ddforge>           80   4.585e+05   2.284e-06   1.389e-02   6.650e+00   95.18    0.10497       7.930e+02
ddforge>           81   4.646e+05   2.508e-06   1.289e-02   6.650e+00   95.19   -0.16646       8.026e+02
ddforge>           82   4.697e+05   2.365e-06   1.084e-02   6.650e+00   95.22   -0.12919       8.122e+02
ddforge>           83   4.743e+05   2.028e-06   1.110e-02   6.650e+00   95.24    0.18948       8.218e+02
ddforge>           84   4.797e+05   2.295e-06   1.291e-02   6.650e+00   95.27    0.02375       8.315e+02
ddforge>           85   4.854e+05   2.484e-06   1.125e-02   6.650e+00   95.29   -0.22301       8.412e+02
ddforge>    11     86   4.899e+05   1.819e-06   8.203e-03   6.650e+00   95.31   -0.00596       8.511e+02
ddforge>           87   4.944e+05   1.858e-06   9.844e-03   6.650e+00   95.33    0.25490       8.610e+02
ddforge>           88   4.997e+05   1.979e-06   1.181e-02   6.650e+00   95.35    0.16621       8.707e+02
ddforge>           89   5.057e+05   2.080e-06   1.094e-02   6.650e+00   95.37   -0.08498       8.802e+02
ddforge>           90   5.109e+05   2.389e-06   1.121e-02   6.650e+00   95.40   -0.10486       8.899e+02
ddforge>           91   5.156e+05   2.306e-06   9.336e-03   6.650e+00   95.41   -0.16474       8.999e+02
ddforge>           92   5.197e+05   2.091e-06   7.102e-03   6.650e+00   95.43   -0.21196       9.101e+02
ddforge>           93   5.231e+05   1.660e-06   7.507e-03   6.650e+00   95.46    0.31350       9.206e+02
ddforge>           94   5.276e+05   1.615e-06   9.008e-03   6.650e+00   95.46    0.37858       9.315e+02
ddforge>           95   5.332e+05   2.070e-06   1.081e-02   6.650e+00   95.48    0.08701       9.421e+02
ddforge>           96   5.384e+05   1.914e-06   9.234e-03   6.650e+00   95.49   -0.08896       9.529e+02
ddforge>    12     96   5.384e+05   1.914e-06   9.234e-03   6.650e+00   95.49   -0.08896       9.529e+02
ddforge>
ddforge> Safe ending time step = 48
ddforge>
ddforge> All done. Program exiting normally.


When a line above indicates a conformation # in the first column, a PDB file is written to disk containing that conformation of the atomic model, named as the concatenation of the original PDB file name and "deform.x", where "x" is the conformation number.

The program will end the trajectory according to a stopping criterion based on the overlap evolution. At the end of the screen output, it will notify the time step when it is safe to stop the trajectory before getting into the overfitting regime. It will look like this:

ddforge>    12     96   5.384e+05   1.914e-06   9.234e-03   6.650e+00   95.49   -0.08896       9.529e+02
ddforge>
ddforge> Safe ending time step = 48
ddforge>
ddforge> All done. Program exiting normally.


The safe ending time step will be quite earlier than the current time step, because sufficient time is needed to assess accurately the start of the saturation region of the overlap, on which the stopping criterion is based. Then, the conformation that was written to disk just before or after the safe ending time step should be taken as the solution. In the above case, the solution would be the file  0_lactoferrin_orig.deform.10.pdb.

Important preparation for the next tutorial steps: To prevent overwriting the flexed files in the subsequent runs below, create a directory "1_flexible", and move the "deform.x" files into it. See the run_tutorial.bash file for the respective UNIX commands for doing this.
Using Residue Constraints

As specified in the ddforge user guide and shown above, one can specify a residue data file that fine-tunes the refinement of specific amino acid residues. In fact, we could have omitted this file in the above run as the default program behavior is full flexibility. However, the two additional input files 0_residue_codes_rigid.txt and 0_residue_codes-H+S_rigid-rest_flexible.txt can be used to demonstrate the effect of full and partial rigidity on the fitted structure. To explore this, run the above code with these two alternative residue data files instead. After each run, save the "deform.x" files to two new directories "1_rigid" and "1_H+S_rigid-rest_flexible", respectively. You should notice that in the fully rigid case the overlap hardly changes and the program terminates without being able to find a proper stopping criterion. The partially flexible case (where helices and bends are rigid and everything else is treated flexible) converges similar to the above full flexibility after 47 steps or the 10th conformation.

Secondary structure can be assigned with tools like DSSP. Setting up residue data files for large PDBs might become labor intensive. You can use the above templates as a start for other applications. Alternatively, we recommend to write a script to generate a template for further editing. Here we show such a script written in Mathematica, but a user can probably translate this to a preferred scripting language without much difficulty:

AllChains = {{"A", 1, 691}};
ResidueData = {"CODE  CH.ORI.  RES.ORI."};
For[ch = 1, ch <= Length[AllChains], ch++,
  chainID = AllChains[[ch, 1]];
  res1 = AllChains[[ch, 2]];
  g = (Length[AllChains[[ch]]] - 1)/2;
  For[s = 1, s <= g, s++,
    i1 = AllChains[[ch, 2*s]];
    i2 = AllChains[[ch, 2*s + 1]];
    For[i = i1, i <= i2, i++,
      record = "  31     " <> chainID <> ToString[PaddedForm[i, 10, NumberSigns -> {"", ""}]];
      AppendTo[ResidueData, record];
    ]
  ]
];
Export["residue_data_file.txt", ResidueData, "Table"];

The first line specifies the chains and number of residues in the PDB. The one above is for a particular example of a PDB with a single chain called A which has 691 residues. If you had, say, 2 chains, A and B, and chain B has 200 residues, you would write instead: AllChains = {{"A", 1, 691}, {"B", 10, 200}};

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 (red) and flexed structures (green: flexible; orange: rigid; cyan: partially flexible) and render them in colored tube representation. The script also renders the target density map in gray.

mol load pdb 0_lactoferrin_orig.pdb
mol load pdb 1_flexible/0_lactoferrin_orig.deform.10.pdb
mol load pdb 1_rigid/0_lactoferrin_orig.deform.4.pdb
mol load pdb 1_H+S_rigid-rest_flexible/0_lactoferrin_orig.deform.10.pdb
mol load situs 0_lactoferrin_target.situs
mol top 0
rotate stop
display resetview
display projection orthographic
mol modstyle 0 0 Lines 2.0
mol modselect 0 0 {name C N CA}

mol modstyle 0 1 Lines 2.0
mol modselect 0 1 {name C N CA}

mol modstyle 0 2 Lines 2.0
mol modselect 0 2 {name C N CA}

mol modstyle 0 3 Lines 2.0
mol modselect 0 3 {name C N CA}
mol modstyle 0 4 Isosurface 50 0 0 1 2 1
mol modcolor 0 0 ColorID 1
mol modcolor 0 1 ColorID 7
mol modcolor 0 2 ColorID 3
mol modcolor 0 3 ColorID 10

mol modcolor 0 4 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: Feature-Based Flexible Fitting

If you have low-resolution (worse than 10A) maps without interior detail, you may be interested in the original feature-based flexible fitting approach we initially developed with Joachim Frank and Seth Darst in the early 2000s. Part II of the tutorial shows how to assign simulated features to the data which can then be used for flexible registration. Moreover, to improve the stereochemical quality, it is possible to constrain the distances between the features to reduce the effect of noise and other experimental limitations. 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 low-resolution applications are demonstrated in the Flexible Docking Tutorial, Part II.

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