RMSD

RMSD, short for root-mean-square deviation, is a numerical measure used to quantify the difference between two molecular structures or conformations. It represents the average distance between corresponding atoms after the structures have been optimally superimposed in three-dimensional space. The standard aim is to assess how similar a structure is to a reference or how much it deviates during a simulation.

Calculation typically involves two sets of N corresponding atomic coordinates, r_i and s_i. The structures are first translated and rotated to minimize the RMSD, often using the Kabsch algorithm to find the best-fit alignment. After alignment, the RMSD is computed as: RMSD = sqrt( (1/N) sum_{i=1}^N || r_i - s_i ||^2 ). In practice, one may choose a subset of atoms (for example, Cα atoms in proteins) and exclude hydrogens.

RMSD is widely used in chemistry and structural biology to compare crystal or model structures, evaluate docking results, and monitor conformational changes in molecular dynamics simulations. In MD, an RMSD trajectory shows how the structure evolves over time relative to a reference. Lower RMSD values indicate closer similarity, but interpretation depends on the system, atom selection, and reference.

Limitations include sensitivity to the chosen atom set and to global superposition; RMSD can mask local differences or domain movements. Other metrics, such as GDT-TS, TM-score, or locality-focused measures, are often used to complement RMSD when assessing structural similarity.