2008/03/01 by Ali R. Mohazab, Ali Reza Mohazab, Steven S. Plotkin
Biochemistry, Genetics and Molecular Biology · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Combinatorics #Computer science #Curvature #Distance measures #Enzyme Structure and Function #Euclidean distance #Euclidean geometry #Geometry #Inverse #Mathematical analysis #Mathematics #Metric (unit) #Piecewise #Protein Structure and Dynamics #Robotic Mechanisms and Dynamics #Topology (electrical circuits) #Transformation (genetics) #cond-mat.other #cond-mat.soft
paper · pdf · doi:10.1088/0953-8984/20/24/244133
Submitted to J. Phys.:Condens. Matter
arxiv created 2008/03/01 · openalex publication_date 2008/05/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The calculation of Euclidean distance between points is generalized to one-dimensional objects such as strings or polymers. Necessary and sufficient conditions for the minimal transformation between two polymer configurations are derived. Transformations consist of piecewise rotations and translations subject to Weierstrass–Erdmann corner conditions. Numerous examples are given for the special cases of one and two links. The transition to a large number of links is investigated, where the distance converges to the polymer length times the mean root square distance (MRSD) between polymer configurations, assuming that curvature and non-crossing constraints can be neglected. Applications of this metric to protein folding are investigated. Potential applications are also discussed for structural alignment problems such as pharmacophore identification, and inverse kinematic problems in motor learning and control.