BA-ARAP-NMA: A Local Geometry Control Nonlinear Normal-Mode Analysis Method

Low-frequency normal-mode analysis (NMA) is widely used to predict collective protein motions, but direct Cartesian scaling progressively distorts the alpha-carbon (Cα) backbone as the amplitude increases. We present backbone-angle-compatible as-rigid-as-possible normal-mode analysis (BA-ARAP-NMA), a nonlinear Cα structure-generation method that constrains first-order changes in adjacent and next-nearest Cα distances during anisotropic network model (ANM) calculations and applies a co-rotational as-rigid-as-possible (ARAP) correction during structure generation. Tests on 35 experimentally characterized two-state protein pairs showed that the geometric constraints retained most of the input-to-second-state displacement information. In 34 of 35 pairs, recalculating the constrained modes increased the concentration of the retained transition information in the leading low-frequency modes. Across matched displacements, BA-ARAP-NMA substantially reduced local Cα distance and angle distortions in every pair. At the protein-pair level, BA-ARAP-NMA generally yielded lower root mean square deviation (RMSD) to the paired state and higher transition coverage than linear Cα-ANM while maintaining improved virtual-angle accuracy. BA-ARAP-NMA therefore extends Cα normal-mode structure generation beyond direct linear scaling, retaining transition-related collective information while providing amplitude-ordered structures with frame-level geometric measurements for subsequent rebuilding and refinement.