F2Dock: fast Fourier protein-protein docking

Abstract

The functions of proteins are often realized through their mutual interactions. Determining a relative transformation for a pair of proteins and their conformations which form a stable complex, reproducible in nature, is known as docking. It is an important step in drug design, structure determination, and understanding function and structure relationships. In this paper, we extend our nonuniform fast Fourier transform-based docking algorithm to include an adaptive search phase (both translational and rotational) and thereby speed up its execution. We have also implemented a multithreaded version of the adaptive docking algorithm for even faster execution on multicore machines. We call this protein-protein docking code F2Dock (F2 = Fast Fourier). We have calibrated F2Dock based on an extensive experimental study on a list of benchmark complexes and conclude that F2Dock works very well in practice. Though all docking results reported in this paper use shape complementarity and Coulombic-potential-based scores only, F2Dock is structured to incorporate Lennard-Jones potential and reranking docking solutions based on desolvation energy .

Fig. 1

(a) Skin and Core regions for complementary space docking. Atoms are drawn as solid circles. The skins regions are colored green while the core regions are red. The skin volume of molecule A is obtained by rolling a solvent ball over its surface. (b) A possible docking of the molecules show a large overlap between the grown layer of molecule A and the surface atoms of molecule B.

Fig. 2

For shape-complementarity scoring skin atoms are assigned a weight of $c^{Re}=\sqrt{w_{ss}}$, and core atoms are assigned weight $c^{Im}=i·\sqrt{w_{cc}}$, where w_ss is the reward factor for skin-skin overlaps, and w_cc is the penalty factor for core-core overlaps.

Fig. 3

Overview of the translational search phase of the F²Dock algorithm. Here f_A and f_B are affinity functions of molecule A and B, respectively. We assume that a given rotation has already been applied on molecule B.

Fig. 4

The docking peak search can be represented as finding the peak positions and values in a grid of overlapping splines.

Fig. 5

Unbound-unbound docking: (a) (1DFJ: Ribonuclease A complexed with Rnase inhibitor) Docking the unmarked chain of 2BNH.pdb (Rnase inhibitor) on chain B (Ribonuclease A) of 9RSA.pdb, (b) (1GHQ: Epstein-Barr virus receptor CR2 complexed with Complement C3) Docking chain A (Complement C3) of 1LY2.pdb on the unmarked chain (Epstein-Barr virus receptor CR2) of 1C3D.pdb, (c) (2PCC: Cyt C peroxidase complexed with Cytochrome C) Docking the unmarked chain (Cytochrome C) of 1YCC.pdb on the unmarked chain (Cyt C peroxidase) of 1CCP.pdb, and (d) (7CEI: Colicin E7 nuclease complexed with Im7 immunity protein) Docking chain B (Im7 immunity protein) of 1M08.pdb on chain D (Colicin E7 nuclease) of 1UNK.pdb. In all cases the first chain is static (colored yellow), and the other chain is moved around for docking. The position of the moving molecule shown in pink corresponds to the true solution (obtained by the best superimposition of each molecule on the corresponding molecule in the bound structure) while red is our final docked position.

Fig. 6

(a & b) Docking 1A2K (Ran GTPase complexed with nuclear transport factor 2): (a) (Bound-Bound) Redocking chains A & B (nuclear transport factor 2) of 1A2K.pdb on it’s chain C (Ran GTPase), (b) (Bound-Unbound) Docking chains A & B (nuclear transport factor 2) of 1OUN.pdb on chain C of 1A2K.pdb. (c & d) Docking 1CGI (Bovine chymotrypsinogen complxed with PSTI):: (c) (Bound-Bound) Redocking chain I (PSTI) of 1CGI.pdb on it’s chain E (Bovine chymotrypsinogen), (d) (Bound-Unbound) Docking the unmarked chain (PSTI) of 1HPT.pdb on chain E of 1CGI.pdb. In (a) & (b) chain C is static (colored yellow), and in (c) & (d) chain E is static, and in all cases the other chain(s) is (are) moved around for docking (the true position in the bound complex is pink, and our final docked position is red).

Fig. 7

Poisson-Boltzmann electrostatics potential on the surface of (a) Ran GTPase, (b) Ran GAP, and (c) complex of Ran GTPase and Ran GAP (1K5D.pdb). The potential ranges from −3.8 k_bT/e_c (red) to +3.8 k_bT/e_c (blue).

Fig. 8

Figures (a) and (b) show Poisson-Boltzmann electrostatics potential on the surface of Ran GTPase and Ran GAP, respectively. The potential ranges from −3.8 k_bT/e_c (red) to +3.8 k_bT/e_c (blue). Figures (c) and (d) show the bound complex of Ran GTPase and Ran GAP (1K5D.pdb). In (c) Ran GAP is drawn semi-transparent while in (d) Ran GTPase is drawn semi-transparent in order to show the electrostatics complementarity at the interface. Figures (e) and (f) show the solution with the lowest RMSD (1.66 Å) from the bound complex among the top 2,000 solutions returned by F²Dock when electrostatics weight was set to 350. Figures (g) and (h) show the solution with the lowest RMSD (2.90 Å) from the bound complex among the top 2,000 solutions returned by F²Dock when electrostatics weight was set to 0.