Protein Docking by the Underestimation of Free Energy Funnels in the Space of Encounter Complexes
Date
2008-10-01
DOI
Authors
Shen, Yang
Paschalidis, Ioannis Ch.
Vakili, Pirooz
Vajda, Sandor
Version
OA Version
Citation
2008. "Protein Docking by the Underestimation of Free Energy Funnels in
the Space of Encounter Complexes," PLoS Computational Biology. vol. 4 issue. 10 .
Abstract
Similarly to protein folding, the association of two proteins is driven
by a free energy funnel, determined by favorable interactions in some neighborhood of the
native state. We describe a docking method based on stochastic global minimization of
funnel-shaped energy functions in the space of rigid body motions (SE(3)) while accounting
for flexibility of the interface side chains. The method, called semi-definite
programming-based underestimation (SDU), employs a general quadratic function to
underestimate a set of local energy minima and uses the resulting underestimator to bias
further sampling. While SDU effectively minimizes functions with funnel-shaped basins, its
application to docking in the rotational and translational space SE(3) is not
straightforward due to the geometry of that space. We introduce a strategy that uses
separate independent variables for side-chain optimization, center-to-center distance of the
two proteins, and five angular descriptors of the relative orientations of the molecules.
The removal of the center-to-center distance turns out to vastly improve the efficiency of
the search, because the five-dimensional space now exhibits a well-behaved energy surface
suitable for underestimation. This algorithm explores the free energy surface spanned by
encounter complexes that correspond to local free energy minima and shows similarity to the
model of macromolecular association that proceeds through a series of collisions. Results
for standard protein docking benchmarks establish that in this space the free energy
landscape is a funnel in a reasonably broad neighborhood of the native state and that the
SDU strategy can generate docking predictions with less than 5 � ligand interface Ca
root-mean-square deviation while achieving an approximately 20-fold efficiency gain compared
to Monte Carlo methods.