A Self-Organizing Algorithm for Modeling Protein Loops

Abstract

Protein loops, the flexible short segments connecting two stable secondary structural units in proteins, play a critical role in protein structure and function. Constructing chemically sensible conformations of protein loops that seamlessly bridge the gap between the anchor points without introducing any steric collisions remains an open challenge. A variety of algorithms have been developed to tackle the loop closure problem, ranging from inverse kinematics to knowledge-based approaches that utilize pre-existing fragments extracted from known protein structures. However, many of these approaches focus on the generation of conformations that mainly satisfy the fixed end point condition, leaving the steric constraints to be resolved in subsequent post-processing steps. In the present work, we describe a simple solution that simultaneously satisfies not only the end point and steric conditions, but also chirality and planarity constraints. Starting from random initial atomic coordinates, each individual conformation is generated independently by using a simple alternating scheme of pairwise distance adjustments of randomly chosen atoms, followed by fast geometric matching of the conformationally rigid components of the constituent amino acids. The method is conceptually simple, numerically stable and computationally efficient. Very importantly, additional constraints, such as those derived from NMR experiments, hydrogen bonds or salt bridges, can be incorporated into the algorithm in a straightforward and inexpensive way, making the method ideal for solving more complex multi-loop problems. The remarkable performance and robustness of the algorithm are demonstrated on a set of protein loops of length 4, 8, and 12 that have been used in previous studies.

Modeling Structures and Motions of Loops in Protein Molecules

“…Recent work in [143] employs structural information extracted from protein structure databases in order to improve the quality of closed conformations. The terminal atoms of the loop are placed in their target positions.…”

“…The terminal atoms of the loop are placed in their target positions. Instead of placing the atoms of the loop in a straight line, the self-organizing method in [143] places the remaining atoms of the loop in random positions in the vicinity of the terminal atoms. An iterative procedure then refines the positions of these remaining atoms with information derived from ideal structural templates obtained for the fragments from a precomputed library.…”

“…The resulting method reproduces native structures of loops of 4, 8, and 12 amino acids with backbone RMSDs no higher than 0.36, 1.5, and 2.7Å, respectively. Extensive analysis in [143] shows that the method is both more accurate and more efficient than CCD.…”

“…The self-organizing method proposed in [143] is one of the most recent close-and-relax approaches to loop modeling. The method aims to simultaneously address the satisfaction of geometric, steric, planarity, and chirality constraints.…”

“…Indicatively, as far as running times are concerned, comparative studies in a dual-core 2 GHZ Intel processor with 1.96 GB 667 MHz DRAM report that search-based methods that employ CCD to close open loop conformations are quite efficient, obtaining a closed conformation of a loop of 12 amino acids in about 0.45 seconds. The self-organizing method in [143] reports further savings over employing CCD, but does not improve time demands over the IK-based method in [58]. Work in [136] shows that the consideration of steric constraints increases these time demands to 17.74 seconds to obtain a closed conformation that is also free of steric clashes for a loop of 25 amino acids.…”