A path planning approach for computing large-amplitude motions of flexible molecules.

MOTIVATION: Motion is inherent in molecular interactions. Molecular flexibility must be taken into account in order to develop accurate computational techniques for predicting interactions. Energy-based methods currently used in molecular modeling (i.e. molecular dynamics, Monte Carlo algorithms) are, in practice, only able to compute local motions while accounting for molecular flexibility. However, large-amplitude motions often occur in biological processes. We investigate the application of geometric path planning algorithms to compute such large motions in flexible molecular models. Our purpose is to exploit the efficacy of a geometric conformational search as a filtering stage before subsequent energy refinements. RESULTS: In this paper two kinds of large-amplitude motion are treated: protein loop conformational changes (involving protein backbone flexibility) and ligand trajectories to deep active sites in proteins (involving ligand and protein side-chain flexibility). First studies performed using our two-stage approach (geometric search followed by energy refinements) show that, compared to classical molecular modeling methods, quite similar results can be obtained with a performance gain of several orders of magnitude. Furthermore, our results also indicate that the geometric stage can provide highly valuable information to biologists. AVAILABILITY: The algorithms have been implemented in the general-purpose motion planning software Move3D, developed at LAAS-CNRS. We are currently working on an optimized stand-alone library that will be available to the scientific community.

Architecture-independent approximation of functions.

We show that minimizing the expected error of a feedforward network over a distribution of weights results in an approximation that tends to be independent of network size as the number of hidden units grows. This minimization can be easily performed, and the complexity of the resulting function implemented by the network is regulated by the variance of the weight distribution. For a fixed variance, there is a number of hidden units above which either the implemented function does not change or the change is slight and tends to zero as the size of the network grows. In sum, the control of the complexity depends on only the variance, not the architecture, provided it is large enough.