Bio Directory Reference

Detailed Description

[Introduction] [Energy landscapes] [Path planning] [Protein loops] [Protein hinges] [References]

Introduction

This folder includes some molecules to test the interface CuikSuite-OpenBabel. This interface allows to define worlds (i.e., mechanical structures) from PDB files (or any other file accepted in OpenBabel). The worlds can be then used to identify all valid conformations. For each conformation the corresponding energy can be computed using again the CuikSuite-OpenBabel interface.

Several issues must be considered before using this interface.The atom positions in the pdb's are not very accurate and they do not fulfilf the rigid geometry assumption (the distance and angle between atoms of the same time slightly vary). Geometrically this has a large consequence (significantly changes the manifold of conformations). Therefore, in when necessary, we use a world (_orig.world) file to generate equations that take into account the exact geometry. These files are used to generate equations (via cuikequations) and then to generate one valid conformation (via cuiknewton). This conformation is then used to get a valid set of atom positions (via cuiksamples2atoms). If available, these atom positions are used when defining the world form the pdb, instead of the atom positions in the pdb. To replace the atom positions, it is very imporant that the atoms in the _orig.word are given in the same order as atoms in the pdb.

When analysing a protein loop, the residues forming the loop (i.e., the flexible residues) are given in a separate file (with extension .res). The residues might not need to be consecutive (if so, rigid parts are considered in between consecutive flexible residues).

When analyzing the motion of rigid parts of a molecule connected by molecular hinges, the atoms forming the solids are given in a separate file (with extension .rigids) and the bonds forming the hinges are given also explicitly in a file (with extension .hinges).

In our experiments pdb's are visualized using Avogadro.

Many of the results reported here are described in detail in Porta and Jaillet 2013.

Energy landscapes

In the cyclooctane case (c8) the conformational space is composed by two manifolds joined by a singularity set. Each manifold can be isolated using the appropriate sample (in c8.joints), using c8_a or c8_b and executing with parameter DETECT_BIFURCATIONS 0 if DETECT_BIFURCATIONS is set to 1 (or to 2) the whole manifold is recovered from the two starting points.

The sequence of commands to perform the analysis of a given molecule is:

  • Generate the world from the pdb For this we take the atom positions from a pre-existing world (c8_orig) modelling the ideal geometry. Note that if the exact atom positions with perfect geometry is not required the first two steps can be skiped:
  • Generate the atlas
  • Compute the energy for each chart center
  • Plot the atlas colored according to the energy
    • bin/cuikplotatlas examples/Bio/c8_a examples/Bio/c8_a_center 0 1 2
    • geomview examples/Bio/c8_a_atlas.gcl
  • Visualize one of the conformations The first one in the file of solutions
    • bin/cuiksols2samples examples/Bio/c8_a examples/Bio/c8_a_center
    • bin/cuiksample2pdb examples/Bio/c8_a.pdb examples/Bio/c8_a_center.pdb
    • [in Mac OS X] open -a avogadro examples/Bio/c8_a_sample.pdb

For the c8_b example is the same but using the second starting point in c8_orig.joints.

The other examples (csh and csh2 can be processed analogously). For instance with csh2 (note the projection variables for cuikplotatlas):

The only problem with csh is that the atlas is too large and some symmetries must be considered (this aspect is not yet included in the CuikSuite).

Path planning

Besides fully generating the atlas and computing the energy, we can perform more local explorations of the energy landscape

  • Generate the world from the pdb For this we take the atom positions from a pre-existing world (c8_orig) modelling the ideal geometry:
  • Perform local minimization Ensure that the first line in c8_planning.joints has the point from where to start the minimization.
  • Generate the atlas To be used as a reference when plotting
  • Plot the atlas and the two minimization paths
    • bin/cuikplotpath examples/Bio/c8_planning examples/Bio/c8_planning_path_0 0 4 6
    • bin/cuikplotpath examples/Bio/c8_planning examples/Bio/c8_planning_path_1 0 4 6
    • bin/cuikplotatlas examples/Bio/c8_planning examples/Bio/c8_planning_center 0 4 6
    • geomview examples/Bio/c8_planning_atlas.gcl examples/Bio/c8_planning_path_0.gcl examples/Bio/c8_planning_path_1.gcl
  • Visualize the conformations along a path There is some shakiness due to the size of the steps in the minimization.

We can also connect two samples along minimum energy paths:

  • Generate the world from the pdb For this we take the atom positions from a preexisting world (c8_orig) modelling the ideal geometry:
  • Determine the path connecting the samples IMPORTANT Ensure that the first two lines in c8_planning.joints have the points to connect. Please, deactivate the DETECT_BIFURCATIONS in the paremeter filem, set the VDW_RATIO very low, e.g. 0.1 since this planner is energy driven and not collision-driven and set DELTA to 0.05
  • Generate the atlas (Also without bifurcations) To be used as a reference when plotting.
  • Plot the atlas and the planned path
    • bin/cuikplotpath examples/Bio/c8_planning examples/Bio/c8_planning_path 0 1 2
    • bin/cuikplotatlas examples/Bio/c8_planning examples/Bio/c8_planning_center 0 1 2
    • geomview examples/Bio/c8_planning_atlas.gcl examples/Bio/c8_planning_path.gcl
  • Visualize the conformations along a path

Protein loops

To analyze the mobility of protein loops we can use:

A similar procedure can be followed to analyze the 3DFR.pdb molecular loop.

Protein hinges

The CuikSuite tools can also be used to model the motion of large rigid parts of a protein connected by some chains forming a protein hinge. This is joint work with Adnan Sljoka that is able to identify the rigid parts of the protein and the chains forming the hinge. The information he provided was used to define the file with the ridigs (2LAO.rigids) and the one with the joints defining the hinge (2LAO.hinges).

To get the atlas (i.e., the full possible motion) of the protein hinge execute:

Use geomview to differentiate between the full atlas (2LAO_atlas.gcl) and the collision free (2LAO_atlas.gcl) part of the atlas. You can get a plot as the one below:

To have a look at the collision-free conformations execute (the cuikplayer take some time to start up)

Some of the configurations are actually in collision since the atlas includes the borders of the collision-free configuration space.

The energy landscape can be obtained executing;

The one dimensional path can be optained as

References

Files

file  c8_orig.world [code]
 The cyclooctane.
 
file  cs_orig.world [code]
 A synthetic molecule with many loops.
 
file  csh2_orig.world [code]
 A synthetic molecule with many loops.
 
file  csh_orig.world [code]
 A synthetic molecule with many loops.