Chandrajit Bajaj

Protein Protein Interaction

 Introduction | Representation | Function | Dynamic structure | Hierarchical model | Protein docking | Simulations | Meshing | Visualization

6. Protein-Protein Docking

F2Dock [CK+10, BCS09, CSB05] is a rigid-body protein-protein docking software developed at CVC (Computational Visualization Center), UT Austin, in collaboration with TSRI (The SCRIPPS Research Institute), California. The major contribution of the original version of F2Dock [BCS09, CSB05] was the use of non-equispaced FFT to speed-up docking calculations while still remaining within a provable error bound. The current implementation of F2Dock [CK+10] focuses both on speed and accuracy, and includes a highly tunable solvation energy based postprocessing tool called GB-rerank [MC+10] for much improved reranking of the potential docking solutions generated by F2Dock. F2Dock is used as a subroutine by F3Dock [BCS08] - a CVC software for flexible protein-protein docking.

Docking Objective Functions/Filters and Postprocessing in F2Dock:

The current implementation of F2Dock [CK+10] uses the following on-the-fly scoring functions and filters, and a solvation energy based postprocessing tool. Following the docking process, MolEnergy and TexMol can be used for further energetics computation and visualization.

  • Exhaustive Search (FFT):
    • Shape Complementarity: This is an improved version of the traditional double-skin layer based shape complementarity function. Unlike the traditional model the receptor skin atoms do not touch the receptor surface, and the weight assigned to a core atom is a function of its location in the molecule. The position and thickness of the skin layers are carefully chosen for accuracy.
    • Electrostatics: This is based on the approximate Coulombic interaction function and designed to reduce discretization errors on the grid.
    • Hydrophobicity: Uses per-atom hydrophonicity values to compute hydrophobic-hydrophobic, hydrophobic-hydrophilic and hydrophilic-hydrophilic interactions.
    • Hbond Correction: This function penalizes hydrogen-bond-like proximity of hydrogens of one molecule to the carbons and electronegative atoms of the other which do not actually form hydrogen bonds.

  • Filters (Multi-level Grid and/or Adaptive Spatial Decomposition):
    • van der Waals (vdW) Filter: This function is used for on-the-fly filtering of docking configurations with vdW potential above some user-defined threshold. This static multi-level grid based implementation computes the near interactions exactly and the far interactions approximately, and runs up to 1500 times faster than the naïve implementation on a molecule of typical size with less than 6% relative error. The approximation scheme is described in [CB10].
    • Clash Filter: Filters all docking poses with the number of steric (atom-atom) collisions above some user-defined threshold.
    • Hydrophobicity Filter: Filters a docking configuration if the ratio of buried hydrophilic area to buried hydrophobic area is outside some user-defined range.
    • Interface Area Filter: Filters a docking pose if the interface area is outside some user-defined range.

  • Postprocessing:
    • GB-rerank (Solvation Energy): This tool reranks the docking configurations obtained from F2Dock by computing an apporoximate change in solvation energy due to each configuration. The polar part of the solvation energy (i.e., polarization energy) is approximated in two phases using the surface-based formulation of Generalized Born (GB) energy [BZ09]. In the first phase the Born radius of each atom is approximated using an octree-based fast summation algorithm. Another octree-based fast approximation algorithm is used in the second phase that computes the polarization energy from the approximated Born radii. Both approximation schemes are described in [CB10]. The non-polar part of the change in solvation energy is approximated by computing an approximate interface area of the two molecules using our fast linear-space Dynamic Packing Grid (DPG) data structure described in [BCR09].
    • MolEnergy: This package allows for more refined energy and binding affinity computations for selected results. This includes software for solving the Poisson-Boltzmann equation and computing associated solvation energies [BCR09].

  • Visualization:
    • TexMol provides a graphical user interface and allows for the visualization of docking and energetics results.
Some Performance Figures (Bound-bound Only; Unbound-unbound Results are in [CK+10]):

The following figure shows how the performance of F2Dock improves as various options described above are added one by one to the docking process. The experiments were run on 60 rigid-body bound-bound test cases from ZDock benchmark 2.0. The test cases are listed here along with some relevant properties (taken from [MC+10]). F2Dock returned 2000 top solutions for each complex, where a hit is any docking configuration that lies within 5Å RMSD of the known solution. RMSD is computed using all atoms of the moving molecule (i.e., ligand) that lie within 5Å of any atom of the static molecule (i.e., receptor) in the known solution. Observe that in 80% of the cases F2Dock reports a hit in the top 5.

