Hierarchical and multi-resolution representation of protein flexibility

Abstract

Conformational rearrangements during molecular interactions are observed in a wide range of biological systems. However, computational methods that aim at simulating and predicting molecular interactions are still largely ignoring the flexible nature of biological macromolecules as the number of degrees of freedom is computationally intractable when using brute force representations. In this article, we present a computational data structure called the Flexibility Tree (FT) that enables a multi-resolution and hierarchical encoding of molecular flexibility. This tree-like data structure allows the encoding of relatively small, yet complex sub-spaces of a protein's conformational space. These conformational sub-spaces are parameterized by a small number of variables and can be searched efficiently using standard global search techniques. The FT structure makes it straightforward to combine and nest a wide variety of motion types such as hinge, shear, twist, screw, rotameric side chains, normal modes and essential dynamics. Moreover, the ability to assign shapes to the nodes in a FT allows the interactive manipulation of flexible protein shapes and the interactive visualization of the impact of conformational changes on the protein's overall shape. We describe the design of the FT and illustrate the construction of such trees to hierarchically combine motion information obtained from a variety of sources ranging from experiment to user intuition, and describing conformational changes at different biological scales. We show that the combination of various types of motion helps refine the encoded conformational sub-spaces to include experimentally determined structures, and we demonstrate searching these sub-spaces for specific conformations.