Cyclooctane.world File Reference

Detailed Description

[Introduction] [Process] [Statistics] [Results] [References]

Introduction

Cyclooctane is a cyclic alkane used as an intermediate in production of plastics, fibers, adhesives, and coatings. It is also known as octomethylene.

The goal here is to compute an exhaustive map of all conformations that are compatible with the rigid-geometry hypothesis (fixed bond lengths and angles, variable torsion angles). To the best of our knowledge, a complete map of such conformations was not known so far. Other previous work on this molecule could only obtain low-energy conformers via sampling and/or local search techniques [Kolossvary and Guida 1993, Manocha and Zhu 1994, Rocha et al. 1998]. The map we provide is exhaustive (it contains all points of the conformational space) and may thus be used to determine its topology, or derive the whole (guaranteed) network of minimum-energy conformers and saddle point transitions between them.

The formulation provided here is not based on distances (as we did in Porta et al. 2007 but on rotation matrices and vectors (as in Porta et al. 2008). In any case, this problem is very hard and we use a cluster of computers to isolate the whole configuration space. The difference is that with the distance formulation days of compuation are necessary, even when using the cluster, and with the vector/matrix formulation few minutes are enough.

Process

This example is treated following this steps (from the main CuikSuite folder):

  • Generate the equations: Ensure that the paremeter REPRESENTATION is set to LINKS (or just not set). When planning it is typically set to JOINTS which is not valid for bin/cuik. Morover, ensure that MAX_NEWTON_ITERATIONS is set to 0 (or just not set) to avoid a slow Newton process for each processed box. This is useful when searching just for one solution. Then, execute:
  • Solve the positional analysis problem: Use the parallel version of cuik. To use this version you have to configure your cluster (set of computer with password less acces from your computer with a shared disc), the list of machines (in share/machines.LINUX) and probably the rmpicuik script. As a reference, we distribute the version that we use:
    • scripts/rmpicuik examples/Cycloalkanes/Cyclooctane
  • Plot and visualize the configuration space (you will see the two-dimensional solution set):
    • bin/cuikplot3d examples/Cycloalkanes/Cyclooctane 11 21 33 0 c8.gcl
    • geomview c8.gcl
  • Generate and visualize the atlas This is an alternative way to isolate the configuration space However, the atlas is limited to the connected component including the initial point (in this case there is no difference since the configuration space only has one component). Ensure that REPRESENTATION is set to JOINTS (this is just to speed up the process), that MAX_NEWTON_ITERATIONS is set to 50 and that DETECT_BIFURCATIONS is set to 1. The execute
  • We can also determine the path between two points on the configuration space For this, deactivate the bifurcation detection (set DETECT_BIFURCATIONS to 0 or just comment it) and execute:
    • rm examples/Cycloalkanes/Cyclooctane.cuik
    • bin/cuikatlasGBF examples/Cycloalkanes/Cyclooctane
    • scripts/cuikplayer examples/Cycloalkanes/Cyclooctane examples/Cycloalkanes/Cyclooctane_path
  • An alternative way to plan:

Please, see the experiments with molecules for additional information about how to deal with the cyclooctane.

Statistics

Characteristics of the problems:

Nr. of loops 1
Nr. of links 8
Nr. of joints 8
Nr. of equations (in the simplified system) 15
Nr. of variables (in the simplified system) 17

Here you have the statistics about the execution (on a grid with 160 cores).

Nr. of empty boxes 127033
Nr. of solution boxes 284244
Solver time (s) 270

Results

The conformational space of the cyclooctane, shown in transparency so that its complexity can be appreciated.

The solution of cuik set includes about 280000 boxes, so the process and visualization would be slow.

This is the atlas obtained with bin/cuikatlas and colored using the potential energy of each conformation.

Please, see our experiments with bio molecules for more information about this how to obtain this output.

Note that the atlas and path planning process can also be directly applied to the world file, but then collisions are taken into account.

Note that the result is a two-dimensional manifold and therefore it is not worth to use tools such as cuiksort or cuikanimate on the solution file (these tools are basically aimed for zero or one-dimensional solution sest).

Morever, you can also get particular configurations (using cuiknewton) and determine a path between them using cuikatlasGBF or cuikatlasrrt. These applications can work on different representations for the problem but they are typically more efficient using a DOF-based representation (set REPRESENTATION parameter to DOF). In this case the samples to connect are read from the dof file. Note that conversion between sample files (containing configuraions in MATRIX representation) and dof files are possible using cuiklinks2joints. It is important to remark that the obtained path does not take into account energetic aspects but only kinematic ones.

Please note that different samples/dof are provided for the cyclooctane corresponding to different set ups for this problem used in our papers. The difference between the experiments is the value of rH (the radii for the hydrogen atoms causing collisions) set in the Cyclooctane.world file.

References

  • I. Kolossvary and W. Guida, "Comprehensive conformational analysis of the four- to twelve-membered ring cycloalkanes: Identification of the complete set of interconversion pathways on the MM2 potential energy hypersurface," Journal of the American Chemical Society, vol. 115, pp. 2107-2119, 1993.
  • D. Manocha, Y. Zhu, "Kinematic Manipulation of Molecular Chains Subject to Rigid Constraints", Proc. 2nd Symposium on Molecular Biology , pp. 285-294, 1994.
  • J. M. Porta, L. Ros, F. Thomas, F. Corcho, J. Cantó,J. Pérez, "Complete Maps of Molecular Loop Conformational Spaces", Journal of Computation Chemistry, Vol. 28, pp. 2170-2189, 2007.
  • J. M. Porta, L. Ros, and F. Thomas, "A Linear Relaxation Technique for the Position Analysis of Multi-loop Linkages", IEEE Transactions on Robotics, 25(2): 225-239, 2009..
  • W. R. Rocha, J. R. Pliego, S. M. Resende, H. F. Dos Santos, M. A. De Oliveira, and W. B. De Almeida, "Ab initio conformational analysis of cyclooctane molecule," Journal of Computational Chemistry, vol. 19, no. 5, pp. 524-534, 1998.

Definition in file Cyclooctane.world.