A Self-Organizing Algorithm for Modeling Protein Loops

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.Author Summary: Protein loops play an important role in protein function, such as ligand binding, recognition, and allosteric regulation. However, due to their flexibility, it is notoriously difficult to determine their 3D structures using traditional experimental techniques. As a result, one can often find protein structures with missing loops in the Protein Data Bank. Their sequence variability also presents a particular challenge for homology modeling methods, which can only yield good overall structures given sufficient sequence identity and good experimental reference structures. Despite extensive research, the construction of protein loop 3D structures remains an open problem, since a sensible conformation should seamlessly bridge the anchor points without introducing steric clashes within the loop itself or between the loop and its surroundings environment. Here, we present a conceptually simple, mathematically straightforward, numerically robust and computationally efficient approach for building protein loop conformations that simultaneously satisfy end-point, steric, planar and chiral constraints. More importantly, additional constraints derived from experimental sources can be incorporated in a straightforward manner, allowing the processing of more complex structures involving multiple interlocking loops.