Optimizing noisy funnel-like functions on the euclidean group with applications to protein docking

Formulated as an optimization problem, the final stages of protein docking can be viewed as optimizing a very noisy funnel-like function on the space of rigid body motions, the (special) Euclidean group SE(3). We have recently introduced a stochastic global optimization method, called semi-definite programming based underestimation (SDU) (Paschalidis et al., 2007), that constructs a convex quadratic under-estimator to the free energy funnel based on a sample of energy function evaluations and uses the quadratic under-estimator to guide future sampling. In this paper we show that the parameterization of SE(3) has a significant impact on the effectiveness of SDU and introduce a parameterization that dramatically reduces the number of very costly energy function evaluations. The resulting algorithm represents a significant gain (more than an order of magnitude) in computational efficiency compared to state-of-the-art Monte Carlo-based algorithms used for the same purpose.