The following figure compares the performance of the shape complementarity function of F2Dock with that of the state-of-the-art docking programs ZDock 2.1 and DOT 2.0. F2Dock performs significantly better than both.

F2Dock's shape complementarity function (with vdW filtering) runs much faster than that of DOT 2.0, but is comparable to that of ZDock 2.1. The figure below shows sequential running times of all three programs on a single core of a 2.33 GHz dual-core Intel Xeon 5140. ZDock's shape complementarity function requires a complex-to-complex FFT in the forward direction and a faster complex-to-real FFT in the backward direction, while F2Dock requires a complex-to-complex FFT in both directions for shape complementarity. But F2Dock speeds up FFT computation by taking advantage of the sparsity of the input/output grids, restricting its search space within a narrow band around the receptor, and using a high performance priority queue in order to maintain the current pool of solutions. Thus F2Dock's running time remains comparable to that of ZDock 2.1. However, ZDock 2.0.1 uses the high performance conv3D package for computing 3D convolution, and as a result runs faster than F2Dock. F2Dock should also be able to achieve similar speed-ups if conv3D is used.

The following figure compares the accuracy of F2Dock, ZDock 3.1 (/3.0.1) and DOT 2.0 when electrostatics is also used with shape complementarity. F2Dock still remains significantly more accurate than both ZDock and DOT.

A detailed evaluation of the scoring functions of F2Dock on both bound-bound and unbound-unbound test cases, comparison of its performance with other similar docking software (e.g., ZDock) as well as its performance on latest CAPRI targets can be found in [KC+10].

A detailed comparative study of the reranking methods used by F2Dock (i.e., GB-rerank), ZDock (i.e., ZRank) and DOT (i.e., ClusPro) can be found in [MC+10].

    [BCR09] Chandrajit Bajaj, Rezaul A. Chowdhury, and Muhibur Rasheed.
A Dynamic Data Structure for Flexible Molecular Maintenance and Informatics.
Proceedings of the ACM Symposium on Solid and Physical Modeling (SPM 2009), San Francisco, California, pp. 259-270, 2009.
    [BCR11] Chandrajit Bajaj, Shun-Chuan Chen, and Alexander Rand.
An Efficient Higher-Order Fast Multipole Boundary Element Solution For Poisson-Boltzmann Based Molecular Electrostatics.
To Appear in the SIAM Journal on Scientific Computing, 2011.
    [BCS08] Chandrajit Bajaj, Rezaul A. Chowdhury, and Vinay Siddavanahalli.
F3Dock: A Fast, Flexible and Fourier Based Approach to Protein-Protein Docking.
The University of Texas at Austin, ICES Report 08-01, January 2008.
    [BCS09] Chandrajit Bajaj, Rezaul A. Chowdhury, and Vinay Siddavanahalli.
F2Dock: Fast Fourier Protein-Protein Docking.
IEEE/ACM Transactions on Computational Biology and Bioinformatics,8(1):45-58, 2011.
    [BZ09] Chandrajit Bajaj and Wenqi Zhao.
Fast Molecular Solvation Energetics and Force Computation.
SIAM Journal on Scientific Computing, 31(6):4524-4552, 2011.
    [CB10] Rezaul A. Chowdhury and Chandrajit Bajaj.
Multi-level Grid Algorithms for Faster Molecular Energetics.
Proceedings of the ACM Symposium on Solid and Physical Modeling (SPM 2010), Haifa, Israel, September 1-3, 2010.
    [CK+10] Rezaul A. Chowdhury, Donald Keidel, Maysam Moussalem, Arthur Olson, Michel Sanner, and Chandrajit Bajaj.
F2Dock 2.0: Improved Fast Fourier Protein-Protein Docking.
Under Preparation, 2010.
    [KC+10] Donald Keidel, Rezaul A. Chowdhury, Maysam Moussalem, Arthur Olson, Michel Sanner, and Chandrajit Bajaj.
F2Dock 2.0 Scoring: An Evaluation.
Under Preparation, 2010.
    [MC+10] Maysam Moussalem, Rezaul A. Chowdhury, Donald Keidel, Arthur Olson, Michel Sanner, and Chandrajit Bajaj.
Comparative Study of Three Reranking Methods for Fast Fourier Transform-Based Protein-Protein Docking Programs.
Under Preparation, 2010.