Collision‐free poisson motion planning in ultra high‐dimensional molecular conformation spaces

Abstract

The function of protein, RNA, and DNA is modulated by fast, dynamic exchanges between three-dimensional conformations. Conformational sampling of biomolecules with exact and nullspace inverse kinematics, using rotatable bonds as revolute joints and noncovalent interactions as holonomic constraints, can accurately characterize these native ensembles. However, sampling biomolecules remains challenging owing to their ultra-high dimensional configuration spaces, and the requirement to avoid (self-) collisions, which results in low acceptance rates. Here, we present two novel mechanisms to overcome these limitations. First, we introduce temporary constraints between near-colliding links. The resulting constraint varieties instantaneously redirect the search for collision-free conformations, and couple motions between distant parts of the linkage. Second, we adapt a randomized Poisson-disk motion planner, which prevents local oversampling and widens the search, to ultra-high dimensions. Tests on several model systems show that the sampling acceptance rate can increase from 16% to 70%, and that the conformational coverage in loop modeling measured as average closeness to existing loop conformations doubled. Correlated protein motions identified with our algorithm agree with those from MD simulations. © 2018 Wiley Periodicals, Inc.

Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion

“…Nonetheless, they show convincing agreement with experimental data. Moreover, kinematic floppy modes that observe hydrogen bond constraints have guided conformational transitions 39,58,59 and revealed coordinated loop motions, 60 often more successful than normal mode based methods. 47,58 Analyses of motions beyond the floppy modes, i.e., in the kinematic flexibility regime, revealed several unexpected insights.…”

“…Nonetheless, they show convincing agreement with experimental data, if energy cutoffs to determine constraints are carefully chosen. Moreover, kinematic floppy modes that observe hydrogen bond constraints have guided conformational transitions 36,68,71 and revealed coordinated loop motions, 72 often more successfully than normal mode based methods. 49,68 Analyses of motions beyond the floppy modes, i.e., in the kinematic flexibility regime, revealed several unexpected insights.…”

Kinematic Vibrational Entropy Assessment and Analysis of SARS CoV-2 Main Protease

“…Atoms inside the neighboring cell within the threshold d cutoff are used to calculate the potential energy. This procedure reduces the computational complexity from to , see refs and . On the basis of the potential energy V x , the Hessian matrix with respect to the atom positions in Cartesian coordinates is where are the positions of atoms i and j and the matrix is the identity matrix, while ⊗ denotes the tensor product.…”

Exploring implicit spaces for constrained sampling-based planning

“…Tangent spaces have been used by Weghe et al (2007) and Stilman (2010) for manipulators under general end-effector constraints. The technique has also seen many applications in curve tracking constraints for redundant manipulators (Cefalo et al, 2013; Oriolo and Vendittelli, 2009; Vendittelli and Oriolo, 2009) and structural biology to generate valid motions of proteins with loop closures (Fonseca et al, 2018; Pachov and van den Bedem, 2015; Zhang and Hauser, 2013).…”