Computational Biology

Presents a concise SVD-based algorithm for finding the optimal rotation and translation between two 3D point sets, with analysis of the degenerate reflection case that Umeyama later corrected.

The matrix-based companion to Horn’s 1987 quaternion method, deriving the optimal rotation as the orthonormal factor in the polar decomposition of the cross-covariance matrix via eigendecomposition of a 3x3 symmetric matrix.

Corrects a flaw in prior SVD-based alignment methods (Arun et al., Horn et al.) that could produce reflections instead of rotations under noisy data, and provides a complete closed-form solution for similarity transformations in arbitrary dimensions.

Derives the optimal rotation between two 3D point sets as the eigenvector of a 4x4 symmetric matrix built from cross-covariance sums, using unit quaternions to enforce the orthogonality constraint.

A foundational 1976 short communication presenting a direct, non-iterative method for finding the best rotation matrix between two point sets via eigendecomposition of a cross-covariance matrix.

This paper introduces DynamicFlow, a full-atom stochastic flow matching model that simultaneously generates ligand molecules and transforms protein pockets from apo to holo states. It also contributes a new dataset of MD-simulated apo-holo pairs derived from MISATO.

Levinthal’s 1969 perspective paper defined the protein folding paradox by demonstrating the impossibility of random search, establishing the need for kinetic pathways that guide folding faster than thermodynamic equilibration allows.