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Two protein domain structures can be aligned by superposing their 3D coordinates, with the aim of minimizing the RMSD of the superposition.
Many algorithms have been developed to optimize this complex task.
The task is complex because of the large number of degrees of freedom between two datasets of points in 3D (each molecule has 6 degrees of freedom). This is just the simple case of 'rigid body' superposition.
Algorithms
Some approaches use quaternerions to reduce the dimensionality of the space without removing any information (isomorphic translation).
A major class of approaches is based on reducing the representation of the complex protein molecules into its secondary structure. Secondary structucture elements can be approximatly represented as vectors and aligned in pairs.
Dynamic programming can be used to find local regions of similarity which are then expanded.
The Dali algorithm (named after Salvador Dali) uses netwrok isomorphism between the contact networks of two proteins to perform alignment.
Sequence similarity between proteins can be used to optimize structural alignmens.
Geometric hashing is a good technique!
Packages
Many tools exist to perform structural alignment and multiple structural alignment.
VMD SSM CE Dali Deep View
... And many many more!