4D Flexible Atom-Pair Kernel

The 4D Flexible Atom-Pair Kernel represents a 4D similarity measure for molecular graphs. The information of a conformational sampling or molecular dynmic simulation is measured by means of atom-pair distance profiles (Figure 1). In a pre-processing step the method detects flexible and rigid atom-pairs of the molecules. For the flexible atom-pairs the approach calculates Gaussian mixture models that encode the distance profile of the atom-pair (Figure 2). Thus, the complete information of the conformational space of a molecule is encoded into a list of Gaussian mixture models. Rigid atom-pairs are stored together with the topological distance information. The method can apply two different regularization techniques to change the atom-pair type from flexible to rigid if the variability of the distance profile is insufficient. As a consequence, the reduction of the information dimension from 4D to 2D for rigid atom-pairs reduces the integration of noisy data to the final model. The kernel convolutes the similarities of the different atom-pairs to a final similarity value.

Figure 1. Example of a flexible atom-pair in the conformational space of the molecule. The different distance measurements between the atoms describe the behaviour in the conformational space.
Figure 2. Visualization of the distance profile as histogram and the corresponding Gaussian mixture model that is used for the similarity calculation. The blue histogram and Gaussian model represents an equal weight contribution of each conformation, whereas the red histogram and model represent a Boltzmann distribution weighting of the conformations.


  • Flexible Atom-Pair Model Creator (FAPModelCreator)
    Pre-processing tool that calculates the Gaussian mixture models based on the conformer list.
    Author: Andreas Jahn
    Source and Binaries
  • 4D Flexible Atom-Pair Kernel (4D-FAP)
    Kernel function that calculates the similarity values of molecules based on the Gaussian mixture models calculated by the FAPModelCreator.
    Author: Andreas Jahn
    Source and Binaries
  • Sample Conformational Data Set
    Sample of a conformational sampled data set to test the software.
    Data Set


  • A. Jahn, G. Hinselmann, N. Fechner, C. Henneges, A. Zell, Probabilistic Modeling of Conformational Space for 3D Machine Learning Approaches, Molecular Informatics, 2010, 29 (5), pp 441-455
  • A. Jahn, G. Hinselmann, L. Rosenbaum, N. Fechner, A. Zell, Boltzmann-enhanced Flexible Atom-Pair Kernel with Dynamic Dimension Reduction, Molecular Informatics, 2011, accepted for publication


Andreas Jahn