Protein Docking by the Underestimation of Free Energy Funnels in the Space of Encounter Complexes

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.

Automatic Detection of Relevant Head Gestures in American Sign Language Communication

An automated system for detection of head movements is described. The goal is to label relevant head gestures in video of American Sign Language (ASL) communication. In the system, a 3D head tracker recovers head rotation and translation parameters from monocular video. Relevant head gestures are then detected by analyzing the length and frequency of the motion signal's peaks and valleys. Each parameter is analyzed independently, due to the fact that a number of relevant head movements in ASL are associated with major changes around one rotational axis. No explicit training of the system is necessary. Currently, the system can detect "head shakes." In experimental evaluation, classification performance is compared against ground-truth labels obtained from ASL linguists. Initial results are promising, as the system matches the linguists' labels in a significant number of cases.